Abstract
An experimental study on the Reynolds stress tensor was conducted in the three-dimensional flow in the plane turbulent wall jet induced by an isolated streamwise vortex generated by the half-delta wing mounted on the wall. Oscillation of the angle of attack of the wing induced a periodic perturbation in the strength of the streamwise vortex. Analysis by triple velocity decomposition and phase averaging shows that the oscillation induces periodic variations in the strength, radius, and position of the streamwise vortex center. The effect of periodic perturbation manifests itself in the magnitude of the Reynolds stress components \(\overline{w^{2}}\) and \(\overline{vw}.\) Simulations prove that the periodic variations in the strength, radius, and position of the vortex center can generate an apparent shear stress, denoted herein as \(\overline{\tilde{V}\tilde{W}}.\)
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Abbreviations
- AR:
-
Aspect ratio of the jet nozzle, nozzle width/height
- b m :
-
Inner layer thickness of the plane wall jet (m or mm)
- b 2 :
-
Half-width of the plane wall jet (m or mm)
- c :
-
Chord length of the half-delta wing (m or mm)
- f :
-
Frequency of the oscillating wing (Hz)
- h :
-
Height of the half-delta wing (m or mm)
- R y :
-
Transverse radius of the streamwise vortex (m or mm)
- R z :
-
Spanwise radius of the streamwise vortex (m or mm)
- S l :
-
Nozzle height (m or mm)
- S yz :
-
Rate of strain in the cross-streamwise plane, \(=\frac{\partial W}{\partial y} + \frac{\partial V}{\partial z}\) (1/s)
- t′:
-
Delay time of phase averaging (s)
- T :
-
Period of oscillation of the angle of attack (s)
- U :
-
Mean streamwise velocity (m/s)
- U e :
-
Velocity in the irrotational flow outside the wall jet (m/s)
- U m :
-
Maximum mean streamwise velocity (m/s)
- U 0 :
-
Velocity excess, =U m − U e (m/s)
- u :
-
Fluctuating streamwise velocity (m/s)
- V :
-
Mean transverse velocity (m/s)
- v :
-
Fluctuating transverse velocity (m/s)
- W :
-
Mean spanwise velocity (m/s)
- w :
-
Fluctuating spanwise velocity (m/s)
- x :
-
Streamwise distance from the trailing edge of the wing (m or mm)
- x 0 :
-
Streamwise distance from the nozzle exit (m or mm)
- y :
-
Transverse distance from the wall (m or mm)
- y c :
-
Transverse distance from the wall to the vortex center (m or mm)
- z :
-
Spanwise distance from the centerline of the test plate (m or mm)
- z c :
-
Spanwise distance from the centerline to the vortex center (m or mm)
- α:
-
Angle of attack of the wing (degree)
- Ω x :
-
Mean streamwise vorticity, \( = \frac{\partial W}{\partial y} - \frac{\partial V}{\partial z}\) (1/s)
- ω x :
-
Fluctuating streamwise vorticity, \( = \frac{\partial w}{\partial y} - \frac{\partial v}{\partial z}\) (1/s)
- ΔT :
-
Time interval for conventional time averaging (s)
- ν:
-
Kinematic viscosity (m2/s)
- \(\overline{Q}\) :
-
Mean value, \(\equiv {\mathop {\lim}\limits_{\Delta T \to \infty}}\frac{1}{\Delta T}{\int\limits_{0}^{\Delta T} {\tilde{q}(t, {\mathbf{x}})\hbox{d}t}}\)
- 〈Q 〉 T :
-
Phase-averaged value, \( \equiv {\mathop {\lim}\limits_{N \to \infty}}\frac{1}{N}{\sum\limits_{k = 0}^{N - 1} {\tilde{q}({\mathbf{x}, }t + kT)}}\)
- \(\tilde{Q}\) :
-
Periodic fluctuating component of \(\tilde{Q}\)
- q′:
-
Random fluctuating component of \(\tilde{Q}\)
- \(\tilde{Q}\) :
-
Instantaneous value of the physical quantity q
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Mochizuki, S., Yamada, S. & Osaka, H. Reynolds stress field in a turbulent wall jet induced by a streamwise vortex with periodic perturbation. Exp Fluids 40, 372–382 (2006). https://doi.org/10.1007/s00348-005-0074-9
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DOI: https://doi.org/10.1007/s00348-005-0074-9