Development of a near-wall domain decomposition method for turbulent flows

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Abstract

In computational fluid dynamics (CFD), there are two widely-used methods for computing thenear-wall regions of turbulent flows: high Reynolds number (HRN) models and low Reynoldsnumber (LRN) models. HRN models do not resolve the near-wall region, but instead use wallfunctions to compute the required parameters over the near-wall region. In contrast, LRNmodels resolve the flow right down to the wall. Simulations with HRN models can take anorder of magnitude less time than with LRN models, however the accuracy of the solution isreduced and certain requirements on the mesh must be met if the wall function is to be valid.It is often difficult or impossible to satisfy these requirements in industrial computations.In this thesis the near-wall domain decomposition (NDD) method of Utyuzhnikov (2006)is developed and implemented into the industrial code, Code_Saturne, for the first time.With the NDD approach, the near-wall regions of a fluid flow are removed from the maincomputational mesh. Instead, the mesh extends down to an interface boundary, which islocated a short distance from the wall, denoted y*. A simplified boundary layer equation isused to calculate boundary conditions at the interface. When implemented with a turbulencemodel which can resolve down to the wall, there is no lower limit on the value of y*. Thereis a Reynolds number-dependent upper limit on y*, as there is with HRN models. Thus forlarge y*, the model functions as a HRN model and as y*→ 0 the LRN solution is recovered.NDD is implemented for the k−ε and Spalart-Allmaras turbulence models and is testedon five test cases: a channel flow at two different Reynolds numbers, an annular flow, animpinging jet flow and the flow in an asymmetric diffuser. The method is tested as a HRNand LRN model and it is found that the method behaves competitively with the scalable wallfunction (SWF) on simpler flows, and performs better on the asymmetric diffuser flow, wherethe NDD solution correctly captures the recirculation region whereas the SWF does not.The method is then tested on a ribbed channel flow. Particular focus is given to investigatinghow much of the rib can be excluded from the main computational mesh. It is found that itis possible to remove 90% of the rib from the mesh with less than 2% error in the frictionfactor compared to the LRN solution.The thesis then focuses on the industrial case of the flow in an annulus where the inner wall,referred to as the pin, has a rib on its surface that protrudes into the annulus. Comparisonis made between CFD calculations, experimental data and empirical correlations. It is foundthat the experimental friction factors are significantly larger than those found with CFD,and that the trend in the friction factor with Reynolds number found in the experiments isdifferent. Simulations are performed to quantify the effect that a non-smooth surface finishon the pin and rib surface has on the flow. This models the situation that occurs in anadvanced gas-cooled nuclear reactor, when a carbon deposit forms on the fuel pins. Therelationship between the friction factor and surface finish is plotted. It is demonstrated thatsurface roughness left over by the manufacturing process in the experiments is not the sourceof the discrepancy between the experimental and CFD results.

Keyword(s)

AGR; Code Saturne; Domain decomposition; RANS; Wall functions

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