Bi-Fo time scaling method in the numerical simulation of transient conjugate heat transfer

Yu Shi ^a, Shuiting Ding ^b, Tian Qiu ^b,*, Chuankai Liu ^b, Shenghui Zhang ^a

a. School of Energy and Power Engineering, Beihang University, Beijing, 100191, China
         b. Research Institute of Aero-Engine, Beihang University, Beijing, 102206, China

Abstract: Reliable transient thermal analysis plays a very important role in the engine safety analysis. Transient conjugate heat transfer simulation is an important way of temperature analysis. But there exists a great disparity in the time scales between solid conduction and fluid convection. The calculation cost of transient conjugate heat transfer analysis is very huge because of the tiny time step of computational fluid dynamics. The Bi-Fo time scaling method is proposed to improve the computational efficiency of transient conjugate heat transfer. On the one hand, this method carries out a similar transformation on solid heat conduction, scaling the calculation time with the product of density and specific heat capacity to maintain the consistency of Fourier number. On the other hand, it takes very short time for the fluid domain to recover stability after a boundary disturbance. Based on the above characteristic, the flow time is directly compressed to the same as that of the solid domain. It is verified by Mark Ⅱ vane that increasing the solid thermal diffusivity can reduce the time scale of heat conduction. In the situation of rapidly stable flow field, scaling flow time does not affect the solid thermal boundary under corresponding dimensionless time. Within the application scope, the Bi-Fo time scaling method can greatly reduce the time cost of transient conjugate heat transfer simulation while maintaining the accuracy of transient temperature analysis.

Keywords: Transient; Temperature analysis; Conjugate heat transfer; Similar transformation; Time scaling

https://doi.org/10.1016/j.jppr.2021.05.005