Carnegie Mellon

Mechanical Engineering

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FEM/ANSYS

## Test F1: Flow Over a Flat Plate

Fluid #1: Flow Over a Flat Plate

Introduction: In this example you will solve for the air flow velocity for flow over the flat plate, based on the specified velocity, pressure boundary conditions, and the plate dimensions.

Physical Problem: Compute and plot the velocity distribution of a flow of air over a flat plate.

Problem Description:

The dimensions of the plate are as shown in the figure.

Objective:
 To plot the velocity profile around the plate.

You are required to hand in print outs for the above.

Dimensions:
 The plate is 2 m long and is very thin.  ANSYS does not allow infinitesimally thin models so the plate is given a thickness of 0.001 m. The plate is situated within a 4 m square.  This arbitrary size serves to set up the boundary conditions of air traveling over the plate. The velocity of the air at infinite distance from the plate is 2 m/s. Atmospheric pressure is assumed on all faces except the face where velocity is input into the system.

Material Properties (Air):
 Density D=1.23 kg/m3 Viscosity ρ = 1.79E-5 N-s/m2

 Figure:

 Create the larger area, then the area defining the plate. Subtract the smaller area from the larger plate. Define the Element Properties as a 2D Air ElementDefine the Material Properties of the Air Element (Density and Viscosity are the important qualities) Mesh the plate with a mesh size of 0.01 on the edges of the inner plate, and 0.2 on the edges of the outer plate. Apply Boundary Conditions (No Slip along the edges of the inner plate, velocity along the left line of the large plate, and Atmospheric Pressure (P=0 in ANSYS) along the top, right and bottom lines of the large plate. Iterate 400 times and solve. (Ideally the iteration count would be at least several thousand times to make sure that the solution converges… but computational time dictates that in order to be able to solve the problem in a reasonable amount of time, the iteration number should be trimmed down to 400) Plotting the Velocity distribution in the X direction, this is the answer you should obtain with 400 iterations: