ML25142A089

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Final Audit Report Kairos Core Design TR Non-Proprietary
ML25142A089
Person / Time
Site: 99902069
Issue date: 11/20/2025
From:
NRC/NRR/DANU
To:
Kairos Power
References
KP-TR-024-P
Download: ML25142A089 (0)
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Text

SUMMARY

REPORT FOR THE REGULATORY AUDIT OF THE KAIROS POWER LLC TOPICAL REPORT KP-TR-024-P, KP-FHR CORE DESIGN AND ANALYSIS METHODOLOGY TOPICAL REPORT AUGUST 2024 - JULY 2025

1.0 BACKGROUND

AND PURPOSE Kairos Power LLC (Kairos) began pre-application discussions with the U.S. Nuclear Regulatory Commission (NRC) staff on its proposed Kairos Power Fluoride-Salt-Cooled, High-Temperature Reactor (KP-FHR) in October 2018. In December 2020, Kairos announced that the Hermes test reactor (henceforth known as Hermes 1 for clarity) would be used to support future development of the KP-FHR. On December 14, 2023, the NRC issued a construction permit (CP) to Kairos for the Hermes 1 facility (Agencywide Documents Access and Management System (ADAMS) Accession No. ML23338A260). Additionally, on November 21, 2024, the NRC issued CPs to Kairos for the Hermes 2 testing facility (ML24324A020).

By letter dated April 3, 2024, Kairos submitted KP-TR-024-P, KP-FHR Core Design and Analysis Methodology Topical Report (ML24095A256), to support future KP-FHR test and power reactor operating license (OL) applications. On June 20, 2024, the NRC staff determined that the topical report (TR) presented sufficient information to begin a detailed technical review (ML24163A021). The NRC staff issued an audit plan on August 22, 2024 (ML24222A276). The purpose of the audit was for the NRC staff to gain a better understanding of KP-TR-024-P by providing an opportunity to review and discuss material used to support statements or conclusions in the TR.

2.0 AUDIT REGULATORY BASES The bases for the audit are the regulations in Title 10 of the Code of Federal Regulations (10 CFR) pertinent to the NRC staffs review of a future Hermes OL application, particularly 10 CFR Part 50, Domestic Licensing of Production and Utilization Facilities, sections 50.34, Contents of applications; technical information, 50.40, Common standards, and 50.57, Issuance of operating license.

3.0 AUDIT OBJECTIVES The primary objective of the audit was to enable a more effective and efficient review of KP-TR-024-P through the NRC staffs review of supporting documentation and discussion with Kairos. A secondary purpose of the audit was to identify any information that will require docketing to support the NRC staffs safety evaluation.

4.0 AUDIT ACTIVITIES The audit was conducted from August 2024 through July 2025 via the Kairos electronic reading UNITED STATES NUCLEAR REGULATORY COMMISSION WASHINGTON, D.C. 20555-0001

2 room (ERR). The NRC staff conducted the audit in accordance with the Office of Nuclear Reactor Regulation (NRR) Office Instruction LIC-111, Revision 1, Regulatory Audits (ML19226A274).

Members of the audit team were selected based on their detailed knowledge of the subject matter and are listed below:

  • Alex Siwy - Senior Nuclear Engineer, Audit Lead
  • Pravin Sawant - Senior Nuclear Engineer
  • Ben Adams - General Engineer
  • Brian Bettes - Project Manager
  • William Wieselquist - Contractor
  • Christopher Boyd - Senior Technical Advisor for Computational Fluid Dynamics (CFD)

The NRC staff reviewed the following items via the ERR:

  • K. Wakao, S. Kaguei and T. Funazkri, "Effect of fluid dispersion coefficients on particle-to-fluid heat transfer coefficients in packed beds," Chemical Engineering Science, vol. 34, pp. 325-326, 1978
  • Nuclear Energy Agency (2015), Best Practice Guidelines for the Use of CFD in Nuclear Reactor Safety Applications - Revision, Organization for Economic Co-operation and Development Publishing, Paris
  • Kairos Power, Appendices (Neutronics PIRT [phenomena identification and ranking table] Table), HER-EN-RPT-110-0003-Rev A
  • Kairos Power, HER-MTHD-000004-Rev 0, Core Thermal Hydraulics Inputs Sensitivity Analysis, April 2, 2024
  • Kairos Power, Technical Report KP-1000002924, Revision 0, FHR Core Thermal-Hydraulics Calculation Guidelines, August 2024
  • American Society of Mechanical Engineers Standard for Verification and Validation in Computational Fluid Dynamics and Heat Transfer 20 - 2009 (R2021)
  • RSS [reactivity shutdown system] Total, Integral and Differential Worth Comparison Calculation Presentation dated November 26, 2024
  • Simcenter STAR-CCM+ User Guide, Version 2021.3, Siemens Digital Industries Software, 2021
  • Presentation slides providing responses to audit questions
  • Proposed markups to the TR Audit meetings were held on the following dates (meetings were virtual unless otherwise noted):

