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On the propagation of naturally-occurring turbulent spots

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Abstract

An experimental investigation of the propagation of turbulent spots occurring naturally during boundarylayer transition was conducted. Wide-bandwidth heat-transfer instrumentation was used in tracking individual cuibulent spots as they progressed down a flat-plate surface toward fully-developed turbulence. The convection rates of the turbulent/non-turbulent interfaces of the spots in the streamwise direction were determined, as were rates of lateral spreading. The separate effects of compressibility and favourable pressure gradients have been assessed, and some typical results have been reported.

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Abbreviations

C ie, C_le:

fractional propagation rate of the spot leading edge,U le/U∞

C m, C_m:

fractional propagation rate of the spot (“mean”),U m/U∞

C te, C_te:

fractional propagation rate of the spot trailing edge,U te/U∞

Cr :

criterion function

D :

detector function

dx :

distance of propagation of the lateral edge of a turbulent spot in the streamwise direction (mm)

dz :

distance of propagation of the lateral edge of a turbulent spot in the cross-stream direction (mm)

h :

sampling period (s)

K :

acceleration parameter, (ν/U 2∞ )dU ∞/dx

m :

relative signal magnitude

M ∞ :

freestream Mach number

n :

turbulent-spot generation rate (s−1 m−1)

P :

freestream static pressure (N/m2)

P 0 :

total pressure (N/m2)

q :

heat flux (kW/m2)

Re u :

freestream unit Reynolds number at the working-section inlet (m−1),U ∞/ν

Re θ :

local Reynolds number based on momentum thickness,U ∞θ/ν

T 0 :

total temperature (K)

T w :

wall temperature (K)

Tu :

freestream turbulence intensity,u′/U ∞

t NT :

amount of time an unsteady heat-transfer signal is non-turbulent (s)

t T :

amount of time an unsteady heat-transfer signal is turbulent (s)

U le :

turbulent-spot leading-edge velocity (m/s)

U m :

turbulent-spot “mean” velocity (m/s)

U te :

turbulent-spot trailing velocity (m/s)

U ∞ :

local freestream velocity (m/s)

w :

weighting factor

x :

distance from the leading edge of the flat plate (m)

x 1 :

distance from the leading edge of the flat plate to the point of transition onset (m)

α:

turbulent-spot spreading angle (degrees)

γ:

intermittency,t T/(tT+tNT)

θ:

boundary-layer momentum thickness (m)

ν:

kinematic viscosity (m2/s)

σ:

Emmons' non-dimensional turbulent-spot propagation parameter

τ 5 :

smoothing period (s)

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Authors and Affiliations

  1. Oxford University, Oxford, U.K.

    J. P. Clark & T. V. Jones

  2. Syracuse University, Syracuse, NY, U.S.A.

    J. E. LaGraff

Authors
  1. J. P. Clark
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  2. T. V. Jones
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  3. J. E. LaGraff
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Clark, J.P., Jones, T.V. & LaGraff, J.E. On the propagation of naturally-occurring turbulent spots. J Eng Math 28, 1–19 (1994). https://doi.org/10.1007/BF02383602

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