Text

LLC Submittal of Topical Report Methodology for the Determination of the Onset of Density Wave Oscillations (Dwo), TR-131981, Revision 0
	ML22364A332
Person / Time
Site:	99902078, 05200050
Issue date:	12/30/2022
From:	Shaver M; NuScale
To:	; Office of Nuclear Reactor Regulation, Document Control Desk
Shared Package
ML22364A331	List: ML22364A332;
References
	LO-133378
	Download: ML22364A332 (1)
	v • d • e

LO-133378 December 3, 2022 Docket No.52-050 U.S. Nuclear Regulatory Commission ATTN: Document Control Desk One White Flint North 11555 Rockville Pike Rockville, MD 20852-2738

SUBJECT:

NuScale Power, LLC Submittal of Topical Report Methodology for the Determination of the Onset of Density Wave Oscillations (DWO),

TR-131981, Revision 0 NuScale Power, LLC (NuScale) hereby submits Revision of the Methodology for the Determination of the Onset of Density Wave Oscillations (DWO), (TR-131981). The purpose of this submittal is to request that the NRC review and approve the evaluation model that provides a method for calculating the margin to the onset of density wave oscillations in steam generator tubes that use an inlet flow restrictor device. NuScale respectfully requests that the acceptance review be completed in 60 days from the date of transmittal. contains the proprietary version of the report entitled Methodology for the Determination of the Onset of Density Wave Oscillations (DWO), TR-131981, Revision 0.

NuScale requests that the proprietary version be withheld from public disclosure in accordance with the requirements of 10 CFR § 2.390. The enclosed affidavit (Enclosure 3) supports this request. Enclosure 1 has also been determined to contain Export Controlled Information. This information must be protected from disclosure per the requirements of 10 CFR § 810. Enclosure 2 contains the nonproprietary version of the report.

This letter makes no regulatory commitments and no revisions to any existing regulatory commitments.

If you have any questions, please contact Jim Osborn at 541-360-0693 or at josborn@nuscalepower.com.

Sincerely, Mark W W. Shaver Manager, Licensing NuScale Power, LLC Distribution: Michael Dudek, NRC Getachew Tesfaye, NRC Bruce Bavol, NRC NuScale Power, LLC 1100 NE Circle Blvd., Suite 200 Corvallis, Oregon 97330 Office 541.360.0500 Fax 541.207.3928 www.nuscalepower.com

LO-133378 Page 2 of 2 12/30/2022 Enclosure 1: Methodology for the Determination of the Onset of Density Wave Oscillations (DWO), TR-131981, Revision 0, proprietary version Enclosure 2: Methodology for the Determination of the Onset of Density Wave Oscillations (DWO), TR-131981, Revision 0, nonproprietary version Enclosure 3: Affidavit of Mark W. Shaver AF-133380 NuScale Power, LLC 1100 NE Circle Blvd., Suite 200 Corvallis, Oregon 97330 Office 541.360.0500 Fax 541.207.3928 www.nuscalepower.com

LO-133378 :

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO),

TR-131981, Revision 0, proprietary version NuScale Power, LLC 1100 NE Circle Blvd., Suite 200 Corvallis, Oregon 97330 Office 541.360.0500 Fax 541.207.3928 www.nuscalepower.com

LO-133378 :

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO),

TR-131981, Revision 0, nonproprietary version NuScale Power, LLC 1100 NE Circle Blvd., Suite 200 Corvallis, Oregon 97330 Office 541.360.0500 Fax 541.207.3928 www.nuscalepower.com

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO)

TR-131981-NP Revision 0 Licensing Topical Report Methodology for the Determination of the Onset of Density Wave Oscillations (DWO)

December 2022 Revision 0 Docket: 52-050 NuScale Power, LLC 1100 NE Circle Blvd., Suite 200 Corvallis, Oregon 97330 www.nuscalepower.com

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO)

TR-131981-NP Revision 0 Licensing Topical Report COPYRIGHT NOTICE This report has been prepared by NuScale Power, LLC and bears a NuScale Power, LLC, copyright notice. No right to disclose, use, or copy any of the information in this report, other than by the U.S. Nuclear Regulatory Commission (NRC), is authorized without the express, written permission of NuScale Power, LLC.

The NRC is permitted to make the number of copies of the information contained in this report that is necessary for its internal use in connection with generic and plant-specific reviews and approvals, as well as the issuance, denial, amendment, transfer, renewal, modification, suspension, revocation, or violation of a license, permit, order, or regulation subject to the requirements of 10 CFR 2.390 regarding restrictions on public disclosure to the extent such information has been identified as proprietary by NuScale Power, LLC, copyright protection notwithstanding. Regarding nonproprietary versions of these reports, the NRC is permitted to make the number of copies necessary for public viewing in appropriate docket files in public document rooms in Washington, DC, and elsewhere as may be required by NRC regulations.

Copies made by the NRC must include this copyright notice and contain the proprietary marking if the original was identified as proprietary.

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO)

TR-131981-NP Revision 0 Licensing Topical Report Department of Energy Acknowledgement and Disclaimer This material is based upon work supported by the Department of Energy under Award Number DE-NE0008928.

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights.

Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO)

TR-131981-NP Revision 0 Table of Contents Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Executive Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.0 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.1 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 SG DWO Stability Evaluation Model Scope. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.0 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.1 Regulatory Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.0 NuScale Power Module Description and Operations . . . . . . . . . . . . . . . . . . . . . . . . 11 3.1 NuScale Power Module Steam Generator Operation . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.2 Evaluation Model Requirements and Figures of Merit . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.3 Description of DWO Phenomenon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 4.0 Phenomena Identification and Ranking and Scaling Analysis . . . . . . . . . . . . . . . . 18 4.1 PIRT Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.2 PIRT Phenomena. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.3 Discussion of High Ranked Phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 4.3.1 ((2(a),(c) . . . . . . . . . . . . 21 4.3.2 (( }}2(a),(c) . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 4.3.3 (( }}2(a),(c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 4.3.4 (( }}2(a),(c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 4.3.5 (( }}2(a),(c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 4.3.6 (( }}2(a),(c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 4.3.7 (( }}2(a),(c) . . . . . . . . . . . . . . . . 23 4.3.8 (( }}2(a),(c) . . . . . . . . . . . . . . . . . . . . . 23 4.3.9 (( }}2(a),(c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 4.3.10 (( }}2(a),(c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4.3.11 (( }}2(a),(c) . . . . . . . . . . . . . . . . . . . 24 4.3.12 (( }}2(a),(c) . . . . . . . . . . . . . 24 4.3.13 (( }}2(a),(c) . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.3.14 (( }}2(a),(c) . . . . . . . . . . . 25 4.4 Scaling Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.4.1 Analysis of TF-2 Scaling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 © Copyright 2022 by NuScale Power, LLC iv

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Table of Contents 4.4.2 Scaling Analysis Objectives, Methodology and Fundamental Requirements . . 27 4.4.3 DWO Phenomena and Experiment Objectives . . . . . . . . . . . . . . . . . . . . . . . . . 28 4.4.4 NPM HCSG Stability Phenomena Identification and Ranking Table . . . . . . . . . 28 4.4.5 TF-2 Facility Operating Conditions and Dimensions . . . . . . . . . . . . . . . . . . . . . 28 4.4.6 Scaling Evaluation using the H2TS Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 4.4.7 NRELAP5 Models for Scaling Assessments . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 4.4.8 Analysis of scaling distortions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.4.9 Scaling sensitivity and Distortion Optimization Methodology . . . . . . . . . . . . . . . 46 4.4.10 Transient Distortions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.4.11 Scaling and Distortion Analysis Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 5.0 NRELAP Code Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 5.1 Quality Assurance Requirements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 5.2 Hydrodynamic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 5.2.1 Field Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 5.2.2 State Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 5.2.3 Flow Regime Maps. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 5.2.4 Momentum Closure Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 5.2.5 Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 5.3 Heat Structure Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 5.4 Trips and Control System Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 5.5 Special Solution Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 5.5.1 Abrupt Area Change. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 5.5.2 Form Loss Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 5.6 Numerical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5.7 Helical Coil Steam Generator Component . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 6.0 NRELAP5 Helical Coil SG Model Development. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 6.1 Helical Coil Tube Friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 6.1.1 Helical Coil Single-Phase Tube Wall Friction . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 6.1.2 Helical Coil Two-Phase Tube Wall Friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 6.2 Helical Coil Tube Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 6.2.1 Helical Coil Single-Phase Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 © Copyright 2022 by NuScale Power, LLC v

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Table of Contents 6.2.2 Helical Coil Two-Phase Subcooled and Saturated Flow Boiling Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 6.2.3 Primary Side Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 6.3 Subcooled Boiling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 6.3.1 Onset of Nucleate Boiling (ONB) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 6.3.2 Onset of Significant Void . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 6.3.3 Subcooled Void Fraction and Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 6.4 Transition to Dryout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 6.4.1 Two Phase to Single Phase Vapor Transition . . . . . . . . . . . . . . . . . . . . . . . . . . 86 7.0 Evaluation Model Description. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 7.1 General Model Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 7.2 Overview of DWO Simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 7.2.1 Overview of BC Methods to Induce DWO Onset . . . . . . . . . . . . . . . . . . . . . . . . 92 7.2.2 Overview of Parameters Impactful on DWO Characteristics . . . . . . . . . . . . . . . 93 7.3 Steady-State NPM Model Needed for Input to NPM SG DWO Analysis . . . . . . . . . . . . 94 7.3.1 BCs Needed for NPM SG DWO Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 7.3.2 Steady-State NPM Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 7.4 Specific Methods for DWO Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 7.4.1 Specific Methods to Induce DWO Onset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 7.4.2 Determination of DWO Stability Boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 7.4.3 Determination of DWO Flow Period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 7.4.4 Application of Specific Methods to Induce DWO Onset . . . . . . . . . . . . . . . . . . 101 7.4.5 SG Separation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 7.5 NPM SG DWO Analysis Model Requirements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 7.5.1 Hydrodynamic Volume and Junction Options . . . . . . . . . . . . . . . . . . . . . . . . . 103 7.5.2 Heat Structure Options. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 7.5.3 Time Step and System Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 7.5.4 Initial Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 7.6 Model Nodalization - SG Primary-Side . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 7.6.1 SG Primary-Side: Inlet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 7.6.2 SG Primary-Side: Upper Downcomer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 7.6.3 SG Primary-Side: Exit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 © Copyright 2022 by NuScale Power, LLC vi

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Table of Contents 7.6.4 SG Primary-Side: Riser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 7.6.5 SG Primary-Side: Riser Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 7.6.6 SG Primary-Side: Upper Plenum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 7.7 Model Nodalization - FW and STM Plenums . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 7.7.1 FW Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 7.7.2 FW Plenum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 7.7.3 STM Plenum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 7.7.4 STM Exit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 7.8 Model Nodalization - HCSG Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 7.8.1 HCSG Tube Inlets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 7.8.2 HCSG Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 7.8.3 HCSG Tube Exits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 8.0 NRELAP5 Assessments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 8.1 Assessment vs TF-1 data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 8.1.1 Test Description and Experimental Procedure. . . . . . . . . . . . . . . . . . . . . . . . . 126 8.1.2 Phenomena Addressed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 8.1.3 NRELAP5 TF-1 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 8.1.4 Performance against TF-1 SET Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 8.1.5 Performance against TF-1 DWO Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 8.1.6 Summary and Conclusions from TF-1 DWO Code-to-Data Comparisons . . . . 145 8.2 Assessment vs TF-2 data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 8.2.1 TF-2 Test Description and Experimental Procedure . . . . . . . . . . . . . . . . . . . . 146 8.2.2 Phenomena Addressed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 8.2.3 Important NRELAP5 Modeling Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 8.2.4 Performance against TF-2 SET Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 8.2.5 Performance against TF-2 DWO IET Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 8.2.6 Summary and Conclusions from TF-2 Code-to-Data Comparisons. . . . . . . . . 161 8.3 Assessment vs POLIMI data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 8.3.1 Test Description and Experimental Procedure. . . . . . . . . . . . . . . . . . . . . . . . . 161 8.3.2 Phenomena Addressed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 8.3.3 NRELAP5 Modeling Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 © Copyright 2022 by NuScale Power, LLC vii

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Table of Contents 8.3.4 POLIMI Code-to-Data Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 8.3.5 POLIMI base model versus cases run with TF-1 Characteristics. . . . . . . . . . . 166 8.3.6 Summary and Conclusions from POLIMI Data to Code Comparisons. . . . . . . 172 9.0 Assessment of Evaluation Model Adequacy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 9.1 Adequacy Demonstration Overview. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 9.2 Evaluation Models and Correlations (Bottom-Up Assessment) . . . . . . . . . . . . . . . . . . 174 9.2.1 Evaluation of Models and Correlations (Bottom-Up Assessment) . . . . . . . . . . 175 9.2.2 Applicability Evaluation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 9.2.3 Bottom-Up Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 9.3 Evaluation of Integral Performance (Top Down Evaluation Summary) . . . . . . . . . . . . 232 9.3.1 Review of Code Governing Equations and Numerics . . . . . . . . . . . . . . . . . . . 233 9.3.2 Evaluations of Integral Tests at SETs and IET. . . . . . . . . . . . . . . . . . . . . . . . . 237 10.0 Uncertainty Evaluation and Margin for NPM with respect to DWO . . . . . . . . . . . . 240 10.1 Uncertainty Analysis Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 10.2 NPM Operation Margin for DWO Onset. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 11.0 Results/Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 12.0 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254 Appendix A EMDAP Process and Roadmap to the DWO EM . . . . . . . . . . . . . . . . . . . . . .A-1 Appendix B Sample Calculation for NPM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .B-1 B.1 NPM DWO Onset Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .B-1 B.2 DWO Model Nodalization and Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .B-1 B.2.1 Percent Nominal Power Equilibrium Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . .B-1 B.2.2 NRELAP5 Model Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .B-5 B.3 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .B-10 B.4 IFR Kinlet Loss Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .B-10 B.5 DWO Number of Channels Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .B-13 B.6 Margin Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .B-16 B.7 Stability Evaluations at 100 Percent Nominal Power Conditions . . . . . . . . . . . . . . . . .B-17 B.8 Stability Evaluations at Off-Nominal 100 Percent Power Conditions . . . . . . . . . . . . . .B-24 B.9 Results and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .B-29 © Copyright 2022 by NuScale Power, LLC viii

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 List of Tables Table 1-1 Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Table 1-2 Definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Table 4-1 Component Designation for Phenomena Identification and Ranking. . . . . . . . . 19 Table 4-2 SG DWO stability PIRT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Table 4-3 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Table 4-4 Index notation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Table 4-5 NPM and TF-2 Steady-State Operating Conditions at 100% Power* . . . . . . . . 29 Table 4-6 NPM and TF-2 SG Design Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Table 4-7 NPM and TF-2 HCSG Row 3 Comparison. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Table 4-8 Field Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Table 4-9 NPM and TF-2 Initial Conditions at Different Power Levels . . . . . . . . . . . . . . . . 40 Table 4-10 TF-2 Distortion for DWO Phenomena Compared with 100% NPM Operating Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 Table 4-11 TF-2 Distortion for DWO Phenomena Compared with 15% NPM Operating Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Table 4-12 Pressure Group Distortion at 100% Power Condition . . . . . . . . . . . . . . . . . . . . 45 Table 4-13 Pressure Group Distortion at 15% Power Condition . . . . . . . . . . . . . . . . . . . . . 45 Table 4-14 Parameter Bounds for the 15% Power Sensitivity Cases . . . . . . . . . . . . . . . . . 47 Table 4-15 Parameter Bounds for the 100% Power Sensitivity Cases . . . . . . . . . . . . . . . . 47 Table 4-16 Distortions for the Optimal Cases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Table 4-17 Transient Pi Group Distortion for TF-2 and NPM 100% . . . . . . . . . . . . . . . . . . . 50 Table 4-18 Transient Pi Group Distortion for TF-2 and NPM 15% . . . . . . . . . . . . . . . . . . . . 50 Table 4-19 Nondimensional Resultant Momentum Oscillation and Frequency Comparison Between TF-2 and NPM at 100% Power . . . . . . . . . . . . . . . . . . . . 51 Table 4-20 Nondimensional Resultant Momentum Oscillation and Frequency Comparison Between TF-2 and NPM at 15% Power . . . . . . . . . . . . . . . . . . . . . 52 Table 5-1 NRELAP5 Code Modifications (DWO specific only). . . . . . . . . . . . . . . . . . . . . . 54 Table 7-1 DWO Stability PIRT vs. NPM SG DWO Model Incorporation . . . . . . . . . . . . . . 90 Table 7-2 NPM Steady-State Operating Parameters Needed for SG DWO Analysis . . . . 94 Table 8-1 Comparison of Geometrical Parameters for NPM and Assessment Tests . . . 122 Table 8-2 NPM T-H Conditions vs. Assessment Test Program Conditions . . . . . . . . . . . 124 Table 8-3 TF-2 DWO Test NRELAP5 Simulation, DWO Onset Total Error Summary Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 Table 9-1 NRELAP5 Models and Correlations Associated with High-Ranked Phenomena Along with Relevant Assessment Test Data . . . . . . . . . . . . . . . . 176 © Copyright 2022 by NuScale Power, LLC ix

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 List of Tables Table 9-2 (( }}2(a),(c) . . . . . . . . . . . . . . . . . . . . . . 190 Table 9-3 ((

                                    }}2(a),(c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 Table 9-4          Numerical Evaluation of the Transverse Temperature Profiles . . . . . . . . . . . . 200 Table 9-5          Summary of Bottom-Up Evaluation of NRELAP5 Models and Correlations. . . 227 Table 9-6          Applicability Summary for High Ranked Phenomena with Originally Knowledge Level 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 Table 9-7          Assessment Test Data and Associated High-Ranked PIRT Phenomena . . . . 233 Table 9-8          Limitations and Improvement Needs Related to DWO. . . . . . . . . . . . . . . . . . . 237 Table 9-9          Top-Down Assessment Summary for IET . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 Table 10-1         NPM Sensitivity Cases at Off-Normal Conditions for DWO Evaluation . . . . . . 250 Table A-1          EMDAP Steps and Associated Document Sections. . . . . . . . . . . . . . . . . . . . . .A-3 Table B-1          NPM Steady State Boundary and Initial Conditions at Various Power Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .B-10 Table B-2          NPM 20 Percent Nominal Power, DWO Comparison for Columns 4 and 12 . .B-16 Table B-3          NPM 100 Percent Nominal Power, DWO Summary Results and Margin . . . .B-24 Table B-4          NPM 100 Percent Nominal Power, Off-Nominal Assumed Control Action and Trip Times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .B-27 Table B-5          NPM 100 Percent Nominal Power, Cases 1 to 16, Margin for Tube with Earliest DWO Onset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .B-27 Table B-6          NPM 100 Percent Nominal Power, Case 11, Margin to DWO Onset for SG Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .B-28 Table B-7          Summary of Margin to DWO Onset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .B-29

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 List of Figures Figure 3-1 NPM Cut Away . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Figure 3-2 Thermal Conversion System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Figure 3-3 NPM Secondary Side Configuration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Figure 3-4 Tube Bundle with the RPV And Riser (Left) and Tube Bundle Only (Right) . . . 15 Figure 4-1 Flow Diagram for the H2TS Analysis (Reference 12.4) . . . . . . . . . . . . . . . . . . . 31 Figure 4-2 HCSG Breakdown into Hierarchical Levels and Primary Operational Modes . . 32 Figure 4-3 NPM HCSG Region Breakdown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Figure 4-4 DWO Onset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Figure 5-1 Schematic of Vertical Flow-Regime Map Indicating Transitions . . . . . . . . . . . . 60 Figure 5-2 Schematic of Horizontal Flow Regime Map with Shaded Regions Indicating Transition (Interpolation) Regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Figure 5-3 Schematic of Horizontally Stratified Flow in a Pipe, with Definition of . . . . . . . 62 Figure 5-4 NRELAP5 Boiling and Condensing Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 Figure 5-5 Physical Meaning of the Courant Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 Figure 6-1 Basic Geometry of a Helical Tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 Figure 7-1 Example of an NPM SG DWO Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 Figure 7-2 EM Input/Output Flow Chart (Simplified) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 Figure 7-3 General FW Flow-Controlled BC Method, Example Illustration . . . . . . . . . . . . . 97 Figure 7-4 Bulk FW Flow-Controlled BC Method, Example Illustration. . . . . . . . . . . . . . . 98 Figure 7-5 DWO Onset Determination Applied to TF-2 DWO test S01-1_00475 . . . . . . . 100 Figure 7-6 Example Illustrating DWO Flow Period Behavior Summary. . . . . . . . . . . . . . . 101 Figure 8-1 Tube-to-Coil Diameter Ratio for NPM and Assessment Test Programs . . . . . 123 Figure 8-2 Secondary Side Parameter Ranges for NPM and Assessment Tests . . . . . . . 125 Figure 8-3 TF-1 Test Section and Instrumentation Configuration . . . . . . . . . . . . . . . . . . . 127 Figure 8-4 Relative Heat Flux vs Position Along the Tube . . . . . . . . . . . . . . . . . . . . . . . . 128 Figure 8-5 NRELAP5 Model of SIET TF-1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 Figure 8-6 TF-1 Differential Pressure for Coil 1 Adiabatic Tests . . . . . . . . . . . . . . . . . . . . 132 Figure 8-7 TF-1 Differential Pressure for Coil 2 Adiabatic Tests . . . . . . . . . . . . . . . . . . . . 133 Figure 8-8 TF-1 Differential Pressure for Coil 3 Adiabatic Tests . . . . . . . . . . . . . . . . . . . . 134 Figure 8-9 TF-1 Differential Pressure for Coil 1 Diabatic Tests . . . . . . . . . . . . . . . . . . . . . 135 Figure 8-10 TF-1 Differential Pressure for Coil 2 Diabatic Tests . . . . . . . . . . . . . . . . . . . . . 136 Figure 8-11 TF-1 Differential Pressure for Coil 3 Diabatic Tests . . . . . . . . . . . . . . . . . . . . . 137 Figure 8-12 TF-1 Fluid Temperature Comparison for Coil 1 . . . . . . . . . . . . . . . . . . . . . . . . 139 © Copyright 2022 by NuScale Power, LLC xi

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 List of Figures Figure 8-13 Fluid Temperature Comparison for Coil 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 Figure 8-14 Fluid Temperature Comparison for Coil 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 Figure 8-15 Wall Temperature Comparison for Coil 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 Figure 8-16 Wall Temperature Comparison for Coil 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Figure 8-17 Wall Temperature Comparison for Coil 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 Figure 8-18 TF-1 DWO Code-to-Data Comparison, DWO Onset Power . . . . . . . . . . . . . . 145 Figure 8-19 TF-2 Secondary-side Tube Bundle Configuration in the Primary-side Flow Annulus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 Figure 8-20 SIET TF-2 Configuration P&ID . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 Figure 8-21 TF-2 NRELAP5 Adiabatic and Diabatic Test Nodalization Diagram . . . . . . . . 150 Figure 8-22 TF-2 DWO Test NRELAP5 Model Nodalization Diagram - Only Row 3 Active . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 Figure 8-23 TF-2 Adiabatic Tests, Primary-side Differential Pressure Comparison . . . . . . 154 Figure 8-24 TF-2 Diabatic Tests, Primary-side Differential Pressure Comparison . . . . . . . 155 Figure 8-25 TF-2 Diabatic Tests, Primary-side Temperature Comparison . . . . . . . . . . . . . 156 Figure 8-26 Predicted vs. Measured FW Flowrate at DWO Onset for the Least Stable Tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 Figure 8-27 Predicted vs. Measured Average DWO Flow Period for the Least Stable Tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 Figure 8-28 Predicted vs. Measured Average DWO Amplitude for the Least Stable Tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 Figure 8-29 Overview of POLIMI Parallel HCSG Configuration . . . . . . . . . . . . . . . . . . . . . 162 Figure 8-30 Schematic of POLIMI Test with Instrumentation Locations . . . . . . . . . . . . . . . 163 Figure 8-31 POLIMI Parallel HCSG Facility NRELAP5 Model Nodalization Diagram . . . . . 165 Figure 8-32 POLIMI Test 46 Code to Data Differential Pressure Along the Tube vs NRELAP5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 Figure 8-33 POLIMI NRELAP5 HCSG Tube Pressure Drop Ratio vs. Pressure (Base Model and Model with TF-1 Characteristics) . . . . . . . . . . . . . . . . . . . . . . . . . . 168 Figure 8-34 POLIMI NRELAP5 DWO Onset Power Ratio vs Pressure (Base Model and Model with TF-1 Coil Characteristics) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 Figure 8-35 POLIMI NRELAP5 HCSG Tube Pressure Drop Ratio vs. Tube A Kinlet . . . . . . 170 Figure 8-36 POLIMI NRELAP5 DWO Onset Power Ratio vs. Tube A Kinlet . . . . . . . . . . . . 171 Figure 8-37 POLIMI NRELAP5 Code-to-Data Comparison, Tube A Axial Wall Temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 Figure 9-1 (( }}2(a),(c) . . . . . . . . . . . . . . 181 Figure 9-2 (( }}2(a),(c) . . . . . . . . . . . . . . 181 © Copyright 2022 by NuScale Power, LLC xii

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 List of Figures Figure 9-3 (( }}2(a),(c) . . . . . . . . . . . . . . 182 Figure 9-4 (( }}2(a),(c) . . . . . . . . . . . . . . . . . . . . . . . . . 182 Figure 9-5 (( }}2(a),(c) . . . . . . . . . . . . . . . . . . . . . . . . . 183 Figure 9-6 (( }}2(a),(c) . . . . . . . . . . . . . . . . . . . . . . . . . 183 Figure 9-7 (( }}2(a),(c) . . . . . . . . . . . . . . . . . . . . . . . . . 184 Figure 9-8 (( }}2(a),(c) . . . . . . . . . . . . . . . . . . . . . . . . . 184 Figure 9-9 (( }}2(a),(c) . . . . . . . . . . . . . . . . . . . . . . . . . 185 Figure 9-10 (( }}2(a),(c) . . . . . . . . . . . . . . . . . . . . . . . . . 185 Figure 9-11 (( }}2(a),(c) . . . . . . . . . . . . . . . . . . . . . . . . . 186 Figure 9-12 (( }}2(a),(c) . . . . . . . . . . . . . . . . . . . . . . . . . 186 Figure 9-13 (( }}2(a),(c) . . . . . . . . . . . . . . . . . . . . . . . . . 187 Figure 9-14 (( }}2(a),(c) . . . . . . . . . . . . . . . . . . . . . . . . . 187 Figure 9-15 (( }}2(a),(c) . . . . . . . . . . . . . . . . . . . . . . . . . 188 Figure 9-16 (( }}2(a),(c) 194 Figure 9-17 ((

                           }}2(a),(c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 Figure 9-18        ((
                           }}2(a),(c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 Figure 9-19        ((                                                                                                }}2(a),(c) . . . . 199 Figure 9-20        ((
                            }}2(a),(c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 Figure 9-21        ((                                                            }}2(a),(c). . . . . . . . . . . . . . . . . . . . . . 204 Figure 9-22        ((                                                            }}2(a),(c). . . . . . . . . . . . . . . . . . . . . . 205 Figure 9-23        ((                                                                                                 }}2(a),(c) . . . 206 Figure 9-24        ((                                                                                               }}2(a),(c) . . . . 207 Figure 9-25        ((                                                                                                 }}2(a),(c) . . . 208 Figure 9-26        ((                                                                                                 }}2(a),(c) . . . 209 Figure 9-27        ((                                                                                                 }}2(a),(c) . . . 210 Figure 9-28        ((                                                                                                 }}2(a),(c) . . . 211 Figure 9-29        ((                                                                                                 }}2(a),(c) . . . 212 Figure 9-30        ((                                                                                                 }}2(a),(c) . . . 213 Figure 9-31        ((
                            }}2(a),(c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 List of Figures Figure 9-32 ((

                                }}2(a),(c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 Figure 9-33        ((
                                }}2(a),(c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 Figure 9-34        ((
                                }}2(a),(c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 Figure 9-35        ((                                                                                  }}2(a),(c) . . . . . . . . . . . 224 Figure 9-36        Physical Meaning of the Courant Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 Figure A-1         Evaluation Model Development and Assessment Process (EMDAP) . . . . . . . .A-2 Figure B-1         100 Percent Nominal Power, Xeq vs HCSG Tube Length . . . . . . . . . . . . . . . . .B-2 Figure B-2         100 Percent Nominal Power, Xeq vs HCSG Tube Length, Detailed View . . . . .B-3 Figure B-3         DWO Model 1, For Evaluations from 70 Percent to 100 Percent Nominal Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .B-4 Figure B-4         Representation of the Primary Side of the NRELAP5 DWO Model . . . . . . . . . .B-8 Figure B-5         Representation of the Secondary Side of the NRELAP5 DWO Model. . . . . . . .B-9 Figure B-6         NPM 20 Percent Nominal Power, DWO Onset in Tube 4, with an IFR Kinlet loss of 800 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .B-12 Figure B-7         NPM 20 Percent Nominal Power, DWO Onset in Tube 4, with an IFR Kinlet loss of 1000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .B-13 Figure B-8         NPM 20 Percent Nominal Power, DWO Onset in Tube 4 . . . . . . . . . . . . . . . .B-14 Figure B-9         NPM 20 Percent Nominal Power, DWO Onset in Tube 12 . . . . . . . . . . . . . . .B-15 Figure B-10        NPM 100 Percent Nominal Power, DWO Onset, Tube 1 . . . . . . . . . . . . . . . . .B-20 Figure B-11        NPM 100 Percent Nominal Power, First Ten Peaks of DWO, Tube 1 . . . . . . .B-21 Figure B-12        NPM 100 Percent Nominal Power, Differential Pressures, Tube 1 . . . . . . . . .B-22 Figure B-13        NPM 100 Percent Nominal Power, Equilibrium Quality Profiles, Tube 1 . . . . .B-23

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Abstract NuScale Power, LLC (NuScale) is requesting the Nuclear Regulatory Commission (NRC) review and approval to use the Steam Generator (SG) Density Wave Oscillation (DWO) Evaluation Model (EM) described herein for analyses of such oscillations during normal and off-normal operating conditions at reactor power levels between 20 and 100 percent nominal. Use of this EM outside of this power range requires justification. The SG DWO EM uses the proprietary NRELAP5 system analysis code. The NRELAP5 code includes models and correlations for heat transfer and pressure drop for the NuScale Power Module (NPM) helical coil SG. Extensive NRELAP5 validation was performed to ensure the DWO EM is applicable for important phenomena and processes. The validation suite includes separate and integral effects test data developed specifically for the NPM application. This EM provides a methodology for analyzing secondary-side instabilities in the NPM SG design, addresses identification of potential DWOs within the SG tubes, and provides information about such transients to support downstream stress and fatigue analysis of applicable portions of the reactor coolant system integral reactor pressure vessel and steam generator. Although not required, this SG DWO EM follows the guidance provided in Transient and Accident Analysis Methods, Regulatory Guide (RG) 1.203. Key aspects of this RG that are addressed include: development of the DWO phenomena identification and ranking table (PIRT), assessment of separate and integral-effects DWO tests, quantification of code uncertainty based on comparisons to test data, EM development, EM adequacy assessment using bottom-up assessment of NRELAP5 models and correlations, and top-down assessment of NRELAP5 models for mass, momentum, and energy conservation, and numerical solution technique. integral effects test facility scaling. For illustrative purposes to aid the reader's understanding of the context of the application of this SG DWO EM, a sample calculation of the implemented EM is provided. Calculations for the NPM SG are performed at 100 percent power. Results show that a ((

               }}2(a),(c) exists at this power.

