Numerical Simulation of Flow over a Surface-mounted Cube with the Vorticity Confinement Method

Over the last several years, Vorticity Confinement has been shown to be a very efficient method to simulate the vortex-dominated flows over complex configurations. To calculate these flows, no high-order numerical scheme and body conforming grids are required for this method and only a fixed, uniform Cartesian grid is employed. First, an overall description of the original Vorticity Confinement method (VC1) is presented, followed by an introduction of the newly developed Vorticity Confinement method (VC2). The advantage of VC2 over VC1 is the ability to conserve the Momentum. Two different numerical schemes are shown for VC1 and VC2. The one for VC2 is much simpler than that of VC1. Results of VC1 and VC2 for convecting vortices and scalars in 1-D and 2-D will be presented. Numerical results are presented for the three dimensional flow over a surface-mounted cube. Comparisons have been made with experimental and Large Eddy Simulation (LES) data. It is observed that with a coarse uniform Cartesian grid, Vorticity Confinement is able to get results in better agreement with the experimental results than the LES simulation results on a fine grid. This method is shown to be more effective than trying to model and discretize more complex system of equations in the traditional methods, when solving complex high Reynolds number flow problems

Towards a solution of the closure problem for convective atmospheric boundary-layer turbulence

We consider the closure problem for turbulence in the dry convective atmospheric boundary layer (CBL). Transport in the CBL is carried by small scale eddies near the surface and large plumes in the well mixed middle part up to the inversion that separates the CBL from the stably stratified air above. An analytically tractable model based on a multivariate Delta-PDF approach is developed. It is an extension of the model of Gryanik and Hartmann [1] (GH02) that additionally includes a term for background turbulence. Thus an exact solution is derived and all higher order moments (HOMs) are explained by second order moments, correlation coefficients and the skewness. The solution provides a proof of the extended universality hypothesis of GH02 which is the refinement of the Millionshchikov hypothesis (quasi- normality of FOM). This refined hypothesis states that CBL turbulence can be considered as result of a linear interpolation between the Gaussian and the very skewed turbulence regimes. Although the extended universality hypothesis was confirmed by results of field measurements, LES and DNS simulations (see e.g. [2-4]), several questions remained unexplained. These are now answered by the new model including the reasons of the universality of the functional form of the HOMs, the significant scatter of the values of the coefficients and the source of the magic of the linear interpolation. Finally, the closures 61 predicted by the model are tested against measurements and LES data. Some of the other issues of CBL turbulence, e.g. familiar kurtosis-skewness relationships and relation of area coverage parameters of plumes (so called filling factors) with HOM will be discussed also

Numerical Simulation of Separating Flows Using Computational Models Based on the Vorticity Confinement Method

The objective of the present research is to investigate the recent development of the vorticity confinement method. First, a new formulation of the vorticity confinement term is studied. Advantages of the new formulation over the original one include the ability to conserve the momentum, and the ability to preserve the centroid motion of some flow properties such as the vorticity magnitude. Next, new difference schemes, which are simpler and more efficient than the old schemes, are discussed. At last, two computational models based on the vorticity confinement method are investigated. One of the models is devised to simulate inviscid flows over bodies with surfaces not aligned with the grid. The other is a surface boundary layer model, which is intended for efficiently simulating viscous flows with separations from the body surfaces. To validate the computational models, numerical simulations of threedimensional flows over a 6:1 ellipsoid at incidence are performed. Comparisons have been made with exact solutions for inviscid simulations or experimental data for viscous simulations, and data obtained with conventional CFD methods. It is observed that both the inviscid and the viscous solutions with the new models exhibit good agreement with the exact solutions or the experiment data. The new models can have much higher efficiency than conventional CFD methods, and are able to obtain solutions with comparable accuracy

Summaries of FY 1995 engineering research

The individual engineering project summaries follow the program overview. The summaries are ordered alphabetically by name of institution and so the table of contents lists all the institutions at which projects were sponsored in fiscal year 1995. Each project entry begins with an institutional-departmental heading. The names of investigators are listed immediately below the title. The funding level for fiscal year 1995 appears to the right of title; it is followed by the budget activity number. These numbers categorize the projects for budgetary purposes and the categories are described in the budget number index. A separate index of Principal Investigators includes phone number, fax number and e-mail address, where available. The fiscal year in which either the project began or was renewed and the anticipated duration in years are indicated respectively by the first two and last digits of the sequence directly below the budget activity number. The summary description of the project completes the entry

1991 Summer Study Program in Geophysical Fluid Dynamics : patterns in fluid flow

The GFD program in 1991 focused on pattern forming processes in physics and geophysics. The pricipallecturer, Stephan Fauve, discussed a variety of systems, including our old favorite, Rayleigh-Bénard convection, but passing on to exotic examples such as vertically vibrated granular layers. Fauve's lectures emphasize a unified theoretical viewpoint based on symmetry arguments. Patterns produced by instabilties can be described by amplitude equations, whose form can be deduced by symmetry arguments, rather than the asymptotic expansions that have been the staple of past Summer GFD Programs. The amplitude equations are far simpler than the complete equations of motion, and symetry arguments are easier than asymptotic expansions. Symmetry arguments also explain why diverse systems are often described by the same amplitude equation. Even for granular layers, where there is not a universaly accepted continuum description, the appropnate amplitude equation can often be found using symmetry arguments and then compared with experiment. Our second speaker, Daniel Rothan, surveyed the state of the art in lattice gas computations. His lectures illustrate the great utility of these methods in simulating the flow of complex multiphase fluids, particularly at low Reynolds numbers. The lattice gas simulations reveal a complicated phenomenology much of which awaits analytic exploration. The fellowship lectures cover broad ground and reflect the interests of the staff members associated with the program. They range from the formation of sand dunes, though the theory of lattice gases, and on to two dimensional-turbulence and convection on planetary scales. Readers desiring to quote from these report should seek the permission of the authors (a partial list of electronic mail addresses is included on page v). As in previous years, these reports are extensively reworked for publication or appear as chapters in doctoral theses. The task of assembling the volume in 1991 was at first faciltated by our newly acquired computers, only to be complicated by hurricane Bob which severed electric power to Walsh Cottage in the final hectic days of the Summer.Funding was provided by the National Science Foundation through Grant No. OCE 8901012

Vorticity Confinement and TVD Applied to Wing Tip Vortices for Accurate Drag Prediction

The vorticity confinement (VC) method was used with total variation diminishing (TVD) schemes to reduce possible over-confinement and applied to tip vortices shed by edges of wings in order to predict induced drag using far-field integration. The optimal VC parameter was determined first by application to 2-D vortices and then to tip vortices shed by a 3-D wing. The 3-D inviscid simulations were post-processed using the wake-integral technique to determine lift-induced drag force. Dependence of the VC parameter on the flight Mach number and the angle of attack was evaluated. Grid convergence studies were conducted for 2-D vortices and for induced drag generated by 3-D wing. VC was used with TVD minmod and differentiable flux limiters to evaluate their effect on the VC method. Finally, the VC approach was combined with the Reynolds stress equation turbulence model, and the results were compared to experimental data of tip vortex evolution.Comment: 40 pages, 12 Figure