Solution of incompressible fluid flow problems with heat transfer by means of an efficient RBF-FD meshless approach

The localized radial basis function collocation meshless method (LRBFCMM), also known as radial basis function generated finite differences (RBF-FD) meshless method, is employed to solve time-dependent, 2D incompressible fluid flow problems with heat transfer using multiquadric RBFs. A projection approach is employed to decouple the continuity and momentum equations for which a fully implicit scheme is adopted for the time integration. The node distributions are characterized by non-cartesian node arrangements and large sizes, i.e., in the order of $10^5$ nodes, while nodal refinement is employed where large gradients are expected, i.e., near the walls. Particular attention is given to the accurate and efficient solution of unsteady flows at high Reynolds or Rayleigh numbers, in order to assess the capability of this specific meshless approach to deal with practical problems. Three benchmark test cases are considered: a lid-driven cavity, a differentially heated cavity and a flow past a circular cylinder between parallel walls. The obtained numerical results compare very favourably with literature references for each of the considered cases. It is concluded that the presented numerical approach can be employed for the efficient simulation of fluid-flow problems of engineering relevance over complex-shaped domains

The aerodynamic flow over a bluff body in ground proximity: CFD prediction of road vehicle aerodynamics using unstructured grids

The prediction of external automobile aerodynamics using Computational Fluid Dynamics (CFD) is still in its infancy. The restrictions on grid size for practical use limit the ability of most organisations to predict the full flow over an automobile. Some insight into the flow over a passenger car can be made by examining the flow over a bluff body in close proximity to the ground. One such body is the Ahmed body composed of a rounded front, straight mid-section and variable slant-rear section. This body exhibits many of the 3D flow structures exhibited by passenger cars. The main feature of the flow around this body is the change in flow structure as the angle of the slant surface at the rear of the body is increased. The flow starts fully attached and ends fully separated. In between these two regimes is a third high drag regime. The flow structure is characterised by strong counter-rotating longitudinal vortices originating from the interaction between the flow from the sides and top of the body, and a small separation from the top/slant edge on the centre-plane of the body. The flow reattaches to the slant surface and the low-pressure fluid within the separation bubble increases the drag considerably. The use of CFD incorporating tine averaged statistical turbulence models to reproduce these flow patterns is assessed in this study. Initial work concentrated on evaluating structured grid methods for this flow type. Some success was achieved with the flow fields for the attached and fully separated cases but the third high drag regime was not predicted. The flow field also exhibited a grid dependent flow structure and drag result. To examine these effects further without high grid overheads an unstructured mesh generator was developed and used to provide meshes with more grid cells clustered around the body and it's wake. Analysis and refinement of the unstructured grids proved successful at removing the grid dependent flow field but still showed no evidence of the third high drag flow regime. Further, the bulk levels of drag in all cases was too high and the fully separated flow regime occurred too late in the slant surface angle sweep, coming at 40° instead of the 30° seen in the wind tunnel results. Further analysis of the flow field using highly refined mixed meshes showed no improvement in the drag or flow field prediction with the high drag flow field still not present. The use of higher order differencing schemes and anisotropic turbulence models reduced the drag levels considerably but not to the levels seen in the wind tunnel results. Comparison of the results from this work with the work of other authors is difficult for two reasons. Firstly, work on the specific body used in this thesis is sparse and, secondly, much of the work done by other authors was in conjunction with automotive manufacturers and details of the specific numerical methods employed are not available. The most important parallel conclusion from the work presented here and that of other authors is the inability of the CFD prediction to capture the change in flow mode as the angle of slant surface is increased. This failure can, in all probability, be attributed to the use of a steady-state CFD solution algorithm to capture the flow field around the body. A small possibility perhaps still exists that further grid refinement, very localised around the body, would help, but the detailed and careful predictions presented in this study make this highly unlikely. The most important piece of further work that could follow this work would therefore be the application of a time-accurate (unsteady) CFD solution algorithm to the bluff body in ground proximity problem. Whether these predictions should be of an unsteady RANS nature, or full LES predictions would be best answered by applying these methods to the present flow problem which is fundamental to the study of automobile aerodynamics

Lattice Boltzmann Methods for Wind Energy Analysis

An estimate of the United States wind potential conducted in 2011 found that the energy available at an altitude of 80 meters is approximately triple the wind energy available 50 meters above ground. In 2012, 43% of all new electricity generation installed in the U.S. (13.1 GW) came from wind power. The majority of this power, 79%, comes from large utility scale turbines that are being manufactured at unprecedented sizes. Existing wind plants operate with a capacity factor of only approximately 30%. Measurements have shown that the turbulent wake of a turbine persists for many rotor diameters, inducing increased vibration and wear on downwind turbines. Power losses can be as high as 20-30% in operating wind plants, due solely to complex wake interactions occurring in wind plant arrays. It is my objective to accurately predict the generation and interaction of turbine wakes and their interaction with downwind turbines and topology by means of numerical simulation with high-performance parallel computer systems. Numerical simulation is already utilized to plan wind plant layouts. However, available computational tools employ severe geometric simplifications to model wake interactions and are geared to providing rough estimates on desktop PCs. A three dimensional simulation tool designed for modern parallel computers based upon lattice Boltzmann methods for fluid-dynamics, a general six-degree-of-freedom motion solver, and foundational beam solvers has been proposed to meet this simulation need. In this text, the software development, verification, and validation are detailed. Fundamental computational fluid dynamics issues of boundary conditions and turbulence modeling are examined through classic cases (Cavity, Jeffery-Hammel, Kelvin-Helmholtz, Pressure wave, Vorticity wave, Backward facing step, Cylinder in cross-flow, Airfoils, Tandem cylinders, and Turbulent flow over a hill) to asses the accuracy and computational cost of developed alternatives. Simulations of canonical motion (falling beam), fluid-structure-interaction cases (Hinged wing and Flexible pendulum), and realistic horizontal axis wind turbine geometries (Vestas v27, NREL 5MW, and MEXICO) are validated against benchmarks and experiments. Results from simulations of the three turbine array at the Scaled Wind Farm Test facility are presented for two steady wind conditions

Projection methods for incompressible flow problems with WENO finite difference schemes

Weighted essentially non-oscillatory (WENO) finite difference schemes have been recommended in a competitive study of discretizations for scalar evolutionary con\-vec\-tion-diffusion equations [20]. This paper explores the applicability of these sche\-mes for the simulation of incompressible flows. To this end, WENO schemes are used in several non-incremental and incremental projection methods for the incompressible Navier-Stokes equations. Velocity and pressure are discretized on the same grid. A pressure stabilization Petrov-Galerkin (PSPG) type of stabilization is introduced in the incremental schemes to account for the violation of the discrete inf-sup condition. Algorithmic aspects of the proposed schemes are discussed. The schemes are studied on several examples with different features. It is shown that the WENO finite difference idea can be transferred to the simulation of incompressible flows. Some shortcomings of the methods, which are due to the splitting in projection schemes, become also obvious