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Executive Summary NuScale Power, LLC (NuScale) is requesting Nuclear Regulatory Commission (NRC) review and approval to use the Steam Generator (SG) Density Wave Oscillation (DWO) Evaluation Model (EM) described in this report for analyses of steam generator oscillations during normal and off-normal operating conditions at reactor power levels between 20 percent and 100 percent nominal. Although not required, this SG DWO EM is consistent with the guidance provided in Transient and Accident Analysis Methods, Regulatory Guide (RG) 1.203 (Reference 12.1), since it contains industry best practices for EM development. This topical report is not intended to provide final design values or results; rather, it contains example values for illustrative purposes to aid the reader's understanding of the context of the application of the SG DWO EM. NuScale developed a small modular reactor (SMR) design that supports operation of multiple NuScale Power Modules (NPMs) at a specific site. Each NPM is an advanced, light-water, integrated pressurized water reactor (PWR) using natural circulation for the primary coolant flow. Within each NPM there are two independent helical coil steam generators (SG) in the upper outer annulus of the primary reactor pressure vessel. Each SG consists of a large number of helical tubes connected in parallel to common feedwater (FW) plenums at the bottom, and common steam plenums at the top. Each SG tube has at its inlet a flow restrictor device that is sized to provide secondary-side hydraulic resistance within the single-phase region to enhance secondary flow stability. Systems that utilize convective boiling flow such as the NPM SGs can be found in a variety of industrial applications, including boiling water reactors, steam boilers, heat exchangers and condensers. Such systems offer the advantage of high heat transfer rates at moderate temperature differences. A drawback though is that these systems are susceptible to thermally induced two-phase DWOs that require additional engineering design to overcome. For the NPM SGs, secondary-fluid boiling within the tubes creates conditions potentially prone to parallel tube DWO. Hydraulic sizing of the tube inlet flow restrictor is important to ensuring acceptable flow stability along with reasonable constraints to power operation. NuScale previously submitted to the NRC a design certification application (DCA) for review and approval of a 12 NPM power plant design. Upon final review and final ACRS meetings, it was determined that a Combined Operating License (COL) item was required to close portions of the reactor coolant system integral reactor pressure vessel and steam generator fatigue analysis to address potential impact of DWO to SG lifetime. A COL item 3.9-14 was created to address these concerns, it states: A COL applicant that references the NuScale Power Plant design certification will develop an evaluation methodology for the analysis of secondary-side instabilities in the steam generator design. This methodology will address the identification of potential density wave oscillations in the steam generator tubes, and qualification of the applicable portions of the reactor coolant system integral reactor pressure vessel and steam generator given the occurrence of density wave oscillations, including the effects of reverse fluid flows within the tubes. This SG DWO EM provides a methodology for analyzing secondary-side instabilities in the NPM SG design, addresses identification of potential DWOs within the SG tubes, and provides information about such transients to support downstream stress and fatigue analysis of © Copyright 2022 by NuScale Power, LLC 2

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 applicable portions of the reactor coolant system integral reactor pressure vessel and steam generator. The methodology for evaluating SG integrity from a thermal fatigue perspective is outside the scope of this report. This SG DWO EM uses the NuScale-proprietary NRELAP5 computer code as the computational tool. This software was derived from the Idaho National Laboratory (INL) RELAP5-3D© computer code. It includes the necessary models for characterization of the NPM hydrodynamics, heat transfer between structures and fluids, modeling of fuel, reactor kinetics models, and control systems. The NRELAP5 code includes models and correlations for heat transfer and pressure drop for the NPM helical coil SG. Validation and verification of the SG DWO EM was conducted following the principles and guidance in the Evaluation Model Development and Assessment Process (EMDAP) of RG 1.203. A phenomena identification and ranking table (PIRT), that identifies the important phenomena and processes impacting SG DWO, was developed. Seventeen phenomena were identified as important to DWO, and thus important to capture in the SG DWO EM. Six of these important phenomena have a low knowledge level (level = 2), and required assessment against test data. Extensive NRELAP5 code assessment was performed to ensure applicability of the SG DWO EM for the important PIRT phenomena over the range of conditions encountered in the NPM. The validation tests included separate and integral-effects DWO tests performed at the Societ Informazioni Esperienze Termoidrauliche (SIET) TF-1 facility in 2016 and new DWO tests performed at the SIET TF-2 facility in 2022. Additional validation was conducted using an external database obtained from Polytechnic University of Milan (POLIMI). For TF-1 and TF-2, predicted-to-measured values of DWO onset are in reasonable-to-excellent agreement. For POLIMI, which has longer tubes and a tighter helix than the NPM SG, NRELAP5 predictions of DWO onset are conservative. EM adequacy for DWO analysis of the NPM SGs is demonstrated through bottom-up and top-down evaluations performed with NRELAP5 for high-ranking PIRT phenomena, and NRELAP5 validation against relevant test data. For the bottom-up assessment, adequacy of the models and correlations in NRELAP5 are examined by considering their pedigree, applicability, and fidelity to appropriate fundamental or separate effects test data, and scalability to the SG DWO conditions. Integral or top-down performance is assessed by evaluating the mathematical models for mass, momentum, and energy conservation; numerical solution techniques employed; and integral effects test predictions of TF-2 where integral system response is present. The conclusion drawn from the bottom-up and top-down assessments is that the EM is adequate for the purpose of predicting SG DWO onset for the NPM. An uncertainty analysis is carried out using TF-1 and TF-2 DWO data. Using a 95 percent confidence interval, the NRELAP5 uncertainty in predicting helical coil SG tube pressure drop and heat transfer is calculated. When highly conservative biasing parameter uncertainty is applied to TF-2 NRELAP5 models, NRELAP5 uncertainty for predicting DWO onset is calculated to be (( }}2(a),(c). This uncertainty is then applied to the NPM SG DWO analysis calculations. © Copyright 2022 by NuScale Power, LLC 3

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 A sample calculation is provided to demonstrate application of the EM in an NPM SG DWO model. This calculation demonstrates that appropriate NRELAP5 modeling can be used to predict DWO onset, with consideration of an inlet flow restrictor Kinlet-loss and expected operating conditions. This methodology application also illustrates how to determine margin to DWO onset, apply code uncertainty, and account for the effect of deviations from nominal conditions in DWO onset predictions. The results of the sample calculation show that margin to DWO onset is possible at all nominal power levels at and above 20 percent power, and at off-nominal 100 percent power conditions that are reasonably expected to be bounded by the final control system design and nominal trip setpoints. © Copyright 2022 by NuScale Power, LLC 4

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 1.0 Introduction 1.1 Purpose This evaluation model (EM) provides a validated method for calculating the margin to onset of density wave oscillations (DWO) in steam generator (SG) tubes that use an inlet flow restrictor (IFR) device. This report is used to size the inlet flow restrictor (IFR) resistance for the NuScale Power Module (NPM) to demonstrate thermal hydraulic stability between 20 percent and 100 percent reactor power (nominal), and to inform the design of nonsafety-related secondary-side control systems. 1.2 SG DWO Stability Evaluation Model Scope The scope of this evaluation model (EM) is limited to the NPM steam generator (SG) and nominal reactor power levels between 20 percent and 100 percent. Use of this EM for components other than SG or outside of the nominal power range requires further justification. Although not required, this EM is consistent with the guidance in Transient and Accident Analysis Methods, Regulatory Guide (RG) 1.203 (Reference 12.1), since it contains industry best practices for T-H EM development. As such, this report describes the NuScale SG design and operation, phenomena identification and ranking table (PIRT), and NRELAP5 input model, correlations, and applicability to SG DWO analysis. In addition, this report also summarizes NRELAP5 assessments against separate effects test (SET) and integral effects test (IET) data. An uncertainty analysis and DWO onset margin methodology is presented. Qualification of NPM structural components such as the integral reactor pressure vessel (RPV) and SG given the occurrence of DWO are outside of the scope of this report, but are taken into consideration as part of the ASME component lifetime fatigue analysis. 1.3 Abbreviations Table 1-1 Abbreviations Term Definition ACRS Advisory Committee on Reactor Safeguards ASME American Society of Mechanical Engineers BC boundary condition CHF critical heat flux COL Construction and Operating License CNV containment vessel DCA Design Certification Application DF distortion factor DOE Department of Energy DT differential temperature DWO density wave oscillation EM evaluation model EMDAP evaluation model development and assessment process © Copyright 2022 by NuScale Power, LLC 5

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Table 1-1 Abbreviations (Continued) Term Definition ESDU Engineering Science Data Unit FoM figures of merit FW feedwater GDF general design framework H2TS Hierarchical Two-Tier Scaling HC helical coil HCSG helical coil steam generator HT heat transfer HTFS heat transfer and fluid flow service IC initial condition IET Integral effects test IFR Inlet flow restrictor INL Idaho National Laboratory LOCA Loss of coolant accident LTR licensing topical report MPS Module Protection System NIST NuScale Integral System Test Facility NPM NuScale Power Module NRC Nuclear Regulatory Commission NSSS nuclear steam supply system ONB onset of nucleate boiling OSV onset of significant void PIRT phenomena identification and ranking table POLIMI Polytechnic University of Milan RCS reactor coolant system RG regulatory guide RTP rated thermal power RPV reactor pressure vessel SDA Standard Design Approval SG steam generator SET separate effects test SIET Societ Informazioni Esperienze Termoidrauliche STM steam TF-1 test facility and test data from SIET - tests described in Section 8.0 TF-2 test facility and test data from SIET - tests described in Section 8.0 T-H thermal-hydraulic US United States © Copyright 2022 by NuScale Power, LLC 6

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Table 1-2 Definitions Term Definition excellent agreement One of the acceptance criteria defined in RG 1.203. Excellent agreement applies when the code exhibits no deficiencies in modeling a given behavior. Major and minor phenomena and trends are correctly predicted. The calculated results are judged to agree closely with the data. The calculation, with few exceptions, lies within the specified or inferred uncertainty bands of the data. The code may be used with confidence in similar applications. figure of merit A parameter selected to characterize and quantify acceptance of results insufficient agreement One of the acceptance criteria defined in RG 1.203. Insufficient agreement applies when the code exhibits major deficiencies. The code provides an unacceptable prediction of the test data because major trends are not predicted correctly. Most calculated values lie outside the specified or inferred uncertainty bands of the data. Selected code models and facility model noding need to be reviewed and modified before the code can be used with confidence in similar applications. minimal agreement One of the acceptance criteria defined in RG 1.203. Minimal agreement applies when the code exhibits significant deficiencies. Overall, the code provides a prediction that is only conditionally acceptable. Some major trends or phenomena are not predicted correctly and some calculated values lie considerably outside the specified or inferred uncertainty bands of the data. Incorrect conclusions about trends and phenomena may be reached if the code were to be used in similar applications and an appropriate warning needs to be issued to users. Selected code models and facility model noding need to be reviewed, modified, and assessed before the code can be used with confidence in similar applications. reasonable agreement One of the acceptance criteria defined in RG 1.203. Reasonable agreement applies when the code exhibits minor deficiencies. Overall, the code provides an acceptable prediction. Major trends and phenomena are correctly predicted. Differences between calculation and data are greater than deemed necessary for excellent agreement. The calculation frequently lies outside but near the specified or inferred uncertainty bands of the data. However, the correct conclusions about trends and phenomena would be reached if the code was used in similar applications. standard deviation Standard deviation provides the estimate of how closely individual data points cluster around the average values standard error Standard error is a measure of how individual values vary from the true values standard error in mean Standard error in mean provides the estimate of how individual mean values vary from the true values uncertainty General definition of data uncertainty is standard deviation of the data divided by the square root of number of data points © Copyright 2022 by NuScale Power, LLC 7

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 2.0 Background The nuclear steam supply system (NSSS) of the NPM is designed to use natural circulation as the means of core heat removal. The nuclear core serves as the heat source for the system while the helical coil SG tubes inside the reactor pressure vessel (RPV) serve as an elevated heat sink. During steady-state conditions, the difference in density and elevation between subcooled liquid water in the core and in the SG tubes creates the buoyancy force that drives primary-side flow. In the secondary-side, feedwater (FW) is pumped into a FW plenum from which it enters the SG tubes. Inside the SG tubes, water is transformed into superheated steam via boiling and convection. This dry superheated steam exits the tubes into a steam plenum before being directed to a turbine. The NuScale NPM utilizes a helical coiled SG in the upper outer annulus of the primary pressure vessel. The NPM has two independent steam generators. The inlet of each tube is connected to one of four feedwater plenums at the bottom of the tube bundle and conclude at one of four steam plenums at the top of the bundle. A large number of tubes are connected in parallel from each of the four common inlet headers. The helical coil tubes have a low inclination angle, but traverse a large vertical height and therefore have behavior of both horizontal and vertical tubes in parallel. Unlike more common once-through steam generators, the secondary side of the NPM SG is inside the SG tubes and the primary side is on the exterior of the tubes. The liquid in each tube undergoes a phase change on the inside of the tube as it travel upward through the SG secondary side where it exits as superheated steam under normal operating conditions. A more detailed design explanation is given in Section 3.1. Helical coil (HC) tube bundles are capable of high thermal performance due to their large surface area per unit height and can accommodate more thermal expansions and flow induced vibration than straight tube bundles. Due to the curved shape of the coil, a centrifugal force acts upon the flowing fluid within the tube. In two-phase flow, this centrifugal force keeps the tube wall wet up to very high qualities, shifting the location at which dry-out occurs toward the vapor region and thus reducing the extension of the post dry-out two phase flow region. Since the tube wall is kept wet for more boiling length, the heat transfer capability increases compared to a vertical straight tube, especially in the high quality region of the channel. Thus, the HC tube promotes mixing of the fluid, thus increasing the heat transfer capability, but at the expense of higher flow pressure drop. Systems based on convective boiling flow are found in a wide variety of industrial applications, such as boiling water reactors, boilers, heat exchangers, condensers. Such systems take advantage of the high heat transfer rates that a boiling fluid can reach at moderate temperature differences. However, those systems are susceptible to thermally induced two-phase flow instabilities. The major concern with a SG located inside an RPV is the fact that boiling takes place inside the tubes, a condition potentially prone to parallel channel flow instability. This concern, though common to once-through designs, could be severe in the NPM due to the HCSG design with a very high ratio of tube length to tube diameter and high pressure drop. © Copyright 2022 by NuScale Power, LLC 8

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Oscillations in SG tube flow, pressure, and tube wall temperature can cause control problems, and thermal fatigue, which can potentially reduce the lifespan of an SG. For the NPM HCSG, excessive secondary flow oscillations can potentially exceed ASME fatigue limits at the FW plenum tube-to-tubesheet weld (i.e. at the SG tube inlet), causing unacceptable cavitation and accelerated wear during oscillations. Thus, SG flow instabilities should be prevented or reduced to acceptable levels. Secondary side instabilities in NPM SG can be mitigated by both design components, such as an inlet flow restrictor, and controlling operational parameters such as steam outlet pressure and superheat. The methodology herein therefore provides the basis for performing calculations in determining stable operating domains and characteristics of the NPM SG in order to prevent or reduce DWO instabilities to acceptable levels. 2.1 Regulatory Requirements General Design Criterion (GDC) 4 requires in part that structures, systems, and components important to safety are designed to accommodate the effects of and to be compatible with the environmental conditions associated with normal operation, maintenance, testing, and postulated accidents. These structures, systems, and components are appropriately protected against dynamic effects, including the effects of missiles, pipe whipping, and discharging fluids, that may result from equipment failures and from events and conditions outside the nuclear power unit. GDC 31 requires in part that the reactor coolant pressure boundary is designed with sufficient margin to assure that when stressed under operating, maintenance, testing, and postulated accident conditions the probability of rapidly propagating fracture is minimized. The design reflects consideration of service temperatures under operating, maintenance, testing, and postulated accident conditions and residual, steady state and transient stresses. NuScale submitted a design certification application (DCA) for review and approval of the US600 power plant design to the U.S. NRC. Upon final review and final ACRS meetings, it was determined that a Combined Operating License (COL) item was required to close portions of the reactor coolant system integral reactor pressure vessel and steam generator fatigue analysis to address potential impact of DWO to SG lifetime. A COL item 3.9-14 was created to address these concerns which states: A COL applicant that references the NuScale Power Plant design certification will develop an evaluation methodology for the analysis of secondary-side instabilities in the steam generator design. This methodology will address the identification of potential density wave oscillations in the steam generator tubes, and qualification of the applicable portions of the reactor coolant system integral reactor pressure vessel and steam generator given the occurrence of density wave oscillations, including the effects of reverse fluid flows within the tubes. This topical report provides the design analysis of secondary-side flow oscillations, that demonstrates that GDC 4 and GDC 31 are met with respect to structural and leakage integrity of the SG tubes from the effects of secondary-side DWO and reverse flow from © Copyright 2022 by NuScale Power, LLC 9

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 20 percent to 100 percent nominal power. As no evaluation methodology for analysis of secondary side instabilities or DWO existed, this LTR describes the methodology and partial closure of this COL item. The EM described herein identifies potential DWO in the SG tubes and provides information about such transients to downstream stress and fatigue analysis. Qualification of the SG tubes as reactor coolant pressure boundary components is accomplished as part of the qualification of the reactor pressure vessel. © Copyright 2022 by NuScale Power, LLC 10

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 3.0 NuScale Power Module Description and Operations 3.1 NuScale Power Module Steam Generator Operation The NPM, shown in Figure 3-1 is the fundamental building block of NuScales small modular reactor based power plant. It consists of a 250 megawatts-thermal reactor core housed with other primary system components in an integral reactor pressure vessel surrounded by a steel containment vessel, which is partially immersed in a large pool of water that serves as the ultimate heat sink. The primary reactor coolant path is upward through the reactor core. Heated water flows upward through the hot riser tube due to buoyancy forces and is turned downward at the pressurizer baffle plate. It then flows over the shell side of the SG, where it is cooled by conduction and convection of heat to the secondary coolant and continues to flow downward until its direction is again reversed at the lower reactor vessel head and turned upward back into the core. Coolant circulation is maintained entirely by natural buoyancy forces of the lower-density heated water exiting the core and the higher-density cooled water exiting the SG annulus. The NuScale design uses the Rankine thermal conversion cycle (Figure 3-2) to produce electricity. In the secondary circuit of each NPM, FW is pumped into four total FW plenums, two per steam generator, where it is heated by the primary-side coolant and boils to produce superheated steam. As shown in Figure 3-3, two main steam lines from each NPM combine into a single line and route the steam to a dedicated turbine-generator system that generates nominally 77 megawatts-electric (gross). Low pressure steam exiting the turbine is condensed and recirculated through three FW heater stages to the FW plenums. The NPM has two independent helical coil SGs in the upper outer annulus of the primary pressure vessel. Each SG tube is connected to one of four FW plenums at the bottom of the tube bundle and terminates at one of four steam (STM) plenums at the top of the bundle as shown in Figure 3-3. A large number of tubes are connected in parallel from each of the four common inlet plenums as shown in Figure 3-4. The HCSG tubes have a low inclination angle, but steeper transition sections at the inlet and outlet and therefore have behavior of both horizontal and vertical tubes in parallel. Unlike more common once-through SGs, the secondary-side of the NPM SG is inside the HCSG tubes and the primary-side is on the exterior of the HCSG tubes. Each tube or set of tubes undergo phase change of the fluid on the inside of the tube as it travels upward through the SG secondary-side where it exits as superheated steam under normal operating conditions. Systems based on convective boiling flow such as the NPM SG are found in a wide variety of industrial applications, such as boiling water reactors, boilers, heat exchangers and condensers. Such systems take advantage of the high heat transfer rates that a boiling fluid can reach at moderate temperature differences. However, these systems are susceptible to thermally induced two-phase DWO instabilities. The concern for the NPM SG is the fact that boiling takes place inside of the tubes, a condition potentially prone to parallel channel DWO. This concern is common to once-through SG designs. © Copyright 2022 by NuScale Power, LLC 11

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Oscillations in SG tube flow and tube wall temperature resulting from DWO can cause thermal fatigue, which can impact SG lifespan. These instabilities can be mitigated both by design features, such as a SG tube IFR, and by controlling operational parameters such as steam outlet pressure and steam superheat. Figure 3-1 NPM Cut Away © Copyright 2022 by NuScale Power, LLC 12

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 3-2 Thermal Conversion System

© Copyright 2022 by NuScale Power, LLC 13

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 3-4 Tube Bundle with the RPV And Riser (Left) and Tube Bundle Only (Right) © Copyright 2022 by NuScale Power, LLC 15

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 3.2 Evaluation Model Requirements and Figures of Merit This EM provides a validated method for calculating the margin to the onset of density wave oscillations in the NPM SG tubes that use a tube IFR device. It is used to size IFR resistance for the NPM to demonstrate thermal hydraulic stability between 20 percent and 100 percent reactor power (nominal). In order to evaluate SG stability with respect to DWO, the following figures of merit (FoMs) are selected:

1. DWO onset

2. DWO flow change amplitude

3. DWO flow rate frequency For this onset methodology, reasonable-to-excellent agreement is needed for prediction of DWO onset (FoMs 1), while minimal agreement is needed for flow change amplitude, and flow rate frequency (FoMs 2 and 3).

The calculation of margin is performed using realistic operating parameters that are used by non-safety related secondary side control systems for monitoring and control of power production. This report provides a description of the NuScale SG DWO EM. The following steps are used to develop EM. They are: Determining the requirements for the EM Developing an assessment base consistent with the determined requirements Developing the EM Assessing the adequacy of the EM Appendix A provides how various sections of this report align to these four principles of the evaluation model development and assessment process (EDMAP). This EM utilizes the NRELAP5 code that was developed from the Idaho National Laboratory (INL) RELAP5-3D© computer code. This report discusses the code and modeling requirements needed to address the phenomenon of the NPM SG design and prediction of DWO. 3.3 Description of DWO Phenomenon DWO occurs in parallel flow channels (e.g. HCSG tubes) due to feedback effects between flow, density, void fraction, and pressure drop. In a two-phase system, density decreases as fluid is heated along the channel. Pressure drop increases in the two-phase region compared to the single-phase region. As flow perturbations are induced at the inlet, the channel axial void fraction distribution changes. There is a time delay between the propagated void fraction change and the flow perturbation. At specific flow oscillations, the pressure drop at the exit becomes completely out of phase with the inlet © Copyright 2022 by NuScale Power, LLC 16

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 perturbation. Because the propagated void fraction change is referred to as a density wave, this 180-degree phase difference causes flow oscillations known as DWO. During NPM startup, shutdown and high power operation, dynamic instability such as DWO is of primary concern. DWO onset in a single tube depends on the tube pressure drop, inlet subcooling, power distribution, flow rate, and IFR pressure drop. For parallel tube configurations, it was experimentally shown that self-sustaining DWO can occur. The FW flow enters the HCSG tubes and is heated via primary-to-secondary heat transfer. Within the tubes, and after the single-phase liquid region, boiling occurs and voiding continues to increase until eventually superheated steam is produced at the exit. This arrangement of a heated channel is subject to DWO. © Copyright 2022 by NuScale Power, LLC 17

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 4.0 Phenomena Identification and Ranking and Scaling Analysis NuScale developed a phenomena identification and ranking table (PIRT) for DWO in the NPM SG. Reference 12.1 outlines the EMDAP which is summarized in Appendix A. Developing the PIRT is the first step of the EMDAP process because it provides critical input to the development of the EM, assessment bases, and methodology of its application. This EM utilized the process as needed to facilitate the PIRT development in tractable manner. 4.1 PIRT Objectives The objectives of the PIRT are to: Establish FoMs Identify phenomena affecting FoM Rank phenomena applicable to the appropriate FoM Identify the knowledge base associated with the phenomena, and provide a recommendation for closing the knowledge gap, as applicable. Determine the high-importance/low knowledge level phenomena to focus the development of the analytical model and to determine additional testing requirements and design improvements. Traditionally the PIRT development uses a simplified nine-step process described in Reference 12.2. Those nine steps were followed as need bases in the development of the NPM SG DWO PIRT. The PIRT supports scaling of separate effects and prototypical testing and design and operation of test facilities. The PIRT identifies the most important thermal-hydraulic phenomena for DWO. 4.2 PIRT Phenomena Phenomena are evaluated and ranked on a component bases. For the NPM HCSG, the necessary components are 1) the FW line, 2) the FW plenum, 3) the HCSG tube internal fluid, 4) the HCSG tube wall metal, 5) the HCSG tube external fluid (i.e. primary side liquid), 6) the steam plenum, and 7) the steam line. These components are grouped as shown in Table 4-1. © Copyright 2022 by NuScale Power, LLC 18

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Table 4-1 Component Designation for Phenomena Identification and Ranking Component Description Identification Tube inside HCSG inside evaluated for T-H phenomena 1 Tube geometry HCSG tube wall thickness, roughness, geometry 2 Tube outside Primary side T-H condition for heat transfer and 3 boundary conditions FW line and FW plenum FW line, FW plenum, and other components upstream 4 to HCSG Steam line and steam Steam line, steam plenum, and other components 5 plenum downstream of HCSG The PIRT Table is organized as follows: The first column lists the components identified for the system. The second column lists the phenomena likely to occur relevant to that component. The FoM columns are split where:

             -    1 refers to DWO onset
             -    2 refers to DWO flow change amplitude
             -    3 refers to DWO temperature change amplitude, and
             -    4 refers to DWO frequency.

The four FoM are important to quantifying tube inlet fluid temperature oscillations that can cause stresses on tube-to-tube sheet welds. The seventh column identifies the importance ranking column (H for high, M for medium, and L for low). The eighth column identifies the knowledge level ranking (where 4 indicates the highest knowledge level). The SG stability PIRT (Table 4-2) lists a total of 25 phenomena or processes for the NPM HCSG related to the following figures of merit (FoM): DWO onset, DWO flow amplitude, DWO temperature amplitude, and DWO frequency. No phenomenon/processes are ranked with a knowledge level of 1. Seventeen are importance ranked H, and a subset of six are importance ranked H with a knowledge level of 2 The subset of six H-2 ranked phenomena are emphasized in bold font in Table 4-2, and are discussed in Section 4.3. © Copyright 2022 by NuScale Power, LLC 19

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Table 4-2 SG DWO stability PIRT ((

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Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 4.3 Discussion of High Ranked Phenomena This section provides a summary of the high ranking phenomena, bases for phenomena ranking and knowledge level. 4.3.1 (( }}2(a),(c) ((

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                                      }}2(a),(c) 4.4      Scaling Analysis 4.4.1         Analysis of TF-2 Scaling This section presents the scaling analysis used to evaluate distortions associated with the existing TF-2 facility relative to the NPM design for density wave oscillation (DWO) experiments. The DWO data obtained from this facility was used for code validation. The scaling and distortion analysis is valuable to establish the adequacy of data for the NPM.

