Real-time estimation of time-dependent heat flux for 3D finite domain employing thermal mode and recursive least square deconvolution

Abstract

This paper presents a novel surface heat flux estimation method for the 3D finite domain experiencing dynamic convection and surface heat flux. The thermal mode parameter is adopted to produce a mathematical relation between the surface heat flux history function and the transient temperature response vector with modal superposition method and to locate specific measurement point which can represent transient temperature change of the domain. The direct solution is obtained using the modal superposition method with thermal modes and modal time constants representing thermal characteristics of domain, and the proposed surface heat flux estimation method is derived by the inverse solution applying the novel recursive least square deconvolution (RLSD). The proposed method is validated by numerical tests and experiments that include two main advanced points: employment of the dynamic convection condition and implementation of efficient computing for real-time estimation. As a result, the root mean square error (RMSE) of numerical tests show the results within 2% for the maximum magnitude of hypothetical heat flux for all cases. Also the estimation result from experiment presents the RMSE within 2.5% for the maximum magnitude of measured heat flux history, achieved in only 49 s of computing time for long-term estimation of 100 min.