September 12, 2024 - Entrance meeting October 29, 2024 November 5, 2024 November 20, 2024 December 3, 2024 December 17, 2024 December 18, 2024

3 January 14, 2025 January 28, 2025 February 11, 2025 February 25, 2025 May 20, 2025 June 6, 2025 July 18, 2025 - Exit meeting The NRC staff transmitted audit questions to Kairos on the following dates:

August 22, 2024 (ML24222A276)

October 18, 2024 (ML24292A169 Public) (ML24292A186 Non Public)

December 6, 2024 (ML24341A201 Public) (ML24341A163 Non Public)

January 8, 2025 (ML25008A259 Public) (ML25008A302 Non Public) 5.0

SUMMARY

OF AUDIT OUTCOME The NRC staffs audit focused on the review of supporting documents associated with the topics identified in the audit plan and subsequently transmitted questions. The NRC staff reviewed information through the ERR and held discussions with Kairos staff to understand and resolve questions. In many cases, Kairos updated KP-TR-024-P to resolve items discussed in the audit.

Gaining access to underlying documentation and engaging in audit discussions about various aspects of the TR facilitated the NRC staffs understanding and aided in assessing the proposed methodology. The table below reproduces the transmitted audit questions and summarizes the resolution of the questions. The equation numbers of the audit questions have been updated in the table below to reflect the numbering in Revision 1 of the TR.

As noted in the table below, Kairos updated the TR based on the audit discussions. These updates are included in Revision 1 of the TR, which was submitted in letter dated June 17, 2025 (ML25168A340). In addition, during audit calls on May 20 and June 6, 2025, the NRC staff shared with Kairos draft limitations and conditions that were under consideration as the NRC staff prepared the draft safety evaluation (SE).

4 Question Number Audit Question Resolution 1.2-1 Section 1.2.2, Principal Design Criteria for the Reactor Core, of the TR discusses the principal design criteria (PDC) that apply to the KP-FHR reactor core. Please explain how the core design tools presented in this TR are used to show compliance with PDC 12. Describe the analyses that would be performed to support the conclusions that the KP-FHR core is inherently stable and that a detection system for power-oscillations is not required are justified. Section 6.2.5, Nuclear Stability, of the TR provides limited qualitative discussion on nuclear stability under the condition of asymmetric rod operation.

However, the scope of PDC 12 is broader. PDC 12 requires the reactor core; associated structures; and associated coolant, control, and protection systems to be designed to ensure that power oscillations that can result in conditions exceeding specified acceptable system radiological release limits (SARRDLs) are not possible or can be reliably and readily detected and suppressed. It is possible that the methodology presented in this TR can play some role in analyses to address PDC 12. However, it is not clear how the proposed methodology can address all the elements of the analyses necessary to perform a PDC 12 evaluation (e.g., adequate modeling of control systems, assurance that the proposed numerical methods are applicable to evaluate the stability).

Kairos updated sections 1.2.2 and 6.2.5 in Revision 1 of the TR to clarify that the methodology is not intended to fully satisfy PDC 12; rather, the methodology will support evaluation of compliance with PDC 12 by calculating neutronics parameters that will allow evaluation for stability in OL applications. These parameters include diffusion length, migration area, and reactivity coefficients. The updates further clarified that instability initiated by the control system is not within the scope of this methodology.

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.

Kairos stated that ZONER uses DEM pebble trajectories (streamlines) and their residence time to generate axial and radial spectral zones discretization. The methodology is able to capture the pebbles batch velocity profile with the desired degree of spectral zone discretization. The Kairos Power Advanced Core Simulator will then simulate fuel materials ascension as described in TR section 4.4.3.

5 Question Number Audit Question Resolution 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.

Kairos stated that the PEM is modeled as one homogenized material with composition and density determined using the total volume fractions of Flibe coolant and steel material. The fueling region is composed of Flibe coolant and pebbles. The power level in the fueling region is homogenized because of the low overall power level.

Kairos modified the TR in Revision 1 to further describe modeling of these regions.

2.3-1 Please explain the two approaches to reactor startup modeling, the mixed bed and critical height approaches, in greater detail than is provided in TR section 2.3, Operational Regimes. For example, describe the assumptions regarding core composition and distribution of pebble types in the core. Explain any other unique methodology features needed to support the startup modeling for the mixed bed approach vs. critical height approach.

Kairos updated section 2.3 in Revision 1 of the TR to (1) remove the mixed bed approach and (2) add information for the critical height approach.

Kairos stated that the proposed startup modeling approach is consistent with American Nuclear Society Standard 19.13, Initial Fuel Loading and Startup Physics Tests for First-of-a-Kind Advanced Reactors.

3.1-1 Section 3.1.1 and appendix C of the TR provide discussion on neutronics PIRT results for the KP-FHR.

