Proceedings of the 2017 25th International Conference on Nuclear Engineering ICONE25 July 2-6, 2017, Shanghai, China ICONE25-66832 CONTROL SYSTEM DESIGN OF SUPERCRITICAL CO2 DIRECT CYCLE GAS FAST REACTOR Xianshan Zhang School of Energy and Power Engineering, Xian Jiaotong University, Xian, Shaanxi, China Peiwei Sun School of Energy and Power Engineering, Xian Jiaotong University, Xian, Shaanxi, China ABSTRACT The Supercritical CO2 Direct Cycle Gas Fast Reactor(SCGFR) is a Generation IV reactor. The thermal properties of supercritical carbon dioxide are different from helium gas. Therefore, it is necessary to develop its dynamic model and study its control system. A mathematical model is developed for the SC-GFR. One prompt neutron group point kinetics equations with six groups of delayed neutrons is applied in the model. The core consists of an assembly of hexagonal fuel elements: the innovative Tube-in-Duct(TID) fuel assembly. Steady-state calculation is performed and the results are compared with the design data. The transient results are analyzed and the responses are reasonable in theory. The transient results show that the model can properly predict the SC-GFR dynamics. The study showed that it is not only feasible to build a numerical model of the SC-GFR, but also the control system can satisfy the design purposes. m mass (kg) n neutron flux (n/(cm2 ·s)) n in Eq.(8): number of fuel assemblies N filter coefficient Nu Nusselt number P pressure (MPa) Pr Prandtl number Q heat flux per unit length (W/m) Re Reynolds numbers t time (s) T K or ◦ C Greek letters α heat transfer coefficient (W/m·K) β delayed neutron fraction ζ pressure loss coefficient κ Thermal conductivity W/(m·K) λ decay constant Λ the average neutron life time (s) µ dynamic viscosity (Pa·s) ρ fluid density (kg/m3 )) Subscripts b bulk fluid c carbon dioxide coolant d cladding f fuel i node number i in Eq.(13–14): group number s inter surface of clad w wall NOMENCLATURE A area of the flow cross-section (m2 ) C specific heat (J/(kg·K)) D diameter (m) f fanning friction factor g gravitational acceleration G fluid mass flow rate (kg/s) h fluid enthalpy per unit mass (J/kg) k gain parameter l length (m) 1 Copyright © 2017 ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use TABLE 1. SC-GFR plant key parameters [3, 4] 1 INTRODUCTION [Matlab & Simulink] Six kinds of Generation IV nuclear reactor concept are proposed in 2000 [1]. In which the Gas-cooled Fast Reactor is a fast-neutron reactor with some advantages other fast-neutron reactors have. In addition, it also operates within a closed fuel cycle which leads to a better utilization of uranium resources, generated little low-level radioactive waste and compliance with nuclear non-proliferation requirements. Various refrigerants may be used in GFR as the coolant, typically helium and carbon dioxide. In order to improve the Breeding Ratio (BR) and prevent positive void coefficient, the neutron capture cross sections need to be low. As a type of the GFR, the Supercritical CO2 Direct Cycle Gas Fast Reactor (SC-GFR) uses the recuperate Brayton cycle of supercritical carbon dioxide, which runs more efficient than the Rankine cycle or recuperate gas Brayton cycles working with Helium. The main advantages of this concept are as follows [2]: ⋄ High thermal efficiency with relatively low reactor outlet coolant temperatures; ⋄ Compact, economical power conversion system; ⋄ Endurable core with a closed fuel cycle; ⋄ Small void reactivity worth from loss of coolant; ⋄ The coolant is stable, non-toxic and easy to obtain; ⋄ Natural convection decay heat removal; ⋄ Prevent nuclear proliferation. A mathematical model is developed for the SC-GFR which implemented with the Matlab & Simulink. One prompt neutron group point kinetics equations are applied in the primary reactor kinetics model. Two reactivity feedback mechanisms are considered. The reactor thermal-hydraulics is developed based on the fundamental conservation of fluid mass, energy and momentum. The mathematical model is built though all these Partial Differential Equations(PDEs) and some other equations. The heat transfer coefficient is derived from the immediate inner wall temperature, the coolant pressure and temperature because the particularity of coolant. By look up the table, all physical and thermodynamic properties are calculated with the local temperature and pressure. The core consists of an assembly of hexagonal fuel elements: the innovative Tube-in-Duct(TID) fuel