This work aimed at the development of a versatile, efficient, and physically accurate commercial software for the solution of a broad range of turbulent flows encountered in energy engineering. In Phase I, the effort focused on achieving dramatic improvements both in speed and efficiency of a Fast Multipole Method (FMM) for computing the velocity field produced by the three-dimensional vortex elements: the most computationally intensive part of the complete algorithm. Results indicated that, for simulations involving on the order of ten million vortex elements, we were getting speedups on the order of 1000 compared to the direct calculations. The Phase II goal was to develop a computer code based on our fast vortex method, which will be able to deliver a significantly higher level of accuracy in predicting complex turbulent flow fields than can be obtained from traditional models - within a competitive cycle time.  The code incorporated a triangle tessellation of complex surfaces, and an adaptive implementation of the parallel FMM.  The applications were focused on automotive external flows (The DaimlerChrysler Corporation and SGI-Cray Division were co-sponsors of this project).

The end result of this project was a fast, grid-free, parallel CFD software for automotive and energy engineering applications.  The code was based on a hybrid vortex filament-sheet method, and incorporates the adaptive fast multipole methodology (FMM) for computational efficiency.  Distributed memory parallelization was achieved using Message Passing Interface (MPI).

We note that vortex methods exhibit several advantages over traditional grid-based methods for the numerical simulation of turbulent flow.  In particular, they have negligible if any numerical diffusion so that high Reynolds number turbulence effects can be represented with high numerical accuracy and fidelity, and they are grid-free so that they can be easily applied to engineering flows in complex geometries.  Moreover, they are naturally adaptive since the computational elements occupy only the relatively small support of the flow field where the vorticity is significant.  Finally, vortex methods offer a direct means for modeling some of the most important dynamical processes of turbulent flow; the energy cascade driven by vortex stretching and the quasi-streamwise vortex regeneration process near boundaries.

During the course of this project and based on its early results, VorCat, Inc. applied for a Registered Trademark and a U.S. Patent. Both were granted (2000 and 2003, respectively).

Results and Images:

Detailed results of several applications and different aspects of the work are given in the publications listed above. Sample results are shown here.

1. Turbulent flow past a prolate spheroid in uniform stream

The following animations show the evolution of the vortex filament distribution.  The filaments are colored according to circulation strength where red corresponds to the strongest circulation and blue to the weakest.  The color contours on the geometry surfaces depict the evolution of the streamwise vorticity component where red indicates the highest values of positive vorticity and blue the highest values of negative vorticity.
Image 1 is an animation of the flow past a prolate spheroid for two Reynolds numbers, Re = 10,000 (top) and Re = 100,000 (bottom), at zero degree angle of attack. In this case all vortons are shown. Image 2 is similar where only top 20% of the vortons (based on strength) are shown.

Images 3 is an animation of the flow over the prolate spheroid at Re = 100,000, 20 degrees angle of attack, top and side views. In this image only 20% of vortons are shown.

Images 4 and 5 are animations of the flow over the prolate spheroid at an angle of attack of 30 degrees, where 100% vortons and only 20% of the vortons are shown, respectively.

Images 6 displays animations of the flows about the spheroid at angles of attack of 20 degrees and 30 degrees as viewed from the top. Image 7 displays compares the same flows as viewed from the side.

2.  "Ahmed" Benchmark Ground Vehicle Geometry

The “Ahmed” geometry is a benchmark configuration used in the automotive industry. Several preliminary simulations of VorCat are shown here.

Image 8 is an animation of the flow over Ahmed geometry at Re=100,000, as viewed from the side, with 50% of vortons (based on strength) shown.

Image 9 is an animation of the flow as in Image 8 as viewed from the back.

Image 10 is an animation of the flow over the Ahmed geometry with wind tunnel boundaries, where Re = 100,000 and all vortons are shown, as viewed from the side.

Image 11 is an animation of the flow as in Image 10, as viewed from the back.

Image 12 is an animation of the flow as in Image 10, as viewed from the top.

3. Ground vortex drawn into aircraft engine intake

The airflow between the intake of an aircraft jet engine at high thrust levels, when the airplane is stationary or taxing, and the ground in the presence of winds may lead to strong vorticity generation (Patterns in the Sky: Natural Visualization of Aircraft Flow Fields, by Campbell, J. F. and Chambers, J. R., 1994, NASA SP-514).  This vorticity appears in the form of small vortices that are generated on the ground and are drawn into the engine inlet.  These vortices present a potential safety hazard because they can create suction forces strong enough to pick up foreign objects from the runway and inject them into the engine or disrupt the flow ahead of the compressor blades and result in compressor stall.

Current Reynolds-Averaged Navier-Stokes (RANS) solvers cannot predict the fundamental vorticity generation by the separated flow induced on the ground by the suction of the aircraft engine.  To demonstrate the capability of VorCat to a US aircraft manufacturer, we considered an idealized fundamental problem where the jet engine is modeled as a cylinder with the same length/diameter and height/diameter ratios (3 and 1.5, respectively) as the actual engine. We performed flow simulations under two conditions: without and with cross wind in the positive spanwise, Z direction. The results clearly demonstrate the capability of VorCat to capture the experimentally observed patterns for both cases. Images 13 and 14 describe streamlines at two locations (upper views, under cross wind), y=0.8 and y=1.0. Animations of the simulated flows are also available and will be posted here in the future.

Relevant Publications:
1. Final Reports (Phase I, 1998 and Phase II, 2000) submitted to DOE.

2. Athanassios Dimas, Pat Collins and Peter Bernard, A Fast, Parallel Vortex Method for Turbulent Flow Simulation, Proceedings of FEDSM 98, ASME Fluids Engineering Division Summer Meeting, June 21-25, 1998, Washington DC.

3. Athanassios Dimas, Peter Bernard and Jacob Krispin, An Adaptive, Fast, Parallel Vortex Method for Numerical Simulations of Turbulent Separated Flows, Proceedings if the 37th AIAA Aerospace Sciences Meeting, AIAA 99-0155, Reno, Nevada.

4. Peter Bernard, Athanassios Dimas, and Pat Collins, Turbulent Flow Modeling Using a Fast, Parallel, Vortex Tube and Sheet method, European Series in Applied and Industrial Mathematics (ESAIM), Vol. 7, 1999, 46-55. Editors: Giovannini A., Cottet, G. H., Ghoneim, A. and Melburg, E.

5. Peter Bernard, Athanassios Dimas, and Isaac Lottati, Vortex Method Analysis of Turbulent Flows, Proceedings of The First International Conference on Vortex Methods, November 4-5, 1999, Kobe, Japan.

6. Pat Collins, Athanassios Dimas and Peter Bernard, A Parallel Adaptive Fast Multipole Method for High Performance Vortex Method Based Simulations, Proceedings of IMECE’99, ASME International Mechanical Engineering Congress and Exposition, November 14-19, 1999, Nashville, Tennessee.

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