# Presentation: 808463

## Case 2:  LUMPED ELEMENT MODELINGOF A ZNMF ACTUATOR INTERACTING WITH A GRAZING BOUNDARY LAYERQuentin Gallas, 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 30, 2004

## Outline

- Model Description
- Linear vs. nonlinear effects
- Grazing flow model
- Implementation & Case-Specific Details
- Results
- 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
*See yesterday’s presentation for more on this modeling approach...*

## LEM for Piezoceramic Driver

## LEM for Voice-Coil Driver

- Boundary Layer Separation Control  McCormick, AIAA 2000-0519, Jan. 2000
- Below shows equivalent circuit model obtained using lumped elements

## Synthetic Jet Formation

- Nonlinear distortion for v(y/d=0.1, r/d=0, t)

## Synthetic Jet Formation

- Seifert, A. and Pack, L.G., “Oscillatory Control of Separation at High Reynolds Numbers”, *AIAA J.*, Vol. 37, No. 9, pp. 1062-1071, Sep. 1999.

## LEM for Grazing Boundary Layer Case

-  ZaO = RaO,lin + jMaO + RaO,nl
-  Nonlinear orifice resistance modeled as
- generalized Bernoulli flow meter

## Model Extraction Using CFD(Mittal et al. GWU)

- Comparison of magnitude and phase of orifice impedance vs. Stokes number *S* using simulations of Mittal et al.

## Grazing Boundary Layer Impedance

- Use of empirical models developed for acoustic liners (flow past Helmholtz resonators)
- BC from the NASA Langley  Zwikker-Kosten Transmission Line (ZKTL) code
- Issues:
- Acoustic models rely heavily on questionable use of experimental two-microphone impedance method and curve-fitting
- Ad-hoc functional forms for the impedance  *f (h/d, S, u**friction**, etc.)*
- Different mathematical models (vortex shedding from the slot, Kelvin-Helmholtz instability, wave equation, potential flow, *steady* bias flow through the orifice,...)

## Effect of Grazing Boundary Layer Impedance

-  Grazing BL impedance increases overall resistance, and slightly decreases reactance

## ResultsTime Domain

-  Effect of nonlinearity is to shift pressure signal to be almost in phase with jet velocity
-  Phase shift is highly dependent upon complex impedance

## Case 2 Implementation

- Piston volume velocity:
- Issue with computing the volume displaced by the piston!
- Unknown dynamics of stretched membrane
- We assumed only rigid piston displaces fluid

## Results and Conclusions

|  |  |  
(peak-to-peak) [Pa] |
| --- | --- | --- |
| Exp. (LDV) | 1.31 | 8648 |
| LEM | 1.72 | 5115 |

- Model over predicts output velocity and under predicts  cavity pressure  possible causes
- Small h/d of beveled orifice violates model assumption of fully developed pipe flow
- Resistance underestimated
-  Boundary layer has little impact at such low Mach number
- Need experimental data for the no-grazing-flow condition required to address this question