Problem Statement Following is the schematic of the 2-D step-wall diffuser with FEMLAB boundary numbering The
problem statement requires that DM
and DP be addressed. The
non-dimensional forms for these conservation principles for incompressible
flow are
DM:
DP:
where P = p/r
is kinematic pressure. The lecture detailed the transformation to
streamfunction-vorticity variables, which produces a very stable PDE system
with tractable BCs. For the definitions
DM
:
kinematics :
The resultant streamfunction-vorticity Navier-Stokes elliptic boundary value problem statement is
BCs: ¶Win : u(y, xin) Þ win, yin via definitions ¶Wout
:
¶Wwall : y = constant by definition
The Galerkin weak statement process GWSN Þ GWSh = Se{WSe} º 0 leads to the template
pseudo-code statements
Since GWSh
is explicitly non-linear, the Newton iterative algorithm form is [JAC]{dQ}p+1 = - {GWSh}
{Q}p+1 = {Q}p
+ {dQ}p+1 for {Q} = {OMG, PSI} and iterative convergence occurs when max|dQ| £ e. Setting-up the problem in FEMLAB
Open the 2D, general non-linear stationary PDE mode in the FEMLAB
model navigator. Set the number of dependent variables to 2 and their names
to psi (y)
and omega (w).
This mode is selected when a built-in mode is not available, hence one must
define the PDE system, which is done under subdomain settings. The subdomain
settings, which define the PDE terms are
Applying the w
BC
In the solver option,
the parametric mode is chosen to enable executing the study for
You are required to compare the reattachment length with the
experimental data. Table 1 lists the experimentally determined primary
recirculation reattachment intercept non-dimensionalized by the step height
s for various Reynolds number. Table 1. Dimensionless reattachment intercept vs. Re.
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