Jay I. Frankel

Slug calorimeters are rugged and proven sensors for hypersonic flight and ground tests. Data reduction through inverse theory is employed to obtain the heat flux from the temperature time history. The unknown heat loss into the surrounding structure introduces inaccuracies. Other than through extensive calibration, the inaccuracies can be addressed by improved and new sensor designs and associated theory. In this paper, a novel design is proposed that addresses the unknown heat loss problem at the back face by adding a stainless steel part with a second thermocouple. This multilayered slug calorimeter design is being tested in a purpose-built laser heat flux facility. Measurements provide validation data for heat transfer simulations that are being employed for design parameter studies. The simulation data are used for the testing of novel inverse theory. The present results demonstrate that the proposed bimetal slug calorimeter, in combination with new inverse theory, can provide accurate heat flux measurements. To evaluate sensor performance in a representative environment, the Mach 18 airflow over a hemisphere was simulated, and the wall heat flux served as input for sensor heat transfer simulations. The analysis revealed a 20% variation in the heat flux prediction depending on the wall catalycity.

Thin-film temperature gauges with nickel and silver sensing elements on a Macor ceramic substrate are evaluated for unsteady heat flux measurements in impulse facilities such as shock tunnels. Unsteady heat transfer simulations with known input heat flux provide resistance and temperature data. The heat flux is then recovered from inverse theory and compared with the known input heat flux. For the nickel-based sensor, the effect of the film thickness and film overlap with the insulator are investigated. Simulations with box and square function heat input demonstrate the dependence of the sensor frequency response on the film thickness. For the silver thin-film gauge, the effect of partial direct heat transfer into the surrounding insulator is investigated. The suitability of the silver thin film for time-resolved heat flux measurements in a turbulent high-speed boundary layer is evaluated. The unsteady wall heat flux is obtained from a large-eddy simulation of a high-enthalpy Mach 5 turbulent boundary layer in thermochemical nonequilibrium. Inverse analysis of the temperature data from the thin-film simulation provides the wall heat flux, which is in good agreement with the heat flux obtained directly from the large-eddy simulation, thus demonstrating that the thin-film gauge is well suited for impulse facility experiments.

In this paper, a parameter estimation approach, based on a least-square method and a quantified heat flux source, is proposed for estimating the effective thermal effusivity of a co-axial thermocou...

A calibration integral equation method is proposed for estimating the surface temperature in the context of a nonlinear inverse heat conduction problem. The temperature-dependent thermophysical properties and probe positioning are implicitly accounted in the integral equation formulation through calibration tests. A first kind Chebyshev expansion is applied to represent the temperature-dependent property transform function. The undetermined expansion coefficients associated with the Chebyshev expansion are then estimated through two calibration tests. Regularization of the ill-posed problem is achieved by the future-time method. The optimal regularization parameter is estimated using a phase plane and cross-correlation phase plane analyses. Numerical simulation for stainless steel yields highly favorable surface temperature prediction.

This paper utilizes concepts extracted from phase-plane and cross-correlation analyses for estimating the optimal regularization parameter required by a nonlinear space marching inverse heat conduction method. The regularization parameter for this approach is based on the cut-off frequency used in a low-pass Gauss digital filter for preprocessing the in-depth temperature data. The simulation uses two in-depth thermocouples which are representative of a physical experiment. Numerical results indicate a high level of robustness as the best prediction is extracted from the prediction space over the spectrum of cut-off frequencies. The feasibility and effectiveness of phase-plane and cross-correlation analyses are discussed.