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Development, Implementation and Testing of an Alternative DDES Formulation Based on Elliptic Relaxation

Ashton, Neil

[Thesis]. Manchester, UK: The University of Manchester; 2013.

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Abstract

A new formulation of Delayed Detached-Eddy Simulation (DDES) based upon elliptic relaxation is derived and implemented within a finite-volume framework. This new formulation is based upon the φ − f RANS model which has previously demonstrated both improved modelling of the near-wall physics and numerical robustness for industrial applications. The φ − f DDES model is calibrated and validated using Decaying Isotropic Turbulence (DIT) to establish the validity of the derivation and to calibrate the model constants. In light of the numeri- cal scheme requirements for DDES, a hybrid numerical scheme is proposed and implemented, which is shown to perform in the intended manner.Initially, three DDES formulations (SA-DDES, SST-DDES and φ − f DDES) are compared on the 2D periodic hills test case at Re = 10590 and Re = 37000. This test case primarily serves as a validation case to evaluate whether the im- plementation and calibration were correct. The flow over a NACA0021 airfoil post-stall at 60o incidence is then evaluated; a test case that DDES was origi- nally devised for (i.e massive separation from an airfoil). The three formulations are then evaluated on a 2D wall-mounted hump which exhibits largely geometry induced separation, but is still sensitive to the modelling of the initial separated shear layer and upstream turbulence levels. The final case is the Ahmed car body which combines both geometry and pressure-induced separation from a 3D surface. This complex flow is challenging for any turbulence modelling approach and is sensitive to the underlying RANS model.A general sensitivity to the underlying RANS model is demonstrated for the majority of the test cases investigated. The φ − f DDES model is shown to have encouraging performance on these wide range of test cases compared to the established SST-DDES and SA-DDES models. Whilst the φ − f DDES model is not a fix for the shortcomings of DDES, it is shown to be a practical and robust alternative to the established SST-DDES and SA-DDES variants that have become the de facto choice for many DDES users.