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Abstract submitted for an oral presentation in the Exterior Ballistics session

Free-Flight Motion Analysis Based on Shock-Tunnel Experiments

P. Wey, F. Seiler, J. Srulijes, M. Bastide, B. Martinez

French-German Research Institute of Saint-Louis (ISL) 5 rue du Général Cassagnou, 68301 Saint-Louis, France

Phone: +33 3 89 69 51 28, Email: Pierre.Wey@isl.eu Extended Abstract

ISL’s shock tunnel STA (Fig. 1) is used as short blowing ground testing facility to analyse the 6 degrees of freedom (6 DOF) motion of a free flying body in order to determine its aerodynamic coefficients. This so-called ”Free-Flight Force Measuring Technique (FFM)” was originally described by Igra and Takayama [1] and has been further developed at ISL’s Shock Tube Laboratory using high-speed cameras for observing the translation and the rotation of the body [2]. This paper presents the three tasks that are required to perform the data reduction: (1) measurement of the time-dependant flow parameters, (2) accurate observation of the body motion and (3) use of motion and fit models to estimate the aerodynamic coefficients. The process is illustrated and validated using the Explosive-Formed Projectile (EFP) model (Fig. 2) detailed in [3].

Steady-state flows in the measurement section after the nozzle can be observed during a very short time interval of about 3 ms. Afterwards, the flow becomes unsteady due to the shock reflections in the driven tube (Fig. 1): the velocity, the density, the temperature and the pressure of the flow vary with time. The flow velocity (Fig. 3a) is measured using the Laser-Doppler-Velocimeter (LDV) developed at ISL [4] and the flow density (Fig. 3b) is obtained from the static pressure as measured at the nozzle wall close to the nozzle exit. As long as the flow is not disturbed by the arrival of the driver gas, the Mach number is only determined by the Laval-nozzle geometry. Considering shock tunnel STA equipped with Mach 3 and Mach 4.5 nozzles, the Mach number remains constant over a time interval of nearly 15 ms.

The motion of the body is observed from two orthogonal directions and recorded at 12 500 frames per second using two high-speed cameras. Fig. 4 displays snapshots of the EFP model displacement at Mach 3 in the case of a zero-angle of attack motion. Extracting the positions of selected body-fixed points is based on image processing algorithms that were developed at ISL. This process is necessary in order to describe motions with both translation and rotation of the body. Fig. 5a and 5b display the trajectory of the EFP nose in the case of a non-zero angle of attack motion in the vertical plane.

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Finally, the last section of the paper presents the aerodynamic data extraction method and compares the results with the EFP reference data. The first step of the method consists in computing the theoretical motion of the model using the flow parameters history and assuming normalized aerodynamic coefficients. The second step is a fit process that minimizes the difference between the theoretical and observed motions. Fig. 6 displays the fit results for the zero-yaw drag force coefficient (CD0). In this case, the fit method is based on two parameters: the first one accounts for the initial perturbations of the observed motion (mainly due to the removal of the fixture system) and the second one is the drag force coefficient that accounts for the linear dependency between the theoretical and observed motions. Drag force coefficients that were extracted at Mach 3 and Mach 4.5 compare well with the reference EFP data (Fig. 7). The overturning moment coefficient derivative (CMα) is extracted from the angular motion of the body using a three parameters fit method (initial perturbations, maximum angle and angular frequency) based on sine functions. Furthermore, changing the location of the model center of mass and comparing the resulting overturning moment coefficients gives the normal force coefficient derivative (CNα). Figures

Fig. 1: ISL’s shock tunnel facility STA

Fig. 2: EFP model and fixture system

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Fig. 3a: Stream velocity (Mach 3) Fig. 3b: Stream density (Mach 3)

Fig. 4: Downstream motion of the EFP model (zero angle of attack motion)

Fig. 5: Motion of the model nose in the vertical plane (non-zero angle of attack motion)

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m3]

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Fig. 6: Fitting observed data to theoretical data (downstream displacement)

Fig. 7: Comparison of extracted data with reference data

0 5 10 15 20 25 0

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Theoretical Displacement [cm]

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cm]

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References

[1] Igra O., Takayama K., "Shock-Tube Study of the Drag Coefficient of a Sphere in a Non-stationary Flow", Proc. R. Soc. London Ser. A-Math. Phys. Eng. Sci. 442 (1915), 231-247, 1993

[2] Seiler F., Mathieu G., George A., Srulijes J., Havermann M., “Development of a Free Flight Force Measuring Technique (FFM) at the ISL Shock Tube Laboratory”, 25th International Symposium on Shock Wave (ISSW25), Bangalore, India, 2005

[3] Winchenbach G., Krieger J., Hathaway W., Whyte R., “EFP Free Flight Test Aerodynamic Results”, Air Force Research Laboratory, AT-98-08-02, 1998

[4] Smeets G., George A., "Instantaneous laser Doppler velocimeter using a fast wavelength tracking Michelson interferometer", Rev. Sci. Instrumentation 49(11), 1589–1596, (1978)

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