Semi-Annual Report for Horizontal Compact High Temperature Gas Reactor (HC-HTGR) Development during Performance Period October 2022-March 2023

Horizontal Compact High Temperature Gas Reactor (HC-HTGR) is being designed by a multi-disciplinary team of nuclear, mechanical, and structural engineers under the support of a DOE-NE Advanced Reactor Demonstration Program’s Advanced Reactor Concepts-20 (ARC-20) award. The objective of this ARC-20 project is to deliver a conceptual design for the proposed HC-HTGR in 3 years and support its commercialization as a safe, low-cost HTGR. Argonne National Laboratory (Argonne) is responsible for the design and analysis of the reactor cavity cooling system (RCCS) as a safety system for passive decay heat removal of the reactor concept. Additionally, Argonne is providing analysis of the primary heat transport system to ensure temperatures in the reactor systems, structures and components with significant safety margins during normal operation and design basis accident scenarios. This third semi-annual report summarized the progress made at Argonne on the two tasks during the first half of FY23. As a part of the RCCS design task, a design process for the water panel and the system configuration was performed to improve the thermal performance of the RCCS. The updated water panel design had achieved enhanced thermal performance with 0.96 MWth capability with major design updates made in structural interfaces with the RPV and initial configuration of the water tanks. The loop configuration of the RCCS has been proposed to have two independently working loops for system redundancy. A water panel material study was performed focusing on the use of carbon steel in water systems.

Additional modeling strategies of primary system thermal fluids analyses were developed to meet modeling needs that are not well suited for the 1D-3D assembly level approach.The first of these is a reduced order assembly model, in which fuel centered unit cells are used to represent a fuel assembly.The 2D approach used in this model is much more computationally efficient, making this model useful for full core transient scenarios where fuel to coolant heat transfer is still the dominant flow path.The next model is the 3D core conduction model to be used to analyze decay heat removal in loss of primary system flow scenarios.Because these scenarios require a large domain to be modeled, a homogenized core model is being pursued to reduce the required computational costs.To accurately model decay heat scenarios it is necessary to couple a RCCS model to the 3D core conduction model.A simplified case is presented to demonstrate how the coupling methodology will be applied to the full core 3D conduction model.

Introduction
The Horizontal Compact High Temperature Gas Reactor (HC-HTGR) is being designed by a multi-disciplinary team of nuclear, mechanical, and structural engineers led by MIT under the support of a DOE-NE Advanced Reactor Demonstration Program's Advanced Reactor Concepts-20 (ARC-20) award.The objective of this ARC-20 project is to deliver a conceptual design for the proposed HC-HTGR in 3 years and support its commercialization as a safe and low-cost HTGR with a focus on minimizing the overnight capital cost of the power-generation system and explicit considerations of functionality, constructability, transportability, modularity, safety, and future licensing.
Argonne National Laboratory ("Argonne") is responsible for the design and analysis of the reactor cavity cooling system (RCCS) as a safety system for passive decay heat removal of the reactor concept and the thermal hydraulics analysis of the primary heat transport system including reactor pressure vessel (RPV) internals for normal operation, shutdown, and accident conditions.
For the RCCS design task, efforts made in the FY22 focused on a scoping calculation in estimating HVAC capability for the HC-HTGR reactor building and preliminary performance analyses for the HC-HTGR RCCS design using RELAP5-3D which includes water panel modeling study, development of a reference RELAP5-3D model of the baseline design of the RCCS, and single-phase natural circulation and panel conduction performance analysis.For the primary system analysis task, efforts focused on preliminary work on the development of a full core reduced order model and high resolution 1D-3D assembly level model, which can be found in [1].This third semi-annual report summarizes the progress made at Argonne on the two tasks during the first half of FY23.Chapter 2 highlights the design updates made to the water panel and the major system configurations implemented to improve the thermal performance of the RCCS for HC-HTGR.A design parametric study was conducted on the water panel geometry and natural circulation loop configurations to enhance the system's efficiency.Recent updates to the RCCS have enabled two independently operating loops in the system configuration.In Chapter 3, additional modeling methodologies that address scenarios unsuitable for 1D-3D assembly level analysis are discussed.A reduced order unit cell modeling approach is being pursued to predict assembly level parameters with high computational efficiency.Furthermore, a 3D core conduction model is being used for loss of primary coolant flow scenarios.

