Surrogate Model for Heat Transfer Prediction in Impinging Jet Arrays using Dynamic Inlet/Outlet and Flow Rate Control

Abstract

This study presents a surrogate model designed to predict the Nusselt number distribution in an enclosed impinging jet arrays, where each jet function independently and where jets can be transformed from inlets to outlets, leading to a vast number of possible flow arrangements. While computational fluid dynamics (CFD) simulations can model heat transfer with high fidelity, their cost prohibits real-time application such as model-based temperature control. To address this, we generate a CNN-based surrogate model that can predict the Nusselt distribution in real time. We train it with data from implicit large eddy computational fluid dynamics simulations (Re < 2,000). We train two distinct models, one for a five by one array of jets (83 simulations) and one for a three by three array of jets (100 simulations). We introduce a method to extrapolate predictions to higher Reynolds numbers (Re < 10,000) using a correlation-based scaling. The surrogate models achieve high accuracy, with a normalized mean average error below 2% on validation data for the five by one surrogate model and 0.6% for the three by three surrogate model. Experimental validation confirms the model's predictive capabilities. This work provides a foundation for model-based control strategies in advanced thermal management applications.

Figures (13)

• Figure 1: Geometries of the two jet active cooling systems: (a) Five by one configuration and (b) Three by three configuration. In these systems, every inlet can be dynamically changed into an outlet and every outlet can be changed into an inlet. Any nozzle can also be shut. The surrogate models estimate the Nusselt distribution on the surface outlined by the green dashed line.
• Figure 2: Side view of the coarsest initial 3D mesh (228,000 elements) used for the mesh convergence analysis. The zoomed sub-image illustrates the mesh refinement along the top boundary.
• Figure 3: Mesh convergence analysis results where jets 0, 1, 2, and 3 are inlets at a Reynolds number of 2,000 and jet number 4 is set as an outlet. We present three simulation results using 228,000 cells, 1.2M cells and 3.0M cells. The three time-averaged Nusselt number curves are taken along the center of the five by one jet active-cooling system ($y = L/2$). The time average is computed from 40s to 60s. Results show mesh independence with a RMSE of 0.07 for 1.2M cells.
• Figure 4: Simulation partitioning for the five by one active cooling system. 83 low Reynolds number simulations (Re < 2,000) are split into training, testing, and validation sets. The training and testing sets are used to train and to select the convolutional neural network's (CNN) hyperparameters. This tuning is done using a k-fold cross validation technique. Performance evaluation of the CNN is done by comparing the predictions to unseen validation simulation results (20%). The predictions at Re=2,000 of the trained CNN are then extrapolated using correlation based technique to Re=10,000. A second validation dataset is then used to validate the performance of the extrapolation.
• Figure 5: Illustration of a transposed convolution operation with a 4 by 4 kernel and a stride of 2. The input feature map (left) is expanded, and the kernel is applied in a sliding-window fashion to produce a larger output feature map (right). The powdered blue highlights the input values of a single channel, while the cyan is the resulting output of the kernel operation. This operation effectively doubles the size of the input.