PHOTON USE
p
gr z 1
msg Grid
msg
vec z 1 sh
MSG Velocity vectors
msg
msg Press return to redraw
pause
gr off; gr ou z 1; red
msg Press return to plot pressure contours
pause
cont p1 z 1 fil;.001
msg
msg Type e to End
ENDUSE
GROUP 1. Run title
TEXT(PRANDTL-MEYER turning in the X-Y: B536
TITLE
DISPLAY
This case simulates Prandtl-Meyer turning. The geometry is
depicted below:
North boundary (not shown)
is curved to follow the
theoretical position of
the streamline.
y ^ /
|---------------------- V
Uniform |
in flow | /
at Mach | /
number | /
1.0 | / \
| / Outlet boundary is set
| / to coincide with a
|----------->-------/ characteristic line.
x
CHAR(ANSW)
mesg(Press return to continue
readvdu(answ,char,y)
The North boundary is impervious to flow because it is
located along a streamline (the location of which is
calculated from Prandtl-Meyer expansion theory). At the exit,
the pressure is fixed to the constant value that pertains to the
characteristic line along which the exit boundary is prescribed
to run. The last row of cells is very thin compared to the
others to ensure the accuracy of this pressure fixation.
The grid lines of constant I are set to be coincident with
the theoretically-calculated locations of the characteristic
lines. The grid lines of constant J are uniformly spaced, and
hence must correspond to streamlines.
The predicted contours of pressure are very close to the
grid lines of constant I, which demonstrates the ability of
EARTH to calculate accurately Prandtl-Meyer turning.
ENDDIS
INTEGER(NI,NJ,NK); REAL(PT,PS,UIN,RHOIN,COEF)
GROUP 3. X-direction grid specification
NX=13
GROUP 4. Y-direction grid specification
NY=5
GROUP 6. Body-fitted coordinates or grid distortion
BFC=T;NONORT=T;NI=NX+1;NJ=NY+1;NK=2
** Set corner points for frame
GSET(P,A,-1.1000E-01,0,0)
GSET(P,C,1.0000E-03,-1.0000E-02,0)
GSET(P,D,3.4756E+00,1.4970E-01,0)
GSET(P,E,-1.1000E-01,1,0)
** Set points for curved part
GSET(P,B,1.0000E-03,-1.0000E-02,0)
GSET(P,D0,-1.0000E-02,1,0)
GSET(P,D1,5.7410E-01,9.9430E-01,0)
GSET(P,D2,9.7960E-01,9.6660E-01,0)
GSET(P,D3,1.5386E+00,8.7760E-01,0)
GSET(P,D4,2.1825E+00,7.0380E-01,0)
GSET(P,D5,2.9870E+00,3.9250E-01,0)
GSET(P,D6,3.4746E+00,1.5970E-01,0)
** Set SOUTH boundaries
GSET(L,L1,A,B,1,1.0)
GSET(L,L2,B,C,NX-1,1.0)
** Set EAST boundary
GSET(L,L3,C,D,NY,1.0)
** Grid north boundary is a theoretical streamline.
GSET(L,L4A,D0,E,1,1.0)
GSET(L,L4B,D0,D1,2,1.5,ARC,2.0000E-01,1,0)
GSET(L,L4C,D1,D2,2,-1.05,ARC,7.9020E-01,9.8310E-01,0)
GSET(L,L4D,D2,D3,2,1.0,ARC,1.2542E+00,9.3040E-01,0)
GSET(L,L4E,D3,D4,2,1.1,ARC,1.8448E+00,8.0400E-01,0)
GSET(L,L4F,D4,D5,2,1.1,ARC,2.5600E+00,5.6980E-01,0)
GSET(L,L4G,D5,D6,1,1.0)
GSET(L,L4H,D6,D,1,1.0)
** Set WEST boundary
GSET(L,L5,E,A,NY,1.0)
** Define frame
GSET(F,F1,A,B,C,-,D,D6.D5.D4.D3.D2.D1.D0,E,-)
** Set grid dimension
GSET(D,NX,NY,1)
** Match frame onto K1
GSET(M,F1,K1,1,NX,1,NY,TRANS)
** Copy K1 to K2
GSET(C,K2,F,K1,+,0,0,1)
GROUP 7. Variables stored, solved & named
SOLVE(P1,U1,V1)
GROUP 9. Properties of the medium (or media)
** Total pressure, inlet velocity and inlet density (with
total density taken to be 1.0)...
PT=1.0E5;UIN=(1.4*PT/1.2)**0.5; RHOIN=1.0/1.57744
** The isentropic gas law is activated which is valid for
expanding flow...
RHO1=COMPRESS;PRESS0=0.0; RHO1A=PT**(-1.0/1.4); RHO1B=1.0/1.4
ENUL=1.E-10
GROUP 11. Initialization of variable or porosity fields
FIINIT(U1)=UIN;FIINIT(P1)=PT*0.5
GROUP 13. Boundary conditions and special sources
** Uniform inflow at Mach 1.0 is prescribed at the inlet plane
INLET(INLET,WEST,1,1,1,NY,1,1,1,1)
VALUE(INLET,P1,RHOIN*UIN)
VALUE(INLET,U1,UIN)
** Constant pressure boundary condition is prescribed at the exit
PATCH(OUTLET,CELL,NX,NX,1,NY,1,1,1,1)
COEF=1000.;PS=PT/7.87329-RHOIN*UIN/(NY*COEF)
COVAL(OUTLET,P1,COEF,PS)
GROUP 15. Termination of sweeps
LSWEEP=100
GROUP 17. Under-relaxation devices
RELAX(U1,FALSDT,0.2/UIN); RELAX(V1,FALSDT,0.2/UIN)
GROUP 22. Spot-value print-out
IYMON=3
GROUP 23. Field print-out and plot control
PATCH(MAP,CONTUR,1,NX,1,NY,1,1,1,1)
PLOT(MAP,P1,0.0,20.0)
TSTSWP=-1