ML24292A169

Kairos Power Pre-App Doc - Audit Questions Related to Kairos Core Design and Analysis Methodology Topical Report

ML24292A169
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Cayetano Santos Sent:

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Tomkins@kairospower.com; Joe-Nimique Cilliers Cc:

Josh Borromeo; Brian Bettes

Subject:

Audit Questions Related to Kairos Core Design and Analysis Methodology Topical Report Attachments:

2nd set of audit questions Kairos core design TR FINAL Public Version_Redacted.pdf Jim and Joe-Nimique, Attached is the second set of audit questions related to the NRC staffs audit of Kaiross core design and analysis methodology topical report. This is the public version in which the proprietary and export-controlled information has been redacted. The non-public version has been shared with Kairos via the Box secure portal.

Please let me know if you have any questions.

Tanny Santos

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Official Use Only - Proprietary and Export Controlled Information Official Use Only - Proprietary and Export Controlled Information KAIROS POWER, LLC - KP-FHR CORE DESIGN AND ANALYSIS METHODOLOGY TOPICAL REPORT SECOND SET OF AUDIT QUESTIONS (EPID NO. L-2024-TOP-0013)

[Question 2.1-1] Provide a more explicit description of the connection between the discrete elements method (DEM), ZONER, and Serpent in terms of the ability to represent batchwise pebbles within each zone and how they are transferred between zones.

[Question 2.1-2] Figure 2-2, Explicit Serpent 2 Model, provides an illustration of the Serpent 2 model for a typical KP-FHR design. Discuss the compositions and materials used to describe the pebble extraction machine (PEM) and fueling regions.

[Question 3.1-5] Provide additional discussion justifying why direct pebble-to-reflector conduction heat transfer, particularly with respect to developing potential hot spots on the reflector surface is not included.

[Question 3.1-4a (follow-up to Question 3.1-4)] Topical report (TR) section 3.1.3, Key Thermal Hydraulics Phenomena, states that, [f]ast neutron fluence and temperatures are used to inform geometrical and thermophysical property correlations that are then used as inputs to the thermal hydraulic model. Question 3.1-4 from the audit plan (ML24222A276) requested discussion on how this was achieved. In response to this question, Kairos stated that the fast neutron fluence and temperature inform constitutive relations in KP-BISON. KP-BISON provides thermal conductivity in pebbles and tri-structural isotropic (TRISO) layers and provides TRISO buffer-IPyC (inner pyrolytic carbon layer) gas layer thickness. Kairos also addressed the potential impact of temperature on the reflector gap or geometry and its effect on the bypass flow.

a. Discuss how the KP-BISON treatment of material thermophysical properties is relevant to the methodology presented in the TR. Discuss the interface between the TR methodology and KP-BISON.

b. Discuss how the material property and geometrical impacts of fluence and temperature are accounted for in the thermal-hydraulic models presented in the TR.

[Question 3.2-2] Discuss how natural circulation flow bypass is calculated or represented in the STAR-CCM+ model.

[Question 3.3-2] Clarify the following regarding the momentum equation (Equation 1) and the drag force equation (Equation 2) for a pebble.

a. Equation 1 does not include space dependence. Explain the time derivative on the left side of Equation 1. Is it a substantial derivative, total time derivative, or ordinary derivative of pebble velocity?

Official Use Only-Proprietary and Export Controlled Information b.

In Equation 1, state if the pebble velocity is a vector quantity.

c.

State whether the pressure field in Equation 2 is a vector quantity or a scalar quantity.

b.

C.

d.

e hether the pressure drop in Equation 2 is the same as the pressure drop in E uation 5 and the si nificance of subscri t "d" in E uation 2.

[Question 3.3-5] Discuss how the DEM and core thermal hydraulics (TH) models are coupled. Flow and pressure drop for the DEM model are obtained from the core TH model while the core porosity calculated by the DEM model is provided as input to the core TH model. Discuss if there is an iterative process to perform these calculations.

Furthermore, the input list for the DEM model does not include core pressure drop.

