Effect of the KRUSTY Reactor Core Insulation Layer on Power

ZHANG Jie1,2,3 LIU Fudong1,2 WANG Kunpeng1,2

1. Nuclear and Radiation Safety Center, Ministry of Ecology and Environment, Beijing 102401
2. State Environmental Protection Key Laboratory of Nuclear and Radiation Safety Regulatory Simulation and Validation, Beijing 102401
3. School of Mechanical and Power Engineering, Shanghai Jiao Tong University, Shanghai 200240

Abstract Small modular reactors have the characteristics of simple structure, convenient construction, and ease of deployment. The heat-pipe reactor is a type of small modular reactor, and it operates in a load-following mode. KRUSTY (Kilowatt Reactor Using Stirling TechnologY), as the prototype of the heat-pipe Kilopower reactor, has undergone relevant testing and achieved satisfactory results. To further optimize the structure of KRUSTY, gain an in-depth understanding of the influence of the insulation layer on the reactor, and improve the efficiency of reactor output energy, a study was carried out. KRUSTY was modeled using the multiphysics software Simscape, and the model was modified to varying degrees according to different schemes (Schemes 1–6). The reactor behavior of each scheme was calculated under the conditions of 0.6 $ reactivity startup, ±40 pcm reactivity insertion, and ±50% load change. Among them, Scheme 6 had the highest energy output efficiency, reaching 79.71%. The results show that, when the number of voids among structures such as the core, vacuum vessel, and reflector is increased, and when a relatively thick insulation layer is contained inside the vacuum vessel, the efficiency of the energy exported from the reactor is higher.

Keywords Simscape; KRUSTY; insulation layer; heat-pipe reactor; transient analysis

CLC number TL333

The effect of insulation layer of KRUSTY on reactor power

ZHANG Jie1,2,3 LIU Fudong1,2 WANG Kunpeng1,2

1. (Nuclear and Radiation Safety Center, Ministry of Ecology and Environment, Beijing 102401, China)

2. (State Environmental Protection Key Laboratory of Nuclear and Radiation Safety Regulatory Simulation and Validation, Beijing 102401, China)

3. (Shanghai Jiao Tong University, School of Mechanical Engineering, Shanghai 200240, China)

Abstract [Background]: Small modular reactor has the characteristics of simple structure, convenient construction and easy deployment. As a type of small modular reactor, the heat pipe reactor operated in load following mode. Kilopower is a typical heat pipe reactor designed to provide 1 to 10 kilowatts of electricity in space or on the surface of a planet or moon. As the prototype of the heat pipe reactor Kilopower, The Kilowatt Reactor Using Stirling TechnologY (KRUSTY) has been tested and achieved satisfactory results. [Purpose]: This study aims to optimize the structure of KRUSTY, understand the influence of insulation layer on the reactor, and improve the efficiency of reactor output energy. [Methods]: Firstly, the multi-physics software Simscape is used as the system analysis tool, and the reactor power calculation module, heat pipe module and so on are added for the simulation of heat pipe reactor. Secondly, taking KURSTY as the object, the system model of different insulation thickness schemes (Case1–Case6) is built. Finally, the reactor behavior under the conditions of 0.6 $ reactivity startup, ±40 pcm reactivity introduction and ±50% load change is studied, and the calculation [[unclear: sentence continues off visible page]]

Fund support: Inherent Safety Integrated Small Fluoride Salt Cooled High Temperature Reactor Technology Research Project (Grant No. 2020YFB1902000)

First author: ZHANG Jie, male, born in 1982, received his doctoral degree from the University of Chinese Academy of Sciences in 2019; research field: reactor thermal hydraulics. E-mail: shenmue@foxmail.com

Corresponding author: LIU Fudong, E-mail: liufudong1968@sina.com

Date received: 2024-00-00; date revised: 2024-00-00

Supported by Inherent Safety Integrated Small Fluoride Salt Cooled High Temperature Reactor Technology Research Project.

