Analysis of Cavity Disk Heat Transfer by Solving Inverse Heat Transfer Problem

Abstract

The flow and heat transfer within compressor rotor cavities of aero-engines is a conjugate problem. The operating conditions buoyancy forces, caused by radial temperature difference between the cold throughflow and the hotter shroud, can influence the amount of entrained air significantly. By this, the heat transfer depends on the radial temperature gradient of the cavity walls, and in turn, the disk temperatures are dependent on the heat transfer. In this article, disk Nusselt numbers are calculated in reference to the air inlet temperature and in comparison to a modeled local air temperature inside the cavity. The local disk heat flux is determined from measured steady-state surface temperatures by solving the inverse heat transfer problem in an iterative procedure. The conduction equation is solved on a 2D mesh using a validated finite element approach, and the heat flux confidence intervals are calculated with a stratified Monte Carlo approach. An estimate for the amount of air entering into the cavity is calculated by a simplified heat balance. The major influences on the Nusselt number were found to be the mass flowrate entering the cavity and the density of the fluid inside the cavity.