Channel Flow simulation using Converge CFD.

Objective: To setup up a channel flow tutorial that is provided by Convergent Science.
To show for all 3 different meshes 
1. Velocity and Pressure contour for all given mesh size.
2. Surface with edges for all base mesh size.
3. Plots for velocity, pressure, mass flow rate and total cell count for all 3 base mesh sizes.

Given:
Different mesh sizes are:

1. dx= 2e-4 m, dy= 2e-4 m, dz= 2e-4 m
2. dx= 1.5e-4 m, dy= 1.5e-4, dz= 1.5e-4
3. dx= 1.0e-4 m, dy= 1.0e-4, dz= 1.0e-4

Theory:

Here, we are going to setup a case of channel flow. In this tutorial we are going to use bunch of softwares that will helps us to  pre and post- process the flow, simulate the flow.

List of Softwares are:
1. Converge studio `->`To pre-process the data needs to simulate the case. It plays an important role in generating the necessary input file only using GUI. It does not run simulation directly it creates input files which then can be used to run the simulation.

2. Cygwin `->` Cygwin is a collection of GNU and open-source tools that provide functionality similar to Linux distribution on windows.

3. Converge-2.3.26_msmpi_64 `->` As we got input files from converge studio we need to process or run these files we use converge-2.3.exe. To run simulation parallelly using nos. of processor we use mpiexec.exe

4. Post convert.exe `->`It convert all output files which are processed by converge-2.3.exe into the file which will be readable for post-processing in ParaView.

5. Paraview `->` This is used for post-processing our obtained results. It is an open-source, multi-platform data analysis and visualization application.

CASE SETUP:

In this case, we are going to set up a simulation of laminar flow through the channel using CONVERGE CFD. 

All the case setup of channel flow simulation has been done the same as shown in the lecture the only changes we need to do are in the simulation time parameter. We know finner the mesh size longer will the simulation time as it requires more time to solve governing equations on all mesh elements. so we made changes in the simulation time parameter accordingly which is required for convergence.

3D Post-Processing Data ParaView:

1. Mesh comparison:

A key ingredient in the implementation of the finite volume method is setting up the geometrical support framework for the problem at hand. This process starts with mesh generation, which replaces the continuous domain by a discrete one formed of a contiguous set of nonoverlapping elements or cells delimited by a set of faces, and the defining of the physical boundaries through the marking of the boundary faces.

We will be looking here on a computational mesh on which the governing equations are subsequently solved

Case-1: dx=2e-4, dy=2e-4, dz=2e-4

Case-2: dx=1.5e-4, dy=1.5e-4, dz=1.5e-4

Case-3: dx=1.2e-4, dy=1.2e-4, dz=1.2e-4

Closer look comparison

Case-1:dx=2e-4, dy=2e-4, dz=2e-4

Case-2:dx=1.5e-4, dy=1.5e-4, dz=1.5e-4

Case-3:dx=1.2e-4, dy=1.2e-4, dz=1.2e-4

The above figures represent, complete domain discretized using a uniform grid system where we discretized along all axis of the domain (0.1*0.001*0.001) with different mesh sizes. As we can see case 1 is much coarse than other cases because we defined mesh size as 0.0002 along all dimensions of the domain.

2. Velocity and Pressure contour comparison:

As we are interested to see the velocity profile inside the computational domain where the flow of fluid takes place at a particular length of the domain from the start of the channel. As the flow taking place inside the channel is LAMINAR it is expected to have a parabolic velocity profile along the Y-axis of the domain and pressure variation along the length of the pipe according to Hagen-Poiseuille Equation.

Case-1: dx=2e-4, dy=2e-4, dz=2e-4

Case-2: dx=1.5e-4, dy=1.5e-4, dz=1.5e-4

Case-3: dx=1.2e-4, dy=1.2e-4, dz=1.2e-4

Here we have Velocity and pressure plots for all mesh sizes. All plots look very much similar to each other as we have already performed simulations for its convergence since we are dealing with different mesh sizes, simulation time plays a major role as we know finner the mesh larger will be the computational time as governing equations are solved for all computational mesh elements.

Computational Time for all different mesh sizes is as:

mesh size: 2e-4

mesh size: 1.5e-4

mesh size: 1.2e-4

From the above data, we can clearly say that Finner the mesh element higher will be the computational time as all governing equations and transport equations are being solved for each and every mesh element of the complete domain.

3. Velocity, Pressure, Mass Flow rate & Total cell count

Here we can see the rate of convergence to the exact solution in every cycle of computation at both boundaries i.e. inflow and outflow.
Based on the size of the mesh element, a certain amount of cycles for computation needed to reach exact solutions.

Case-1: mesh size 2e-4 (15000 cycles)

Average Velocity:

Total Pressure:

Average Mass Flow Rate:

Total Cell Count:

Case-2: mesh size 1.5e-4 (32000 cycles)

Average Velocity:

Total Pressure:

Average Mass Flow Rate:

Total Cell Count:

Case-3: mesh size 1.2e-4 (40000 cycles)

Average Velocity:

Total Pressure:

Average Mass Flow Rate:

Total Cell Count:

Simulations for all Mesh elements:

Case-1: dx=2e-4, dy=2e-4, dz=2e-4

Simulation clip:

Case-2: dx=1.5e-4, dy=1.5e-4, dz=1.5e-4

Simulation clip:

Case-3: dx=1.2e-4, dy=1.2e-4, dz=1.2e-4

Simulation clip:

All the above images are to show to end results of simulation after running the case for a certain amount of cycles(in order to achieve converged solution). 

In the simulation, we can see the completely spurious results and a higher rate of convergence until certain time steps achieve. Once we attain that time step we started getting most likely outcomes till the last time step. And in the end time step, we got a converged solution from that we can draw all possible exact outcomes like velocity, pressure, species information, etc.

Conclusion:

1. From all the above graphs, we can say that finner the mesh higher will be the computational time as all the governing equations are being solved for all computational mesh.

2. Although computational time is higher for finner mesh, we surly expect greater accuracy in the end results. As we all know the higher the order of the error the faster it will decrease with mesh refinement.

3. Memory usage and memory storage increase with a decrease in mesh size.