Task 1 Update: RCCS Design
For the RCCS design task, efforts made in the second half of FY22 focused on a scoping calculation in in estimating heating, ventilation, and air conditioning (HVAC) capability for the reactor building, modeling study for the water panel with CFD support, and preliminary performance analysis for the HC-HTGR RCCS design using RELAP5-3D.
The water panel modeling study was conducted previously with CFD support by informing important phenomena expected in the RCCS conditions.The RELAP5-3D model for the HC-HTGR RCCS was developed and preliminary performance analyses for the HC-HTGR RCCS design were conducted.Single phase natural circulation performance and panel conduction performance was evaluated for the design conditions and candidate materials for the water panel.The baseline design of the RCCS for the HC-HTGR was initially evaluated with a vertical straight water panel to have ~0.56MWth heat removal performance when the RPV surface temperature of 472 °C [2], in spite of the riser inlet water temperature of 30 °C with potential convection by air flow through gap between the RPV and the panel.Therefore, the design efforts have been made to improve thermal performance of HC-HTGR RCCS by exploring various design options under considerations.
This section summarizes the efforts made in the first half of FY23 focused on the design updates on the water panel and the system configurations made to enhance system performance, including design parametric study.The updated RCCS system configuration was proposed with recent design updates of the system to have some redundancy.The material study of the water panel in use of carbon steel in the water system is discussed.

Design updates on the water panel
Previous analyses were conducted with design conditions considering sufficiently low water temperature with additional heat removal assisted by HVAC.The reference design condition has then been updated for operation conditions in a more conservative manner as below: -Average RPV surface temperature of constant 420 °C -The emissivity of 0.8 for all surfaces participating in radiation heat transfer -Single-phase operation with higher water temperature throughout the loop -Air convection at both RPV outer surface and water panel surface is ignored.
-Thermal radiation heat transfer from the water panel to the cavity concrete wall is ignored.
-Radiative heat transfer between the RPV and top and bottom tanks is ignored.
Under such design constraints and reference design conditions for the RCCS of HC-HTGR, prioritized strategies to improve the thermal performance of the water panel were addressed as maximizing the water panel surface area and minimizing loss of radiation from the RPV to environment/structures other than the water panel.A potential water panel design update has been proposed to improve the RCCS performance to achieve the target heat removal rate of ~ 1 MWth in the design condition within a limited vertical elevation change allowed to the water panel maintaining the top located in the reactor building.Figure 1 and Table I show the major design changes of the water panel of HC-HTGR RCCS.
After several attempts, it was found that the water panel surface area is the major design parameter under such design constraints.A target heat removal rate of over 1 MWth was achieved only with the updated water design which has increased both the number of riser tubes per water panel from 33 to 66 and the water panel width to 1.5 m making its surface area to be double.Even though the maximum allowable span for a single water panel located between the adjacent vertical support is 1.5 m, however, the project team has limited it to 1.0 m to leave the design space for the vertical supports.Closely interacting with the overall project team, design changes of the HC-HTGR RPV and relevant structures have been made for sufficient heat removal from the water panel of the RCCS. Figure 2 shows a HC-HTGR RPV design change recently made by the project team.The vertical supports design has been revisited and updated to have more coverage area of the RPV.The vertical supports were intended to have 9 on each side of the RPV equally spaced, so the water panel connecting with top and bottom collectors is located between adjacent supports.A total of 8 top and bottom collectors are positioned on each RPV side with a span of 1.5 m.Now, the updated design has the number of vertical supports reduced from 9 to 2 on each RPV side and relocated two remaining vertical supports at both ends in the axial direction.The RPV outer diameter was the same as 4.1 m.The active core is in between supports, which are 8.4 m long, and the core is about 11.5 m long including reflectors and shielding.These changes enable to have a single long length water panel without any breaks from the vertical supports.However, the overall heat transfer area for 1 panel with a 9 m width is still smaller than previously targeted for the 8 water panels with the 1.5 m, which had 0.85 MWth heat transfer performance at the reference design condition.
* Used under the terms of the CC BY license (https://creativecommons.org/licences/by/4.0/)a) Initial configuration of the RPV [3] b) Potential design updates (as of December 2022) Figure 2 The initial concept and the potential design update of the vertical load supports Design parametric study on the loop configuration and the total length of the water panel was conducted for the updated water panel design.First, top tank injection elevation (X) and the top tank elevation (Y) were investigated with a unit water panel having a single riser tube model using RELAP5-3D.Table II shows the summary of the RCCS performance with the updated water panel design by natural circulation loop configurations.1.0 m is the maximum allowable margin for both the top tank elevation to be located inside the reactor building and for the top tank injection elevation to have at least 30 % of the level of the top tank water inventory as the depletion state from the given top tank size.As expected, the two parameters brought a favorable impact on promoting natural circulation flow rate, but they had insignificant enhancement of overall thermal performance.This indicates that the system performance evaluated at the reference design condition is primarily limited by the thermal radiation from the RPV.For the ideal case of a cylindrical shell shaped water panel with a smooth surface covering the entire RPV area, radiation heat transfer from the RPV is calculated by equation (1), where e is the emissivity, s is Stephan-Boltzman coefficient, A is the surface area, and D is the diameter [4].It is estimated 0.95 MWth in the reference design condition with a panel temperature of 65 °C and an emissivity of 0.8, which is close to the target thermal performance.This also confirms the main design parameter of the RCCS is the water panel surface area.Since the RPV side surface covered by the water panel is partially blocked by the top and bottom tanks, it led to another major system design updates.By locating the top tank other than above the RPV, it is expected to improve the thermal performance by utilizing additional RPV area participating in radiation heat transfer to the water panel with minimizing loss to the structures and extending water panel height to promote natural circulation flow.Mass flow rate [kg/s] 6.0e-3 6.2e-3 6.4e-3 6.7e-3 6.2e-3 6.4e-3 6.7e-3

