# Presentation: 171295

## Reduced-Order Model for Zero-Mass Synthetic Jet Actuators

_*Nail K. Yamaleev*_
- North Carolina A&T State University
- and
*Mark H. Carpenter*
- NASA Langley Research Center

## 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?

## Current Practices and Algorithms

## Reduced-Order Model

## 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:_
- Doesn’t account for 2-D/3-D effects in the actuator

##                   Previous ResultsThe 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 geometryN. Yamaleev and M. H. Carpenter, “ A reduced-order model for efficient simulation of synthetic jet actuators”, NASA/TM-2003-212664.

## Wavelength of diaphragm vibration

## 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.

- 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****.*

## 4th-order Numerical Method

- 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

## Synthetic Jet in Quiescent Air

## Grid Refinement Study

## Time-history of the vertical velocity at x=0, y=0.1 mm

## Time-averaged vertical velocity at y=1 mm.

## Contours of the vertical velocity component after 10 periods.

## Vorticity contours obtained with the quasi-1-D and full 2-D models after 1 period

## Synthetic Jet in a Crossflow

## Time-history of the vertical velocity at y=0.1 mm

## Time-averaged vertical velocity at y=1 mm

## Time-averaged vertical velocity along the center of the orifice

## 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;
-       - *Re*orifice>500, *L*interface>2*d*.
- Computational cost of the quasi-1-D model
-      -  1⁄2 of the full 2-D model
-      - 10% overhead as compared with the 0-D models