assembly, and its temperature distribution has been numerically calculated by the PDE Toolbox in Simulink. The property of the clad and fuel, especially the thermal conductivity is also calculated with a higher accuracy. A mathematical model is developed for the SC-GFR which implemented with the Matlab & Simulink. Point kinetics with one prompt neutron group with six groups of delayed neutrons is applied in the reactor neutron dynamics. Two reactivity feedback mechanisms are considered. Based on the first law of thermo-dynamics, developed the reactor thermal-hydraulics model by the balances of mass, energy and momentum. The Parameter Value Core Thermal Output 2400 MWth Specific Power 20.7 kW/kgHM Power Density 85.4 kW/L Active Core Diameter 1.54 m Effective Core Diameter 4.81 m Reflector Ti(axial),S-CO2 (radial) Core Flow 1.1708 × 104 kg/s Plant Electrical Output 1200 MWe Coolant Inlet Temperature 485.5 ◦ C Coolant Outlet Temperature 650 ◦ C Coolant volume fraction 25% Peak Coolant Pressure 20 MPa Fuel emissivity 0.79 Plant Lifetime 60 years mathematical model is built though all these Partial Differential Equations(PDEs) and some other equations. Because of the particularity of the coolant, the heat transfer coefficient is derived from real-time inner wall temperature, the coolant temperature, pressure and flow rate. By looking up the table, all physical and thermodynamic properties are calculated by the local temperature and pressure in real time. The core consists of a new type of assembly: the innovative Tube-in-Duct(TID) fuel assembly, and its temperature constant distribution has been numerically calculated by the PDE Toolbox in Simulink. The property of the clad and fuel, especially the thermal conductivity is also calculated with a higher accuracy. 2 S-CO2 GAS-COOLED FAST REACTOR There are two main design directions in the international research on SC-GFR. First, the research has been done by MIT mainly in the USA, and is pretty deep. This research has adopted the CO2 re-condensation direct loop which has no CO2 condensation. Using the columnar core component, and cancel the plutonium proliferation that traditional fast reactor has, turn to employ a new “Tube-in-Duct”(TID) assembly to enlarge the portion of fissionable material. 2 Copyright © 2017 ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use FIGURE 2. FIGURE 1. Simplified Plant Layout (Top view). Simplified Plant Layout (Front view). Second, the Tokyo Institute of Technology’s Advanced Gas Reactor represent another direction of SC-GFR, in the core it uses Partial pre-cooling direct cycle, which can reduce the heat taken by condensation, in the primary design they think pebble or rod type fuel element could be used in S-CO2 cooled AGR and receive fairly good effect. To obtain the dynamic characteristics of SC-GFR, a MIT concept [5] is chosen in this study, and some supercritical carbon dioxide Brayton cycle and design is refereed to work done by Dostal [6, 7] and by Moisseytsev [8]. While the research presented in this work deals mainly with the simulation of plant and its control system, it is important to understand the larger framework into which it fits. Figure 1 and Fig.2 show the layout of the plant. Figure 1 shows two parallel 600 MWe turbo-machinery sets (turbine, re-compressor, main compressor, and electric generator) each served by four heat exchanger trains (high and low temperature recuperators, and pre-cooler) in two pairs on both upper and lower floors, straddling the shaft. The Fig.1 is a top-view drawing, due to the angle, only the two upper floor trains per shaft can be seen. Turbine capacity is limited at about 600 MWe, based on keep in the affordable limit of turbine blades and shaft rpm to 1800, a standard electric generator value. And the diameter of pipe limits to about 1 meter to conform the attempted practice, therefore the heat exchanger train capacity limit to about 320 MW, corresponding to about 150 MWe. Finally, the Printed Circuit Heat Exchangers (PCHE) produced by Heatric™meet the needs of design, which FIGURE 3. 