The reduction of ill-posedness of the inverse heat transfer problem in rotating disc cavities using the wall temperature characteristics as the priori knowledge

Abstract

Solving the heat conduction equation using surface measurement temperature as boundary conditions to obtain surface heat flux is an ill-posed inverse heat transfer problem, in which small temperature errors can create large uncertainties in heat flux. This paper proposes a RBF (Radial Basis Function) + BP (Back Propagation) neural network approximation method that uses the wall temperature characteristics as priori knowledge to reduce the ill-posedness of the inverse heat transfer problem in rotating disc cavities of aero-engines. The wall temperature characteristics are described using first-order derivative, which are discussed and obtained through analytical solution and fluid-thermal coupling numerical simulation. Bayesian inference theory is used to construct neural network training objective function with regularization term and the RBF + BP neural network approximation method with uncertain regularization coefficient is proposed. Numerical experiments were conducted based on numerical simulation data to verify the effectiveness of the proposed method. The results show that the method can effectively suppress the ill-posed nature of the inverse heat transfer problem and can reduce the heat flux relative error level by 1 ∼ 2 orders of magnitude compared with several traditional data fitting methods commonly used in rotating disc cavities. The method of densifying measurement points combined with priori knowledge revision near the air impact point can effectively capture the local heat flux characteristics caused by airflow impact. The RBF + BP approximation method can reduce the demand for measurement points by approximately 44 ∼ 60 % under the error of 3σ = 0 K ∼ 0.9 K compared with Bayesian inference method.