Investigation Into the Effect of Uncertainty in Thermal Properties on Turbomachinery Disc Heat Transfer Using Both a Monte Carlo Simulation Technique and a Taylor Series Uncertainty Propagation Method

Abstract

The effect of uncertainties in the thermal properties of components and surrounding fluids is often ignored in the field of experimental turbomachinery heat transfer. The work reported here uses two different methods of uncertainty analysis to help quantify these effects: 1) a stochastic Monte Carlo simulation and 2) a Taylor series uncertainty propagation. These two methods were used on a steady state free disc test case having a turbulent flow regime. The disc modelled was made from IMI 318 titanium and had an inner and outer radius of 0.115 m and 0.22 m respectively, representative of engine and test rig geometry. The disc thickness was 0.016 m. Convective boundary conditions were derived from the relevant equation for local Nusselt number. The applied boundary conditions resulted in local heat transfer coefficients in the range of approximately 120 W/m2 K to 170 W/m2 K. Uncertainties for these heat transfer coefficients were a near identical match between the two different uncertainty methods and were found to be ± 0.66%. Calculated heat flux values fell within the range of approximately 1500 W/m2 and 5200 W/m2. The Monte Carlo uncertainty method returned uncertainty values varying from ± 1.17% to ± 0.47% from the inner and outer radii respectively. An extended Taylor series of uncertainty propagation returned uncertainties varying from ± 1.82% to ± 0.96%, from the inner and outer radius respectively and increased and decreased a number of times in between. These differences are due to assumptions and simplifications which need to be made when using the Taylor series method and shows that a Monte Carlo simulation analysis offers a better way of quantifying the uncertainties associated with disc to air heat transfer as it is more realistic. Studying the magnitudes of uncertainty allows the analyst to understand the impact that uncertainties in thermal properties can have on calculated values of disc to air heat fluxes and heat transfer coefficients.