Property-Embedded Parameterized Physics-Informed Neural Network for Modeling Supercritical Pressure Fluid Convective Heat Transfer

Quantifying velocity and temperature fields is essential for understanding convective heat transfer. However, for supercritical pressure fluids with dramatic thermal property variations as temperature arises, the complex heat transfer behaviors pose significant challenges in the acquisition to the measurement and prediction of the physical fields. To overcome this challenge, we develop a physics-informed deep learning framework to derive the physical fields from the sparse experimental measurements and numerical simulations, named property-embedded parameterized physics-informed neural network. This approach addresses two key issues in modeling supercritical pressure fluid convective heat transfer, the gradient derivation problem for thermal properties and the time dimension inconsistency between the steady-state experiment and transient physical constraint. To evaluate the model, numerous numerical experiments are conducted. The results reveal that, the models achieve an average absolute mean error of below 0.01 when trained with less than 1% of the available data. Compared with the baseline framework, the model’s generalization and robustness are improved by 52.9% and 29.1%, respectively, and the proposed multi-head structure is effective in enhancing model convergence. Furthermore, this framework is applied in practical experiment scenarios, and successfully invert the sparse wall temperature measurement results into a detailed temperature field, with a resulted average error below 6% for convective heat transfer coefficient. This represents the first demonstration of the potential of a physics-informed deep learning framework to directly quantify physical fields from limited boundary data in a multi-physics coupling systems.

This work can be sited as:

Qingyan Weng, Yuli Cao, Peixue Jiang, Zhihe Li, Ruina Xu. Property-embedded parameterized physics-informed neural network for modeling supercritical pressure fluid convective heat transfer, AI Thermal Fluids, 2025: 100003

View full paper on ScienceDirect:

https://www.sciencedirect.com/science/article/pii/S3050585225000023

We have opened the DNS data and P3INN code involved in this article, which corresponds to the convective heat transfer process of supercritical pressure CO2 flowing upward in a vertical circular tube. The working conditions are shown in the following table. The data format is .mat, and can be read into a dictionary using the scipy.io.loadmat command in Python.

Source file name Case Mesh for x×r R* (mm) L* T0* (K) p0* (MPa) 2×Re0 qw* (kW/m²)
Junjie Yan[1] q27.matC1 2304×64 0.4765 180 R* 296.15 7.6 3600 27
q42.35.matC242.35
q48.matC348
q55.59.matC455.59
q63.matC563
Yuli Cao[2] 1_p7.75q49.matC6 3072×72 0.5 240 R* 296.15 7.75 3540 78
3_p7.75q78.matC749
Yuli Cao[3] P8.8q549d99C8 3840×56 0.496 300 R* 297.35 8.8 3800 548.8

References:

[1] Yan, J. Researches on Turbulent Heat Transfer Mechanism and Thermal Cracking of Supercritical Pressure Fluids. Ph.D. Dissertation 2018 (Beijing: Tsinghua University) (in Chinese).
[2] Cao YL, Xu RN, Yan JJ, He S, Jiang PX. Direct numerical simulation of convective heat transfer of supercritical pressure in a vertical tube with buoyancy and thermal acceleration effects, J Fluid Mech 2021:927.
[3] Cao Y, Ruina Xu, He S, Jiang P. Accelerating turbulence in heated micron tubes at supercritical pressure. J Fluid Mech 2023;972:A13.

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