Provide the pebble and reflector mechanical properties needed as input to the DEM model.

[Question 3.5-2] The table 3-2, "Model Paradigm Summary," description of the porous media (PM) model is not consistent with the descri tion rovided in section 3.5, "Thermal H draulics Modelin Paradi m."

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[Question 3.5-3] Provide nomenclature for the parameters in Equations 5 - 8 (e.g.,

Reynolds number; m; A; and non-dimensional parameters including the length and velocity scales used in these parameters). The TR states that the implementation of the heat transfer correlation is in section 4.3.1.3. However, since this section does not exist; clarify the appropriate reference in the TR.

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[Question 3.5-4]

a. Discuss how the Flibe properties (density and viscosity) are calculated for use in the Reynolds number in Equation 6.

b. Reference 7 of the TR shows a limiting curve for the applicability of the empirical pressure drop correlation (German Nuclear Safety Standards Commission (KTA) correlation in Equations 5 and 6) based on the Reynolds number and the bed-to-pebble diameter ratio. Confirm that the correlation is used within its geometric parameter applicability range for the Hermes test reactor and KP-FHR power reactor designs.

c. Discuss how the experimental data that is used for the derivation of the KTA pressure correlation is applicable to the Hermes test reactor and KP-FHR power reactor designs.

d. The inertial or turbulent pressure drop term in the KTA pressure drop correlation (Equations 5 and 6 or 17) is almost three times higher than the similar term in well-established porous media pressure drop correlations (e.g., the Ergun equation or Burke-Plummer equation [Ergun, Sabri. "Fluid flow through packed columns." Chem. Eng. Prog. 48, 1952]. Discuss the fundamental reason for this discrepancy in these two empirical correlations.

[Question 3.5-5] Specify the range of applicability for the Wakao correlation (Equation 7) and the ((

)) Discuss the basis for the selection of these correlations and the applicability of experimental data used for the development of these correlations to the Hermes test reactor and KP-FHR power reactor designs.

[Question 3.5-6] Explain the sentence, "The LTNE [local thermal non-equilibrium] porous media model also models power distribution between core materials as shown in table 3.5". Describe how this power distribution is calculated.

[Question 3.5-7] From Equation 9 it appears that the packed-bed porosity is defined as the volume fraction of Flibe in the whole packed bed.

a. Discuss the implication of this assumption of uniform porosity throughout the packed bed.

b. State if the methodology accounts for non-uniform distribution of porosity.

c. Porosity is a function of how the bed is packed. The KP-FHR bed is expected to be packed during the initial pebble addition phase under the buoyancy force.

Since the pressure drop in a packed-bed is a function of bed porosity, discuss how the methodology accounts for the impact of uncertainty in the bed porosity on pressure drop.

[Question 3.5-8]

a. Density is a term in Equation 16 for the body force. State if this should be Flibe density consistent with the mass balance Equation 12 and the momentum balance Equation 14.

b. If Equation 13 is a standard equation of continuity and velocity is a vector field, then there should be a dot product (i.e., divergence) between 'del' and rest of the parameters in the equation rather than simple gradient as shown. Please clarify this equation.

c. Clarify if in Equation 14, the left-hand side should be a divergence or dot product while the first term on the right-hand side should be a gradient.

d. Provide all the equations in this TR in standard vector and tensor notations.

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[Question 3.5-9] Equation 14, the Flibe-phase momentum transfer equation, includes a separate term to account for pressure losses in a porous bed (porous resistance force).

However, the standard velocity shear stress tensor also accounts for some of the same forces. Discuss how the shear stress tensor term is different from the porous resistance force. Provide the closing relations used for the shear stress tensor term.

[Question 3.5-1 O] Explain the significance of terms containing shear velocity tensor and body force in energy Equation 22.

[Question 3.5-11]

a.

Describe how the coupling of mass, energy, and momentum for Flibe in the porous bed and the Flibe in the reflector are represented in the model.

b.