Design updates on the system configuration
The initial concept of the RCCS has top and bottom tanks located above and below the RPV to have a compact configuration of the RCCS as shown in Figure 3.The top tank location above the RPV would have a chance to directly receive the radiation heat transfer even during normal operation.In addition, since the top tank was intended to be an additional heat sink by boiling off the inventory in accident condition, it would accelerate suppressing natural circulation flow, which is the main heat transfer mechanism of the RCCS.With that, relocating the top tank location was proposed to the project team.To support the design of top tank configuration, transient simulations were conducted using RELAP5-3D, and the results of two cases were compared -one is the top tank surface adjacent to the RPV receives the radiation heat transfer from the RPV directly (Case 1), and the other is the top tank is isolated and not receiving any radiation heat transfer from the RPV (Case 2).The transient scenario considered for the analyses is the simplified Depressurized Conduction Cooldown (DCC) event, which adopted the RCCS heat load evolution by time from a reference HTGR design [5].The power profile was then normalized to have a designed power level of HC-HTGR and set as a heat flux boundary condition.Started with the steady state natural circulation flow (0 s), heat sink to maintain the top tank temperature turned off.
Figure 4 Heat load to RCCS during DCC adopted from a reference HTGR design [5] Figure 5 shows the comparison of case 1 and case 2 in RPV temperature and natural circulation flow rate evolutions during DCC.Both cases showed the peak RPV temperature near 120 hr, and case 2 had 2 C higher than that of case 1. Case 1 had maximum RPV location at the center as the top tank is isolated with the RPV, while case 2 did at the top of the RPV.With continuous heating of the top tank by thermal connection with the RPV, case 2 had a lower natural circulation flow rate and started boiling earlier than case 1.The results support avoiding the potential heat transfer to the top tank or any structures near the top tank which suppress the heat transfer and accelerate the inventory of the top tank boil-off.Based on the investigations, a potential RCCS design with the updated water panel design has been proposed.It has the same top tank elevation and injection rate with the same distance between the RPV and the water panel of 0.1 m with the initial concept.Then, the bottom tank was replaced to the header to have the same function, and the top tank above the RPV was divided into two tanks and relocated to the top corner of the reactor building.With the changes made for the top and bottom tanks, the water panel had 165 % of area increase to cover more RPV area including top and bottom regions where those were previously blocked by the tanks as shown in Figure 6.This change still has a compact system configuration but has better heat transfer performance.In the reference design condition, 0.975 MWt of thermal performance is expected with the enhanced natural circulation flow rate of 5.02 kg/s, which was 4.48 kg/s for the previous design.Splitting the top tank into two separate tanks would configure the system with multiple independent loops for system redundancy.The RCCS of the Framatome's SC-HTGR have two independent loops with designed headers at the top and the bottom of the RPV connected with the riser tube assembly making two redundant system configurations [6].Inspired by Framatome's configuration, a potential system configuration of the RCCS for the HC-HTGR has been proposed to have two independently operating loops with designed top and bottom headers located at both ends of the water panel connecting riser tubes with cross connecting headers for each loop but not connecting each adjacent riser tube to the same header.These preliminary assumptions will be revisited when a more detailed system design process is made.With the new RCCS configuration, design parametric study on system performance was performed with respect to the tank elevation.Moving the top tank to other than above the RPV and splitting into two separate tank enables to have a potential design space for the top tank elevation to improve the thermal performance.Figure 8 shows the system temperature changes and natural circulation flow rate by tank elevation.Here, 0 m for the tank indicates the location at the top corner of the reactor building internal as a reference, and top tank elevation increasing up to 10 m indicates potential top tank location outside and above the reactor building.Increasing top tank elevation helps decreasing system temperature variation having better natural circulation performance in the reference design condition.In normal operation condition of TRPV=220 °C and Twater=30 °C, system temperature difference would have 20 °C when the tank is just above the reactor building.

