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On the vorticity characteristics of lobe-forced mixer at different configurations

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Abstract

Lobe-forced mixer is one typical example of the passive flow controllers owing to its corrugated trailing edge. Besides the spanwise Kelvin–Helmholtz vortex shedding, streamwise vortices are also generated within its mixing layer. The geometrical configuration of the lobe significantly affects these two types of vortices, which in turn affects the mixing performance of the mixer. In the present investigation, characteristics of mixers with five different configurations were examined and evaluated for two velocity ratios (r = 1, 0.4). The mixers have only one lobe in order to eliminate any possible interactions between neighboring vortices generated by the adjacent lobes. Hot-wire anemometer was used to examine the Kelvin–Helmholtz vortices via the spectrum analysis while laser Doppler anemometer was employed to examine the streamwise vortices. It was found that there were two main frequencies for the Kelvin–Helmholtz vortices in the wake of the mixer; and the Strouhal numbers approached their respective maximum values at high Reynolds number. The rectangular mixer had similar mixing performance with the semicircular one; and both of them were better than the triangular mixer. The scalloping modification enhanced mixing by generating additional streamwise vortices while the scarfing modification could not improve the mixing performance.

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Abbreviations

A wake :

Wake area of the lobe-forced mixer flow (m2)

C I :

Normalized streamwise circulation \( C_{\text{I} } = \frac{{\Upgamma_{I} }}{{\overline{U} \times \lambda }} \)

R :

Radius of the semi-circle part of the lobe trailing edge (m)

Re :

Reynolds number \( Re = \frac{{\rho \overline{U} \lambda }}{\mu } = \frac{{\overline{U} \lambda }}{\nu } \)

St :

Strouhal number \( St = \frac{\lambda }{{\lambda_{\text{{K}\text{--} \text{H}}} }} = \frac{f \times \lambda }{{\overline{U} }} \)

U 1 and U 2 :

Upper and lower stream velocity (m/s)

\( \overline{U} \) :

Mean velocity (nominal velocity) \( \overline{U} = \frac{{U_{1} + U_{2} }}{2}, \) (m/s)

\( \overline{U} ,\overline{V} ,\overline{W} \) :

Mean velocities in the streamwise, spanwise and traverse directions, respectively (m/s)

\( u',v',w' \) :

rms (root-mean-square) velocities in the streamwise, spanwise and traverse directions, respectively (m/s)

X, Y, Z :

Cartesian coordinate system (streamwise, spanwise and traverse directions accordingly)

f :

Kelvin–Helmholtz vortex shedding frequency (Hz)

h :

Height of the lobe (m)

r :

Velocity ratio of the on-coming streams, \( r = \frac{{U_{1} }}{{U_{2} }} \)

ΓI :

Mean streamwise circulation of the plane I, \( \Upgamma_{\text{I}} = \int\nolimits_{{\overrightarrow {\text{AB}} }} {\overline{V} \times {\text{d}}y} + \int\nolimits_{{\overrightarrow {\text{BC}} }} {\overline{W} \times {\text{d}}z} + \int\nolimits_{{\overrightarrow {\text{CD}} }} {\overline{V} \times {\text{d}}y} + \int\nolimits_{{\overrightarrow {\text{DA}} }} {\overline{W} \times {\text{d}}z} \)

ε :

Penetration angle (half divergence angle) of the lobe-forced mixer

λ:

Wavelength of the lobe (m)

\( \lambda_{K - H} \) :

Average K–H vortex wavelength (m)

ω :

vorticity \( \overrightarrow {\omega } = \nabla \times \overrightarrow {U} \)

ω x :

Streamwise vorticity \( \overrightarrow {{\omega_{x} }} = (\frac{\partial W}{\partial y} - \frac{\partial V}{\partial z}) \times \overrightarrow {i} \)

1:

Upper stream

2:

Lower stream

C:

Point C of the mixer trailing edge

L:

Point L of the mixer trailing edge

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Authors and Affiliations

  1. Faculty of Civil Engineering, Delft University of Technology, Delft, The Netherlands

    R. Mao

  2. School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore, Republic of Singapore

    S. C. M. Yu & L. P. Chua

  3. School of Civil and Resource Engineering, University of Western Australia, Crawley, Australia

    T. Zhou

Authors
  1. R. Mao
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  2. S. C. M. Yu
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  3. T. Zhou
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  4. L. P. Chua
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Correspondence to R. Mao.

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Mao, R., Yu, S.C.M., Zhou, T. et al. On the vorticity characteristics of lobe-forced mixer at different configurations. Exp Fluids 46, 1049–1066 (2009). https://doi.org/10.1007/s00348-009-0613-x

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  • DOI: https://doi.org/10.1007/s00348-009-0613-x

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