Table 4-3 provides nomenclature associated with the scaling analyses provided below. Table 4-4 provides index notations associated with the scaling analyses provided below. © Copyright 2022 by NuScale Power, LLC 25

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Table 4-3 Nomenclature Variable Definition A 2 Area ( m ) D Diameter ( m ) e Specific energy ( J kg ) - includes enthalpy, kinetic, and potential energies e Specific energy ( J kg ) without pressure and density definition g 2 Gravitational pull ( m s ) h Specific enthalpy ( J kg ) H Axial coil pitch j Quantity flux W k Thermal conductivity ( -------- ) mK L Length ( m ) F Forces in momentum equation, separated as friction, gravity, shear, and form loss fg Variable associated with transition from liquid to vapor. m Mass ( kg ) - equivalent to V P Pressure ( Pa ) q 2 Heat flux ( J m s ) Q Heat transfer ( J s ) v Velocity ( m s ) V 3 Volume ( m ) 3 Density of some quantity X ( X m ) Steam quality z Elevation of the center of mass ( m ) Void fraction or volume fraction The SG tube angle from horizontal - a subscript is used if the angle is different from average SG tube angle 3 Water mass conversion rate from liquid to vapor per volume ( kg m s ) latent heat of vaporization 3 Density ( kg m ) t Time ( s ) Characteristic time ( s ) T Temperature ( K ) W Work done by fluid ( J )

                                                   -1 Characteristic frequency ( s )

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Table 4-4 Index notation Index Part Definition B Buoyancy. Indexes used in the steam generator region to indicate ( u ) the unheated liquid region, u, c, s, v, h ( c ) the subcooled liquid region, ( s ) the two-phase saturated region, ( v ) the single-phase vapor region, and ( h ) steam header region f, g Indexes used to indicate ( f ) liquid and ( g ) gas or vapor h Heated length when applied to a L variable Steam header ( h ) at exit to steam generator tubes ( e ) for tube 1, tubes 2 through n-1 he1, hex, hen ( x ), and tube n i, o Inlet or outlet to a region as determined by the standard operational direction of flow out, in The outer diameter or inner diameter of a tube m Term used to indicate the property is part of the momentum analysis Or The orifice to a region w Index used to indicate the property is the wall F Frictional pressure loss G Gravitational head I Interfacial shear pressure loss L Pressure loss due to other loss terms such as orifice sat Saturated sub Subcooled T Variable associated with the combined steam generator tubes T1 Variable associated with a single steam generator tube 0 Initial condition value

         -         The bar above a property indicates that it is not pressure dependent
        ~          The tilde on a property indicates that the property is the value of the surrounding body

Indication term is a flow rate 4.4.2 Scaling Analysis Objectives, Methodology and Fundamental Requirements The main objective of this scaling analysis is to evaluate the distortion resulting from physical dimensions and operating conditions of a scaled test facility capable of simulating the important flow and heat transfer behavior of the NPM secondary side under steady-state and DWO conditions. Distortions are evaluated with specific objectives for each operational mode of interest identified below:

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 The similarity criteria that should be preserved or distortions between the test facility and the full-scale prototype are calculated. The priorities for preserving the similarity criteria for testing are established or reducing distortions for testing are determined. Specifications for the test facility modifications are established, if required. Biases due to scaling distortions are identified. To assure that the scaling objectives are met in an organized and clear traceable manner, a GDF was established. The model for this framework includes features drawn from Reference 12.4. 4.4.3 DWO Phenomena and Experiment Objectives The first task outlined by the GDF is to specify the experimental objectives. The experimental objectives define the types of tests that are performed to address specific design or certification needs. These objectives determined the general modes of operation that should be simulated in the test facility. There are practical limits concerning what can be studied in a single facility. The TF-2 test facility primarily focuses on evaluating steady-state operation and DWO onset criteria with operational margin. The objectives of DWO testing at TF-2 are to obtain qualified data to benchmark computer codes and models that are used to evaluate the NPM secondary side. These objectives include: 1) measurements of steady-state thermal hydraulic conditions on the secondary side and 2) characterization of DWO phenomena. 4.4.4 NPM HCSG Stability Phenomena Identification and Ranking Table The second task outlined by the GDF is the development of a PIRT. PIRT information is presented in Section 4.1 through Section 4.3. DWO phenomena identification and ranking are provided in Table 4-1. The PIRT table results are presented in Table 4-2. 4.4.5 TF-2 Facility Operating Conditions and Dimensions This section presents preliminary TF-2 facility operating conditions and physical dimensions and compares them to the corresponding preliminary values for the full-scale NPM. 4.4.5.1 Secondary Side Steady-State Operating Conditions This section provides the physical dimensions and operating conditions for the NPM and TF-2 facility. For NPM, operating conditions at 100 percent power is provided. For TF-2, test facility technical specifications and maximum allowable operation range from the existing data are provided. For evaluating distortions, © Copyright 2022 by NuScale Power, LLC 28

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 discrete NPM operating conditions are compared with corresponding TF-2 conditions. TF-2 facility underwent a power upgrade to better cover NPM conditions. The TF-2 maximum power is 8.5 megawatts thermal. Due to the power limitations of TF-2, different modeling schemes are used for 15 percent power and 100 percent power simulations. Table 4-5 provides nominal conditions for NPM and TF-2 to allow variations in the boundary conditions to reduce distortions. Table 4-5 NPM and TF-2 Steady-State Operating Conditions at 100% Power* Parameter (range) NPM TF-2 Units Core Power/tube (maximum) 33.73 (all rows) 181.2 kW 163.46 (row 3 only) Primary Pressure 2000 (137.9) 1450 (100) psia (bar) Secondary side SG DT 357.1 (453.74) 243 (408) °F (K) Secondary side FW pressure 545.7 (37.63) 507.63 (35) psia (bar) Secondary side steam plenum pressure 500 (34.48) 482.98 (33.3) psia (bar) Secondary side inlet temperature 200 (366.4) 200 (366.4) °F (K) Secondary side FW flow/tube 0.0705 0.05 kg/sec Inlet loss coefficient (K) (( }}2(a),(c).ECI (( }}2(a),(c),ECI N/A

Note: The best available information used for scaling analysis Table 4-6 NPM and TF-2 SG Design Comparison Parameter NPM TF-2 Units Tube material Alloy 690 AISI 304L N/A

of tubes 1380 252 N/A Tube outside diameter 15.88 16.07 mm Tube inside diameter 13.34 13.17 mm Tube length (active) 22.4 to 25.9 25.01 m Tube thickness 1.27 1.45 mm Single tube inside flow area 139.66 136.24 mm2 Helical coil radius (( }}2(a),(c),ECI (( }}2(a),(c),ECI m Table 4-7 NPM and TF-2 HCSG Row 3 Comparison NPM TF-2 Parameter Units Column 3 Row 3 Coil radius (( }}2(a),(c),ECI (( }}2(a),(c),ECI m Active length 24.91 25.01 m
of tubes per column 52 52 N/A Inclination angle 13.69 13.978 degrees Single tube, interior fluid volume 0.0035 0.0036 m3 Inside Heat Transfer Area 1.044 1.1079 m2 Tube material Alloy 690 AISI 304L N/A Table 4-6 shows TF-2 and NPM geometry parameter comparison. Tube ID and length are very close, which enhances in-tube thermal hydraulic scaling. The tube

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 thickness is 15 percent larger for TF-2, which increases the primary to secondary heat transfer resistance somewhat, but the tube metal is not the dominant resistance to heat transfer, and heat flux can be increased with an increased primary Thot. Table 4-7 provides a geometry comparison specifically for row 3. As can be seen in Table 4-7, the TF-2 row 3 geometrical parameters closely match the NPM column 3 parameters. 4.4.6 Scaling Evaluation using the H2TS Method The next step in GDF method requires performing scaling analysis for each of the hierarchical levels (e.g., systems and subsystems) and their modes of operation, as defined in the previous section. This section describes the Hierarchical Two-Tier Scaling (H2TS) method. This method has been used previously to develop the similarity criteria necessary to scale NIST for LOCA transients. The H2TS method was developed by the USNRC and is fully described in Reference 12.4. It was expanded upon in Reference 12.5, Reference 12.6, and Reference 12.7. Figure 4-1 presents the four basic elements of the H2TS analysis method. The first element consists of subdividing the plant into a hierarchy of systems. Each system is subdivided into interacting subsystems that are further subdivided into interacting modules that are further subdivided into interacting constituents (materials) that are further subdivided into interacting phases (liquid, vapor, or solid). Each phase can be characterized by one or more geometrical configurations and each geometrical configuration can be described by three field equations (mass, energy, and momentum conservation equations). Each field equation can incorporate several processes. © Copyright 2022 by NuScale Power, LLC 30

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 4-1 Flow Diagram for the H2TS Analysis (Reference 12.4) © Copyright 2022 by NuScale Power, LLC 31

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 4-2 HCSG Breakdown into Hierarchical Levels and Primary Operational Modes © Copyright 2022 by NuScale Power, LLC 32

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 4-2 presents the breakdown of the NPM into hierarchical levels and high-level processes to be scaled. It provides a roadmap used to structure the subsequent scaling analyses. The RCS and the HCSG tubes are the focus of this scaling study. 4.4.6.1 Scaling Analysis Methodology The basic objective of the H2TS scaling method is to develop a set of characteristic time ratios for the physical processes that play a significant role in the system response. For DWO phenomena, different physics (or terms in the system equations) are dominant in different regions of the HCSG tube. Thus the HCSG tube region is divided into regions where different terms are dominant. Figure 4-3 NPM HCSG Region Breakdown © Copyright 2022 by NuScale Power, LLC 33

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 As shown in Figure 4-3, the HCSG secondary side is divided into five regions: four regions for the HCSG tube and a fifth steam header region where the HCSG tubes merge. The FW header provides a boundary condition. An orifice at the inlet to the HCSG region plays an important role in stabilizing DWO behavior and is included in the model as part of an entrance unheated section of the tube. In order to induce the DWO behavior, the orifice is modeled as a valve that slowly opens over the simulation. Note that the TF-2 experiment includes a section of pipe following the orifice that is heated, while the NPM does not include an unheated section of pipe after the orifice. This configuration is followed by the heated single-phase liquid region, the two-phase mixture region, and the single-phase vapor region. Lengths of the heated regions depend on initial and boundary conditions. The length of the subcooled region are established by the onset of significant void if void information is available. When insufficient void information is available, but heat transfer data are available, the length of the single-phase region can be estimated by the amount of heat addition required for the water to reach saturation conditions. Since systems typically exhibit some subcooled boiling, the use of void fraction data is the preferable method to calculate the boundary of the subcooled and two-phase regions. The boundary between the two-phase region and the single-phase vapor region is determined by the energy required to heat the liquid entering the HCSG to saturated conditions and then convert it to steam. 4.4.6.2 Fluid Field Equations As part of the two-tiered hierarchical scaling analysis, after the system is divided into relevant systems, subsystems, modules, constituents, phases, and geometrical configurations, then the relevant field equations, for a particular geometrical configuration, are scaled. The basic field equations, which are the mass continuity equation, the energy equation, and the momentum equation, are shown in Table 4-8. © Copyright 2022 by NuScale Power, LLC 34

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Table 4-8 Field Equations Field Field Equation Mass dm

              ------- - m* i + m* o = V, m* =  Av, m =  V = ( i.e. for two phase (  V ) )

dt Energy d ( me -) - m* e + m* e = Q - W

              --------------          i i       o o dt 1 2                   P 1 2                                  1 2 e = h + --- v + gz = u + --- + --- v + gz , e = u + --- v + gz 2                      2                                    2 Momentum d ( mv ) *
                 --------------- - m i v i + m* o v o = -PA + F G + F I + F L + F F dt or d(Lv)                     2        2                    FG FI FL FF
                  ------------------ -  i v i +  o vo = -P + ------       - + ----- + ------ + ------

dt A A A A F G (Gravitational Force), F I (Interfacial Force) F L (Form Loss), F F (Frictional Force) The typical definition of P (i.e., the downstream pressure minus the upstream pressure) leads to a negative P value for pressure driven flow. In order to obtain positive Pi group values, the definition is reversed (upstream pressure minus downstream pressure). In the heated region, the enthalpy and internal energy terms are much larger than the kinetic and potential energy terms. At an operating pressure of 2000 psia, the enthalpy of vaporization is (( }}2(a),(c), and the change in internal energy is (( }}2(a),(c). At 100 percent power, the exit velocity of the HCSG tubes is about (( }}2(a),(c), which equates to the kinetic energy of (( }}2(a),(c). The difference in elevation across the HCSG tube ( h ) is about (( }}2(a),(c). HCSG change in potential energy across the HCSG tubes is about (( }}2(a),(c) ( gh ). Thus, enthalpy and internal energy are over three orders of magnitude larger than kinetic and potential energy in the heated region and the kinetic and potential energy are ignored in this region. W represents the work due to pressure loss terms. Neglecting the kinetic energy and potential energy terms lead to the following simplified energy equation, which is used in the heated region of the HCSG tube. d ( mu ) *

                                                          --------------- - m i h i + m* o h o = Q - W                     Equation 4-1 dt

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 As noted previously, the steam generator tube is divided into four regions, with the steam header comprising the fifth region. The field equations are evaluated in each of these regions. These regions are an unheated region, a subcooled liquid region, a two-phase vapor generation region, a single-phase vapor region, and the steam header region. The subscripts i and o are used to indicate boundary terms at the inlet and outlet of the HCSG tube region. A subscript is used with the field equations to identify variables associated with each region with u for the unheated region, c for the subcooled region, s for the saturated two-phase region, v for the single-phase vapor region, and h for the steam header region. Thus, for example, v so indicates the velocity at the outlet of the two-phase region. The boundary between the subcooled liquid region and the two-phase region is determined by the onset of significant void when void data are available. Since the onset of the significant void can occur when the bulk temperature is below saturation conditions, the two-phase region may contain some liquid that is not yet at saturation conditions. For the single-phase liquid and single-phase vapor regions, the vapor generation term and the interfacial friction force term F I are zero. This condition is also true in the two-phase region when considered as a mixture since the liquid and vapor equations each have an equal and opposite vapor generation. The interfacial friction and buoyancy terms also have equal and opposite forces between the liquid and vapor, which cancel when liquid and vapor equations are summed. 4.4.6.3 Evaluation of Scaling Analysis Equations The scaling analysis calculations are based on NRELAP5 models of the NPM and the TF-2 facility. Calculations are summed over cells within the models, and many of the calculations are summed only over the cells in a particular region. For example, the length of the subcooled region is determined by the location of the onset of significant void, which is defined as void of 0.5 percent. The location typically includes only a fraction of a cell. Once the cells have been defined for a region, calculations for quantities defined over the region are evaluated by summing the quantities over the cells in the region. The summation symbol is implied for the region calculations. At the edges of a region, when only a fraction of a cell is included in the region, linear interpolation is used to partition the calculated value between the adjacent regions. As an example, in the subcooled region the gravitational Pi group is defined as: c0 gL c0 cG = -------------------- sin ( c ) Sm © Copyright 2022 by NuScale Power, LLC 36

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 4.4.6.4 Calculating Temporal Scales and Frequencies The two-tiered hierarchical scaling methodology defines a methodology for calculating temporal scales associated with processes in order to group processes into those of the same order of magnitude when examining a control volume in order to determine the relative importance. The temporal scale characterizes a process that occurs across a boundary into a control volume. The formula for calculating the temporal scale is:

                                                      = V       -
                                                           -------                                     Equation 4-2 Aj V is the control volume being analyzed and A is the area of the boundary across which a transfer process occurs  . is a quantity density (i.e., quantity per volume) and j is the quantity flux (i.e., transfer of quantity per area) associated with the field equation being analyzed. For example, the quantity may be mass and the density is mass density. The flux would represent mass flux across a boundary or possibly a mass conversion process such as condensation. In a case like condensation, where the rate may be expressed as a volumetric rate, the Aj would need to be replaced by V   , where represents the transfer rate per volume.

It is also common for quantities to be specified on a per mass basis . The temporal scale for mass transfer in the volume, which is used commonly in development of the non-dimensional Pi groups, is:

                                                       = m  ---*-                                     Equation 4-3 m

A non-dimensional Pi group is defined for each term in the field equations. Given the time scale associated with a Pi group, the Pi groups can be decomposed into the product of the temporal scale and a specific frequency of the process as follows:

                                                     =                                              Equation 4-4 4.4.6.5            The Phase Change Number and Subcooled Number The standard parameters used to characterize DWO stability are the phase change (or Zuber) number and the subcooling number, which are defined as:

Q f - g N pch.eq = ------------

                                                         *          ------------------                 Equation 4-5 m hf g g

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 h i f - g N sub = ------------ ------------------ Equation 4-6 h f g g These are useful for comparing results to the literature. While these parameters have proved useful for generating a stability map for individual systems, it is well known that the stability results do not directly translate to other systems. However, different systems are expected to show similar stability map trends relative to these parameters. 4.4.6.6 Selecting the Time Point for Performing Scaling Analysis The scaling analysis is used to characterize conditions at the onset of DWO. For both the NPM and TF-2 models, the orifice loss for the steam generator tubes is set high enough that the model is initially in a stable state that exhibits no DWO phenomenon. In order to induce DWO in the NRELAP5 model the orifice loss is reduced by slowly opening the valve. As the orifice resistance goes below some critical threshold, density wave oscillations are observed. Non-dimensional numbers are also used to evaluate the onset of DWO. DWO typically shows the flow/velocity oscillation, HCSG outlet velocity is chosen as a parameter to indicate the onset of DWO. For non-dimensionalization, inlet liquid velocity that is fixed from the boundary condition is used as a non-dimensional parameter. The ratio of the HCSG tube outlet vapor velocity to the inlet liquid velocity is selected to identify the onset of DWO because it provides a good indication of the onset of DWO. This ratio is defined as v and is related to the Zuber and phase change number that are commonly used to characterize the onset of DWO. Below is an example plot of v for the TF-2 facility at 15 percent power. From Figure 4-4 it is apparent that density wave oscillations start at about (( }}2(a),(c) so this time is used as the time point for performing the non-dimensionalization. While (( }}2(a),(c) shows that oscillations beginning at a later time, each case can only have one point where the non-dimensionalization time starts. The onset of DWO can be seen in the ratio of the HCSG outlet velocity to the fixed inlet velocity during DWO onset and full cycle DWO. © Copyright 2022 by NuScale Power, LLC 38

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 4-4 DWO Onset ((

                                                                                                                 }}2(a),(c) 4.4.7         NRELAP5 Models for Scaling Assessments NPM cases are selected to cover 100 percent power range and 15 percent power range. Power level of 100 percent is important as the plant is expected to be operated at this level most often. 15 percent power condition represents the low power condition where the full set of TF-2 rows are operational. Table 4-9 lists the steady-state parameters expected for the NPM and TF-2 secondary side at selected power levels.

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Table 4-9 NPM and TF-2 Initial Conditions at Different Power Levels ((

                                                                                                                }}2(a),(c) 4.4.7.1            TF-2 Models for 15 Percent and 100 Percent Power For 100 percent power, a ((
                                                                                                   }}2(a),(c) 4.4.7.2            NPM DWO Scaling Models for 15 Percent and 100 Percent Power NPM NRELAP5 inputs are created for 15 percent and 100 percent power.

((

                                            }}2(a),(c) 4.4.8         Analysis of scaling distortions Nondimensional PI groups are derived for the system governing equations to allow comparison of the TF-2 test facility results with the NPM simulation results. The PI

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 groups help establish the relative importance of different terms in the governing equations. PI group development allows separating relevant and irrelevant DWO phenomena. The TF-2 and NPM PI groups are compared to determine if the scale model geometry, boundary, or initial conditions introduce significant scaling distortions. The effect of distortion in the model for a specific process can be quantified as follows: [ i ]P - [ i ]m DF = ----------------------------------

                                                                                -                       Equation 4-7

[ i ]P Where index m indicates the reduced scale model (TF-2 experimental model) that is used for validation purposes and P is full-scale prototype (NPM). The distortion factor, (DF), represents the fractional difference in the amount of conserved property transferred through the evolution of a specific process in the prototype to the amount of property conserved through the same process in the model during the respective residence time. The degree to which a specific transfer process could impact a particular transient can be determined by comparing the maximum characteristic time ratio for each of the transfer processes that arise during the transient. A global distortion factor is defined that combined the individual distortion factors, weighted by the relative magnitude of the Pi groups in order to give proper weighting to the distortion factors. The global distortion is calculated for each of the simulations that is executed. Results are summarized in Table 4-10 and Table 4-11 which tabulates values of the Pi groups with the distortion from Equation 4-7. ((

                                              }}2(a),(c)

The scaling analysis gives rise to several Pi groups. Pi groups are defined for each of the SG tube regions (unheated, subcooled, two-phase, single-phase vapor, and steam header), with Pi groups being calculated for both the primary and secondary side. A Pi group is defined for each term of each of the field equations used to characterize the behavior in a region. Not all of the Pi groups are important for characterizing DWO behavior. Pi groups that provide similar information are not included; for example, several single-phase vapor Pi groups and steam header Pi groups provide the similar flow information. Therefore, only one set of Pi groups are used. Pi groups are also calculated for the primary side flow across the steam generator tubes. While these Pi groups provide some information about the source of heat transfer to the secondary side, it is the overall heat transfer to each region that is of primary importance. Heat transfer is already characterized by the secondary side heat © Copyright 2022 by NuScale Power, LLC 41

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 transfer Pi groups. Thus, the primary side Pi groups tend to provide repeated information. In order to determine which of the SG secondary side Pi groups are important, it is useful to look at the Pi groups values. Note that the Pi group terms for the momentum equation in each of the regions is scaled by the total pressure drop across the tubes rather than scaling the region by a pressure drop across the region. Scaling by total pressure drop across the tubes is done in order to allow Pi groups in different regions to be compared directly to determine the relative importance of each momentum Pi group over the tube region. Similarly, the energy equation in each region is scaled relative to the energy needed to convert the liquid entering the region from saturated liquid to saturated vapor. Thus, the energy Pi groups in each region can be compared for relative importance. Based on the values of Pi groups, only the dominant Pi groups are presented in the scaling analysis. Table 4-10 TF-2 Distortion for DWO Phenomena Compared with 100% NPM Operating Condition ((

                                                                                                                 }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Table 4-10 TF-2 Distortion for DWO Phenomena Compared with 100% NPM Operating Condition (Continued) ((

                                                                                                                }}2(a),(c)

Table 4-11 TF-2 Distortion for DWO Phenomena Compared with 15% NPM Operating Condition ((

                                                                                                                }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Table 4-11 TF-2 Distortion for DWO Phenomena Compared with 15% NPM Operating Condition (Continued) ((

                                                                                                                }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Table 4-12 provides the comparison between pressure drop Pi groups for the regions between NPM and TF-2 at 100 percent power levels. Note that overall region lengths are comparable between NPM and TF-2. Table 4-13 provides the comparison of pressure drop Pi groups for the regions between NPM and TF-2. Table 4-12 Pressure Group Distortion at 100% Power Condition ((

                                                                                                                }}2(a),(c)

Table 4-13 Pressure Group Distortion at 15% Power Condition ((

                                                                                                                }}2(a),(c)

((

                                              }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 ((

                      }}2(a),(c) 4.4.9         Scaling sensitivity and Distortion Optimization Methodology The baseline boundary conditions for the TF-2 tests are selected to align with boundary conditions in the NPM at equivalent power. Ideally the TF-2 tests for the given power levels would have zero distortion relative to the NPM plant at the equivalent power. Due to difference in the TF-2 facility and the NPM steam generator some distortion is expected. However, it is desirable for this distortion to be as small as possible. Minimizing distortion is accomplished via optimization, where the objective of optimization is to identify adjusted TF-2 boundary conditions at which to run the system in order to have the smallest distortion. However, given that a separate distortion factors are calculated for each Pi group, it is useful to devise a method to combine the Pi groups into a single system wide distortion factor that can be minimized in order to determine whether a change in boundary conditions leads to a smaller overall distortion.

The List of Pi groups included to calculate the global distortion is: (( }}2(a),(c) A set of sensitivity cases is run and global distortions are calculated to identify conditions that leads to minimal distortions. There are several parameters that can be varied in the experiments that have an impact on the Pi groups and the associated distortions. The following five parameters are selected that are likely to have an impact: ((

                                            }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 ((

                             }}2(a),(c)

For each parameter, a lower and an upper sensitivity bound is select around the baseline parameter value. A sensitivity analysis is performed on each of the parameters individually. A summary of the results are provided in Table 4-14, Table 4-15, and Table 4-16. Table 4-14 Parameter Bounds for the 15% Power Sensitivity Cases ((

                                                                                                                  }}2(a),(c)

Table 4-15 Parameter Bounds for the 100% Power Sensitivity Cases ((

                                                                                                                  }}2(a),(c)

Table 4-16 Distortions for the Optimal Cases ((

                                                                                                                  }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Table 4-16 Distortions for the Optimal Cases ((

                                                                                                                  }}2(a),(c) 4.4.10         Transient Distortions The PI groups associated with a steady-state analysis are useful for characterizing conditions at DWO onset. The amplitude and frequency of oscillations are also of interest. Currently, there is no analytical closed form model available to predict the amplitude and frequency of oscillations as a function of operating parameters.

For the current scaling analysis, the momentum equation is non-dimensionalized over the whole tube. The same base momentum equation is used, with the terms calculated for the whole tube, rather than region specific terms used in the steady state analysis. (( Equation 4-8

                                                                                               }}2(a),(c)

The non-dimensionalization of the whole SG tube is similar to the non-dimensionalization of the different regions of the SG tube. The same scaling factor 1 P T1 is used for whole tube scaling. However, the left hand momentum terms are divided into three PI groups. The nondimensionalized equation after applying the scaling factor is: (( Equation 4-9

                                                                                               }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Pi Groups P , g , F , and O are a natural extension of the associated PI groups from each of the SG tube regions, being the sum of the associated PI groups over a SG tube region. The PI group definitions for each of the terms is shown below: (( Equation 4-10 Equation 4-11 Equation 4-12 Equation 4-13 Equation 4-14 Equation 4-15 Equation 4-16

                                                                                             }}2(a),(c)

The variables m and v are whole tube quantities defined below, where subscript i is an index associated with NRELAP5 cells in the SG tube region. A subscript 0 indicates the value evaluated at the time selected for nondimensionalization. For the transient analysis, DWO onset point is used as the time for nondimenisonalization.

                                                                    +  m-m =   mi ,             m = ------

m0 Equation 4-17 mi vi

                                                                     +   v v = ------------------ , v = -----                            Equation 4-18 v0 mi The non-dimensional time is defined as:
                                                       +          t t       = --                                       Equation 4-19 Where  is defined as m  m* . It represents the time required to transport liquid through the tube, or equivalently, the time required to replace the fluid in the tube. In order to examine the frequency of oscillation/time period, the non-dimensionalized momentum

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 term is expanded as shown below. Thus, plots of this term represent the change in momentum with time scaled by the pressure force applied across the tubes. (( Equation 4-20

                                                                                           }}2(a),(c)

For comparing non-dimensionalized transient scaling factor and evaluating distortions, NPM and TF-2 NRELAP5 cases are run beyond the DWO onset and allowed to reach the limit cycle. DWO onset and transient parameters are used to evaluate the transient Pi groups. Transient Response for TF-2 ((

                                                           }}2(a),(c)

Transient PI groups for 100 percent and 15 percent power between NPM and TF-2 are shown in Table 4-17 and Table 4-18 below. Table 4-17 Transient Pi Group Distortion for TF-2 and NPM 100% ((

                                                                                                                }}2(a),(c)

Table 4-18 Transient Pi Group Distortion for TF-2 and NPM 15% ((

                                                                                                                }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 ((

                                      }}2(a),(c)

Table 4-19 and Table 4-20 present the DWO amplitude (or resultant delta oscillation) and frequency distortions between NPM and TF-2 for 100 percent and 15 percent power. ((

                     }}2(a),(c)

Table 4-19 Nondimensional Resultant Momentum Oscillation and Frequency Comparison Between TF-2 and NPM at 100% Power ((

                                                                                                                   }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Table 4-20 Nondimensional Resultant Momentum Oscillation and Frequency Comparison Between TF-2 and NPM at 15% Power ((

                                                                                                                  }}2(a),(c) 4.4.11        Scaling and Distortion Analysis Conclusion Scaling analysis on TF-2 is performed using H2TS method to identify the important Pi groups providing relative comparison of phenomena important to DWO onset between NPM and TF-2 in non-dimensional space. Scaling optimization is also performed to reduce the distortions by optimizing the test conditions at TF-2.

Transient scaling analysis is also performed to evaluate relative distortions in comparing oscillation magnitude and frequency in non-dimensional space. The purpose of TF-2 is not to provide a direct simulation of NPM conditions, but rather for generating applicable validation test data. TF-2 provides an adequately scaled prototypic test facility for providing validation data for NPM DWO over a range of power conditions. © Copyright 2022 by NuScale Power, LLC 52

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 5.0 NRELAP Code Description The NuScale DWO EM is based on the NRELAP5 system thermal-hydraulics code. The NRELAP5 code includes models for characterization of hydrodynamics, heat transfer between structure and fluids, modeling of fuel, reactor kinetics models, and control systems. NRELAP5 uses a two-fluid, non-equilibrium, non-homogeneous model to simulate system thermal-hydraulic responses. This section provides a general overview of the code structure, models, and correlations. This section also addresses specific code models and improvements implemented to address unique design features and phenomena for the NPM. The adequacy of code models and correlations essential for modeling the high-ranked PIRT phenomena is discussed in Section 4.0. The full details of the models and correlations that makeup NRELAP5 can be found in the NRELAP5 Theory Manual (Reference 12.8). RELAP5-3D©, version 4.1.3, was used as the baseline development platform for the NRELAP5 code. RELAP5-3D© was procured and as part of the procurement process for commercial grade dedication, which was performed by NuScale to establish the baseline NRELAP5 code. Subsequently, features were added and changes made to NRELAP5 to address the unique aspects of the NPM design and licensing methodology. Those aspects of NRELAP5 that are new or revised specifically for the NPM application include: helical coil SG heat transfer and pressure drop models core CHF models wall condensation models critical flow models interfacial drag models for large-diameter pipes core CHF limit stop The first item on the above list is of particular importance to prediction of DWO, and is detailed in Section 6.0. Code modifications of importance to DWO are listed and described in Table 5-1. The RELAP5 series of codes were developed at the INL under sponsorship of the DOE, the US NRC, members of the International Code Assessment and Applications Program, members of the Code Applications and Maintenance Program, and members of the International RELAP5 Users Group. Specific applications of the code have included simulations of transients in light water reactor systems, such as LOCAs, anticipated transients without scram, and anticipated operational occurrences, such as loss of feedwater, loss of offsite power, station blackout, and turbine trip. The RELAP5 code, including the RELAP5-3D© version that was used as the development platform for NRELAP5, has an extensive record of usage and acceptable performance for nuclear safety analysis. RELAP5-3D© is the latest version of the RELAP5 code that has been under continuous development since 1975, first under NRC sponsorship and then with additional DOE sponsorship beginning in the early 1980s. © Copyright 2022 by NuScale Power, LLC 53

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 While NRC sponsorship ended in 1997, the DOE continued sponsorship of RELAP5-3D© to meet its own reactor safety assessment needs. The RELAP5 code was chosen by DOE as the thermal-hydraulic analysis tool because of its widespread acceptance. Table 5-1 NRELAP5 Code Modifications (DWO specific only) ((

                                                                                                                }}2(a),(c) 5.1      Quality Assurance Requirements The NRELAP5 code is developed following the requirements of the NuScale QAPD (Reference 12.9). The NuScale corporate Software Configuration Management Plan provides a framework for NRELAP5 configuration management and change control in conformance with the requirements outlined in the NuScale Software Program Plan. The NuScale QAPD complies with the requirements of 10 CFR 50 Appendix B, Quality Assurance Criteria for Nuclear Power Plants and Fuel Reprocessing Plants (Reference 12.10) and American Society of Mechanical Engineers (ASME) NQA-1-2008 and NQA-1a-2009 Addenda, Quality Assurance Program Requirements for Nuclear Facility Applications, (Reference 12.11).

5.2 Hydrodynamic Model The NRELAP5 hydrodynamic model is a transient, two-fluid model for flow of a two-phase vapor-gas-liquid mixture that can contain non-condensable components in the vapor-gas phase as well as a soluble component (i.e., boron) in the liquid phase. The two-fluid equations of motion that are used as the basis for the NRELAP5 hydrodynamic model are © Copyright 2022 by NuScale Power, LLC 54

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 formulated in terms of volume and time-averaged parameters of the flow. Phenomena that depend upon transverse gradients, such as friction and heat transfer, are formulated in terms of the bulk properties using empirical transfer coefficient formulations. In situations where transverse gradients cannot be represented within the framework of empirical transfer coefficients, such as subcooled boiling, additional models specially developed for the particular situation are employed. The system model is solved numerically using a semi-implicit, finite-difference technique. 5.2.1 Field Equations The NRELAP5 thermal-hydraulic model solves eight field equations for eight primary dependent variables. The primary dependent variables are pressure, phase-specific internal energies, vapor or gas volume fraction, phasic velocities, non-condensable quality, and boron density. For the one-dimensional equations, the independent variables are time and distance. Non-condensable quality is defined as the ratio of the non-condensable gas mass to the total vapor or gas phase mass. The secondary dependent variables used in the equations are phasic densities, phasic temperatures, saturation temperature, and non-condensable mass fraction in the non-condensable gas phase for the ith non-condensable species. The basic field equations for the two-fluid, non-equilibrium model consist of two phasic continuity equations, two phasic momentum equations, and two phasic energy equations. The equations are time averaged and one-dimensional. The phasic continuity equations are shown in Equation 5-1 and Equation 5-2. 1 ( g g ) + --- ( g g v g A ) = g Equation 5-1 t Ax ( ) + - ( v A ) = Equation 5-2 t f f Ax f f f f Continuity consideration yields the interfacial condition of Equation 5-3. f = -g Equation 5-3 The interfacial mass transfer model assumes that total mass transfer can be partitioned into mass transfer at the vapor/liquid interface in the bulk fluid ( ig ) and mass transfer at the vapor/liquid interface in the thermal boundary layer near the walls ( w ) as defined by Equation 5-4. g = ig + w Equation 5-4 The phasic momentum equations are in the form of Equation 5-5 and Equation 5-6. © Copyright 2022 by NuScale Power, LLC 55

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 2 v 1 v P g g A -------g- + --- g g A -------g- = - g A ------ + g g B x A - ( g g A )FWG v g t 2 x x

                                          +  g A ( v gI - v g ) - (  g  g A )FIG  ( v g - v f )                         Equation 5-5

( vg - vf ) v g v f

                                          - C  g  f  m A ------------------------
                                                                                   - + v f -------- - v g -------

t x x 2 v 1 v P f f A -------f + --- f f A -------f- = - f A ------ + f f B x A - ( f f A )FWF v f t 2 x x

                                             -  g A ( v fI - v f ) - (  f  f A )FIF  ( v f - v g )                      Equation 5-6

( vf - vg ) v f v g

                                        - C  f  g  m A ------------------------
                                                                                 - + v g ------- - v f -------- .

t x x The force terms on the right sides of Equation 5-5 and Equation 5-6 are, respectively, the pressure gradient, the body force (i.e., gravity and pump head), wall friction, momentum transfer due to interface mass transfer, interface frictional drag, and force due to virtual mass. The terms FWG and FWF are part of the wall frictional drag, which are linear in velocity, and are products of the friction coefficient, the frictional reference area per unit volume, and the magnitude of the fluid bulk velocity. The coefficients FIG and FIF are part of the interface frictional drag; two different models (drift flux and drag coefficient) are used for the interface friction drag, depending on the flow regime. Conservation of momentum at the interface requires that the force terms associated with interface mass and momentum exchange sum to zero as shown by Equation 5-7. ( vg - vf ) g Av gI - ( g g A )FIG ( v g - v f ) - C g f m A ----------------------- t Equation 5-7 ( vf - vg )

                    -  g Av f I - (  f  f A )FIF  ( v f - v g ) - C  f  g  m A ------------------------- = 0 t

The phasic thermal energy equations are defined by the following two equations: 1 g P ( g g U g ) + --- ( g g U g v g A ) = - P --------- - --- g v g A t A x t Ax Equation 5-8

                                              + Q wg + Q ig +          ig h g     + w hg      + DISS g 1                                        f P

( f f U f ) + --- ( f f U f v f A ) = - P -------- - --- ( f v f A ) t Ax t A x Equation 5-9

                                             + Q wf + Q if -         ig h f     -   w hf   + DISS f .

