sci.math.num-analysis

SUNA54, Ideal internal Flow globally
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Geometrical dimensions of a prototype Neratoom Intermediate Heat exchanger are:

Outer diameter of inner shell          R1 = 0.460 m ;
Inner diameter of outer shell          R2 = 0.960 m ; see picture below.
Height of inflow (and outflow) opening  H = 0.370 m ;

It is remarked that the above measures were designed in such a way that:

      2.pi.R2.H = pi.(R2.R2 - R1.R1)      approximately.

Hence the flow velocity at the inflow opening will be the same as the velocity
in the middle of the bundle. (I guess this is NO coincidence. But maybe I _did_
mess up radii and diameters ;-).

The flow field becomes parallel (that is: uninteresting) after 2 or 3 times the
height of the inlet perforation  H . The grid contains five meshlines in radial
direction and 3 times = 15 meshlines in axial direction. There is a 5 x 5 grid
in the inlet region. The rest of the flow field doesn't have to be calculated,
either because it is trivial, or (at the outlet) symmetrical with respect to
the inlet region.

Repeatable elements are those with the same inner and outer radii  r1 , r2 .
That's the reason why all elements are assembled in the  z  direction first,
in order to take advantage, namely, of their repeatability in that direction.

So far so good, all about the BULK elements in the flow. Equally important are
the Boundary Conditions. For our numerical experiments, we employed two types:
         __________                    __________
    R1 >|  v = 0   |                  |  v = 0   |
        |          |                  |          |
        |        H | u = -1           |          | v = 0
        |          |_^^^^^^           |          |_^^^^^
        |          |                  |          |
        |          |                  |          |
        |          |                  |          |
  u = 0 |          | u = 0      u = 0 |          | u = 0
        |          |                  |          |
        |          |                  |          |
        |          |                  |          |
        |  u = 0   |< R2              |  v = -1  |
           ^^^^^                         ^^^^^^
           Type 1                        Type 2

Three BASIC programs were developed: NERAGEN.BAS, NERAFLOW.BAS, NERAPLOT.BAS .

The following files are created by NERAGEN: GENER*.BIN, COORD*.BIN, TOPOL*.BIN,
UNKNO*.BIN and BOUND*.BIN, where (*) stands for the numbers below: 11 up to 14.
The velocities calculated by NERAFLOW are stored into the file VELOC*.BIN .
A special "BINARY" sub-directory, containing the "BIN" files, must be created
before you start any of the calculations !

Results are visualized on the CGA (emulated) screen by the NERAPLOT program.

Cases investigated (defined by the file CURRENT.DAT):

11 = Reduced quadrilaterals with B.C. type 1
12 = Reduced quadrilaterals with B.C. type 2
13 = Midside quadrilaterals with B.C. type 1
14 = Midside quadrilaterals with B.C. type 2

Results:

11 = the only really GOOD looking flow field !!!
12 = merely a disaster, due to the other B.C.
13 = not very good, element-wise unstable result
14 = merely a disaster, due to the other B.C.

Conclusions: The boundary conditions for this problem should be of type (1).
             and the Reduced Quadrilateral with velocities at the vertices is
             by far the _best_ element for Ideal (internal) Flow.

At least for the time being. IMNSHO, this result is not very satisfactory.
Especially the unexpected failure of case 13 must be investigated further.

To be continued ...
-
* Han de Bruijn; Applications&Graphics | "A little bit of Physics * No
* TUD Computing Centre; P.O. Box 354   | would be NO idleness in  * Oil
* 2600 AJ  Delft; The Netherlands.     | Mathematics" (HdB).      * for
* E-mail: Han.deBruijn@RC.TUDelft.NL --| Fax: +31 15 78 37 87 ----* Blood