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Once-Through Steam Generator Model Analysis Using Python and Advanced Optimization Tools (Summer Internship Report)

This study focuses on the parametric analysis of design parameters for a once-through steam generator (OTSG) model, using python and advanced optimization tools to facilitate applications such as the flowing autoclave steam generator (FASG) test cases. Building on previous research involving another OTSG with a different design, this project aims to enhance our understanding of how steam generators (SGs) behave and how their outputs are influenced by changes in design. The reason for this design change is to allow for more precise modeling and optimization of SG performance, to provide a comparative analysis between the two designs, and to set up the model for integration with the FASG test case. The OTSG python-model is a mathematical representation (including fluid flow and heat transfer equations/models/correlations) of a steam-generating unit in a pressurized water reactor-type small modular reactor system. Design studies involve changing the model’s input design parameters to observe the resulting effects on the output of the system. By using advanced optimization tools, such as the Risk Analysis Virtual Environment (RAVEN) developed at Idaho National Laboratory, detailed design parametric studies and model optimization were performed. Six input parameters—pressure, temperature, and mass flow rate for the inlet of the primary-side (hot fluid) and secondary-side (cold fluid), respectively, of the SG—were randomly perturbed via RAVEN’s Monte Carlo Sampler module, using uniform distributions (i.e., ±1%, ±5% and ±10% relative changes) for 600 samples. The analysis provides valuable insights into SG optimization and can be used for sensor placement optimization to effectively monitor and obtain experimental data in other tests.

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A dynamic model of once-through steam generator (OTSG) for prototypical advanced reactor - 374

new design of Small Modular Reactor, the Prototypical Advanced Reactor (PAR), features two sodium primary systems each connected to dedicated steam generators (SGs) and sharing a balance of plant (BOP) system. PAR adopts once-through steam generators (OTSG) for its compact structure. The existence of superheated steam in a OTSG improves turbine design by eliminating the need of bulky moisture separator in SG. The two cores and SGs' design enable PAR to adjust power flexibly, as a result, introduce more challenges to the control. Therefore, a fast simulation model with high accuracy OTSG model is needed. In this paper, a dynamic model is built for OTSG of PAR based on the conservation of mass, momentum, and energy. The OTSG is simulated as lumped pipe and divided into subcooled, evaporating, and superheated regions by moving boundaries. SIMULINK is adopted to this OTSG simulation to be merged into existing PAR system models easily. The steady state results show that key parameters are rational. The 5% step increase of feedwater enthalpy transient demonstrates that the model is capable to respond to the perturbations. Since the basic laws and algebraic method used in this paper are suitable for other fluids, the model can be easily applied to any other OTSG. Future work will also focus on model optimization, merging and improved control. The final aim is to perform full scope realtime simulations for PAR under normal operational transients. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Steam generator model design parameter sensitivity study for small modular reactor system

Here, this study focuses on design parameter sensitivity studies pertaining to several Once-Through Steam Generator (OTSG) model cases both with and without a riser using python and advanced risk assessment and optimization tool, i.e. Risk Analysis Virtual Environment (RAVEN) developed at Idaho National Laboratory (INL), to support a Small Modular Reactor (SMR) system. The presented Steam Generator (SG) python-based model is a mathematical representation of a steam-generating unit for a Pressurized Water Reactor (PWR)-type SMR system, including fluid flow and heat transfer equations, models, and correlations. Design studies involve changing the model’s input design parameters (e.g., temperature, pressure, mass flow rate) to observe the resulting effects on the output of the system, such as the Heat Transfer Coefficient (HTC), Reynolds number, Nusselt number, and heat transfer performance. Sensitivity studies analyze the degree to which system output and/or desired parameters (e.g., HTC or heat transfer performance) are sensitive to changes in the input parameters. By using RAVEN, detailed design parametric sensitivity studies. Six input parameters—namely, the pressure, temperature, and mass flow rate for the inlet of the primary-side (hot fluid) and secondary-side (cold fluid) of the SG—were randomly perturbed via RAVEN’s Monte Carlo Sampler module, using uniform distributions (i.e., ±1%, ±5% and ±10 % relative changes) for 600 samples. The analysis results give valuable insights into SG system performance, and provide justification for further research and development such as optimized sensor placement, design verification, validation, and optimization.

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Model-free adaptive control for MHTGR-based nuclear steam supply systems - 144

Modular high temperature gas-cooled reactor (MHTGR) uses helium as coolant and graphite as both moderator and structural materials. Due to its inherent safety feature, MHTGR has been regarded as an important candidate for next generation of nuclear plants. By coupling with the once-through steam generator (OTSG), MHTGR can be utilized to form the nuclear steam supply system (NSSS) for producing superheated steam, which can be adopted for nuclear plants with high efficiency. Power-level control of is important for the stable and efficient operation of the MHTGR-based NSSS, and it is necessary to develop the power-level control law that is robust to physical and thermal parameters and can guarantee the closed-loop stability in normal and even abnormal conditions. In this paper, a model-free adaptive power-level control law is developed for the MHTGR-based NSSS, which is free from physical and thermal-hydraulic parameters, takes the simple forms of proportional-integral (PI) or proportional-differential (PD) feedback law, and can provide globally asymptotic closed-loop stability. Then, it is applied to the NSSS control of the two modular high temperature gas-cooled nuclear plant HTR-PM. Numerical simulation results in normal power maneuver and some typical abnormal cases show that this new control law can provide satisfactory closed-loop stability as well as transient performance. (authors)

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Control system design for a small pressurized water reactor - 141