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 In the phasic energy equations, Q wg and Q wf are the phasic wall heat transfer rates per unit volume. These phasic wall heat transfer rates satisfy Equation 5-10 where Q is the total wall heat transfer rate to the fluid per unit volume. Q = Q wg + Q wf Equation 5-10 The vapor generation (or condensation) consists of two parts, vapor generation that results from energy exchange in the bulk fluid ( ig ) and energy exchange in the thermal boundary layer near the wall ( w ) (Equation 5-4). Each of the vapor generation (or condensation) processes involves interface heat transfer effects. The interface heat transfer terms ( Q ig and Q if ) appearing in Equation 5-8 and Equation 5-9 include heat transfer from the fluid states to the interface due to interface energy exchange in the bulk and in the thermal boundary layer near the wall. The vapor generation (or condensation) rates are established from energy balance considerations at the interface. The phasic energy dissipation terms, DISS g and DISS f , are the sums of wall friction, pump, and turbine effects. The dissipation effects due to interface mass transfer, interface friction, and virtual mass are neglected. 5.2.2 State Relations The six-equation model uses five independent state variables with an additional equation for the non-condensable gas component. The independent state variables are chosen to be P , g , U g , U f , and X n . The remaining thermodynamic fluid variables (temperatures, densities, partial pressures, qualities, etc.) are expressed as functions of these five independent state variables (Equation 5-11). In addition to these variables, several state derivatives are needed for some of the linearizations used in the numerical scheme. g g f f

                       --------g-  , ----------      ,  ---------  ,  -------- ,  ---------

P U g, X n U Equation 5-11 g P, X n X n P, U g P f U f U P The interphase mass and heat transfer models use an implicit (linearized) evaluation of the temperature potentials T I - T f and T I - T g . The quantity T I is the temperature that exists at the phase interface. The implicit (linearized) evaluation of the temperature potentials in the numerical scheme requires the derivatives of the phasic and interface temperatures defined by Equation 5-12. © Copyright 2022 by NuScale Power, LLC 57

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 T

                             --------g-            T g              T g                T f P  U g, Xn  U                                             P  U f g P, X n  X n P, U g Equation 5-12 T f                  s             T s             T s T
                              --------- ,  -------- U , X ,  ----------     ,  ---------

U f P P g n U g P, X X n P, U n g 5.2.2.1 Water Property Tables The set of basic properties for light water is used for the calculations. Implementation is activated by the user. These thermodynamic tables tabulate saturation properties as a function of temperature, saturation properties as a function of pressure, and single-phase properties as a function of pressure and temperature. The tables are based on the 1995 Steam Tables from the International Association for the Properties of Water and Steam (IAPWS) and are known as IAPWS-95. The temperature and pressure range covered in the property table is 273.16 K (32.018 degrees F) to 5000 K (8540.33 degrees F) and 611.6 Pa (0.0887 psia) to 100 MPa (14,504 psia). The properties and derivatives in the tables are saturation pressure, saturation temperature, specific volume ( ), specific internal energy, specific entropy, and three derivatives: the isobaric thermal expansion coefficient ( ), the isothermal compressibility ( ), and the specific heat at constant pressure (Cp). Liquid properties are obtained from the thermodynamic tables, given P and Uf. The desired density and temperature derivatives can then be obtained from the derivatives of f , f , and Cpf . In the case of the vapor being subcooled or the liquid being superheated, (i.e., metastable states) the calculation of v , T , , , and C p incorporates a constant pressure extrapolation from the saturation state for the temperature and specific volume. 5.2.3 Flow Regime Maps The one-dimensional nature of the field equations for the two-fluid model used in NRELAP5 precludes direct simulation of effects that depend upon transverse gradients of physical parameters, such as velocity or energy. Consequently, such effects must be accounted for through algebraic terms added to the conservation equations. The mapping for flow conditions to a specific flow regime is required to provide closure to the two-fluid equations. The selected flow regime determines the constitutive relationships that are applied for interphase friction, the coefficient of virtual mass, wall friction, wall heat transfer, and interphase heat and mass transfer. The flow regime maps are based on the work of Taitel and Dukler (Reference 12.12 and Reference 12.13) and Ishii (Reference 12.14, Reference 12.15, and Reference 12.16). Taitel and Dukler have simplified flow regime classifications and © Copyright 2022 by NuScale Power, LLC 58

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 developed semi-empirical relations to describe flow regime transitions. However, some of their transition criteria are complex, and further simplification have been carried out in order to efficiently apply these criteria in NRELAP5. The flow regime maps for the volumes and junctions are identical but used differently as a result of the finite difference scheme and staggered mesh used in the numerical scheme. The volume map is based on volume quantities. It is used for interphase heat and mass transfer, wall friction, and wall heat transfer. The junction map is based on junction quantities and is used to calculate the interfacial friction coefficient. Three flow-regime maps in both volumes and junctions for two-phase flow are used in the NRELAP5 code: (a) a horizontal map for flow in pipes; (b) a vertical map for flow in pipes, annuli, and bundles; and (c) a high mixing map for flow through pumps. Wall heat transfer depends on the volume flow regime maps in a less direct way. Generally, void fraction and mass flux are used to incorporate the effects of the flow regime. Since the wall heat transfer is calculated before the hydrodynamics, the flow information is taken from the previous time step. 5.2.3.1 Vertical Volume Flow Regime Map The vertical volume flow regime map is for upflow, downflow, and counter current flow in volumes whose inclination (vertical) angle is such that 60 < 90 degrees. An interpolation region between vertical and horizontal flow regimes is used for volumes whose absolute value of the inclination angle is between 30 and 60 degrees. This map is modeled as nine regimes: four regimes for pre-CHF heat transfer - bubbly, slug, annular-mist, and dispersed (droplet or mist) four regimes for post-CHF heat transfer - inverted annular, inverted slug, mist, and dispersed (droplet or mist) one regime for vertical stratification A schematic of the vertical flow regime map as coded in NRELAP5 is shown in Figure 5-1. The schematic is three-dimensional to illustrate flow-regime transitions as functions of void fraction g , average mixture velocity v m , and boiling. © Copyright 2022 by NuScale Power, LLC 59

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 5-1 Schematic of Vertical Flow-Regime Map Indicating Transitions 5.2.3.2 Horizontal Flow Regime Map The horizontal volume flow regime map is for volumes whose inclination angle is such that 0 < 30 degrees. The inclination angles for NPM, and the three acceptance tests are less than 30 degrees (Table 8-1) so horizontal flow regimes are applicable to the helical coils. A schematic of the horizontal volume flow regime map as coded in NRELAP5 is illustrated in Figure 5-2. Transition regions used in the code are indicated with shaded areas. Such transitions are included in the map primarily to preclude discontinuities when going from one correlation to another. Details of the interpolating functions employed between correlations are given in the sections that describe the various correlations in Reference 12.8. © Copyright 2022 by NuScale Power, LLC 60

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 5-2 Schematic of Horizontal Flow Regime Map with Shaded Regions Indicating Transition (Interpolation) Regions The bubble-slug transition void fraction is: 2 0.25 G m 2000 kg m s BS = 0.25 + 0.00025 ( G - 2000 ) 2000 < G < 3000 kg m 2 s Equation 5-13 m m 2 0.50 G m 3000 kg m s Where the mixture mass flux is: Gm = g g vg + f f vf Equation 5-14 The transition region between slug flow and annular mist flow is defined by DE = 0.75 and SA = 0.80 . The annular mist to dispersed transition criterion is AM = 0.80 . The criterion defining the horizontally stratified regime is based on the one developed by Taitel and Dukler (Reference 12.13). According to Taitel and Dukler, the flow field is horizontally stratified if the vapor/gas velocity satisfies the condition v g < v crit Equation 5-15 12 1 ( f - g )g g A v crit = --- ----------------------------------- ( 1 - cos ) Equation 5-16 2 g D sin © Copyright 2022 by NuScale Power, LLC 61

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 where is the angle from vertical of the stratified liquid level, defined in Figure 5-3. Figure 5-3 Schematic of Horizontally Stratified Flow in a Pipe, with Definition of The algebraic relationship between vapor fraction g and angle is: g = - cos sin Equation 5-17 The flow is horizontally stratified if the phasic relative velocity and the mass flux satisfies the condition: 2 v g - v f < v crit and G m < 3000 kg m s Equation 5-18 If the conditions in Equation 5-18 are met, the flow field undergoes a transition to the horizontally stratified flow regime. If the conditions are not met, then the flow field transitions to the bubble, slug, annular mist, or mist pre-CHF flow regime. The lower transition limit of the interpolation region for v g - v f is and for G m is 2 2500 kg m s 5.2.3.3 Junction Flow Regime Maps The junction map is based on both junction and volume quantities. It is used for the interphase drag and shear, as well as the coefficient of virtual mass. The flow regime maps used for junctions are the same as used for the volumes and are © Copyright 2022 by NuScale Power, LLC 62

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 based on the work of Taitel and Dukler (Reference 12.12 and Reference 12.13), Ishii (Reference 12.16), and Tandon, et. al. (Reference 12.17) As with the volumes, three junction flow regime maps are used: horizontal map for flow in pipes vertical map for flow in pipes/bundles high mixing map for flow in pumps The vertical flow regime map is for junctions whose junction inclination (vertical) angle j is 60 < j 90 degrees. The horizontal flow regime map is for junctions whose junction inclination angle j is 0 < j 30 degrees. An interpolation region between vertical and horizontal flow regimes is used for junctions whose junction inclination angle j is 30 < j 60 degrees. This interpolation region is used to smoothly change between vertical and horizontal flow regimes. Junction quantities used in the map decisions are junction phasic velocities, donored (based on phasic velocities) phasic densities, and donored (based on superficial mixture velocity) surface tension. The junction void fraction ( ) is calculated from either of the volume void g,j fractions of the neighboring volumes, g,k or g,L , using a donor direction based on the mixture superficial velocity j m . 5.2.4 Momentum Closure Relations NRELAP5 uses two different models for the phasic interfacial friction force computation, the drift flux method and the drag coefficient method. The choice of which model to use depends upon the flow regime. The methods are described in the following two subsections. 5.2.4.1 Drift Flux Model The drift flux approach is used only in the bubbly and slug-flow regimes for vertical flow. The drift flux model specifies the distribution coefficient and the vapor/gas drift velocity. These two quantities must be converted into a constitutive relation for the interfacial frictional force per unit volume. Such a relation can be found by assuming that the interfacial friction force per unit volume is given by Equation 5-19. F i = C i v R v R = f g ( f - g )g Equation 5-19 © Copyright 2022 by NuScale Power, LLC 63

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 where the interfacial frictional force per unit volume is balanced by the buoyancy force per unit volume where C i is an unknown coefficient and v R is the relative velocity between the phases. Within the context of the drift flux model, the relative velocity between the phases is not the difference between the phasic velocities but is a weighted difference between the phase velocities given by Equation 5-20. vR = C1 vg - C0 vf Equation 5-20 where C 0 is given by the drift flux correlations and C 1 is given by Equation 5-21. 1 - g C0 C 1 = --------------------- - Equation 5-21 1 - g Substituting these relations into Equation 5-19 gives the interfacial friction force per unit volume in terms of the phasic velocities, given by Equation 5-22. Fi = Ci C1 vg - C0 vf ( C1 vg - C0 vf ) Equation 5-22 Here the coefficient C i is yet undetermined. The drift flux model also specifies that the relative velocity ( v R ) can be written as the ratio of the vapor/gas drift velocity and the liquid volume fraction, and is given by Equation 5-23. v gj v R = ------ - Equation 5-23 f where the vapor/gas drift velocity ( v gj ) is given by the drift flux correlations. Substituting this value of the relative velocity into Equation 5-19 allows the coefficient C i to be determined from Equation 5-24. 3 g f ( f - g )g C i = -------------------------------------- Equation 5-24 2 v gj 5.2.4.2 Drag Coefficient Model The drag coefficient approach is used in flow regimes other than vertical bubbly and slug-flow. The model uses correlations for drag coefficients and for the computation of the interfacial area density. The constitutive relation for the frictional force on a body moving relative to a fluid is given by Equation 5-25. © Copyright 2022 by NuScale Power, LLC 64

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 1 2 F = --- v C D A Equation 5-25 2 where, F = drag force

                   = fluid density, v = velocity of body relative to the fluid, C D = drag coefficient, and A = projected area of the body.

Expressing the frictional force for a group of bodies moving relative to a fluid (e.g., bubbles moving through liquid or droplets moving through vapor/gas) in terms of the frictional force for each body leads to the constitutive relation of Equation 5-26 for the interfacial frictional force per unit volume: 1 F i = --- c v g - v f ( v g - v f )C D S F a gf = C i v g - v f ( v g - v f ) Equation 5-26 8 where, F i = interfacial friction force per unit volume, 1 C i = --- c C D S F a gf 8 c = density of continuous phase a gf = interfacial area per unit volume, and S F = shape factor. The additional factor of 1/4 comes from the conversion of the projected area of 2 2 spherical particles (i.e., r ) into the interfacial area (i.e., 4 r ) and the shape factor is included to account for non-spherical particles. The drag coefficient model for the global interfacial friction coefficient is reduced to the specification of the continuous density, drag coefficient, interfacial area density, and shape factor for the flow regimes. Once these quantities have been computed, the interfacial friction force per unit volume ( F i ) is computed from Equation 5-20 from which the global interfacial friction coefficient can be computed. © Copyright 2022 by NuScale Power, LLC 65

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 5.2.4.3 Wall Friction The wall friction is determined based on the volume flow regime map. The wall friction force terms include only wall shear effects. Losses due to abrupt area change are calculated using mechanistic form-loss models. Other losses due to elbows or complicated flow passage geometry are modeled using energy-loss coefficients that must be input by the user. The semi-implicit scheme, one-dimensional, finite difference equations for the sum momentum equation and the difference momentum equation contain the terms of Equation 5-27 that represent the phasic wall frictional pressure drop. n n+1 n n+1 FWG j ( v g ) j x j t and FWF j ( v f ) j x j t Equation 5-27 These terms represent the pressure loss due to wall shear from cell center to cell center of the cell volumes adjoining the particular junction that the momentum equation is considering. The wall drag or friction depends not only on the phase of the fluid, but also on the flow regime characteristics. The wall friction model is based on a two-phase multiplier approach in which the two-phase multiplier is calculated from the heat transfer and fluid flow service (HTFS) modified Baroczy correlation. The individual phasic wall friction components are calculated by apportioning the two-phase friction between the phases using a technique derived from the Lockhart-Martinelli model (Reference 12.18). The model is based on the assumption that the frictional pressure drop may be calculated using a quasi-steady form of the momentum equation, as used by Chisholm. This wall friction partitioning model is used with the drag coefficient method of the interphase friction model. The Lockhart-Martinelli model computes the overall two-phase friction pressure drop in terms of the liquid-alone and vapor/gas-alone wall friction pressure drop as shown in Equation 5-28. dP 2 dP 2 dP

                                                            =  f  ------- =  g  -------                   Equation 5-28 dx  2                  dx  f         dx  g Here  f and  g are the liquid-alone and vapor/gas-alone two-phase Darcy-Weisbach friction multipliers, respectively. The phasic wall friction pressure gradients are expressed by Equation 5-29 for the liquid and vapor/gas alone.

2 2 f Re f M f g Re g M g dP dP

                                   ------- = ------------------------ and ------- = -------------------------   Equation 5-29 dx  f                        2           dx  g                     2 2D  f A                              2D  g A

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Here the prime indicates the liquid and vapor/gas-alone Darcy-Weisbach friction factors, respectively, calculated at the respective Reynolds numbers given by Equation 5-30. Mf D Mg D Re f = ----------- - and Re g = ----------- - Equation 5-30 f A g A The liquid and vapor/gas mass flow rates, respectively, are defined by Equation 5-31. M f = f f v f A and g g v g A Equation 5-31 The overall two-phase friction pressure gradient is calculated using two-phase friction multiplier correlations. The multipliers are interrelated using Equation 5-23 and Equation 5-24 and the Lockhart-Martinelli ratio defined by Equation 5-32. dP

                                                                     -------        2 2         dx  f         g
                                                        = --------------- = -----                             Equation 5-32 2

dP

                                                                    -------       f dx  g The HTFS correlation is used to calculate the two-phase friction multipliers. This correlation is chosen because it is correlated to empirical data over broad ranges of phasic volume fractions, phasic flow rates and phasic flow regimes. The correlation is also shown to give good agreement with empirical data.

The HTFS correlation for the two-phase friction multiplier is expressed with Equation 5-33. 2 f = 1 + --- C- + ----- 1 and = + C + 1 2 2 Equation 5-33 2 g C is the correlation coefficient and is the Lockhart-Martinelli ratio given by Equation 5-32. If the HTFS correlation is combined with the wall friction formulations by combining Equation 5-28, Equation 5-29, Equation 5-31, Equation 5-32, and Equation 5-33, then the combined two-friction pressure drop is expressed by Equation 5-34. dP

                              ------- =  f  dP 2
                                                ------- =  g  dP 2                  1
                                                                      ------- = ------

2

                                                                                      - ( {  f f ( f vf ) )

dx 2 dx f dx g 2D Equation 5-34 2 2 12 2

                             + C [ f f ( f vf ) g g ( g vg ) ]                    + g g ( g vg ) }

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 The phasic wall friction coefficients are defined by Equation 5-35 and Equation 5-36. 2 dP Z FWF ( f f v f )A = f p f = f ------- -------------------------2 A Equation 5-35 dx 2 g + f Z dP 1 FWG ( g g v g )A = g p g = g ------- -------------------------2 A Equation 5-36 dx 2 + Z g f Here Z is defined by Equation 5-37. 2 fw f ( Re f ) f v f -------- 2 f Z = ------------------------------------------

                                                                                             -                                 Equation 5-37 2  gw g ( Re g )  g v g ----------

g Taking the sum of these two equations gives the overall quasi-static, two-phase wall friction pressure gradient as shown by Equation 5-38. dP FWF ( f f v f )A + FWG ( g g v g )A = ------- A Equation 5-38 dx 2 The phasic friction factors used in the wall friction model are computed from correlations for laminar and turbulent flows with interpolation in the transition regime. The friction factor model is simply an interpolation scheme linking the laminar, laminar-turbulent transition, and turbulent flow regimes. The laminar friction factor is calculated by Equation 5-39. 64 L = ------------ for 0 Re 2200 Equation 5-39 Re S Here S is a user-input shape factor for non-circular flow channels ( S is 1.0 for circular channels). The friction factor in the transition region between laminar and turbulent flows is computed by reciprocal interpolation with Equation 5-40.

                                                     ,250 L, T =  3.75 -------------
                                                               - (             -  L, 2200 ) +  L, 2200 Re  T, 3000                                                             Equation 5-40 for 2200 < Re < 3000

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Here L, 2200 is the laminar factor at a Reynolds number of 2,200, T, 3000 is the turbulent friction factor at a Reynolds number of 3,000, and the interpolation factor is defined to lie between zero and one. The turbulent friction factor is given by the Zigrang-Sylvester approximation (Reference 12.19) to the Colebrook-White correlation (Reference 12.20) with Equation 5-41, where is the surface roughness. 1 2.51 21.25

                         ---------- = - 2log 10  ------------ + ---------- 1.14 - 2log 10  ---- + -------------

T 3.7D Re D Re 0.9 Equation 5-41 for Re 3000 5.2.5 Heat Transfer The liquid and vapor/gas energy solutions include the wall heat flux to liquid or vapor-gas. During boiling, the saturation temperature based on the total pressure is the reference temperature, and during condensation the saturation temperature based on the partial pressure is the reference temperature. The general expression for the total wall heat flux is defined by Equation 5-42: q total = h wgg ( T w - T g ) + h wgspt ( T w - T spt ) + h wgspp ( T w - T spp ) Equation 5-42

                                           + h wff ( T w - T f ) + h wf spt ( T w - T spt )

where, h wgg = heat transfer coefficient to vapor/gas, with the vapor/gas temperature as the reference temperature (W/m2 K), h wgspt = heat transfer coefficient to vapor/gas, with the saturation temperature based on the total pressure as the reference temperature (W/m2 K), h wgspp = heat transfer coefficient to vapor/gas, with the saturation temperature based on the vapor partial pressure as the reference temperature (W/m2 K), h wff = heat transfer coefficient to liquid, with the liquid temperature as the reference temperature (W/m2 K), h wfspt = heat transfer coefficient to liquid, with the saturation temperature based on the total pressure as the reference temperature (W/m2 K), T w = wall surface temperature (K), T g = vapor/gas temperature (K), © Copyright 2022 by NuScale Power, LLC 69

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 T f = liquid temperature (K), T spt = saturation temperature based on the total pressure (K), and T spp = saturation temperature based on the partial pressure of vapor in the bulk (K). A boiling curve is used in NRELAP5 to govern the selection of the wall heat transfer correlations when the wall surface temperature is above the saturation temperature (superheated relative to the saturation temperature based on total pressure). When a hydraulic volume is voided and the adjacent surface temperature is subcooled, vapor condensation on the surface is predicted. If non-condensable gases are present, the phenomena are more complex because condensation is based on the partial pressure of vapors present in the region. When the wall temperature is less than the saturation temperature based on total pressure, but greater than the saturation temperature based on vapor partial pressure, a convection condition exists. Figure 5-4 illustrates these three regions of the curve. Figure 5-4 NRELAP5 Boiling and Condensing Curves Boilingregion CHFpoint Heatflux Nucleate Transition Film [Tspp -Tw ] [Tw-Tspt ] Condensingregion Convectionregion The boiling curve uses the Chen boiling correlation (Reference 12.21) up to the CHF point. © Copyright 2022 by NuScale Power, LLC 70

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 5.3 Heat Structure Models Heat structures provided in NRELAP5 permit calculation of the heat transfer across solid boundaries of hydrodynamic volumes. Modeling capabilities of heat structures are general and include fuel pins or plates with nuclear or electrical heating, heat transfer across SG tubes, and heat transfer from pipe and vessel walls. Temperatures and heat transfer rates are computed from the one-dimensional form of the transient heat conduction equation. Heat structures are represented using rectangular, cylindrical, or spherical geometry. Surface multipliers are used to convert the unit surface of the one-dimensional calculation to the actual surface of the heat structure. Temperature-dependent and space-dependent thermal conductivities and volumetric heat capacities are provided in tabular or functional form either from built-in or user-supplied data. Finite differences are used to advance the heat conduction solutions. Each mesh interval may contain different mesh spacing, a different material, or both. The spatial dependence of the internal heat source, if any, may vary over each mesh interval. The time-dependence of the heat source can be obtained from reactor kinetics, one of several tables of power versus time, or a control system variable. Boundary conditions include symmetry or insulated conditions; a heat transfer correlation package; and tables of surface temperature versus time; heat flux versus time; heat transfer coefficient versus time; and heat transfer coefficient versus surface temperature. The heat transfer correlation package can be used for heat structure surfaces connected to hydrodynamic volumes. The heat transfer correlation package contains correlations for convective, nucleate boiling, transition boiling, and film boiling heat transfer from the wall to the fluid, and it contains reverse heat transfer from the fluid to the wall including correlations for condensation. The heat conduction model also includes a gap conduction model and a radiation enclosure model. The integral form of the heat conduction equation is defined by Equation 5-43. T Cp ( T, x ) ----- t

                                              - ( x, t )dV =

k ( T, x )T ( x, t ) ds + S ( x, t )dV Equation 5-43 V S V where, k ( T, x ) = thermal conductivity, s = surface, S = internal volumetric heat source, t = time, T = temperature, V = volume, © Copyright 2022 by NuScale Power, LLC 71

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 x = space coordinates, and C p = volumetric heat capacity. The boundary conditions applied to the exterior surface have the form of Equation 5-44. T ( t ) A ( T )T ( t ) + B ( T ) ------------- = D ( T, t ) Equation 5-44 n The n denotes the unit normal vector away from the boundary surface. Thus, if the desired boundary condition is that the heat transferred out of the surface equals a heat transfer coefficient ( h ) times the difference between the surface temperature ( T ) and the sink temperature ( T sk ) as shown by Equation 5-45. T

                                                   - k ------ = h ( T - T sk )                                    Equation 5-45 n

then the correspondence between the above expression and Equation 5-44 yields A = h , B = k , and D = T sk Equation 5-46 One-dimensional heat conduction in rectangular, cylindrical, and spherical geometry can be used to represent the heat structures in the components in NRELAP5. The equations governing one-dimensional heat conduction are defined by Equation 5-47, Equation 5-48, and Equation 5-49. T T C p ------ = ----- k ------ + S for rectangular geometry Equation 5-47 t x x T 1 T C p ------ = --- ----- rk ------ + S for cylindrical geometry Equation 5-48 t r r r T 1 2 T C p ------ = --- ----- r k ------ + S for spherical geometry Equation 5-49 t r r r Heat may flow across the external heat structure boundaries to either the environment or to the working fluid. For heat structure surfaces connected to hydrodynamic volumes containing the working fluid, a heat transfer package is provided containing correlations for heat transfer from wall-to-liquid and reverse heat transfer from liquid-to-wall. Any number of heat structures may be connected to each hydrodynamic volume, or heat transfer coefficient versus surface temperature can be used to simulate the boundary conditions. © Copyright 2022 by NuScale Power, LLC 72

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 The heat conduction equation can be solved by various numerical techniques. NRELAP5 uses the Crank-Nicolson method (Reference 12.22) for solving this equation. 5.4 Trips and Control System Models The control system provides the capability to evaluate simultaneous algebraic and ordinary differential equations. The capability is primarily intended to simulate control systems typically used in hydrodynamic systems, but it can also model other phenomena described by algebraic and ordinary differential equations. Another use is to define auxiliary output quantities, such as differential pressures, so they can be printed in major and minor edits and be plotted. The control system consists of several types of control components. Each component defines a control variable as a specific function of time-advanced quantities. The time-advanced quantities include hydrodynamic volume, junction, pump, valve, heat structure, reactor kinetics, trip quantities, and the control variables themselves (including the control variable being defined). This approach permits control variables to be developed from components that perform simple, basic operations. The trip system consists of the evaluation of logical statements. Each trip statement is a simple logical statement that has a true or false result and an associated variable. Two types of trip statements are provided (variable and logical trips). 5.5 Special Solution Techniques Certain models in NRELAP5 have been developed to simulate special processes. Special process models are used in NRELAP5 to model those processes, which are sufficiently complex that they must be modeled by empirical models. The following sections summarize those models. Special process models include choked flow, entrainment/pull through model, thermal stratification model, counter-current flooding, form-loss model and abrupt area change. Choked flow, stratification, and counter-current flooding are not important to DWO. Discussion of abrupt area change and form losses follows. 5.5.1 Abrupt Area Change The general reactor system contains piping networks with many sudden area changes and orifices. To apply the NRELAP5 hydrodynamic model to such systems, analytical models for these components are included in the code. The basic hydrodynamic model is formulated for slowly varying (continuous) flow area variations; therefore, special models are not required for this case. The abrupt area change model, is based on the Borda-Carnot formulation (Reference 12.23) for a sudden (i.e., sharp, blunt) enlargement and standard pipe flow relations, including the vena-contracta effect for a sudden (i.e., sharp, blunt) contraction or sharp-edge orifice or both. This type of change is referred to as the full © Copyright 2022 by NuScale Power, LLC 73

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 abrupt area change model. It does not include the case where an enlargement, contraction, or orifice is rounded or beveled. Quasi-steady continuity and momentum balances are employed at points of an abrupt area change. The numerical implementation of these balances is such that hydrodynamic losses are independent of upstream and downstream nodalization. In effect, the quasi-steady balances are employed as jump conditions that couple fluid components having abrupt changes in cross-sectional area. This coupling process is achieved without change to the basic numerical time-advancement schemes. The basic assumption used for the transient calculation of two-phase flow in flow passages with points of abrupt area change is that the transient flow process can be approximated as a quasi-steady flow process that is instantaneously satisfied by the upstream and downstream conditions (that is, transient inertia, mass, and energy storage are neglected at abrupt area changes). However, the upstream and downstream flows are treated as fully transient flows. The volume of fluid and associated mass, energy, and inertia at points of abrupt area change is generally small compared with the volume of upstream and downstream fluid components. The transient mass, energy, and inertia effects are approximated by lumping them into upstream and downstream flow volumes. Finally, the quasi-steady approach is consistent with modeling of other important phenomena in transient codes (that is, heat transfer, pumps, and valves). Activation of the full abrupt area change model in NRELAP5 results in the code internally calculating the form and interfacial losses across a junction. Utilization of the partial area change model allows the user to specify the form loss while allowing the code to internally calculate the interfacial loss. Activation of the smooth area change model allows the user to specify the form loss with no internal calculation of the interfacial losses. More detailed discussion concerning this model can be found in the NRELAP5 theory manual (Reference 12.8). 5.5.2 Form Loss Model The form loss model in NRELAP5 allows specifying a user defined form loss coefficient to calculate the friction pressure drop for complicated geometry. The form loss coefficient in NRELAP5 calculates the pressure drop term HLOSSG (for vapor) and HLOSSF (for liquid) in the phasic momentum equation. 1 HLOSSG = --- ( K g + K in ) V g,j Equation 5-50 2 1 HLOSSF = --- ( K f + K in ) V f,j 2 © Copyright 2022 by NuScale Power, LLC 74

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Where K in is user-specified loss coefficient either the forward loss K F or reverse loss K R , depending on the phasic velocity direction. The code-calculated abrupt area loss terms K g and K f as discussed in the previous section. In many cases the form loss coefficient is specified as a function of the Reynolds number. The user-specified form loss for Reynolds number dependency can be expressed as

                                                                -C F K R = A F + B F Re Equation 5-51
                                                                -C R K R = A R + B R Re Where A F , A R , B F , B R , C F , and C R , are user-defined constants and Re is the Reynolds number based on the mixture fluid properties.

