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The uncertainty in heat transfer data derived from theoretical turbomachinery disc temperatures has been investigated using Monte Carlo simulation methods. Two specific test cases of relevance to turbine disc heat transfer have been considered, a free disc with laminar flow and a free disc with turbulent flow. This study explores and quantifies uncertainties for the test cases considered by looking at three factors: measurement noise, the order of magnitude of the polynomial fit used for interpolation through the data points and the number of data points utilised within the polynomial. The local heat flux uncertainty arising from using a 5th order polynomial for the laminar case varied between approximately ± 40 % and ± 600 % and for the turbulent case between approximately ± 4 % and ± 1000 %. This study provides guidelines for similar analyses and the resulting uncertainty and how test data can be presented.

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This article describes a Monte Carlo simulation-based error and an uncertainty analysis for values of disc to air heat fluxes as part of the design of an experimental axial turbine test rig. This work is of interest for those who study heat transfer and measurement or the design and use of experimental test rigs. An inverse analysis of theoretical disc surface temperatures was performed for different thermocouple configurations to compare the errors and uncertainties resulting from each to establish whether there was any configuration that would return the lowest magnitudes of error and uncertainty and hence influence the location of the proposed instrumentation. It is shown that great care needs to be taken when using an analysis of this kind together with temperature measurements having realistic and typical uncertainty values. This is because such an analysis is purely analytical, and any small fluctuations in the inputs, such as typical thermocouple uncertainties and noise, result in the process of an inverse analysis becoming unstable. This instability has two effects: (a) the returned values of heat flux have an inbuilt bias error and (b) the magnitudes of uncertainty can exceed>100 per cent.

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.