|M.Sc Student||Hantsis Zvi|
|Subject||Hybrid methods in computational fluid mechanics:|
Application of hybrid RANS/LES model to internal
|Department||Department of Mechanical Engineering||Supervisor||Professor Steven Howard Frankel|
|Full Thesis text|
The Partially-Averaged Navier-Stokes (PANS) method, originally devised by Girimaji et. al., was an important milestone in the evolution of hybrid methods, specifically in the category of Variable-Resolution (VR) methods. Nevertheless, the original implementation of the method, using the k-ε and k-ω RANS models, suffers from a major drawback as it is only applicable to a uniform filter (or slowly varying filter) in both time and space. This meant that the formulation is only be applicable when the control parameter is constant, meaning the whole domain can either be solved as RANS or LES, but not both. Some attempts were made to allow some variation of the control parameter spatially, however these were based on the constant parameter formulation.
In this work, the original k-ω PANS formulation was extended to be mathematically consistent with both spatially and temporally varying filter, yielding a solution that can vary from LES to RANS on the same domain. This allows for a very efficient use of computational resources and the use of RANS time steps. The commutation error term, which results from explicitly changing the filter-width, is also treated within the framework of eddy-viscosity. This new formulation can retain the fidelity of the solutions with a substantially lower computational cost in comparison to an equivalent LES simulation.
The validation of the new formulation was done using the fully-developed turbulent channel flow test case for different Reτ (from 180 to 2,000) and comparison to DNS data, RANS solutions and LES solutions. The simulations were done using high-order spatial and temporal schemes. However, coarse meshes were employed, similarly to what is expected in real-life scenarios of limited resources.
Results show that the new formulation showed better agreement with DNS data when compared with RANS (using the k-ω model) and LES (using the Vreman model) over the same meshes. Additionally, the treatment of the commutation error improved the agreement even further. The original PANS k-ω formulation presented bad agreement, as expected from the mathematical inconsistency with varying control parameter.