Subgrid and hybrid RANS/LES models for scalar transport and boundary layer transition

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Date
2022-08
Authors
Bader, Shujaut H
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Durbin, Paul A
Ward, Thomas
Sippel, Travis R
Leifsson, Leifur T
Simon, Jacob B
Luo, Songting
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Altmetrics
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Aerospace Engineering
Abstract
The present study consists of three campaigns - (i) on the development of a dynamic subgrid scale (SGS) model for the turbulent flux of a passive scalar; (ii) on the formulation of a hybrid RANS/LES model for transitional flows; and (iii) on the large eddy simulation (LES) of passive scalar transport in transitional boundary layer over a flate plate and development toward an improved Higher Order Generalized Gradient Diffusion Hypothesis (HOGGDH) model. In the first project, a dynamic subgrid-scale (SGS) scalar-flux model, based on the exact rate of production of turbulent scalar fluxes, is proposed. The model is derived from an assumption that the pressure-scalar correlation in the equation for turbulent scalar flux is a vector that is approximately aligned with the scalar flux itself. The formulation then yields a tensor diffusivity which allows nonalignment of the SGS scalar fluxes with respect to the resolved scalar gradient. In contrast to eddy diffusivity models and to general gradient diffusion hypothesis models, for which the diffusivity tensor is symmetric, the present formulation produces an asymmetric diffusion tensor; for theoretical and experimental reasons, that tensor is known to be very asymmetric. The model contains a single coefficient, which is determined dynamically. The model is validated in fully developed turbulent channel flow and in separated and reattaching flow over a backstep. In the second project, a simple alternative to locally compute the model coefficient CDES in the ℓ2 − ω Delayed Detached Eddy Simulation (DDES) model is presented. The formula for the coefficient is derived from the structural function Bβ of Vreman. It, therefore, does not involve explicit filtering or averaging procedures. By virtue of the variable coefficient being based on Bβ, the model is expected to retain the property of relatively small dissipation in transitional and nearwall regions. This property enables the present formulation to be an excellent candidate to predict transitional flows. The formulation is validated in the canonical, fully developed turbulent channel flow and backward facing step flows, followed by simulations of the orderly, bypass and separation induced laminar-to-turbulent transition in a spatially developing boundary layer over a flat plate. In the third project, flat plate transition under freestream turbulence with heat transfer is studied using subgrid dynamic scalar-flux models. The advantage of adopting tensorial subgrid diffusivity is quantified. A set of Reynolds Averaged scalar-flux models is also evaluated using the LES data. Based upon the observations, an improved Higher Order Generalized Gradient Diffusion Hypothesis (HOGGDH) model is proposed with a modified, spatially varying model coefficient. The model coefficient is made a function of the turbulent Reynolds number RT , which enables it to detect the near wall region, thereby increasing the accuracy down to the wall. The mean temperature predictions and the scalar fluxes in the wall-normal as well as the streamwise directions by the improved version of the HOGGDH model are shown to be accurate compared to the HOGGDH model with a constant coefficient and other considered models.
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