Multiphysics Multiscale Coupling Modeling for Nuclear Reactor and Its Uncertainty Quantification
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Jun Sun, Ximing Sun, Yanhua Zheng, "Transient Study on the HTRPM with TINTEvPower Coupling Code Package", Science and Technology of Nuclear Installations, vol. 2020, Article ID 5090597, 14 pages, 2020. https://doi.org/10.1155/2020/5090597
Transient Study on the HTRPM with TINTEvPower Coupling Code Package
Abstract
The hightemperature gascooled reactor pebblebed module (HTRPM) nuclear power plant consists of two nuclear steam supply system modules, each of which drives the steam turbine by the superheated steam flow and is fed by the heatedup water flow. The shared steam/water system induces mutual effects on normal operation conditions and transients of the nuclear power plant, which is worthy of safety concerns and intensive study. In this paper, a coupling code package was developed with the TINTE and vPower codes to understand how the HTRPM operated. The TINTE code was used to analyze the reactor core and primary circuit, while the vPower code simulated the steam/water flow in the conventional island. Two TINTE models were built and coupled to one vPower model through the data exchange in the steam generator models. Using this code package, two typical transients were simulated by decreasing the primary flow rate or introducing the negative reactivity of one module. Important parameters, including the reactor power, the fuel temperature, and the reactor inlet and outlet helium temperatures of two modules, had been studied. The calculation results preliminarily proved that this code package can be further used to evaluate working performance of the HTRPM.
1. Introduction
Modular hightemperature gascooled reactor (HTR) is wellknown for the high safety, high efficiency, and processing heat applications capability. A commercialscale 200 MWe pebblebed modular hightemperature gascooled reactor (HTRPM) has been designed and is now under construction in Shandong Province, China [1]. Most of the construction and installation work have been finished, and the connection to the electric grid will be expected in the end of 2020.
The HTRPM nuclear power plant (NPP) consists of two nuclear steam supply system (NSSS) modules, each of which contains independent reactor core, steam generator (SG), and passive reactor cavity cooling system (RCCS). The steam generated in two NSSS modules is supplied to one steam turbine [2]. After following through the condenser and deaerator, the water is pumped by two pumps, respectively, and fed back to two SGs again. Furthermore, the 600 MWe commercial NPP with six similar NSSS modules and only one steam turbine is in the standard design phase. With this typical multimodule design, the transient or perturbation in one module will inevitably influence the operating features of other modules. Study on this coupling or interaction characteristics is important for further understanding and safe operation of the plant.
Engineering simulators have been developed to study the operating features of multimodule HTRs, especially for the intermodule influences during power load regulations or accidents [3, 4]. Benefited from the fullscope models and realtime simulations, engineering simulators can present coupled dynamic behaviors of the whole NPP by wellbalanced computational cost and accuracy. In the integral supporting system of vPower code, reactor core models are simplified, while appropriate models of helium blowers, SGs, RCCSs, secondary systems, control systems, and electric system are coupled and managed in data transfer [5]. Without adequate detailed reactor core model, the vPower code of engineering simulator can only match the main parameters of the NPP and loses accuracies of distribution parameters.
To further improve the simulation accuracy, a coupling code package was developed with the TINTE and vPower codes. TINTE code is used to carry out the analysis of reactor core and primary circuit, while vPower code performs the secondary circuit calculation, including the primary side of the SGs. These two codes are connected through components of SGs. In this paper, two cases, including the primary flow rate decrease and the reactivity introduction of one module, were simulated with this code package. The phenomena in two modules, including some important parameters such as the reactor power, the fuel temperature, and the helium temperatures, were studied.
HTRPM is shortly described in Section 2. Sections 3 and 4 provide description of the TINTE code and vPower code, and the coupling method between different circuits with these two codes is shortly discussed in Section 5. The calculation results are presented in Section 6. Finally, Section 7 presents the summary and conclusion.
