An Iterative Neural Operator to Predict the Thermo-Fluid Information in Internal Cooling Channels

Abstract

Abstract The design of internal cooling channels played an important role in turbine cooling. Distributions of thermo-fluid information, including surface distributions, cross section distributions and projected distributions are common forms of data for internal cooling research. For over half a century since 2-D thermo-fluid data were obtainable, there were very few universal tools to regress images. While several mathematical methods worked well with regressing zero-dimensional data, they were hardly compatible with 2-D data. Recent progress in the deep learning domain provided capability for image regression by using a convolutional feature encoding-decoding process. However, deep learning models usually had a huge number of trainable parameters, which substantially reduced the generalization accuracy on small datasets. Therefore, the convective heat transfer field has been continuously searching for reduced ordered models to regress images that could generalize on an obtainable small dataset. This study proposed a reduced ordered model to regress thermo-fluid image data by integrating the physics nature of thermo-fluid problems with neural networks. This effort started from a general partial differential equation and utilized a series of derivation to convert the equations into a recurrent convolutional neural networks. By releasing the convolutional kernels to trainable parameters and using data to train the kernels, a single layer convolutional neural networks could accurately replace a spatial advancing step of the thermo-fluid image within an iteration step. The recurrent convolution neural networks were tested on a convective heat transfer dataset obtained from simulating a cooling channel with random surface patterns on one side. The tested data included the temperature distribution on the cooled solid surface, the projected heat flux image on the fluid-solid interfaces, and the pressure distribution in the middle cross section. Results indicated an excellent regressing accuracy of the presented model for the three types of data, which was elevated as compared with a widely used cGAN deep learning model. Most importantly, the proposed model only consumed 1/290 trainable parameters as compared with the cGAN model. The key features that led to the success of proposed reduced ordered model included: the matching between the differential nature of a convention-diffusion phenomenon and the convolution calculation process, the compliance of the time evolution nature of thermo-fluid images with the recurrent structure of the model, the embedding of boundary condition images into the inputs, and the introduction of hidden state images into the networks.