NICOGRAPH International 20xx, pp. 1234-1237

A Flow Representation for EFD/CFD Integrated Visualization
Kaori Hattanda1)
Shigeya Watanabe2)

Takayuki Itoh1)

Shigeru Kuchi-ishi2)

Kanako Yasue2)

1) Department of Information Sciences, Ochanomizu University
2) Japan Aerospace Exploration Agency{kaori-h, itot}@itolab.is.ocha.ac.jp, {shigeyaw, shigeruk}@chofu.jaxa.jp, yasue.kanako@jaxa.jp

Abstract
EFD (Experimental Flow Dynamics) and CFD (Computational Flow Dynamics) are two major research fieldsfor analysis of flow phenomena. We focus on development of EFD/CFD integrated visualization which aims
comparison and analysis of results of EFD and CFD. We especially have attempted to visualize the pressure andairflow around airplanes obtained as results of EFD and CFD, and have already presented a visualization of airpressure on the surfaces of airplanes. As the second step of our work, this paper presents a visualization ofairflow around the airplanes obtained as results of EFD and CFD. Our representation is effective for thecomparison of vortices as well as vector fields between results of EFD and CFD.

1.

Introduction

2.1 EFD/CFD Integration

Experimental Fluid Dynamics (EFD) and Computational

There are few well-known systems on the integration of EFD

Fluid Dynamics(CFD) are two major research fields for analysis

and CFD in the field of aerospace. ViDI (Virtual Diagnostics

and of flow phenomena. EFD technologies measure directions

Interface System)[2] by NASA Langley laboratory is a typicaland velocities of airflows by using special equipments such as

EFD/CFD integrated system. It compares real-time EFD results

wind tunnels. EFD has relatively longer history and therefore

and pre-computed CFD results and quickly visualizes their

many researchers feel EFD is more reliable; however, it has

difference. Also, JAXA (Japan Aerospace Exploration Agency)

several limitations including costs and schedules. CFD isis developing a concurrent EFD/CFD integration system sorelatively easier to have more variety of results; however, wecalled Digital/Analog hybrid wind-tunnel[3]. In such systems,

need to verify the results of CFD by comparing withvisualization is a very important technical component to help

corresponding results of EFD. Integration of both techniques isusers compare and understand the results of EFD and CFD.

more effective to complement the drawbacks, and bring better

2.2 EFD/CFD Integrated Visualization

knowledge from each technique.

We have presented an EFD/CFD integrated visualization

We have been focusing on integrated visualization of EFD andtechnique and applied to air pressure on the surfaces of

CFD for the comparison of both results and supplement of their

airplanes [1]. It firstly integrates mesh structure between EFD

drawbacks. As the first step of the work, we have presented anand CFD, and then visualizes their scalar fields and differences

integrated visualization technique of scalar fields of EFD andbetween them calculated on the integrated mesh. The technique

CFD[1], especially for air pressure on the surfaces of airplanes.

also overlays sharp-gradient lines of EFD and CFD. The

This paper presents our development on integrated visualization

sharp-gradient lines are often observed around critical regionsof vector fields of EFD and CFD, especially airflow aroundsuch as shockwaves around airplanes, and therefore comparison

airplanes as results of EFD and CFD, as the second step of ourof the sharp-gradient lines between EFD and CFD is anwork. This paper demonstrates the effectiveness by applying theimportant process to verify these results each other.

airflow around an airplane.

2.3 Vortex-oriented Flow Visualization
Critical points such as vortices are always important for flow
analysis, and therefore they are often emphatically drawn in

2. Related Workflow

This section introduces related studies on EFD/CFD
integration,

EFD/CFD

integrated

visualization,visualization.

Our

techniquefeaturesintegrated

visualization of vortices between EFD and CFD. It applies aandcritical point extraction method[4], which extracts positions thatvortex-oriented flow visualization.

the velocity of a vector fields is zero as critical points. The1

NICOGRAPH International 20xx, pp. 1234-1237
critical points can be theoretically divided into several types:

velocity values of the three triangles. Finally, the scheme calculates

vortices, saddles, and so on.

the velocity v at Ve’, as the average of the velocities at thecell-vertices while weighting by the areas of three triangles.

