Lfl FOR PEPSIG (CORNER VORTEX VERSION)PEPSIG (CORNER VORTEX VERSION) N REPORT NO. R88920028-F (b) Ralph Levy Scientific Research Associates P.O. Box 1058, 50 Nye Road Glastonbury,

, i1iC FILE CO

ANALYSIS OF THE SUBMARINE APPENDAGE FLOW FJELD

USER'S MANUALLfl FOR

PEPSIG (CORNER VORTEX VERSION)

REPORT NO. R88920028-F (b)N

Ralph Levy

Scientific Research AssociatesP.O. Box 1058, 50 Nye Road

Glastonbury, Connecticut 06033

DTICELECTE l"'

Contract No. N000167-86-C-0048 _ SEP 141989 U

Sponsored by: B

Office of Naval Research

800 Quincy St.

Arlington, VA 22217

Under the Applied Hydrodynamics Research Program

APPROVED FOR PUBLIC RELEASE;

DISTRIBUTION UNLIMITED

August 1988

89 9 14 067

NAVY USERS MANUAL INPUT I

PEPSIG (CORNER VORTEX VERSION)INPUT DESCRIPTION

Input to PEPSIG (Corner Vortex version) consists of an initial card specifying thetype of calculation to perform and a title, plus three namelists. Many of the inputparameters have default values and do not need to be specified by the user unlesssome other value is desired. The type (REAL or INTEGER) of the input parametersfollows standard FORTRAN convention, unless stated otherwise. (I.e., those startingwith I, J, K, L, M, or N are INTEGER, and the remainder are REAL).

TITLE CARD

MODE An integer in column 1 specifying the type of calculation to beperformed, as follows:3 to compute and store geometric parameters for potential

flow calculation.2 to perform potential flow calculation.1 to perform viscous flow calculation.0 to terminaie jun.

TITLE A descriptive title in columns 2-33 used on the printed output and inthe plot file.

NAMELIST RESTRT

The parameters specified in this namelist are primarily used to control where arestart file is read and/or written. A restart file must be used when changing thepolynomials used to specify the geometry, the marching step size DT, the type ofoutput desired, etc.

IRSTIN Marching station number to be read from restart file. IRSTIN = 0implies this is not a restart case. The default value is 0.

IRSTOT The interval for writing onto the restart file (i.e., at stationIRSTIN+IRSTOT, IRSTIN+2*IRSTOT, etc.). If IRSTOT = 0 no restart fileis written. The default value is 0.

NFILE The sequence number in the restart file of the station to be read.E.g., if stations 1, 5, 20, and 24 have been written onto the restartfile, and a restart at station 20 is desired, then NFILE should be 3.The default value is 1.

NSAVED The number of stations in the restart file to be saved. E.g., ifstations 1, 5, 20, and 24 have been written onto the restart file, andNSAVED = 3, then when a restart is next written stations 1, 5, and 20will be saved and station 24 will be overwritten. The default value isNFILE. Note that if JRSTIN = JRSTOT (see below) and NFILE = NSAVED,the same file can be used for reading and writing restart data withdestroying any previously saved data.

NAVY USERS MANUAL INPUT 2

NOTE: In practice NFILE and NSAVED are both usually defaulted,which results in each write to the restart file overwriting thepreviously saved station.

JRSTIN Fortran unit number from which restart data will be read. Thedefault value is 11.

JRSTOT Fortran unit number onto which restart data will be written. Thedefault value is 11.

NAMELIST FLUIDS

The first group of parameters in this namelist apply to all cases, and are used to setreference conditions, initial profiles, and boundary conditions.

IUNITS 1 Dimensionless input and output.2 SI units in input and output.3 English units in input and output.The default value is 1.

INPOPT Eight options are available for specifying a consistent set ofreference conditions. These conditions are also used to set up theinitial profiles to start the viscous marching calculation. ForINPOPT = 1 to 8, the parameters to be specified by the user aresummarized as follows:

NPOPT PARAMETERS SPECIFIED Acoession For1 CMACH REY YZERO TZERO PZERO NTIS GP,&I2 UZERO REY YZERO TIRO FZERO DTIC TAB 0l3 CMACH REY YZO TERO RZERO Unannounced [4 UZERO REY YZERO TZERO RZERO Justification5 CMACH REY YZERO SOUND PZERO6 UZERO REY YZERO SOUND PZERO By-7 CMACH REY YZERO SOUND RZERO a /

8 UZERO REY YZERO SOUND RZERO -Availability Codes

The default value is 1. iAvall and/orDist [Special

KTURB 0 Laminar flow.1 Turbulent flow. AIThe default value is 0. I

CMACH Reference Mach number. The default value is 0.01.

REY Reference Reynolds number, based on RZERO, UZERO, and

YZERO. The default value is 1.

UZERO Reference velocity. The default value is 1.

YZERO Reference length. The default value is 1.


TZERO Reference static temperature. The default value is 1.

PZERO Reference static pressure. The default value is 1.

RZERO Reference static density. The default value is 1.

SOUND Reference speed of sound. There is no default value.

RG Gas constant. The default value is 1716., which works for bothIUNITS = 1 and 3.

CPR Reference value for specific heat at constant pressure, used informula for specific heat as a function of temperature. The defaultvalue is 6006., which also works for both IUNITS = 1 and 3.

BLD A 6-element array giving the initial boundary layer thicknesses onthe four computational surfaces, and on the inner and outer lobesurfaces for a mixer case. The default values are 0., 0., 0., 0.2, 0., and0.

VGEN(J,20) Coefficients of the polynomial specifying the houndary layerthickness along the vertical wall. The independent variable in thispolynomial is the height, z. Up to a second-order polynomial maybe specified (i.e., J = 1 to 3). J = n corresponds to the z to the (n-1)'thterm in the polynomial.