2. HTRPM
As mentioned above, there are two pebblebed modular reactors in the HTRPM NPP coupling with one steam turbine generators, whose total power is 500 MWt and its electrical efficiency is about 42%. For each reactor module, it consists of a hightemperature pebblebed reactor and a oncethrough steam generator, as well as its connecting horizontal coaxial tube. The helium goes through the reactor core and is heated up to 750^{∘}C, then transfers the heat to the secondary circuit water in the SG, and finally produces the highpressure superheated steam. The helium at the SG outlet is cooled to about 250^{∘}C by the secondary circuit water. Then, this cold helium, driven by the helium blower, enters the reactor again through the outer annular channel of the coaxial duct [6, 7]. Each equilibrium state reactor core has an average in height of 11 m and a diameter of 3.0 m, which is a randomly packed pebble bed by roughly 420,000 spherical fuel elements.
The flow diagram of power conversion is shown in Figure 1, and the key parameters are provided in Table 1.

3. TINTE Code and Model
3.1. TINTE Code
The TINTE (TImedependent Neutronics and TEmperatures) is a specialdesigned and welldeveloped code by the Research Center Jülich to evaluate the nuclear and thermal transient behavior of pebblebed hightemperature gascooled reactors. The performance of TINTE has been validated by the wellknown open/blind benchmarks [8–11] and has been widely used in the pebblebed hightemperature reactor design [12–14], such as the HTRPM in China and PBMR in South Africa. VSOP99 (also developed for pebblebed hightemperature gascooled reactor by the Research Center Jülich) is used to prepare state parameters, e.g., the cross sections, the power, and burnup histories, for TINTE calculation. There are several computational modules in TINTE to consider the complex multiphysics coupling effect in the pebblebed high temperature reactor, such as the 2D neutronic diffusion module, 2D thermalhydraulic module, the corrosion module, and the automatic control module. In this work, we focus on the thermalhydraulic module, whose conservation equations and main correlations are as follows [15, 16].(1)Pebblebed heat conservation equation: where the term and represent the heat flux from the fuel element and the convective heat transfer term between the pebble bed and coolant helium, respectively. is the effective thermal conductivity, which considers the effects of radiation, gas and solid conduction, and contact conduction. The detail discussion about the correlations of effective thermal conductivity in the pebblebed region could be found in [17–21].(2)Helium continuity equation:(3)Helium momentum equation: where the resistance coefficient could be determined as follows [22]:(4)Helium energy equation: where the heat transfer coefficient of the surface of spherical fuel elements could be calculated, according to the German safety guide KTA3102.2 [23].
3.2. TINTE Model of HTRPM
The calculation models for the HTRPM have been established based on some reasonable approximations and simplifications. The 2D heat conduction and gas convection model of HTRPM reactor is shown in Figure 2, including the pebblebed core, reflectors, carbon bricks, core vessel, RPV, water cooling panel of RCCS, and reactor building. In this model, the pebblebed core, a porous medium with the void fraction of 0.39, is divided into 6 nodes along the radius and 20 nodes along the height.
A 1D model for the primary circuit is also built and shown in Figure 3. In this model, rectangular figures represent the different components such as the hotgas duct, the SG, and the blower, while circular figures are the nodal points used to connect the components. The 1D primary circuit model is through two nodal points (“core inlet” and “core outlet”) connected to the 2D model via two corresponding components (“core inlet cavity” and “core outlet” shown in Figure 2).
In the below, one 2D model along with the connected 1D model is called as one TINTE model for a HTRPM reactor module. To analyze the coupling behavior of the HTRPM, two same models are built.
4. VPOWER Code and Model
4.1. vPower Code
The vPower code is an integrated simulation software developed by Beijing Neoswise Science and Technology Limited Company in China. The vPower code has user friendly interfaces (see Figure 4) based on Windows operation system and has many integrated, objectoriented graphical modeling tools, which can solve the builtin thermal fluid networks and electrical power flow networks. Powerful toolboxes are capable of simulating typical components of power plants, such as pipes, valves, steam turbines, deaerators, pumps, condensers, separators, and a variety of heat exchangers. Control systems and electrical supply of those components also have respective toolboxes. Moreover, the vPower code also supplies graphical tools to draw digital operating interfaces. Wellorganized code architecture creates levels of data management and time schedule [5] and makes the vPower code widely serve for many simulators of coalfired plants in China.
