Abstract
The possibilities of applying the pure Lagrangian vortex methods of computational fluid dynamics to viscous incompressible flow simulations are considered in relation to various problem formulations. The modification of vortex methods—the Viscous Vortex Domain method—is used which is implemented in the VM2D code developed by the authors. Problems of flow simulation around airfoils with different shapes at various Reynolds numbers are considered: the Blasius problem, the flow around circular cylinders at different Reynolds numbers, the flow around a wing airfoil at the Reynolds numbers and , the flow around two closely spaced circular cylinders and the flow around rectangular airfoils with a different chord to the thickness ratio. In addition, the problem of the internal flow modeling in the channel with a backward-facing step is considered. To store the results of the calculations, the POD technique is used, which, in addition, allows one to investigate the structure of the flow and obtain some additional information about the properties of flow regimes.
Highlights
Flow simulation problems and, more generally, computational fluid dynamics (CFD)problems, are among the most difficult problems of computational mathematics, mainly due to the nonlinearity of the governing equations and the need to take into account a large number of factors which have both a physical nature, and are related to the requirements of the necessary properties of the numerical scheme, such as accuracy, conservatism, stability, monotony, etc.There is, a rather wide range of problems, for example, fluid–structure interaction (FSI) problems, where it is necessary to estimate hydro- or aerodynamic loads acting on the structure
Despite the fact that the drag force coefficient is overestimated in numerical simulations, the main result of this simulation is the following: two-dimensional simulation permits to obtain correct results at rather high Reynolds numbers, if the airfoil with a sharp edge is considered, and the flow separation takes place at this point; the viscous vortex domains method allows for correct resolving the viscosity effect that is especially clearly seen for the lift coefficient dependency against the angle of attack (AoA)
All the considered numerical simulations were performed by using the VM2D code
Summary
More generally, computational fluid dynamics (CFD). problems, are among the most difficult problems of computational mathematics, mainly due to the nonlinearity of the governing equations and the need to take into account a large number of factors which have both a physical nature (heat transfer, convection, chemical reactions, cavitation, etc.), and are related to the requirements of the necessary properties of the numerical scheme, such as accuracy, conservatism, stability, monotony, etc. In addition to the fact that the problems of numerical flow simulation are traditionally time-consuming, in many cases, the problem of storing and analyzing the simulation results is actual, especially when an unsteady flow is simulated and it is required to store snapshots at many time steps This problem sometimes wrongly seems to be not essential or at least much more simple in comparison to flow numerical simulation itself, in practice, it has nearly the same importance. Despite the rather narrow range of applicability, which will be outlined below, such methods can be extremely efficient in engineering applications, when it is necessary to estimate unsteady loads acting on the structure and to predict the most significant properties of the flow, such as large vortex structures, etc. Technique for the results of flow simulations storing and further reconstruction, as well as for different flow regimes distinguishing
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