Page 221 - Finite Element Analysis with ANSYS Workbench

212 Chapter 11 Incompressible Flow Analysis

v
and v  v  A  p

P
P
a v P y 
while p is obtained by solving the differential equation,
  A  u p     A  v p      u     v   



 x a u P x      y a v P y       x  y    


which is in the form of the Poisson’s equation.

Step 3 Check whether the solutions u, v and p converge to the
correct solutions. This is equivalent to the values of ,u v and p


u
are closed to zero, so that u  u  , vv and p  p . If the , v

and p are not converged to the specified tolerance, reset u  , u


v  and p  p , then repeat the iteration process. The process
v
continues until u, v and p for all cells converge to the correct
solutions.
During the iteration process, many software packages
,
show plot of the solutions u v and p that change with the
iteration numbers. The plot provides good information to ensure
convergence of the solutions.

11.3 Academic Example

We will use Fluent which is embedded in ANSYS
through the Workbench to analyze flow circulation in a cavity and
flow past a cylinder in a channel.

11.3.1 Lid-Driven Cavity Flow
A unit square cavity filled with a fluid is shown in the
figure. The specified velocity along the top edge induces flow
circulation in the cavity. The flow behavior depends on the
Reynold’s number defined by,