Small Pressurized Water Reactors (SPWR) have unique designs from the commercial large Pressurized Water Reactors (PWRs). Integral design is adopted. There are no hot legs and cold legs between the reactor core and the steam generators like in the PWR. Strong interactions exist among different loops. The pressure vessel is large in volume and the coolant inventory is also in a large amount. The inertia of the coolant is large and it takes more time for the primary system to respond to disturbances. The steam generator adopts the once-through design and the water inventory is small. The steam generator is very sensitive to disturbances. These unique characteristics challenge the control system design of SPWR. Relap5 is used to model the SPWR. Steady-state simulation is performed to verify the correctness of the model. In the reactor power control system, both the reactor fission power and the coolant average temperature are regulated by the control rod reactivity. In the feedwater flow control system, the coordination between the reactor and the turbine is considered and coolant average temperature is adopted as one measurable disturbance for the control system. The coolant pressure is adjusted based on the heaters and spray in the pressurizer. The water level in the pressurizer is controlled by the charging flow and the letdown flow is compensated to calculate the charging flow needed. Transient simulations are carried out to evaluate the control system performance. When the reactor is perturbed, the reactor can be stabilized under the control system. (authors)

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Simulation and control of a passively cooled small modular reactor Samet - 142

This work regulates a small modular reactor (SMR) with traditional control methodologies and analyzes its response to typical disturbances. An analytical model for the passively cooled NuScale SMR is developed to represent the essential dynamics. The MATLAB/Simulink based model consists of reactor core, steam generator, pressurizer, hot leg riser and downcomer, and turbine representations. The point kinetics equations with a single combined neutron precursor group and the lumped parameter representations with single-phase natural circulation account for the neutronics and thermohydraulics in the reactor core. A lumped parameter, moving-boundary approach forms the basis of the nonlinear model adopted for the once-through helical-coil heat exchangers in which boundaries between regions of different fluid states (i.e., subcooled, boiling, and superheated) vary over time. A proportional-integral-derivative controller employing a sliding-average temperature strategy commonly used for pressurized water reactors is implemented. The responses of the SMR to two different disturbances are analyzed and discussed in detail. For the first scenario, a 5% step increase in the load is applied to the system, which results in a change in the steam valve opening. For comparison, two different simulations under this same disturbance are run: one including and one excluding the control systems. The second scenario tests the effectiveness of the control system to increase (or decrease) the reactor thermal power to a certain level within a desired time period. The simulation results show that important system variables are kept at the desired values by the proposed control strategy. (authors)

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Dynamic Behavior of Oval-Twisted Helical Tube Heat Exchanger: Numerical Study with RELAP5-3D

Convective heat transfer characteristics and theoretical thermal stress behaviors are numerically calculated using RELAP5-3D for the helical-coiled once-through steam generator (H-OTSG) and the novel heat exchanger design known as the oval-twisted helically coiled heat exchanger (OTHCHX) under (1) fluctuating wall temperature conditions, (2) square-wave pulsating flow conditions, and (3) the combined effects of fluctuating wall temperature and square-wave pulsating flow conditions. Heat transfer coefficient models for the H-OTSG and OTHCHX were developed based on existing data and implemented into RELAP5-3D, successfully capturing the N⁢uavg behavior within 8% to 10% of the reported data. Under fluctuating wall temperature conditions, the OTHCHX displayed higher N⁢u avg behavior than the H-OTSG. As 𝑓 increased, the $𝜎^{𝑚⁢𝑎⁢𝑥}_{𝑡⁢ℎ}$ decreased. The $𝜎^{𝑚⁢𝑎⁢𝑥}_{𝑡⁢ℎ}$ was higher for the OTHCHX than for the H-OTSG under fluctuating wall temperature conditions. Under pulsating flow conditions, the H-OTSG and OTHCHX displayed much higher 𝑁⁢𝑢 𝑎𝑣𝑔 than under constant flow conditions. The H-OTSG displayed a higher $𝜎^{𝑚⁢𝑎⁢𝑥}_{𝑡⁢ℎ}$ over the OTHCHX. Under combined fluctuating wall temperature and pulsating flow conditions, the augmented heat transfer behavior from the pulsating flow was counteracted by the wall temperature fluctuations, producing slightly higher 𝑁⁢𝑢 𝑎𝑣𝑔 over constant wall temperature, constant flow conditions, but much lower than only constant pulsating flow under constant wall temperature conditions. The effects of simultaneous wall temperature fluctuations and square-wave pulsating flow caused higher $𝜎^{𝑚⁢𝑎⁢𝑥}_{𝑡⁢ℎ}$ than that of only wall temperature fluctuations or pulsating flow. As the Reynolds number (Re) increased, $𝜎^{𝑚⁢𝑎⁢𝑥}_{𝑡⁢ℎ}$ increased. However, when 𝑓=𝑓$_{\dot{m}}$, the $𝜎^{𝑚⁢𝑎⁢𝑥}_{𝑡⁢ℎ}$ showed decreasing values as Re increased. In conclusion, the results indicate that thermal-fluid resonance can help mitigate thermal stresses.

Thermal stress↗

Model-free adaptive control of advanced power plants

A novel 3-Input-3-Output (3.times.3) Model-Free Adaptive (MFA) controller with a set of artificial neural networks as part of the controller is introduced. A 3.times.3 MFA control system using the inventive 3.times.3 MFA controller is described to control key process variables including Power, Steam Throttle Pressure, and Steam Temperature of boiler-turbine-generator (BTG) units in conventional and advanced power plants. Those advanced power plants may comprise Once-Through Supercritical (OTSC) Boilers, Circulating Fluidized-Bed (CFB) Boilers, and Once-Through Supercritical Circulating Fluidized-Bed (OTSC CFB) Boilers.

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