  • The advanced high-temperature reactor (AHTR) PIRT is used as the reference PIRT. Please explain how the unique KP-FHR design features are addressed in the PIRT.
  • Please explain the sentence "The outcome of benchmarking the methodology against the PIRT revealed adequacy of the fidelity in the best estimate methods to capture the physics of the FHR core" in section 3.1.1 of the TR and the process of benchmarking the methodology against a PIRT. The staff notes that a PIRT usually guides methodology development. Fidelity of a methodology to capture the physics of important phenomena identified in the PIRT Kairos updated TR section 3.1.1 in Revision 1 of the TR to clarify that the internal KP-FHR PIRT described in Appendix C of the TR was not used to develop the methodology. Instead, the KP-FHR PIRT was used as a tool to confirm that the developed methodology is capturing the relevant physics.

Kairos also noted that the AHTR PIRT was reviewed as part of the literature review prior to beginning the internal KP-FHR PIRT because the material, conditions, tri-structural isotropic (TRISO) fuel, and coolant were similar to those of the FHR.

6 Question Number Audit Question Resolution is usually demonstrated by performing validations against applicable data (analytical and experimental).

Initial PIRT rankings could be based on expert input and/or analysis. The PIRT rankings could be further validated using the experimental data or limited sensitivity calculations. It is essential for staff to understand the process used to develop the PIRT and how it is confirmed that all the high ranked phenomena are properly identified and characterized.

3.1-2 Section 3.1.2, Key DEM Phenomena, of the TR identifies factors important for modeling in the DEM model. The staff would expect fluid or coolant thermophysical properties (including temperature/composition effect) to play a critical role in determining the forces on the pebble. Similarly, the staff believes that coolant flow distribution could be an important input for the DEM model analysis. However, these factors are not identified in section 3.1.2 as factors influencing the DEM figures-of-merit (FOMs). Please clarify all the factors/phenomena/boundary conditions that are important for the DEM model and discuss why core pressure gradient, temperature and coolant flow distribution, thermophysical properties, etc. are not identified as factors influencing the FOMs in section 3.1.2.

Kairos stated that the phenomena of pressure gradient, temperature and coolant flow distribution, and thermophysical properties are implicitly included in the Pebble drag forces as seen in TR Equations (2) and (19). Kairos stated that they confirmed all the physics important to modeling FOMs were included in the methodology by (1) conducting literature surveys, (2) performing global sensitivity analyses, and (3) performing validation studies.

Kairos confirmed that the phenomena identified by the NRC staff are treated as important phenomena in the TR.

3.1-3 In section 3.1.3, Key Thermal Hydraulics Phenomena, of the TR, the approach used to identify the phenomena important for core thermal-hydraulic (TH) analysis is not clear. It appears that the methodology considers phenomena identified for the steady state conditions from the Kairos Power thermal fluid PIRT. Section 3.1.3 also states that the importance ranking in the reference PIRT was "outside the scope" of core TH applications, and sensitivity analysis is used for the identification of important phenomena.

Kairos stated that the TH methodology was selected prior to the PIRT analysis. The PIRT was used for confirmation of the model. In addition, global sensitivity analyses and dedicated studies were performed to validate the modeling assumptions.

Kairos stated that the most important phenomena affecting core design FOMs are listed in the TR and updated the TR to clarify treatment of select additional phenomena.

Question Number 3.1-4 3.1-4a 7

Audit Question

  • Please explain how the generic thermal fluid PIRT for postulated events was adopted for the core steady-state TH analysis. Please explain similarities and differences between the thermal fluid PIRT and the conclusions reached in TR section 3.1.3 (e.g., FOMs, transient vs. steady state) and the process/justifications used to identify the applicable PIRT phenomena from the generic Kairos Power thermal fluid PIRT.
  • Section 3.1.3 identifies the phenomena/processes that must be modeled to calculate core TH FOMs reliably.

Why are the following phenomena/processes not considered as important for core-TH analysis:

  • Core power distribution boundary condition
  • Core heat transfer mechanisms such as conduction, radiation, and conduction inside pebbles and layers of TRISO particles
  • Fluid thermophysical properties
  • 3-D or asymmetric temperature and flow distributions and other phenomena specific to large ower reactors Please explain how fast neutron fluence and temperatures are used to inform geometrical and thermophysical property correlations as stated in TR section 3.1.3.

(Follow-up to Question 3.1-4) 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 Ian ML24222A276 Resolution 0

I I

o ermop ysIca prope Ies an

-D spatial effects are captured explicitly in the evaluation model.

Kairos clarified that the reflector temperature distribution is calculated using a 3-D model.

Similarly, the porous media model for flow distribution is a 3-D model.

Kairos stated that these effects, including the potential impact of temperature on the reflector gap or geometry and its effect on the bypass flow, are accounted for in the fuel performance code, KP-BISON.

The NRC staff issued Question 3.1-4a as a follow-up to this uestion.

Kairos stated in audit discussions that the methodology is not linked to any prescribed fuel performance code or interface and can use any thermophysical or geometrical properties as input to the thermal models described in TR section 3.5.1.3. KP-BISON is one tool Kairos may use in develo ing the methodolog in ut.

Question Number 3.1-5 8

Audit Question 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 tristructural isotropic (TRISO) layers and provides TRISO buffer-lPyC (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.

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.