5.6 Numerical Methods NRELAP5 solves the one-dimensional two-fluid model equations. The local instantaneous equations are developed for each phase. These equations are then averaged over time and cross-sectional area to generate governing equations that are solved numerically. The difference equations implement mass and energy conservation by equating accumulation to the rate of mass or energy inflow and outflow through the cell boundaries, minus the rate of mass or energy out through the cell boundaries, plus source terms such as heat input. This approach necessitates defining mass and energy volume average properties and requiring knowledge of velocities at the volume boundaries. The velocities at the cell edges are defined through the use of momentum control volumes centered on the mass and energy cell boundaries. This approach results in a numerical scheme having a staggered spatial mesh with the momentum control volumes extending from the mass and energy cell centers to the neighboring mass and energy cell centers. The scalar properties of the flow (pressure, specific internal energies, and void fraction) are defined at mass and energy cell boundaries. The governing equations are discretized in time and space, and are solved numerically using a semi-implicit finite-difference technique. A nearly-implicit finite-difference technique, which allows violation of the material Courant limit, is also available. However, the DWO EM and the supporting assessment calculations use only the semi-implicit numerical scheme. The semi-implicit numerical solution scheme is based on replacing the system of differential equations with a system of finite difference equations partially implicit in time. NRELAP5s semi-implicit solution scheme A) behaves like a classic explicit scheme and B) introduces numerical diffusion (which acts to damp inlet perturbations). The amount of © Copyright 2022 by NuScale Power, LLC 75

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 numerical diffusion can vary considerably as it is dependent on A) the number of nodes used and B) the Courant number C, which is the time-step size normalized to the transport time through a volume per Equation 5-522: C = vt x Equation 5-52 Where v is the velocity (m/s), t is the time step (s), and x is the node length (m). The physical meaning of C, illustrated in Figure 5-5, is the distance a fluid particle travels in a time step ( vt ), divided by the node length ( x ). It is desirable to keep the distance traveled less than the node length (ex, C=0.4, as seen on the left). If the distance traveled exceeds the node length (C=1.2, as seen on the right) information may not be correctly propagated from node to node. Figure 5-5 Physical Meaning of the Courant Number For the NRELAP5 semi-implicit scheme, the range of allowable values is 0 < C < 1. In an NRELAP5 simulation, if the velocity in a node (i.e. either liquid velocity or gas velocity) would cause C > 1, the time-step is automatically reduced such that C < 1. Note that in NRELAP5, nodes use the same time-step. Often, NRELAP5 models with uniform nodalizations have their time step controlled by the node with the highest velocity, so more course nodalization in high velocity regions is sometimes used to keep the time step from becoming very small, impacting the overall solution time. When generating a solution of finite difference equations there is a possibility that the solution may not be converged. This could be the result of an ill-posed problem, inappropriate time step size selection, inadequate spatial nodalization, or an instability. Sensitivity studies have proven useful to assure convergence and stability of the NRELAP5 solutions. © Copyright 2022 by NuScale Power, LLC 76

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Adherence to the known modeling limitations and requirements of RELAP5, discussed in Section 9.0, assist in assuring that the governing equations are well posed. Requirements for nodalization and time step sensitivity studies assure converged solutions. Solutions are examined to identify unstable or unphysical behavior. ((

                                                                                     }}2(a),(c) 5.7      Helical Coil Steam Generator Component A new hydrodynamic component and heat transfer package is added to NRELAP5 to model flow and heat transfer inside a helical coil SG. This model is developed based on helical coil geometry-specific heat transfer and wall friction correlations. The need for improved models is based on inadequate agreement with pressure drop and heat transfer performance with the baseline RELAP5-3D© code results against prototypic helical coil SG testing performed at SIET. Improvements and adequacy of the implemented models in NRELAP5 are demonstrated through prototypic assessments of the NuScale helical coil SG using SIET test data (Section 8.1 and Section 8.2). These tests assessed heat transfer and pressure drop on both the secondary side (within tubes) and primary side (external to tubes) of the helical coil SG.

A wide range of pressure drop and heat transfer correlations were investigated for analyzing the inside of the helical coils. A down selection is performed of these investigated models for implementation into the NRELAP5 code based on the applicability of the models to the NPM helical coil SG. These models are described in Section 6.0. © Copyright 2022 by NuScale Power, LLC 77

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 6.0 NRELAP5 Helical Coil SG Model Development Models developed specifically for helical coil steam generator are described in this section. Additional details of the model development and supporting data can be found in Reference 12.8. Figure 6-1 shows a schematic of a helical coil as a visual reference for the parameters used in helical coil heat transfer and pressure drop correlations found in open literature. The pipe has an inner diameter di. The coil diameter is represented by Dcoil (measured between the centers of the pipes). The distance between two adjacent turns, called axial pitch is H. The ratio of pipe diameter to coil diameter (di/Dcoil) is called curvature ratio. The ratio of pitch to developed length of one turn (H/Dcoil) is termed torsion. Consider the projection of the coil on a plane passing through the axis of the coil. The angle, which projection of one turn of the coil makes with a plane perpendicular to the axis, is called the tube inclination angle, (degrees). Consider any cross-section of the pipe created by a plane passing through the coil axis. The side of the pipe wall nearest to the coil axis is termed the inner side of the coil and the farthest side is termed as the outer side of the coil. © Copyright 2022 by NuScale Power, LLC 78

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 6-1 Basic Geometry of a Helical Tube Similar to the Reynolds number for flow in pipes, the Dean number is used to characterize the flow in a helical pipe. The predominant parameter governing the physics of flow within helical tubes is the Dean number De: di De = Re ------------ Equation 6-1 D coil Dean number couples inertial and centrifugal effects. © Copyright 2022 by NuScale Power, LLC 79

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 6.1 Helical Coil Tube Friction 6.1.1 Helical Coil Single-Phase Tube Wall Friction ((

                               }}2(a),(c)

(( Equation 6-2 Equation 6-3 Equation 6-4

                                                                                                                    }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 6.1.2 Helical Coil Two-Phase Tube Wall Friction (( Equation 6-5 Equation 6-6 Equation 6-7 Equation 6-8 Equation 6-9

                                                                                                                }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 6.2 Helical Coil Tube Heat Transfer A new heat transfer package is added to NRELAP5 and differs from that of the standard RELAP5 pipe geometry in the single-phase heat transfer and two-phase flow boiling heat transfer. A new geometry type represents the inside of the helical tubes. ((

                                                                                                       }}2(a),(c) 6.2.1          Helical Coil Single-Phase Heat Transfer

(( Equation 6-10 Equation 6-11 Equation 6-12

                                                                                                                }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 6.2.2 Helical Coil Two-Phase Subcooled and Saturated Flow Boiling Heat Transfer The saturated flow boiling heat transfer correlation is used for both subcooled and saturated flow boiling conditions. This correlation is similar to the treatment of a standard pipe component, though the heat transfer coefficient is slightly different for helical tubes. (( Equation 6-13 Equation 6-14 Equation 6-15 Equation 6-16

                                                                                                                }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 (( Equation 6-17 Equation 6-18

                                                                                                                }}2(a),(c) 6.2.3         Primary Side Heat Transfer During normal NPM operation, the primary-side is expected to be in single-phase liquid conditions throughout the entire operating range. ((

Equation 6-19 Equation 6-20

                                                                                                                }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 6.3 Subcooled Boiling 6.3.1 Onset of Nucleate Boiling (ONB) ((

                                   }}2(a),(c) 6.3.2         Onset of Significant Void Onset of Significant Void (OSV) signifies the transition from the single-phase liquid region to the two-phase region. OSV is sometimes called the point of Net Vapor Generation (NVG) or the bubble departure point in the external literature (Reference 12.37).

In NRELAP5, OSV is calculated using the Saha-Zuber model (Reference 12.33). The Saha-Zuber model uses the Peclet number to determine if the heat flux at OSV is related to the Nusselt Number (low flow, thermally controlled bubble growth) or the Stanton number (high flow, hydrodynamically controlled bubble growth). The correlation for the liquid enthalpy at OSV is: St C pf h - Pe > 70, 000 f, sat 0.0055 - 0.0009 F ( p ) h cr = Equation 6-21 Nu C pf h f, sat - ----------------- Pe 70, 000 455 Where: q di f Nu = ---------

                                 -            Nu-St  = --------

kf Pe Gd i C pf Pe = RePr = ----------------- kf q = wall heat flux to the liquid f G = mass flux (mass flow rate / tube area) k f = liquid thermal conductivity C pf = liquid heat capacity at constant pressure © Copyright 2022 by NuScale Power, LLC 85

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 The value of F ( p ) in the denominator of the Stanton number criterion is a function of pressure defined as: 1.0782 F ( p ) = -------------------------------------------------------------------------------------- Equation 6-22 p

                                                                 --------------------------------- - - 140.75 3

6.894757 x10 1.015 + e -------------------------------------------------------------- 28 When the local enthalpy exceeds h OSV , a fraction of the wall heat flux goes to vapor generation, and the remainder goes to heating the liquid. This partitioning of the heat flux continues until the liquid reaches the saturation temperature, then the heat flux goes into vapor generation. This heat partitioning fraction (called Mul in Reference 12.34, Eq. 4.7-11) is calculated in NRELAP5 using a model developed by Lahey (Reference 12.35). 6.3.3 Subcooled Void Fraction and Quality The quality x in the subcooled flow region can be estimated according to Levy in Reference 12.36. This equation holds for straight channel flow. x th x = x th - x th@NVG exp --------------------- - - 1 Equation 6-23 x th@NVG Where x th is the thermodynamic equilibrium quality and x th@NVG is the thermodynamic equilibrium quality at the point of net vapor generation. 6.4 Transition to Dryout The helical coil component is exclusively used to model a steam generator. ((

                                                                                                                                }}2(a),(c) 6.4.1         Two Phase to Single Phase Vapor Transition In NRELAP5 the transition from nucleate boiling heat transfer and heat transfer to single-phase vapor is accomplished by an interpolation between the two-phase and single-phase vapor heat transfer starting at a void fraction of 0.995 and continues until a void fraction of 0.9999, where heat transfer to pure vapor takes over. This transition is the natural occurrence of the onset of dryout.

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 7.0 Evaluation Model Description This section provides a detailed description of the NPM SG DWO EM. The nodalization and modeling options selected for each NPM component are discussed along with the rationale for each choice. Justifications are provided for the boundary conditions (BCs) and initial conditions (ICs) selected for the model. A description of how DWO is analyzed and interpreted is included. This analysis follows the recommended best practices for the preparation of a RELAP5-3D input per Reference 12.34 that are applicable to the NRELAP5 DWO model as well as NuScale-specific DWO best practices per Reference 12.8. The NPM SG DWO model is consistent with conclusions from DWO SET assessments, DWO IET assessments, and related engineering analysis (e.g. nodalization studies) as detailed in Section 8.0. The results of DWO analysis of the NPM SG are summarized in Appendix B. 7.1 General Model Overview The NRELAP5 model for analyzing SG DWO within the NPM is developed through a process that reviews different NPM operating conditions, the key phenomena described in the NPM SG PIRT per Section 4.2, and the numerical behavior of NRELAP5. The model describes the key components of the NPM participating in SG DWO as follows: The SG primary-side:

             -    The upper downcomer
             -    Other adjacent regions, if desired.

The SG secondary-side:

             -    The FW and STM plenums
             -    The HCSG tubes An example of a general nodalization for these three components is shown in Figure 7-1, which presents the schematic for a model with ((
                                                                                                             }}2(a),(c)

(Section 7.5 through Section 7.8). Note that the specifics of model nodalization, including the number of boiling channels needed, depend on the BC method applied (Section 7.4 and Section 7.8). Figure 7-2 shows an example flow chart of the EM content, inputs to the EM, and outputs from the EM. © Copyright 2022 by NuScale Power, LLC 87

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Table 7-1 provides a cross-walk between the NPM SG T-H stability PIRT and the model described herein, for which details are described in the following sections. Figure 7-1 Example of an NPM SG DWO Model ((

                                                                                                                 }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0

                                                                                                                                          }}2(a),(c)

Table 7-1 DWO Stability PIRT vs. NPM SG DWO Model Incorporation ((

  © Copyright 2022 by NuScale Power, LLC 90

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0

                                                                      }}2(a),(c)

Table 7-1 DWO Stability PIRT vs. NPM SG DWO Model Incorporation ((

            © Copyright 2022 by NuScale Power, LLC 91

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 7.2 Overview of DWO Simulation 7.2.1 Overview of BC Methods to Induce DWO Onset The methods described herein rely on a quasi-steady-state analysis of NPM SG stability relative to DWO. Section 7.4 provides the determination of DWO characteristics. The stability of a system over different operating conditions is typically examined by introducing a user-defined perturbation at steady-state, such as a pulse. The perturbation causes flow oscillations, which either grow if the system is unstable or decay to the pre-perturbation state if the system is stable. Often decay ratios or other quantifications are used a stability parameters. However, due to non-linear effects, fully-developed DWO has large-amplitude oscillations with a decay ratio of 1.0 (sometimes referred to as limit-cycle oscillations if they do not grow further). Therefore, while decay ratio can be used to quantify how quickly oscillations grow from initially stable conditions, this DWO development time is not considered as important in simulations as the DWO flow behavior itself (e.g. the flow amplitude and flow period). The DWO flow behavior informs the impact of DWO on a system (e.g. potential stresses - which are not further discussed herein). To determine whether a system is stable at given conditions, a simulation is run at specific conditions. For an unstable system, a very small perturbation can trigger DWO onset by allowing the system response to occur at the resonant DWO frequency (often characterized via period due to more convenient values). Within SGs, a method of BC changes can be applied to perform a quasi-steady-state analysis wherein very small perturbations are constantly being introduced. For example, the slow ramping of a BC from a higher value to a lower value is called down ramping (e.g., decreasing FW flow rate). When sufficient BC changes are applied to an initially stable condition, the system transitions from stable conditions to large-amplitude DWO via DWO onset. This method allows for the analysis of a stability boundary (i.e., where the system transitioned between stable and unstable states). Comparison of stability boundaries allows for a determination of the distance that any stable condition has to potential instability (i.e., the margin in that BC to the stability boundary). While BC step-changes can be used to determine stability boundaries, the introduction of larger perturbations generally reduces the resolution of the determined stability boundary. Therefore, BC step-changes are not further discussed herein. From a given set of initial conditions, DWO onset can usually be induced by ramping of many different BCs. For this EM, the selected methods focus on the ramping of the FW flow rate. FW flow rate is used because it can both change the overall system conditions (e.g., the total primary-to-secondary heat transfer) and local HCSG tube conditions (e.g., the void fraction, pressure drop) within a specific HCSG tube volume. © Copyright 2022 by NuScale Power, LLC 92

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 This approach allows for sufficient perturbations to allow for stability boundary investigation. 7.2.2 Overview of Parameters Impactful on DWO Characteristics The dynamic behavior of boiling systems depends on their geometry and operating conditions. This section discusses effects of different parameters on stability relative to DWO for the NPM HCSG tubes. Total power and its effects on stability is easier to interpret for boiling channels with two-phase exit conditions. Therein, increases in power results in increased exit quality and increased average tube quality, which are generally destabilizing. ((

                                    }}2(a),(c)

FW flow is an important parameter to stability. Increased flow results in longer single-phase liquid within boiling channels, and thus lower average tube quality, which tends to generally decrease the relative weight of two-phase and single-phase gas pressure drop. In addition, both the boiling channel inlet pressure drop (i.e. due to Kinlet) and the wall friction pressure drop are dependent on the inlet mass flow rate. Increasing FW flow generally leads to more stable conditions. FW temperature can have different effects on stability. For subcooled inlet conditions, increased subcooling is generally stabilizing as it lowers the average tube quality. Boiling channel pressure - most commonly referred to via STM pressure - affects pressure drop and density. Increasing pressure decreases the density ratio between the liquid and gas phases, which helps to weaken disturbances in two-phase conditions. Furthermore, increasing pressure decreases the relative dependence of two-phase pressure drop on local quality. Therefore increasing system pressure generally leads to more stable conditions. The boiling channel pressure drop profile (i.e. the pressure drop as a function of channel length) plays an important role in determining the stability of the system. A large concentrated pressure drop at the channel inlet (e.g., Kinlet) enables the system to compensate for fluctuations in total channel pressure drop due to small perturbations, and thus leads to stability. Thus, generally more Kinlet leads to more stable conditions. Conversely, increasing Kexit is equivalent to increasing the pressure drop of the two-phase and/or single-phase gas regions of the boiling channel, and generally makes the system less stable. © Copyright 2022 by NuScale Power, LLC 93

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 7.3 Steady-State NPM Model Needed for Input to NPM SG DWO Analysis 7.3.1 BCs Needed for NPM SG DWO Analysis Table 7-2 details the BCs needed to perform NPM SG DWO analysis. The details regarding the NRELAP5 Location column are provided in the following subsections. To determine values for Table 7-2, simulations of realistic operating conditions (i.e., primary-side and secondary-side steady-state parameters) are needed. For example, a simulation performed at 30 percent power conditions run to convergence. Section 7.3.2 provides more details on high-level requirements for such models. Section 1.1 states that this EM is applied to NPM conditions between 20 percent and 100 percent power. The FW temperature entry in Table 7-2 is applied just before the HCSG tube inlet and therefore, accounts for any heat transfer in the FW line to or from the CNV. If this heat transfer results in a temperature change smaller than 5 °C, it is considered negligible. The FW pressure entry in Table 7-2 is applied just before the HCSG tube inlet and therefore, accounts for any pressure drop along the FW line. The entries in Table 7-2 are at the following NPM nominal operating conditions: 100%, 90%, 80%, 70%, 60%, 50%, 40%, 30%, and 20% power.

                  -    These conditions reflect TF-2 DWO test conditions per Section 8.2.
                  -    Additional operating conditions in this range may be evaluated if desired.

For any condition above 5 percent power where nominal operating conditions may include one or two active SGs, simulations are needed for both configurations. For any condition above 5 percent power that include step-changes as a function of power (e.g. rapid FW changes as a result of disabling/enabling pre-heaters), simulations are needed before and after the step change. Table 7-2 NPM Steady-State Operating Parameters Needed for SG DWO Analysis System Parameter NRELAP5 Location RCS hot temperature Primary-side inlet Primary-side RCS mass flow rate Primary-side inlet Upper downcomer exit pressure Primary-side exit Main steam pressure STM exit Secondary-side FW temperature FW inlet FW mass flow rate FW inlet © Copyright 2022 by NuScale Power, LLC 94

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 7.3.2 Steady-State NPM Model This section defines the models that provide inputs to NPM SG DWO analysis per Table 7-2. The three regions modeled are the primary-side, the secondary-side, and the CNV. 7.3.2.1 Primary-Side Models The primary-side modeling provides an accurate simulation of the natural circulation flow within the RPV. The natural circulation flow is driven by heat transfer from the core paired with heat removal from the SG. Therefore, requisite steady-state models include sufficient detail to capture significant contributors to A) primary-side energy balance and B) primary-side pressure drop. For example, a detailed primary-side circulation loop with hydrodynamic volumes and heat structures for the core, riser, upper plenum, pressurizer, upper downcomer, downcomer, and lower plenum must be determined. Note that per Section 7.6 this level of detail is not required for DWO analysis models. Because bulk conditions are needed per Table 7-2, it is considered acceptable to use 1-D components to model primary-side hydrodynamic volumes even though numerical study places emphasis upon HCSG tube outside liquid A) flow distribution and B) temperature distribution. Section 9.2.2.7 details how TF-2 DWO test data illustrates the appropriateness of a 1-D primary-side component. As steady-state operating conditions are modeled, the simulation of systems like the emergency core cooling system are not needed as long as they do not have a significant impact on the steady-state operating conditions. 7.3.2.2 Secondary-Side Models The secondary-side provides an accurate simulation of the forced flow and total heat transfer between the inlet to the FW plenums and the exit of the STM plenums. Therefore, models include sufficient detail to capture significant contributors to A) secondary-side energy balance and B) secondary-side pressure drop. For example, a detailed once-through system with hydrodynamic volumes and heat structures for the FW line, FW plenum, HCSG tubes, STM plenum, and STM lines must be determined. As steady-state operating conditions are modeled, the simulation of systems like the decay heat removal system are not needed as long as they do not have a significant impact on said steady-state operating conditions. © Copyright 2022 by NuScale Power, LLC 95

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 7.3.2.3 CNV Models The CNV provides an accurate simulation of any significant heat transfer to/from the primary-side and secondary-side. Therefore, models include sufficient detail to capture significant contributors to A) primary-side energy balance and B) secondary-side energy balance. For example, a detailed system with hydrodynamic volumes and heat structures for the CNV components and a representation of the ultimate heat sink is included. 7.4 Specific Methods for DWO Simulation 7.4.1 Specific Methods to Induce DWO Onset Although other methods can be used to induce DWO onset, this EM focuses on A) the general FW flow-controlled BC method and B) the bulk FW flow-controlled BC method. The latter is used to determine the relative stability between NPM HCSG tube columns. The former is used with that information to analyze DWO stability with a less detailed model. Section 7.4.2 contains the analysis of stability boundaries. For either method, a FW flow-controlled BC method relies on directly ramping the simulated FW mass flow rate. Figure 7-3 and Figure 7-4 provide graphical representations, and Section 7.8 provides more information regarding HCSG tube nodalization. Flow ramping steps are provided below: ((

                             }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 7-3 General FW Flow-Controlled BC Method, Example Illustration ((

                                                                                                                }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 7-4 Bulk FW Flow-Controlled BC Method, Example Illustration ((

                                                                                                                }}2(a),(c) 7.4.2         Determination of DWO Stability Boundaries For the BC methods discussed in Section 7.4.1, the stability boundary encountered is DWO onset during FW flow ramp down. The determination of the points associated with these stability boundaries is described below. Section 7.4.3 contains content regarding the determination of the DWO flow period.

((

                                                                                                               }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 The following method of DWO onset determination is applied: ((

                                               }}2(a),(c)

Figure 7-5 provides an example of this method applied to a set of TF-2 DWO test data. The blue line shows tube inlet mass flow rate (row 3 tube #11). The red line shows the relative error. The green line denotes the DWO onset time. © Copyright 2022 by NuScale Power, LLC 99

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 7-5 DWO Onset Determination Applied to TF-2 DWO test S01-1_00475 ((

                                                                                                                   }}2(a),(c) 7.4.3         Determination of DWO Flow Period An effective and consistent method for determining DWO period is needed.

This method is illustrated in Figure 7-6. Each cycle is defined by a return to the minima value, and the calculated DWO flow period is an average of the flow period for each cycle within the time window selected for analysis. ((

                                      }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 7-6 Example Illustrating DWO Flow Period Behavior Summary ((

                                                                                                                }}2(a),(c) 7.4.4         Application of Specific Methods to Induce DWO Onset NPM SG DWO analysis simulations are performed at the conditions for which BCs are sourced per Section 7.3.1. Each condition is first assessed via the ((
                                               }}2(a),(c) Section 7.8 contains HCSG tube nodalization details. Ramping is then applied per Section 7.4.1 and then DWO stability boundaries for different columns is determined per Section 7.4.2.

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 ((

                                                             }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 7.4.5 SG Separation Section 7.6, Section 7.7, and Section 7.8 detail methods for modeling any number of HCSG tubes, which includes anything between one HCSG tube and 1,380 HCSG tubes. ((

                                                     }}2(a),(c) within Section 7.6, Section 7.7, and Section 7.8.

7.5 NPM SG DWO Analysis Model Requirements In NRELAP5 methodologies, various assumptions and approximations are made to represent a physical configuration via a numerical model. This section discusses the general assumptions and approximations made in the NPM SG DWO analysis model. Note that NRELAP5 models used to produce steady-state NPM operating conditions per Section 7.3.2 do not need to follow these requirements. 7.5.1 Hydrodynamic Volume and Junction Options This section discusses the general assumptions and approximations made relative to hydrodynamic components. Specific discussion is provided for flags related to hydrodynamic volume velocity (i.e. the homogeneous flag) and to the hydrodynamic volume temperature (i.e. the equilibrium flag). Other flags are discussed more succinctly. 7.5.1.1 Non-Homogeneous Flag ((

                                                              }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 ((

                            }}2(a),(c) 7.5.1.2            Non-Equilibrium Flag

((

                                                 }}2(a),(c) 7.5.1.3            Other Hydrodynamic Volume Flags The following hydrodynamic volume control flags are applied within the NPM SG DWO model.

((

                           }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 7.5.1.4 Other Hydrodynamic Junction Options The following hydrodynamic junction control flags are applied within the NPM SG DWO model. ((

                                                          }}2(a),(c) 7.5.2         Heat Structure Options This section discusses the general assumptions and approximations made relative to heat structures. Section 5.3 provides more details on the specifics of the NRELAP5 heat transfer numerics and correlations.

In the NPM SG DWO analysis model, the key use of heat structures is to facilitate primary-to-secondary heat transfer. Other heat structure applications (e.g., approximating primary-side or secondary-side heat losses) are significantly less important. Because no core heat structures are included, many models are not needed. ((

                                                  }}2(a),(c)

For general applications, the heat transfer type 101 boundary condition are used. ((

                                                                                   }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 ((

                           }}2(a),(c) 7.5.3         Time Step and System Options The semi-implicit time scheme is applied for hydrodynamic components. Section 5.6 contains more details on the specifics of NRELAP5 time step numerics.

Starting from user-inputs for minimum and maximum time step sizes, NRELAP5 determines the appropriate global time step such that: ((

                                                               }}2(a),(c) The heat structure time scheme is implicitly coupled to the hydrodynamic solution.

Besides preventing significant mass error accumulation, concerns regarding time step size mostly focus on A) reducing numerical instabilities in the model (e.g. artificial perturbations introduced by flow-regime or heat transfer flip-flopping) and B) reducing numerical diffusion in the HCSG tubes (i.e. artificial damping of perturbations). As the BC methods discussed in Section 7.4.1 rely on the introduction of perturbations to the HCSG tubes, it is important that HCSG tube models not include egregious amounts of numerical diffusion. ((

                                                                                          }}2(a),(c)

Because both the primary-side and secondary-side operate in a once through configuration (Section 7.6 and Section 7.7), the system-wide mass error checks may be disabled. Disabling mass error checks only prevents code termination based on cumulative mass error buildup (i.e. at 1 percent of total system mass), it does not prevent time-step controls based on mass error accumulation during the current time step. 7.5.4 Initial Conditions For the NPM SG DWO analysis model, ICs are set to values which allow for simulation convergence within a reasonable period of time (e.g. ~2,000 seconds) before ramping begins per Section 7.4. Herein, simulation convergence refers to behavior wherein BCs are fixed at values and that conditions within individual © Copyright 2022 by NuScale Power, LLC 106

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 components (e.g. HCSG tubes, upper downcomer, etc.) are not noticeably changing as a function of time. Generally, poorly tailored ICs only lead to the need for extended convergence times. However, sometimes very poor ICs can lead to initial instability. In these cases, it can take some time for convergence to occur. Therefore suggestions for IC tailoring is provided for each relevant component in Section 7.6 through Section 7.8. 7.6 Model Nodalization - SG Primary-Side The required components for the SG primary-side are the primary-side inlet, the upper downcomer (i.e. the upper section containing the HCSG tubes), and primary-side exit. The optional components for the SG primary-side are the riser, the riser holes, and the upper plenum. 7.6.1 SG Primary-Side: Inlet ((

                                                                }}2(a),(c) 7.6.1.1            SG Primary-Side: Inlet BCs

((

                                                                           }}2(a),(c)

Section 7.3.1 provides more information on BCs. 7.6.2 SG Primary-Side: Upper Downcomer ((

                                                                             }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 ((

                              }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 7.6.2.1 SG Primary-Side: Upper Downcomer Heat Structures ((

                                                                                                 }}2(a),(c) 7.6.2.2            SG Primary-Side: Upper Downcomer ICs

((

                                                                                                             }}2(a),(c) 7.6.3         SG Primary-Side: Exit

((

                             }}2(a),(c) 7.6.3.1            SG Primary-Side: Exit BCs

((

                                                             }}2(a),(c) 7.6.4         SG Primary-Side: Riser This component is not required.

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 ((

                                                              }}2(a),(c) 7.6.4.1            SG Primary-Side: Riser Heat Structures These heat structures are not required.

((

                                                                                                   }}2(a),(c) 7.6.4.2            SG Primary-Side: Riser ICs Pressure is set to values similar to initial BCs per Section 7.6.3.1. Temperature is set to initial BCs per Section 7.6.1.1. Mass flow rate is set to initial BCs per Section 7.6.1.1.

7.6.5 SG Primary-Side: Riser Holes This component is not required. ((

                                                         }}2(a),(c)

If included, the riser holes must include realistic and accurate flow area, hydraulic diameter, and loss coefficient inputs. 7.6.5.1 SG Primary-Side: Riser Holes ICs (( }}2(a),(c) 7.6.6 SG Primary-Side: Upper Plenum This component is not required. © Copyright 2022 by NuScale Power, LLC 110

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 ((

                             }}2(a),(c) 7.6.6.1            SG Primary-Side: Upper Plenum Heat Structures Any HCSG tubes in the upper plenum require heat structures. Other heat structures are not required for this component.

7.6.6.2 SG Primary-Side: Upper Plenum ICs Pressures are set to values similar to initial BCs per Section 7.6.3.1. Temperatures are set to initial BCs per Section 7.6.1.1. Mass flow rates are set to initial BCs per Section 7.6.1.1. 7.7 Model Nodalization - FW and STM Plenums ((

                                                                                                                 }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 7.7.1 FW Source ((

                             }}2(a),(c) 7.7.1.1            FW Source: Inlet BCs

((

                                                                      }}2(a),(c)

Section 7.3.1 provides more information on BCs. 7.7.2 FW Plenum ((

                                                                                  }}2(a),(c) 7.7.2.1            FW Plenum: Heat Structures

((

                                             }}2(a),(c) 7.7.2.2            FW Plenum: ICs Pressure is set to values slightly higher than initial STM pressure BCs per Section 7.7.3. Temperature is set to initial FW temperature BCs per Section 7.7.1.

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 7.7.3 STM Plenum The STM plenum is a mandatory component for flow-controlled BC methods. ((

                                                                                                }}2(a),(c) 7.7.3.1            STM Plenum: Heat Structures:

((

                                             }}2(a),(c) 7.7.3.2            STM Plenum: ICs Pressure is set to the initial values per Section 7.7.3. Temperature is set to Thot initial values per Section 7.6.1.1.

