Experimental Demonstration of Inverse Heat Transfer Methodologies for Turbine Applications

Abstract

Gas turbines operate at extreme temperatures and pressures, constraining the use of both optical measurement techniques as well as probes. A strategy to overcome this challenge consists of instrumenting the external part of the engine, with sensors located in a gentler environment, and use numerical inverse methodologies to retrieve the relevant quantities in the flowpath. An inverse heat transfer approach is a procedure that is used to retrieve the temperature, pressure, or mass flow through the engine based on the external casing temperature data. This manuscript proposes an improved digital filter inverse heat transfer method, which consists of a linearization of the heat conduction equation using sensitivity coefficients. The sensitivity coefficient characterizes the change of temperature due to a change in the heat flux. The heat conduction equation contains a non-linearity due to the temperature-dependent thermal properties of the materials. In previous literature, this problem is solved via iterative procedures that however increase the computational effort. The novelty of the proposed strategy consists of the inclusion of a non-iterative procedure to solve the non-linearity features. This procedure consists of the computation of the sensitivity coefficients in the function of temperature, together with an interpolation where the measured temperature is used to retrieve the sensitivity coefficients in each timestep. These temperature-dependent sensitivity coefficients are then used to compute the heat flux by solving the linear system of equations of the digital filter method. This methodology was validated in the Purdue Experimental Turbine Aerothermal Laboratory (PETAL) annular wind tunnel, a two-minute transient experiment with flow temperatures up to 450 K. Infrared thermography is used to measure the temperature in the outer surface of the inlet casing of a high-pressure turbine. Surface thermocouples measure the endwall metal temperature. The metal temperature maps from the IR thermography were used to retrieve the heat flux with the inverse method. The inverse heat transfer method results were validated against a direct computation of the heat flux obtained from temperature readings of surface thermocouples. The experimental validation was complemented with an uncertainty analysis of the inverse methodology: the Karhunen–Loeve expansion. This technique allows the propagation of uncertainty through stochastic systems of differential equations. In this case, the uncertainty of the inner casing heat flux has been evaluated through the simulation of different samples of the uncertain temperature field of the outer casing.