2D and 3D Rendering of a Hex-nut fuel Pellet of TID assembly. offers a compact solution, the ability of working with a very large pressure difference between the hot side and the cold side in the heat exchanger, a low pressure drop and high thermal effectiveness [9]. The plant layout can fit inside a diameter of 54m containment, able to remove decay heat after LOCA. The reactor core uses a new type of fuel assemblies called Tube-in Duct (TID). The TID fuel assembly consists of a hexagonal outer tank having a cylinder coolant channel placed in the fuel center, between the fuel layer and coolant is the clad, which manufactured by INCOLOY alloy MA956, whose melting point is 1480 ◦ C, density is 7.25 g/cm3 . This metal obtained by mechanical alloying, allowing the clad has excellent anti-oxidation and prevent carbon corrosion characteristics, has been selected as lining material of the aero engine combustion chamber. The TID fuel assemblies is displayed at Fig.3, note the fuel and coolant have switch places, compared to original design. The selection of TID fuel assembly rather than traditional 3 Copyright © 2017 ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use PIN type fuel assembly, it is a compensation measures, and it cancels the external blankets. Compare to same pitch to diameter ratio, this design allows a higher fuel volume fraction than PIN type, it is favorable for numerous neutronic reasons. It has advantages in terms of anti-nuclear proliferation, because the isotopes which could produce nuclear weapons(e.g., 239 Pu) would mixed with other fission products, make it difficult to extract. Compared to PIN type, TID assembly also has advantage in thermal-hydraulics, TID type have a lower fuel temperature and less pressure drop than PIN type at a certain fuel volume fraction. Besides, TID fuel assembly need no spacer grid either, which reduce further pressure drop. PIN type would result in less favorable thermal hydraulic performance to achieve the same neutronics target. Much work has gone into development of a S-CO2 Brayton Re-compression Cycle for use as a nuclear plant both in USA and Japan, the main feature of the cycle which distinguished it from the original Brayton cycle is that its compression operates near the critical point, where density is very high, and it uses another compressor called re-compressing compressor, which sets before the pre-cooler. It different from the traditional Brayton cycle where there is typically only one recuperator as well [6]. This arrangement can avoid the pinch point in the recuperators which usually happens when a simple Brayton cycle was adopted. In order to get the accurate physical properties such as specific heat capacity and density, used Look-up block of Simulink. As mentioned in the above chapter, set the main compressor operated near the critical point of CO2 , where density is very high, to improve its efficiency. It is worth noting that because of the difference in physical properties, the start-up period is quite different from helium-cooled fast reactor. balance: dm = Gin − Gout dt (1) d(mh) = Gin hin − Gout hout + Q dt (2) Energy balance: Momentum balance: pout = pin − ζ G2in ρ (3) In the reactor core, the fission energy is released into the fuel assemblies in the form of heat, then transferred into the clad through the gas gap by conduction and to the middle coolant channel afterwards by convection. This process can be described as Eq.(4) in each fuel node: d (mf,i hf,i ) = P − (hA)fc,i (Tf,i − Tc,i ) dt (4) And the variations in temperature of carbon dioxide coolant satisfied Eq.(5): d (mc,i hc,i ) = (hA)fc,i (Tf,i − Tc,i ) + Gi−1 hi−1 − Gi hi dt (5) The subscripts number i − 1 in Eq.(4) and Eq.(5) turn into “inlet” when the i equals 1. Outlet fluid mass flow rate and the variations of fluid density satisfied Eq.(6) 3 GOVERNING EQUATIONS This chapter includes the derivation of the simplified dynamic models for each of the considered operating units. A model constructed based on the combination of mass, energy and momentum balance. The following simplifying modeling assumptions are considered: Vi ⋄ The reactor is regarded as a united system with 5 operating nodes of core and two reflectors as two operating nodes, and the properties such as pressure, temperature and flow in every nodes are uniform; ⋄ The initial reactivity is considered as 0; ⋄ One dimensional fluid flow model is utilized. dρ = Gi−1 − Gi dt (6) 3.2 Heat transfer For each node, the thermal power can be related to the temperature drop from fuel to coolant via the overall heat transfer resistance as: (hA)fc = First law of thermo-dynamics Considered the principle of conservation, the reactor model is bounded by the balance of mass, energy and momentum: Mass P Tf − Tc (7) 3.1 And the heat transfer resistance can be described by the summation of thermal resistance of the fuel, the gas gap, the 4 Copyright © 2017 ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use 3.4 Neutron dynamics The neutrons behavior in the SC-GFR core can be described with a point kinetics model, consisting of six energy groups. cladding and the convective heat transfer resistance in carbon dioxide coolant. Hence, the (hA)fc can be formulated as: (hA) f c = n 1 4πκf,i + 2π r 1 f,i hg,i + rf +tg +Tc 1 1 2πκf,i ln( rf +tg ) + π dhs (8) The gap heat transfer coefficient hg is calculated by: κg hg = + tg 1 εc σ + ε1 − 1 f ( 4 Tf,inner − Td4 ( κw κb )0.22 ( µw µb )−1.13 (9) TABLE 2. Fast neutron fission parameter for 235U in SC-GFR 3.3 Pressure drop Based on the assumptions mentioned above, momentum balance equations can be summed up as a summation of frictional pressure drop and form-loss pressure drop. L G2 ( fh + 1.2) 2ρ D ] [ 8qw 1 ∂ρ fh = f + − ( ) m Gc p ρ ∂t 0.316Re−1/4 for Re ≤ 2 × 104 0.184Re−1/5 for Re ≥ 2 × 104 βi λi /s−1 τi 1 0.000251 0.0127 78.74 2 0.001406 0.0317 31.55 3 0.001241 0.115 8.70 4 0.002687 0.311 3.22 5 0.000845 1.40 0.714 6 0.000172 3.87 0.258 Summation β =0.00660 β /λ =0.084 Regarded the initial steady state as 0, the temperature variation of fuel and coolant results in a reactivity change, which would feedback to stabilize the system by itself, and complied the thermal-hydraulics and the neutronics, ρ = ρext + αf ∆Tf + αc ∆Tc (11) (15) Where the αf = −0.45 ¢/K and αc = −0.38 ¢/K are the temperature coefficient of the TID assemblies and Supercritical CO2 at the Beginning of Cycle (BOC) [3]. For turbulent flow in smooth tube, the friction factor ( f ) is given by: f= Group (10) The frictional pressure drop is calculated by Eq.(10), Where Hydraulic drag ( fh ) is given by [11]: { (14) Where the i = 1, 2, . . . , 6, noted that the SC-GFR is different from typical PWR, it is a fast reactor with a different coolant. The parameter of neutron in the SC-GFR are shown in Tab.2 [9]. Guptas correlation was developed for Super Critical CO2 by the experimental data within a range of thermodynamic parameterspressures belongs to 7.4–8.8 MPa, mass fluxes 900– 3000 kg/m2 ·s and inlet fluid temperatures 20–40 ◦ C. Due to the Dittus-Boelter correlation was better applied to sub-critical CO2 , and CO2 is very sensitive to temperature and pressure within the pseudo-critical and critical ranges, therefore chose the Eq.9 rather than Dittus-Boelter correlation. pout − pin = dci βi = n − λiCi dt Λ Tf,inner − Td )0.93 ( ρw ρb (13) ) And the heat transfer coefficient hs can be calculated by the work of Gupta [10]: Nu = 0.01Re0.89 Pr−0.14 6 dni ρ − βi = n + ∑ λi ci dt Λ i=1 (12) 4 DYNAMIC MODEL OF SC-GFR 4.1 Dynamics model of SC-GFR without controller The thermal power of reactor can be calculated by the neutron flux, firstly, rearrange the Eq.(4) and Eq.(5), then Laplace Above equation is valid for supercritical CO2 within the range of Re ≤ 1.5 × 105 . 5 Copyright © 2017 ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use FIGURE 4. control. Simulink representation of reactor model without PID FIGURE 5. control. Simulink representation of reactor model with two PID transform is used to combine outlet and input. hf,i = 1 [P − (hA)fc,i (Tf,i − Tc,i )] mf,i s constant control strategy, to avoid the influence from coolant temperature continuous rise, to avoid the thermal stress-cracking in TID assemblies and structures in vessel. However, it drew higher demand in turbine. In the primary control system design, considered two individual mechanisms: to by the control rod and to by the valve opening. Adopted a combination of two PID controllers, through the PID controllers export two signals, passed to the stepper motor, to adjust the control rod and valve opening, to change the reactivity and inlet coolant flow rate. And to avoid the frequent action of control rod, after the calculation of outlet temperature and target temperature, there is a dead zone allowing a certain error. This model with two PID controller is shown in Fig.5. The PID controllers are weighted according to the independent gain parameter kP , kI , and kD [12]. The transfer function of a PID in Simulink is shown in Eq.(18): (16) And the variations in temperature of carbon dioxide coolant satisfied Eq.(5): hc,i = 1 [(hA)fc,i (Tf,i − Tc,i ) + Gi−1 hi−1 − Gi hi ] mc,i s (17) The thermal properties of supercritical carbon dioxide change due to coolant temperature and pressure at the moment, hence, use Look-up block to obtain properties of coolant. As Eq.