Moreover, the vPower code has unique functions of embedding a series of userdeveloped models, which extends the application of the vPower code into NPP simulators. Since 2009, Tsinghua University employed the vPower code to establish the HTRPM engineering simulator by developing typical models of reactor core neutronics, helium flow, fuel pebbles, graphite blocks, helium circulators, oncethrough helical coil SGs, and control rods. Besides the newly developed models of the nuclear island, the conventional island components, as well as necessary human machine interfaces (HMIs), were also developed to form the fullscope simulation capability. Great efforts have been made to balance the computational cost and model accuracy in two aspects. As one challenge, the neutronic behavior is described by the improved quasistatic method to solve the threedimensional spacetime dynamic equations. The efficient solver also contributes to get the solutions of each step fast enough [24]. The other challenge is from the complicated threedimensional gas flow and heat transfer inside the reactor core. Since the builtin thermal fluid network assumes it as the combinations of many onedimensional flow paths and heat transfer paths, flow network and heat transfer network models can represent the reactor core flow and heat transfer and save computational time significantly [25]. After 3 years of effort, the engineering simulator of HTRPM was able to perform the normal operation conditions well and basic abnormal scenarios in real time [5]. Following that, the engineering simulator was used to simulate the startup and shutdown processes of the HTRPM NSSS modules step by step and supported the confirmation of commissioning programs and detailed procedures [26, 27].
4.2. vPower Model of HTRPM
The HTRPM engineering simulator models by the vPower code mainly consist of reactor core section, SG, secondary loop section, control system, and electric system. The reactor core section has been described in many previous papers [5, 24, 25, 27]. In the current paper, the SG model and the secondary loop section are introduced to be coupled with the TINTE model of reactor core.
Each NSSS module of the HTRPM has independent SG using helical coil heat transfer tube bundles. The engineering simulator developed a new component model of the helical coil heat transfer tube bundle to calculate the pressure drops and heat transfers in both the helium flow side and the steam/water side, as well as the heat transfer from helium to steam/water through the tube walls [26], shown in Figure 5(a). The matrix of SG model shows the configuration of 19 bundles, each one of which is divided into 16 subsections in height. In Figure 5(b), 19 × 16 components are connected by flow nodes and flow links to simulate helium flows in the primary side, while in Figure 5(c), the same components are again connected in the secondary side to simulate water/steam flows. The reuse of the SG component model can couple the calculations of flow and heat transfer of primary and secondary sides. Correlations of pressure drop and convection in both the primary and secondary sides were also described in [28]. Since the function of SG is significant to transfer reactor core heat into water/steam flow, the SG model is key to couple nuclear and conventional islands. In the engineering simulator of the HTRPM, the vPower code is carefully tested and agrees well with design data [27, 28].
(a)
(b)
(c)
Seen from Figure 1, the water/steam side of SG serves as part of secondary side of the HTRPM NPP. The engineering simulator of the HTRPM also establishes models for components of the highpressure and lowpressure cylinders of the steam turbine, the condenser, the condensate pumps, the lowpressure and highpressure heaters, the deaerator, feedwater pumps, and many valves. These components are connected by onedimensional pipes to form the complete water/steam flow network, which is solved by builtin thermal fluid solver. Several HMIs indicate more details of the secondary side models in Figures 6 and 7. Models and operation data of the secondary side of HTRPM engineering simulator were also carefully tested to match the design parameters, which can continue to support the coupling with the TINTE code.
5. Coupling between Different Circuits
A coupling code package based on TINTE code and vPower code has been developed to study the coupling characteristics of the HTGR plants with more than one reactor module, and the data communication between these two codes can be controlled by an independent platform. In HTRPM analysis, two TINTE models are connected to one vPower model.