First author: ZHANG Jie, male, born in 1982, graduated from University of Chinese Academy of Sciences with doctoral degree in 2019, focusing on reactor thermohydraulic.

Corresponding author: LIU Fudong, E-mail: liufudong1968@sina.com

results under different schemes are compared. [Results]: Among them, the energy output efficiency of case 6 is the highest, reaching 79.71%. Moreover, the influence of each working condition on the energy output efficiency of case 6 is also minimal. [Conclusions]: The results show that the efficiency of the reactor's energy output is higher when the number of gaps is increased between the core, the vacuum tank, the neutron reflector and other structures, and the vacuum tank contains a thick insulation layer.

Key words　Simscape, KRUSTY, insulation layer, Heat pipe cooled reactor, Transient analysis

As reactors develop toward miniaturization, research and development of small modular reactors (SMRs, small modular reactors) have improved markedly. For scenarios with relatively small power demand, small modular reactors can not only provide energy but, compared with full-scale light-water reactors, also have the characteristics of being more economical, safer, and easier to construct. Microreactors, as still smaller reactors, can be built in a factory environment, facilitating deployment and transport, and they have abundant application scenarios. For example: supplying power to remote areas, supplying power to islands, and supplying power to planetary-surface bases.

A typical example of a microreactor is Kilopower, proposed by the U.S. National Aeronautics and Space Administration (NASA, National Aeronautics and Space Administration)[1-2]. This reactor aims to provide 1 to 10 kW of electric power for spacecraft or landers, and its prototype was named KRUSTY. As the representative of the 5 kW-thermal Kilopower space reactor, KRUSTY had design, R&D, manufacturing, and testing costs of less than USD 20 million, and final testing was completed in March 2018[3].

The heat-pipe reactor type adopted by KRUSTY has many differences from the design of traditional reactors[4-6]. This paper takes KRUSTY as the target and studies the significance of a core insulation layer and its influence on reactor power[7].

1　Significance of the Insulation Layer

In traditional reactors, in order to reduce the core temperature after shutdown and avoid the influence of decay heat on reactor safety, it is often necessary to set up various heat-dissipation systems. However, in KRUSTY or any low-power high-temperature reactor, this heat-dissipation phenomenon needs to be avoided as much as possible. The reason is that the process of outward heat transfer accompanying the high temperature of the reactor will waste a large amount of thermal energy; the lost heat seriously affects the thermal efficiency of the reactor and thereby affects the overall performance of the reactor. By contrast, the relatively low power makes the influence of core decay heat very weak and does not pose a serious threat to reactor safety[6,8].

To reduce heat loss, work must be carried out in two respects. One is to maintain a vacuum environment around the core, thereby reducing the effects of heat conduction and thermal convection; the other is to use insulating materials to construct an insulation layer outside the core, so that it is difficult for thermal energy acquired by structural materials such as the core reflector layer to diffuse further into the external environment.

In space, the vacuum environment of a space reactor is relatively easy to obtain. However, the requirements for insulation materials are very stringent. Traditional insulation materials not only have large mass and are unsuitable for use in space reactors; more importantly, a larger thickness will also increase neutron absorption, thereby affecting core reactivity. In response, the use of multilayer insulation (MLI, multilayer insulation) has become the preferred solution to this problem. Because it is small in volume and light in mass, and has multiple radiation gaps, it can greatly reduce the thermal conductivity of the material.

In KRUSTY, the MLI is composed of aluminum foil and fused-silica braided strands that separate the layers of aluminum foil. Aluminum has the characteristics of low emissivity, high-temperature resistance, and acceptable neutron absorption; fused-silica braided strands have the characteristics of high-temperature resistance and low thermal conductivity. This composition limits the potential contact between aluminum foils, thereby reducing thermal conductivity, and is the ideal choice for MLI.

2　Research Method

By simulating the reactor state under different core-insulation-layer configurations, the significance of the insulation layer for KRUSTY and further optimization recommendations are obtained.

