[Preeti Rani]

In CFD, we know SIMPLE algorithm is used to solve governing equations. There we have pressure term in all momentum equation(say x, y, z). What if there is no pressure gradient term in y and z momentum(i.e. exist only in x-momentum)? What will be the control volume for y and z momentum? Is it will be scalar cell or we have to use v-cell and w-cell as we always do in staggered grid?

[Hamidzoka]

When you are applying finite volume to solve 3D flows, you should never think of zero pressure gradient at certain directions. It is always needed to assume that there is a gradient and if the flow physics impose a zero gradient at a certain direction, simulation outputs will show it as you postprocess it.
another thing to note is that, when we are talking about a 3D flow, we normally encounter with sophisticated velocity field, rotations, separations,... . In other words, these x,y,z directions are not isolated ones and it is rather impossible to have exactly zero pressure gardient in one direction and non-zero values in other direction.

Best

[Preeti Rani]

Originally Posted by Hamidzoka

When you are applying finite volume to solve 3D flows, you should never think of zero pressure gradient at certain directions. It is always needed to assume that there is a gradient and if the flow physics impose a zero gradient at a certain direction, simulation outputs will show it as you postprocess it.
another thing to note is that, when we are talking about a 3D flow, we normally encounter with sophisticated velocity field, rotations, separations,... . In other words, these x,y,z directions are not isolated ones and it is rather impossible to have exactly zero pressure gardient in one direction and non-zero values in other direction.

Best

Thank you for your reply....
I attached a file of governing equations which contains pressure only in x-direction. We use staggered grids because of existence of pressure gradient term. But here pressure is only in x-direction. So is it correct to apply only u-velocity control volume as in staggered and for v and w momentum use the same control volume which is for pressure and temperature cell? And in SIMPLE algorithm we find out pressure correction term. Is it contains only east and west face value coz equations does not contains pressure in all direction?

[FMDenaro]

Generally, that is the case you have a base and constant pressure gradient in one direction that enters as a forcing term into the momentum. But the pressure fluctuation you have to solve is 3d.

[Hamidzoka]

Hi,
You can't use SIMPLE with staggered control only on x direction while keeping it non-staggered on other directions. The reason is, pressure correction equation includes coefficiencts and constant term,b, which needs to be calculated at staggered grid. So, if you insist on using non-staggered (co located) control volumes on other directions you need to revise the eqations carefully before application.
There is a more important issue taht I am trying to explain below:

What normally happens in SIMPLE algorithm is: Solution starts with an initial guess of presusre field, calculation of velocity, calculation of pressure correction term and then velocity correction term and then updaing them. Your case, however, needs to keep the pressure constant in y and z directions. In order to make it happen, you need to modify pressure and velocity correction equations such that they only include e,w,E and W (x-direction) components. Therefore, pressure correction terms other than p'w and p'e needs to be removed. Accordingly, y and z components of the velocity correction needs modifications and p' terms on y and z directions should get zero.
If you do not change it and use the conventional SIMPLE algorithm, there will be no guarantee to have zero pressure gradients on y and z. In other words, besides the momentum equations you have two extra equations i.e. dp/dy=0 and dp/dz=0 which need to be reflected in SIMPLE or any other algorithm you use.

Best

[Preeti Rani]

Originally Posted by Hamidzoka

Hi,
You can't use SIMPLE with staggered control only on x direction while keeping it non-staggered on other directions. The reason is, pressure correction equation includes coefficiencts and constant term,b, which needs to be calculated at staggered grid. So, if you insist on using non-staggered (co located) control volumes on other directions you need to revise the eqations carefully before application.
There is a more important issue taht I am trying to explain below:

What normally happens in SIMPLE algorithm is: Solution starts with an initial guess of presusre field, calculation of velocity, calculation of pressure correction term and then velocity correction term and then updaing them. Your case, however, needs to keep the pressure constant in y and z directions. In order to make it happen, you need to modify pressure and velocity correction equations such that they only include e,w,E and W (x-direction) components. Therefore, pressure correction terms other than p'w and p'e needs to be removed. Accordingly, y and z components of the velocity correction needs modifications and p' terms on y and z directions should get zero.
If you do not change it and use the conventional SIMPLE algorithm, there will be no guarantee to have zero pressure gradients on y and z. In other words, besides the momentum equations you have two extra equations i.e. dp/dy=0 and dp/dz=0 which need to be reflected in SIMPLE or any other algorithm you use.

Best

Thank you so much to clear this step. Can you please refer me any book or any article by which i can prove it that pressure correction terms other than p'w and p'e needs to be removed.

[Hamidzoka]

I suggest "Numerical Heat Transfer and Fluid Flow" by Patankar.