Considerations on RCCS Water Panel Materials
The use of carbon steel for the riser tubes can offer improved heat transfer performance when compared against a stainless steel option due higher emissivity and thermal conductivity material properties.In an untreated system, however, oxidation will occur due to a cathodic reaction between iron in the steel and oxygen in the water.This corrosion mechanism may introduce an oxide layer on the riser tube walls which will result in degradation of the convective heat transfer and ultimately overall performance of the RCCS.Additionally, the surface will experience loss of material due to this corrosion mechanism and overtime will cause damage due to pitting and erosion [7].
For systems that feature heat exchange surfaces, such as boilers, shell and tube heat exchangers, cooling towers, etc. fouling can be expected and if left untreated can result in significant degradation of heat transfer performance.In broader terms, fouling is the result of material build-up on the walls and can be attributed to chemical, biological, deposition, and corrosion mechanisms.Regardless of the type, they result in a decrease in heat transfer efficiency.Estimates can be made to quantify the decreased efficiency, which is defined in terms of a fouling resistance, Rf, and varies based on a given system design and flow conditions such as water quality, temperature, velocity, etc. Considering a system representative of the RCCS (untreated cooling water at temperatures up to 115°C and flow velocity less than 1 m/s) a fouling resistance of ~0.0005 K/W-m 2 may be expected.The impact on the overall heat transfer coefficient can be determined based on equation ( 2), where Uf is the overall heat transfer with fouling, Rf is the fouling factor, and Uc is the heat transfer coefficient of a clean system [8].
At normal conditions where the RPV temperature is ~220°C and RCCS is operating with a water inlet temperature of 30 °C, models indicate that water in the riser tubes will flow at ~0.065 m/s and transfer heat from the walls at a convective rate in the range of 900 -1,500 W/m 2 -K.If a fouling resistance of 0.0005 K/W-m 2 is introduced, this convective rate drops to a range of 620 -750 W/m 2 -K.One of the primary factors for this high level of fouling is the velocity, which becomes significant at low flow velocities, shown in Figure 9. Furthermore, this rate of heat transfer degradation will continue with to decrease time and is likely to follow either a log or power dependence as shown in Figure 10.Since fouling impacts many applications across various industry, a large amount of work has been made to identify effective techniques to control against its impact.In cooling water systems, the most common is the addition of chemicals corrosion inhibitors, which form a protective film or barrier on the metal surfaces.This method may impact heat transfer by the fluid due to film build-up and reduced fluid thermal performance and requires regular monitor to ensure chemical levels are adequate for continued protection.Commercially available corrosion inhibitors typically require dilution levels in the range of 10 -100 mL/L, or between 1 -10% of the total water volume [10].A wide range of other additive-based options, such as nanoparticles, polymers, organic compounds, etc., are also available and widely used in various applications [11].Another commonly used technique is the introduction of cathodic protection via a sacrificial anode such as zinc or magnesium, however, is difficult to control and requires frequency replacement of the anode material [12].
In consideration for possible treatment methods of a water based RCCS, requirements specific to nuclear safety present unique demands and limit the range of viable options.Furthermore, the reliance on natural circulation heat transfer to maintain adequate levels of decay heat removal performance excludes many of the chemical solutions where the build-up of protective film would hinder the convective performance of the cooling panel tubes.
The reduction of dissolved oxygen (DO) is identified as one viable method as it maintains the simplicity in design and operation without chemical or mechanical additives.Removal of DO can be achieved with several techniques, including but not limited to sustained boiling, purging with an inert gas, and sonication.A comparison of these was made by Butlter et al, 1994 [13] and determined that purging with nitrogen gas was the most effective and adequately cost effective for most applications.In their work, a 1.0 L tank of deionized water (initial DO concentration of ~8.5ppm) was purged over a 60-minute period with purified nitrogen at a gas rate of 25 mL/sec.Within 10 minutes DO levels dropped to ~0.5-ppm, and after 30 minutes of purging dropped to 0.3-ppm.Additional purging beyond saw diminishing returns, reducing to only 0.25-ppm after a total of 60-minutes.It was also noted that ultra-high purity nitrogen was no more effective for removing oxygen than the cheaper pre-purified (laboratory) grade gas.
Currently, the design of the full size HC-HTGR RCCS contains a total water volume of approximately 230-tons, or ~234,000-L of water.Preserving the nitrogen to fluid ratios identified by Butler, 372,000 ft 3 of nitrogen would be needed to reach a DO concentration below 0.3-ppm.This volume falls conventionally within the capacity of a standard tanker truck, which can hold 500,000 ft 3 of compressed liquid N2.Though this method would provide acceptable water quality levels initially, ingress of ambient outside air (for example via breather ports for water expansion/contraction in the system) would create a pathway for the reintroduction of oxygen into the system.Thus, additional considerations would need to be made for a continuous and long-term method for maintaining water quality.Possibilities include maintaining a small positive pressure within the gas space above the tank water level, which would create a blanket of cover gas shielding the water surface from the oxygen rich environment.An inert gas such as argon would reduce the amount of gas flow needed to maintain the blanket given the higher density and lower potential for egress by diffusion.Similarly, a slow-flow continuous purge of nitrogen through the piping, etc. gas space may also be able to achieve this goal.Further evaluation of design and operating details would be needed to confirm the effectiveness of such a system, including an assessment of the reliability, long-term operational costs, failure points, and their impacts.
Based on the design study, the RCCS of the HC-HTGR has been updated to have improved thermal performance for the reference design condition.The HC-HTGR RCCS design will be finalized based on the calculations for the cases of particular interest in the design process such as the case of a quarter or half of the riser tubes not working.Then, the RCCS design will be integrated into the primary system analysis using SAM to simulate selective accident scenarios of interest.It will also continue interacting with other efforts made in the project such as shielding structural/seismic, and primary system thermal hydraulics, which would have system interfaces with the RCCS.