2.1　Simulation Tool

Simscape is a modeling and simulation tool for multidomain physical systems. It runs in the Simulink environment and can conveniently and rapidly create physical system models. In this paper, Simscape will be used, and custom component models such as the point reactor and heat pipe will be created using the MATLAB-based Simscape language. With the aid of Simscape, a heat-pipe reactor physical component model based on physical connections is built, and system analysis is carried out.

2.2 Simulation Method

2.2.1 Neutron-physics model

The point-reactor neutron-kinetics equations with six delayed-neutron groups are used to treat the transient characteristics of reactor power.

$$ \frac{dn(t)}{dt}=\frac{\rho(t)-\beta}{\Lambda}n(t)+\sum_{i=1}^{6}\lambda_i C_i(t) \tag{1} $$

$$ \frac{dC_i(t)}{dt}=\frac{\beta_i}{\Lambda}n(t)-\lambda_i C_i(t)\qquad i=1,2,\ldots,6 \tag{2} $$

where \(n(t)\) is the neutron density (power level), \(\mathrm{m^{-3}}\); \(\rho(t)\) is the total reactivity; \(\beta_i\) is the delayed-neutron fraction of the \(i\)-th group; \(\beta\) is the total delayed-neutron fraction; \(C_i\) is the concentration of precursor nuclei of the \(i\)-th delayed-neutron group, \(\mathrm{m^{-3}}\); \(\lambda_i\) is the decay constant of this group, \(\mathrm{s^{-1}}\); and \(\Lambda\) is the neutron generation time, \(\mathrm{s}\).

$$ \rho(t)=\rho_{ext}(t)+\sum_{j=1}^{N}\rho_{j,e}(t) \tag{3} $$

$$ \rho_{j,e}(t)=\alpha_{j,e}\left(\overline{T_j}(t)-T_{j,0}\right) \tag{4} $$

where \(\rho_{ext}(t)\) is the externally introduced reactivity; \(\rho_{j,e}(t)\) is the reactivity introduced by the temperature change in region \(j\); \(\alpha_{j,e}\) is the temperature-reactivity feedback coefficient of region \(j\), \(\mathrm{K^{-1}}\); \(\overline{T_j}(t)\) is the average temperature of region \(j\), \(\mathrm{K}\); and \(T_{j,0}\) is the initial temperature of region \(j\), \(\mathrm{K}\).

2.2.2 Thermal model

An improved thermal-resistance-network method is used to simulate the heat pipe (as shown in Fig. 1): on the basis of the traditional thermal-resistance-network method \([9\text{-}11]\), more nodes are divided \([12\text{-}13]\), and vapor thermal resistance is considered.

Fig. 1 Division method of heat pipe block

The radial heat-transfer thermal resistance \((\mathrm{K\cdot W^{-1}})\) of the pipe wall and wick is:

$$ R_r=\frac{\ln\left(\frac{r_o}{r_i}\right)}{2\pi l\lambda} \tag{5} $$

The axial heat-transfer thermal resistance \((\mathrm{K\cdot W^{-1}})\) of the pipe wall and wick is:

$$ R_z=\frac{l}{\pi\left(r_o^2-r_i^2\right)\lambda} \tag{6} $$

Here, \(r_o\) and \(r_i\) are the outer and inner radii, respectively, of the heat-pipe wall (or wick) corresponding to the divided segment block, m; \(l\) is the length of the heat-pipe region corresponding to the divided segment block, m; and \(\lambda\) is the thermal conductivity of the segment block, \(\mathrm{W\cdot(m\cdot K)^{-1}}\).