(8) has shown, the (hA)fc would change with the power, flow rate and temperature of fuel and coolant, therefore, during the model founding, it could be calculated by dynamic properties. In order to get the accurate thermal resistant, use the reactor thermal properties such as power, flow rate and temperature of a unit time step before the current time. The model is using a Matlab ODE solver called ODE45. The equations above can be solved directly via the Matlab & Simulink platform. The structure of the SC-GFR dynamic model (without control system) is shown in Fig.4. 1 N Gc (s) = kP + kI + kD s 1 + N 1s (18) 5 SIMULATION RESULTS There are four inputs in the model: the temperature (Tc,in ), pressure (pin ) and flow rate (Gin ) of inlet coolant, the reactivity introduced by outside ((ρext )). The ρext can be considered as disturbance. set it to 0, and the other inputs set as a constant conform with design, the outputs values are shown in Tab.3, outputs are corresponded with design propose. To investigate the dynamic characteristics of the reactor model without any control system, for the comparisons to show the control system effect. In each case, one input variable 4.2 Control system based on dynamics analysis In order to adjust the cycle in such a way that the plant produces electricity as expected, chose the reactor parameters that can describe the difference between power level and the grid demand, there chose a plan of average coolant temperature 6 Copyright © 2017 ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use TABLE 3. Steady-state Values and Design values P/MW Gout /kg·s−1 pout /MPa Tc,out /◦ C Design values 2400 1.78×104 18.2 650 Model values 2400 1.779×104 18.223 649.45 is change from its design values, while other inputs are kept unchanged. 5.1 A step increase in reactivity without PID The responses to the step increase in reactivity from 0 to 5¢at 50s without PID controller have shown in Fig.6-Fig.8, as a result, the final reactor power increases because of the increase of neutron flux, then the temperature of fuel increases which lead to the increase of coolant by thermal transfer, and because of the reactivity-feedback from both fuel and coolant as Eq.15 described, the reactor power decrease slightly and stabilizes at 102.13% FP (Full Power equals 2400WM). During this process, the fuel average temperature finally increases 17.6◦ C to 827.6◦ C, the coolant average temperature increases 3.85◦ C. These results change trend has same shape with similar HTR model [13]. FIGURE 7. Fuel temperature responses to a step increase in reactivity. FIGURE 8. reactivity. Coolant temperature responses to a step increase in TABLE 4. FIGURE 6. Power responses to a step increase in reactivity. Parameters of two PID controllers. Number kP kI kD N 1 Pset -1.27×10−3 -9.442×10−3 -1.627×10−5 55.41 2 Tc,ave 80.66 43.57 0 100 The responses to the 5% FP step increase in power set have shown in Fig.10-Fig.12 at the beginning, the reactor stabilizes at the design value; after the step increase in power set introduces at 10s, the PID controllers pass the difference value between the power and power set to the stepper motor, then changes the valve opening and the control rod, which leads to changes in reactivity 5.2 A step increase in power set The parameters of two PID controllers are designed with the help of Optimization block of Simulink toolbox, there are the optimize process in Fig.9. The final two PID controllers parameters set values are shown in Tab.4. 7 Copyright © 2017 ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use FIGURE 9. A process of Optimization. FIGURE 11. Fuel temperature response to a step increase in Power set and inlet flow rate, finally the reactor power stabilizes at 105% FP due to the reactivity feedback and PID controller, and the valve opening decreases, to balance the increase of coolant temperature caused increase in pass through flow rate. The fuel temperature finally increases by about 10◦ C. FIGURE 12. Power set. FIGURE 10. Coolant temperature response to a step increase in in temperature set pass an increase of valve opening, it increases the inlet coolant flow rate, make the coolant temperature promote more through the reactor core, with higher temperature in reactor core, it drives the negative reactivity feedback mechanisms thereby resulting in the reactor power stabilizes at 100% FP as set after the slightly shake, and the fuel temperature increases by 10.4◦ C, average coolant temperature increases at the new set point of 572.75◦ C. Power response to a step increase in Power set. 5.3 A