VGEN(J,19) Coefficients of the polynomial specifying the boundary layerthickness along the horizontal wall. The independent variable inthis polynomial is the distance from the corner, y. Up to a second-order polynomial may be specified (i.e., J = I to 3). J = n correspondsto the y to the (n-1)'th term in the polynomial.

QRATIO For internal flows - ratio of the average initial velocity at the startof the viscous run to the inlet velocity in the potential flow run.This parameter is used in setting the potential flow pressure field,and is most important when the initial station in the viscous rundoes not have the same mass flow as the initial station in thepotential flow run. To determine what value to use: (1) set QRATIO -1.0 and run the viscous calculation one step; (2) check the printedoutput for the value of the average velocity at the initial station(UBAR); (3) run the complete viscous case with QRAT - TJBAR. Thedefault value is 1.

NS1 0 Symmetry boundary condition on computational surface 1.I Solid wall boundary condition on computational surface 1.The default value is 0.

NS2 0 Symmetry boundary condition on computational surface 2.1 Solid wall boundary condition on computational surface 2.The default value is 0.

NS3 0 Symmetry boundary condition on computational surface 3.1 Solid wall boundary condition on computational surface 3.


The default value is 0.

NS4 0 Symmetry boundary condition on computational surface 4.1 Solid wall boundary condition on computational surface 4.The default value is 1.

ISYM Degree of symmetry in the cross-section, i.e., ISYM = 1 for a full 360degree polar cross section, ISYM = 2 for a 90 degreecalculation,ISYM = 4 for a 90 degree calculation, etc. The defaultvalue is 2.

IPRD 0 No periodic boundary condition.1 Periodic boundary condition in the circumferential direction.The default value is 0.

NOTE - IPRD = I only applies to the NGEOM = 2-5 and 12-15 geometryoptions. In addition, when IPRD = 1 stretched meshes in thecircumferential direction cannot be used.

ILAW 0 Compute the laminar viscosity coefficient from Sutherland'slaw.

1 Compute the laminar viscosity coefficient by assuming it isproportional to temperature to the 0.76 power.

2 Hold the laminar viscosity coefficient constant at its inputvalue (computed from YZERO, UZERO, RZERO, and REY).


IVT 0 Hold the specific heat at constant pressure (CP) and the ratio ofspecific heats (GAMMA) constant at their input values(computed from TZERO).

1 Treat CP and GAMMA as variable functions of temperature.The default value is 0.

FLRFC Flare approximation criteria for separated flow regions. If U <FLRFC*UAVG, U is reset to FLRFC*UAVG. The default value is 0.025.

The following parameters also apply to all cases, and are used to specify thedistribution of grid points in the streamwise direction, and the number of gridpoints in the ttansverse directions. The distribution of grid points in thetransverse directions is controlled by parameters in namelist GEOM.

T Marching parameter, or streamwise computational coordinate.This is the independent variable used in evaluating thepolynomials PCL and PGEO in namelist GEOM. The value of T must bespecified at the initial station. After a restart, however, the value istaken from the restart file. There is no default value.

DTE(K) Step size in T for marching step from station IRSTIN to IRSTIN+l.There is no default value. Up to 10 piecewise continuous sections,each beginning at TSECT(K), can be specified. (default K=I).

AP(K) Ratio of successive step sizes in T. I.e., AP =(T(I+l)-T(I))/(T(l)-T(I-1)). Ihe default value is 1.0, corresponding to a constant step size.

N NAVY USERS MANUAL INPUT 5

Up to 10 piecewise continuous sections, each beginning at TSECT(K),can be specified. (default K=l).

NS Number of last streamwise station to be computed. I.e., the code willmarch from station IRSTIN to station NS. There is no default value.

NEY Number of grid points in the circumferential direction. There is nodefault value.

NEZ Number of grid points in the radial direction. There is no defaultvalue.

The following parameters apply to all cases and control the type and amount ofoutput to be printed and/or written to the plot file. (ICOEF also controls otheraspects of the calculation).

ICCEF A 6x20 array containg various switches, limits, etc. See the separatewrite-up on ICOEF for the details.

IWSTA A 101-element array specifying station numbers at which outputwill be printed. This option is activated when ICOEF(2,3) < 0. Thedefault values are all 0.

KPRT(I) An array of up to 15 elements used to specify additional printoutbeyond the standard printout. This is done by setting KPRT(I) equalto an integer corresponding to the variable desired. For valuesfrom 1 to MVARP (a PARAMETER equal to the number of variablesin the Z array), the corresponding variable from the Z array isprinted. Additional variables may also be printed. Table ? lists thevariables stored in the Z array, plus the others that may be printed.For example, setting KPRT(l) = 62 and KPRT(2) = 71 results inprofiles of turbulence mixing length and Mach number beingprinted.The default values are all 0.

IPLOT 0 Do not write a plot file.I Write a file for later post-processing. The stations written into

the file are controlled by the values of ICOEF(2,4), ICOEF(2,5),and IPSTA.


IPSTA A 101-element array specifying station numbers at which outputwill be written into the plot file. This option is activated whenICOEF(2,5) < 0. The default values are all 0.

NPLT Number of variables written into the plot file at each station. Themaximum allowed is MVARP + 10. The default value is 14.

KPLT(I) An array of NPLT elements specifying which variables are to bewritten into the plot file. This is done in the same way as thespecification of additional printout using KPRT. The defaults forKPLT are such that the following 14 variables are stored in the plotfile:


1 Reference Cartesian coordinate in x-direction. Here"reference coordinate" refers to a fixed coordinate system, asopposed to one that is perpendicular to a duct centerline, forexample.