Resolution KP-BISON predicts the evolution of pebbles' and TRISO particles' thermal conductivities and layer thicknesses with burnup. The core design methodology provides KP-BISON with the following inputs: pebble surface temperature, pebble residence time, pebble power, and fast neutron flux.

Kairos further stated that material properties are scope dependent and clarified that the fluence and temperature dependence of fuel pebble and TRISO particle properties and geometry (e.g., thicknesses of TRISO layers) is accounted for in the inputs to the methodology.

The NRC staff asked about accounting for the uncertainties in the input properties and how frequently the properties will be updated during the iterative TH and neutronics calculations. In response, Kairos added discussion to TR section 3.1 in Revision 1 of the TR on how thermophysical property and geometric changes due to temperature and fluence can be accounted for.

TR section 5.2.3.2 describes the overall treatment of input uncertainties, including uncertainties in thermophysical properties and geometrical parameters, with reference to figure 5-12.

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Question Number 3.1-6 9

Audit Question Resolution Kairos updated section 3.1.3 in Revision 1 of the TR based on these discussions.

Kairos stated the followino:

Question Number Audit Question 10 3.1-7 Section 3.1.3, "Key Thermal Hydraulic Phenomena,"

states that e

e 1

unce aIn Ies for ((

~----f.-l--)) in the me o o ogy.

3.2-1

'1Tisiiotc:1ear from the discussion in TR section 3.2, "General Modeling Approach," if the reactor vessel wall is part of the core TH model. Please explain how the heat transfer or heat loss from the reactor vessel to the decay heat removal system (DHRS) and its impact on the reactor vessel temperature are accounted for in the model.

Resolution Kairos stated that the reactor vessel temperature distribution is not part of the FOMs encompassed by the core thermal-hydraulic methodology. An assumption of constant temperature is used instead. The boundary condition is not predefined and can be flexible to account for variations in reactor vessel wall temperature.

Kairos also clarified that the neutronic methodology includes the reactor vessel wall region.

Kairos u dated section 3.5 in Revision 1 of the TR to

11 Question Number Audit Question Resolution clarify the modeling approach.

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

Kairos asked for clarification regarding what is meant by natural circulation flow bypass. The NRC staff stated that the question was asking about modeling of flow through the natural circulation flow path. Kairos stated that bypass flow is design-dependent but not significant given the temperature margins.

3.3-1 It appears there may be a typographical error in Equation 3 in TR section 3.3, DEM Modeling Paradigm.

Please confirm the accuracy of Equation 3 as written in the TR and as coded in the model.

Kairos updated Equation 3 in Revision 1 of the TR to correct the typographical error. Kairos also confirmed that the correlation as coded is correct.

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?

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.

Kairos stated the following in audit discussions:

a) Equation 1 represents the Lagrangian formulation of a single DEM particle expressed in the form of Newtons second law of motion. The particle velocity is a function of time and position; hence, the derivative can be considered as the total time derivative.

b) The pebble velocity is a vector, as suggested by the notation on the right-hand side of Equation 1. A vector accent was added in Revision 1 of the TR.

c) The pressure field is a vector field.

Kairos stated that particle velocity is a Lagrangian field, while the pressure field is a Eulerian field.

In response to NRC follow-up discussion, Kairos stated that the STAR-CCM+ theory manual describes contact forces in the DEM model as a typical variant of the spring-dashpot model and not as frictional/drag forces.

The contact forces (normal and tangential) represent repulsive forces pushing particles apart and viscous damping and allow the simulation of forces in the collision of particles. ((

Question Number 3.3-3

b.

C.

d.
e.

12 Audit Question same as the pressure drop in Equation 5 and the Resolution Kairos updated section 3.3 in Revision 1 of the TR based on these discussions.

Kairos stated the following in audit discussions:

a) The pressure gradient in Equation 2 is not the same as the pressure drops in Equation 5. The pressure gradient in Equation 2 is the same as the one described in section 3.5.1.3, b) c)

d) e)

E uation 19. The subscri t "d" refers to dra.

Question Number 3.3-4 3.3-5 13 Audit Question n qua I0n, rag an o y orces uoyancy orce are identified as separate forces; explain this discre anc.

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 Resolution on ics are not in the scope of the TR.

Kairos updated sections 3.3 and 5.3 in Revision 1 of the TR as a result of these discussions.

Kairos stated in audit discussions that drag and buoyancy forces are kept and modeled separately in Equation 1. Further characterizations of these forces are provided in Equations 2 and 3.

Kairos updated section 3.3 in Revision 1 of the TR to clarif that

Question Number 3.5-1 14 Audit Question Resolution properties needed as input to the DEM model.

pressure drop. Provide the pebble and reflector mechanical ro erties needed as input to the DEM model.

+----------

Discuss if the scope of the ((

11 includes local conjugate heat rans er e een libe and the reflector.

Kairos stated that the ((

local conjugate heat trans er reflector.

11 includes 1 e and

-+---

-+---

3.5-2 3.5-3 3.5-4 The table 3-2, "Model Paradigm Summary," description of the porous media (PM) model is not consistent with the description provided in section 3.5, "Thermal H draulics Modelin Paradi rov, e 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; clari the a ro riate reference in the TR.