Task 2 Update: Primary System Heat Removal Analysis
The preliminary analysis of the primary heat transport system begun in the second half of FY22.Various modeling approaches were identified to provide different fidelity levels.An assembly level approach utilizing a coupled 1D fluid and 3D solid model using System Analysis Module (SAM) [14] was considered first to produce a high-resolution prediction of the temperature distribution in selective core assemblies.This method allows locally asymmetric designs of typical HTGRs to be fully resolved while still utilizing the advantages in computational efficiency and robustness of 1-D fluid modeling for the coolant channel assembly level modeling.Using this method works best at steady state conditions where fuel assembly temperature distributions can be assumed to be independent from the conditions of adjacent assemblies.This model was applied to analyze a peak power assembly design.A peak fuel temperature at nominal operating conditions, and the impact of the bypass channel cooling with resulting impact on fuel temperature was investigated to inform the core design.
Although the 1D-3D method provides some computational efficiency compared to a 'Fully 3D model', it is still too costly to be used widely as a full core and transient analysis tool.To address these limitations, additional modeling methodologies are being developed.In the second half of FY22, preliminary work on the development of a reduced order model was done.This model is suited to predict the core wide coolant flow distribution, average and peak fuel and coolant temperatures, and to model certain operational and accidental transients.This section summarizes the progress in the first half of FY23 on the primary system heat removal analysis.A single assembly reduced order model has been tested and analyzed with a direct code-to-code comparison against the 3D-1D assembly model.This model can now be expanded to the entire core, though additional considerations are needed to address the impacts of bypass flows.Along with the single assembly model, a homogenized assembly model was pursued to allow the full core to be modeled with a much coarser mesh thus reducing computational costs.Lastly, a demonstration case study was performed integrating a simplified 3D-core model with the RCCS model, potentially applied in the transient safety analyses of HC-HTGR design basis accidents.