2 Reference Cartesian coordinate in y-direction.

3 Reference Cartesian coordinate in z-direction.

4 Inviscid velocity (from potential flow file) in relativeCartesian y-direction.

5 Inviscid velocity (from potential flow file) in relativeCartesian z-direction.

6 Static pressure from solution of Poisson pressure equation.

7 Static pressure coefficient.

8 Inviscid static pressure coefficient (from potential flow file).

9 Streamwise gradient of invisciu static pressure.

10 Velocity in relative Cartesian y-direction, non-dimensionalizedby UZERO. Here "relative Cartesian" refers to a coordinatesystem whose x-axis is normal to the plane of thecomputational station (and therefore the y-z axes are in theplane). The x-direction is often referred to as the streamwiseor primary flow direction.

11 Velocity in relative Cartesian z-direction, non-dimensionalizedby UZERO.

12 Velocity in relative Cartesian x-direction (i.e., streamwisedirection), non-dimensionalized by UZERO.

13 Vorticity component in the streamwise direction, non-dimensionalized by UZERO/YZERO.

14 Secondary stream function, non-dimensionalized byUZERO*YZERO.

The following parameters apply to all cases, and control the starting procedure forthe initial marching step, and the sequence of solution of the equations.

KSTART 0 Original PEPSIG starting procedure.I Iterative starting procedure.2 Split the first marching step into substeps.The default value is 0.

DXSTRT Initial marching parameter step size for KSTART = I option. Thedefault value is T+AP*DT.


NSTART Number of iterations in the starting sequence if KSTART = 1, ornumber of substeps if KSTART = 2.The default value is 1.

ISEQ 0 Original equation solving sequence in PEPSIG.1 Optional equation solving sequence.2 Another optional equation solving sequence.The default value is 0.

IBETA 0 Use the small scalar approximation.1 Use the pressure approximation.The default value is 1.

The remaining variables in namelist FLUIDS are either not used, apply to optionscurrently being developed, or are for output only.

NAMELIST GEOM

The following parameters specify the geometry being analyzed.

NGEOM 2 Superelliptic cross-sections, set up through subroutine TUBE,with the semi-major axis, ratio of semi-major to semi-minoraxis, and exponent specified.

3 Superelliptic cross-sections, set up through subroutine TUBE,with the semi-major axis, semi-minor axis, and exponentspecified.

4 Same as NGEOM = 2 but with elliptical centerbody.5 Same as NGEOM = 3 but with elliptical centerbody.12 Same as NGEOM = 2 but going through ANYGEO and GEOTUB

instead of TUBE.13 Same as NGEOM = 3 but going through ANYGEO and GEOTUB



instead of TUBE.21 Rectangular cross-sections.The default value is 2.

NOTE: The NGEOM = 2-5 options will eventually be replaced by the NGEOM = 12-15options. Similarly, the NGEOM = 21 option may also eventually bereplaced by an ANYGEO equivalent. See the separate write-up onANYGEO for details on how to add additional user-written geometrypackages.

TSECT(K) The geometry can be specified in up to 10 piecewise continuoussections. Section K begins at TSECT(K) (default K=I).

PCLD(J,1,K) Coefficients of the polynomial specifying the y Cartesiancomponent of the centerline location, if ICOEF(1,9) = 1; thecurvature CNU of the centerline (i.e., the reciprocal of the local


radius of curvature), if ICOEF(1,9) = 0; or the Frenet framecurvature CAPPA of the centerline, if ICOEF(l,9) - 2. Theindependent variable in this polynomial is the marchingparameter T. Up to a tenth-order polynomial may be specified(i.e., J = 1 to 11). J = n corresponds to the x to the (n-1)'th term inthe polynomial. The default values are all 0, corresponding to astraight centerline. Up to 10 piecewise continuous sections, eachbeginning at TSECT(K), can be specified. (defau' K=1).

PCLD(J,2,K) Coefficients of the polynomial specifying the z Cartesiancomponent of the centerline location, if ICOEF(1,9) = 1; thecurvature CETA of the centerline (i.e., the reciprocal of the localradius of curvature), if ICOEF(1,9) = 0; or the Frenet frame torsionTAU of the centerline, if ICOEF(1,9) = 2. The independent variablein this polynomial is the marching parameter T. Up to a tenth-order polynomial may be specified (i.e., J = I to 11). J = ncorresponds to the x to the (n-1)'th term in the polynomial. Thedefault values are all 0, corresponding to a straight centerline. Upto 10 piecewise continuous sections, each beginning at TSECT(K),can be specified. (default K=1).

PCLD(J,3,K) Coefficients of the polynomial specifying the x Cartesiancomponent of the centerline location, if ICOEF(1,9) = 1, or the arclength along the centerline, if ICOEF(1,9) = 0 or 2. Theindependent variable in this polynomial is the marchingparameter T. Up to a tenth-order polynomial may be specified(i.e., J = 1 to 11). J = n corresponds to the x to the (n-1)'th term inthe polynomial. The default values are all 0, except PCL(2,3) = 1.,which says that the marching parameter T is the Cartesian xcoordinate. Up to 10 piecewise continuous sections, eachbeginning at TSECT(K), can be specified. (default K=1).

PGEOD(J,I,K) Coefficients of the polynomial specifying the ratio of the semi-major to semi-minor axis, if NGEOM = 2, 4, 32, or 34, or the semi-minor axis itself if NGEOM = 3, 5, 33, or 35. The independentvariable in this polynomial is the marching parameter T. Up to atenth-order polynomial may be specified (i.e., J - 1 to 11). J = ncorresponds to the x to the (n-l)'th term in the polynomial. Thedefault values are all 0, except PGEO(l,1) = 1. Up to 10 piecewisecontinuous sections, each beginning at TSECT(K), can be specified.(default K=1).