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 (KT A) 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 KT A pressure correlation is applicable to the Hermes test reactor and KP-FHR ower reactor designs.

Kairos stated in audit discussions that they agree with the NRC staff's observation. Kairos u dated table 3-2 in Revision 1 of the TR to ((

11 Kairos stated in audit discussions that the correct reference is TR section 3.5.1.3. The nomenclature was clarified in Revision 1 of the TR.

Kairos stated the following:

a) Equations 5 and 6 report the original formulation of pressure drops in the KT A document (Reference 7). The baseline porous media model uses the rearranged form in section 3.5.1.3 Equations 17, 18, and 19 (Darcy-Dupuit-Forchheimer). The equations are then evaluated in the local differential formulation in Equation 14.

In this formulation, density and viscosity are evaluated locally at the cell volume center.

Section 3.5.1.1 points to section 3.5.1.3 for implementation details.

b) This was addressed in response to Question 3.3-3e.

c) This was addressed in response to Question 3.3-3e. Kairos also referenced a

Question Number 3.5-5 3.5-6 15 Audit Question

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.

Specify the range of applicability for the Wakao correlation Equation 7) and the ((----

)) Discuss the basis ~

ese corre ations and the applicability of experimental data used for the development of these correlations to the Hermes test reactor and KP-FHR power reactor designs.

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.

d)

Resolution discussion in TR section 5.3.1.

s app,ca 1 1 y rs assessed w,

Ig - 1 e I y CFO benchmarks as described in TR section 5.3. Other porous media pressure drop correlations were not assessed since they are outside the scope of this methodology.

Kairos updated section 3.5 in Revision 1 of the TR based on these discussions.

Kairos stated that ((

-- )) applica 1 1 range are no prov, ed in this

~us media models for mass, momentum and energy transfer in KP-FHRs are validated using high-fidelity CFO models. These models confirm the applicability of ressure dro and heat transfer correlations [

))

for specific core opera Iona s a es.

e me o o ogy also provides bias and confidence intervals to bound temperature calculations.

Kairos updated section 3.5 in Revision 1 of the TR based on these discussions.

Kairos stated that the sentence refers to the capability of the porous media models to include the following power deposition inside the core: neutron and gamma power deposition in Flibe, neutron and gamma power deposition in moderator pebbles, neutron and gamma power deposition in fuel pebbles, and fission power in fuel pebbles. These power distributions are used as a power density source term in TR Equations 20 and 23.

The ower densit distributions are calculated using

Question Number 3.5-7 3.5-8 16 Audit Question 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.

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.

Resolution Ser ent.

Kairos stated that yes, the packed-bed porosity is defined as the volume fraction of Flibe in the whole packed bed.

a and b. Kairos updated section 3.5.1.3 in Revision 1 of the TR to address these uestions. Kairos also reiterated that sec I0n..

c. Kairos stated that DEM modeling can provide baseline best-estimate porosity values as well as bounding values (plus uncertainties). For the latter, the baseline DEM model can be used to produce highly packed and loosely packed configurations aligned with FHR physics and design. The current baseline TH porous media model uses best-estimate and bounding value ranges to assess the im act on relevant FOMs.

Kairos stated that Flibe density in Equation 16 is the same one used in previous equations. Kairos revised the equations and notations in Revision 1 of the TR to address items b - d.

Question Number 3.5-9 3.5-10 3.5-11 17 Audit Question

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

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.

Explain the significance of terms containing shear velocity tensor and body force in energy Equation 20.

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 transport processes are modeled.

Resolution Kairos stated that the porous resistance force provides the local momentum sink term in Equation 14 to model the flow resistance due to the presence of the porous medium. For FHR beds, this includes the presence of a randomly packed bed of spheres and their wall boundary (reflector core cavity). For FHR cores, the porous resistance force term represents the largest momentum sink inside the core region. The shear stress tensor models the remainin sources of momentum.

Kairos updated section 3.5.1 in Revision 1 of the TR based on these discussions.

Kairos stated in audit discussions that the term containing the shear stress tensor and body force represents the work done per unit time on the fluid b the viscous forces and bod forces.

b.

1 e-1 e energy transfer is captured by Equation 20 in the conduction and advection terms.

Flibe-reflector energy transfer is modeled as described in TR section 3.5.1.3.

_J C. ([

Question Number 3.5-12 3.5-13 3.5-14 18 Audit Question Resolution

))

7

)) ----+------------------1

a.

escn e e process or es,ma,on o e,_

effective solid thermal conductivity and volumetric energy source term in Equations 23 and 24.

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 23 and 24) and the Flibe porous media energy transport equation (Equation 20) use the same nodalization.

Kairos stated the following:

a. The solid-phase thermal conductivity for pebbles is an input to the model. The volumetric energy source term is imported from Serpent.
b. Yes, the total power deposited is accounted for in the Serpent calculations.
c. The model uses the formulation described in Equation 23. Conduction heat transfer within the same solid hase is modeled with E uation 24.

computational mesh (discretized domain).