Development of Primary System Reduced Order Model
The reduced order model is best suited for full core steady state and operational transients where fuel to coolant channel heat transfer is the dominant heat transfer path.In cases where core wide heat transfer becomes significant, as is the case for loss of primary flow scenarios, a full core 3D heat transfer model is needed.Modeling the full core with each fuel pin and coolant channel resolved presents challenges from a computational cost perspective.
The reduced order model for a single assembly was developed to provide a less computationally demanding alternative to the 1D-3D coupled model that was originally developed for thermal hydraulic analysis of HC-HTGR fuel assemblies.This model uses a fuel-coolantmatrix unit cell to represent a full assembly or assembly sub-region.The unit cell is then reduced from three dimensions to two (X-Z) dimensions to significantly reduce the computation size.As shown in Figure 11, a fuel centered unit cell was chosen in an effort to reduce distortions in the peak fuel temperature predicted by the model, a key safety parameter.When developing this reduced order model, several parameters were conserved in an effort to improve the utility of the model.To preserve the thermal inertia of the unit cell, the volume of each component is preserved in the reduced dimension model.Because a fuel centered unit cell was chosen, the fuel volume is inherently preserved in the reduced order model.For the graphite matrix this is done by manipulating the outer radius.To accurately predict the peak fuel temperature, it was necessary to ensure the thermal resistance between the fuel and coolant is preserved in the reduced order model.To do this, a numerical model of the unit cell was compared against Equation 3gives the equation for the thermal resistance of the analytically calculated thermal resistance of the reduced order model given by equation (3).
Where:  ; is the outer matrix radius,  0 is the outer fuel radius, k is thermal conductivity.
The analytical unit cell model, shown in Figure 12, had a uniform volumetric heat generation applied in the fuel pin and constant temperature condition applied at the coolant channel boundaries.The thermal resistance was then calculated using equation ( 4). Where: T ? 1 ,ABC is the average temperature on the outer radius of the fuel, T DEE2A3F is temperature boundary condition applied at the coolant channel, Q is the heat flux.It was found that with the same matrix thermal conductivity used both models, the thermal resistance was a factor of 2.5 greater in the unit cell model compared to the reduced order model.This is due to a combination of two factors: the matrix thickness between fuel and coolant is 1.25 times greater in the reduced order model in order to preserve the total graphite volume; and only half of the matrix cross section in the unit cell provides a path to the coolant.Thus, a factor of 1/2.5 is applied to the matrix thermal conductivity in the reduced order model.Figure 13 shows a comparison of the temperature distribution predicted by a 1D-3D model of the unit cell and the reduced order model.In addition to the steady state case, a transient test was performed.The test conditions, shown in Figure 14, involve a power reduction followed by a coolant flow reduction, both to half of the initial condition.Results for peak fuel temperature and average graphite temperature in each model are shown in Figure 15.As a demonstration case, the reduced order model was applied to the assembly with the peak power generation and compared with a 1D-3D model.As shown in Figure 16, two reduced order models were used, one representing the peak power unit cell and one with the average power of the remaining unit cells.The reduced order model predicted a peak fuel and coolant temperatures of 1549 K and 1468 K respectively while the 1D-3D model predicted peak fuel and coolant temperatures of 1581 K and 1472 K, respectively.This discrepancy indicates that the reduced computational costs of the reduced order model likely come at the expense of accuracy indicating the need for both the reduced order model and 1D-3D assembly model to predict peak fuel temperatures.It should also be noted that this analysis did not include impacts of the bypass flow channels on the side surfaces of the fuel assembly.This complexity is difficult to include in the reduced order model and should be investigated in future efforts if the need arises.
Figure 16 Discretization of an assembly using the reduced order model.

