Visualizing Flow Field Solutions From ...

Visualizing Flow Field Solutions From Computational Fluid Dynamics Using Streamball Techniques Hans-Christian Rodrian Hans Hagen

Kelly Gaither Robert Moorhead

University of Kaiserslautern Germany

Mississippi State University USA

Abstract Visualizing CFD solutions has become an increasingly important tool in the analysis of ow around complex con
gurations. Streamlines, Streaklines, Timelines and Pathlines are vital methods for exploring the behavior of the ow
eld solutions. This paper presents the streamball method for displaying these ow lines as a part of an integrated solution visualization system. Actual simulation data is used, and visualization results are presented and discussed.

Introduction The de nition of a
uid can be given as a substance that deforms continuously under the application of a shear stress 1]. Given this de nition, we can easily see that
uids comprise the liquid and gas phases of the physical forms in which matter exists. A clear understanding of the eld of
uid mechanics is essential to adequately analyze any system in which a
uid is the working medium. There are basically three approaches to solving problems in
uid mechanics. They can be classi ed as 2]: Experimental Theoretical Numerical Experimental research has the potential for giving the most realistic answers, but the cost associated with simulating the conditions can be prohibitive. Theoretical research provides the results in a formula, but is limited to simple geometries. The physics are usually restricted to linear problems. The numerical approach

makes a limited number of simplifying assumptions and uses high-speed computers to solve the numerically approximated governing equations. The process of approximating these governing equations and solving them numerically is called Computational Fluid Dynamics (CFD). Because the cost of numerical calculations have signi cantly decreased over the past decade, CFD is being used to solve the
ow around more complex con gurations. Visualizing these CFD results has become an e ective tool for analyzing these solutions. For example, streamlines, streaklines, pathlines and timelines are important entities to visualize because of the information that each portray 1]. (THE FOLLOWING IS IDENTICAL TO THE VIS94 ARTICLE. I WOULD PROPOSE TO DROP IT) Streaklines - are the lines joining
uid particles that have passed through a xed reference point at some previous time. Timelines - are the the lines joining adjacent
uid particles in a
ow eld at a given instant in time. Pathlines - are the paths or trajectories of moving
uid particles. Streamlines - are the lines drawn in the
ow eld so that at a given instant they are tangent to the direction of the
ow at every point in the
ow eld. Given steady
ow, streaklines, timelines, pathlines and streamlines are equivalent. This paper focuses on visualizing the
ow lines through the use of a technique called streamballs. The basic concepts behind the computation of streamballs

is reviewed, and the use of streamballs in an interactive visualization system is discussed. A discussion of the details of the underlying grid and the physical parameters under which the solution is computed is given. Visualization results are presented to show the quality of the information that streamballs are capable of displaying on actual CFD simulations. Conclusions of the visualization results are given and a scope for future work is discussed.

Streamballs The premise for visualizing
ow data with streamballs is to use the positions of particles in the
ow as skeletons for the construction of implicit surfaces, which by blending with each other form three- dimensional streamlines, stream surfaces etc. The particle positions pi are given by tracing
ow lines through a
ow eld in discrete timesteps. Considering each of the particle positions pi as a single skeleton si results in producing discrete streamballs. Grouping several particle positions to form polylines and using these as skeletons results in producing continuous streamballs. Depending on the geometry of the skeletons si 2 S, a three-dimensional potential eld F(S x) x 2 Ri ) = 0 where ri is the radius of one single, separated streamball generated by si and Ri is the maximal range of in
uence of this streamball, i.e. the distance where the in
uence of the streamball drops to zero. The quartic function 2 eliminates the need to evaluate the square root for the distance calculations thus greatly reducing the calculation costs. The maximal radius Ri for each skeleton is chosen indirectly by giving a radius ri and a smoothness smi : 0 0

Ri = ri  (1 + smi ) (5) This approach provides the advantage of having just one scale-dependent parameter (ri ) associated with the streamballs. All other parameters which in
uence the shape of the streamballs are chosen in relation to this parameter, thus allowing a simple scalability of the scene.