step increase in coolant temperature set As discussed in chapter 4, in this model there used a plan of average coolant temperature constant control, so the average coolant temperature set is another control object. The responses to the 5◦ C step increase in average coolant temperature set values are shown in Fig.13-Fig.15, at the beginning, the reactor stabilizes at the design value because there is no disturbance; after the step increase in temperature set introduces at 10s, the increase 6 CONCLUSIONS Steady-state calculation is performed and the results are compared with the design data. The errors are small and the dynamic model is verified. In order to study the dynamic behaviors of the reactor system, step disturbances are introduced. The 8 Copyright © 2017 ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use FIGURE 13. Power response to a 5◦ C step increase in Tc,ave set. FIGURE 15. Tc,ave set. Coolant temperature response to a 5◦ C step increase in and the Project-sponsored by SRF for ROCS, SEM. REFERENCES [1] A technology roadmap for generation iv nuclear energy systems. Report GIF-002-00, US DOE Nuclear Energy Research Advisory Committe and the Generation IV International Forum, 2002. [2] Parma, E. J., Wright, S. A., Vernon, M. E., Fleming, D. D., Rochau, G. E., Suo-Anttila, A. J., Rashdan, A. A., and Tsvetkov, P. V., 2011. “Supercritical co2 direct cycle gas fast reactor (sc-gfr) concept”. SANDIA REPORT. [3] Handwerk, C. S., 2007. “Optimized core design of a supercritical carbon dioxide-cooled fast reactor”. Department of Nuclear Science and Engineering. [4] Pope, M. A., 2006. “Thermal hydraulic design of a 2400 mw direct supercritical co-cooled fast reactor”. Thesis. [5] Gibbs, J. P., Hejzlar, P., Gong, Y., and Driscoll, M. J., 2007. “Plant layout for a 1200 mwe direct brayton cycle gfr”. Transactions of the American Nuclear Society, 96, pp. 793–794. [6] Dostal, V., Driscoll, M. J., and Hejzlar, P., 2004. A supercritical carbon dioxide cycle for next generation nuclear reactors. Report. [7] Dostal, V., Hejzlar, P., and Driscoll, M. J., 2006. “Highperformance supercritical carbon dioxide cycle for nextgeneration nuclear reactors”. Nuclear Technology, 154(3), pp. 265–282. [8] Moisseytsev, A., Kulesza, K. P., Sienicki, J. J., Division, N. E., and Univ., O. S., 2009. Control system options and strategies for supercritical co2 cycles. Report ANL-GENIV-081; TRN: US1000457 United States 10.2172/958037 TRN: US1000457 ANL ENGLISH, ; FIGURE 14. Fuel temperature response to a 5◦ C step increase in Tc,ave set. transient results are analyzed and the responses are reasonable in theory. The transient results show that the model can properly predict the SC-GFR dynamics. After the lumped parameter modeling, two PID controllers are designed with the help form the Simulink Design Optimization block in Simulink to yield desired steady-state error and a faster response. The study shows that it is not only feasible to build a numerical model of the SCGFR using the Matlab & Simulink, and also the control system can satisfy the design purposes. ACKNOWLEDGMENT This project is supported by the National Natural Science Foundation of China (Grant No.11405126), the China Postdoctoral Science Foundation (Grant No.2014M552455), the Fundamental Research Funds for the Central Universities (xjj2014040) 9 Copyright © 2017 ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Argonne National Laboratory (ANL). [9] Gezelius, K., 2004. “Design of compact intermediate heat exchangers for gas cooled fast reactors”. Thesis. [10] Gupta, S., Saltanov, E., Mokry, S. J., Pioro, I., Trevani, L., and McGillivray, D., 2013. “Developing empirical heat-transfer correlations for supercritical co2 flowing in vertical bare tubes”. Nuclear Engineering and Design, 261, pp. 116–131. [11] Sarkar, J., Bhattacharyya, S., and Ramgopal, M., 2008. “Pressure drop for in-tube supercritical co2 cooling: Comparison of correlations and validation”. 19th National & 8th ISHMT-ASME Heat and Mass Transfer Conference. [12] Li, Y., Ang, K. H., and Chong, G. C., 2006. “Pid control system analysis and design”. IEEE Control Systems, 26(1), pp. 32–41. [13] Li, H., Huang, X., and Zhang, L., 2008. “A simplified mathematical dynamic model of the htr-10 high temperature gas-cooled reactor with control system design purposes”. Annals of Nuclear Energy, 35(9), pp. 1642– 1651. 10 Copyright © 2017 ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use

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