# Wind-tunnel studies on maneuvering slender bodies

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## Abstract

In this paper, the first experimental results of tests with a new model support designed for simulations of high frequency and high amplitude pitching maneuvers are presented. A generic missile model with a blunt nose was used for which static test data from earlier experiments with a conventional model support were existing. At the beginning, static tests were done for comparison purposes to judge the influence of the new setup (model support, sting for the model, pivot arm) on the measured forces and moments. Afterwards, dynamic tests with sine oscillations at frequencies of \(f_{\rm a}=0.05\ldots 4\,\hbox{Hz}\) and angles of attack varying between \(\alpha = 0^{\circ} \ldots 45^{\circ}\) were performed. Beside the qualification of this new test rig, the tests were used to study the “Phantom Yaw Effect” and to prove an interactive method of its control. This phenomenon is characterized by unwanted yawing moments resulting from asymmetric vortices which can occur on slender bodies at high angles of attack. In the tests, a lee-vortex control device with symmetrically arranged longitudinal slot nozzles producing “air-jet strakes” was demonstrated to decrease the yawing moments both under static and dynamic conditions.

## Keywords

Phantom Yaw Maneuver simulation Asymmetric vortices Slender bodies Flow control Experiments## List of symbols

## Greek symbols

*α*Angle of attack

- \(\Updelta\alpha\)
Pitching amplitude

- \(\alpha_{\rm AV}\)
Onset angle asymmetric vortices

- \(\alpha_{\rm SV}\)
Onset angle symmetric vortices

- \(\alpha_{\rm UV}\)
Onset angle unsteady vortices

- \(\alpha_{\rm N}\)
Effective angle of attack at model’s nose

*δ*Offset angle of

*x*-axis and radius to pivot for a POI*ω*Angular velocity

- \(\dot{\omega}\)
Angular acceleration

*σ*Standard deviation

## Roman symbols

*a*Acceleration

- \(c_x, c_y, c_z\)
Aerodynamic force coefficients

- \(c_l, c_m, c_n\)
Aerodynamic moment coefficients

- \(c_{x,{\rm {bp}}}\)
Axial force coefficient at model base

*D*Model diameter

- \(F_x, F_y, F_z\)
Force in

*X*-,*Y*- or*Z*-direction- \(F_{\rm act}\)
Actuation force of hydraulic system

- \(f_{\rm a}\)
Actuation frequency

- \(f_{\rm s}\)
Sampling frequency

*J*Moment of inertia

*L*Model length

*M*Mach number

- \(M_x, M_y, M_z\)
Moment around

*X*-,*Y*- or*Z*-axis*m*Model mass

- \(q_\infty\)
Free stream dynamic pressure

- \(p_\infty\)
Free stream static pressure

- \(p_0\)
Stagnation pressure

- \( p_{\rm B}\)
Base pressure

- \(Re_D\)
Reynolds number (based on model diameter)

*r*Distance to the pivotal point

*t*Time

- \(t_{\rm m}\)
Measurement time

- \(\Updelta x\)
Distance between 2 points on

*x*-axis- \(\Updelta z_0\)
Distance wind tunnel wall to main body axis

## Abbreviations

- AoA
Angle(s) of attack

- BRP
Balance reference point

- CAD
Computer-aided design

- CG
Center of gravity

- DLR
German Aerospace Center

- MCS
Model coordinate system

- MEMS
Microelectromechanical systems

- POI
Point of interest

- RCS
Rotation coordinate system

- RMS
Root mean square

- RP
Reference point

- RS
Reference (coordinate) system

- TWG
Transonic wind tunnel Göttingen

## Subscripts

*x**X*-direction of corresponding coordinate system*y**Y*-direction of corresponding coordinate system*z**Z*-direction of corresponding coordinate system- M
Model (coordinate system)

- N
Model nose

- CG
Center of gravity

- Acc
Accelerometer parameter

- in
Inertial

- BRP
Referring to balance reference point

- bpc
Base pressure corrected

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