The vapor–liquid interfacial thermal resistance \((\mathrm{K\cdot W^{-1}})\) is:

\[ R_{lv}=\frac{R_0T_v^2}{h_{fg}^2P_vr_vl}\sqrt{\frac{R_0T_v}{2\pi}} \tag{7} \]

The vapor heat-transfer thermal resistance \((\mathrm{K\cdot W^{-1}})\) is:

\[ R_v=\frac{4T_v\mu_vl}{\pi\rho_v^2r_v^4h_{fg}^2} \tag{8} \]

Here, \(R_{lv}\) is the vapor–liquid interfacial thermal resistance, \(\mathrm{K\cdot W^{-1}}\); \(R_v\) is the vapor heat-transfer thermal resistance, \(\mathrm{K\cdot W^{-1}}\); \(R_0\) is the gas constant of the working fluid, \(\mathrm{J\cdot(kg\cdot K)^{-1}}\); \(T_v\) is the vapor temperature, K; \(P_v\) is the (saturated) vapor pressure, Pa; \(h_{fg}\) is the latent heat of vaporization of the working fluid, \(\mathrm{J\cdot kg^{-1}}\); \(r_v\) is the vapor-cavity radius, m; \(l\) is the axial length of the vapor cavity in the computational domain, m; \(\mu_v\) is the dynamic viscosity, \(\mathrm{Pa\cdot s}\); and \(\rho_v\) is the (saturated) vapor density, \(\mathrm{kg\cdot m^{-3}}\).

Meanwhile, the vapor heat-transfer part also needs to consider the effect of the heat-transfer limit. When the heat transfer exceeds the maximum heat-transfer capacity at that temperature, the vapor heat-transfer thermal resistance changes accordingly, so that the heat transfer is equal to the maximum heat-transfer capacity at that temperature.

2.3 System model

A KRUSTY model is established[^14]. The segmentation scheme is shown in Fig. 2, in which the outermost side of the reflector or shielding layer exchanges heat with the external environment by thermal radiation. The schematic of the core cross section is shown in Fig. 3.

Fig. 2 KRUSTY segment diagram
Fig.2 Block diagram of KRUSTY

Fig. 3 Core schematic diagram
Fig.3 Core schematic

For convenience of study, the condenser sections of all heat pipes are cooled with nitrogen, that is, the simulator cooling scheme used in the KRUSTY experiment, rather than the Stirling engine scheme.

To study the effects of the MLI insulation layer and the vacuum isolation between components on the core power, the following schemes were simulated, and the calculation results were compared[^15-^17]:

1) No insulating material MLI; the core, vacuum vessel, and reflector are in direct contact
2) No insulating material MLI; the core, vacuum vessel, and reflector are not in direct contact
3) With insulating material MLI; the core, vacuum vessel, and reflector are in direct contact
4) With insulating material MLI; the core, vacuum vessel, and reflector are not in direct contact
5) Same as 4, with the MLI thickness reduced to 0.5 times the original value
6) Same as 4, with the MLI thickness increased to 2 times the original value

Among these, Case 4 is the configuration adopted by KRUSTY. Its specific arrangement is as follows: 8 layers of MLI are placed between the fuel/clamp and the vacuum vessel, and 4 layers of MLI are placed between the fuel and the axial reflector.

3 Calculation Results

3.1 Startup with 0.6 $ reactivity

Taking the method of introducing reactivity in Case 4 as the standard, the other cases (Cases 1, 2, and 3) are also introduced with the same reactivity at the same time, ultimately yielding the following results (Fig. 4). As can be seen from Fig. 4a, when the same reactivity is introduced, the power change in Case 1 is the largest, and it finally stabilizes at around 16700 W; the power change in Case 3 is also relatively large and finally stabilizes at around 2150 W; the power changes in Cases 2 and 4 are the smallest, eventually oscillating at about 500 W.

It is not difficult to see from the model structure that, because of the lack of sufficient thermal insulation measures, the heat generated in the core in Case 1 can readily diffuse to the reflector, causing the reflector temperature to rise. Since the temperature reactivity coefficient of the reflector is positive, the temperature increase further promotes an increase in core power, ultimately causing the core power to be far higher than in the other cases and to remain at a high power level.

In Case 3, the presence of the insulating material MLI hinders, to a certain extent, the diffusion of heat from the core to the reflector, so that the core power is only slightly higher than that in Case 4 and far lower than that in Case 1.

