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Multi component Doppler Global Velocimetry in the ISL

supersonic wind tunnel

B. Martinez*

Institut franco-allemand de recherches de St Louis (ISL), B.P. 70034,68301 St Louis, France

A description of a Doppler Global Velocimetry (DGV) setup is presented in this article.

The principles of the method are reminded and the technical solution used to obtain

measurements is explained. The method is here dedicated to the study of supersonic flows in

a wind tunnel facility. We show in this article, how we validated our experimental knowledge

with an academic flow around a wedge at a free stream Mach number of two. The main

difficulties encountered dealt with calibration and multi components measurements.

Nomenclature

1,2,3, … = index for the several measurement configuration -1 = exponent symbol for the inverse of the current matrix

c = velocity of light in vacuum

L = unity vector of light propagation direction, descended from the laser source

p = projection vector, related to L and R vectors

R = unity vector of light propagation direction, heading to the optical setup

Slab = laboratory orthonormal space coordinate system

Sproj = non-orthonormal space coordinate system based on the several projection vectors p T = exponent symbol for the transpose of the current matrix

V = vector of the physical velocity

Vm = Doppler velocity measured by the optical setup (scalar)

Vproj = measured velocities vector (each component made of a Vm )

ν = light frequency

ν0 = laser light frequency

Δν = Doppler frequency shift

Π = projection matrix

I. Introduction

elocity field measurements are classically achieved by efficient methods like PIV and LDV. However these

methods have, in some cases, limitations. Doppler Global Velocimetry, also referred as DGV is a relatively

young velocimetry method 3, which may provide solutions and in opposition with PIV, DGV is insensitive to flow

direction problems especially in 3D cases. Presently, DGV provides new possibilities for investigators to explore

flow fields without making well-known methods like PIV and LDV obsolete. It contributes to the research effort

efficiency. This paper presents how DGV has been developed and applied at ISL. Those developments are mainly

concerned with problems of geometrical calibration and seeding.

II. Fundamentals

As shown in figure 1, DGV is a Doppler effect based method designed to investigate flow velocity fields. The

simplified local Doppler effect described in Eq. 1 links the observation R and illuminating L direction vectors and

the velocity vector V to the Doppler frequency shift Δν. The physical quantity ν0 is the laser light frequency, when

c is the light velocity in vacuum.

* Aerodynamics Researcher, Supersonic Experimental Aerodynamics Department (AES), 5, rue du général

Cassagnou, B.P. 70034, 68301 St Louis, France /martinez@isl.tm.fr

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44th AIAA Aerospace Sciences Meeting and Exhibit9 - 12 January 2006, Reno, Nevada

AIAA 2006-46

Copyright © 2006 by french-german Research Institut of Saint Louis. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

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( )L-RV.c

νν-ν∆ν 0

0 == (1)

With : ( )L-RV.Vm = (2)

and L-Rp = (3)

For one local measurement, the idea is to reach ∆ν and to convert it into Vm. Vm is the projection of V on the

non-intuitive vector R-L also referred as the projection vector p. Since V is a three component vector, it is possible

to calculate it if we know three independent Vm projections. These three projections are realized thanks to several

points of view and/or several points of illumination. The prerequisite is to have all these points calibrated, actually,

to know precisely where those points are in the laboratory space (Slab).

Like PIV, DGV is able to measure velocity fields of the frame part of a laser sheet. Considering that Doppler

effect is local and can be estimated on each point of the laser sheet, the process only needs to be repeated

automatically for each pixel.

Figure 1. Doppler effect.

Figure 2. Wind tunnel typical configuration

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In order to measure the Doppler shift ∆ν, we use a frequency to intensity converter which is the heart of the

DGV system. This converter is an iodine cell, which is temperature regulated. The received frequency information is

transformed into grey levels information thanks to the frequency selective transmission of the iodine molecules.

III. Experimental setup

Figure 3 shows a schematic of the single camera system used at ISL. As a transmission is measured, a reference

image and an iodine filtered image are required. The transmission field is the result of the division pixel by pixel of

the two images. The idea is to generate those two DGV images side by side on the same CCD sensor instead of

using two cameras.

The main practical issue of measuring the velocity is the seeding of the test section. It is quite difficult to use

LDV typical seeding like DEHS (Di-ethyl-hexyl Sebacate) because Laskin nozzles produce too few particles.

Therefore, we have decided to use small ice tracers. These are obtained by moistening the air of the settling chamber

so that water condensates in the supersonic area 4, 5. The ice tracer was compared to the DEHS particle thanks to

velocity profiles through an oblique shock wave obtained by means of LDV measurements. As a result it was

demonstrated the capability of the moistening method to give useful particles, in a dense fog.

IV. Velocity field reconstruction

The calibration issues deal with two main points: image correction and geometrical calibration. The first point

was already presented in a publication 6. It mainly concerns the correction of transmission between the two beam

paths of the system thanks to flat images. The second point, which is of major importance for 3D measurement

expressed in the laboratory space, concerns the projection vector of Eq. 3.

The principle is that three measurements Vm1, Vm2 and Vm3 were made and are respectively associated with the

three known projection vectors p1, p2 and p3. Those measurements can be obtained by several optical setups and/or

laser sheets. The velocity vector is then Vproj = (Vm1 ,Vm2 ,Vm3)T in the non-orthonormal space coordinate system

Sproj (p1, p2, p3 ).At this point, it is possible to shift to the laboratory orthonormal space coordinate system Slab

(X,Y,Z) by means of a matrix Π, the rows of which are made of the coordinates in the laboratory space of the three

projection vectors p1, p2 and p3 . In Slab , the velocity vector can be written as :

V = Π-1.Vproj (4)

With: ( )T

labS 321 p,p,pΠ = (5)

That is the reason why Π must be non-singular, and the three projection vectors independent i.e. not in the same

plane. It should be noticed that in our case, a single observation system was used and the several measurements were

made independently. This is possible in the case of a steady flow.

