An Analytical Approach for Calculating Instantaneous Multilayer-Coated Wall Surface Temperature in an Engine 2020-01-0160

Thermal swing coatings that have low volumetric heat capacity and low thermal conductivity are attractive because they have the potential to significantly reduce heat transfer to the combustion chamber walls. This paper presents an analytical method for determining the exact solution of the time-resolved wall temperature during the engine cycle for any number of coating layers and properties using the Laplace transformed heat diffusion equation. The method relies only on material properties and the past heat flux history, and represents the exact solution of the heat diffusion equation. The analytical nature of the solution enables fast computation and, therefore, application to system-level optimization calculations. The model relies on an assumption of one-dimensional heat flow, and constant material properties. The major advantage of this approach compared to the standard finite difference approach, wherein the wall is finely discretized, is that there is no approximation and the accuracy is guaranteed, i.e., it does not depend on nodal density. Results are presented for both a quasi-steady operating condition and for an engine transient event. In the latter case a 200-fold reduction in computation time relative to a finite difference code was realized.