[mostanad]

Originally Posted by arjun

The way to elimniate the pressure from solid bodies is to pretend that they are not there.

In simple terms

1. when constructing the pressure equation, just ignore the control volume faces that has one side a solid cell or both of them are solid cells (left and right cells to a control volume face). That is solids do not participate in the pressure matrix construction.

2. Construct and solve the pressure system made up of only fluid cells.

3. Get the pressure correction and then extrapolate the pressure correction to those solid cells while looping over the control volume faces. (like you would do if there was a boundary).

Apply the pressure correction.

Forcing is fancy term people use for addition of extra term to momentum equation so that when it is solved the cell velocity is equal to solid velocity.

However you can just set the velocity equal to solid velocity and mostly it works without problems.

In which point I can set the particle velocity as I am doing it after Navier-Stokes step. So in Navier-Stokes, this velocity field is used as Initial condition and the outcome of NSE is a manipulated particle velocity.

[mostanad]

Originally Posted by arjun

The way to elimniate the pressure from solid bodies is to pretend that they are not there.

In simple terms

1. when constructing the pressure equation, just ignore the control volume faces that has one side a solid cell or both of them are solid cells (left and right cells to a control volume face). That is solids do not participate in the pressure matrix construction.

2. Construct and solve the pressure system made up of only fluid cells.

3. Get the pressure correction and then extrapolate the pressure correction to those solid cells while looping over the control volume faces. (like you would do if there was a boundary).

Apply the pressure correction.

Forcing is fancy term people use for addition of extra term to momentum equation so that when it is solved the cell velocity is equal to solid velocity.

However you can just set the velocity equal to solid velocity and mostly it works without problems.

Thanks again for your kind reaponse. Do you have any reference that i can use about this method?
Cheers

[FMDenaro]

Originally Posted by mostanad

So what if we impose a high viscosity value for inside the particle? Does it make any problem for pressure field? The algorithm designed for solving NSE with fluid properties in entire domain and finding "intermediate velocity". Look at the attached files. They are the results of Newtonian case. The first one is the result of NSE pressure. The second one talks about the final result of time step with corrections due to satisfying divergence-free condition. This result is used for drag value calculation.
So now I want to change the NSE calculation based on viscoplastic Herschel-Bulkley model. Because of low strain-rate inside the particle, the viscosity should be high. However, the original approach assumes constant viscosity value for the entire region. What does the original algorithm tell us?


NSE intermediate pressure:




pressure at the end of time step:

I think you miss some basic point. As an example, I suppose you are aware of the panel method for solving the inviscid flow around an airfoil. You have a fictious geometry, you just distribute sources, sinks, vortex in such a way to mimic the presence of the airfoil. The resulting velocity field induced by such kind of distribution exists also inside the airfoil, you simply disregard it.
So my question is: you have a solid particle and you want to study only the flow around it? If yes, you have to simply disregard any fluid variable inside the particle. You can do that also in the graphic post-processing. The only relevant issue is that you have to check the normal velocity component at the wall to ensure that mass is conserved.

[mostanad]

Originally Posted by FMDenaro

I think you miss some basic point. As an example, I suppose you are aware of the panel method for solving the inviscid flow around an airfoil. You have a fictious geometry, you just distribute sources, sinks, vortex in such a way to mimic the presence of the airfoil. The resulting velocity field induced by such kind of distribution exists also inside the airfoil, you simply disregard it.
So my question is: you have a solid particle and you want to study only the flow around it? If yes, you have to simply disregard any fluid variable inside the particle. You can do that also in the graphic post-processing. The only relevant issue is that you have to check the normal velocity component at the wall to ensure that mass is conserved.

No Filippo
I can't disregard it. I am calculating drag force on particle using Gauss Theorem. So, the pressure drag force is obtained using volume integral or the pressure value inside the particle. As I said, I am solving entire domain. So the pressure will have a non-zero value in the particle field.

Yes I wanna study the terminal velocity of a particle settling in fluid. Therefore, in every time step I should find drag force using:





So I need the values inside the particle. To this end, let's look at the images in previous post. Can you interpret for me the distribution of pressure after NSE and after imposing particle velocity?

