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Probabilistic methods for the quantification of uncertainty and error in computational fluid dynamics simulations

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Abstract

The life of engine components is determined by a combination of the material properties and the applied stresses and temperatures. As a consequence of variability in these parameters, the component life is not fixed (deterministic) but stochastic (random) and may be characterised by a probability density function (PDF). In order to reduce the cost of ownership of ADF aircraft these PDFs need to be determined as accurately as possible. Probabilistic techniques offer significant potential for accurate and realistic estimates of component lives by quantifying stochastic elements of an analysis rather than introducing excessive conservatism to allow for them. This report examines the feasibility of using a probabilistic approach for modelling the component temperatures in an engine using CFD (Computational Fluid Dynamics).

Executive Summary

DSTO has developed a risk and reliability management capability for mechanical components in propulsion systems. This includes an assessment of relative airworthiness risks resulting from modifications to life limits as a consequence of operational, logistic and repair requirements. It will expand the understanding of the fundamental mechanisms and processes responsible for the statistical distribution of lives in aircraft dynamic components. The overall purpose of this capability is to provide technical airworthiness advice to the RAAF on those critical factors that underpin the promulgation of operational lives of propulsion system components, and on the risks associated with varying these life limits. The life of engine components is determined by a combination of the material properties and the applied stresses and temperatures. As a consequence of variability in these parameters, the component life is not fixed (deterministic) but stochastic (random) and may be characterised by a probability density function (PDF). In order to reduce the cost of ownership of ADF aircraft these PDFs need to be determined as accurately as possible. Probabilistic techniques offer significant potential for accurate and realistic estimates of component lives by quantifying stochastic elements of an analysis rather than introducing excessive conservatism to allow for them. The objective is to devise a methodology that brings together probabilistic and deterministic approaches in a manner that best supports improved component life estimates. This will reduce under-utilisation and cost of spare parts, and increase safety. This report examines the feasibility of using a probabilistic approach for modelling the component temperatures in an engine using CFD (Computational Fluid Dynamics). Currently, CFD analysis for engine temperature uses deterministic inputs. Small variations in these inputs may have a significant effect on the resultant component temperatures and in turn the predicted life. This is especially important for creep life assessment when a change of 20°C can halve the creep life. The CFD discipline is less mature than the linear finite element stress analysis discipline because CFD requires much greater computer power to solve problems of practical engineering interest. For this reason probabilistic methods have been too computationally expensive to be widely adopted in CFD. Computer power has now increased to the point where probabilistic CFD has become a very active area of research. This report untangles some of the confusion and debate which currently surround the definitions of "error", "uncertainty" and "variability" in computational simulation, and the three distinct processes of verification, validation and uncertainty analysis. It critically reviews a range of probabilistic and non-probabilistic methods which may be used to propagate the uncertainty from the input variables, through the model, to the output variables. Finally it makes recommendations for the application of the probabilistic methods to CFD.

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