In the results presented below, we consider a 2D flow so that the out of plane velocity component is zero. We

need to measure two components of the velocity, that is to say, to make only two Doppler measurements Vm1 and

Figure 3. DGV experimental setup

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Vm2. The last one, Vm3 was arbitrarily affected a zero value and its projection vector p3 was given a direction,

perpendicular to the measurement plane.

V. Optical calibration

The importance of the projection vector has been exposed in the previous section. This paragraph explains how

to estimate this vector. The knowledge of the laser source and the observation system position are the basis of this

process. It is necessary to calibrate the position of the laser source and of the observation system because they lead

to the illumination direction vector and the observation direction vector. The difference between those two vectors is

the projection vector “p” as defined in Eq. 3.

A. Laser source positioning The main idea is to estimate the position of the light source. As light propagates in straight lines and a

commercial comb is inserted in the light path, it is possible to generate as shown in figure 4, a series of converging

beams 7.

The point of convergence is the origin of light. A Matlab script was written in order to detect the position and the

direction of the beams as shown in figure 5. As a result we obtain straight line equations and therefore we are able to

calculate the best converging point for the beams of light, thanks to a least square method. Once the light source is

detected, we calculate the light propagation vector L. This is made by normalizing the vector originated in the light

source, and heading to the current point in the test area.

B. Observation system positioning This part is certainly the most difficult one because of the number of parameters involved in this problem.

Classical methods are described by quite a few papers 1,2,8. Globally, our approach was to use the Direct Linear

Transformation method to find a first approximation to the transformation. This solution gives the initial guess for

an optimization process. We use ten parameters which include the four intrinsic parameters (horizontal and vertical

focus length and coordinates of the principal point on the CCD sensor) and the six extrinsic parameters (rotation and

translation between the laboratory coordinate system and the camera’s coordinate system). In our case, no distortion

is parameterized. The optimization process is based on Levenberg-Marquart algorithm.

Figure 4. Converging beams

Figure 5. Converging beams detected

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Practically, a 3D test card made out of three inner sides of a cube generates a series of 3D calibrated points. A

picture of this 3D test card is taken as shown in figure 6 and the 3D coordinates of the calibrated points are linked

with the 2D coordinates of their image in the picture. In order to estimate the ten parameters, we use a merit

function. The good parameters are found when the merit function is minimized i.e. when the images and the

projections of the 3D calibrated points are as close as possible.

VI. Results

The last experiments conducted at ISL in order to improve the DGV method, consisted in measuring a supersonic

flow over a wedge. Figure 7 shows the obtained velocity field and the streamlines in the vicinity of the wedge at a

Mach number of 2. The horizontal ad vertical scales are expressed in pixels. Two pixels represent one millimetre.

We shall notice that the deviation angle is about 12.5°, which is the half angle of the wedge. An upstream velocity of

about 520m/s ahead the shock and a velocity of 445m/s behind the shock were expected from the theory. By

comparison, one can note a small difference between theory and measurements. The mean velocity difference is

about 6% ahead the shock and 8% after the shock. This mean error can be explained by the scattered light emitted

from the wedge. As a matter of fact, in this configuration, the wedge is on the laser sheet path and reflects the light

Figure 6. 3D-calibration card image

Figure 7. Velocity field (m/s) and streamlins over a wedge (Mach = 2)

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back into the flow, so that in the vicinity of the surface the particles are illuminated from a new direction. This may

disturb the measurement of the Doppler effect.

In addition, the scattered light emitted from the wedge prevented us to use the adapted exposure time, because

of saturation phenomenon on the CCD sensor of the camera. Actually, in case of saturation, the smearing

phenomenon, changes the grey values measured by the CCD device.

Figure 8 represents the combination of a shadowgraph and of the DGV measurement in order to compare the

flow structure observed by the two means. It should be noticed that the shock wave originated from the tip and the

expansion area are well-detected by the mean of DGV. Figures 9 and 10 represent the horizontal and vertical

velocities measured by DGV. It is important to notice that the vertical velocity before the shock is almost zero and

uniform. It is even possible to locate the end of Mach rhomb. After this rhomb, the supersonic flow is not guaranteed

any more to be at the right Mach number. This phenomenon is due to the end of the nozzle shape in the wind tunnel.

Figure 8. Velocity field over a wedge (Mach = 2):

streamlines (DGV) and shadowgraph

Figure 9. Horizontal velocity field

measured over a wedge (Mach = 2)

Figure 10. Vertical velocity field

measured over a wedge (Mach = 2)

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VII. Conclusion

We demonstrated that the DGV method is useful for a supersonic flow investigation at ISL. We still have to

improve our experimental setup, due to the problems of velocity drift, of unwanted scattered light and of a lack of

high grey level information, although the results show the possibility of measurement of a multi component velocity

in a supersonic flow field. Another problem deals with the fact that the precision of the measurements is not clearly

quantified for the moment. In the future this is a point that should be developed at ISL.

Acknowledgments

The author thanks the wind tunnel staff for their efficiency and their know-how especially mister Bidino. The

author is also indebted to mister Jaeggy and doctors Schaefer, Wernert and Leopold for their help.

References

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