PGEOD(J,2,K) Coefficients of the polynomial specifying the semi-major axis.The independent variable in this polynomial is the marchingparameter T. Up to a tenth-order polynomial may be specified(i.e., J = 1 to 11). J = n corresponds to the x to the (n-l)'th term inthe polynomial. The default values are all 0, except PGEO(1,2) = 1.Up to 10 piecewise continuous sections, each beginning atTSEC[(K), can be specified. (default K=l).

PGEOD(J,4,K) Coefficients of the polynomial specifying the exponent of thesuperellipse. The exponent must be greater than or equal to 2.0and should be less than or equal to 10.0. The independent variablein this polynomial is the marching parameter T. Up to a tenth-

NAVY USERS MANU INPUT 9

order polynomial may be specified (i.e., J = 1 to 11). J = ncorresponds to the x to the (n-1)'th term in the polynomial. Thedefault values are all 0, except PGEO(1,4) = 1. Up to 10 piecewisecontinuous sections, each beginning at TSECT(K), can be specified.(default K=1).

PGEOD(J,5,K) Coefficients of the polynomial specifying the semi-major axis ofthe elliptical centerbody. The independent variable in thispolynomial is the marching parameter T. Up to a tenth-orderpolynomial may be specified (i.e., J = 1 to 11). J = n corresponds tothe x to the (n-1)'th term in the polynomial. The default valuesare all 0. Up to 10 piecewise continuous sections, each beginningat TSECT(K), can be specified. (default K=l).

PGEOD(J,6,K) Coefficients of the polynomial specifying the semi-minor axis ofthe elliptical centerbody. The independent variable in thispolynomial is the marching parameter T. Up to a tenth-orderpolynomial may be specified (i.e., J = I to 11). J = n corresponds tothe x to the (n-1)'th term in the polynomial. The default valuesare all 0. Up to 10 piecewise continuous sections, each beginningat TSECT(K), can be specified. (default K=1).

RTUBE Radius of small tube surrounding polar coordinate singularity atthe centerline. The recommended value is half the distance to thefirst grid point from the centerline. The default value is 0.01.

ARC Centerline arc length at the start of the calculation.The default value is 0.0.

IDUCT 0 External flow case. (Requires input reference point forpressure. See ICOEF(2,16) and (2,17)).

1 Internal flow case.The default value is 1.

ITUBE 0 Print grid point locations in relative Cartesian coordinates.1 Print grid point locations in polar coordinates.

The default value is 1.ITUBE is automatically set equal to 0 if NGEOM > 20.

The following parameters control the distribution of grid points in the transversedirections.

IPA 1 Pack grid points in the circumferential direction usingsubroutine KGRID, as specified by NCTRK, XAK, and EPSK.

2 Uniformly spaced circumferential grid.3 Pack grid points in the circumferential direction

automatically, based on the cross-section geometry.The default value is 2.

IPB 1 Pack grid points in the radial direction using subroutineKGRID, as specified by NCTRK, XAK, and EPSK.

2 Uniformly spaced radial grid.3 Pack grid points in the radial direction as specified by VIS.The default value is 2.


VIS Radial grid packing parameter used when IPB = 3. A value of 0.15gives a loosely packed grid near the outer wall, and a value of 0.6gives a very tightly packed grid near the outer wall. For laminarflow, values of 0.15 to 0.4 are recommended. For turbulent flow,values of 0.4 to 0.6 are recommended. The default value is 1. (why,I don't know).

NCTRK(J) Number of locations between end points, in transversecomputational coordinate directions (J = 1 and J = 2) about whichgrid points are to be packed using KGRID. The maximum valueallowed is 10. There are no default values.

XAK(I,J) Non-dimensional locations (i.e., from 0.0 to 1.0), in transversecomputational coordinate directions (J = I and J = 2) about whichgrid points are to be packed using KGRID. XAK(1,J) andXAK(NCTRK(J)+2,J) should always be 0.0 and 1.0, respectively. Thesubscript I runs from 1 to NCTRK(J)+2. There are no defaultvalues.

EPSK(I,J) Parameter specifying the degree of packing about the pointXAK(I,J). It can be thought of as the length of the interval aboutXAK(I,J) in which points a',. packed. Smaller values of EPSKresult in tighter packing. If EPSK(I,J), corresponding to thelocation XAK(I,J), is greater than the distance to the locationXAK(I-1,J) or XAK(I+1,I), no packing is done about XAK(I,J).Therefore, since XAK(I,J) can at most be 1.0, an easy way to notpack at XAK(I,J) is to set EPSK(I,J) = 1.0. There are no defaultvalues.

NAMELIST VORTEXThe parameters specified in this namelist define the forced vortex at the initial

value surface.

RCORE Radius of the core of the forced vortex.

QTEDGE Strength of the forced vortex specified as the velocity at the edgeof the core. Within the core the vortex strength isf2=2*QTEDGE/RCORE.

ZZERO Location of the center of the forced vortex in the transverseinitial value surface. ZZERO is a complex number, so the y,zlocation of the vortex is specified in the form (y,z).

NAVY USERS MANUAL ICOEF OPTIONS 1

PEPSIG (CORNER VORTEX VERSION)ICEF OPTIONS

ICOEF is a 6x20 array read in namelist FLUIDS that contains various switches,limits, etc. Some of these apply to both the potential flow (MODE=2) and viscousflow (MODE=l) calculations, some to only one or the other, and some to features inthe code that are still under development. For the average user, many, if not most,of these options will have little significance. Those most likely to be needed by thetypical user are marked with an asterisk. Except where noted, setting the value to0 turns the option off. Except where noted, the default values are all zero.

