A Vortex-particle Mesh Method for Large Eddy Simulation of Bluff Body Aerodynamics

This dissertation presents a vortex-particle mesh method for bluff body aerodynamics using iterative Brinkman penalization, local mesh refinement and large-eddy-simulation. The method relies on regularized Green’s function solutions to the unbounded Poisson equation. The Poisson solver is based on the convolution approach by Hockney and Eastwood (1988) and is extended to a mixture of unbounded, periodic and homogeneous Dirichlet or Neumann conditions. A mixture of unbounded and periodic conditions is achieved using the technique of Chatelain and Koumoutsakos (2010), where the Poisson equation is initially Fourier transformed in the periodic directions. For each discrete wavenumber a modified Helmholtz equation of reduced dimensionality is then solved. The rate of convergence corresponds to the order of the regularization function used, either Gaussian or an ideal low-pass filter, which is demonstrated for test problems. Homogeneous Dirichlet or Neumann conditions are achieved using the method of images. The Poisson solver is implemented in parallel and demonstrated to be highly scalable. It is used within a remeshed vortex-method and the consistency of this combination is demonstrated for a semi-periodic problem of an unstable system of two parallel vortex pairs also considered by Chatelain and Koumoutsakos (2010).
The vortex method is extended to handle solid bodies using the iterative Brinkman penalization technique by Hejlesen et al. (2015a) for three dimensional flow. An accurate prediction of bluff body flow requires that the solid interface is well resolved, hence a multiresolution formulation of the method is applied based on refinement patches. The technique depends on a superposition of solutions to a scale-decomposed Poisson equation, which are obtained level wise in a mesh hierarchy. The multiresolution method is applied for the flow past a circular cylinder at low Reynolds number (Re = 300) in three dimension.The obtained results are found to be in excellent agreement with what is reported in the literature, in terms of force coefficients, growth rate and the topology of spectral profile of the primary unstable mode of the transition from two- to three dimensional flow.
Large-eddy-simulations using two different subgrid-scale stress models are implemented and verified for benchmark cases of homogeneous turbulence. Subsequently, the models are applied for bluff body flow at moderate Reynolds number (Re ≥ 10⁴). A qualitative good agreement is obtained with experimental and numerical results from the literature, but several challenges of the method applied for such applications are also identified.