Spectral Heat Transfer Coefficient for Thermal Design Analysis—Part II: Leveraging Diabatic Wall Conditioning for Nonlinear Regime

Abstract

There are two main issues of interest in the context of Newton's law of cooling as applied to turbine aerothermal designs. First, in a linear aerothermal regime in which both the conventional wisdom in general and the law of cooling in particular are notionally established, how do we deal with a non-isothermal wall where the wall surface temperature is non-uniform? Secondly, what can we do if an aerothermal system becomes nonlinear, manifested by qualitatively large changes in the flow field affected by heat transfer? In Part 1, a new spectral heat transfer coefficient (SHTC) method has been introduced for blade thermal analysis subject to non-isothermal walls in a linear aerothermal regime. It has been demonstrated definitively that the SHTC approach enables markedly more accurate thermal design analyses of a solid temperature field than the conventional method. Part II is devoted to address the issue of nonlinearity when the temperature field actively interacts with the velocity field as in many practical aerothermal problems. It is noted that the conventional approach rests heavily on an adiabatic state, so much so that its working range becomes overly restrictive. To move away from the adiabatic state, we take advantage of a smooth (“differentiable”) heat flux-wall temperature relation afforded by strong solid diffusion. A local linearization can be utilized by decomposing a full thermal variable into a nonlinear base as the reference and a locally linear perturbation. This split enables us to directly compute a nonlinear base as well as to carry out a linearized scaling with the SHTC (or HTC for isothermal wall) on top of the selected nonlinear aerothermal base state. The framework method has been implemented with relatively minor changes to the linear SHTC scaling method as presented in Part 1. The results of the present computational case studies clearly and consistently support the validity and effectiveness of the present approach.