Simulating a 2-D flow in a rectangular channel for different mesh sizes using CONVERGE CFD

INTRODUCTION:

In this project, we will be simulating a 2-D flow through a rectangular channel. The size of the mesh will be varied (from coarse - fine - very fine) to compare the results. The setup is done using CONVERGE Studio and the results are post-processed in Paraview. The geometry is a simple box (channel) with a square cross-section of `0.01` `m` X `0.01` `m` with a channel length of `0.1` `m`. The boundaries are named according to the boundary conditions. The inlet and outlet are named as "inlet" (brown) and "outlet" (yellow). The top and bottom walls are named as "walls" (orange) and the front and back walls are named "faces_2D" (purple). The front and back walls will be assigned the "2D" boundary condition to simulate a 2D channel flow.

MESHING:

Three different mesh sizes are used to set up the simulation. The mesh sizing is entered for each of the three cartesian vectors (x, y and z) as follows:

`{:(ul{text{Mesh}},,ul{text{dx [m]}},,ul{text{dy [m]}},,ul{text{dz [m]}}),(text{Coarse},,0.0002,,0.0002,,0.0002),(text{Fine},,0.00015,,0.00015,,0.00015),(text{Very Fine},,0.0001,,0.0001,,0.0001):}`

The screenshots for the three mesh are shown below:

SETUP OF THE FLOW PHYSICS:

The simulation is a pressure-based steady state simulation using air as the predefined mixture. Since we are not interested in any reaction mechanisms, the species solver is neglected from the solution. The simulation is run for `15000` cycles with a minimum time step of `1times 10^{-9}` `s` and a maximum time-step of `1` `s`. A volumetric region is created from the entire domain and boundary conditions are applied for this region. The inlet (boundary id: 1) is assigned an INFLOW boundary condition with a pressure of `1` `Pa` above `1` `ba r`, which is `100001` `Pa`. The outlet (boundary id: 2) is assigned an OUTFLOW boundary condition with a pressure of `1` `ba r`, which is `100000` `Pa`. The top and the bottom surfaces are assigned a NO-SLIP WALL boundary condition. Since the pressure difference between the inlet and the outlet is only `1` `Pa`, no turbulence is expected for the flow and hence turbulence modeling is turned off for this simulation. The front and back walls are assigned TWO_D boundary condition which assumes that the flow will not  change in the z-directions (essentially a 2D flow). The temperature of the entire domain is kept constant at `300` `K` to exclude the energy equation. The solution is initialized with air as the mixture (oxygen: 0.23 and nitrogen: 0.77 mass fraction) at a temperature of `300` `K` and pressure of `100000` `Pa`. The base grid is initialized as per the table shown above for different mesh sizes. The simulation is run using this setup conditions in parallel using Cygwin with `2` processors.

RESULTS AND DISCUSSIONS:

The different results during the simulation and at the end of the simulation are shown below for different mesh sizes. The "bound_id_1" and "bound_id_2" in the graphs refer to the "inlet" and the "outlet" respectively.

Mesh 1 (Coarse):

Cell Count

The coarse mesh utilizes a total of `25551` cells distributed as `12597` and `12594` cells across the `2` processors.

Average Mass Flow Rate:

Average Velocity Magnitude:

Average Total Pressure:

Average Static Pressure:

Velocity Contours:

Pressure Contour:

Velocity at Outlet:

Mesh 2 (Fine):

Cell Count

The coarse mesh utilizes a total of `45424` cells distributed as `22688` and `22736` cells across the `2` processors.

Average Mass Flow Rate:

Average Velocity Magnitude:

Average Total Pressure:

Average Static Pressure:

Velocity Contours:

Pressure Contour:

Velocity at Outlet:

Mesh 3 (Very Fine):

Cell Count

The coarse mesh utilizes a total of `101101` cells distributed as `50532` and `50569` cells across the `2` processors.

Average Mass Flow Rate:

Average Velocity Magnitude:

Average Total Pressure:

Average Static Pressure:

Velocity Contours:

Pressure Contour:

Velocity at Outlet:

The graphs indicate that the mesh 2 and 3 simulations have not developed fully in `15000` cycles. A coarse mesh can be initially utilized to validate the flow physics and then the finer meshes can be run for longer times to get more accurate results. The velocity profile for a fully developed flow should be of parabolic shape. Since the pressure difference is very small (`1` `Pa`), the maximum velocity magnitude obtained is only about `1` `m"/"s` giving a Reynolds number of only about `700` which falls in the laminar flow region. The mesh can further be made finer near the walls to get the velocity as close to `0` `m"/"s` near the walls. The computation time increases significantly with the use of smaller and smaller mesh, hence a proper mesh convergence study is helpful in finding a balance between accuracy and computational resources.