Inverse estimation of hot-wall heat flux using nonlinear artificial neural networks. (August 2021) - Wang, Hui; Zhu, Tao; Zhu, Xinxin; Yang, Kai; Ge, Qiang; Wang, Maogang; Yang, Qingtao
Highlights: A modified, inverse-estimation analytical model of heat flux is presented; The nonlinear inverse model is approximated by an artificial neural networks; A hot-wall heat flux sensor for the nonlinear inverse estimation is developed. Abstract: Compared with cold-wall heat flux measurement, hot-wall heat flux indicates more information from dynamic heat transfer between the aerothermodynamic boundary layer and the true model's surface; thus, hot-wall heat flux measurement has become predominant in the aerothermodynamic measurement field. In harsh aerothermodynamic in-flight or ground tests, the hot-wall heat flux must be determined from time history temperature measurements at one or more interior locations. Therefore, accounting for the temperature dependence of the thermophysical properties, hot-wall heat flux measurement essentially results in the solution of the nonlinear inverse heat conduction problem (IHCP). In this paper, a novel inverse estimation of hot-wall heat flux using nonlinear artificial neural networks (ANN) is presented. First, motivated by the hybrid method proposed by Clayton A. Pullins, David O. Hubble, and Tom E. Diller et al., [2010], a modified hybrid heat flux measurement method using two in-depth thermocouples is proposed, which avoid to directly measure surface temperature of gauge or model under harsh aerodynamic heating environments; accounting for the unknown temperature dependent thermophysical properties, a new heat flux inverse estimation model of a nonlinear ANN is proposed and identified to approximate the modified hybrid measurement method through calibration experiment. This heat flux inverse estimation method does not need to solve a first kind Volterra integral equation and to obtain the information about the thermophysical properties of heat conduction body, and the thermal inertia, locations of thermocouples. This paper presents xenon lamp calibration and arc-heated wind tunnel experiments that validate the new inverse estimation method combined with the fabricated hot-wall heat flux sensor and its probe. These experimental results show that, in general, the dynamical hot-wall heat flux estimated based on the proposed method agree well with the known calibrated values and the stagnation heat fluxes of the classic slug calorimeter.