Laminar Flow - Velocity Profile
 

I compared the velocity profile of the circular pipe (in ANSYS Fluent) with the velocity profile of the laminar flow in accordance with the theory of the parabolic curve of laminar flow.

In the first case, I only use pipes with mesh in the fluid section only without any solid walls on the edges. Then in the second case, I use the same pipe but by adding a solid wall.

By doing a flow simulation only (without an energy calculation) I get different results. The pipe without a solid wall obtained perfect results in accordance with the theory of the parabolic curve of laminar flow, but the pipe with a solid wall there is a difference in the amount of velocity in the area approaching the wall.



Why did this happen?

Mesh
 

Adding a solid without energy equation does not make a difference. Even if a solid is added and energy equation is solved, as long as temperature is a passive field, it will not have any effect. The effect that you are observing is because of the difference in the meshes.

But in this case, I have not entered the energy equation, only a flow simulation, but still the results have a difference when I add a solid wall.

Solid and Thermal Energy
 

My post states the same; it does NOT matter whether you have the energy equation enabled or not, the presence of solid will not make a difference to the flow profile until the transport properties and density are function of temperature. So, in your case, the difference is purely because of mesh and nothing else.

Thank you for your answer

What if in my case the dimensions of the circular channel are very small (Diameter 3 mm) and I have meshed the smallest size I can make. Is there a way to improve the condition of the mesh?

Mesh Size
 

There is no smallest mesh size that you can make as far as meshing tools are concerned. You can go all the way down to the machine precision, provided RAM of the machine is capable of handling it.

For the time being, I'd suggest you to do one thing. Load the case with solid in Fluent, go to Mesh > Zones > Delete and then delete the solid zone. Run the simulation. Then compare it with the simulation where you have solid included. This way, you will have same mesh for fluid since you use the same case.