1. 1 CASE 2: Modeling of a synthetic jet in a cross flow Williamsburg, Virginia, USA March 29 th -31 th 2004 C. Marongiu 1, G. Iaccarino 2 1 CIRA Italian Center for Aerospace Research 2 CTR Center for Turbulence Research Stanford University

2. 2 OUTLINE 1.Objectives 2.Synthetic jet modeling 3.Determination of the jet parameters 4.The computational grid 5.Preliminary results i.The effect of the turbulent kinetic energy assignment ii.The mean field iii.The phase averaged field

3. 3 Objectives Investigation of a boundary condition for the RANS approach to simulate the flow control device. Development a spatial&time model for the flow ( , u,v,w,p) and the turbulence (k, , , …) variables The benefits saving very complicated and time- consuming moving mesh calculations. becoming suitable for design and optimization tools. The disadvantages Need to characterize the synthetic jet behavior (flow conditions, jet geometry) Suitable turbulence modeling at jet exit

4. 4 Methodology: logical process Boundary Condition Model (BCM) ,u,v,w,p,k, ,  Characterization of the (synthetic) jet parameters Experiments Complete Numerical Simulations Simulation with BCM Validation Final product: a BC model, for cheaper computations suitable for design and optimization tools

5. 5 Synthetic Jet Modeling Turbulent variables at jet orifice ? Cross Flow U  Movable Plate A p Jet Orifice A J UJUJ BC S.J Cavity Not Simulated

6. 6 Determination of the jet parameters: U Jmax where s(t) is the plate displacement Two ways are possible: A P, movable plate area A J, jet orifice area Max Volume variation  V = A p s m  m=  V  Mass flux into an half period Mean velocity into an half period Using a cosine law, and equaling his mean value (over an ½ period) to the mean velocity, Max Mass variation

7. 7 Fluid Domain and Boundary Conditions OUTFLOW CONDITIONS Free stream exit No slip wall INFLOW CONDITIONS From experiments x z y JET CONDITIONS Half domain has been considered, with the symmetry condition at y=0 Slip wall Symmetry condition

8. 8 CIRA CODE: U-ZEN + Compressible RANS equations + Multiblock structured grids. + Second order cell centered finite volume + Explicit artificial dissipation + Dual Time Stepping unsteady procedure + Multigrid and Residual Averaging + Myong and Kasagi k -  turbulence model Preliminary results The case 2 is still in progress. Some preliminary results will be shown, obtained by the CIRA U-ZEN code. SIMULATION 45 time steps per period

9. 9 Grid and topology details 12 blocks  z w = 0.001 775680 cells xz plane topology Grid detail xy plane Jet orifice

10. 10 u profiles at x =63.28, y=0 Mean field- Effect of the turbulent variables setting w contour levels k, ,  T extrapolated from inside.

11. 11 Mean field - u velocity profiles

12. 12 Mean field- w velocity profiles

13. 13 Phase alignment w component at P  (50.63, 0, 0.4)

14. 14 Phase averaged field. u profiles. x/c = 63.28, y=0  = 0°  = 90°  = 180°  = 270°

15. 15 Unsteady Control Velocity w contour plot on xz and yz planes

16. 16 Conclusions The weak points of the actual boundary condition model seem to be: Turbulent variables setting: an improvement of the solution has been achieved by the extrapolation from inside of the turbulence variables. The time law : the sine/cosine is not a realistic law, as can be seen before. The spatial shape : a top hat profile has been used. Each of these points will be the scope of our future investigations. The preliminary results are encouraging