Research on the Step-reduction Model of Thermal Power Steam Pressure Reducing Valve

Recently, the special control valve research team of Zhejiang University has conducted systematic research on the thermohydraulic characteristics of key regulating components of steam pressure reducing valves in thermal power plants. The related research results have formed an academic paper titled "Rapid Prediction of Thermohydraulic Characteristics of Steam Pressure Reducing Valves in Thermal Power Plants Based on Order Reduction Model". and was published in the journal International Communications in Heat and Mass Transfer (a TOP journal in the second zone of the Chinese Academy of Sciences). In response to the limitations of traditional CFD numerical simulation and experimental research methods in terms of efficiency and cost, a reduced-order model (ROM) based on eigenorthogonal decomposition (POD) was constructed, achieving rapid reconstruction and efficient prediction of complex flow fields. This significantly improved computational efficiency while ensuring engineering accuracy.

Steam pressure reducing valves are key regulating components in thermal power plants. Due to the high computational cost and time requirements, it is rather difficult to analyze their complex thermal-hydraulic characteristics. To address this issue, this study developed a reduced-order model (ROM) using eigenorthogonal decomposition (POD). Firstly, the flow field under different outlet pressures and strokes was numerically simulated; Secondly, use POD to extract spatial modes and modal coefficients; Finally, through fitting methods such as the Kriging model, support vector machine regression, and physics-based support vector regression, the relationship between modal coefficients and working conditions was established.

The results show that, compared with CFD simulation, ROM has increased the computational efficiency by more than four orders of magnitude. The maximum error of the ROM result is 13.59%. The ROM predicts the distribution of pressure, temperature and entropy, with a relative root mean square error (RRMSE) of less than 2%. This work proposes a new reduced-order modeling framework for predicting the distribution of physical quantities within pressure reducing valves.

In addition, this study provides a reference for developing rapid and accurate prediction models for engineering components in fluid dynamics applications.

Research Background

The steam pressure reducing valve is a key regulating component in the steam system of thermal power plants. It is responsible for reducing the pressure of high-temperature and high-pressure superheated steam (about 2 MPa, 574℃) to the required pressure downstream and controlling the flow rate by adjusting the opening degree. With the increasing demand for power peak shaving, valves need to operate frequently. If there is clogged flow (Ma>=1) inside them, it may lead to a decrease in efficiency or even equipment damage. Therefore, real-time monitoring of the internal flow field is crucial for safe operation. However, the interior of the valve is in an extremely high-temperature and high-pressure environment, making it impossible to install sensors at critical locations such as throttle holes. It is difficult to grasp the true internal pressure, speed and temperature distribution. At present, research on steam pressure reducing valves mainly relies on experiments and CFD simulations, but there are obvious shortcomings in terms of efficiency and cost. Therefore, this paper constructs a reduced-order model (ROM) based on eigenorthogonal Decomposition (POD). The core idea is: to extract the main flow modes from a small number of high-precision CFD results and reconstruct the flow field. Subsequently, a simple mapping between the working condition parameters and the modal coefficients is established. Under the new working conditions, the complete flow field can be quickly reconstructed without re-solving the complex fluid mechanics equations.

Research methods

The foundation for building a reduced-order model is to establish a high-quality training sample library. The study selected four outlet pressures (1.2 MPa, 1.4 MPa, 1.6 MPa, 1.8 MPa) and six valve strokes (20 mm to 120 mm), and combined them to form 24 sets of steady-state calculation conditions, covering the typical working condition range of this steam pressure reducing valve.

Verified by the on-site data of the thermal power plant, the maximum deviation between the CFD calculated flow rate and the measured value is 9.70%, which meets the engineering accuracy requirements and ensures the reliability of the subsequent ROM input data.

The EigenOrthogonal Decomposition (POD) method is adopted to reduce the dimension of CFD snapshot data. Arrange each group of flow field physical quantities (density, pressure, velocity, temperature, Mach number, entropy) as row vectors to construct a snapshot matrix X (m×n dimensions, where m=24 is the number of samples and n≈8×10⁶ is the number of grid nodes).

POD: X ≈ UΣV beta is achieved through Singular Value Decomposition (SVD). Among them, U contains the modal coefficient information, V contains the Spatial Modes, and the diagonal elements of Σ are singular values, representing the energy contribution of each mode. After being arranged in descending order of energy, the first mode accounts for 85.72% of the pressure field energy and 88.00% of the entropy field. The cumulative energy of the first 12 modes reaches 99%, so the truncation order k=12 is selected, and the higher-order modes are discarded to filter out numerical noise.

To achieve the prediction of new working conditions, it is necessary to establish the mapping relationship between the working condition parameters (outlet pressure p, valve stroke h) and the modal coefficient α, α=f(p, h). The study compared three regression methods: polynomial regression, Kriging, and support vector regression.