3. Implementation DetailOur implementation of the presented technique consists of two
major components: data integration and cortex extraction. Figure 1
shows a dataset we visualized in this work. Air pressure on thesurface of the airplane is represented by the color of the surface. Air
flow behind the airplane is represented by a set of arrows on a plane.
The left side of the figure is the result of CFD, and the right side ofFigure 2. Integration of results of CFD onto the mesh structure

the figure is the result of EFD.

of EFD.

v13 =v + v 3 + v1
3v 23 =v12 =v + v2 + v33v + v1 + v 2
3v + v2 + v3v + v 3 + v1 ⎞1 ⎛ v + v1 + v 2v = ⎜ S12+ S23+ S31⎟⎠333S⎝
Figure 1. Example of visualization of air pressure and airflow as

Figure 3. Velocity interpolation.

the results of EFD and CFD.
Our implementation calculates the differences of velocities between

3.1 Data Unification

EFD and CFD after the unification process. It finally represents thedistribution of velocities (or their differences) by colors.

We suppose that both EFD and CFD datasets form mesh

3.2 Vortex Extraction

structure. Generally we cannot expect that mesh structures of
EFD and CFD datasets are similar. It is necessary to unify theVortex observation is important in flow visualization, becausemesh structure so that we can calculate the differences ofairflow around vortices is often unstable, and therefore it may

velocity between EFD and CFD. Our implementation calculatescause damages or energy inefficiency. Visualization of vortices

velocities of results of CFD at the cell-vertices of EFD, because

behind airplanes assists understanding of forces to airplanes due

basically we would like to trust the results of EFD and therefore

to the airflow. Figure 4 shows an example of vortex behind thefit the results of CFD onto the results of EFD. The following iswing tip of an airplane.

the processing flow of integration of results of CFD onto themesh structure of EFD, where Figure 2 shows the correspondence
between mesh structures of EFD and CFD:
1.

Project the position of a cell-vertex Ve in the mesh structure2.

Specify the cell Cc which encloses Ve’.

3.

Calculate the velocity value at Ve’ by interpolating velocityof EFD at the position Ve’ in the mesh structure of CFD.
Figure 4. Example of vortex behind an airplane.

values at the cell-vertices of Cc.
4.

Velocity is zero at the center of a vortex. In other words, vortices

Repeat 1. to 3. for all the cell-vertices of the mesh structure

can be discovered by extracting the position where the velocities areof EFD.

zero, and then dividing the positions according to the numeric

Figure 3 shows the interpolation scheme applied to the velocity atfeatures of vector fields around them. Our implementation applies aa point inside a triangular cell. The scheme firstly divides thetechnique [3] which extracts zero-velocity positions to generate

quadrilateral cell into two triangles and specify the one of them

meaningful streamlines for flow visualization. Supposing that awhich encloses the position Ve’. It then calculates the areas of threevector field is given on an XY-plane, the processing flow fortriangles, S12, S13, and S23. Here, the triangle which encloses Ve’ isextracting zero-velocity positions is as follows:

divided to generate the three triangles, by connecting each of its

1.

Determine if a zero-velocity position exists in a cell Cc.

cell-vertices and Ve’. Also, it calculates v12, v13, and v23, average

2.

Calculate the position where the velocity is zero, if it is2

NICOGRAPH International 20xx, pp. 1234-1237

4.1 Vortex Extraction

determined that the position exists in Cc.
3.
4.

Determine if the zero-velocity position is the center ofFigure 5 shows an example of vortex extraction result, wherevortex or not.

centers of vortices in the EFD result are indicated as green

Repeat 1. to 3. for all of cells.

squares in the left side, and ones in the CFD result are indicated

Our implementation determines the existence of zero-velocity

in the right side. Several vortices were observed as the result ofpositions as follows. Let a cell Cc triangular, positions of its

turbulent flow behind the engines. Vortices are also observed

three cell-vertices (y0, z0), (y1, z1) and (y2, z2), and velocity of aaround the wing tips.

flow at the three cell-vertices (v0, w0), (v1, w1) and (v2, w2). Our
implementation calculates the real values p and q satisfying thefollowing equation:⎛ 0 ⎞ ⎛ v0 ⎞⎛ v1 ⎞⎛ v2 ⎞⎜⎜ 0 ⎟⎟ = ⎜⎜ w0 ⎟⎟ × p + ⎜⎜ w1 ⎟⎟ × q + ⎜⎜ w2 ⎟⎟ × (1 − p − q)⎝ ⎠ ⎝ ⎠⎝ ⎠⎝ ⎠
It determines that a zero-velocity position exists in Cc, if p andq satisfies the following equation:

0 ≤ p,0 ≤ q,0 ≤ 1 − p − q
In this case, the zero-velocity position is calculated by theFigure 5. Centers of vortices displayed as green/blue squares.

following equation:
We projected the center of a vortex behind the wing tips from⎛ y2 ⎞⎛ y1 ⎞⎛ y ⎞ ⎛ y0 ⎞⎜⎜ ⎟⎟ = ⎜⎜ ⎟⎟ × p + ⎜⎜ ⎟⎟ × q + ⎜⎜ ⎟⎟ × (1 − p − q)
⎝ z2 ⎠⎝ z1 ⎠⎝ z ⎠ ⎝ z0 ⎠EFD to CFD. Also, we projected the one from CFD to EFD.