A portion of the core Flibe energy is exchanged between the core and the reflector by direct exchange of Flibe mass between these two regions. A portion of the core Flibe energy is also directly transferred to the solid reflector phase.

Describe how these two different trans ort recesses are modeled.

C.

[Question 3.5-12]

a.

Describe the process for estimation of the "i-th" effective solid thermal conductivity and volumetric energy source term in Equations 25 and 26.

b.

Discuss if the volumetric energy source term accounts for the energy deposited in all the pebble layers.

c.

Discuss if the model accounts for fuel pebble-to-pebble heat transfer by direct contact. Additionally, discuss if the pebble energy transport equations (Equations 25 and 26) and the Flibe porous media energy transport equation (Equation 22) use the same nodalization.

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[Question 3.5-19] Identify the inputs needed for the reflector CFO-RANS model along with the justifications (e.g., meshing type and parameters selected, turbulence model and other closing relations such as wall models selected and numerical method related inputs such as time steps, convergence criteria, under/over relaxation, and any other closing relations). Describe the basis for the selection of the RANS model.

[Question 3.5-20] Please address the discrepancy in scope of the RANS model in section 3.5 and in table 3.2, "Model Paradi m Summa."

[Question 4.1-1] Section 4.1, "Process Flow," describes the process flow and coupling between the DEM, neutronics (Serpent 2), and thermal hydraulics (TH, PM, RANS) modules. However, the inputs and outputs for each of the main three models or modules (i.e., DEM, neutronics, core TH) are not clearly identified and defined.

a.

Describe the inputs and outputs of each computational module.

b. Clarify the data flow presented in figure 4-1, "High Level Process Flow Diagram of the Core Design and Analysis Methods," by explicitly identifying code modules.

[Question 4.2-2] Section 4.2, "STAR-CCM+," states that Kairos Power made no modifications to the base STAR-CCM+ code. Describe how the equations described in section 3.5.1.3, "LTNE Porous Media Formulation," were implemented. State if these equations are available as standard options for a user to select in ST AR-CCM+. Discuss if there was any need for developing user defined functions or modules to implement the fundamental equations and closing relations.

[Question 4.3-1] TR section 4.3, "Serpent 2," states that "Kairos Power made no modifications to the base Serpent 2 code." Provide the version of Serpent 2 code used.

Describe the quality assurance plan for updating the code.

[Question 4.3-2] Equation 38 describes nuclide transmutation, removal, and decay (i.e.,

the Bateman equations). As expressed, it appears to require negative values for A.ii parameters describing removal. Provide this equation in a form such that it is clear how nuclide balance is being tracked.

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[Question 4.4-1) Section 4.4.4, "Wrapper Codes," states that KPATH is the Kairos-developed data transfer interface that connects STAR-CCM+ to Serpent 2.

However, the process flow illustrated in figure 4-1 does not identify any connection between the KPATH and STAR-CCM+. Please explain this discrepancy.

o4.4-2) Section 4.4.2, "KACEGEN," states that "[

-))" Discuss how was this chosen. Discuss if the e ec rn e paper, ncorrec resonance escape probability in Monte Carlo Code due to the threshold approximation of temperature-dependent scattering," by Gabriel Lentchner et.al. (Annals of Nuclear Energy, Vol. 207, 2024, 110717) was investigated. This paper claims that modifications to the Serpent source code are necessary for the correct scattering with temperature.

[Question 5.2-2) Provide additional justification for evaluating the simplified KP-FHR models presented in section 5.2.1.1, "Simplified KP-FHR model," at isothermal conditions. Explain if there are any temperature dependent effects missed by this simplified approach.

[Question 5.2-3) Discuss the location of the reactivity control elements in the simplified models. State if both in-blade and in-reflector locations are accounted for.

[Question 5.2-4] In section 5.2.3, "Uncertainty Quantification," it appears that input parameter uncertainty quantification is performed for SCALE. Describe if such analysis was performed for Serpent 2.

