# Presentation: 280837

## Case 1:  LUMPED ELEMENT MODELINGQuentin Gallas, Ryan Holman,Rajat Mittal, Mark Sheplak, & Louis CattafestaInterdisciplinary Microsystems GroupDepartment of Mechanical & Aerospace Engineering University of Floridahttp://www.img.ufl.edu CFD Validation of Synthetic Jets & Turbulent Separation Control ~ NASA-LaRC WorkshopMarch 29, 2004

## Outline

- Background  Model Description & Validation
- Implementation & Case-Specific Details
- Results & Issues
- Conclusions

## Model Description

- Zero-net mass flux (ZNMF) actuator is a coupled electro-mechanical-acoustic-fluidic system
- Device behavior is determined by geometry and material properties
_**L**_umped _**E**_lement _**M**_odeling (LEM) models the dynamic behavior using a compact analytical formulation
- Goal of LEM is to provide low-order model of local interaction region as a design tool, desirable for
- Device design
- Control algorithm testing
- Numerical boundary condition implementation
- Physical insight

## Lumped Element Model w/o Boundary Layer(Gallas et al., AIAA Journal, Vol. 41, No. 2, pp. 240-247, February 2003 )

## Implementation

- Model of the piezoelectric diaphragm that drives the actuator
- Linear composite plate theory [Prasad et al.†]
- Provides mode shape and fd

-  large uncertainties & tolerances with dimensions
-  can “tune” the device parameters within tolerances to match the natural frequency

- †Prasad, S., Horowitz, S., Gallas, Q., Sankar, B., Cattafesta, L., and Sheplak, M., “Two-Port Electroacoustic Model of an Axisymmetric Piezoelectric Composite Plate,” AIAA Paper 2002-1365, April 2002.

## Synthetic Jet Lumped Element Model w/o Grazing Boundary Layer

- Vac=50 Vpp

**(******** experiment, ********  model)**

- Model validated for orifice aspect ratio *h/d >>1* via LDV measurements of *u(0)* vs. freq.

## Implementation & Circuit Analysis

- 4th-order coupled oscillator  2 resonant frequencies ***f******1*** and ***f******2***
- s = j= 0,  Qout = 0
- s  0, Qout  Vacdawhere da= Vol/Vac
- s  , Qout  -3

## Circuit Implementation & Analysis

- Resonance frequencies      and       influenced by natural frequency of diaphragm and Helmholtz frequency:
- Output parameter is the volume flow rate (spatially and phase averaged over ejection portion of cycle)

## Cavity Compressibility Effect

**Cavity Compressibility Effect**

_**4**__**th**__** order system**_** **
****
_**2**__**nd**__** order system**_

_*Case 1*_
*AIAA J. LEM Paper*

- Incompressible when cavity volume
*f**1* and *f**2* are resonant peaks

_*Case 1*_* *
*NASA Workshop*

## ResultsFrequency Domain

|  |              [m/s] |                  [m/s] |
| --- | --- | --- |
| Exp. (LDV) | ~25 |  |
| LEM |  | ~24 |

-  1st peak dictated by diaphragm natural frequency
-  2nd peak dictated by cavity Helmholtz frequency
-  LEM also provides frequency response

## Measurement Issues

- LEM requires accurate phase-locked velocity measurements near the orifice/slot and p across the slot as a function of Strouhal number to model nonlinearity
- Methods
- HW
- Problems with free convection near zero velocity
- Directional ambiguity  rectification issues due to free convection
- Sensitivity to normal velocity (both significant near orifice/slot)
- Issues with large fluctuation levels near zero mean velocity
- Temperature correction
- LDV
- Spatial resolution issues (probe volume length)
- Velocity bias
- PIV
- Spatial resolution issues (interrogation spot and sheet thickness)
- Particle dynamics

## Experimental DataHigh Resolution PIV Setup

-  10o phase-locked movie   36 frames
-  Spatial resolution across the orifice: 15 or more measurements w/ 50% overlap
-  Field of view is 7.7 mm x 7.7 mm

## Experimental Data High Resolution LDV Setup

-  Probe volume is ~ 60 m
-  3 beam recombiner used for near wall measurements
-  90o off-axis receiving optics with 200 mm lens and bellows extender to limit prove volume length (normally 0.5 mm) to be O(30 m)
-  Obtain 27 independent coincident (ur,uz) velocity measurements across d=1.65 mm orifice
-  Need to characterize particle dynamics and velocity bias

## Experimental DataComparison between PIV & LDV ~ same location

- S=10, measurement at same location (0.1d), Red=20
- PIV data acquired 3 months before LDV data

- axial velocity

- radial velocity

## Comparison with Theory

- Fully-developed, oscillatory pressure-gradient pipe flow = f(pressure difference, frequency)
- Need improved model for small h/d

## Experimental DataComparison between PIV & LDV ~ same location

- axial velocity

- radial velocity

***Experimental Data******Comparison between PIV & LDV ~ same location***

- S=15, measurement at same location (0.1d), Red=110
- Nonlinear effects evident due to jet formation

## Conclusions

- Model results are in close agreement with experimental measurements for this case
- Bonus: gives response over the entire frequency domain
- Model gives reasonable estimate (typically within 20%) with minimal effort, function of signal input, device geometry, material and fluid properties
- Power of LEM:
- Simplicity
- Design tool
- Issues:
- Output variable only at the orifice exit
- Model needs additional data for small h/d, different slot geometries, grazing BL flow