Week 8 - BlockMesh Drill down challenge

Objective: To make block Mesh of different gradings using Cavity solver and finding the behaviour of velocity and pressure distribution along y-direction.

Regarding Solver: IcoFoam solver solves, momentum equation for velocity along with PISO solver (for pressure determination).

Block Mesh that was used is as shown below.

Boundary conditions:

• Inlet velocity is defined as 1 m/s (in x-direction only). considering inlet flow is unidirectional and uniform.
• exit velocity is defined as zero gradient .
• Inlet pressure is defined as zero gradient
• Outlet pressure is defined as 0 `N/m^2`and uniform.
• Considering no flow in z-direction. Thus, flow variables are expected to change only in x and y directions.
• Left end along the x-direction in the above image is considered as inlet and right end along the x-direction in the above image is considered as exit.
• Top and bottom ends (along y-axis) are considered as closed walls. And at 0.8 m from left end of x-axis, the face below having unit normal along -ve x-axis is also considered as closed wall.

Constants :

• Kinematic Viscosity is `10^(-6) m^2/s` at `22^0 C``
• Time step considered as `10^(-5) s`. Such a small number is considered after analysing the courant number value in different time steps.
• Initial time=0 s and final time =0.5 s.
• No.of grids along x-axis are 200 , no.of grids along y-axis are 20 and number of grids along z-axis are 1. Grading is changed for three different cases and velocity profile is analysed

Case-1: Lets consider grids are uniformly distributed along all directions. That leads to mesh of the below kind.

Problem soving using uniform grids at an intermediate time step.

After reaching steady state velocity and pressure profiles are as follows,

After looking at the above final state of image, velocity at the line of examination it is very clear to find a whril near the bottom boundary and after that there is a uniform velocity found. Such a whirl has been experienced due to, sudden expansion of fluid at 0.8 m from origin along x-axis, thus leading to point of seperation. Now along the line of examination observing the whirl since it is due to a forced vortex as the radius decreases velocity decreases (near the core) and soon after the core is crossed radius of the whirl is going to increase so velocity increases correspondingly (i.e with in a whirl due to forced vortex velocity is directly proportional to radius). Such a behaviour is clearly visible in the below image from 0.001 m to 0.01 m. After a whirl there is a uniform flow fluid, at the external radius of whirl velocity being much less than the uniform velocity region thus leads to high gradient in the velocity as shown below (i.e after 0.01 m).

In a forced vortex (i.e with in the whirl region), pressure is directly proportional to square of velocity. Thus, with in this region as the radius is decreasing pressure also started to decrease and soon after the center of the core is crossed pressure started to increase upto external radius of the whirl (i.e at 0.01 m). Soon after the whirl, there being only uniform velocity region such an effect cannot be well described directly for pressure. But in short it can be said that, pressure gradient along y-direction will be very close zero in uniform flow region that can be seen from the below image from 0.01 to 0.02 (i.e generally used assumption while solving a navier stokes equation).

Note: In the uniform flow region, pressure gradient looks to be large but infact as the graph is magnified it is looking to be high.

Note: The above two explanations for velocity and pressure behavouir as discussed in above graphs, the same would be resembled in every below case. But now below, the only difference comes with change in whirl dimension leading to velocity change behaviour.

0.8 grading mesh near walls

Final Steady state reaching below

0.5 grading mesh near walls

Finally after reaching steady state velocity contour for a 0.5 graded mesh.

0.2 grading mesh

Intermediate phenomenon of velocity contour for a 0.2 graded mesh

Finally after reaching steady state velocity contour for a 0.2 graded mesh.

Final Comparision:From above, for different gradients meshes it is very clear that as the grade mesh value decreases, near the walls the mesh becomes more finer (i.e more number of computational points does exist). As an engineer, our keen observation will be on abrupt phenomenon occuring on flow variables. Thus, increasing the computational points near the walls and point of seperation that lead to more clearer phenomenon of whirl velocities as the grade meshing decreasing from 1 to 0.2 near the walls.