## CFD simulation of a channel with a backward step

**Figure-1-** Two-Dimensional, isothermal, incompressible flow over a backward step.

# Abstract

The Objective of this report is to:

- Generate an appropriate computational grid to a channel with a backward step and apply the boundary conditions for both the inlet and outlet of the 2 dimensional channel shown in
*Figure-2-*. - Studying the distribution of pressure and velocity in the channel and producing a set of data in variable points of coordinate or simply in a particular coordinate and calculate the Reynolds number out of it.

-Perform 4 simulations implementing 1 type of fluid and a mixture of 2 fluids using 2 models and generate an analytical comparison at the end.

The Results obtained in this report are calculated, simulated and graphed by Ansys fluent for the solver and drawn by Ansys ICEM CFD.

# Theory

Computational fluid dynamics is a wide and branched topic that deals with the behavior of fluid in action based on the Navier Stock equations that formulize the second law of Newton in Fluids.

Many methods in this domain have been published in an attempt to solve fluid dynamic problems. Methods as: “Central difference, Quick and power law” where some have limitations like the central difference method due to its inability of identifying the direction of the flow.

For the first Task in this report the focus will be on the ”SIMPLE” scheme for the pressure velocity coupling using a 2^{nd} order upwind method for the discritization of the momentum equation.

The first step of applying any computational fluid method is to make a grid of the fluid in action space by meshing the space with discrete panels.

Every fluid dynamic problem has boundary conditions that are essential to the computation, for example:” the inlet velocity” and “the outlet total pressure” of a certain pipe.

Selecting the type of fluid in flow is essential and all its properties as the density, viscosity and temperature etc…

# Simulation-1- Laminar Flow

Ansys Fluent as a standalone package is unable to resolve a grid out of a geometry so the need of another package as ICEM CFD from Ansys is critical in order to mesh our system whether is it two dimensional or 3 dimensional.

It is possible to draw the system in ICEM CFD or to import it from another CAD program like Solidwork or Autocad .

The second step is meshing the space by assigning the inlet and the outlet to the appropriate edges and choose the gridding system after blocking the fluid zone.

**Figure-3***-Backward facing step channel –mesh grid. *

The grid comprise of 132 vertical lines on the top side , 120 vertical lines on the bottom side, 6 horizental lines on the inlet side and 12 on the outlet side.

The next step is using Fluent by importing the mesh and adding the input boundary conditions.

For the first task the inlet boundary condition are: 16kg/m^{2}.s and 1000/kg/m^{3} for the density.

Concerning the boundary condition at the outlet an environmental pressure of “0 PA” gauge is added.

The case studied is considered laminar due to a quick guess from the mass flux , the density and the channel diameter to get an estimated value of the Reynolds number which is less than 2300 .

Running the simulation after selecting the correct boundary conditions, keeping the under relaxation factor for the pressure at: “0.3” and for the momentum at”0.7”in which these 2 values have a role in damping the solution if instability occurs:

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# Results

Figures: 5 and 6 show the pressure contour and the velocity vector distribution in the channel at 16kg/m^{2}.s mass flux.

**Figure-5-** Pressure distribution.

**Figure-6-** Velocity vector distribution.

It is evident in the figure below that there are 2 circulations in the channel, one right before the step where the center of it is at x = 0.18 m and the second one is at the top of the channel at x=0.5m.

**Figure-7-** Location of the circulations

**Figure-8-** velocity vector at the vortices at x=0.18m **Figure-9-** Velocity vectors at the top vortices at x=0.5m

The behavior of this flow and the appearance of the circulations after the step is because of the change in the geometry of the channel which in its turns created a negative pressure a “vaccum” that caused the circulation at the top of the channel.

Figures: 10 and 11 show the pressure and velocity plots distributed along the X-axis at 16kg/m^{2}.s of mass flux.

**Figure-10-** Pressure distribution along Xaxis*

**Figure-11**– Velocity along Xaxis*

Reynolds number is a dimensionless number that indicate whether the flow is turbulent or laminar.

Re=ρ.V_{m}.D_{h}/µ.

Re: Reynolds number. ρ**: **Density = 1000kg/m3

V_{m}: Mean velocity

D_{h}: Hydraulic diameter = 0.05m

µ: Dynamic viscosity = 0.001 kg/m-s

The mean velocity right on the step at the top is found using an option in fluent called surface integral where the mean velocity among many other options can be found:

**Figure-12-** the line in which the mean-velocity is calculated.

Facet average is selected in surface integral and velocity field variable with the line shown in the figure above is assigned to compute the mean velocity which is equal to: 0.01602347 m/s.

Putting all the values in the Reynolds number equation gives:

Re=ρ.V_{m}.D_{h}/µ.

Re=801.1