Application of conjugate gradient method for estimation of the wall heat flux of a supersonic combustor

In this paper, conjugate gradient method (CGM) considering variations in material properties with temperature is developed to solve transient inverse heat conduction problems. With CGM, the measured outer wall temperatures of supersonic combustor are used as input data to recover the heat flux and temperature on the inner wall. Numerical test has been done to study the effect of temperature measurement noises on accuracy of the inversion result. It indicates that the inversion results are very close to the exact heat flux with a maximum error of less than 5% when the measurement noise is less than ±3 K. At the same time, a series of experiments are conducted on a Mach 3 supersonic combustor test facility with varied fuel injection conditions. The heat fluxes on the inner wall are recovered by measured outer wall temperatures via CGM. The inversion results of heat flux agree satisfactorily with the values measured by heat flux sensors and a maximum difference of less than 5% is found. The present comparison results prove the validity and accuracy of the CGM developed in the paper for estimation of the wall heat flux of supersonic combustor.