In addition, the research attempted physical information support vector machine regression. The residual term of the momentum equation is introduced into the SVR loss function, and the gradient descent algorithm is adopted to optimize the hyperparameter ε, so that the predicted flow field satisfies the momentum conservation constraint of the steady-state N-S equation on the symmetry plane.

However, the results show that since the POD basis function has been extracted from the CFD snapshot that satisfies the control equation, the basis function itself contains sufficient physical information; In the case of limited samples, the basic SVR has approached the upper limit of accuracy of this representation framework. Introducing physical constraints as secondary optimization terms did not significantly reduce the prediction error (RRMSE 1.16% vs 0.87%), but instead might lead to an increase in local regional bias due to excessive constraints.

The online prediction process of the final ROM is as follows: Input the target operating condition parameters (p, h), obtain 12 modal coefficients α youdaoplaceholder7 through Kriging model interpolation, and linearly superposition the pre-stored spatial modes at u(X)=Σα dv ϕ and dv (X) to reconstruct the complete flow field distribution. The computational complexity of this process is O(k×n). On the computing platform equipped with AMD EPYC 7763, a single prediction takes approximately 4.8 seconds, which is four orders of magnitude higher than the 11,665 seconds of CFD.

Research results

Taking the pressure prediction results as an example, the prediction results of the symmetric plane pressure field by the reduced-order model based on the Kriging model show that the RRMSE is 0.79% and the maximum relative error is 16.49%. The RRMSE of the model based on Support Vector Machine regression (SVR) is 0.87%, and the maximum relative error is 15.38%. Both methods control the relative error of the pressure distribution within the engineering acceptable range of 20%, and the RRMSE of both is less than 1%.

It is worth noting that in the annular gap area between the outer sleeve and the inner sleeve, due to the sudden expansion of the flow area, the flow rate decreases, and the pressure shows a significant rebound phenomenon, with the pressure value rising to between 1.53 MPa and 1.88 MPa. Subsequently, the steam flows through the throttling hole of the inner sleeve (secondary throttling), and the pressure drops again, eventually balancing with the pressure at the downstream outlet. This non-monotonic pressure distribution characteristic of "pressure reduction - rebound - pressure reduction again" was accurately captured by the ROM model. Whether it is the Kriging or SVR method, their prediction curves are in good agreement with the CFD reference values, with only minor deviations in the region with the maximum local gradient.

In the main body area of the valve cavity and the inlet and outlet pipeline areas, the pressure changes are relatively gentle, and the relative error is generally less than 5%, with some areas even less than 1%. The maximum relative error of 16.49% occurs at the local position near the wall at the outlet of the throttle hole of the outer sleeve. Here, the flow separation is intense, and the detail loss caused by the high-order mode interruption is most obvious. Despite this, the error level is still within an acceptable range for pressure trend judgment and overall load assessment in engineering applications.

The performance of the three fitting methods in flow field prediction was compared: The Kriging model with an RRMSE accuracy of 0.79% was slightly better than the SVR's 0.87%, and the two were comparable at the maximum error level (approximately 15-16%). The PI-SVR method with physical information constraints introduced does not show an advantage in pressure prediction. Its RRMSE is 1.16%, the maximum error reaches 17.67%, and the error distribution range in the high-gradient area of the throttle hole is expanded compared with the basic SVR.

This phenomenon indicates that for physical quantities like pressure, which have strong nonlinearity but relatively fixed spatial structure, Kriging interpolation based on Gaussian processes can better handle small sample and non-parametric mapping relationships. Therefore, for the rapid prediction of the flow field of steam pressure reducing valves, the Kriging model was determined to be the optimal solution.

Research Prospects

The research results provide a feasible technical path for the digital twin construction of pressure reducing valves. This ROM model can achieve real-time reconstruction and visual monitoring of key parameters such as the internal pressure field and temperature field of the valve, solving the "black box" problem caused by the inability of traditional sensors to be installed inside the throttling component.

However, it should be pointed out that the reduced-order model established in this study has clear applicable boundaries. Firstly, the effective range of the model is strictly limited to the parameter space covered by the training data and does not have the ability to extrapolate to unsampled geometries or different boundary conditions. Secondly, the current model is constructed based on steady-state snapshots and is only applicable to steady-state working condition prediction, unable to capture the transient flow evolution during the rapid action of the valve.

Subsequent research will deepen and expand the current work from the following two aspects:

The first is transient flow modeling. By combining time series analysis methods (such as Dynamic Mode Decomposition DMD or Long Short-Term Memory Network LSTM), a dynamic reduced-order model capable of predicting unsteady flow evolution is constructed.

The second is the optimization of physical information methods. Re-examine the implementation strategies of physical information machine learning, explore the introduction of physical constraints in the modal extraction stage rather than the regression stage, or adopt a multi-fidelity framework combined with low-resolution CFD and physical information neural networks to improve the model's extrapolation ability and physical consistency in sample sparse regions.