NESC0719 NATRAN2

1. NAME OR DESIGNATION OF PROGRAM:  NATRAN2

3. DESCRIPTION OF PROBLEM OR FUNCTION

NATRAN2  analyzes  short-term
pressure-pulse transients in a  closed hydraulic system consisting
of a  two-dimensional  axisymmetric  domain connected  to  a  one-
dimensional  piping  network.   The  one-dimensional  network  may
consist of  series or  parallel piping,  pipe junctions,  diameter
discontinuities, junctions of three to  six branches, closed ends,
surge  tanks,  far  ends,   dummy  junctions,  acoustic  impedance
discontinuities, and rupture disks.  By default, the working fluid
is assumed  to be  liquid sodium  without cavitation;  but another
working fluid  can be  specified in  terms of  its density,  sonic
speed, and  viscosity.  The source  pressure pulse can  arise from
one of the following:  a  pressure-time function specified at some
point in the two-dimensional domain, a pressure-time function or a
sodium-water reaction  specified   at  some  point  in   the  one-
dimensional  domain.   The  pressure  pulse  from  a  sodium-water
reaction is assumed to be generated according to the dynamic model
of Zaker and Salmon.

4. METHOD OF SOLUTION

For the two-dimensional  region, NATRAN2 uses
a  numerical  integration  technique,  based   on  the  method  of
characteristics  and formulated  for  the  system of  quasi-linear
hyperbolic equations describing fluid-hammer phenomena in a closed
two-dimensional axisymmetric domain.  The set of nonlinear partial
differential equations is first converted  to a system of integral
equations  written  along  bicharacteristics.    The  solution  is
constructed  in  a  step-by-step procedure  by  approximating  the
integral  equations  by  the trapezoidal  formula  and  using  the
resulting difference  relations along  four bicharacteristics  and
one streamline  through each  point.  Spatial  derivatives of  the
dependent variables are eliminated  from the difference relations.
The solution at any point then  is obtained explicitly by a linear
combination of the remaining difference relations.

5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

The        program
currently provides for maxima of:
     1 two-dimensional cylindrical region
    30 grid points in the r-direction
    60 grid points in the z-direction
    50 one-dimensional pipe branches
   120 nodes per pipe branch
    50 junctions
    10 surge tanks
   Cavitation is  assumed to  be absent.   In the  two-dimensional
analysis, viscosity  effects are neglected.  A  sufficiently large
length-to-diameter ratio must be allowed for extended regions both
upstream and downstream  of the two-dimensional domain,  since the
matching of the boundary conditions at the interfaces neglects any
two-dimensionality close to the interface.

6. TYPICAL RUNNING TIME

Execution  of the  sample problem  requires
approximately 135 CPU seconds on an IBM370/195.

7. UNUSUAL FEATURES OF THE PROGRAM:

8. RELATED AND AUXILIARY PROGRAMS

The   NATRANSIENT    code   (NESC
Abstract 718)  is used  as  a subroutine  within  NATRAN for  one-
dimensional system  calculations.  Related programs  include WHAM6
(NESC  Abstract 278),  COMPARE (NESC  Abstract  702), HAMOC  (NESC
Abstract 710), and NAHAMMER (NESC Abstract 717).

10. REFERENCES

Y. W.  Shin and Richard A.  Valentin, Two-dimensional
Fluid-hammer Analysis by the Method of Characteristics in a Closed
Axisymmetric Cylindrical Domain, ANL-8090, August 1974.
             T. A. Zaker and M. A. Salmon, Effects of Tube Rupture
in  Sodium   Heated  Steam   Generator  Units,   ASME  Publication
69-WA/NE-18, November 1969.

11. MACHINE REQUIREMENTS

452K  bytes of  storage  are required.   If
plotting information is  to be written on logical unit  10, a disk
or tape unit is needed for this purpose.

13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED:   OS/360,370.

14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS

    To
execute the  sample problem,  specify file  FT10F001 as  dummy, or
with RECFM=FB, LRECL=40, and a  BLKSIZE appropriate to the storage
unit being used.

15. NAME AND ESTABLISHMENT OF AUTHORS

                 Y. W. Shin and R. A. Valentin
                 Components Technology Division
                 Argonne National Laboratory
                 9700 South Cass Avenue
                 Argonne, Illinois  60439

File name	File description	Records
NESC0719_01.001	SOURCE PROGRAM (F4,EBCDIC)	2085
NESC0719_01.002	SAMPLE PROBLEM INPUT DATA	21
NESC0719_01.003	SAMPLE PROBLEM PRINTED OUTPUT	4610