Spectral Heat Transfer Coefficient for Thermal Design Analysis—Part 1: Augmenting the Cooling Law for Non-Isothermal Wall

Abstract

There are two major issues of interest in relation to Newton's law of cooling. The first is its applicability to flow bounded by a nonisothermal wall where the wall surface temperature is nonuniform. The second is the restriction by the basic linear assumption. In terms of the first issue, a general Green's function-based framework exists but its implementation as a working method has been lacking, attributable to the inherent locality of Green's function. Instead of setting up and solving the local–local influence and response, a new spectral heat transfer coefficient (SHTC) method takes a different avenue. It sets up and solves global-to-local temperature-heat flux influences for a small number of low order spectral modes of wall temperature disturbances. The SHTC approach covers a range of physically relevant and numerically resolvable length scales, which have been missing in the conventional cooling law. The present work is aimed at applying the SHTC methodology to turbine blade aerothermal analysis. Two aerothermal regimes are considered, respectively. In the first part (Part 1 of the two-part article), the SHTC approach is described and case-studied for a linear aerothermal regime where the flow energy equation behaves linearly and the corresponding temperature (thermal) field is passively dictated by the velocity (momentum) field. In the companion paper (Part II), the methodology will be extended to a nonlinear regime, where the temperature field will be actively interacting with (rather than passively influenced by) the velocity field.