7.7.4 STM Exit ((

                                   }}2(a),(c) 7.7.4.1            STM Exit: Exit BCs

((

                                        }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 7.8 Model Nodalization - HCSG Tubes The HCSG tubes are composed of the tube inlet(s), the tubes, and the tube exit(s). Different BC methods, which are discussed in more detail in Section 7.4, make use of different numbers of boiling channels. 7.8.1 HCSG Tube Inlets ((

                                                                      }}2(a),(c) 7.8.1.1            HCSG Tube Inlets: ICs

((

                                                                                                         }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 7.8.2 HCSG Tubes ((

                          }}2(a),(c) 7.8.2.1            HCSG Tubes: Columns

((

                                              }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 7.8.2.1.1 ((

                                  }}2(a),(c)

((

                                                                }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 7.8.2.1.2 ((

                                  }}2(a),(c)

((

                                                                                                        }}2(a),(c) 7.8.2.2            HCSG Tubes: Sections

((

                                                      }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 ((

                                }}2(a),(c) 7.8.2.3            HCSG Tubes: Main Section General Nodalization

((

                                                                        }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 ((

                                                                          }}2(a),(c) 7.8.2.4            HCSG Tubes: Heat Structures

((

                                      }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 7.8.2.5 HCSG Tubes: ICs ((

                                                                                                              }}2(a),(c)

Mass flow rates are set consistent with Section 7.8.1.1. 7.8.3 HCSG Tube Exits ((

                     }}2(a),(c) 7.8.3.1            HCSG Tube Inlets: ICs

((

                                                       }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 8.0 NRELAP5 Assessments The following section provides a summary of SET and IET assessment that have been completed for NRELAP5 application to SG DWO. The results of these assessments support Section 9.0 to justify the adequacy of NRELAP5 for modeling high-ranked phenomena identified in the SG stability PIRT described in Section 4.0. Three experimental programs used in the assessment of NRELAP5 are summarized below: SIET TF-1: Electrically heated test facility with three full-length HCSG tubes. The testing was performed to characterize pressure drop, heat transfer coefficients and DWO in parallel coiled tubes. SIET TF-2: Primary fluid heated test facility with 252 HCSG tubes in five rows, which includes the effect of primary-to-secondary heat transfer through the tube walls. Testing included a large-scale facility, near-prototypic HCSG tube geometry, and NPM-based operating conditions. POLIMI: Electrically heated test facility with two HCSG tubes in parallel fed by a single FW line. Both tubes were connected to a shared FW header and steam header. For each assessment, the following information is summarized in Section 8.1, Section 8.2, and Section 8.3: Brief description and purpose of the experimental facility Summary of the phenomena addressed Experimental procedure Important NRELAP5 modeling techniques Comparison of NRELAP5 calculations against data Table 8-1 provides a comparison of geometrical parameters for the NPM and the three assessments. A graph showing the HCSG tube diameter ratio (di/Dcoil) for the NPM and the three experimental programs is shown in Figure 8-1. It is observed that TF-1 covers the full NPM range of tube diameters. TF-2 models the five innermost tube rows of the NPM SG, and as such, covers the upper range of di/Dcoil. POLIMI tests a larger diameter ratio, representing larger centrifugal forces than those that would exist in NPM. The NPM operating conditions from 5 percent to 100 percent power are shown Table 8-2 along with T-H parameter ranges from the three test programs. Figure 8-2 plots (as a horizontal bar) secondary side parameter ranges for STM pressure, FW temperature and flow per tube for NPM and the three assessment tests. The plot includes both DWO and non-DWO conditions. For the three parameters, TF-2 fully covers the NPM range. © Copyright 2022 by NuScale Power, LLC 121

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Table 8-1 Comparison of Geometrical Parameters for NPM and Assessment Tests Parameter NPM TF-1 TF-2 POLIMI Tube material Alloy 690 AISI 304L AISI 304L SS AISI 316 Number of tubes 1380 tubes in 21 3 tubes 252 tubes in 5 2 tubes columns rows (2 for DWO) Tube outside diameter (mm) 15.88 15.88 16.07 17.15 Tube inside diameter (mm) 13.34 13.086 13.17 12.53 Tube length (active, m) 22.4 to 25.9 26.82 25.01 to 26.42 32 Tube thickness (mm) 1.27 1.397 1.45 2.31 Tube Inclination (deg.) 12.8 to 15.1 C1(1) 10.0 13.6 to 14.5 14.3 (13.69 for C3) C2 14.0 C3 14.0 Helical coil radius (m) (( (( (( 0.5

                                              }}2(a),(c),ECI          }}2(a),(c)          }}2(a),(c),ECI Tube ID to Coil Dia.                ((                     ((                  ((                      0.0125 Ratio(di/Dcoil)
                                              }}2(a),(c),ECI          }}2(a),(c)          }}2(a),(c),ECI Tube Length to Tube IDRatio 1679 to 1942                   2052                1899 to 2006            2554 (Ltube/di)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 8-1 Tube-to-Coil Diameter Ratio for NPM and Assessment Test Programs ((

                                                                                                                }}2(a),(c)

Table 8-2 NPM T-H Conditions vs. Assessment Test Program Conditions

     © Copyright 2022 by NuScale Power, LLC TF-1           TF-1             TF-2           TF-2           POLIMI Parameter              Units        NPM (non-DWO/SET)       (DWO)        (non-DWO/SET)      (DWO)           (DWO)

Secondary-side exit Psi 200 - 700 217.5 - 464 211 - 233 450 178-769 130 - 1,100 pressure MPa 1.38 - 4.83 1.50 - 3.20 1.46 - 1.61 3.10 1.23 - 5.30 0.90 - 7.58 FW temperature oF 120 - 250 149 - 417 145 - 324 300 73 - 384 274 - 488 oC 48.9 - 121.1 65 - 214 62.8 - 162.2 148.9 22.8 - 195.6 134.4 - 253.3 Total flow rate/tube lb/sec 0.015 - 0.164 0.023 - 0.124 0.022 - 0.128 0.002 - 0.115 0.037 - 0.22 0.05 - 0.164 (average) kg/sec 0.007- 0.074 0.01 - 0.056 0.01 - 0.058 0.001 - 0.052 0.017 - 0.10 0.023 - 0.074 Power/tube kW 15.6 - 158 23 - 131 20 - 120 20 - 110 18.3 - 151.2 7 - 97 (average) Tube exit steam oF 20- 94 0 - ~200 0 - ~120 0 - 104

                                                                                                               ~0 (usually)                                         ~0 superheat               oC         11 - 52         0 - ~111                         0 - ~67          0 - 58 Methodology for the Determination of the Onset of Density Wave Oscillations (DWO)

Primary-side Thot oF 409 - 598 533.9 - 588.4 481 - 582 n/a n/a n/a oC 209 - 314 279 - 309 249 - 306 Primary-side Tcold oF 387 - 482 524.2 - 560.0 440 - 540 n/a n/a n/a oC 197 - 250 273 - 293 227 - 282 Primary-side flow lb/sec 510 - 1,611 22.5 - 333.6 50.7 - 134.9 n/a n/a n/a kg/sec 231 - 731 10.2 - 151. 23.0 - 61.2 TR-131981-NP 124 Revision 0

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 8-2 Secondary Side Parameter Ranges for NPM and Assessment Tests © Copyright 2022 by NuScale Power, LLC 125

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 8.1 Assessment vs TF-1 data 8.1.1 Test Description and Experimental Procedure The TF-1 test facility at SIET was operated to perform a series of testing in 2016. The main components and loops of the SIET TF-1 facility in the NuScale HCSG test configuration are described here and shown in Figure 8-3. A pump system drives water from a water storage tank to the pre-heating zone where it is brought to the specified operating conditions and sent to a FW header. The FW header provides inlet flow to the three HCSG tubes of the test section (Coil 1, Coil 2, and Coil 3) that can be activated by valves singularly or two in parallel. Superheated steam exits the test section toward a header connected to the separation and discharge system. Steam enters a water-steam separator that allows the two phases to be discharged separately. Electric power is provided to the pre-heaters and to the desired test section coils by a direct current generator. For the adiabatic tests, no electric power is provided to the test section coils. For the diabatic tests and the DWO tests, the power generator connections to the coils are suitable to deliver heat to the sub-cooled, saturated and superheated zones, which can be controlled independently. The TF-1 tube geometry and coil geometry details are provided in Table 8-1. The instrumentation details are also shown in Figure 8-3. The run number prefix (which appears on some of the plots) of TA stands for adiabatic testing, TD for diabatic testing, and TO for DWO testing. © Copyright 2022 by NuScale Power, LLC 126

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0

                                                                                                                                           }}2(a),(c)

Figure 8-3 TF-1 Test Section and Instrumentation Configuration ((

  © Copyright 2022 by NuScale Power, LLC 127

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 The relative heat flux profile along the tube for the three zones is shown in Figure 8-4. The three zones are intended to approximately simulate differing heat inputs in the single phase, boiling two phase, and superheated steam regions of the steam generator. Figure 8-4 Relative Heat Flux vs Position Along the Tube ((

                                                                                                                 }}2(a),(c) 8.1.2         Phenomena Addressed Phenomena addressed by TF-1 data include single-phase and two-phase pressure drop, single-phase and two-phase heat transfer, void fraction, and interfacial drag.

Several of the highly ranked phenomena are addressed by TF-1 (Section 9.0). The facility lacks primary-side fluid, so primary-side heat transfer effects are not addressed as per TF-2 testing (Section 8.2). 8.1.3 NRELAP5 TF-1 Model For SET simulation, the NRELAP5 input model of the TF-1 test facility is depicted in Figure 8-5. © Copyright 2022 by NuScale Power, LLC 128

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 8-5 NRELAP5 Model of SIET TF-1 ((

                                                                                                                 }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 ((

                                                                                                            }}2(a),(c) 8.1.4         Performance against TF-1 SET Data TF-1 SETs include analyses of pressure drop (described in Section 8.1.4.1) and heat transfer via wall and fluid temperatures (described in Section 8.1.4.2).

8.1.4.1 Pressure Drop Comparison This section presents an assessment of NRELAP5 with respect to single and two-phase pressure drop in the HCSG tubes using TF-1 data. The TF-1 experiments included both adiabatic and diabatic test configurations. TF-1 non-DWO testing consisted of 77 adiabatic (unheated) test runs (TA-0001 to TA-0077) and 84 diabatic (heated) test runs (TD-0001 to TD-0084). TF-1 DWO (integral effects) testing consisted of 22 runs. For the adiabatic tests, liquid and vapor flow was injected through the FW line and pressure drop was measured across the channels at different locations as indicated in Figure 8-3. The TF-1 tube geometries are comparable with the NPM (Table 8-1 and Figure 8-1). It is apparent from Table 8-2 and Figure 8-2 that the TF-1 adiabatic tests cover a significant range of the plant operation. The assessment of different tubes at TF-1 for pressure drop comparison demonstrates that the NRELAP5 capability to predict the pressure drop for NPM. NRELAP5 Code Assessment For TF-1 SET code-to-data comparisons, agreement herein is determined as follows: Within +/-10 percent: Excellent Within +/-20 percent: Reasonable Within +/-40 percent: Minimal More than 40 percent: Insufficient © Copyright 2022 by NuScale Power, LLC 130

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 In the following figures, the purple lines provide boundaries within 15 percent of the data value. NRELAP5 was assessed against the TF-1 adiabatic tests to establish its capability to predict the two-phase pressure drop. Figure 8-6, Figure 8-7, and Figure 8-8 show the pressure drop comparison from adiabatic tests for coil 1, coil 2, and coil 3. The majority of points are within 15 percent, though some are outside 15 percent. NRELAP5 was assessed against the TF-1 diabatic tests to establish its capability to predict pressure drop and fluid and wall temperature along the HCSG tubes at several locations. Figure 8-9, Figure 8-10, and Figure 8-11 show the pressure drop comparison from adiabatic and diabatic tests for coil 1, coil 2, and coil 3. Most points are within 15 percent. Overall, the calculated two-phase pressure drops along the coil are in reasonable-to-excellent agreement with the adiabatic and diabatic test data. © Copyright 2022 by NuScale Power, LLC 131

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 8-6 TF-1 Differential Pressure for Coil 1 Adiabatic Tests ((

                                                                                                                }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 8-7 TF-1 Differential Pressure for Coil 2 Adiabatic Tests ((

                                                                                                                }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 8-8 TF-1 Differential Pressure for Coil 3 Adiabatic Tests ((

                                                                                                                }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 8-9 TF-1 Differential Pressure for Coil 1 Diabatic Tests ((

                                                                                                                }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 8-10 TF-1 Differential Pressure for Coil 2 Diabatic Tests ((

                                                                                                                }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 8-11 TF-1 Differential Pressure for Coil 3 Diabatic Tests ((

                                                                                                                  }}2(a),(c) 8.1.4.2            Fluid and Wall Temperature Comparison TF-1 TD diabatic cases are used to assess two-phase heat transfer. The incoming FW is heated and eventually becomes a two-phase mixture. Diabatic tests measure pressure drop, and fluid and wall temperature along the HCSG tubes at several locations. The accuracy of wall and fluid temperature comparison between NRELAP5 and test data directly depends on the heat transfer coefficient prediction.

Figure 8-2 lists the TF-1 diabatic test condition range and comparison with NPM operating condition. It is apparent from the table that overall diabatic test conditions cover the NPM operation range. Although the power per tube in TF-1 is lower than NPM, TF-1 tubes undergo a wide quality range and therefore provide the effect of quality on two-phase heat transfer. © Copyright 2022 by NuScale Power, LLC 137

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Fluid temperature code-to-data comparisons with NRELAP5 are shown in Figure 8-12, Figure 8-13, and Figure 8-13 for the three coils. Values are within 15 percent. Excellent predictions of fluid temperatures by NRELAP5 indicate the heat input to the fluid is correctly modeled. Predicted versus measured wall temperatures are plotted in Figure 8-15, Figure 8-16, and Figure 8-17 for the three coils. Most values are within 15 percent. Reasonable agreement of wall temperature predictions indicates the accuracy of the heat transfer coefficient model in NRELAP5. Some over-prediction of wall temperature is observed, which is believed to be due to NRELAP5 predicting tube dryout upstream of where it is observed in the test. For TF-1, if the NRELAP5 dryout location is only slightly (e.g., 10 cm) off near the step change in heat flux (Figure 8-4), a large temperature error occurs. This heat flux step change due to the application of electrical heating in not typical of the NPM or TF-2 HCSG tubes. © Copyright 2022 by NuScale Power, LLC 138

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 8-12 TF-1 Fluid Temperature Comparison for Coil 1 ((

                                                                                                                }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 8-13 Fluid Temperature Comparison for Coil 2 ((

                                                                                                                }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 8-14 Fluid Temperature Comparison for Coil 3 ((

                                                                                                                }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 8-15 Wall Temperature Comparison for Coil 1 ((

                                                                                                                }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 8-16 Wall Temperature Comparison for Coil 2 ((

                                                                                                                }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 8-17 Wall Temperature Comparison for Coil 3 ((

                                                                                                                  }}2(a),(c) 8.1.5         Performance against TF-1 DWO Data A code-to-data NRELAP5 comparison of DWO onset power is plotted in Figure 8-18.

Predictions are generally within +/- 15 percent, with the exception of seven data points which are more conservative (i.e. NRELAP5 predicts DWO onset at a lower power). Of these cases, six of the seven (indicated with a blue circle) were observed to be oscillating at the starting power of the test. This result indicates that NRELAP5 is capable of simulating DWO onset with reasonable-to-excellent agreement, and furthermore, that the simulations were generally conservative for the TF-1 application. Predictions of DWO flow behavior and DWO flow amplitude are more challenging due to the electrically heated nature of TF-1. NRELAP5 produced minimal-to-reasonable agreement for both (not shown), but was largely conservative for DWO flow amplitude, which is deemed acceptable. © Copyright 2022 by NuScale Power, LLC 144

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Previous analysis demonstrated alternative TF-1 NRELAP5 modeling methods that could be used to produce excellent code-to-data agreement for DWO flow period and reasonable-to-excellent agreement for DWO flow amplitude. These are not presented herein as the focus of the TF-1 assessment is the DWO onset prediction with the more optimized model. Figure 8-18 TF-1 DWO Code-to-Data Comparison, DWO Onset Power ((

                                                                                                                }}2(a),(c) 8.1.6         Summary and Conclusions from TF-1 DWO Code-to-Data Comparisons Prediction of pressure drop, and fluid and wall temperature are generally within
             +/-15 percent, which is considered reasonable-to-excellent agreement.

Prediction of DWO onset powers are generally within +/-15 percent, which is considered reasonable-to-excellent. The seven case that are outside +/-15 percent are on the conservative side from a code prediction perspective and as such, are deemed © Copyright 2022 by NuScale Power, LLC 145

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 acceptable. In other words, NRELAP5 predicts DWO onset before it occurs in the experiment. 8.2 Assessment vs TF-2 data 8.2.1 TF-2 Test Description and Experimental Procedure The TF-2 test facility at SIET was operated to perform one series of testing around 2015 and another around 2022. TF-2 is a fluid-heated test facility where the secondary-side fluid is heated by the primary-side fluid. Boundary conditions (e.g. primary-side and secondary-side flow, temperature, and pressure) are varied during testing for DWO investigation. The objective of TF-2 testing was to obtain quality HCSG data with fluid-heated HCSG tubes. Testing was performed to characterize primary-side characteristics (e.g. pressure-drop and heat transfer), and secondary-side DWO characteristics (e.g. DWO onset, DWO flow amplitude, and DWO flow period). To accomplish these objectives, the TF-2 test program was divided into two-phases. During the first phase, testing was conducted to simulate the T-H behavior of the primary-side and secondary-side of NPM HCSG . A small set of initial DWO runs were obtained and analyzed with NRELAP5 . During the second phase, testing was focused on obtaining HCSG tube data for DWO characteristics during simulated NPM conditions. Lessons learned from the first set of DWO testing were implemented. DWO tests were performed by varying boundary conditions (e.g. FW flow) until DWO onset occurred, after which testing continued, if possible. For many tests, measurement of DWO behavior continued while boundary conditions were ramped towards stability (e.g. increased FW flow) until DWO cessation. Sets of facility characterization data were also collected . The TF-2 facility test section consists of a bundle of 252 HCSG tubes split between five rows as shown in Figure 8-19. The five tube rows are placed in an annulus formed by two cylindrical barrels installed axially within the pressure vessel. Each row of HCSG tubes (i.e. groups of 48 or 52 tubes) is fed by a row-specific FW header (which is mounted inside the vessel) that distributes water to each tube inlet as shown in Figure 8-20. Steam exiting the tubes is collected on a per-row basis by a steam header and driven out through the top nozzle. The five rows of the SG can either operate together or individually (i.e., FW flow is delivered on a per-row basis). TF-2 testing was conducted in both single-row and multi-row configurations. TF-2 adiabatic and diabatic tests involve a series of single-row and multi-row tests with conditions designed to analyze primary-side flow behavior. TF-2 DWO tests involve a series of single-row and multi-row tests with scaled NPM operating conditions and sensitivity parameter variations. row 3 is the most highly instrumented for HCSG tube inlet differential pressure, which is used to calculate tube inlet flow. © Copyright 2022 by NuScale Power, LLC 146

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Geometric information for TF-2 HCSG tubes is provided in Table 8-1. The TF-2 HCSG tubes represent geometries that are similar to the five innermost columns of the NPM HCSG at the time the facility was first commissioned in terms of diameter, length and helical coil characteristics. Compared to the latest version of the NPM design, the TF-2 HCSG tubes have a very similar inside diameter, a slightly longer tube length, a helical radius within the NPM range, and a tube inclination angle within the NPM range. Therefore, TF-2 provides a valuable assessment base for analyzing DWO in the NPM. TF-2 test condition ranges are provided in Table 8-2. Figure 8-19 TF-2 Secondary-side Tube Bundle Configuration in the Primary-side Flow Annulus ((

                                                                                                                }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 8-20 SIET TF-2 Configuration P&ID ((

                                                                                                                 }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 8.2.2 Phenomena Addressed TF-2 tests were run to assess primary-side behavior (i.e. adiabatic and diabatic tests) and DWO behavior (i.e. the DWO tests). Phenomena covered by TF-2 testing are pressure drop (single-phase and two-phase), heat transfer (single-phase and two-phase), and primary-to-secondary heat transfer. Due to the presence of boiling channels and primary-to-secondary heat transfer, TF-2 tests cover a wide range of applicable phenomena. TF-2 DWO tests are used to assess the FoMs of DWO onset, DWO flow period, and DWO flow amplitude. 8.2.3 Important NRELAP5 Modeling Techniques TF-2 adiabatic and diabatic tests involve SG operation with primary-to-secondary heat transfer. ((

                              }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 8-21 TF-2 NRELAP5 Adiabatic and Diabatic Test Nodalization Diagram ((

                                                                                                                  }}2(a),(c)

((

                             }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0

                                                                                                                                               }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 ((

                                                                                                              }}2(a),(c) 8.2.4         Performance against TF-2 SET Data TF-2 is equipped with thermocouples and DP sensors across the primary-side of the test section. TF-2 adiabatic and diabatic tests were carried out to evaluate primary-side pressure drop and heat transfer. Primary-side pressure drop is dominated by cross-flow over tubes. Primary-side temperature conditions are dominated by primary-to-secondary heat transfer.

Adiabatic tests were run without primary-side heating and without secondary-side flow. Diabatic tests were performed to evaluate primary-side pressure drop and heat © Copyright 2022 by NuScale Power, LLC 152

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 transfer. These tests characterized the thermal performance of the HCSG tubes for a range of primary-side and secondary-side flows and temperatures. For TF-2 SET code-to-data comparisons, agreement herein is determined as follows: Within +/-10 percent: Excellent Within +/-20 percent: Reasonable Within +/-40 percent: Minimal More than 40 percent: Insufficient In the following figures, the purple lines provide boundaries within 15 percent of the data value. Adiabatic experimental data are used to assess modeling of primary-side friction and form losses in NRELAP5. Figure 8-23 shows a comparison of predicted and measured primary-side pressure drop with instrument uncertainty for adiabatic tests. NRELAP5 values provide excellent code-to-data agreement. © Copyright 2022 by NuScale Power, LLC 153

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 8-23 TF-2 Adiabatic Tests, Primary-side Differential Pressure Comparison ((

                                                                                                                }}2(a),(c)

Figure 8-24 shows a comparison of predicted and measured primary-side pressure drop with uncertainty for diabatic tests. Code-to-data agreement is reasonable-to-excellent. Figure 8-25 shows the primary-side temperature prediction by NRELAP5 for diabatic tests. For most of the test conditions. NRELAP5 closely predicted the change in the primary side temperature. Code-to-data agreement is reasonable-to-excellent. For TF-2 diabatic tests, NRELAP5 validation shows reasonable-to-excellent agreement with test data for primary-side pressure drop, primary-side fluid temperatures, HCSG tube wall temperatures, HCSG tube dryout locations, and HCSG tube fluid temperatures. Based on the primary-side and secondary-side fluid temperatures and tube wall temperatures predicted by NRELAP5, it is concluded that the heat transfer coefficients of both the primary-side and secondary-side are well-predicted by NRELAP5. © Copyright 2022 by NuScale Power, LLC 154

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 8-24 TF-2 Diabatic Tests, Primary-side Differential Pressure Comparison ((

                                                                                                                }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 8-25 TF-2 Diabatic Tests, Primary-side Temperature Comparison ((

                                                                                                                 }}2(a),(c) 8.2.5         Performance against TF-2 DWO IET Data For TF-2 DWO test simulation, both base and biased NRELAP5 cases were run to quantify uncertainty for DWO onset. The biased cases include conservative values for input parameters with potentially large impacts (i.e. higher HCSG tube inlet K-loss, colder FW temperature, and higher total FW flow). The magnitudes of these biases were determined per uncertainty estimates.

Table 8-3 provides a summary for the base and biased results. An NRELAP5 case showing DWO onset at a higher FW flowrate is considered conservative. A positive error denotes a conservative prediction, while a negative error denotes a non-conservative prediction. For NRELAP5 code-to-data comparisons of DWO onset, relative error is calculated separately for row 3 and also for all rows. © Copyright 2022 by NuScale Power, LLC 156

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 For uncertainty analysis, row 1 and row 5 results are included along with row 3 results. While row 3 is the most highly instrumented and thus provides the highest level of resolution, row 1 and row 5 also are instrumented and therefore provide useful information. Besides just providing additional tube measurements, row 1 and row 5 have slightly different geometries. The NRELAP5 base cases are overall conservative for DWO onset (i.e. NRELAP5 predicts DWO onset at a higher FW flow vs. the test data). When 95 percent confidence uncertainty is applied, NRELAP5 base cases become slightly non-conservative. The NRELAP5 biased cases are overall non-conservative for DWO onset (i.e. NRELAP5 predicts DWO onset at a lower FW flow vs. the test data). When 95 percent confidence uncertainty is applied, NRELAP5 biased cases become slightly more non-conservative. To account for uncertainty of NRELAP5 in predicting DWO onset, the one-sided uncertainty results are defined as the overall NRELAP5 uncertainty. For NRELAP5 downstream usage for predicting DWO onset, a one-sided bias uncertainty of

             -13.6 percent with a 95 percent confidence interval is recommended.

Table 8-3 TF-2 DWO Test NRELAP5 Simulation, DWO Onset Total Error Summary Results ((

                                                                                                                }}2(a),(c)

Figure 8-26, Figure 8-27, Figure 8-28 show code-to-data comparisons for DWO onset, DWO flow period, and DWO flow amplitude for the least stable tube. The NRELAP5 values are from the base cases. For code-to-data comparisons of these FoM, the criteria stated below were applied to determine code-to-data agreement. Less than -40 percent: Minimal Between -40 percent and -10 percent: Reasonable Between -10 percent and 10 percent: Excellent © Copyright 2022 by NuScale Power, LLC 157

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Between 10 percent and 20 percent: Reasonable Between 20 percent and 40 percent: Minimal More than 40 percent: Insufficient For DWO onset, a negative percent value means that NRELAP5 DWO onset occurs at a lower FW flow rate. For DWO flow period, a negative value means that NRELAP5 has a smaller period. For DWO flow amplitude, a negative value means that NRELAP5 has a smaller amplitude. For DWO onset, NRELAP5 base cases show reasonable-to-excellent agreement. The vast majority of cases were within 15 percent agreement, and most cases outside of 15 percent agreement were conservative. For DWO flow period, NRELAP5 base cases show generally reasonable agreement. Some outliers are outside of 15 percent agreement. For DWO flow amplitude, NRELAP5 base cases show generally reasonable agreement. While many cases were outside of 15 percent agreement, overall agreement is deemed reasonable because often minimal or insufficient agreement for the majority of cases is due to NRELAP5 over-predictions, which are considered conservative and acceptable, and is consistent with the EM requirements in Section 3.2. It is important to note an important difference between characterizing DWO onset vs. characterizing DWO flow amplitude and period. Within most tests, values tend to change based on tube (i.e., are not constant between the tubes within a row) and time (i.e., are not constant throughout the test). Therefore, the values presented herein are largely simplified to give a high-level overview of DWO flow behavior. © Copyright 2022 by NuScale Power, LLC 158

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 8-26 Predicted vs. Measured FW Flowrate at DWO Onset for the Least Stable Tube ((

                                                                                                                }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 8-27 Predicted vs. Measured Average DWO Flow Period for the Least Stable Tube ((

                                                                                                                }}2(a),(c)

Figure 8-28 Predicted vs. Measured Average DWO Amplitude for the Least Stable Tube ((

                                                                                                                }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 8.2.6 Summary and Conclusions from TF-2 Code-to-Data Comparisons NRELAP5 simulations of TF-2 adiabatic and diabatic data show reasonable-to-excellent code-to-data agreement for primary-side pressure drop and heat transfer. NRELAP5 simulations of TF-2 DWO data allowed for assessment for DWO behavior. The primary FoM is the ability of NRELAP5 to predict DWO onset. For DWO onset: The base model results predicted row 3 DWO onset with reasonable-to-excellent agreement. The base model results were generally slightly conservative, but slightly non-conservative at the 95 percent confidence level. The biased model results were used to determine a ((

                                                                                                            }}2(a),(c)

For DWO flow period and DWO flow amplitude: The base model results for DWO flow period showed reasonable agreement. The base model results for DWO flow amplitude showed minimal agreement overall, but were mostly conservative and thus considered acceptable per Section 3.2 EM requirements. 8.3 Assessment vs POLIMI data This section provides a summary of the testing activities and subsequent code-to-data comparisons for the Polytechnic University of Milan (POLIMI) data. The test data presented in this section is from the POLIMI Parallel HCSG tests. Because POLIMI data was not developed under NQA-1 2008/2009a, the data was qualified for use in this EM following the NuScale Procedure for the Qualification of Existing Data . 8.3.1 Test Description and Experimental Procedure The POLIMI Parallel HCSG configuration included two electrically heated HCSG tubes in parallel fed by a single FW line as shown in Figure 8-29, both coils were connected to a shared FW header and steam header. During testing, BCs such as inlet mass flow, pressure, and temperature were kept relatively constant while the electrical power supplied to heat the coils was increased. Heat was applied uniformly to the lower 3/4 of the tube, while the last 1/4 was unheated. Power was increased until DWO onset occurred. The two tubes were identical, except one did not have DP instrumentation as shown in Figure 8-30. © Copyright 2022 by NuScale Power, LLC 161

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 8-29 Overview of POLIMI Parallel HCSG Configuration © Copyright 2022 by NuScale Power, LLC 162

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 8-30 Schematic of POLIMI Test with Instrumentation Locations

  © Copyright 2022 by NuScale Power, LLC 163

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 8.3.2 Phenomena Addressed Phenomena addressed by the POLIMI tests include single-phase and two-phase pressure drop, wall-to-secondary heat transfer (wall temperatures), and DWO onset. 8.3.3 NRELAP5 Modeling Techniques Figure 8-31 shows the nodalization diagram for the NRELAP5 model. Connections are axial, and arrows entering/exiting from the sides of the box indicate a horizontal component, and not use of crossflow. ((

                                   }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 8-31 POLIMI Parallel HCSG Facility NRELAP5 Model Nodalization Diagram ((

                                                                                                                 }}2(a),(c) 8.3.4         POLIMI Code-to-Data Comparisons The POLIMI testing was published in several PhD theses (along with some unpublished data) at the University of Milan. Therefore, the POLIMI DWO test conditions and HCSG tube geometry are not as close to NPM values as TF-1 and TF-2, as illustrated in Figure 8-1 and tabulated in Table 8-1.

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 ((

                            }}2(a),(c)

From a total of 126 test runs, a set of 45 cases were selected for code-to-data comparison as they were deemed to be the most applicable to NPM conditions. 8.3.5 POLIMI base model versus cases run with TF-1 Characteristics The POLIMI test series evaluated herein has similarities to the TF-1 TO test series in both facility geometry (i.e. two parallel HCSG tubes) and in the test procedure (e.g. gradual power increases until DWO onset occurs). However, as discussed previously the geometry of the POLIMI HCSG tubes are more tightly wound than those used in TF-1 testing, as shown by the di/Dcoil ratio plotted in Figure 8-1. Tightly wound tubes result in greater centrifugal forces on the fluid than for TF-1, which may exceed the range of parameters upon which the two-phase pressure drop model was developed. ((

                                       }}2(a),(c)

Figure 8-32 plots the POLIMI Test 46 code-to-data comparison for differential pressure (DP) along the instrumented HCSG tube (Tube A). The first DP, low in the tube (where single-phase liquid is present) shows excellent agreement, however higher up the tube in the two-phase region, a significant over prediction of pressure drop by NRELAP5 is observed. This trend was observed for the vast majority of POLIMI NRELAP5 code-to-data comparisons. The NRELAP5 over-prediction of two-phase pressure drop is considered conservative for DWO onset predictions as a higher two-phase pressure drop is destabilizing for DWO onset. © Copyright 2022 by NuScale Power, LLC 166

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 8-32 POLIMI Test 46 Code to Data Differential Pressure Along the Tube vs NRELAP5 ((

                                                                                                                   }}2(a),(c)

To study HCSG tube geometry impacts on NRELAP5 pressure drop predictions, POLIMI NRELAP5 cases were also run with TF-1 HCSG tube characteristics. NRELAP5 was run as a sensitivity using the TF-1 HCSG tube inner diameter (di) and di/Dcoil ratio, with results discussed below. These sensitivity cases were called TF-1 Characteristics cases. Note that these changes also have an effect on heat transfer terms etc. The full set of POLIMI cases were run in NRELAP5 both with and without TF-1 HCSG tube characteristics. Figure 8-33 presents the HCSG tube pressure drop ratio vs. HCSG tube pressure. The pressure drop ratio is the NRELAP5 total HCSG DP divided by the data total HCSG DP. So a value greater than 1 is an under-prediction of pressure drop. For the base model, every test except one test shows an under prediction. For the model with TF-1 HCSG tube characteristics, the prediction is significantly improved with the mean DP ratio decreasing from 1.44 to 1.09. The trend lines indicate increasing over prediction with decreasing pressure, and the model with TF-1 coil characteristics matches the DP data reasonably well for P > 3.0 MPa, with the trend line passing through 1.0 at 4 MPa. © Copyright 2022 by NuScale Power, LLC 167

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 8-33 POLIMI NRELAP5 HCSG Tube Pressure Drop Ratio vs. Pressure (Base Model and Model with TF-1 Characteristics) ((

                                                                                                                  }}2(a),(c)

Figure 8-34 presents the HCSG tube DWO onset power ratio. The DWO onset power ratio is the NRELAP5 power at DWO onset divided by the data power at DWO onset. Therefore values less than one mean that NRELAP5 predicted DWO onset at a lower power than the data, i.e. was conservative. Both the base cases and TF-1 characteristics cases have power ratios less than 1 for most tests. © Copyright 2022 by NuScale Power, LLC 168

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 8-34 POLIMI NRELAP5 DWO Onset Power Ratio vs Pressure (Base Model and Model with TF-1 Coil Characteristics) ((

                                                                                                                  }}2(a),(c)

Figure 8-35 and Figure 8-36 show the previously discussed pressure drop ratio and power ratio, but vs. the Tube A test-specific HCSG tube Kinlet values. It is observed that both ratios improve (move toward one) as Kinlet increases. This observation is noteworthy because the higher POLIMI Kinlet values are closer to TF-2 values and also to expected NPM Kinlet values (i.e. in the range at or above a Kinlet of (( }}2(a),(c)). © Copyright 2022 by NuScale Power, LLC 169

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 8-35 POLIMI NRELAP5 HCSG Tube Pressure Drop Ratio vs. Tube A Kinlet ((

                                                                                                                }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 8-36 POLIMI NRELAP5 DWO Onset Power Ratio vs. Tube A Kinlet ((

                                                                                                                }}2(a),(c)

Taken together, these plots show that both pressure and Kinlet are significant parameters for ratios with higher pressures and Kinlet values greater than 100 giving improved code-to-data agreement. The trends show that for values that move towards the range of NPM conditions (e.g. higher Kinlet and higher exit quality), improved code-to-data agreement occurs. Tube inside wall temperature measurements are compared to calculations in Figure 8-37. Code-to-data comparisons are made at the five axial locations shown in the legend (i.e. meters along the tube from the tube inlet). Code-to-data agreement is reasonable-to-excellent, with most of the data predicted to within +/-10K. High code-to-data agreement indicates that wall heat transfer to the fluid is accurately modeled by NRELAP5. © Copyright 2022 by NuScale Power, LLC 171

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 8-37 POLIMI NRELAP5 Code-to-Data Comparison, Tube A Axial Wall Temperature ((

                                                                                                                }}2(a),(c) 8.3.6         Summary and Conclusions from POLIMI Data to Code Comparisons For the POLIMI DWO tests and NRELAP5 predictions agreement rankings of Excellent, Reasonable, Minimal, and Insufficient agreement are assigned. The different agreement levels for POLIMI are stated below. Note that A) the definition of excellent agreement herein is quite restructured, and B) that these definitions are not necessarily applicable to code-to-data comparisons in other situations.

