Simultaneous estimation of reference temperature and heat transfer coefficient in transient film cooling problems

Abstract

This paper aims to simultaneously estimate the reference temperature and heat transfer coefficient in film cooling situations from transient temperature measurements. The exist-ing steady-state technique is a tedious process and employs distinct boundary conditions to evaluate each parameters of the film cooling. Applying different boundary conditions may lead to errors in the estimated parameters due to differences in aerodynamic condi-tions. On the other hand, a transient technique can estimate both parameters in a single test by utilizing short-duration transient temperature data. Hence, the present study uses a novel approach for solving transient film cooling problems based on the inverse heat con-duction approach, which can simultaneously estimate heat transfer coefficient and refer-ence temperature. The present method employs an optimization technique known as the Levenberg-Marquardt Algorithm. The objective function for the inverse algorithm is con-structed using the analytical solution of a transient one-dimensional semi-infinite body. The transient surface temperature data required for the present analysis is obtained through a numerical simulation of film cooling arrangement over a flat surface. Laterally averaged effectiveness and heat transfer coefficient for blowing ratios of 0.5, 0.8, and 1.0 are analyzed using the present technique and compared against the steady-state simulation results to demonstrate the methodology. An average deviation of around 7% for the estimated effec-tiveness and 4% for the heat transfer coefficient values are observed between the present IHCP method and the steady state simulation results. The deviation in heat transfer coeffi-cient predominately occurred near the film hole exit of x/d < 5, which might have occurred due to the conjugate solution employed in the present work.