Kairos updated section 3.5.1 in Revision 1 of the TR as a result of these discussions.

+-

Kairos stated that ((

Question Number 3.5-15 3.5-16 3.5-17 19 Audit Question Resolution s men,one m e TR, e

mo e prov, es the fuel pebble outer surface temperature distributions. The fuel pebble surface temperature field is used as a boundary condition for the 1 D pebble model." Kairos updated section 3.5 in Revision 1 of the TR to clarify the definitions of the temperatures in Equations 31 and 32 as well as assum tions and characterization of ower.

Question Number 3.5-18 3.5-19 3.5-20 3.5-21 20 Audit Question Identify the inputs needed for the [

)) along with the justifications e.g., mes mg pe aiicfparameters 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 closin~

ions). Describe the basis for the selection of the ((- )) model.

Please address the discrepancy in scope of the

((-)) model in section 3.5 and in table 3.2, "Model ParactTcim Summar."

I I

I Resolution Kairos updated section 3.5 in Revision 1 of the TR to state that The resolution of this question is covered through dis osition of uestion 3.5-21.

7 Kairos updated section 3.5.3 in Revision 1 of the TR to align with table 3-2.

TR revision 1, section 3.5 was updated to address this question as well as 3.5-19 and 4.2-1. Kairos provided the following additional information regarding this question:

a.

Question Number Audit Question discuss and, if applicable, provide the following information on the 21 Resolution 7

Question Number 4.1-1 4.2-1 22 Audit Question

e. Fluid and Solid Properties: Please discuss how the fluid and solid properties are modeled and how any buoyancy forces are accounted for.
f. Meshing: Provide details of the mesh type, design, sizing, and any quality metrics used to grade the mesh. Discuss the results of any mesh dependency studies performed to support the selected mesh. What is the estimated grid dependency?
g. Numerical solution: Discuss differencing schemes used for the model equations and methods used to monitor and confirm solution conver ence.
h.

Section 4.1, "Process Flow," describes the process flow and coupling between the DEM, neutronics (Serpent 2),

and thermal hydraulics (TH, PM, ((-))) modules.

However, the inputs and outputs foreach 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.

A multi-physics CFO code, STAR-CCM+, is used for the DEM and core TH modeling. The staff notes that, as a generic purpose CFO tool, STAR-CCM+ includes numerous user o tions that allow a user to exercise a Resolution Kairos stated the following in audit discussions:

a. Computational module specifics are described in their dedicated sections in the report and are illustrated in figure 4.1. Calculational outputs from core analysis are summarized in section 3.6.
b. Figure 4.1 is not a process flow diagram with inputs and outputs. It is used to illustrate connections between modules.

Kairos revised figure 4.1 in Revision 1 of the TR to clarify the data flow in the design and analysis methods and to ex licitl identif code models.

Kairos stated that internal user guidelines have been developed to ensure model configuration control.

The resolution of this uestion is covered through

Question Number 4.2-2 4.3-1 23 Audit Question wide range of field equations, discretization options, closing relations, constitutive equations, nodalization, and numerical methods. It is essential to ensure that the code models, correlations, and various code options selected in the methodology application calculations remain the same as those used in the supporting validations. Please explain how this control is achieved in the methodology (e.g., user guidelines):

  • Please identify the code inputs that have an impact on selected field equations, discretization, and numerical methods. The closing/constitutive relations selected should be clearl identified in the TR.

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 STAR-CCM+. Discuss if there was any need for developing user-defined functions or modules to implement the fundamental equations and closing relations.

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.

Resolution disposition of question 3.5-21.

Kairos updated the TR in Revision 1 to clarify these oints.

Kairos stated that Serpent version 2.2.1 was used for the calculations in the TR. The code is maintained with best practices in a GitHub repository and utilized on computational resources under a configuration control management program. A complete code-to-code benchmark is performed for new versions with defined criteria evaluated for acceptance. Release of successive code versions will be managed under the Kairos software quality assurance program.

The NRC staff noted that SE approval is typically based

Question Number 4.3-2 4.4-1 4.4-2 24 Audit Question Equation 39 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.

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 KPATH and STAR-CCM+. Please explain this discre anc~.

Section 4.4.2, "KACEGEN," states that ((

)) Discuss how Is was c osen. Iscuss I e e ec in the paper, "Incorrect 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.

Resolution on specific code versions, theory manuals, and user manuals. A description of the process to evaluate continued applicability will provide flexibility to use subsequent versions of the code.

Kairos updated the TR in Revision 1 to provide the code version and describe the change rocess.

Kairos revised Equation 39 in Revision 1 of the TR to include a more complete description of the Bateman equation.

Kairos revised the flow chart in Revision 1 of the TR to clarify the connection between KPATH and STAR-CCM+.

Question Number 5.1-1 5.2-1 5.2-2 Audit Question Please discuss or provide further background/contexUdocumentation on the appropriateness of the simplified KP-FHR model described in section 5.2.1.1.

25 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.

Resolution Kairos updated the TR in Revision 1 to remove the T1,

T2, and T3 placeholders and to address the scattering issue.

