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Research Papers: Flows in Complex Systems

An Experimental and Analytical Investigation of Rectangular Synthetic Jets

[+] Author and Article Information
Gopi Krishnan

Department of Aerospace Sciences, University of Colorado, Boulder, CO 80309-429

Kamran Mohseni1

Department of Aerospace Sciences, University of Colorado, Boulder, CO 80309-429mohseni@colorado.edu

1

Corresponding author.

J. Fluids Eng 131(12), 121101 (Nov 10, 2009) (11 pages) doi:10.1115/1.4000422 History: Received November 29, 2008; Revised September 25, 2009; Published November 10, 2009; Online November 10, 2009

In this paper the flow field of a rectangular synthetic jet driven by a piezoelectric membrane issuing into a quiescent environment is studied. The similarities exhibited by synthetic and continuous turbulent jets lead to the hypothesis that a rectangular synthetic jet within a limited region downstream of the orifice be modeled using similarity analysis just as a continuous planar jet. Accordingly, the jet is modeled using the classic two-dimensional solution to a continuous jet, where the virtual viscosity coefficient of the continuous turbulent jet is replaced with that measured for a synthetic jet. The virtual viscosity of the synthetic jet at a particular axial location is related to the spreading rate and velocity decay rate of the jet. Hot-wire anemometry is used to characterize the flow downstream of the orifice. The flow field of rectangular synthetic jets is thought to consist of four regions as distinguished by the centerline velocity decay. The regions are the developing, the quasi-two-dimensional, the transitional, and the axisymmetric regions. It is in the quasi-two-dimensional region that the planar model applies, and where indeed the jet exhibits self-similar behavior as distinguished by the collapse of the lateral time average velocity profiles when scaled. Furthermore, within this region the spanwise velocity profiles display a saddleback profile that is attributed to the secondary flow generated at the smaller edges of the rectangular orifice. The scaled spreading and decay rates are seen to increase with stroke ratio and be independent of Reynolds number. However, the geometry of the actuator is seen to additionally affect the external characteristics of the jet. The eddy viscosities of the synthetic jets under consideration are shown to be larger than equivalent continuous turbulent jets. This enhanced eddy viscosity is attributed to the additional mixing brought about by the introduction of the periodic vortical structures in synthetic jets and their ensuing break down and transition to turbulence. Further, a semi-empirical modeling approach is proposed, the final objective of which is to obtain a functional relationship between the parameters that describe the external flow field of the synthetic jet and the input operational parameters to the system.

Copyright © 2009 by American Society of Mechanical Engineers
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References

Figures

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Figure 2

Schematic of the evolution of a rectangular synthetic jet

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Figure 3

Schematic of an incompressible actuator model, where the volume of fluid displaced by the diaphragm is ejected through the orifice in the form of a slug

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Figure 4

Experimental setup

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Figure 5

Actuator with a rectangular slot orifice along side a dime provided for scale

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Figure 6

The dynamic deflection response of the center of the piezoelectric diaphragm to the variation in driving frequency. Actuator 1, Vd=30 V.

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Figure 7

The dynamic deflection response of the piezoelectric membrane at the center to the variation in driving voltage. Actuator 1, f=560 Hz.

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Figure 8

Variation in the time average centerline velocity with axial distance, displaying the I: developing, II: quasi-two-dimensional, III: transition, and IV: axisymmetric regions (Actuator 2, see Table 2 for details of cases)

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Figure 9

Dependence of centerline decay rate on stroke ratio for both actuators

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Figure 10

Streamwise evolution of turbulence intensity at the centerline (Actuator 1, see Table 1 for details of cases))

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Figure 11

Normalized time average streamwise velocity profile (Case 1a)

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Figure 12

Normalized fluctuating streamwise velocity profile (Case 1a)

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Figure 13

Time average velocity profile along the major axis at different axial locations (Case 1a)

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Figure 14

Variation in jet half width with axial distance (Case 1a)

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Figure 15

Variation in spreading rate with increasing stroke ratio for both actuators

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Figure 16

Dependence of eddy viscosity (ε) on stroke ratio for the two synthetic jet actuators. The eddy viscosity of equivalent turbulent continuous jets are shown for comparison: CJ-continuous jet and SJ-synthetic jet.

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Figure 17

Comparison of the analytical model and experimental data of a synthetic jet (Case 1a)

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Figure 1

Schematic of synthetic jet operation

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