ICOEF( 1 ,n)

n Description

1 1 Print initial station values before starting procedure.

2 1 Momentum integral boundary layer calculation for straightpipe flow, with the correct area variation, as a basis forcomputing the turbulence mixing length.


3 Maximum number of iterations in ADI for scalar potential solutionand for Poisson pressure equation solution. The default value is 200.

4 Maximum number of iterations in ADI3D for potential flow solution.The default value is 200.

5 Maximum number of iterations in PRIMRY for computation of one-dimensional viscous pressure gradient correction. The defaultvalue is 10.

6 0 Linear interpolation on the potential flow file.I Potential flow pressure coefficient set equal to 0.2 Quadratic interpolation on the potential flow file.The default value is I.

7 Not used.

8 1 Print the Jacobian matrix at each giid point.

9 0 Specify the centerline shape (array PCL) by the distribution ofcurvature and arc length.

I Specify the centerline shape (array PCL) by Cartesiancoordinate location.

2 Specify the centerline shape (array PCL) by Frenet frameparameters.

iAVY USERS MANUAL ICOEF OPTIONS 2

10 1 Print the secondary velocities in the orthogonal referencecoordinates as computed during the scalar potential andcoupled vorticity-stream function solutions.

1 1 Print the final computed velocities in the orthogonalreference coordinates.

12 <0 Print iteration data in ADI2X2 during the coupled vorticity-stream function solution every IICOEF(1,12)I iterations.

0 Print namelist SCL2X2 in subroutine SCALE.1 Same as 0, plus print of coefficients of input equations (first

iteration only), plus iteration data every iteration.2 Same as 1, plus print of coefficients of equations sent to matrix

inverter each sweep, and resulting solution.3 Same as 2, plus print from mairix inverter.The default value is -5.

13 <0 Print iteration data in ADI during solution of scalar potentialand Poisson pressure equations every IICOEF(I,13)I iterations.

0 Print iteration data every iteration.1 Same as 0, plus print of namelists TRMDMP, DTADI2, and DUMP

in subroutine ADI.2 Same as 1, plus print of coefficients of input equations (first

iteration only).3 Same as 2, plus print of coefficients of equations sent to matrix

inverter each sweep, and resulting solution.4 Same as 3, plus print from matrix inverter.5 Same as 1.The default value is -5.

14 4) Print iteration data in ADI during solution of streamwisemomentum every IICOEF(1,13)I iterations (if ICOEF(5,5) = 0).

0 Print iteration data every iteration.1 Print namelists TRMDMP, DTADI2, and DUMP in subroutine ADI

during solution of streamwise momentum equation.2 Same as 1, plus print of coefficients of input equations (first


inverter each sweep, and resulting solution.4 Same as 3, plus print from matrix inverter.5 Same as 1.The default value is -5.

15 1 Print from subroutine FRAME.

16 1 Print of initial profiles from subroutine IPROF, MXPROF, orMYPROF.

17 2 Print coefficients of Laplace's equation during potential flowsolution.

18 1 Print ..t 'iysical coordinates, computational coordinates, anddf fer ..... weights.


19 1 Print of data read from potential flow file.

20 For KSTART = 1 or 2 option, output is printed during startingprocedure every ICOEF(1,20)'th iteration or sub-step.

ICOEF(2,n)

n Description

1 Maximum number of iterations in ADI2X2 for coupled vorticity-stream function solution. The default value is 200.

2, 3 For ICOEF(2,3) greater than or equal to zero, computed profiles areprinted every ICOEF(2,3)'th station starting at station ICOEF(2,2). IfICOEF(2,3) is less than zero, profiles are printed at stations specifiedby the array IWSTA. The defaults are 0 for ICOEF(2,2) and 1 forICOEF(2,3).

4, 5 For ICOEF(2,5) greater than or equal to zero, computed results arewritten into the plot file every ICOEF(2,5)'th station starting atstation ICOEF(2,4). If ICOEF(2,5) is less than zero, results are writteninto the plot file at stations specified by the array IPSTA. Thedefaults are 0 for ICOEF(2,4) and 1 for ICOEF(2,5).

6 If ICOEF(2,6) = 1, the reference Cartesian velocity components u, w,and v are put into positions 4, 5, and 6 in the plot file (overwritingKPLT(4), KPLT(5), and KPLT(6)). These values are useful forparticle tracing routines.

7-12 Not used.

13 1 Print non-convergence message in ADI.

14 1 Non-dimensionalize all printed velocities by the averagestreamwise velocity at the initial station.

15 Used by the code to keep track of the number of points in separatedflow regions.

16 Grid point index in the circumferential direction specifying thelocation of the reference pressure when using the external flowoption (IDUCT = 0).

17 Grid point index in the radial direction specifying the location ofthe reference pressure when using the external flow option (IDUCT= 0).

18 1 Print KGRID output.2 Print KGRID output, plus KGRID iteration data.

19 1 Print cross-plane grid point coordinates when ICOEF(2,20) = 1.


20 1 Print geometry parameters computed during a MODE = 3calculation (geometry set-up for potential flow).

ICOEF(3,n)

n Description

1-2 Not used.

3 Results are printed at every (ICOEF(3,3)+I)'th grid point in the IY(circumferential) direction.

4 Results are printed at every (ICOEF(3,4)+I)'th grid point in the JZ(radial) direction.

5 Results are stored in the plot file at every (ICOEF(3,5)+I)'th gridpoint in the IY (circumferential) direction.

6 Results are stored in the plot file at every (ICOEF(3,6)+I)'th gridpoint in the JZ (radial) direction.

7 0 Ignore phi-velocity terms when computing transversevelocity gradients as part of the computation of transversepressure gradients in the Poisson pressure equation, and inthe computation of the vorticity vector.

