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Theoretical and experimental investigations of wall adaptation control in wind tunnel and hybrid wind tunnel testing

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Abstract

The hybrid wind tunnel principle is an economical alternative to classical wind tunnels. Wall adaptation tests are reported which are performed in a small scale arrangement duplicating original kinematic relations. A new method for controlling the quality of wall adaptation is presented which is based on the pressure distribution at the rigid wall. This procedure may also be applied for wall adaptation in conventional wind tunnel technique.

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Abbreviations

c p :

pressure coefficient (=(pp )/q ≈−2u/u )

d :

diameter

h :

height of test section

k :

constant for cross flow pressure drop through perforated wall

l :

length

Ma :

Mach number

p :

pressure

q :

dynamic pressure \(\left( { = \frac{\kappa }{2}pMa^2 } \right)\)

r :

radius

s :

gap width

t :

time

u, v :

disturbance velocity

w :

flow velocity

x :

coordinate in flow direction

β :

Prandtl factor \(\sqrt {1 - {\text{Ma}}_\infty ^{\text{2}} } \)

δ :

boundary layer thickness

k :

ratio of specific heats

ψ:

adaptation coefficient \( = \frac{{c_p }}{{(c_p )_r }}\)

$$ = \left[ {{{\left( {\mathop \smallint \limits^1 c_p^2 (x)dx} \right)} \mathord{\left/ {\vphantom {{\left( {\mathop \smallint \limits^1 c_p^2 (x)dx} \right)} {\left( {\mathop \smallint \limits^1 (c_p )_r^2 (x)dx} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {\mathop \smallint \limits^1 (c_p )_r^2 (x)dx} \right)}}} \right]^{1/2} $$

(subcritical flow)

θ :

flow inclination

λ :

shape factor

μ :

Mach angle

( ) a :

adapted wall (slotted or foam coated, not necessarily optimized)

( ) bl :

blockage

( ) g :

gas

( ) i :

image

( ) l :

lift

( ) m :

model

( ) r :

impermeable rigid wall

( ) :

undisturbed flow

(¯):

mean values

( )1;2 :

flow ahead and behind an oblique pressure wave

( )3 :

flow behind a reflected oblique pressure wave

References

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Additional information

The experimental investigations reported here have been carried out by the following students in the course of undergraduate work: Ch. Bauer, C. Schultes, Th. Reimer and U. Walter. I am very grateful for their great care accomplished contributions.

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Hottner, T. Theoretical and experimental investigations of wall adaptation control in wind tunnel and hybrid wind tunnel testing. Experiments in Fluids 19, 233–240 (1995). https://doi.org/10.1007/BF00196471

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  • DOI: https://doi.org/10.1007/BF00196471

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