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NESC0755 VARR2

VARR2 VARRLXSG, 2-D Transient Fluid Flow and Heat Transfer in X-Y and Cylindrical Geometry

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1. NAME OR DESIGNATION OF PROGRAM:  VARR2
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2. COMPUTERS
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Program name Package id Status Status date
VARR2 NESC0755/01 Tested 01-APR-1980

Machines used:

Package ID Orig. computer Test computer
NESC0755/01 CDC 7600 CDC 7600
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3. DESCRIPTION OF PROBLEM OR FUNCTION

VARR2  is  a  two-dimensional
transient slightly-compressible fluid dynamics program.  It solves
the complete unsteady Navier-Stokes equation, the energy equation,
and the  continuity equation in  either Cartesian  or axisymmetric
cylindrical geometry.  Slight density variations are accounted for
by use of  the Boussinesq approximation, which  couples the energy
and  momentum equations.   At  a cell  face,  the normal  velocity
component may be inward, outward, or zero; the tangential velocity
component  may specify  free  slip, no  slip, or  no  slip with  a
turbulent velocity profile.  For heat transfer problems, adiabatic
or constant  heat flux boundary  conditions can be  specified.  By
specifying  the totality  of cell-face  boundary  conditions in  a
self-consistent manner,  the user can  specify a wide  spectrum of
overall  boundary conditions;  for  example,  those called  rigid,
continuative, periodic, inflow/outflow, or derived.
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4. METHOD OF SOLUTION

The  governing  differential   equations  are
replaced  by finite  difference  equations  of explicit  type  and
solved  over a  region of  fixed  rectangular cells  by using  the
simplified marker and cell technique  (SMAC) of Amsden and Harlow.
The continuity  equation  is  solved through  a  successive  over-
relaxation  (SOR) iterative  process  on  a Poisson  equation  for
pressure.
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5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

With       current
dimensioning, the maximum number of cells is about 1600; roughly a
40  x   40  mesh.   The   problem  geometry  must   be  reasonably
approximated by a two-dimensional net of rectangular cells, either
in Cartesian geometry or transformed from axisymmetric cylindrical
geometry.  Interior obstacles are allowed.   The working fluid may
be specified  as either sodium or  water if the  built-in material
property coefficients are used.  Otherwise,  the properties of the
working fluid may be entered as part of the problem input.
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6. TYPICAL RUNNING TIME

Generally, if the  mass balance convergence
criterion is  modest, approximately  one-tenth of  one percent  or
greater, running  time is less than  1 millisecond per  mesh point
per time  step.  The sample  problem was  executed in about  38 CP
seconds.
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7. UNUSUAL FEATURES OF THE PROGRAM

VARR2  is especially  suited  to
the study  of turbulent flows.   The program solves  the transport
equations for  the turbulence  kinetic energy  and the  turbulence
kinematic viscosity.  These  quantities are then coupled  into the
momentum and energy  transport equations.  The very  high velocity
gradients  encountered  in  turbulent flows  at  rigid  walls  are
represented by analytic functions to  ensure that the correct wall
shear stress will be predicted.
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8. RELATED AND AUXILIARY PROGRAMS

SOLA,SOLA-SURF   (NESC   Abstract
651), and SOLA-ICE (NESC Abstract 723)
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9. STATUS
Package ID Status date Status
NESC0755/01 01-APR-1980 Tested at NEADB
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10. REFERENCES

James  L. Cook  and Paul  I.  Nakayama, VARR  II -  A
Computer Program for Calculating Turbulent Fluid Flows with Slight
Density Variation,  CRBRP-ARD-0106, Vols.  1, 2,  and 3,  November
1976.  (WARD-D-0106 has identical contents.)
             W-ARD Addendum, August 1975.
             SD 4060 Stored Program Recording System, Programmer's
Reference  Manual  for  the Integrated  Graphics  Software  System
(I.G.S.), Vol. 2, October 1976.
             Argonne Code Center Note 78-24, May 24, 1978.
NESC0755/01, included references:
- J.L. Cook and P.I. Nakayama:
  VARR II - A Computer Program for Calculating Turbulent Fluid Flows
  with Slight Density Variation
  CRBRP-ARD-0106, Vol. 1  (November 1976)
- J.L. Cook and P.I. Nakayama:
  Appendix A - Flow Diagram for the VARR II Program
  CRBRP-ARD-0106, Vol. 2  (November 1976)
- J.L. Cook and P.I. Nakayama:
  Appendix B - Fortran IV Index Listing of the VARR II Program
  CRBRP-ARD-0106, Vol. 3  (November 1976)
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11. MACHINE REQUIREMENTS

147,000  (octal) words  of  SCM and  14,400
(octal) words  of LCM  storage are used.   Plotting is  done using
SD-4060 Stored Program Recording System.
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12. PROGRAMMING LANGUAGE(S) USED
Package ID Computer language
NESC0755/01 FORTRAN+ASSEMBLER
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13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED:     SCOPE   2.0,
SCOPE 2.1.3.
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14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS

It is
assumed  that the  operating system  will zero  the memory  before
overlay  generation  and  before each  execution.   To  achieve  a
significant increase  in the number  of mesh points  available, it
probably will be necessary to place more arrays in LCM.  Reference
to LCM is by Level 2 declarations.  The Integrated Graphics System
plotting  software is  included with  the  program.  The  plotting
software probably  will not be useful  unless a SD-4060  system is
available.
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15. NAME AND ESTABLISHMENT OF AUTHORS

                 J. L. Cook and P. I. Nakayama
                 Science Applications Incorporated
                 P. O. Box 1393
                 La Jolla, California  92037
   Contact       T. Andreychek
                 Advanced Reactors Division
                 Westinghouse Electric Corporation
                 Waltz Mill Site
                 Box 158
                 Madison, Pennsylvania  15663
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16. MATERIAL AVAILABLE
NESC0755/01
File name File description Records
NESC0755_01.001 SOURCE (EBCDIC) 3133
NESC0755_01.002 SOURCE (EBCDIC) 97
NESC0755_01.003 SOURCE (EBCDIC) 17
NESC0755_01.004 SOURCE (EBCDIC) 71
NESC0755_01.005 SOURCE (EBCDIC) 8791
NESC0755_01.006 SOURCE (EBCDIC) 1479
NESC0755_01.007 INPUT FOR S.P. 50
NESC0755_01.008 AUXILIARY PROGRAM/INFO 2579
NESC0755_01.009 AUXILIARY PROGRAM/INFO 61
NESC0755_01.010 OUTPUT OF S.P. 5197
NESC0755_01.011 JCL,INFORMATION 46
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17. CATEGORIES
  • H. Heat Transfer and Fluid Flow

Keywords: Boussinesq approximation, Navier-Stokes equation, cylinders, finite difference method, fluid flow, fuel assemblies, heat transfer, hydrodynamics, transients, turbulence, turbulent flow, two-dimensional.