Coupling method between different circuits with these two codes can be explained as follows:(1)Two TINTE models are, respectively, connected to one vPower model through the SG components, as shown in Figure 8.(2)In the TINTE model, only the behavior of reactor core and primary circuit is analyzed, which means the heat load Q (the heat transferred from the helium side to the water/steam side in the SG) needs to be set as a boundary condition.(3)In the vPower model, the behavior of the secondary circuit, but also including the helium side of the SG, will be analyzed. With the given value of the inlet temperature (T_{in}), inlet pressure (P_{in}), and mass flow rate (F) in the helium side, the heat transfer between the primary circuit and the secondary circuit can be calculated.(4)A steady state needs to be achieved firstly. To perform a steadystate calculation, for example, for the HTRPM in normal operation of 100% rated power, some input parameters should be set according to the design, including the heat reactor nuclear power, the SG heat load (Q), the helium mass flow rate (F), and core inlet helium temperature (T_{out}) for two TINTE models, as well as the SG inlet helium temperature (T_{in}), SG inlet feedwater temperature, helium mass flow rate (F), and feedwater mass flow rate for one vPower model. The resistance coefficients in the above models also need to be adjusted according to the design so as to get the correct pressure drops. Thus, an initial steady state for TINTE models and vPower model can be reached, and the values of Q, F, T_{in}, and T_{out} in different models are consistent.(5)During the transient calculation, for example, in the time point t_{0}, calculation will firstly be performed in two independent TINTE codes. Then, the calculation results of each module, including the SG inlet helium temperature (T_{in}), inlet pressure (P_{in}), and helium mass flow rate (F), will be transmitted to act as the input data of the corresponding SG component, and the calculation will be performed by the vPower code. Finally, the calculation results of the vPower code, including the SG heat load (Q) and the SG outlet temperature (T_{out}), will be transmitted back to the TINTE model and act as the input data for calculation of next time point.(6)After calculation in a certain time point has finished, TINTE code can selfadjust the next time step, Δt, according to the calculation error. In this code package, after calculation in the time point t_{0} has finished, two time steps, Δt_{1} and Δt_{2}, will be given by two independent TINTE codes. The platform then will compare these two time steps and select the smaller one to determine the time point for next TINTE and vPower calculation.
6. Calculation Results
It is assumed that both NSSS modules of HTRPM are initially operated in 100% rated power when an unexpected transient or perturbation occurs in the #2 module. Two cases are simulated in this paper: Case 1: the primary flow rate decreases linearly from 100% to 80% rated flow rate in 15 minutes Case 2: a negative reactivity of 0.1% Δk/k is introduced in 2 minutes linearly
These cases aim to test the ability of this coupling code package to analyze the interaction behavior between two modules. The possible operator action, as well as the automatic response of the reactor protection system, is not considered.
6.1. Primary Flow Rate Decrease in Module One
Figures 9–14 show some calculation results of case 1. The decrease in the primary flow rate will result in the decrease of the heat quantity transferred from the primary helium side to the secondary water/steam side in the SG, as shown in Figure 9 (dashed line). The heat transfer between the reactor core and primary coolant is also impaired, resulting in the increase in the fuel temperature, as shown in Figure 10. It also can be seen that the increase in the average fuel temperature during the first several minutes is very small, which is due to the large heat capacity of the HTRPM core (totally about 80 t fuel elements and 250 t reflector graphite in one reactor module). With the increase in the fuel temperature, the reactor power will decrease by negative temperature feedback, as the solid line in Figure 9 shows, which will result in the subsequent decrease in the average fuel temperature.
In the HTRPM, primary coolant flows from the top to the bottom in the pebblebed core and the maximum fuel temperature appears at the bottom of the core. With the decrease in the primary helium flow rate, the maximum fuel temperature and the resulting core outlet (namely, the SG inlet) helium temperature will increase continuously, but very slowly, as the dashed lines in Figures 10 and 11 show. These two curves begin to decline in about 15 minutes affected by the power decrease. It also can be seen from Figure 11 that, because of the larger mass flow rate of the secondary side compared to that of the primary side, the SG outlet helium temperature will decrease continuously.
