Reduced-Order Model for Zero-Mass Synthetic Jet Actuators

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Reduced-Order Model for Zero-Mass Synthetic Jet
Actuators

• Nail K. Yamaleev
• North Carolina AT State University
• and
• Mark H. Carpenter
• NASA Langley Research Center

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Motivation

• Can near full fidelity be achieved with
  reduced-order models?
• - which geometries are amenable to the
  reduced-order
• approximation
• - actuator regions that are inherently
  multidimensional
• - geometrical features that are not important
• What is the magnitude of errors committed by
  reduced-order models?

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Current Practices and Algorithms
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Reduced-Order Model
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Quasi-1-D Model

• The quasi-1-D Euler equations
• A- area variation, - 1-D moving
  grid.
• Advantages
• Fully conservative
• Includes area variation, volume, deflection of
  diaphragm and synthetic jet/BL interaction
• Accounts for the resonance phenomenon
• Computationally efficient
• Can be used for a large array of actuators,
  design and optimization studies
• Disadvantages
• Doesnt account for 2-D/3-D effects in the
  actuator

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Previous ResultsThe quasi-1-D
model provides practically the same accuracy
(2-3 error) as compared with the full 2-D
Navier-Stokes simulation if 1)
2) the quasi-1-D/2-D interface should be
located at least 2d away from the
orifice exit 3) the quasi-1-D geometry
exactly coincides with the real
actuator geometryN. Yamaleev and M. H.
Carpenter, A reduced-order model for efficient
simulation of synthetic jet actuators,
NASA/TM-2003-212664.
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Wavelength of diaphragm vibration
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• The actuator size is much less than the
  wavelength of diaphragm vibration
• The vortex energy ingested into the cavity is
  much less than the gas energy inside the
  actuator
• Acoustic resonance frequency depends on the
  actuator volume, neck length, and orifice size,
  but does not depend on the actuator shape.

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• 4th-order Numerical Method
• Spatial approximation
• 4th-order upwind-biased finite difference
  method
• The spatial error at all the grid interfaces
  was less
• than 0.5.
• Temporal approximation
• Explicit low-storage 4th-order Runge-Kutta
  method
• Temporal error was in the range of

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Synthetic Jet in Quiescent Air
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Grid Refinement Study
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Time-history of the vertical velocity at x0,
y0.1 mm
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Time-averaged vertical velocity at y1 mm.
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Contours of the vertical velocity component after
10 periods.
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Vorticity contours obtained with the quasi-1-D
and full 2-D models after 1 period
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Synthetic Jet in a Crossflow
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Time-history of the vertical velocity at y0.1 mm
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Time-averaged vertical velocity at y1 mm
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Time-averaged vertical velocity along the center
of the orifice
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Conclusions

• Quasi-1-D model provides near full fidelity (2-3
  error)
• in the exterior flowfield if
• - Volume, neck length, diaphragm area, and
  diaphragm
• deflection of the quasi-1-D geometry
  should be
• equal to those of the 3-D actuator
• - Actuator size should be much less than
  the
• wavelength of diaphragm oscillation
• - Reorificegt500, Linterfacegt2d.
• Computational cost of the quasi-1-D model
• - ½ of the full 2-D model
• - 10 overhead as compared with the 0-D
  models