Page 175 - Process Modelling and Simulation With Finite Element Methods

162 Process Modelling and Simulation with Finite Element Methods

4.4 Linking the 2-D Buffer Tank to the l-D Heterogeneous Reactor
The 2-D buffer tank model of $4.2 has unit flow rate inlet and unit
concentration inlet conditions. However, neither is the outflow from the
heterogeneous reactor a unit flow rate nor a unit concentration. Nominally the
flow rate was set at u=0.5 in 04.1, but the throughput varies with the recycle rate.
So tanku(x,y), tankv(x,y), tankp(x,y) will need to be scaled as initial conditions if
the steady tankheterogeneous reactor solution is to be used as an initial
condition for the linked unit operations. If u2 is the actually reactor outflow rate,
then as initial conditions u=u2*tanku, v=u2*tankv, p=p*~2~*tankp. The last is
the inertial scaling for pressure, appropriate at Re=100.
It should be noted that we have two scalars to model in the 2-D buffer tank,
since the concentration of species U and V can both vary independently. So we
need to add another scalar transport mode.
Pull down the Multiphysics menu and select AddEdit modes.

Multiphysics AddEdit modes (c2)
Select the coefficient mode, time-dependent
Name the independent variable c2
Element: Lagrange - quadratic
0
0 Apply/OK
the Boundary menu and select boundary settings

Boundary Mode
0 Set up boundary 1 Dirichlet h=l; r=l; (fixed c2=1)
Set up bnd 2,3,5,6,7 Neumann q=O; g=O
Auulv/OK

Now pull down the Subdomain menu and select Subdomain settings.

Subdomain Mode
Select domains 1&2
Select c2 mode

Before we can move on to the linked model, we also need to follow our recipe
for building initial conditions for the reactor. Open flowsheet.mat from the
FEMLAB GUI, and export fern structure to the workspace. Then in MATLAB,
execute the following commands to store the steady solution: