# Presentation: 504463

## Case 2 : Synthetic Jet in a crossflow

**Julien Dandois****1****, **_**Eric Garnier**__**1**_** ****and**** Pierre Sagaut****2,3**

***1******Applied Aerodynamic Department, ONERA, France***
***2******Laboratoire de Modélisation pour la mécanique, UPMC, France***
***3******CFD and Aeroacoustic Department, ONERA, France***

**CFDVAL2004 Workshop, March 29-31, Williamsburg, Virginia, USA**

## Numerical Method and Subgrid scale modelMesh and boundary conditionsParameters studyTime stepActuator boundary conditionMesh size 

**CFDVAL2004 Workshop, March 29-31, Williamsburg, Virginia, USA**

## Outine

**Numerical Method and Subgrid scale model**
**Mesh and boundary conditions**
**Parameters study**
- Time step
- Actuator boundary condition
- Mesh size

## Numerical Method : Large Eddy Simulation

**CFDVAL2004 Workshop, March 29-31, Williamsburg, Virginia, USA**

**. Unsteady, three dimensional, compressible Navier-Stokes equations**
**. FLU3M solver :   - cell centered finite volume technique**
**	****                  ****- structured multiblock meshes**
**. Implicit time integration**** ****: backward scheme of Gear (second-order-accurate):**
**To compute the implicit term, a Newton-Raphson method is used. At each iteration of this inner process, the inversion of the linear system relies on the Gauss Seidel method.**

## . Spatial scheme : AUSM+(P) deprieved of shock capturing propertiesEuler fluxes :where U1 denotes the interface fluid velocity and L/R the left and right third order MUSCL interpolation.Q   is defined as				          and      is given byUdis characterizes the numerical dissipation acting on the velocity components :To enforce the pressure/velocity coupling in low-Mach-number zone, a pressure stabilization term is added to the interface fluid velocity:

**CFDVAL2004 Workshop, March 29-31, Williamsburg, Virginia, USA**

## Subgrid scale model : Selective mixed scale model

**CFDVAL2004 Workshop, March 29-31, Williamsburg, Virginia, USA**

**The expression of the subgrid viscosity is :**
**where :    - C****m**** = 0.6 **
**                 ****- ******** = 0.5**
**                 ****- f****s**** is a selection function which tests the tridimensionality of the flow and q****c ****is the kinetic energy of the smallest resolved scales which is evaluated with a test filter with a cutoff                    where      is the cubic root of the cell volume :**

## Mesh

**CFDVAL2004 Workshop, March 29-31, Williamsburg, Virginia, USA**

_**Computational domain’s size :**_
**streamwise : 24D (8D upstream and 16D downstream)**
**spanwise : 12D**
**vertical : 12D**
******x****+**** = 100**
******y****+**** = 36**
******z****+**** = 3**
******x = 1.16 mm**
******y = 0.44 mm**
******z = 0.036 mm**
**Insufficient resolution for LES of boundary layers**

## Mesh

**CFDVAL2004 Workshop, March 29-31, Williamsburg, Virginia, USA**

_**Cells repartition:**_
**External field : 1.25 million**
**Orifice : 263 000**
**Cavity : 98 000**

## Boundary Conditions

**CFDVAL2004 Workshop, March 29-31, Williamsburg, Virginia, USA**

**On the whole cavity ’s bottom surface : blowing/suction condition with a top-hat distribution in order to simulate the diaphragm movement :**
**                     ****u(x,t) = U****0**** . cos(2******** f .t) with U****0**** = 0.273 m.s****-1**** and f = 150 Hz**
**The inflow boundary condition is based on a steady RANS mean velocity profile**

## Time step and number of sub-iterations study

**CFDVAL2004 Workshop, March 29-31, Williamsburg, Virginia, USA**

**Case designation   Time step   Number of subiterations**
**             ****A                      1 ********s                          4**
**             ****B                      1 ********s                          6**
**             ****C                     0.5 ********s                        4**

**Results averaged on only 2 periods**
**In the posted case, 8 subiterations have been used.**
**The average has been performed on 8 periods**

## Actuator boundary condition study

**CFDVAL2004 Workshop, March 29-31, Williamsburg, Virginia, USA**

| Case designation | Surface of the boundary condition | U0 (m.s-1)
 |
| --- | --- | --- |
| A | Piston +
diaphragm | 0.273 |
| D | Piston | 0.725 |

## Conclusions

**CFDVAL2004 Workshop, March 29-31, Williamsburg, Virginia, USA**

**Sensivity on numerical parameters (time step, number of sub-iterations)**
**Influence of inflow turbulence and mesh size remains to be caracterised**
**Physical understanding of  the synthetic jet  ?**

**Transfer function ?**