[mostanad]

Originally Posted by arjun

1. You can get rid of pressure in the solid region by taking it out of the calculation domain.

The way to do it is to treat any control volume face that has one side fluid and one side solid as Neumann boundary condition and then NOT solve in the solid region for pressure.

This way you can get better pressure values.

2. You can now set the viscosity how so ever you like in the solid region but just know that momentum equation is no longer valid in this region (since no pressure gradient available). All you can do is to add forcing term that shall make the velocity equal to solid velocities.

3. Pressure is there in the solid region because you solve for it. You can avoid by doing (1).
In past I did the approach in (1) because the pressure in solid region was messing up the lift forces. So i got rid of pressure in solid like this. Worked good.

Sorry Arjun for bothering you again. So you don't have any pressure field inside the particle and still using Cartesian grid. A problem remains unsolved. How do you find drag force on this Cartesian grid? Using surface integral while the grid are not conforming solid body? Or volume integral which still uses inside particle values?

[arjun]

Originally Posted by mostanad

In which point I can set the particle velocity as I am doing it after Navier-Stokes step. So in Navier-Stokes, this velocity field is used as Initial condition and the outcome of NSE is a manipulated particle velocity.

Typically you would have the velocities set up at initialization stage and then immediately after the velocity and pressure correction steps.

There is no references because the company where i worked is more interested in patents and this could not be patented (we had few patents related to solver but they are were about different parts).

[arjun]

Originally Posted by mostanad

Sorry Arjun for bothering you again. So you don't have any pressure field inside the particle and still using Cartesian grid. A problem remains unsolved. How do you find drag force on this Cartesian grid? Using surface integral while the grid are not conforming solid body? Or volume integral which still uses inside particle values?

The drag and lift forces are found by integrating on the solid surface while the pressure is interpolated to surface grid from background cartesian (or polys) meshes.

Assuming you have the solid surface grid.

[mostanad]

Originally Posted by arjun

Typically you would have the velocities set up at initialization stage and then immediately after the velocity and pressure correction steps.

There is no references because the company where i worked is more interested in patents and this could not be patented (we had few patents related to solver but they are were about different parts).

Because you said me in last post "immediately after momentum equation". I think it should be applied after momentum equation and before pressure correction or continuity as we need to have divergence free condition at the need of time step. Is it correct?

[mostanad]

Originally Posted by arjun

The drag and lift forces are found by integrating on the solid surface while the pressure is interpolated to surface grid from background cartesian (or polys) meshes.

Assuming you have the solid surface grid.

So we no longer need to use Gauss theorem as we don't have any pressure field inside the particle. Yes?

[mostanad]

Originally Posted by arjun

The drag and lift forces are found by integrating on the solid surface while the pressure is interpolated to surface grid from background cartesian (or polys) meshes.

Assuming you have the solid surface grid.

So Arjun. You are the only one who I found during last two years has the experience working with this algorithm. So can You please tell me how having pressure inside the solid region can be correct as I am getting correct results with this method for Newtonian cases?
Cheers mate,
I am thirsty to learn from you.

[arjun]

Originally Posted by mostanad

So we no longer need to use Gauss theorem as we don't have any pressure field inside the particle. Yes?

You are still using Gauss theorem. In our case the solid is represented by a surface mesh, typically triangular mesh. So all we need to do is to find the values of pressure on these nodes. Then the forces are integrated by Gauss Theorem by looping over these triangles (or polys it shall not matter).

NOTE that the surface grid lies on the cells where the pressure is available. The solid marking algorithm actually exchanges this information passing the velocities to the background grid while acquiring the pressure from backgroud.

Not so difficult.

[mostanad]

Originally Posted by arjun

You are still using Gauss theorem. In our case the solid is represented by a surface mesh, typically triangular mesh. So all we need to do is to find the values of pressure on these nodes. Then the forces are integrated by Gauss Theorem by looping over these triangles (or polys it shall not matter).

NOTE that the surface grid lies on the cells where the pressure is available. The solid marking algorithm actually exchanges this information passing the velocities to the background grid while acquiring the pressure from backgroud.

Not so difficult.

Still I cant get why we need to use volume integration while all pressure gradient is happening on interface with your approach.