I Include the phi-velocity terms.The default value is 1.

8-9 Not used.

10 0 Potential flow pressure coefficient from potential flow file.1 Potential flow velocity from potential flow file.To get potential flow pressure coefficient and velocity frompotential flow file. ICOEF(3,10) is automatically set equal toICOEF(5,11) if ICOEF(5,11) = 0 or 1. If ICOEF(5,11) = 2, ICOEF(3,10) canbe 0, 1, or 2.

11 Not used.

12 1 Smooth the potential flow pressure coefficient (or velocity ifICOEF(5,11) = 1) in the streamwise direction.

13 1 Print normalized arc-lengths when ICOEF(2,20) = 1.

14 1 Print absolute Cartesian coordinates when ICOEF(2,20) = 1.

15 1 Print elements of Jacobian grid transformation matrix whenICOEP(2,20) = 1.

16-20 Not used.

NAVY USERS MANUAL ICOEF OPTIONS,5

ICOEF(4,n)

n Description

1 Maximum pseudo-time step size used in ADI for solution of the scalarpotential, energy, and swirl equations is divided by the factor2**ICOEF(4,1).

2 Minimum pseudo-time step size used in ADI for solution of the scalarpotential, energy, and swirl equations is divided by the factor2**ICOEF(4,2).

3 0 BETA = 1.0 (backward streamwise differencing) in ADI.I BETA = 0.5 (Crank-Nicholson streamwise differencing) in ADI.

4 0 Use local minimum time step in ADI.1 Use local maximum time step in ADI.

5 Maximum pseudo-time step size used in ADI2X2 for solution of thecoupled vorticity-stream function equations is divided by the factor2**ICOEF(4,5).

6 Minimum pseudo-time step size used in ADI2X2 for solution of thecoupled vorticity-stream function equations is divided by the factor2**ICOEF(4,6).

7 Maximum pseudo-time step size computed by SCALE for the sourceterm in the solution of the coupled vorticity-stream functionequations is divided by the factor 2**ICOEF(4,7).

8 0 BETA = 1.0 (backward streamwise differencing) in ADI2X2.1 BETA = 0.5 (Crank-Nicholson streamwise differencing) in

ADI2X2.

9 Maximum pseudo-time step size used in ADI3D for solution of thepotential flow equation is divided by the factor 2**ICOEF(4,9).

10 Minimum pseudo-time step size used in ADI3D for solution of thepotential flow equation is divided by the factor 2**ICOEF(4,10).

11 - I Use local mean time step in ADI3D.0 Use local minimum time step in ADI3D.1 Use local maximum time step in ADI3D.The default value is -1.

12 0 BETA = 1.0 (backward streamwise differencing) in ADI3D.I BETA = 0.5 (Crank-Nicholson streamwise differencing) in

ADI3D.

13 Convergence criteria in ADI for scalar potential, Poisson pressure,energy, and swirl equations is multiplied by the factor10**ICOEF(4,13).


14 Convergence criteria in ADI2X2 for the first equation (vorticity) ismultiplied by the factor 10**ICOEF(4,14).

15 Convergence criteria in ADI2X2 for tLc second equation (streamfunction) is multiplied by the factor 10**ICOEF(4,15).

16 Convergence criteria in ADI3D is multiplied by the factor10**ICOEF(4,16).

17 Number of time step cycles used in ADI3D for iterative solution ofthe potential flow equation. The maximum number is 3. The defaultvalue is 3.

18 1 Base the pseudo-time step for the first cycle in ADI3D on acombination of the magnitudes of the finite-differenceoperators in the circumferential, radial, and streamwisedirections.

2 Base the time step on a combination of the circumferential andradial directions.

3 Base the time step on a combination of the radial andstreamwise directions.

4 Base the time step on a combination of the circumferential andstreamwise directions.

5 Base the time step on the circumferential direction.6 Base the time step on the radial direction.7 Base the time step on the streamwise direction.The default value is 5.

19 Same as ICOEF(4,18), except for second cycle. The default value is 6.

20 Same as ICOEF(4,18), except for third cycle. The default value is 7.

ICOEF(5,n)

n Description

1 1 Set the rotational part of the cross-flow velocity (computedduring the coupled vorticity-stream function solution) to zero.

2 - 1 Solve the Poisson pressure equation, but get the density fromthe potential flow pressure.

0 Solve the Poisson pressure equation, and get the density fromthe viscous flow pressure.

I Skip solving the Poisson pressure equation, and get the densityfrom the potential flow pressure.

The default value is -1.

3 Used by the program in subroutine COEFVS. Do not change.

'NAVY USERS MANUAL ICOEF OPTIONS 7

4 0 First order wall vorticity boundary condition.1 Second order wall vorticity boundary condition.

5 0 Iterate the primary momentum equation to convergence eachmarching step (mainly important in separated flow regions).If used, convergence criteria (controlled by ICOEF(5,8)) shouldbe tightened.

1 No iteration. The default value is 1.

6 Maximum pseudo-time step size used in ADI for solution of theprimary momentum equation is divided by the factor 2**ICOEF(5,6).This only applies if iteration is used (ICOEF(5,5) = 0).

7 Minimum pseudo-time step size used in ADI for solution of theprimary momentum equation is divided by the factor 2**ICOEF(5,7).This only applies if iteration is used (ICOEF(5,5) = 0).

8 Convergence criteria in ADI for primary momentum equation ismultiplied by the factor 10**ICOEF(5,8). This only applies ifiteration is used (ICOEF(5,5) = 0).

9 <0 if estimated initial velocity profiles are given as velocitycomponents in the body-fitted computational coordinate system(instead of the centerline coordinate system).

10 0 No slip of secondary velocities.1 Slip of secondary velocities.The default value is 0 for IBETA = 1, and I for IBETA = 0.

