Computer Programs
NESC0755 VARR2
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NESC0755 VARR2

VARR2, 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 PROGRAM 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. METHODS

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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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. HARDWARE 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. SOFTWARE REQUIREMENTS

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, CA 92037, USA

 

Contact: T. Andreychek

         Advanced Reactors Division

         Westinghouse Electric Corporation

         Waltz Mill Site, Box 158, Madison, PA 15663, USA

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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.