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

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 Mean field - u velocity profiles

12 Mean field- w velocity profiles

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

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

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

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