Abstract
We compare two turbulent boundary layers produced in a low-speed water channel experiment. Both are subjected to an identical streamwise pressure gradient generated via a lateral contraction of the channel, and an additional spanwise pressure gradient is imposed on one of the layers by curving the contraction walls. Despite a relatively high streamwise acceleration, hot-film probe measurements of the mean-velocity distributions show that the Reynolds number increases whilst the coefficient of friction decreases downstream. Visualization of the viscous layers using hydrogen bubbles reveal an increase in the non-dimensional streak spacing in response to the acceleration. Changes in statistical moments of the streamwise velocity near the wall suggest an increased dominance of high-velocity fluctuations. The near-wall streaks and velocity statistics have little sensitivity to the boundary layer three-dimensionality induced by the spanwise pressure gradient, with the boundary-layer crossflow velocity reaching 11 % that of the local freestream velocity.
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Abbreviations
- Q, Q e :
-
Mean and freestream velocities in the mean-flow direction
- Q τ :
-
Friction velocity (τ w/ρ)1/2
- Q + :
-
Non-dimensional mean velocity in inner units, Q/Q τ
- γ, γ e :
-
Local mean-flow and freestream-directions, respectively
- x, z :
-
Channel coordinates
- y :
-
Channel floor and boundary-layer wall-normal coordinate
- x +, y +, z + :
-
Non-dimensional channel coordinates scaled in inner units; xQ τ /υ, yQ τ /υ, zQ τ /υ
- s :
-
The streamwise distance from the entrance of the pressure gradient geometry
- q′ :
-
Fluctuating velocity in the local mean-flow direction
- S q , K q :
-
Skewness and kurtosis of velocity in the local mean-flow direction
- C f :
-
Coefficient of friction, 2τ w/ρQ 2 e
- Re θ :
-
Momentum thickness Reynolds number, Q e δ θ /ν
- K :
-
Acceleration parameter (υ/Q 2 e ) (dQ e /ds)
- H :
-
Shape factor, δ */δ θ
- τ w :
-
Wall shear stress
- δ :
-
Boundary-layer thickness where Q/Q e = 0.99
- δ θ , δ * :
-
Boundary layer momentum and displacement thicknesses, respectively
- l +, d + :
-
Non-dimensional hot-film probe length and diameter in inner units, lQτ/υ, dQ τ /υ
- t + :
-
Non-dimensional time in inner units, tυ/Q 2 τ
- U, W :
-
Mean velocity in the freestream and crossflow directions, respectively
- \( \bar{\lambda }^{ + } \) :
-
Non-dimensional mean spanwise spacing of the near-wall streaks
- \( \sigma^{ + }_{\lambda } \) :
-
Non-dimensional standard deviation of the near-wall streak spacing distribution
- S λ , F λ :
-
Skewness and kurtosis of the near-wall streak spacing distribution
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Pearce, N.F., Denissenko, P. & Lockerby, D.A. An experimental study into the effects of streamwise and spanwise acceleration in a turbulent boundary layer. Exp Fluids 54, 1414 (2013). https://doi.org/10.1007/s00348-012-1414-1
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DOI: https://doi.org/10.1007/s00348-012-1414-1