As in the HTRPM, the steam from two SGs will converge and then flow into one turbine, and the power decrease in #2 module will also result in the small decrease in the feedwater temperature back to the SGs (as shown in Figure 12), so as to result in the small decrease in the SG outlet helium temperature in #1 module (Figure 13). The helium flows back to the reactor core with a little lower temperature and will then cause a little increase in the reactor power in #1 module due to the negative temperature feedback (Figure 14).
6.2. Reactivity Introduction of Module One
In this case, a negative reactivity of about 0.1% is introduced into #2 module in 2 minutes, resulting in decrease in power (solid line in Figure 15) and the consequent decrease in fuel temperature (Figure 16) and core outlet helium temperature (dashed line in Figure 17, the SG inlet helium temperature). The decrease in the SG inlet helium temperature will also cause the decrease in outlet helium temperature after it transfers the heat to the water/steam in the secondary circuit and flows back to the reactor (solid line in Figure 17).
It can be seen from Figure 17 that the core outlet helium temperature will decrease from about 750^{∘}C to less than 720^{∘}C in 20 minutes due to the decrease in the reactor power, while the decrease in the SG outlet helium temperature is only about several degrees. This can be explained by the coinstantaneous decrease in the heat transfer capacity between two sides of the SG, as the dashed line in Figure 15 shows.
As shown in Figure 15, the reactor power will rise over again due to the fuel temperature decrease and the resulting negative temperature feedback. After a little fluctuation, the power maintains a stable value lower than the initial rated power.
Again, the power decrease in #2 module will result in the small decrease in the feedwater temperature back to the SGs (Figure 18), so as to result in the small decrease in the SG outlet helium temperature in #1 module. The helium flowing back to the reactor core with a little lower temperature will then cause a little increase in the reactor power in #1 module due to the negative temperature feedback (Figure 19).
7. Summary and Conclusion
The modular HTGR is recognized as a candidate for the generation IV nuclear energy system technology and has wellknown inherent safety features. The commercialscale 200 MW HTRPM consists of two NSSS modules and one turbine. Furthermore, the design with more NSSS modules connected to one turbine will be considered in the future. It would be very important and necessary to understand the coupling characteristics between these modules, especially when some transients occur at part of the modules.
A coupling code package has been developed based on the TINTE code and vPower code. These two codes are connected through components of SG. TINTE code is used to carry out the analysis of reactor core and primary circuit, while vPower code performs the secondary circuit calculation, including the primary side of the SGs. A platform is used to transfer data between these two codes, including time steps.
Two cases, including the primary flow rate decrease and the negative reactivity introduction of one module, had been simulated with this code package, and the calculation results were introduced in this paper. The preliminary calculation results can explain the phenomena during the transients. It shows that the coupling code package has the ability to analyze the coupling and interaction behavior between two modules.
Besides, the code package needs to be further improved and optimized, and more simulation should be performed. Further analysis on the coupling behavior between different modules would provide important support for the future development of the modular HTGRs.
Nomenclature
:  Helium heat capacity 
:  Helium temperature 
:  Pebblebed heat capacity 
:  Pebblebed temperature 
:  Diameter of fuel element 
:  Helium velocity 
:  Gravity acceleration 
:  Convective heat transfer coefficient 
:  Nusselt number 
:  Porosity of the pebble bed 
:  Helium pressure 
:  Helium density 
:  Prandtl number 
:  Pebblebed density 
:  Heat flux from the fuel element 
:  Pebblebed effective thermal conductivity 
:  Reynolds number 
:  Helium thermal conductivity. 
Data Availability
The data used to support the finding of this study, for example, the data used to build the model of HTRPM, have not been made available because these belong to engineering design parameters and could not be available at present.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
This paper was supported by the National S&T Major Project (Grant no. ZX06902013) and Tsinghua University Initiative Scientific Research Program (20197050014).
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Copyright © 2020 Jun Sun et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.