In Case 2, its power differs very little from that of Case 4. This phenomenon indicates that the thermal insulation effect of vacuum is far superior to that of the insulating material. However, to avoid the operating condition in which components come into contact with one another due to accidents, it is necessary to add insulating material. Otherwise, the condition of Case 1 would occur. Moreover, when the vacuum level is insufficient, a condition similar to Case 1 will also occur.

As can be seen from Fig. 4b, the energy removed through the heat pipe is the greatest in Cases 2 and 4, with the peak value reaching about 730 W and eventually stabilizing at around 300 W. The energy removed in Case 3 is around 130 W; the energy removed in Case 1 is almost 0. This result once again demonstrates the significance of Case 4: it can remove more energy at a lower reactor-core power.

Figures 4c and 4d show that, in general, the differences in core temperature among the cases are relatively small; only the minimum core temperature in Case 1 differs greatly from those in the other cases, being about 160°C lower.

a) Core power curve

a) Fission power

b) Heat-pipe energy removal curve

b) Energy derived from heat pipe

c) Maximum temperature of outer wall of the core

d) Minimum temperature of outer wall of the core

Fig. 4 Data from 0.6 $ run

3.2 Transient condition with introduction of 40 pcm reactivity

To further investigate the influence of the insulation material MLI in Scheme 4, the system was simulated by introducing reactivity and changing the load, and the results were compared with those of Schemes 2, 5, and 6. As can be seen from Fig. 5a, the reactor powers of the various schemes are very close: the initial power is approximately 3000 W, the peak power is approximately 4470 W, and the final power stabilizes at around 3130 W. Fig. 5b shows the energy extracted through the heat pipes. Scheme 2 has the lowest initial power, about 2300 W, and also the lowest output power in the steady stage, about 2370 W, with the power increasing by about 70 W. Scheme 6 has the highest initial output power, about 2380 W, and also the highest output power in the steady stage, about 2460 W, with the power increasing by about 60 W. Table 1 lists the energy output efficiency (i.e., heat-pipe output power/total power). It is not difficult to find that the thickness of the insulation material MLI has a certain influence on the output power in the heat-pipe condensation section. When the total reactor power is fixed, the thicker the insulation layer, the greater the power extracted through the heat pipes. Figs. 5c and 5d show the core temperature. It can be seen that the thicker the insulation layer, the better the insulation effect, and the higher the reactor-core temperature.

a) Fission power

b) Energy derived from heat pipe

c) Maximum temperature of outer wall of the core

d) Minimum temperature of outer wall of the core

Fig. 5 Calculation results of 40 pcm reactivity introduction accident

Table 1 Energy output efficiency after 40 pcm reactivity introduction

3.3 Transient condition with introduction of -40 pcm reactivity

Similar to the condition with the introduction of 40 pcm reactivity, among Cases 2, 4, 5, and 6, the scheme with the thicker insulation layer has a higher steady-state core temperature and thus exports more energy.

From the conditions with the introduction of $\pm 40\ \mathrm{pcm}$ reactivity, the following conclusion can be drawn: when the initial reactor core total power is fixed, the thicker the insulation layer, the better the insulation effect, and the more energy is exported through the heat pipes. This conclusion is not altered by the introduction of reactivity.

