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The automatic control of boundary-layer transition — Experiments and computation

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Abstract

In recent years there has been an increasing interest in the control of boundary-layer transition through the use of wall suction. In the current work suction is provided through one or more suction panels situated close to the leading edge of a plate. Experiments show that boundary-layer pressure fluctuation measurements can be used to identify the position of transition. Transition can be maintained at a desired location with minimum power consumption by employing an automatic adaptive feedback control loop which regulates the suction flow rates of two independent suction panels. This can be expressed as a constrained optimization problem. To allow the suction flow rates to be updated, a modified least mean squares algorithm is used within the control loop. Experimental measurements show that the control algorithm allows fast and stable convergence towards the optimum suction distribution for a double suction panel configuration. Numerical simulations have also been performed. The two-dimensional boundary layer was calculated allowing the viscous boundary layer to interact with the inviscid outer flow. Following linear stability theory the spatial growth rates are calculated by solving an Orr-Sommerfeld type eigenvalue problem, with the streamwise location of transition predicted via thee N -method. Applying the same optimization strategy as in the experiments, good qualitative agreement between computations and experiments was found. The optimization algorithm has been applied to computer models where the relation between suction flow rates and transition location is described by an empirical analytical function. This shows that the controller can in principle be applied to systems with more than two suction panels.

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Abbreviations

b :

transition location with zero suction

d :

desired transition location

e(k):

error signal

k :

iteration index

p :

rms pressure

p ref :

reference rms pressure

r :

sum of the reference pressure

u :

streamwise velocity

u e :

external velocity

\(u_{e_0 } \) :

inviscid external velocity

A :

wave amplitude

F(\(\vec u\)):

cost function

I:

identity matrix

N :

maximum amplification factor

P:

projection matrix

R:

Reynolds number

Re:

Reynolds number based on the boundary-layer thickness

R:

matrix of weights

Tu:

turbulence level

\(\vec u\) :

vector of suction flow rates

v :

normal velocity

v wall :

suction velocity at the surface

x :

streamwise coordinates

x m :

microphone location

x T(k):

measured transition location

y :

normal coordinate

y(k):

sum of the measured pressures

w(k):

noise

\(\tilde L\) :

plate length

α :

αr +iα i

\(\tilde U_\infty \) :

free stream velocity

δ*:

displacement thickness

\(\vec \theta \) :

gradient vector

λ :

Lagrange multiplier

μ :

controller gain

ϕ :

disturbance stream function

φ :

disturbance amplitude

θ :

wave frequency

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Authors and Affiliations

  1. Department of Aeronautics and Astronautics, The University of Southampton, SO9 5NH, Southampton, Hampshire, England

    Petra Hackenberg & Owen R. Tutty

  2. Institute of Sound and Vibration Research, The University of Southampton, SO9 5NH, Southampton, Hampshire, England

    Jean-Luc Rioual & Philip A. Nelson

Authors
  1. Petra Hackenberg
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  2. Jean-Luc Rioual
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  3. Owen R. Tutty
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  4. Philip A. Nelson
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= complex wave number

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Hackenberg, P., Rioual, JL., Tutty, O.R. et al. The automatic control of boundary-layer transition — Experiments and computation. Appl. Sci. Res. 54, 293–311 (1995). https://doi.org/10.1007/BF00863515

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  • DOI: https://doi.org/10.1007/BF00863515

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