Kairos described ((

R to Kairos u dated the TR section 5.2.1 in Revision 1 to

Question Number 5.2-3 26 Audit Question Discuss the location of the reactivity control elements in the simplified models. State if both in-blade and in-reflector locations are accounted for.

Resolution clarify that this assumption is justified through sensitivity studies.

Kairos stated that the simplified models ((

is Kairos updated section 5.2 in Revision 1 of the TR to

+--------------------1-n_ote how ((

))

5.2-4 5.2-5 5.2-6 In section 5.2.3, "Uncertainty Quantification," it appears that input parameter uncertainty quantification is performed using SCALE. Describe if such analysis was performed for Serpent 2.

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.

Kairos state a inpu parame er supporting regulatory submissions was not done using Serpent 2.

The Serpent 2 methods to explore bias are demonstrated in tables A.1-12, A.1-13, and A.1-14 for isothermal temperature coefficient (ITC) and shutdown margin.

Kairos stated that the ranges of bias corrections are given to account for whether overprediction or underprediction is conservative for safety. The TR includes a method to update nuclear reliability factors (NRFs) in section 5.4. Kairos u dated section 5.4 of the TR to clarif that

Question Number 5.2-7 5.2-8 5.2-9 Audit Question Please explain the use of multiple "+/-" operators in Equation 42.

27 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.

Regarding table 5-26, "Bias Corrections," clarify how the applicability of experiments such as the molten salt reactor experiments was determined. Clarify which Resolution Kairos updated the TR in Revision 1 to clarify the basis for the results in figure 5-4.

Kairos stated that the "£' operators in Equation 42 represent the principle that margin applied to the FOMs will account for whether overprediction or under rediction is conservative for safe.

Kairos updated the TR in Revision 1 to clarify the use of the "+/-" operators with respect to the NRF methodolog.

Kairos revised the title of table 5-2 in Revision 1 of the TR to "Code-to-Code Comparison Model Naming Convention."

Question Number 5.2-10 5.2-11 5.2-12 Audit Question equations are being used to map the basis to bias correction factors.

28 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.

Resolution

Question Number 5.2-13 5.2-14 29 Audit Question 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 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.

Resolution

Question Number 5.3-1 5.4-1 30 Audit Question Section 4, "Modeling Tools," states that "[t]he verification process consists of software benchmarking and numerical solution verification and is described further in Section 5."

However, no substantial description is found on verification of numerical solution in section 5, "Validation, Verification, and Uncertainty Analysis." Section 5.3.4, "Numerical Error and Solution Verification," brief!

describes ISCUSS o serva ions an rmpo an cone us,ons for the methodolog from this recess.

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.

--+---

5.4-2 Equations 46, 47, and 48 appear to require the best estimate to be a single value, as in Equation 46, not an array (subscripted by index i) as in Equations 47 and 48.

a. Describe the treatment of the best estimates in Equations 47 and 48.
b. Discuss the distributions of the measurement(s) M for which the treatment in Equations 46 through 48 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 47 and 48.

Resolution Kairos updated section 5.2 in Revision 1 of the TR based on these discussions.

Kairos stated that software benchmarking refers to Monte Carlo code-to-code verification and is described in TR section 5.2.1. Serpent 2 code-to-code h

k.

is performed with ((--

)) for validation of ~ntended pp cations. Numerical solution verification for CFO is described in TR section 5.3.4. A lication of CFO best ractices based on operational measurements for a reactor, including how different core states are accounted for, will be addressed in the OL application.

Kairos stated the following:

a. The best-estimate (BE) term corresponds to the best estimate for the same condition that the measurements Mare performed. The measurements must be performed for the same or equivalent conditions. The TR Equations 48 and 49 were revised to remove the subscript "i" from the BE term.
b.

J

Question Number 5.4-3 5.5-1 31 Audit Question Section 5.4, "Methodology for U Operatic

," describe Resolution Kairos corrected Equations 48 and 49 and updated section 5.4 of the TR in Revision 1 to explain conditions under which NRF adjustments would be made.

-+---

Kairos stated that FOMs ((

Kairos stated that the methodology is suited for assessing the non-linearity of reactivity coefficients.

Non-linearity assessments were performed for the Hermes and Hermes-2 PSARs.

Question Number 5.5-2 6.1-1 32 Audit Question Discuss how pebble and coolant displacement within the packed bed is accounted for in the reactivity shutdown system worth methodology.

Resolution In addition, Kairos referred to TR revisions made in response to audit question 4.4-2.

airos s a e a

e an wo results in section A.1.1.2 model the RSS insertion by cutting pebbles and removing Flibe from the overlapping location of the RSS rods. When the rods are inserted, there is less fuel and

Question Number 6.1 -2 6.1 -3 6.2-1 33 Audit Question Provide additional explanation of the 1 /v method used for prompt lifetime evaluation. State the purpose of including a B-1 0 term within Equation 55.

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.

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

Resolution Kairos updated section 3.4 in Revision 1 of the TR to further describe RSS and RCS modeling.

