Time-resolved heat flux determination from fast-responding temperature-sensitive paint measurement in a shock tunnel using transient in-situ calibration

Measurement of the global heat flux using fast-responding temperature-sensitive paint (fast TSP) in a shock tunnel is crucial to understanding complex aerothermal effects, but its accuracy is limited by the simplified inverse algorithm as well as the uncertainty in the thermal properties and the thickness of the TSP. In the present work, an in-situ transient calibration method is proposed to determine important parameters in one-dimensional double-layer semi-infinite heat conduction for TSP measurement via heat flux gauges. A fast-converging iterative scheme based on the Levenberg-Marquardt algorithm is used to search for the optimal parameters that minimize the difference between the transient experimental and simulated temperature histories. Furthermore, the heat flux history is determined using the impulse method according to the calibrated parameters. A fast-TSP measurement of 34 degrees ramp flow was conducted at 75 kHz in a Mach-12.1 shock tunnel to validate the proposed method. The results show that the heat flux histories obtained from the TSP and the heat flux gauge results are in good agreement throughout the test period of 11 ms. Moreover, the use of multiple gauges in the calibration further improves the overall consistency of the heat flux amplitude. The in-situ transient calibration method effectively improves the accuracy of the measurement of time-resolved heat flux with relatively low hardware and computational costs.