3D Core Conduction Model
A helium circulator trip resulting in a pressurized conduction cooldown (PCC) is a key scenario that must be evaluated to establish a safety case for the HC-HTGR.In this scenario decay heat produced in the fuel pins must be transferred across the core to the reactor cavity cooling system (RCCS) outside the core barrel.Unlike the normal operating condition where the overwhelming majority of the energy produced in fuel pins is removed by neighboring coolant channels, a PCC involves heat transfer across the entire core.This domain size makes a PCC computationally costly to model unless efforts are made to reduce the domain size.For example, Hua et al. [15] implemented the ring model approach proposed by Strydom et al. [16] to analyze a PCC scenario in the High Temperature Test Facility (HTTF).The horizontal orientation of the HC-HTGR makes the assumption of azimuthal symmetry used to develop the ring model invalid due to several factors.First, the RCCS must still operate with a flow rate against gravity, perpendicular to the core flow direction giving an asymmetric heat transfer boundary condition at the outer surface of the reactor pressure vessel.Additionally, bypass gaps will accumulate at the top of the reactor while gravity pushes the core downwards creating additional asymmetries in the core.Because of these factors, only one axis of vertical symmetry can be applied to the core for PCC analysis compared to the full azimuthal symmetry required for the ring model.
A half-core model with every fuel pin and coolant channel resolved will result in excessive computational costs making additional simplifications necessary.To address this, a homogenized core approach is being pursued.With this method, fuel pins and coolant channels are not resolved in the mesh; instead, a coarse mesh with uniform material properties is used.The density and heat capacity of this material are determined by a weighted average of assembly materials.To determine the effective thermal conductivity, a numerical study is performed in which a small temperature gradient (2K) is applied across opposite ends of an assembly and the heat flux measured, allowing the effective thermal conductivity to be calculated.This procedure is repeated for a range of temperatures to produce the temperature dependent thermal conductivity curve shown in Figure 17.Because the fuel assemblies are not designed with 90° rotational symmetry, this process was repeated with the temperature gradient applied in the x and y dimensions, though the difference in the effective thermal conductivity was found to be negligible.To understand how the homogenized core modeling approach might impact the accuracy of decay heat removal, a PCC scenario was modeled in a fully resolved 3D assembly with adiabatic boundary conditions.Figure 18 shows the peak fuel temperature and peak matrix temperature during the transient.After about 20 seconds the temperature difference between the two drops to only a few degrees K, indicating that for a large majority of a PCC transient it is not necessary to resolve individual fuel pins to approximate the peak temperature in the core.Figure 18 also shows extended transient results using the isolated assembly model to give additional insight into how the full core will behave in a PCC.Despite decay heat energy being added to the assembly with no heat removal modeled, the peak fuel and matrix temperature remains below the initial nominal steady state temperature for over 4 hours.This is because the large thermal inertia of the graphite matrix acts as an effective heat sink during this phase of a PCC transient.In reality, the assembly will not be isolated, instead, heat will flow outward to the reactor cavity cooling system which acts as the ultimate heat sink allowing temperatures in the reactor to remain below safety limits indefinitely.Thus, to ensure the transient is accurately modeled, the RCCS must be included in the full core model.Its inclusion is discussed in chapter 3.3.

Integration of RCCS into SAM Primary System Analysis
The RCCS of the HC-HTGR aims to remove sufficient decay heat to prevent fuel and other structural components within the core from exceeding their temperature safety limits.It is designed to operate relying on natural circulation flow driven by density difference and gravity, where the RCCS flow is perpendicular to the axial dimension of the core from unique horizontal core of the HC-HTGR.In the initial stages of the HC-HTGR RCCS design and analysis, it was modeled with an assumed temperature condition on the RPV wall.This model was used primarily to assess how RCCS design changes impacted to its heat removal capabilities [2]. Figure 19 shows the schematic of the latest water panel design of HC-HTGR RCCS with the core.In the event of a primary system failure, decay heat must be conducted from the fuel assemblies (red), across the reflector (light grey), and reactor pressure vessel (dark gray) where it is transferred to the RCCS water panel (green) via thermal radiation.Since the RPV temperature is dependent on the condition within the reactor core, which may vary widely throughout a decay heat removal transient.Therefore, it is necessary to create a model that incorporates the RCCS with the primary system analysis for a complete performance analysis of the RCCS.To demonstrate the framework developed to thermally couple the HC-HTGR core with the RCCS, a simplified domain for the HC-HTGR with RCCS water panel has been prepared.The MOOSE heat conduction module is used to model a two-dimensional cross section of the core, and this model is coupled with a one-dimensional fluid SAM model of a segment of the RCCS water panel using the MOOSE MultiApp system.For simplicity, a 550 K boundary condition was applied at the outer surface of the active core region.The inlet conditions of the RCCS were determined based on temperature and flow rate obtained from RELAP5 analysis of the full RCCS in this demonstration case.This shows potential extension of integrating between SAM and RELAP5 model of the RCCS with a "loose" coupling scheme between SAM and RELAP5 models of the RCCS for further model development.The coolant inlet conditions of the riser tubes are supplied to SAM via the RELAP5 model while the power removed by the RCCS calculated by SAM is given to the RELAP5 model.This allows the SAM model can have high-fidelity primary system analysis results with taking advantages of full RCCS RELAP5 model.
The coupling scheme for the reactor core-RCCS model is shown in Figure 20.The twodimensional heat conduction model contains the reactor core and a plane representing the corefacing surface of the RCCS water panels.Using the "ConstantViewFactorSrufaceRadiation" MOOSE UserObject, the radiation heat transfer between the outer RPV surface and the water panel wall is calculated and applied to the outer wall of the one-dimensional RCCS SAM model.The view factor between adjacent RPV and RCCS surfaces is currently assumed to be one for simplicity, though this will be updated with calculated view factors in future iterations of the model.The riser wall temperature distribution calculated by SAM is then transferred to water panel wall.This process is repeated until the convergence condition is met.In the current iteration of the model, the outer RPV wall and the water panel are discretized with six surfaces, two for each straight segment of the water panel.When the model is expanded to a full 3D representation of the core, additional discretizations will be made in the axial direction.The number of discretizations will be investigated to determine the impact on model accuracy and computational costs.The water panel of the RCCS is modeled with SAM's PBPipe component.This model approximates the water panel as a one-dimensional fluid component and an axisymmetric twodimensional wall component.To confirm that this reduced order approximation will not introduce a significant error into the model, a three-dimensional model of a segment of the water panel was modeled and compared to the reduced order results.The three-dimensional water panel was modeled by SAM using the coupled 3D solid-1D fluid technique.As shown in Figure 21 (a), there is only a 0.5 K temperature range across the panel cross section, which is consistent with 3-D CFD results [1].When this three-dimensional temperature distribution compared to the outer wall temperature in the reduced order model is observed less than 0.5 K difference, thus the axisymmetric model is not expected to introduce a significant error to the core-RCCS coupled model, despite the asymmetric riser panel shape and heat flux.Along with the reduced order model, the three-dimensional model of the water panel would be adopted as needed for any transient simulations when a significant temperature gradient across the water panel is expected.A simplified demonstration case of the reactor core-RCCS coupled model was compared with the RCCS only model using RELAP5-3D, summarized in Table III.With a 550 K temperature condition applied at the outer boundary of the active core region, the model predicts that the for the half of the core modeled, 12.5 kW would be transferred to the water panel per meter of core length.This equates to 0.225 MW of heat removed by the RCCS.At this boundary condition, the average temperature is 470 K and 315 K on the RPV outer wall and water panel wall, respectively.By comparison, RCCS only model using RELAP5-3D predicted 0.220 MWth heat removed with a 493 K applied temperature condition at the RPV outer wall, indicating a good agreement between the two model.As discussed, there are several items that can be addressed to increase the utility of this model.Most importantly is the active core region model.Additional development of the homogenized core model is needed before it can be fully implemented into the full core 3D conduction model.For example, a method to map the steady state initial condition onto the homogenized mesh must be developed and verified.It also must be demonstrated that homogenized mesh does not result in significant errors early in the transient when there are greater temperature variations between fuel pins and the surrounding matrix.Finally, several gaps exist within the core (between adjacent assemblies, between assemblies and reflector, between reflector and pressure vessel) that may significantly impact the heat transfer paths in a decay heat removal transient.These gaps must be modeled accurately without adding significant computational costs to the model.Additionally, a multi-scale modeling approach will be utilized such that the location where the hottest fuel pin is expected will be modeled explicitly using boundary conditions determined by the homogenized model.This will confirm that temperature safety limits will be exceeded in fuel pins.