0.2 Continuous Streamballs For the continuous streamballs, the eld function is given as a sum of integrals over the single line segments si = pi pi+1 of a polyline S:

X Z F (x)ds Z X = a d(x s ) + b d(x s ) + c ds (6)

F(S x) =

i si 2S i si 2S

i

i

i

i

4

i

i

2

i

i

with ai, bi , and ci chosen to generate a continuous streamline with a radius of ri and a maximal in
uence radius of Ri. When discrete streamballs are placed very close to each other, they will produce a continuous streamline. The radius of this streamline, however, in general will be much bigger than the given radius ri due to the addition of the individual eld functions. Continuous streamlines provide the possibility to produce continuous three-dimensional streamlines with full radius control over the entire length.

0.3 Mapping Techniques As three-dimensional objects, streamballs provide a couple of mapping techniques changing either shape or appearance.

0.3.1 Mapping Techniques Changing Shape

Radius-mapping uses the possibility of assigning different radii to every centerpoint to visualize the absolute value of a scalar parameter of the
ow eld. To simulate stream ribbons, every skeleton point is assigned with a vector perpendicular to the
ow at that skeleton point. By scaling the streamballs in respect to this vector, (i.e.
attening them) a simulation of the stream ribbon technique is produced, maintaining all other mapping techniques associated with the streamballs. In the discrete case, assigning a 3D-vector to each of the centerpoints and scaling the single streamballs in respect to the direction and magnitude of this vector, ellipsoids are produced instead of spherical objects. The orientation of these ellipsoids shows the direction, their shape the magnitude of the given vector. Thus, not only the direction of the vector but also its magnitude can be mapped at the same time. Using particle positions equidistant in space along streamlines, the smoothness parameter of discrete streamballs can be controlled to show the magnitude of a value by a di erent blending behaviour of the streamballs. All of these shape-changing mapping techniques can be applied at the same time, but in most cases applying more than one shape- changing mapping technique produces confusing results. However, the combination of a continuous streamline showing shape and direction and disk-shaped ellipsoids showing the position of the single particle positions along this streamline gives a good idea of the velocity of the particles in di erent areas of the eld. Additionally, the size of the disks can be used to emphasize the velocity or to map a di erent scalar parameter.

0.3.2 Mapping Techniques Changing Appearance The color and transparency of each skeleton can be chosen either xed or dependent on di erent scalar parameters from the eld. The color spot mapping technique assigns a speci c color to a couple of surface points on the streamballs based on the value of a scalar parameter along the underlying streamline. The higher the value of the scalar parameter at a segment of the streamline, the higher the density of the color spots on the surface of the streamballs. Thus, the density of the color spots maps the absolute value of the scalar parameter. (SHOULD WE DROP THE NEXT SENTENCE?) For the generation of streamballs by triangulation, the use of the

color spot mapping technique may be doubted, as it demands a high number of triangles to be produced. Using ray-tracing, however, it shows good results. As the colors of blending streamballs are merged together, it is possible to use the color mapping techniques to visualize merging processes in the
ow.

0.4 Streamballs in an Interactive Visualization System We have completely implemented streamballs as a part of an integrated solution visualization system. Figure Get a gure number shows the various parameters that a user may change to produce
ow lines as streamballs.

Visualization Results Summary and Conclusions References 1] R.W. Fox, A.T. McDonald: Introduction To Fluid Mechanics, Wiley, Third Edition 2] D.A. Anderson, J.C. Tannehill, R.H. Pletcher: Computational Fluid Mechanics and Heat Transfer, Hemisphere Publishing 3] J. Blinn: A Generalization of Algebraic Surface Drawing, ACM Transactions on Graphics Vol. 1, No. 3, 1982, pp. 235-256 4] NASA Workshop on \Future Directions in Surface Modeling and Grid Generation", NASA Ames Research Center, December, 1989. 5] M. Brill, H. Hagen, H.C. Rodrian, W. Djatschin, and S. Klimenko: Streamball Techniques for Flow Visualization, Proceedings of Visualization '94, pp. 225-231