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In this example, we will investigate the Poiseuille flow in a plain 2D channel. The objectives of this example is to introduce how to:
Here is the list of test cases to learn these features in Musbi and some hints on when to use what: ToDo: Update points/characteristics below.
The Poiseuille flow is the fully developed laminar flow between two parallel plates induced by a constant pressure drop in a channel of length L. In general, the flow can be induced by any of the following way:
Here, the flow is induced by pressure boundary condition at inlet (west)
and outlet (east) boundaries as shown in figure below.
The pressure drop along the channel per unit length is ∇pL=pinlet−poutletL=8UmρνH2 where,
The Reynolds number is defined as Re=ˉUHν where, ˉU - the mean velocity. For the parabolic velocity profile, the mean velocity can be computed with ˉU=2Um/3.
The analytical velocity profile along channel height is given as U(x,y)=4Umy(H−y)H2, the analytical pressure profile along the channel length is p(x,y)=p0+∇p(L−x) and wall shear stress profile along the channel height is σ=2ν|y−H/2|Um(H/2)2. The error between analytical solution (ua) and simulated results (us) are defined by the L2 relative error norm as L2 relative error norm=√∑i(ua(i)−us(i))2∑iua(i)2.
Here are the results from the simulation.
Velocity along the height of the channel:
Pressure across the length of the channel:
Wall shear stress along the height of the channel:
To create these plots, run python plot_track.py to create the plots. Before running the plot script, open 'plot_track.py' and update path to Gleaner script in 'glrPath'. Download Gleaner script using hg clone https://geb.inf.tu-dresden.de/hg/gleaner