Excellent agreement: If the ratio is within +/-5 percent. Reasonable agreement: If the ratio is within +/-15 percent Minimal agreement: If the ratio is within +/-30 percent Insufficient agreement: If the ratio is greater than +/-30 percent © Copyright 2022 by NuScale Power, LLC 172

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Each test run was assigned one of the above rankings. Overall, the agreement is described as follows: ((

                           }}2(a),(c)

The overall conclusions from the POLIMI DWO NRELAP5 simulations are: NRELAP5 substantially over predicts pressure drop and under predicts the power needed for DWO onset (i.e. conservatively predicts DWO onset). Based on the runs of POLIMI with TF-1 helical coil characteristics, the NRELAP5 DP over prediction may be due to coil geometry being out of range of the specific correlations implemented in the HLCOIL logic of NRELAP5. As the NRELAP5 predictions of DWO onset are generally conservative, and often very conservative when (( }}2(a),(c), this work suggests that NRELAP5 may be used to conservatively determine the DWO stability boundary for HCSG tube systems. Prediction of wall temperatures is reasonable-to-excellent, indicating the wall to fluid heat transfer modeling is satisfactory. Trends show that for parameters that move towards the range of NPM conditions (e.g. higher Kinlet and higher exit quality), NRELAP5 shows better predictions, while poorer NRELAP5 predictions with considerable conservatism are associated with conditions which are quite different from NPM conditions. © Copyright 2022 by NuScale Power, LLC 173

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 9.0 Assessment of Evaluation Model Adequacy The adequacy of the NRELAP5 code for analysis of DWO in the NPM SG is demonstrated by 1) closure model and correlations reviews and 2) assessments against relevant SET and IET experimental data. 9.1 Adequacy Demonstration Overview The EM adequacy for DWO analysis of the NPM SGs is demonstrated with bottom-up and top-down evaluations performed with NRELAP5 for high ranking PIRT phenomena and NRELAP5 validation against relevant test data. The adequacy of the SG DWO EM is demonstrated through the following steps: Section 9.2 documents the bottom-up assessment of the NRELAP5 models and correlations to determine their adequacy to predict the high-ranked phenomena. The code models used to represent each high-ranked phenomena are identified with emphasis on the phenomena with low-knowledge level. These assessments address the fidelity of the models and correlations to the appropriate fundamental or SET data. Fidelity of the assessments is evaluated using the criteria of excellent, reasonable, minimal, and insufficient. These criteria are defined in Table 1-2. The comparisons to SET data can identify modeling deficiencies that could impose limitations on the application of the NRELAP5 based SG DWO EM. Section 9.3 covers the top-down assessment of the EM including a review of EM governing equations and numerical solution scheme to determine their applicability to NPM SG DWO analysis, and evaluation of the integral code performance based on the assessments of the EM against relevant IETs. 9.2 Evaluation Models and Correlations (Bottom-Up Assessment) The adequacy of the models and correlations in NRELAP5 for modeling the high-ranked phenomena per Section 4.2 are examined by considering their pedigree, applicability, and fidelity to appropriate fundamental or SET data (established by assessment of the EM against legacy and NuScale-specific SET data), and scalability to the NuScale DWO scenario. During the PIRT process there were no high-ranked phenomena identified with knowledge level 1 (the lowest knowledge level). © Copyright 2022 by NuScale Power, LLC 174

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 ((

                                                                }}2(a),(c)

The pedigree of the identified closure relations and correlations was first established based on their historical development and subsequent assessment in the literature. Section 8.0 describes comparisons of NRELAP5 to the three assessment tests (TF-1, TF-2, and POLIMI), which included both SETs for evaluation of the fundamental models (bottom-up evaluation), and IETs to validate the integral performance of the models working together to predict DWO onset and DWO flow behavior (top-down evaluation) Assessment cases were then identified to demonstrate the capability of NRELAP5 to predict the experimental data. The applicability of NRELAP5 to model the subject phenomena is established by demonstrating that the assessment cases cover the range of parameters that approximate the NPM range and evaluating how NRELAP5 compares with test data. 9.2.1 Evaluation of Models and Correlations (Bottom-Up Assessment) Table 9-1 identifies the dominant code models/correlations for the PIRT high ranked phenomena. Key parameters that are influenced by the dominant models and correlations are listed, along with phenomenological and separate effects cases that are used to assess the model/correlation capabilities. The absence of data for a © Copyright 2022 by NuScale Power, LLC 175

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 phenomena does not necessarily mean that it was absent within the relevant test facility, but rather it often means that measurement or assessments of that phenomena were not made. This information is used to establish adequacy of the dominant code models/correlations for NPM SG DWO applications. Table 9-1 NRELAP5 Models and Correlations Associated with High-Ranked Phenomena Along with Relevant Assessment Test Data ((

                                                                                                                   }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Table 9-1 NRELAP5 Models and Correlations Associated with High-Ranked Phenomena Along with Relevant Assessment Test Data (Continued) ((

                                                                                                                }}2(a),(c)

Table 8-2 provides a summary of the estimated range of key parameters that each test program covered and a comparison with NPM operating conditions. Parameter ranges obtained are intended to identify the minimum range that should be covered; the applicability of models and correlations are not restricted to these ranges. Ranges are provided per NPM beginning of life conditions (best estimate). 9.2.2 Applicability Evaluation To determine the adequacy of the models and correlations used to simulate the high-ranked phenomena, the results of assessments against phenomenological and SETs are discussed. The assessments results are drawn from the NRELAP5 assessment report for each experimental program. 9.2.2.1 Overview A graded approach is used to address the bottom-up evaluation method. More emphasis is given to high-ranked phenomena with a low knowledge level. Less emphasis is placed on phenomena that are well understood with a high knowledge level, including well-accepted or engineering handbook models. © Copyright 2022 by NuScale Power, LLC 177

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Each of the following four areas is evaluated to the extent that they are relevant for each high ranked phenomenon: Background of the model development is described, including pedigree and experimental data used in development of the model or correlation. Assumptions and limitations attributed to the model are identified. Applicability Range identifies the range covered by the model(s) and correlation(s) based on the initial development and subsequent assessments. The models range is compared to the range of the NPM application. The manner of addressing the limitations for the NPM application is discussed. Validation of the model(s) and correlation(s) evaluates the fidelity of the models and correlations to appropriate fundamental or SET data. Results of the comparison to experimental data are summarized. Scalability evaluates whether there are scaling effects resulting from the development of the model, which would impose a limitation on the application of the model to full-plant geometries and operation conditions. The scalability evaluation is limited to whether the specific model or correlation is appropriate for application to the configuration and conditions of the plant and transient under evaluation. 9.2.2.2 High-Ranked Phenomena The PIRT identified some phenomena within specified components as high importance phenomena. These high importance phenomena are given the highest focus in the development of the SG DWO EM. The high importance, low knowledge phenomena are addressed first, followed by the other high ranked phenomena listed in Table 9-1. 9.2.2.3 (( }}2(a),(c) 9.2.2.3.1 Background ((

                                                                                                }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 9.2.2.3.2 Technical Evaluation ((

                              }}2(a),(c) 9.2.2.4            ((                                       }}2(a),(c) 9.2.2.4.1              Background

((

                                         }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 9.2.2.4.2 Technical Evaluation ((

                                        }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 9-1 (( }}2(a),(c) ((

                                                                                                                }}2(a),(c)

Figure 9-2 (( }}2(a),(c) ((

                                                                                                                }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 9-3 (( }}2(a),(c) ((

                                                                                                                }}2(a),(c)

Figure 9-4 (( }}2(a),(c) ((

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Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 9-5 (( }}2(a),(c) ((

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Figure 9-6 (( }}2(a),(c) ((

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Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 9-7 (( }}2(a),(c) ((

                                                                                                                }}2(a),(c)

Figure 9-8 (( }}2(a),(c) ((

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Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 9-9 (( }}2(a),(c) ((

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Figure 9-10 (( }}2(a),(c) ((

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Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 9-11 (( }}2(a),(c) ((

                                                                                                                }}2(a),(c)

Figure 9-12 (( }}2(a),(c) ((

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Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 9-13 (( }}2(a),(c) ((

                                                                                                                }}2(a),(c)

Figure 9-14 (( }}2(a),(c) ((

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Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 9-15 (( }}2(a),(c) ((

                                                                                                                      }}2(a),(c)

The following is concluded regarding these code-to-data comparisons: ((

                                   }}2(a),(c) 9.2.2.5            ((                                      }}2(a),(c) 9.2.2.5.1              Background

((

                                           }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 ((

                                      }}2(a),(c) 9.2.2.5.2              Technical Evaluation

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                                                                    }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 9.2.2.6 (( }}2(a),(c) 9.2.2.6.1 Background ((

                                                                                                    }}2(a),(c) 9.2.2.6.2              Technical Evaluation

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                                                }}2(a),(c)

Table 9-2 (( }}2(a),(c) ((

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Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 9.2.2.7 (( }}2(a),(c) 9.2.2.7.1 Background ((

                                                                   }}2(a),(c) 9.2.2.7.2              Technical Evaluation

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                                                                                                }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Table 9-3 ((

}}

((

                                                                                                                }}2(a),(c)

((

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Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 ((

                                                                       }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0

                                                                    }}2(a),(c)

}}2(a),(c) Figure 9-16 (( ((

© Copyright 2022 by NuScale Power, LLC 194

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 ((

                                  }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0

                                                                    }}2(a),(c)

}}2(a),(c) Figure 9-17 (( ((

© Copyright 2022 by NuScale Power, LLC 196

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 ((

                                                                                      }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0

                                                                    }}2(a),(c)

}}2(a),(c) Figure 9-18 (( ((

© Copyright 2022 by NuScale Power, LLC 198

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 9-19 (( }}2(a),(c) ((

                                                                                                                }}2(a),(c)

((

                                             }}2(a),(c)measurement uncertainty).

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0

                                                                            }}2(a),(c)

Table 9-4 Numerical Evaluation of the Transverse Temperature Profiles ((

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Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 9-20 ((

                                                       }}2(a),(c)

((

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Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 ((

                                      }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 9.2.2.8 (( }}2(a),(c) 9.2.2.8.1 Background ((

                                                     }}2(a),(c) 9.2.2.8.2              Technical Evaluation

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                                                                                                  }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 9-21 (( }}2(a),(c) ((

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Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 9-22 (( }}2(a),(c) ((

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Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 9-23 (( }}2(a),(c) ((

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Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 9-24 (( }}2(a),(c) ((

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Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 9-25 (( }}2(a),(c) ((

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Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 9-26 (( }}2(a),(c) ((

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Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 9-27 (( }}2(a),(c) ((

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Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 9-28 (( }}2(a),(c) ((

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Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 9-29 (( }}2(a),(c) ((

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Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 9-30 (( }}2(a),(c) ((

                                                                                                                }}2(a),(c) 9.2.2.9            ((                                             }}2(a),(c) 9.2.2.9.1              Background

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                                                                              }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 9.2.2.9.2 Technical Evaluation ((

                                                                                      }}2(a),(c) 9.2.2.10           ((                                                                        }}2(a),(c) 9.2.2.10.1             Background

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Figure 9-31 ((

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Figure 9-32 ((

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                                      }}2(a),(c) 9.2.2.11           ((                                                        }}2(a),(c) 9.2.2.11.1             Background

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                                                                                            }}2(a),(c) 9.2.2.11.2             Technical Evaluation

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Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 ((

                                                               }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 9-33 ((

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Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 9-34 ((

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                                                 }}2(a),(c) 9.2.2.13           ((                                                                }}2(a),(c) 9.2.2.13.1             Background

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Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 9.2.2.14 (( }}2(a),(c) 9.2.2.14.1 Background ((

                                      }}2(a),(c) 9.2.2.14.2             Technical Evaluation

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Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure 9-35 (( }}2(a),(c) ((

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                               }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 9.2.2.15.2 Technical Evaluation ((

                                                 }}2(a),(c) 9.2.2.16           ((                                                                          }}2(a),(c) 9.2.2.16.1             Background

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                                                          }}2(a),(c) 9.2.2.16.2             Technical Evaluation

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Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 9.2.2.17 (( }}2(a),(c) 9.2.2.17.1 Background ((

                                  }}2(a),(c) 9.2.2.17.2             Technical Evaluation

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                                                               }}2(a),(c) 9.2.3         Bottom-Up Summary Results of the bottom-up evaluation are summarized in Table 9-5, which tabulates for:

each high-ranked phenomena the dominant NRELAP5 model/correlation, a statement of the pedigree of the model/correlation, applicability range restrictions (if any), and fidelity to fundamental and SET test data. The scalability evaluation was limited to whether the specific model or correlation is applicable for the NPM configuration over the range of conditions encountered in DWO events. The geometric parameters presented in Table 8-1 for NPM, TF-1 and TF-2 indicate excellent similarity. The T-H conditions presented in Table 8-2 and Figure 8-2 indicate TF-1 and TF-2 test conditions span the range of NPM operating conditions. Table 9-6 provides a summary for high-ranked phenomena with an original knowledge level of two per Section 4.0. © Copyright 2022 by NuScale Power, LLC 226

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0

                                                                                                                                                     }}2(a),(c)

Table 9-5 Summary of Bottom-Up Evaluation of NRELAP5 Models and Correlations ((

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Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0

                                                                                                                                                                          }}2(a),(c)

Table 9-5 Summary of Bottom-Up Evaluation of NRELAP5 Models and Correlations (Continued) ((

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Table 9-5 Summary of Bottom-Up Evaluation of NRELAP5 Models and Correlations (Continued) ((

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Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0

                                                                                                                                                           }}2(a),(c)

Table 9-6 Applicability Summary for High Ranked Phenomena with Originally Knowledge Level 2 ((

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Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0

                                                                                                                  }}2(a),(c)

Table 9-6 Applicability Summary for High Ranked Phenomena with Originally Knowledge Level 2 ((

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Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 9.3 Evaluation of Integral Performance (Top Down Evaluation Summary) Integral or top-down performance is assessed by evaluating: mathematical models for mass, momentum, and energy conservation; numerical solution techniques employed; and IET test predictions where integral system response is present. The code governing equations and numerical solution are reviewed for their underlying assumptions and whether those assumptions are appropriate for the NPM DWO analysis. The governing equations are appropriate to model DWO phenomena. The NRELAP5 numerical solution tends to be diffusive. However, appropriate nodalization and time-step control is shown to mitigate numerical diffusivity (Section 9.2.2 - (( }}2(a),(c) The integrated performance of the code is assessed against IETs conducted at different test facilities. NuScale utilized three test programs to evaluate NRELAP5 for DWO. TF-1 and POLIMI are SETs that cover the range of high ranking phenomena, but they also provide integral response to a limited extent. TF-2 is an IET, which models the underlying high ranked phenomena, but due to the complex configuration and by design cannot realistically include instrumentation for detailed measurements at all locations. A scaling analysis was performed to demonstrate the sufficiency of the TF-2 facility to represent the phenomena and processes that are important to DWO . Calculations are performed in the scaling analysis to evaluate differences and distortions between the TF-2 facility and NPM design, and to establish the capability of NRELAP5 to scale-up the phenomena and processes to the full scale NPM. For the top-down evaluation of NRELAP5 for DWO, integral effects of the high ranking phenomena are evaluated based on the NRELAP5 applicability in predicting FoMs in the TF-2 facility such as, DWO onset, DWO flow period, and DWO flow amplitude. Results of the adequacy evaluation based on the SIET IETs are summarized in Table 9-9. To ensure maximum fidelity of the assessments, the NRELAP5 DWO analysis models were developed using consistent nodalization and option selection. Table 9-1 provides an overview of the phenomena present in the DWO tests discussed herein vs. the high-ranked PIRT phenomena per Section 4.0. © Copyright 2022 by NuScale Power, LLC 232

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Table 9-7 Assessment Test Data and Associated High-Ranked PIRT Phenomena ((

                                                                                                                   }}2(a),(c) 9.3.1         Review of Code Governing Equations and Numerics The field equations solved by NRELAP5 are discussed in Section 2.1 of Reference 12.8. Herein, the applicability of the field equations to represent the processes and phenomena that can occur in the NPM is evaluated, along with an assessment of the ability of the NRELAP5 numerical solution to approximate the set
  © Copyright 2022 by NuScale Power, LLC 233

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 of governing field equations. This evaluation addresses the mathematical models implemented in NRELAP5 for the NPM DWO analysis, and considers the applicability of the assumptions and processes involved in developing the NRELAP5 system of governing equations, related physical, and thermodynamic and transport property representations. 9.3.1.1 Conservation of Mass, Momentum and Energy The one-dimensional equations and numerical solution scheme have been used in various versions of the RELAP5 codes for many years so their pedigree is well established by code assessments and applications. The semi-implicit solution technique used by NRELAP5 has been in the RELAP5 code as the primary solution technique for the governing conservation equations since the codes initial development. The solution technique continues to be used in NRELAP5 as discussed in Section 2.1.3 of the Reference 12.8. The basic governing equations for mass, momentum and energy conservation utilize a lumped parameter approach with two fields, a vapor field and a liquid field. Mass, momentum, and energy conservation equations are written for each phase, resulting in what is referred to as a six-equation model. A single pressure is assumed for both phases. Mass, energy, and momentum transfer between the two fields is modeled by various closure relations and correlations that depend on the physical and thermodynamic state of the phases. The interaction of each phase with the flow boundaries also depends on the physical and thermodynamic state of each phase, and also on the relative amount of each phase, described by the vapor (or void) fraction. The closure relations are defined for various flow regimes that are based on the flow structure. The flow regimes determine the appropriate closure relationships used to model heat transfer, interfacial drag, and flow losses. The numeric solution evaluation considers conservation of physical properties, convergence and stability of code calculations performed to solve the set of governing equations for an NRELAP5 NPM model. The objective of this evaluation is to summarize information regarding the domain of applicability of the numerical techniques and user options that may impact the accuracy, stability, and convergence of NRELAP5 calculations. User guidelines for model development and execution were developed based on lessons learned during the code reviews and assessments. The guidelines include requirements for assuring convergence of solutions, accounting for uncertainty in results and monitoring code function to assure that the basic conservation equations are being solved correctly. As part of the CGD of RELAP5-3D© to serve as the development platform for NRELAP5, NuScale performed acceptance testing and receipt inspection as documented in a CGD dedication report. The testing and inspection verified that RELAP5-3D© has the necessary critical characteristics to be used as the code development platform for NRELAP5. The critical characteristics include the suitability of the basic governing equations described above for the NuScale © Copyright 2022 by NuScale Power, LLC 234

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 application. The review identified 12 limitations of RELAP5-3D© as the code development platform for NRELAP5 (Table 9-8). Limitations 2 and 10 are related to DWO, and are discussed in Section 9.3.1.3. Some of the limitations derived from the numerical solution techniques used to discretize and solve the governing equations. These are discussed in the next section. 9.3.1.2 Numerical Solution Techniques The governing equations are discretized in time and space. The lumped parameter approach consists of dividing the T-H domain into a number of control volumes (also called mesh cells or nodes) that include the entire fluid domain of interest. The control volumes are connected by flow junctions. The difference equations implement mass and energy conservation by equating accumulation to the rate of mass or energy inflow and outflow through the cell boundaries, minus the rate of mass or energy out through the cell boundaries, plus source terms such as heat input. This approach necessitates defining mass and energy volume average properties and requiring knowledge of velocities at the volume boundaries. The velocities at the cell edges are defined through the use of momentum control volumes centered on the mass and energy cell boundaries. This approach results in a numerical scheme having a staggered spatial mesh with the momentum control volumes extending from the mass and energy cell centers to the neighboring mass and energy cell centers. The scalar properties of the flow (pressure, specific internal energies, and void fraction) are defined at mass and energy cell boundaries. The governing equations for the system model are solved numerically using a semi-implicit finite-difference technique. A nearly-implicit finite-difference technique, which allows violation of the material Courant limit, is also available. However, the DWO EM and the supporting assessment calculations use only the semi-implicit numerical scheme. The semi-implicit numerical solution scheme is based on replacing the system of differential equations with a system of finite difference equations partially implicit in time. For HCSG tube propagation the NRELAP5 semi-implicit solution scheme behaves like a classic explicit scheme and introduces numerical diffusion (which acts to damp inlet perturbations). The amount of numerical diffusion can vary considerably as it is dependent on the number of nodes used and the Courant number C , which is the time-step size normalized to the transport time through a volume per Equation 9-1: C = vt x Equation 9-1 Where v is the velocity (m/s), t is the time step (s), and x is the node length (m). The physical meaning of C , illustrated in Figure 9-36, is the distance a fluid particle travels in a time step ( vt ), divided by the node length ( x ). It is desirable to keep the distance traveled less than the node length (ex, C=0.4, as © Copyright 2022 by NuScale Power, LLC 235

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 seen on the left). If the distance traveled exceeds the node length (C=1.2, as seen on the right) information may not be correctly propagated from node to node. Figure 9-36 Physical Meaning of the Courant Number For the NRELAP5 semi-implicit scheme, the range of allowable values is 0 < C < 1. In an NRELAP5 simulation, if the velocity in a node (i.e. either liquid velocity or gas velocity) would cause C > 1, the time-step is automatically reduced such that C < 1. Note that in NRELAP5, the nodes use the same time-step. Often, NRELAP5 models with uniform nodalization have their time step controlled by the node with the highest velocity, so more course nodalization in high velocity regions is sometimes used to keep the time step from becoming very small, which has the effect of impacting the overall solution time. When generating a solution of finite difference equations there is a possibility that the solution may not converge. Lack of convergence could be the result of an ill-posed problem, inappropriate time step size selection, inadequate spatial nodalization, or an instability. Sensitivity studies have proven useful to assure convergence and stability of the NRELAP5 solutions. Adherence to the known modeling limitations and requirements of NRELAP5, discussed in the next section, assist in assuring that the governing equations are well posed. Solutions are examined to identify unstable or unphysical behavior. ((

                                   }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 9.3.1.3 Limitations on Applicability for DWO Limitations of RELAP5-3D for the NuScale LOCA applications were identified during the CGD and acceptance testing of RELAP5-3D© and in subsequent NRELAP5 code assessments. This report documents three limitations that impact DWO analysis which are provided in Table 9-8. Table 9-8 Limitations and Improvement Needs Related to DWO How limitation was Baseline acceptance Limitation / needed improvement addressed testing section

2. Improve modeling of heat transfer in the helical SS plant model 4.3 coil steam generator tubes TF-1 4.11 10a. Improve CHF correlation to accurately TF-1 simulate fluid and wall temperatures in the upper Note (1) 4.11 third of the steam generator coils.

10b. Improve the two phase pressure drop Literature Data correlation needed to accurately simulate DWO Note (2) 4.11 in the HCSG ((

                                                                               }}2(a),(c) 9.3.2         Evaluations of Integral Tests at SETs and IET TF-1, TF-2, and POLIMI assessment for DWO characteristics are presented in Section 8.0. These assessment provide comparison of geometrical parameters and conditions between the NPM and different test programs. Geometrical distortions/deviations are also explained. Variations in test conditions and their impact regarding deviations on DWO behavior is evaluated.

Results from the adequacy evaluation based on TF-1, TF-2, and POLIMI are summarized in Table 9-9. Additional details are provided below for each assessment. POLIMI: The purpose of the POLIMI code-to-data comparisons are to provide sufficient assurance that the NRELAP5 model is robust for DWO analysis, i.e. that NRELAP5 can be used for other helical coil configurations than TF-1 or TF-2. © Copyright 2022 by NuScale Power, LLC 237

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 The POLIMI test data was primarily used to predict DWO onset. Data-wide comparisons to DWO flow period and DWO flow amplitude were not made as they were not the focus of the analysis. NRELAP5 is conservative in predicting DWO onset for POLIMI, indicating the code performed adequately for a non-NPM HCSG system. TF-1: NRELAP5 is conservative in predicting DWO onset for TF-1 with overall reasonable-to-excellent agreement. NRELAP5 comparisons to DWO flow period and DWO flow amplitude are more varied, with the latter being most often conservative (i.e. larger), which still meets the EM requirements for minimal agreement. TF-1 is an electrically heated system and therefore DWO flow period and DWO flow amplitude are affected as energy addition is unbounded by the secondary side-conditions. This configuration makes predictions sensitive. For these parameters, code-to-data comparisons to systems with primary-to-secondary fluid heating (e.g. TF-2) are considered more applicable. Separate NRELAP5 models were developed for improved DWO flow period and DWO flow amplitude predictions (not presented in this report). TF-2: NRELAP5 provides reasonable-to-excellent agreement for DWO onset vs. TF-2 data. When conservative biases are applied, the code results are slightly non-conservative for DWO onset. NRELAP5 provides reasonable agreement for DWO flow period and DWO flow amplitude vs. TF-2 data. NRELAP5 predictions of DWO flow amplitude are conservative (i.e. larger), and exceed the requirement of minimal agreement. It is noted that both DWO flow period and DWO flow amplitude are complex and TF-2 data are not easily simplified to a single value. TF-2 tests continued varying ramped parameters (e.g. FW flow) beyond DWO onset, which induces multiple frequencies and amplitudes. A different modeling scheme would be required to better predict the range of DWO frequencies and amplitudes observed during each DWO tests (not presented in this report). © Copyright 2022 by NuScale Power, LLC 238

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Table 9-9 Top-Down Assessment Summary for IET Test Integral Effects Tests (IETs) Facility DWO Onset DWO Flow Period DWO Flow Amplitude POLIMI Conservatively predicted by Not compared Not compared NRELAP5(i.e. DWO onset predicted by (DWO) NRELAP5 at lower power vs. data) TF-1 Reasonable-to-excellent agreement, Minimal-to-reasonable Minimal-to-reasonable conservative overall. agreement agreement (mostly (DWO) conservative) TF-2 Reasonable-to-excellent agreement Reasonable agreement Reasonable agreement (conservative) (DWO) © Copyright 2022 by NuScale Power, LLC 239

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 10.0 Uncertainty Evaluation and Margin for NPM with respect to DWO This section describes the methodology for uncertainty quantification and margin evaluation applied to the NRELAP5 calculation of DWO for the NPM SG. The uncertainty methodology used takes into account code input uncertainties stemming from a variety of sources (e.g., initial/boundary conditions, models/correlations, etc.), as well as output uncertainty associated with the code calculations. Code predictions of both SETs and IETs are used to assess how well important phenomena and processes are predicted, as well as overall system response. Margin to DWO onset is calculated for the NPM SGs by reducing feedwater flow from nominal conditions until onset occurs. The difference between the FW flow rate that requires, automatic control system or operator response, or produces a protective trip, and the FW flow rate at DWO onset taking into consideration NRELAP5 code uncertainty, is the margin to DWO for the NPM. For the NPM SG, a best estimate methodology is applied using a combination of conservative and realistic input data and boundary/initial conditions. Uncertainty is assessed using the methodology described in the following section, which considers both code input and output-phase uncertainties. 10.1 Uncertainty Analysis Methodology Reference 12.47 provides an integrated methodology for uncertainty quantification wherein uncertainty evaluation is divided into two distinct parts - the input-phase and the output-phase. Input uncertainty quantification focuses on the identification of uncertainties in code input parameters, and those associated with the models and sub-models of the code. Sources of input uncertainty include: Model parameters, Boundary/initial conditions, and Uncertainties in the structure of sub-models. Input uncertainty includes the sources of code uncertainties that can be explicitly accounted for and are propagated through code calculations. SET data that is used to assess code models and correlations, is also used for input-based uncertainty quantification. The output-phase of uncertainty accounts for the impact of uncertainties associated with the FoM output. For NRELAP5, applicable experimental data come from IET facilities designed to provide information on system behavior. Output phase uncertainty can be characterized by comparing measured IET data to NRELAP5 calculated values. © Copyright 2022 by NuScale Power, LLC 240

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 ((

                                                                                                }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 (( Equation 10-1 Equation 10-2 Equation 10-3

                                                                                                               }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 (( Equation 10-4 Equation 10-5

                                                                                                               }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 (( Equation 10-6 Equation 10-7

                                                                                                               }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 (( Equation 10-8 Equation 10-9

                                                                                                               }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 ((

                                                                                                               }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 ((

                        }}2(a),(c) 10.2     NPM Operation Margin for DWO Onset For evaluating NPM operating margin for DWO onset, sensitivity analysis is used. The sources of uncertainty for the NPM full-plant calculation with respect to DWO are identified. Effects of these uncertainty parameters on DWO are evaluated using IETs/SETs, plant design conditions, operating conditions, design basis safety analysis assumptions/limits, and literature.

