An Investigation Into the Uncertainty of Turbomachinery Disc Heat Transfer Calculations Using Monte Carlo Simulation Methods

Abstract

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.

Radially resolved measurement of stator heat transfer in a rotor–stator disc system

“…The method offers high spatial resolution and does not interfere with the flow, although for accurate results it requires in-situ calibration with known surface temperature reference points. Also, as Cooke [16] shows, solving for heat transfer by inverse analysis of temperature differences can produce very large uncertainties in certain scenarios. 4.…”

Heat Transfer Analysis in a Rotating Cavity With Axial Through-Flow

“…The Nusselt number profile in Figure 12 clearly illustrates that by decreasing the number of measurement points used in the temperature fit there is both an increase in Nusselt number in the outer part of the disc and that the confidence interval increases considerably. This result is unsurprising given that by using a reduced number of measurement point in the curve fit, the fit becomes less restrained leading to a larger spread in the results and is consistent with [2].…”

“…In the context of this paper, Monte Carlo simulation is used as a stochastic alternative to Taylor series uncertainty propagation analysis, which requires independent parameters and is considerably more complicated. It has been previously shown to offer practical results for evaluating disc surface heat fluxes [2]. To conduct a Monte Carlo simulation the model is repeatedly run, on the same mesh, using boundary conditions based on experimentally measured temperatures modified with a randomly generated (Gaussian probability distribution) uncertainty within the bounds of ±0.5 K. For each test case, the solver is run 10,000 times, which is considered sufficient [19] and the surface normal heat fluxes recorded.…”

“…Previously, Owen [1] used fitted curves to the data points to smooth the data and minimise uncertainty in calculated heat fluxes whilst Cooke et al [2] extended this using Monte Carlo simulation. Both used finite-difference approximations applied to simplified grids representative of turbine/compressor discs of gas turbine engines, similiar approaches were followed by Alexiou [3] and Patounas [4].…”

A disc to air heat flux error and uncertainty analysis applied to a turbomachinery test rig design

“…References [9] and [10] showed that for certain radial and axial temperature gradients across a disc, it was possible to decrease the magnitude of heat transfer coefficient uncertainty by increasing the instrumentation density. This was seen to be based on the fact that including more data points in the fitting of an interpolation curve imposed tighter constraints on the interpolated values, by definition of a curve fitting process.…”