11 0 Potential flow solution from a pressure file (or to store apressure file if MODE = 2).

1 Potential flow solution from a velocity file (or to store avelocity file if MODE = 2).

2 Potential flow solution from a file containing both pressurecoefficient and velocity (but this is not currently availablethrough PFLOW).

12 1 Include rotationality of inviscid velocity in COEFVS.

13 0 Ignore phi-velocity terms when computing streamwisevelocity gradients as part of the computation of transversepressure gradients in the Poisson pressure equation.

1 Include the phi-velocity terms.

14 Maximum pseudo-time step size used in ADI for solution of thePoisson pressure equation is divided by the factor 2**ICOEF(5,14).

15 Minimum pseudo-time step size used in ADI for solution of thePoisson pressure equation is divided by the factor 2**ICOEF(5,15).


16 4O Print iteration data in ADI during solution of energy equationevery IICOEF(5,16)I iterations.

0 Print iteration data every iteration.1 Same as 0, plus print of namelists TRMDMP, DTADI2, and DUMP



inverter each sweep, and resulting solution.4 Same as 3, plus print from matrix inverter.5 Same as 1.

17 4 Print iteration data in ADI during solution of swirl equationevery IICOEF(5,17)I iterations.

0 Print iteration data every iteration.I Same as 0, plus print of namelists TRMDMP, DTADI2, and DUMP



inverter each sweep, and resulting solution.4 Same as 3, plus print from matrix inverter.5 Same as 1.

18 Not used.

19 1 Update streamwise velocity and turbulent viscosity coefficientwhen using KSTART - 1 option.

20 Not used.

ICOEF(6,n)

None of these options are currently being used.

NAVY USERS MANUAL "Z" ARRAY 1

PEPSIG (CORNER VORTEX VERSION)"Z" ARRAY PRINTOUT AVAILABLE

WITH KPRT OPTION

This table lists the variables that may be printed and/or written into theplot file using the KPRT and KPLT arrays. Variable numbers 1 through 70 arestored in the Z array. Those above 70 are additional variables that may be printedand/or written into the plot file. In this table, "n" refers to the upstream station,and "n+l" refers to the station most recently computed.

MNEMONIC

No. VARIABLE NAME DESCRIPTION

1 u NUN Streamwise velocity at n

2 u NU Streamwise velocity at n+1

3 v NVN Velocity at n in relative Cartesian y-direction

4 v NV Velocity at n+1 in relative Cartesian y-direction

5 w NWN Velocity at n in relative Cartesian z-direction

6 w NW Velocity at n+1 in relative Cartesian z-direction

7 p NRHON Static density at n

8 p NRHO Static density at n+1

9 Q NVORN Streamwise vorticity at n

10 Q NVOR Streamwise vorticity at n+1

11 cp NCPIN Inviscid pressure coefficient at n

12 Cp NCPI Inviscid pressure coefficient at n+1

13 A MUN Laminar viscosity coefficient at n

14 9 MU Laminar viscosity coefficient at n+1

15 9t MUTN Turbulent viscosity coefficient at n

16 I MUT Turbulent viscosity coefficient at n+1

17 p NPRESN Static pressure at n from Poisson pressureequation

NAVY USERS MANUAL "Z" ARRAY 2

18 p NPRES Static pressure at n+l from Poisson pressureequation

19 v NVPHN Scalar potential velocity in relative Cartesiany-direction at n

20 v NVPH Scalar potential velocity in relativ Cartesiany-direction at n+l

21 w NWPHN Scalar potential velocity in relative Cartesianz-direction at n

22 w NWPH Scalar potential velocity in relative Cartesian

z-direction at n+l

23 y NXYZA Reference Cartesian coordinate in y-direction

24 z NXYZA+I Reference Cartesian coordinate in z-direction

27 x NXYZA+I Reference Cartesian coordinate in x-direction

26-34 NEIll+ Elements of Jacobian matrix at n+l

35-43 NENI1+ Elements of Jacobian matrix at n

44 2D:D NDD Dissipation function

45 h NUN Orthogonal metric scale factor at n

46 h NH Orthogonal metric scale factor at n+1

47 vi NVIN Inviscid velocity at n in relative Cartesiany-direction

48 v i NVI Inviscid velocity at n+l in relative Cartesiany-direction

49 wi NWIN Inviscid velocity at n in relative Cartesianz-direction

50 wi NWI Inviscid velocity at n+l in relative Cartesianz-direction

51 NPX1 y-component of the transverse pressure gradient

52 NPX2 z-component of the transverse pressure gradient

53 NRADI x-component of the distance vector to the centerof rotation

NAVY USERS MANUAL '2" ARRAY 3

54 NRAD2 y-component of the distance vector to the centerof rotation

55 NRAD3 z-component of the distance vector to the centerof rotation

56 v NVPSN Vector potential velocity in relative Cartesiany-direction at n

57 v NVPS Vector potential velocity in relative Cartesiany-direction at n+l

58 w NWPSN Vector potential velocity in relative Cartesianz-direction at n

59 w NWPS Vector potential velocity in relative Cartesianz-direction at n+l

60 u i NUIN Inviscid streamwise velocity at n

61 u i NUI Inviscid streamwise velocity at n+l

62 1 NLEN Turbulence mixing length

63 V NPSI Secondary flow stream function

64 NPHI Secondary flow scalar potential

65 T NTEMN Static temperature at n

66 T NTEM Static temperature at n+l

67 E0 NEON Total enthalpy at n

68 E0 NEO Total enthalpy at n+l

69 NDPIDX Inviscid streamwise pressure gradient

70

71 Mn NLOCMA Mach number

72 P NDSTPR Static pressure

73 Pt NDTOPR Total pressure

74 p NDRHO Static density

75 cp NDCP Static pressure coefficient

76 Tt NDTlOTM Total temperature

NAVY USERS MANUAL PARAMETERS 1

PEPSIG (CORNER VORTEX VERSION)PARAMETERS

In PEPSIG, the sizes of the dimensioned arrays, and hence the storage required for theprogram, are set using PARAMETERs. These PARAMETERs themselves are set in COMDECKCPARAM. Larger or smaller dimensions can be set for the entire program simply bychanging the appropriate PARAMETERs in COMDECK CPARAM, and then recompiling theprogram. The basic PARAMETERs are defined as follows:

NDYP - Maximum number of grid points in the circumferential direction forthe viscous flow calculation. Currently setequal to 55.