The zero-velocity positions can be divided into centers ofregions denote the centers of vortices of EFD and CFD. Thevortices and others. Here, the Jacobian matrix of the airflow indistance between the two centers was about 0.001 times of theCc is calculated by the following equation:

width of an airplane. It denotes that the measurement and⎡ ∂V⎢ ∂yJv = ⎢⎢∂W⎢⎣ ∂yFigure 6 shows the result, where two squares in the zoomed

simulation results around the wing tips were very reliable.

∂V ⎤ ⎡∂v ∂w⎤ ⎡∂V ∂W ⎤∂z ⎥ ⎢∂y ∂y ⎥ ⎢ ∂v ∂v ⎥×⎥=∂W ⎥ ⎢⎢∂v ∂w⎥⎥ ⎢∂V ∂W ⎥⎢⎥∂z ⎥⎦ ⎣∂z ∂z ⎦ ⎣∂w ∂w ⎦−t⎡y − y y − y ⎤ ⎡V −V V −V ⎤= ⎢ 0 2 1 2⎥ × ⎢ 0 2 1 2 ⎥⎣ z0 − z2 z1 − z2 ⎦ ⎣Z0 − Z2 Z1 − Z2⎦t

The position is a center of vortex if the eigenvalue of Jv iscomplex and its real part is not zero.
Our implementation displays vorticity by colors as well as
positions of vortices. Vorticity is a metric for degree of rotationof a vortex, where its absolute value denotes the strength of theFigure 6. Projection of centers of vortices between EFD and CFD.

vortex, and its sign denotes the direction of the flow. It

4.2 Vorticity

calculates the vorticity on the YZ-plane by the followingequation:

Figure 7 shows a result of vorticity calculation, where bluerotV = ∇ × V =∂w ∂v−∂y ∂zportions denote clockwise rotation, and red portions denotecounterclockwise rotation. Figure 7(Upper) shows only the
distribution of vorticity, and Figure 7(Lower) shows the4. Example

distribution of vorticity and flow direction.

This section shows examples of visualization by ourFigure 8 shows a zoom up of vorticity distribution around wing

implementation. We applied an airplane model DLR-F6,tips, where the result of CFD is horizontally reversed. In this

supposing Much number as 0.75, and angle of attack as 0.19.

figure red portions have nearly zero values of vorticity, andFlow fields measured behind the airplane is recorded on an

non-red regions have clockwise rotations. This visualization

YZ-plane. The EFD result is drawn at the left side, while thedenotes that vorticity in the EFD result was much stronger than

CFD result is drawn in the right side in the following examples.

vorticity in the CFD result, and therefore the EFD result
demonstrated much stronger resistance to the body of the3

NICOGRAPH International 20xx, pp. 1234-1237
environments. CFD also may cause errors due to various

airplane than the CFD result.

computational errors, and incompleteness of discrete analysis
models and formulations. Our visualization system willcontribute to understand the errors between EFD and CFD andimprove them.

Figure 7. Vorticity.

Figure 10. A zoom up of the difference of velocity between EFD
and CFD around wing tips.

5. Conclusion
This paper presented a flow representation running on ourEFD/CFD integrated visualization system. As future issues, wewould like to develop more sophisticated error visualization
Figure 8. Vorticity behind wing tips.

schemes considering gaps between centers of vortices. Also, we
would like to develop a scheme to effectively visualize

4.3 Difference

distribution of errors. We will apply more variety of airplanemodels and prove the effectiveness of our system.

Figure 9 shows the difference of the YZ-element of velocity
between EFD and CFD. Here, red portions denote that velocityof EFD is larger, while blue portions denote that velocity ofReferences

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error in maximum, while normalizing the velocity values so thatthe predefined standard velocity is 1.
This kind of visualization is useful for error analysis of EFD
and CFD. EFD may cause errors due to errors and aging ofmodels, skill of engineers, and uncertainness of experiment
4in

anIrregular

Volume,Engineeringwith