Figure 1
Figure 1 Major design changes of the water panel of HC-HTGR RCCS (Not scaled)

1 )
Table II Thermal performance by top tank injection elevation and top tank elevation in the reference design

Figure 3
Figure3Initial concept of the RCCS for the HC-HTGR[3]

Figure 5
Figure 5 RPV temperature and natural circulation flow rate during DCC (natural circulation flow rate after boiling mass flow rate was omitted.)

Figure 6 A
Figure 6 A schematic of the updated RCCS loop configuration as of March 2023

Figure 7
Figure 7 Potential RCCS configuration for the HC-HTGR to have 2 independently operating loops.

Figure 8
Figure 8 System temperature changes and natural circulation flow rate by tank elevation

Figure 9 Figure 10
Figure 9 Fouling resistance versus change in flow velocity, based on correlation from [9]

Figure 12
Figure 12 Numerical unit cell model.

Figure 13
Figure 13 Comparison of axial temperature distribution between the reduced order model (2D) and unit cell model (3D).

Figure 14
Figure 14 Power and coolant flow conditions of transient test.

Figure 15
Figure 15 Peak fuel (left) and average graphite (right) temperatures during transient test for the reduced order (RO) models and 3D unit cell model.

Figure 17
Figure 17 Comparison of component thermal conductivities with the numerically determined effective thermal conductivity.

Figure 18
Figure 18 Comparison of peak fuel temperature and peak matrix temperature in an isolated assembly model.

Figure 19 A
Figure 19 A schematic of HC-HTGR core and RCCS (cross sectional view)

Figure 20 A
Figure 20 A schematic of coupling scheme showing transferred parameters between 3D core -1D riser tube of the RCCS coupled model Figure 21 Three-dimensional water panel model results

Table I A
comparison of design specifications of the water panel

Table III
Summary of core-RCCS coupled and RCCS only models for the demonstration case