NDZP - Maximum number of grid points in the radial direction for theviscous flow calculation. Currently set equal to 50.

NDXPA - Maximum number of grid points in the streamwise direction for thepotential flow calculation. Currently set equal to 50.

NDYPA - Maximum number of grid points in the circumferential directionfor the potential flow calculation. Currently set equal to 20.

NDZPA - Maximum number of grid points in the radial direction for thepotential flow calculation. Currently set equal to 20.

MVARP - Total number of variables stored in the Z array. Currently setequal to 70.

Several additional PARAMETERs are defined in COMDECK CPARAM as functions ofthose listed above. The following PARAMETERs are used in various common blocks,DIMENSION statements, and EQUIVALENCE statements:

NDP = Maximum of NDYP, NDZP, NDYPA, and NDZPA.

NDYNDZ NDYP*NDZP.

NDP2 = NDP**2

NDPM2 = NDP - 2

NDZP1 = NDZP + 1

NDPA = Maximum of NDYP, NDZP, NDXPA, NDYPA,NDZPA.

NPFA = 18*NDXPA*NDYPA*NDZPA

NAVY USERS MANUAL PARAMETERS 2

NPF - 18*NDXPA*NDYPA*NDZPA - 15*NDYP*NDZP- 35*NDYP*NDZP -18&NDP**2- MVARP*NDYP*NDZP

The PARAMETER NPF may require some explanation. The total amount of storagerequired in the C array (common block BLKMM) for the potential flow calculation is18*NDXPA*NDYPA*NDZPA. However, the total amount required in common block BLKMMfor the viscous calculation is only 15*NDYP*NDZP (for array C), plus 35*NDYP*NDZP +18*NDP**2 (for array CQVQ1), plus MVARP*NDYP*NDZP (for array Z). The arrayCPFLOW(NPF) is therefore added to common block BLKMM to make it large enough for thepotential flow calculation. If BLKMM is already large enough, NPF is equal to 1.

In addition to the above PARAMETERs, the following are used in the BLOCK DATAroutine:

NDC = 15*NDYP*NDZP

NZV = MVARP*NDYP*NDZP

MVARP1 = MVARP + 1

MVARP2 = MVARP+ 2

MVARP3 =MVARP+ 3

MVARP4 = MVARP + 4

MVARP5 = MVARP + 5

MVARP6 = MVARP+ 6

MVARP7 = MVARP + 7

MVARP8 = MVARP + 8

MVARP9 = MVARP + 9

MVAR4 = MVARP - 4

MVAR69 = MVARP - 69

NDANG = 4*NDYPA

NDRAD = 4*NDZPA

NDCPI = 4*NDYPA*NDZPA

NAVY USERS MANUAL SAMPLE INPUT

RUNNING A CASE WITH PEPSIG

(CORNER VORTEX VERSION)

This input runstream is stored as [LEVY.VOR]VOR.JOB.

JOB, JN=VOR,MFL=900000,T=200,US=DEFER.ACCOUNT,AC=28X162X8, US=LEVY, UPW=PEPSIG.COP YD.REWIND, DN=$ IN.ACCESS, DN=OBJECT, PDN=PGB*VOR, ID=SRA.ACCESS, DN=UTIL, PDN=LIB*UTILB, ID=SRA, OWN=DEJONG.LDR, DN=OBJECT, LIB=UTIL, NA.EXIT./ EOF1 FLOW WITH VORTEX

&RESTRT& END&FLUIDSNS1=-1, NS2=-l, NS3=1,NS4=-2,BLD=.004,0., .02,0.,VGEN (1,20) =0.004,0.000,0.,VGEN (1, 19) =0.010,0.085,0.,REY=1 .E6,KTURB=1, IBULEV=0,IPLOT=1, AP=1 .07,NEY=4 9, NEZ=4 9,T=0 .038, DTE=. 00811,NS=33,ICOEF (1,1) =0,ICOEF (1,6) =1,ICOEF (2,1) =500,ICOEF (1,2) =0, ICOEF (1,5) =10,ICOEF (1, 12) =-20, ICOEF (1, 13)=-20, ICOEF (1, 14)=-20,ICOEF (2,3) =-1000, ICOEF (2,5) =-1000,ICOEF (2, 16) =40, ICOEF (2, 17) =40,ICOEF (5, 2) =-l,IWSTA=5, 12, 33,IPSTA=5, 12, 33,ISKPL=1,JSKPL=1,NY1PL=1,NZ1PL=1, NY2PL=45,NZ2PL=44,ISKPR=1, JSKPR=1,NY1PR=1,NZ1PR=1, NY2PR=45,NZ2PR=44,&END&GEOMIDUCT=0,VIS=. 004, .9434, .002, 1.,NGEOM=2 1,PGEOD=1000*0.,PGEOD (1, 1)=.2,PGEOD(1, 2)=.116,& END& VORTEXZZERO=(.023, .0077),QTEDGE=0 .35,RCORE=0 .0023,& ENDSTOP

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