# Numerical Study Of Computation Fluid Dynamics: Facing Step Flow

Submitted By ZhongxinBao1
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Numerical study of 2D turbulent backward-facing step flow

MSc Mechanical Engineering 2012
Couse: Computation Fluid Dynamics
Main Tutor: Dr. Zhiyin Yang
The Summary Word Count: words
The Main Text Word Count: words
Submission Date: 28. Feb. 2013

Summary
In this case the mostly task is to obtain results of numerical investigations of air flows over a two-dimensional backward-facing step are presented and then will analyse and discuss the turbulent flow in a rectangular channel by constructing the geometry, generating a suitable grid and measuring instantaneous velocity using ANSYS workbench. I will give own answer based on my understanding of fluid flow.

Contents

1. Introduction
It is true that there are some phenomenon of turbulent flow including the separation of the flow, reattachment to a solid surface and subsequent recirculation in many systems. Such as “these applications are flows over aerofoils at large angles of attack, in a channel whose area suddenly increases, and in gas turbines and heat transfer devices” . In the present study the numerical and experimental methods are still far from perfect as the complexity of the flow associated with the flow separation and reattachment.

“In order to obtain a better understanding, either numerically or experimentally, of the complex fluid flow following separation and including reattachment, the two-dimensional flow past a backward-facing step is a standard test problem as well as a building-block flow for workers developing turbulence models, and it has been addressed by numerous authors using a variety of numerical and experimental methods” . 2. Description of the problem 3.1. Geometry
The geometry of the turbulent flow is shown in Dia 2.1

Diagram 2.1. Flow geometry
Because the flow I used is incompressible so the Mach number must be lower than 0.3.
I specify a value to h h=0.01m, L=3h
So to obtain total measurements are shown in Dia 2.2

Diagram 2.2. Flow geometry 3.2. Boundary conditions
According to the coursework use velocity inlet boundary condition at inflow, pressure outlet at outflow, symmetry at the top and sold wall for the bottom.
See Dia 2.3

Diagram 2.3. Diagrammatic sketch about boundary condition 3.3. Inlet velocity calculation
In this coursework a density and viscosity need to be specified. Because I use air as a kind of fluid so the density equals 1.225kg/m3 and the viscosity equals 1.7894×10-5.
According to the Reynolds equation 2.1
Re=ρUhμ (2.1)
And Re = 5100 is given in the Dia 2.1
So to obtain the velocity U
5100=1.225×U×0.011.7894×10-5
U=7.45m/s 3. Grid generation
As the quality of the grid generations play a direct role in the quality of the analysis, the most important things in this case is to set different grid generation and then compare the former and the latter. Each grid should be significantly finer than the previous grid.

Therefore, I decide to set three different grids. The first one is a gird of 100 × 30 and then double the number of grid points in each co-ordinate direction.
The first one is shown in Dia 3.1

Diagram 3.1. Grid generation 100 × 30
The second one is shown in Dia 3.2

Diagram 3.2. Grid generation 200 × 60
The third one is shown Dia 3.2

Diagram 3.3. Grid generation 400 × 120 4. Demonstration and discussion of convergence
“The flow equations which are basically the partial differential equations can only produce an exact solution for the low flow values and not for the turbulent or laminar flows. Hence for this these flow equations are discretized into their algebraic form and the solution is then calculated by performing iterations. The