[Question 5.2-5) Table 5-26, "Bias Corrections," gives the range of bias correction factors for nuclear analysis figures of merit, including reactivity coefficients. State which of these are limiting when applied within safety analysis calculations. State if the safety analysis will be re-done when operating data is obtained and bias corrections are updated.

[Question 5.2-7) Please explain the use of multiple"+/-" operators in Equation 41.

[Question 5.2-8) Table 5-2, "V&V Model Naming Convention," contains verification information. Discuss why validation is in the title of table 5-2 or edit the title to accurately reflect the contents.

[Question 5.2-9) Regarding table 5-26, "Bias Corrections," clarify how the applicability of experiments such as the molten salt reactor experiments was determined. Clarify which equations are being used to map the basis to bias correction factors.

[Question 5.2-10) Justify the use of simple hexagonal lattice approximations to TRISO and pebble bed geometries in the MCNP and SCALE models described in table 5-2, as compared to more physically representative hexagonal close-packed lattices.

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[Question 5.2-13] Section 2.5.1, "Serpent 2," of TR KP-TR-012-P, "KP-FHR Mechanistic Source Term Methodology" (ML22088A230), states that the use of Serpent 2 to generate core inventory will undergo verification and validation (V&V) as part of the core design and analysis methodology. Discuss the plans to execute the V&V of the Serpent 2 core inventory analysis.

[Question 5.4-1] Provide the frequency of operational measurements that will be used to update nuclear reliability factors. Discuss if there will be accounting for core composition (i.e., relative fraction of pebbles with given pass numbers/burnups). State how these measurements will be performed.

[Question 5.4-2] Equations 45, 46, and 47 appear to require the best estimate to be a single value, as in Equation 45, not an array (subscripted by index i) as in Equations 46 and 47.

a.

Describe the treatment of the best estimates in Equations 46 and 47.

b.

Discuss the distributions of the measurement(s) M for which the treatment in Equations 45 through 47 is valid (i.e., should it be normal?). Discuss how the normality would be tested. Discuss how many independent measurements would be required in Equations 46 and 47.

[Question 5.5-1] Reactivity coefficients should be assessed as continuous functions (e.g., of temperature), as they may be non-linear. By understanding the de ree of non lineari one can develo some conservative estimates if desired.

[Question 6.1-1] Discuss how pebble and coolant displacement within the packed bed is accounted for in the reactivity shutdown system worth methodology.

[Question 6.1-2] Provide additional explanation of the 1/v method used for prompt lifetime evaluation. State the purpose of including a 8-10 term within Equation 55.

[Question 6.1-3] Section 6.1.5.2, "General Depletion," states that modeling Flibe as a fresh Flibe at equilibrium core conditions is conservative. Discuss the impact of modeling the Flibe as fresh in the overall reactivity balance.

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[Question 6.2-1) State any plans to perform uncertainty quantification on predicted end of-life fluence. If plans exist, state the expected acceptance criteria margin.

[Question A.1-1) In the shutdown margin calculations performed in table A.1-2, "Hermes

.,\\-and Q-Core Shutdown Margin," discuss if the worth of each individual contributor is determined via explicit eigenvalue calculations at each perturbed core state or using temperature/density coefficients to estimate worths between different states.

[Question A.1-2) Regarding table A-1.15, "Determination of ITC [isothermal temperature coefficient] Bounds of Uncertainty Based on Determination of Nuclear Reliability Factor,"

provide mathematical justification for the interval sums utilized in this table to arrive at the final conservative bounds.

[Question A.1-3) The comparisons shown in section A.1.1.3.1.1, "Carbon Cross-Section and Thermal Scattering Nuclear Data Bias," demonstrate the calculation of bias for the isothermal temperature coefficient (ITC) and reactivity shutdown system (RSS) worth using the free gas and thermal scattering library approximations. The difference between these two approximations is used as a measure of bias due to uncertainty in graphite thermal scattering neutron data. However, the actual bias is between the chosen approximation and physical data. Please provide justifications for the approach used for the estimation of bias for the ITC and RSS worth.

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