a) Fission power

b) Energy derived from heat pipe

c) Maximum temperature of outer wall of the core

d) Minimum temperature of outer wall of the core

Fig. 6 Calculation results of -40 pcm reactivity introduction accident

Table 2 Energy output efficiency after −40 pcm reactivity introduction

3.4 Load-Increase Transient Condition

As the reactor operating under load-following mode, the heat-pipe reactor uses its load to directly determine the magnitude of the reactor power. In the present simulation scheme, because a simulator cooling scheme was adopted—i.e., the heat pipes were cooled by nitrogen—load increase was simulated by increasing the flow velocity by 50%. As can be seen from Fig. 7a, the total core power increases from 3000 W to approximately 4500 W, and finally stabilizes at about 4000 W. At the same time, the power conducted out through the heat pipes increases from 2300 W to approximately 3300 W (Fig. 7b). Among them, Scheme 2 is the lowest, increasing from 2302 W to 3205 W, an increase of about 903 W; Scheme 6 is the highest, increasing from 2391 W to 3331 W, an increase of about 940 W. Table 3 lists the energy output efficiency. It is not difficult to understand that the energy conducted out through the heat pipes is basically the same as the load magnitude; it is lower than the total reactor power, and the difference is mainly transferred to the outside in the form of heat through materials such as the reflector and shielding layer. Therefore, enhancing the thermal insulation effect of the core is of positive significance for reducing this portion of energy loss.

a) Fission power

b) Energy derived from heat pipe

c) Maximum temperature of outer wall of the core

d) Minimum temperature of outer wall of the core

Fig. 7 Results of load increase conditions

Table 3 Energy output efficiency after 50% increase of load

3.5 Load-Reduction Transient Condition

Similar to the load-increase condition, the load-reduction condition was simulated by reducing the flow velocity by 50%. As seen from Fig. 8, the steady-state temperature of the core in Scheme 6 is the highest, and the energy derived through the heat pipe is the greatest; the corresponding total reactor power is the same as that of the other schemes (or even slightly lower).

From the load-increase/decrease conditions, the following conclusion can be drawn: when the initial total reactor power is fixed, the thicker the insulation layer, the better the thermal-insulation effect, and the more energy is derived through the heat pipe. This conclusion does not change with variations in load.

a) Fission power

b) Energy derived from heat pipe

c) Maximum temperature of outer wall of the core

d) Minimum temperature of outer wall of the core

Fig. 8 Results of load decrease conditions

Table 4 Energy output efficiency after 50% decrease of load

Tables 1–4 record the energy output efficiency (i.e., heat-pipe output power/total power) of each scheme from the steady-state 3 kW power condition to each operating condition. It can be seen that increasing/decreasing the load has the greatest impact on energy output efficiency. This is because part of the energy generated by the reactor is exported through the heat pipes, while another part is transferred to the reflector and shielding layer and ultimately to the outside. Therefore, increasing the load can effectively increase the energy exported by the heat pipes and, without significantly increasing other energy losses, markedly improve the energy output efficiency. It is thus not difficult to understand that, when the power exported through the heat pipes is sufficiently large (MW power level), the influence of the core thermal-insulation scheme (i.e., the gaps between components and the thickness of the insulation layer, etc.) on energy output efficiency will become very small.

4 Conclusion

The 0.6 $ reactivity startup condition, the ±40 pcm reactivity insertion condition at 3 kW steady-state power, and the ±50% load-change condition were simulated, and the behavior of schemes 1–6 under these conditions was compared. The results show that whether components such as the core, vacuum vessel, and reflector are in direct contact has the greatest effect on the total reactor power and the energy exported through the heat pipes; whether the vacuum vessel contains an insulation layer (MLI) and the thickness of the insulation layer also affect the total reactor power and the energy exported through the heat pipes. For example, compared with the original design scheme (scheme 4), scheme 6 improves the efficiency by no less than 1% for all operating-condition indicators. In addition, increasing the system load and ultimately increasing the total reactor power can effectively improve the energy export efficiency (by about 4%). Therefore, under 3 kW steady-state power, provided that the neutron-physics and structural-mechanics requirements of the reactor are not affected, appropriately increasing the number of gaps between the core and external components, increasing the thickness of the insulation layer, and raising the load level all have positive effects on the efficiency of energy exported from the reactor.

Author contributions statement Zhang Jie was responsible for designing the simulation schemes, simulation calculations and data organization, and drafting the manuscript. Liu Fudong was responsible for technical guidance. Wang Kunpeng was responsible for assisting with the analysis and interpretation of the calculation results.

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