Prediction of the Turbine Tip Convective Heat Flux Using Discrete Green Functions

[+] Author and Article Information
Valeria Andreoli

School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907

David Gonzalez Cuadrado

School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907

Guillermo Paniagua

School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907

1Corresponding author.

ASME doi:10.1115/1.4039182 History: Received July 18, 2017; Revised November 30, 2017


The heat fluxes across the turbine tip gap are characterized by large unsteady pressure gradients and shear from the viscous effects. The classical Newton heat convection equation, based on the turbine inlet total temperature is inadequate. Previous research from our team relied on the use of the adiabatic wall temperature. In this paper, we propose an alternative approach to predict the convective heat transfer problem across the turbine rotor tip using Discrete Green Functions. The linearity of the energy equation in the solid domain with constant thermal properties can be applied with a superposition technique to measure the data extracted from flow simulations to determine the Green's function distribution. The Discrete Green Function is a matrix of coefficients that relate the temperature spatial distribution with the heat flux. This methodology is first applied to a backward facing step, validated using experimental data. The final aim of this paper is to demonstrate the method in the rotor turbine tip. A turbine stage at engine-like conditions was assessed using a CFD software. The heat flux pulses were applied at different locations in the rotor tip geometry, and the increment of temperature in this zone was evaluated for different clearances, with a consequent variation of the Discrete Green Function coefficients. Ultimately, a detailed uncertainty analysis of the methodology was included based in the magnitude of the heat flux pulses used in the Discrete Green Function coefficients calculation and the uncertainty in the experimental measurements of the wall temperature.

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