National University of Sciences and TechnologyCollege of Electrical & Mechanical EngineeringAssignment-3: Computational Fluid Dynamics-I

Solution of unsteady incompressible flow problem

Two parallel plates extended to infinity are a distance h = 4 cm apart. The fluid within theplates has a kinematic viscosity of 0.000217m2/s and density of 800 kg/m3. The upper plateis stationary and the lower plate is suddenly set in motion with a constant velocity of 40m/s.A constant streamwise pressure gradient of dp/dx is imposed with in the domain at the instantof start. A spatial grid size of ∆x = 0.001m is specified. The governing equation for this flow,reduced from Navier-Stokes equation, is given as

∂u

∂t= ν

∂2u

∂y2− 1

ρ

∂p

∂x

Tasks

(a) Use the FTCS explicit scheme with time step of ∆t = 0.002 s to compute the velocity within the domain for

(i) dp/dx = 0

(ii) dp/dx = −20000Pa/m

(iii) dp/dx = 20000Pa/m

Plot the velocity profiles at time level 0.0, 0.18 and 1.08 s for each pressure gradient caseon the same graph ( one graph for three velocity profiles for each pressure gradient case).

(b) Use the Lasseonen implicit to compute the velocity within the domain for

(i) ∆t = 0.002, dp/dx = 0

(ii) ∆t = 0.01, dp/dx = 0

(iii) ∆t = 0.1, dp/dx = 0

Plot the velocity profiles at time level 0.0, 0.18 and 1.08 s for each pressure gradient caseon the same graph. TDMA solution would be required in this case.

(c) Discuss the results obtained in part a) and b).

Submission Guidelines

• The soft copy of this assignment, along with computer program, should be submittedlatest by 06/11/2014.

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• To submit your program, include the source code, executable and a description of program.The description must include the flowchart of the program and the guidelines on how torun your source code.

• Any programming language (Fortran,C/C++, Matlab,... ) can be used for coding.

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