Inverse problem of transpiration cooling for estimating wall heat flux by LTNE model and CGM method

In this work, a transient inverse problem of transpiration cooling is investigated in detail. The heat flux on the wall to be cooled is estimated by single point temperature measurement. The local thermal non-equilibrium (LTNE) model is utilized to describe the energy conservation of transpiration cooling process, and the conjugate gradient method (CGM) is extended to solve the inverse problem. The accuracy of the solutions of the inverse problem is examined through three given heat fluxes with given measurement errors. The examination shows that with the LTNE model and CGM, satisfactory solutions can be obtained. The influences of the variation in thermal properties, compressibility and the location of sensor on the accuracy of the solutions are analyzed. The analysis indicates that the variation in thermal properties and compressibility should be considered when a large temperature gradient exists, and the sensor location should be as close as possible to the hot wall. The inverse solutions obtained by the measurements of solid and fluid temperatures are compared. Through the comparison, it is found that using the solid temperature measurement as the input of the inverse problem is better than using the fluid temperature measurement.