SYNTHETIC JET blrgn MODEL
{ \ SHARMA frequency force phase cavDepth cavOrificeRat \ lossCoeff dampCoeff DiaDensityThk natFreq helmFreq | \ { MCMILLAN | WHALEN } frequency voltage phase | \ SINUSOIDAL frequency amplitude phase \ } [inclination_angle [ { ABOUT_Z | ABOUT_NORMAL | ABOUT_BODY } [azimuthal_angle] ] ] |
A synthetic jet is an active flow control device that consists of a diaphragm located at the bottom of a small cavity and an orifice in the opposite face that leads to the main flow passage. The diaphragm is forced to oscillate at a prescribed frequency, causing pressure oscillations within the cavity. During the upward stroke, directed fluid from the cavity is expelled through the orifice. As the flow is expelled out the other side of the orifice, a shear layer develops between the jet and the surrounding fluid. The vorticity within this shear layer generates a vortex ring, which quickly propagates away from the device. On the downward stroke of the diaphragm, outside fluid from the region surrounding the orifice is sucked back into the cavity. Because the vortex ring has propagated away from the orifice, there is no significant interaction between it and the fluid entering the cavity.
Averaged over a period of the diaphragm oscillation, this device introduces no net mass flow to the system. However, because the expelled fluid is a directed pulse and the entering fluid is entrained from the entire surroundings, the jet does produce a non-zero mean jet velocity. The non-zero net momentum pulse of the jet can be used to excite the fluid flowing past the orifice location.
Low-order synthetic-jet modeling is an enabling approach to simulating the complex physics resulting from unsteady, synthetic-jet actuation in a flowfield. The model serves to replace an actuator with a boundary condition that accurately simulates the actuator performance. The result is a considerable time saving for grid generation and computations, as the need to model the actuator cavity and diaphragm motion is replaced by the implementation of a relatively simple boundary condition. Various approaches to synthetic-jet low-order modeling may be applied, ranging from the development of actuator-dependent analytical models to device-independent response surface model approaches based on statistically designed experiments. Some of these models are described below.
To use the synthetic jet models, the grid boundary condition must
be set to type BLEED and the bleed region number
specified with the keyword above must match that in the grid file.
SHARMA frequency force phase cavDepth cavOrificeRat \ lossCoeff dampCoeff DiaDensityThk natFreq helmFreq |
frequency | Frequency of applied forcing, f_{f} (Hz) | ||
---|---|---|---|
force | Amplitude of applied forcing, F (lbf) | ||
phase | Phase shift of applied forcing, φ (deg) | ||
cavDepth | Cavity depth, L (inches) | ||
cavOrificeRat | Ratio of the cavity orifice area to the diaphragm area, A_{o}/A_{w} | ||
lossCoeff | Orifice loss coefficient, K (between 0 and 1) | ||
dampCoeff | Damping coefficient of the diaphragm, ζ_{w} (between 0 and 1) | ||
DiaDensityThk | Diaphragm mass per unit area, m_{w}/A_{w} (slug/ft2) | ||
natFreq | Natural frequency of the diaphragm, f_{w} (Hz) | ||
helmFreq | Helmholtz frequency of the cavity, f_{h} (Hz) |
Note that all of the inputs listed above must be greater than zero.