((

                                                                                                               }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 ((

                              }}2(a),(c)

The methodology for calculating margin for DWO involves accounting for uncertainties in different geometric parameters and operating conditions. Sensitivity analysis is carried out accounting for uncertainties in margin calculation. The methodology for calculating margin identified important uncertainty contributors for DWO. These contributors are derived from the SG stability PIRT, code validation, NPM operating parameters, and safety analysis limits/assumptions. The uncertainty contributors are divided into three categories - analytical uncertainties/T-H model and correlation uncertainties; geometrical uncertainties; and the plant conditions uncertainties. These parameters are varied in a parametric evaluation to ensure that uncertainties are adequately addressed in the evaluation of margin. ((

                                      }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 ((

                                                                                                               }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 ((

                                                                                                           }}2(a),(c)

Table 10-1 NPM Sensitivity Cases at Off-Normal Conditions for DWO Evaluation ((

                                                                                                                }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Table 10-1 NPM Sensitivity Cases at Off-Normal Conditions for DWO Evaluation ((

                                                                                                                }}2(a),(c)

((

                                        }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 11.0 Results/Conclusions This topical report presents the EM used to evaluate DWO in the NPM HCSG during normal and off-normal operating conditions. Although not required, this DWO EM is consistent with guidance provided in the EMDAP of Transient and Accident Analysis Methods, Regulatory Guide 1.203. The DWO EM uses the proprietary NRELAP5 code as the computational tool. NRELAP5 includes the necessary models for the characterization of the NPM hydrodynamics, heat transfer between structures and fluids, modeling of fuel, reactor kinetics models, and control systems. Additional models and correlations are added to model the NPM helical coil configuration. Validation and verification of the EM and NRELAP5 code are conducted using a well-established process. A PIRT, which identifies the important phenomena and processes for HCSG stability is developed. A total of 17 phenomena are identified as high-ranked and thus important to capture in the DWO EM. Extensive NRELAP5 code validation is performed to ensure that the EM is applicable for the important phenomena and processes over the range encountered in NPM operation. The validation suite includes SETs and IETs developed and run specifically for the NPM SG application. The FoM for IETs are DWO onset, DWO flow period, and DWO flow amplitude. SETs were performed at the TF-1 facility. TF-1 provided data on pressure drop and heat transfer for the secondary-side. TF-1 also provided DWO test data with DWO onset, DWO flow period, and DWO flow amplitude. SETs and IETs were performed at the TF-2 facility. TF-2 SETs provided data on primary-side heat transfer and pressure drop. TF-2 also provided DWO test data with DWO onset, DWO flow period, and DWO flow amplitude. Additional validation of NRELAP5 is carried out with an external DWO database obtained from POLIMI. POLIMI DWO test data validation shows that NRELAP5 is conservative in predicting DWO onset for a non-prototypical HCSGs with longer tubes and a tighter helix. The NRELAP5-based SG DWO EM is evaluated for applicability to analyze DWO in the NPM. The applicability of NRELAP5 for high-ranking phenomena is demonstrated by comparing NRELAP5 predictions to data from SETs and IETs. Reasonable-to-excellent agreement obtained via comparison establishes the applicability of NRELAP5 to accurately predict DWO onset phenomena at both the SETs and IETs. Uncertainty analysis is carried out based on TF-1 SET data and TF-2 DWO IET data. Using a 95 percent confidence interval, the ((

                                                                                       }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 The report also contains the methodology for evaluating margin to DWO onset in the NPM at normal and off-normal operating conditions and is applied for NPM reactor power levels between 20 percent and 100 percent nominal. The sample calculation in Appendix B demonstrates application of the EM in an NPM SG DWO NRELAP5 model. The sample results show that DWO onset does not occur in the NPM SG at the nominal, steady state 100 percent power level if the minimum IFR loss coefficient value is ((

                        }}2(a),(c) Results are conservatively biased for code uncertainty. Margin to DWO onset is demonstrated at nominal power levels and at off-nominal 100 percent power conditions that are reasonably expected to be bounded by the final control system design and nominal trip setpoints.

The evaluation model developed herein has an established pedigree and is determined to be adequate for downstream NPM SG analysis for DWO onset. Use of NRELAP5 for accurate prediction of DWO flow period and DWO flow amplitude requires additional evaluation, which may involve nodalization changes and/or methodology improvement. © Copyright 2022 by NuScale Power, LLC 253

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 12.0 References 12.1 U.S. Nuclear Regulatory Commission, Transient and Accident Analysis Methods, Regulatory Guide 1.203, December 2005. 12.2 Boyack, B.E. and G.E. Wilson, Lessons Learned in Obtaining Efficient and Sufficient Applications of the PIRT Process, Best Estimates 2004, Washington DC, November 14-18, 2004. 12.3 Convective Boiling and Condensation, 3rd Edition, JG Collier and J.R. Thome, Clarendon Press - Oxford, 1994. 12.4 U.S. Nuclear Regulatory Commission, An Integrated Structure and Scaling Methodology for Severe Accident Technical Issue Resolution, Draft Report for Comment. Appendix D, NUREG/CR-5809, November 1991. 12.5 Zuber, N., The effects of complexity, of simplicity, and of scaling in thermal-hydraulics, Nuclear Engineering and Design, 204 (1-3), Number 1: pp. 1-27, 2001. 12.6 Zuber, N., U.S. Rohatgi, W. Wulff, and I. Catton, Application of fractional scaling analysis (FSA) to loss of coolant accidents (LOCA) Methodology development, Nuclear Engineering and Design, 237:1593-1607, 2007. 12.7 Catton, I., W. Wulff, N. Zuber, and U. Rohatgi, Application of Fractional Scaling Analysis to Loss of Coolant Accidents: Component Level Scaling for Peak Clad Temperature, ASME Journal of Fluids Engineering, 131 (12) pp. 1-8, 2009. 12.8 SwUM-0304-17023, Rev. 10, NRELAP5 Version 1.6 Theory Manual. 12.9 MN-122626, Rev. 0, NuScale Topical Report: Quality Assurance Program Description for the NuScale Power Plant. 12.10 U.S. Code of Federal Regulations, Domestic Licensing of Production and Utilization Facilities, Part 50, Title 10, Appendix B, Quality Assurance Criteria for Nuclear Power Plants and Fuel Reprocessing Plants, (10 CFR 50 Appendix B). 12.11 American Society of Mechanical Engineers, Quality Assurance Program Requirements 12.12 Y. Taitel and A. E. Dukler, A Model of Predicting Flow Regime Transitions in Horizontal and Near Horizontal Gas-Liquid Flow, AIChE Journal, 22, 1976, pp. 47-55 12.13 Y. Taitel, D. Bornea, and A. E. Dukler, Modeling Flow Pattern Transitions for Steady Upward Gas-Liquid Flow in Vertical Tubes, AIChE Journal, 26, 1980, pp. 345-354 © Copyright 2022 by NuScale Power, LLC 254

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 12.14 M. Ishii and G. De Jarlais, Inverted Annular Flow Modeling, Advanced Code Review Group Meeting, Idaho Falls, ID, July 27, 1982 12.15 M. Ishii and T. C. Chawla, Local Drag Laws in Dispersed Two-Phase Flow, NUREG/CR-1230, ANL-79-105, Argonne National Laboratory, December 1979 12.16 M. Ishii and K. Mishima, Study of Two-Fluid Model and Interfacial Area, NUREG/CR-1873, ANL-80-111, Argone National Laboratory, December 1980 12.17 T. N. Tandon, H. K. Varma, and C. P. Gupta, A New Flow Regime Map for Condensation Inside Horizontal Tubes, Journal of Heat Transfer, 104, November 1982, pp. 763-768. 12.18 R. W. Lockhart and R. C. Martinelli, Proposed Correlations of Data for Isothermal Two-Phase, Two-Component Flow in Pipes, Chemical Engineering Progress, 45, 1, 1949, pp. 39-48 12.19 D. J. Zigrang and N. D. Sylvester, A Review of Explicit Friction Factor Equations, Transactions of the ASME, Journal of Energy Resources Technology, 107, 1985, pp. 280-283 12.20 C. F. Colebrook, Turbulent Flow in Pipes with Particular Reference to the Transition Region between Smooth and Rough Pipe Laws, Journal of Institute of Civil Engineers, 11, 1939, pp. 133-156 12.21 Chen, J.C., "A Correlation for Boiling Heat Transfer to Saturated Fluids in Convective Flow," Process Design and Development, (1966), 5:322-327. 12.22 Crank, J., and P. Nicolson, A Practical Method for Numerical Evaluation of Solutions of Partial Differential Equations of the Heat Conduction Type, Proceedings of the Cambridge Philosophical Society, (1947): 43:50-67. 12.23 J. K. Vennard, One-Dimensional Flow, in: V. L. Streeter (ed.), Handbook of Fluid Dynamics, 1st Edition, New York: McGraw Hill, 1961 12.24 Ito, H., "Friction factors for turbulent flow in curved pipes, Transactions of the ASME, Journal of Basic Engineering, (1959): 81:123-124. 12.25 Sreenivasan K.R., and P.J. Strykowski, "Stabilization Effects in Flow Through Helically Coiled Pipes," Experiments in Fluids 1, 1983, pp. 31-36. 12.26 Prasad, B.V.S.S.S, D.H. Das, and A.K. Prabhakar, Pressure drop, heat transfer and performance of a helically coiled tubular exchanger, Heat Recovery Systems and CHP, (1989), 9: 249-256. 12.27 Dittus, F.W., and L.M.K. Boelter, Heat transfer in automobile radiators of the tubular type, International Communications in Heat and Mass Transfer, (1985), © Copyright 2022 by NuScale Power, LLC 255

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Vol 12, Issue 1, pp. 3-22. Originally published in University of California Publications in Engineering, Vol. 2, No. 13, October 13, 1930, pp. 443-46. 12.28 Green, D.W. and Perry, R.H., Perrys Chemical Engineers Handbook, 8th Edition, McGraw-Hill, New York, NY, 2008. 12.29 J. C. Chen, A Correlation for Boiling Heat Transfer to Saturated Fluids in Convective Flow, Process Design and Development, 5, 1966, pp. 322-327 12.30 Seban, R.A., and E.F. McLaughlin, "Heat transfer in tube coils with laminar and turbulent flow," International Journal of Heat and Mass Transfer, (1963): 6:387-395. 12.31 Donaldson, A.J., Once-through steam generator heat transfer models for SIR, Dynamics and control in nuclear power stations, Thomas Telford, London, (1991). 12.32 Yang, S.H., et al., Experimental validation of the helical steam generator model in the TASS/SMR code, Annals of Nuclear Energy, Volume 35, Issue 1, pp. 49-59, (2008). 12.33 Saha, P. and Zuber, N. (1974). Point of net vapor generation and vapor void fraction in subcooled boiling, Proceedings of the 5th international heat transfer conference, Tokyo, Paper B4.7. 12.34 The RELAP5-3D© Code Development Team, RELAP5-3D© Code Manual, Volume IV: Models and Correlations, INEEL-EXT-98-00834, Revision 4.1, September 2013. 12.35 R. T. Lahey, A Mechanistic Subcooled Boiling Model, Proceedings of the 6th International Heat Transfer Conference, Toronto, Canada, August 7-11, 1978, Volume 1, pp. 293-297 12.36 Levy, S. (1967). Forced convection subcooled boiling prediction of vapor volumetric fraction. Int. J. Heat Mass Transfer, 10, pp 951-965. 12.37 Neil Todreas and Mujid Kazimi, Nuclear Systems Volume 1, 3rd edition, CRC Press (2021). 12.38 Lee, S. C., Dorra, H., and Bankoff, S. G. (1992). 'A critical review of predictive models for the onset of significant void in forced convection subcooled boiling'. Presented in Fundamentals of Subcooled Flow Boiling HTD-Vol. 2 1 7, pp. 33-39. Paper presented at ASME Winter Ann. Mtg, Anaheim, CA. 12.39 Ishii, M., Thermally Induced Flow Instabilities in Two-Phase Mixtures in Thermal Equilibrium, Georgia Institute of Technology 1971. © Copyright 2022 by NuScale Power, LLC 256

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 12.40 The RELAP5-3D© Code Development Team, RELAP5-3D© Code Manual, Volume I: Code Structure, System Models and Solution Methods, INEEL-EXT-98-00834, Revision 4.1, September 2013. 12.41 Handbook of Hydraulic Resistance, 3rd Edition, I.E.Idelchik, 1994. 12.42 Szilard, R.H., et. al., Industrial Application Emergency Core Cooling System Cladding Acceptance Criteria Problem Statement, INL/EXT-35073. 12.43 M. Colombo, A. Cammi, D. Papini, and M. E. Ricotti, RELAP5/MOD3.3 study on density wave instabilities in single channel and two parallel channels, Progress in Nuclear Energy, vol. 56, pp. 15-23, 2012. 12.44 Colombo, M., Experimental Investigation and Numerical Simulation of the Two-Phase Flow in the Helical Coil Steam Generator, Ph.D. thesis, Doctoral program in Energy and Nuclear Science and Technology, Politecnico di Milano, (2013). 12.45 Santini, L., et al., Two-phase pressure drops in a helically coiled steam generator, International Journal of Heat and Mass Transfer 51, pp. 4926-4939, (2008). 12.46 Zhao, L., et al., Convective boiling heat transfer and two-phase flow characteristics inside a small horizontal helically coiled tubing once-through steam generator International Journal of Heat and Mass Transfer, Vol. 46, Issue 25, pp. 4779-4788. 12.47 M. Mohammad, M. Modarres, Integrated Methodology for Thermal-Hydraulic Code Uncertainty Analysis, Prepared for USNRC office of research, CRR Report 2007-M3, March 2007. 12.48 Taylor B.N. and Kuyatt, C.E., Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results, NIST Technical Note 1297 1994 Editiion. 12.49 Mann P. S. and Lacke, C.J., Introductory Statistics, 7th Edition, John Wiley and Sons, 2010. © Copyright 2022 by NuScale Power, LLC 257

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Appendix A EMDAP Process and Roadmap to the DWO EM The RG 1.203 defines four elements for the EMDAP process (Reference 12.1). These elements are divided into 20 different steps that can be followed in creating an EM. Figure A-1 shows various elements of the EMDAP as defined in RG 1.203. Table A-1 provides a roadmap that relates the sections of this report to the elements of the EMDAP. The EMDAP described by RG 1.203 provides a structured approach, which is widely used in the industry, and has been applied to guide the development of this EM. © Copyright 2022 by NuScale Power, LLC A-1

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure A-1 Evaluation Model Development and Assessment Process (EMDAP) © Copyright 2022 by NuScale Power, LLC A-2

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Table A-1 EMDAP Steps and Associated Document Sections EMDAP Element Description EM Section Element 1 Establish Requirements for Evaluation Model Capability 1.2 and 3.3 Element 2 Develop Assessment Base 4.0 and 8.0 Element 3 Develop Evaluation Model 7.0 Element 4A Assess Evaluation Model Adequacy Closure Relations (Bottom-up) 9.2 Element 4B Assess Evaluation Model Adequacy Integrated EM (Top-down) 9.3 © Copyright 2022 by NuScale Power, LLC A-3

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Appendix B Sample Calculation for NPM B.1 NPM DWO Onset Calculations This sample calculation of the implemented EM is provided for illustrative purposes to: demonstrate that the NPM SG DWO model, created in accordance with EM specifications, models DWO onset consistently in multiple configurations, show that the NPM SG DWO model, coupled with an IFR Kinlet-loss designed to prevent DWO, predicts stability at 100 percent nominal power conditions, and calculates the margin to expected setpoints when accounting for code uncertainty, illustrate that the NPM SG DWO model is not subject to DWO at off-nominal 100 percent power conditions, with margin to expected setpoints when accounting for uncertainty and operational deviations. B.2 DWO Model Nodalization and Development A bulk FW flow-controlled boundary condition NRELAP5 model similar to Figure 7-4 is created to match the NPM SG geometry and characteristics. B.2.1 Percent Nominal Power Equilibrium Profile Equilibrium quality (Xeq) profiles from SG-averaged and column-averaged steady state models are extracted and evaluated to determine the DWO model nodalization required to evaluate stability at 100 percent nominal power. The model nodalization is fixed during the DWO onset evaluation yet the optimum nodalization sizing is related to the quality profile as discussed in Section 7.8.2.3. Quality profiles are evaluated against HCSG tube length. First, the equilibrium profiles for all column-averaged and total SG-averaged tubes are plotted versus tube length along the helical axis. Figure B-1 shows an overall plot of equilibrium quality and tube length, while Figure B-2 shows a detailed view of the 55 to 70 length. ((

                                                                        }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Generally, as power decreases, changes in NPM conditions (e.g. pressures, temperatures, flow) cause the length of the subcooled liquid and two-phase regions to decrease while the single-phase steam region of the HCSG tube increases. From comparing the nature of these shifts, a model is developed that provides a similar width of variation in the two-phase region. The model encompasses the equilibrium quality profiles between 70 percent and 100 percent nominal power, while other models with other nodalizations are developed to evaluate other powers. ((

                     }}2(a),(c)

Figure B-1 100 Percent Nominal Power, Xeq vs HCSG Tube Length ((

                                                                                                                 }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure B-2 100 Percent Nominal Power, Xeq vs HCSG Tube Length, Detailed View ((

                                                                                                                }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure B-3 DWO Model 1, For Evaluations from 70 Percent to 100 Percent Nominal Power ((

                                                                                                                }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 B.2.2 NRELAP5 Model Development The development of the full-plant NRELAP5 SG DWO model is performed in conjunction with the methodology presented in Section 7.0. The DWO model features ((

                                                              }}2(a),(c)

Figure B-4 shows a representation of the primary fluid of the NRELAP5 DWO Model. Figure B-5 shows a representation of the secondary fluid portion. A brief description illustrating the numbering scheme of the hydraulic components and heat structures follows as a bulleted list. ((

                             }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 ((

                                             }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 ((

                                                                             }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure B-4 Representation of the Primary Side of the NRELAP5 DWO Model ((

                                                                                                                }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure B-5 Representation of the Secondary Side of the NRELAP5 DWO Model ((

                                                                                                                }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 B.3 Boundary Conditions The primary fluid boundary conditions applied to the NPM SG DWO model includes the primary hot temperature, the primary pressure, and the primary mass flow rate. The primary hot temperature is applied at the inlet time dependent volume, while the primary mass flow rate is applied at the time dependent junction. The primary pressure is applied at the exit time dependent volume. The secondary fluid boundary conditions applied to the NPM SG DWO model includes the FW temperature, the FW mass flow rate, and the steam pressure. ((

                                        }}2(a),(c)

Table B-1 lists the steady state boundary and initial conditions applied to the DWO model. Table B-1 NPM Steady State Boundary and Initial Conditions at Various Power Levels ((

                                                                                                                     }}2(a),(c)

B.4 IFR Kinlet Loss Selection The SG IFR is a restricting orifice designed to induce a large pressure drop as the subcooled fluid enters the HCSG tube from the FW plenum. If the IFR pressure drop is sufficiently sized, DWO is prevented and secondary stability is maintained. The Kinlet loss of the IFR is therefore a crucial component of secondary side stability. The NPM SG IFR is a thick orifice, with a ((

                                     }}2(a),(c),ECI

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 ((

                                                                                }}2(a),(c),ECI

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure B-6 NPM 20 Percent Nominal Power, DWO Onset in Tube 4, with an IFR Kinlet loss of 800 ((

                                                                                                                }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure B-7 NPM 20 Percent Nominal Power, DWO Onset in Tube 4, with an IFR Kinlet loss of 1000 ((

                                                                                                                }}2(a),(c)

B.5 DWO Number of Channels Comparison The NRELAP5 DWO model developed according to the EM features ((

                                                  }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 ((

                         }}2(a),(c)

Figure B-8 NPM 20 Percent Nominal Power, DWO Onset in Tube 4 ((

                                                                                                                }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure B-9 NPM 20 Percent Nominal Power, DWO Onset in Tube 12 ((

                                                                                                                }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Table B-2 NPM 20 Percent Nominal Power, DWO Comparison for Columns 4 and 12 ((

                                                                                                                     }}2(a),(c)

B.6 Margin Calculation Section 10.0 reports a code uncertainty value of ((

                     }}2(a),(c) with a 95 percent confidence interval. In this analysis, the NRELAP5 code uncertainty included in the calculation of DWO onset time is increased to

(( }}2(a),(c) for additional conservatism. Margin to DWO onset is calculated by comparing the lowest onset time, adjusted for NRELAP5 code uncertainty, with assumed operational limits. For the NPM DWO stability assessment, these assumed limits include an automatic control action taken when there is a: ((

                                                                                              }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 ((

                     }}2(a),(c)

Margin is calculated as: m* onset M arg in = 1 - -----------------

                                                                      -                                Equation B-1 m action where m* onset (lbm/s) is the FW mass flow rate at the time of DWO onset, accounting for code uncertainty, m action (lbm/s) is the FW mass flow rate at the time of operator action or nominal trip setpoint.

B.7 Stability Evaluations at 100 Percent Nominal Power Conditions The following calculation demonstrates the stability of the NPM SG to DWO at nominal conditions for 100 percent power. The evaluations initiate from boundary conditions correlated to the nominal, best estimate, beginning-of-life steady state conditions. The IFR Kinlet loss evaluated corresponds to the minimum Kinlet loss discussed in Section B.4. ((

                            }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 DWO onset in single average-tube channels is identified using the methodology presented in Section 7.4.2. Least stable columns and significant margin to DWO are defined according to Section 7.4.4. A code uncertainty is accounted for as an adjustment of the FW mass flow rate corresponding to DWO onset, as described in Section 10.1. Margin to DWO onset is defined through comparison of the FW mass flow rates corresponding to DWO onset, including code uncertainty, and FW mass flow rates that are expected to form conservative bounds for NPM operation. The NPM DWO model is used to evaluate the 100 percent nominal power condition by applying the boundary conditions described in Section B.3. ((

                                                                                          }}2(a),(c)

Geometrical differences between the 21 column-averaged tubes in the NPM DWO model result in small differences in mass flow rates per column at all steady flow conditions. Total feedwater flow ramping results in symmetrical changes to columnar mass flows that are proportional to the original mass flow distribution. ((

                                                                                                  }}2(a),(c) The DWO onset times for the tubes at the 100 percent nominal power condition are shown in Table B-3.

The earliest DWO onset occurs at ((

                                                                             }}2(a),(c) Figure B-10 illustrates a zoomed in view of DWO onset as determined per Section 7.4.2. The red line in the figure (which represents the relative error of a 100 second moving average) exceeds 20 percent at the vertical green line, indicating DWO onset. The first ten peaks of DWO following onset are shown in Figure B-11.

Figure B-12 shows several differential pressure calculations for tube one. These include the total pressure drop from the center of the FW plenum to the center of the first tube cell (representing the IFR pressure drop and friction and static head between the two cells), the pressure drop through the single-phase liquid region (fixed by the model nodalization), and the differential pressure of the two-phase region (fixed by model nodalization). As the single-phase liquid and two-phase region entries are fixed by model nodalization to define the initial region lengths, they may include other regions as FW flow is ramped (i.e. single-phase steam as the two-phase region moves lower in the tube), but they remain representative of proportional tube pressure drop terms. Accounting for the NRELAP5 code uncertainty as described in Section 10.1, ((

                                                                                                         }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure B-13 shows two equilibrium quality profiles, one at the initial nominal FW flow rate for the 100 percent nominal power condition, and the second 2000 seconds before the code calculated DWO onset. The difference between these quality profiles reflects the approximate change in tube conditions prior to DWO onset. ((

                                                }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure B-10 NPM 100 Percent Nominal Power, DWO Onset, Tube 1 ((

                                                                                                                }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure B-11 NPM 100 Percent Nominal Power, First Ten Peaks of DWO, Tube 1 ((

                                                                                                                }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure B-12 NPM 100 Percent Nominal Power, Differential Pressures, Tube 1 ((

                                                                                                                }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Figure B-13 NPM 100 Percent Nominal Power, Equilibrium Quality Profiles, Tube 1 ((

                                                                                                                }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Table B-3 NPM 100 Percent Nominal Power, DWO Summary Results and Margin ((

                                                                                                                }}2(a),(c)

B.8 Stability Evaluations at Off-Nominal 100 Percent Power Conditions Section B.7 describes stability and margin to DWO onset at 100 percent nominal power. The properties and parameters at these different power levels are predicted using a best estimate, beginning-of-life, NPM conditions. However, during steady-state operation, properties and parameters pertinent to secondary side stability may fluctuate or deviate in a quasi-steady manner. Additionally, uncertainty in critical correlations and geometrically-based variations introduce uncertainty into the FoMs most relevant to secondary side stability. Consequently, the operating space at a prescribed power level needs to be wide and account for quasi-steady fluctuations. Off-nominal conditions are considered at the 100 percent nominal power condition, as that is the condition expected for the majority of the service life of the NPM SG. To evaluate stability and margin to DWO onset in off-nominal conditions requires the construction of reasonably bounded but conservative assumptions about the control system setpoints and correlation uncertainties. ((

                                       }}2(a),(c) described in Table 10-1 of Section 10.2.

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 ((

                                                                                               }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 ((

                }}2(a),(c)

Table B-6 details the DWO onset times and margins for the SG tubes for case 11. Accounting for the NRELAP5 code uncertainty as described in Section B.6, ((

                                            }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Table B-4 NPM 100 Percent Nominal Power, Off-Nominal Assumed Control Action and Trip Times ((

                                                                                                                     }}2(a),(c)

Table B-5 NPM 100 Percent Nominal Power, Cases 1 to 16, Margin for Tube with Earliest DWO Onset ((

                                                                                                                     }}2(a),(c)
    © Copyright 2022 by NuScale Power, LLC B-27

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 Table B-6 NPM 100 Percent Nominal Power, Case 11, Margin to DWO Onset for SG Tubes ((

                                                                                                                }}2(a),(c)

Methodology for the Determination of the Onset of Density Wave Oscillations (DWO) TR-131981-NP Revision 0 B.9 Results and Conclusions The NPM SG is stable with respect to secondary side instabilities at the nominal, steady state 100 percent power level if the minimum IFR loss coefficient value is ((

                        }}2(a),(c) Results are conservatively biased by including a one-side bias code uncertainty value of ((
                                                                           }}2(a),(c)

Margin to DWO onset is demonstrated at all nominal power levels and at off-nominal 100 percent power conditions that are reasonably expected to be bounded by the final control system design and nominal trip setpoints. Minimum margins at nominal and off-nominal conditions are summarized in Table B-7. Table B-7 Summary of Margin to DWO Onset ((

                                                                                                                   }}2(a),(c)

LO-133378 : Affidavit of Mark W. Shaver AF-133380 NuScale Power, LLC 1100 NE Circle Blvd., Suite 200 Corvallis, Oregon 97330 Office 541.360.0500 Fax 541.207.3928 www.nuscalepower.com

NuScale Power, LLC AFFIDAVIT of Mark W. Shaver I, Mark W. Shaver, state as follows: (1) I am the Licensing Manager of NuScale Power, LLC (NuScale), and as such, I have been specifically delegated the function of reviewing the information described in this Affidavit that NuScale seeks to have withheld from public disclosure, and am authorized to apply for its withholding on behalf of NuScale (2) I am knowledgeable of the criteria and procedures used by NuScale in designating information as a trade secret, privileged, or as confidential commercial or financial information. This request to withhold information from public disclosure is driven by one or more of the following: (a) The information requested to be withheld reveals distinguishing aspects of a process (or component, structure, tool, method, etc.) whose use by NuScale competitors, without a license from NuScale, would constitute a competitive economic disadvantage to NuScale. (b) The information requested to be withheld consists of supporting data, including test data, relative to a process (or component, structure, tool, method, etc.), and the application of the data secures a competitive economic advantage, as described more fully in paragraph 3 of this Affidavit. (c) Use by a competitor of the information requested to be withheld would reduce the competitors expenditure of resources, or improve its competitive position, in the design, manufacture, shipment, installation, assurance of quality, or licensing of a similar product. (d) The information requested to be withheld reveals cost or price information, production capabilities, budget levels, or commercial strategies of NuScale. (e) The information requested to be withheld consists of patentable ideas. (3) Public disclosure of the information sought to be withheld is likely to cause substantial harm to NuScales competitive position and foreclose or reduce the availability of profit-making opportunities. The accompanying report reveals distinguishing aspects about the method by which NuScale develops its Methodology for the Determination of the Onset of Density Wave Oscillations (DWO). NuScale has performed significant research and evaluation to develop a basis for this method and has invested significant resources, including the expenditure of a considerable sum of money. The precise financial value of the information is difficult to quantify, but it is a key element of the design basis for a NuScale plant and, therefore, has substantial value to NuScale. If the information were disclosed to the public, NuScale's competitors would have access to the information without purchasing the right to use it or having been required to undertake a similar expenditure of resources. Such disclosure would constitute a misappropriation of NuScale's intellectual property, and would deprive NuScale of the opportunity to exercise its competitive advantage to seek an adequate return on its investment. (4) The information sought to be withheld is in the enclosed report entitled Methodology for the Determination of the Onset of Density Wave Oscillations (DWO).The enclosure contains the designation Proprietary" at the top of each page containing proprietary information. The information considered by NuScale to be proprietary is identified within double braces, "(( }}" in the document. AF-133380 Page 1 of 2

(5) The basis for proposing that the information be withheld is that NuScale treats the information as a trade secret, privileged, or as confidential commercial or financial information. NuScale relies upon the exemption from disclosure set forth in the Freedom of Information Act ("FOIA"), 5 USC § 552(b)(4), as well as exemptions applicable to the NRC under 10 CFR §§ 2.390(a)(4) and 9.17(a)(4). (6) Pursuant to the provisions set forth in 10 CFR § 2.390(b)(4), the following is provided for consideration by the Commission in determining whether the information sought to be withheld from public disclosure should be withheld: (a) The information sought to be withheld is owned and has been held in confidence by NuScale. (b) The information is of a sort customarily held in confidence by NuScale and, to the best of my knowledge and belief, consistently has been held in confidence by NuScale. The procedure for approval of external release of such information typically requires review by the staff manager, project manager, chief technology officer or other equivalent authority, or the manager of the cognizant marketing function (or his delegate), for technical content, competitive effect, and determination of the accuracy of the proprietary designation. Disclosures outside NuScale are limited to regulatory bodies, customers and potential customers and their agents, suppliers, licensees, and others with a legitimate need for the information, and then only in accordance with appropriate regulatory provisions or contractual agreements to maintain confidentiality. (c) The information is being transmitted to and received by the NRC in confidence. (d) No public disclosure of the information has been made, and it is not available in public sources. All disclosures to third parties, including any required transmittals to NRC, have been made, or must be made, pursuant to regulatory provisions or contractual agreements that provide for maintenance of the information in confidence. (e) Public disclosure of the information is likely to cause substantial harm to the competitive position of NuScale, taking into account the value of the information to NuScale, the amount of effort and money expended by NuScale in developing the information, and the difficulty others would have in acquiring or duplicating the information. The information sought to be withheld is part of NuScale's technology that provides NuScale with a competitive advantage over other firms in the industry. NuScale has invested significant human and financial capital in developing this technology and NuScale believes it would be difficult for others to duplicate the technology without access to the information sought to be withheld. I declare under penalty of perjury that the foregoing is true and correct. Executed on 12/3/2022. Mark M k W.W Shaver Sh AF-133380 Page 2 of 2}}

v t e Letter Sequence Request
EPID:L-2022-TOP-0019, LLC Submittal of Topical Report Methodology for the Determination of the Onset of Density Wave Oscillations (Dwo), TR-131981, Revision 0 (Open)
Initiation Request Acceptance... Administration Questions Answers Results Approval... Other: ML22364A276, ML23068A158, ML23068A159, ML23265A123, ML23265A124
MONTHYEAR2023-03-17 [Table View]

ML22364A332

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