[Moreza7]

Hello,

I want to solve Couette flow without pressure gradient using stream function - vorticity formulation.

I need two boundary conditions for each plate.

I know that velocity and stream function values are zero on lower plate. Also, for the upper plate, the derivative of stream function equals to the velocity (U).

I need one more boundary condition.

Which boundary condition should I use for the upper moving plate?

[FMDenaro]

Originally Posted by Moreza7

Hello,

I want to solve Couette flow without pressure gradient using stream function - vorticity formulation.

I need two boundary conditions for each plate.

I know that velocity and stream function values are zero on lower plate. Also, for the upper plate, the derivative of stream function equals to the velocity (U).

I need one more boundary condition.

Which boundary condition should I use for the upper moving plate?

You have the BCs for the vorticity on the upper wall, it is just du/dy at the wall.

[Moreza7]

Originally Posted by FMDenaro

You have the BCs for the vorticity on the upper wall, it is just du/dy at the wall.

Thank you! Can I set the upper boundary streamline value equal to the volumetric flow rate as the velocity profile is linear? [psi(@up) = Uh/2]

[FMDenaro]

Originally Posted by Moreza7

Thank you! Can I set the upper boundary streamline value equal to the volumetric flow rate as the velocity profile is linear? [psi(@up) = Uh/2]

yes but why you would use (h/2)? Isn't the height h?

[Moreza7]

Originally Posted by FMDenaro

yes but why you would use (h/2)? Isn't the heigh h?

Because Q=A*Vavg
And Vavg= U/2 & A=h*1

[FMDenaro]

yes, that's from u = dpsi/dy



psi(y)-psi(0)= Int[0,y] u dy = (Uw/h) Int[0,y] y dy


psi(y)=psi(0) + (Uw/h)*y^2/2


Are you using periodic condition in x?

[Moreza7]

Originally Posted by FMDenaro

yes, that's from u = dpsi/dy



psi(y)-psi(0)= Int[0,y] u dy = (Uw/h) Int[0,y] y dy


psi(y)=psi(0) + (Uw/h)*y^2/2


Are you using periodic condition in x?

Yes I use periodic B.C.