[mostanad]

Originally Posted by arjun

You are still using Gauss theorem. In our case the solid is represented by a surface mesh, typically triangular mesh. So all we need to do is to find the values of pressure on these nodes. Then the forces are integrated by Gauss Theorem by looping over these triangles (or polys it shall not matter).

NOTE that the surface grid lies on the cells where the pressure is available. The solid marking algorithm actually exchanges this information passing the velocities to the background grid while acquiring the pressure from backgroud.

Not so difficult.

Sorry mate. Can I ask you more questions? I need your opinion about a simulation using this algorithm.

[arjun]

Originally Posted by mostanad

Still I cant get why we need to use volume integration while all pressure gradient is happening on interface with your approach.

You need to make the surface integration over the whole body.

[arjun]

Originally Posted by mostanad

Sorry mate. Can I ask you more questions? I need your opinion about a simulation using this algorithm.

You can ask but just know that we are all limited by what we have done and what worked for us.

[mostanad]

Originally Posted by arjun

You need to make the surface integration over the whole body.

Ok. So as you told me I can follow one of following approaches:


1- Solving the momentum and pressure equations in entire domain and following Patankar's method, as I am doing now and giving me reasonable results for Newtonian cases.
2- Only solving fluid domain for pressure and enforcing the solid particle velocity after momentum equation. SO in this method we can impose any viscosity value for particle domain.


OK. I think both these methods should be equivalent for a particle settling in a Newtonian fluid. But what about non-Newtonian? By non-Newtonian, I mean Herschel-Bulkley method which changes the viscosity according to strain-rate. look at these two figures:





and





As you see, for a rigid body, we need to know the viscosity value because it is non-Newtonian fluid and the momentum equation is solved in the entire domain. In Newtonian case it is simply solve by assuming constant fluid viscosity.



So, if I wanna apply the first method, do you think this method can be used for a particle but with a high viscosity value?

I mean in Patankar's method, the first step (solving NSE for intermediate velocity) with changing viscosity not only for fluid but also the solid region.

Doesn't it make any problem for pressure or velocity solution?


Or I have only the chance to follow second approach?


This is my question.
Cheers mate.

[FMDenaro]

Originally Posted by mostanad

No Filippo
I can't disregard it. I am calculating drag force on particle using Gauss Theorem. So, the pressure drag force is obtained using volume integral or the pressure value inside the particle. As I said, I am solving entire domain. So the pressure will have a non-zero value in the particle field.

Yes I wanna study the terminal velocity of a particle settling in fluid. Therefore, in every time step I should find drag force using:





So I need the values inside the particle. To this end, let's look at the images in previous post. Can you interpret for me the distribution of pressure after NSE and after imposing particle velocity?

You don't have to compute the volume integral. You have to compute the surface integral, no need to use Gauss!

[mostanad]

Originally Posted by FMDenaro

You don't have to compute the volume integral. You have to compute the surface integral, no need to use Gauss!

Dear Filippo. Please read the following steps carefully. I hope you can help me to figure out this problem. I think from this discussion we can learn so many things.


Why do you think this? We are distributing the surface pressure into the particle domain because after imposing particle velocity, the continuity is violated. So we need to solve a Poisson equation to have divergence-free condition once again. Therefore, the pressure comes inside the particle domain because of this correction. look at these figures:


NSE outcome:








Then imposing particle velocity:





Then, having discontinuity in velocity field (divU):





So need to correct velocity and pressure fields using phiIB (Poisson equation):





The corrected fields are:








These fields are then used for drag force calculation using Gauss theorem:







The important points are:
1- pressure fields at the end of timestep are nonphysical (pressure inside the particle) but suitable for drag calculation using Gauss theorem
2- NSE tries to makes the non-zero pressure inside the particle closer to zero, so the step that makes pressure non-zero is Poisson equation for correcting discontinuity.
3- If I become able to do the correction in Poisson step in a different way, then the pressure inside the particle remains zero. Its the problem I have.


I there any way?

[mostanad]

Originally Posted by arjun

You can ask but just know that we are all limited by what we have done and what worked for us.

Can you please just look at my latest reply.
Sorry for bothering again.