The SHARMA model is based on a forced, second-order, single-degree-of-freedom mechanical system with fluid coupling to include cavity pressure and orifice velocity. The fluidic coupling is derived based on the unsteady continuity equation and Bernoulli's equation with a loss term to account for non-ideal effects of the orifice. The resulting coupled set of equations is given by:
A_{o} | Area of the orifice | ||
---|---|---|---|
A_{w} | Area of the diaphragm wall | ||
F(t)_{} | Force used to displace the diaphragm | ||
K_{} | Orifice loss coefficient | ||
l_{e} | Effective length of the air jet/slug | ||
m_{w} | Mass of the diaphragm | ||
p_{i} | Pressure within the cavity | ||
p_{o} | Pressure of the ambient air | ||
t_{} | Time | ||
V_{o} | Volume of the cavity, A_{w}L | ||
v(t)_{} | Velocity through the cavity orifice | ||
y_{w}(t) | Diaphragm displacement | ||
γ | Ratio of specific heats | ||
φ | Phase shift of applied forcing | ||
ρ_{a} | Density of the ambient air | ||
ω_{f} | Forcing frequency applied to the diaphragm, 2πf_{f} | ||
ω_{h} | Helmholtz frequency of the cavity, 2πf_{h} | ||
ω_{w} | Natural frequency of the diaphragm, 2πf_{w} | ||
ζ_{w} | Damping coefficient of the diaphragm |
The model calculates a cavity exit velocity based on the current time-step, which is then applied as a boundary condition to the flow equations.
The Sharma model has proven effective for simulating synthetic jets that operate at or near resonance frequency. However, not all actuators are designed to operate at those conditions, and this model does not do well for those devices. In addition, the results may be sensitive to errors in the estimation of the input parameters. In those cases, the models described below may be more useful.
Reference:
{ MCMILLAN | WHALEN } frequency voltage phase |
frequency | Operating frequency (Hz) | ||
---|---|---|---|
voltage | Operating voltage (Vrms) | ||
phase | Operating phase shift (deg) |
Note that the frequency and voltage must be positive.
Synthetic jets have a periodic output such that the pressure and jet velocity may be accurately represented in terms of a sine wave of a given amplitude, frequency, and phase. In the McMillan and Whalen models, the amplitude of the wave is determined from a response surface method (i.e., curve-fit) as a function of the input voltage and frequency. The models differ in the type of curve-fit applied.
Reference:
SINUSOIDAL frequency amplitude phase |
frequency | Operating frequency (Hz) | ||
---|---|---|---|
amplitude | Peak jet velocity (ft/s) | ||
phase | Operating phase shift (deg) |
Note that the frequency and voltage must be positive.
This model simply sets the jet velocity to be sinusoidally varying
at the specified amplitude, frequency, and phase. The amplitude
for this model remains constant.
[inclination_angle [ { ABOUT_Z | ABOUT_NORMAL | ABOUT_BODY } [azimuthal_angle] ] ] |
inclination_angle | Inclination injection angle (deg). Must be positive. The default is 0.0. | ||
---|---|---|---|
azimuthal_angle | Azimuthal injection angle (deg). The default is 0.0. |
The synthetic jet direction is set by the input inclination and azimuthal angles.
The inclination_angle is the angle between the blowing direction and the projection of the x-axis onto the surface. If the ABOUT_BODY option is used, then the inclination_angle is the angle between the blowing direction and the projection of the "downstream" aerodynamic axis onto the surface.
If ABOUT_Z is specified, the azimuthal_angle is the angle between the blowing direction and the projection of the surface normal onto a z-constant plane. Starting from the projection of the x-axis onto the surface, the blowing direction is thus determined by rotating about the projection of the surface normal onto a z-constant plane by the azimuthal_angle, then "up" from the surface by the inclination_angle.
If ABOUT_NORMAL is specified, the azimuthal_angle is the angle between the blowing direction and the surface normal itself. Starting from the projection of the x-axis onto the surface, the blowing direction is thus determined by rotating about the surface normal by the azimuthal_angle, then "up" from the surface by the inclination_angle.
If ABOUT_BODY is specified, the azimuthal_angle is the angle between the blowing direction and the "up" aerodynamic axis. Starting from the projection of the "downstream" aerodynamic axis onto the surface, the blowing direction is thus determined by rotating about the "up" aerodynamic axis by the azimuthal_angle, then "up" from the surface by the inclination_angle.
If neither ABOUT_Z, ABOUT_NORMAL, or ABOUT_BODY is specified, then ABOUT_Z is assumed and azimuthal_angle will have its default value of 0.0.
Last updated 1 Apr 2016