Kairos updated section 6.1 in Revision 1 of the TR to describe that the 1/v method introduces small amounts of 1/v absorber uniformly throughout the system. The prompt neutron lifetime of the system is calculated as the limit of Ip as the concentration of boron approaches zero.

Kairos stated that ((

Kairos updated section 6. 1 in Revision 1 of the TR to further describe Flibe modeling.

Kairos stated that downstream applications for fluence information will have their own methodologies for adding margin and conservatively accounting for uncertainty.

The scope of this TR addresses using ((- )) for UQ for the s ecificall identified FOMs th~e used

Question Number 7-1 7.1-1 C.

34 Audit Question ease identify the specific FOMs which demonstrate the safe operation of the test reactor, as related to the core methodologies in the topical report, and provide the safety limits for each figure of merit Section 7.1, "Conclusions" states "The DEM methodology described in Section 3.3 of this topical report is acceptable for generating both a random packed pebble bed and TRISO distributions to use for a Serpent 2 baseline model geometry (Section 3.4) in thermal hydraulic validation benchmarks. These benchmarks, described in Section 5.3, are then used to inform the porous media models described in Section 3.5." Please describe how the Resolution Kairos stated the followino:

a.
b.

ors eady-state operations, the methodology ensures materials remain within their qualification (i.e., fuel, SiC temperature, and graphite temperature), stability of the core, and the shutdown margins shown in table A.1-2. Table 6-5 was added to the TR to show FOMs and acce tance limits.

C.

Kairos updated section 7 of the TR and added table 6-5 in Revision 1 of the TR based on these discussions.

Kairos updated section 7.1 in Revision 1 of the TR to state the following:

"The DEM methodology described in Section 3.3 of this topical report is acceptable for generating both a random packed pebble bed and TRISO distributions to use for a Serpent 2 baseline model geometry (Section 3.4) and for thermal hydraulic validation benchmarks. These benchmarks, described in Section 5.3, are also used to inform the thermal hydraulic uncertainty quantification described in Section 5.3.3."

Question Number A.1-1 A.1-2 A.1-3 A.1-4 35 Audit Question In the shutdown margin calculations performed in table A.1-2, "Hermes A-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.

Regarding table A.1-15, "Determination of ITC 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.

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 ITC and 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.

Section A.1. 1.2, "Demonstration of Uncertainty Analysis Tool," states Resolution Kairos updated appendix A in Revision 1 of the TR to clarif that Kairos stated that the conservative bounds are calculated consistent with the description in TR section 5.2.5 and as clarified by the response to question 5.2-7. Multiple sources of bias and quantified uncertainty are added to the best-estimate value of ITC.

The direct addition of each parameter is conservative.

Kairos updated appendix A in Revision 1 of the TR based on these discussions.

Kairos updated appendix A of the TR in Revision 1 to clarif that the a roach Kairos updated appendix A in Revision 1 of the TR to clarify the statement. In addition, Kairos stated in audit discussions that

Question Number A.2-1 B.1-1 36 Audit Question Also, section A.1.2.1.1 does not exist in the TR. Provide the reference to the correct section.

Figure A.2-1, "S Tern DEM Model Validation ((

Resolution Kairos stated the following:

Kairos expanded the discussion in appendix B in Revision 1 of the TR to address these questions. In addition, Kairos clarified durin audit discussions that 7

Question Number B.2-1 B.2-2 B.2-3 C-1 37 Audit Question Please escribe the reflector geometry used for the results plotted in section B.2.2.1.2 "Reflector Heat Transfer."

Resolution Kairos updated appendix B in Revision 1 of the TR to provide additional details. In addition Kairos stated that ion?

urations,"

which cylinder is the most representative of the test reactor core?

Section B.2.1.1, "Pressure Drop," states that ((

-+------------------------1 Kairos updated appendix B in Revision 1 of the TR to ex lain wh

Question Number Audit Question 38 Resolution

39 6.0 EXIT BRIEFING The NRC staff conducted an audit closeout meeting on July 18, 2025. At the closeout meeting, the NRC staff reiterated the purpose of the audit and discussed their activities.

7.0 ADDITIONAL INFORMATION RESULTING FROM AUDIT As a result of the audit, the NRC staff did not identify any requests for additional information related to this TR. However, Kairos revised the subject TR to address questions discussed during the audit.

8.0 OPEN ITEMS AND PROPOSED CLOSURE PATHS Not applicable. There were no deviations from the audit plan.

Package: ML25142A086 Draft proprietary version: ML25142A152 Final Proprietary version: ML25142A088 Final Nonproprietary version: ML25142A089 Transmittal email for Final Report:ML25324A354

  • concurred by email OFFICE NRR/DANU/UAL1:PM NRR/DANU/UAL1:LA NRR/DANU/UTB1:LEAD NAME CSantos DGreene*

PSawant DATE 7/2/2025 7/14/2025 7/23/2025 OFFICE NRR/DANU/UTB1:BC NRR/DANU/UAL1:BC NRR/DANU/UAL1:PM NAME CdeMessieres JBorromeo CSantos DATE 9/24/2025 9/24/2025 9/24/2025

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