The VULCAN code provides seven methods that can be used to initialize the flow within the computational domain.

The ordering of each initialization option is as follows during the initialization process:

1) The propagations are first performed depending on the REGION they belong to.
2) The non-BLEND propagations are then performed depending on their IN-ORDER number.
3) The BLENDed propagations are then performed after all the non-BLEND propagation boundary conditions and all the CUT and PATCH propagation conditions are performed in each REGION.

The hydrogen/air mixing example presented in figure 1 can be used to illustrate how the methods described in table XI. can be used to initialize a multi-block computational domain. Choosing to solve the flow in the computational domain with a spatially elliptic algorithm and as a single region containing all 3 blocks means that the flow in all the blocks must be initialized in a sensible and self consistent manner.

Figure 9. Sample computational domain for initialization

The default initialization (method 1 in table XI.) used by VULCAN would initialize the flow to the reference conditions. A sample input file given below would result in all 3 blocks being initialized to Mach 1.9336062 flow of a gas mixture containing 76.86 percent N2 and 23.14 percent O2 by mass. However, this is a poor initialization in block 2 and the upper half of block 3 given that figure 9 shows block 2 has a supersonic flow of pure H2 as its I-MIN boundary condition. If this initialization were used the code must convect the H2 through blocks 2 and 3. The large density gradients present during the convection process due to the large difference in the molecular weight of the two gas mixtures would require a low initial CFL no. to keep the code stable.

Table XII. Sample input file for flow initialization

$*********************************************************************$ $*********************************************************************$ $**************** Sample VULCAN Input File ***************************$ $*********************************************************************$ $*********************************************************************$ $**************** Beginning of general control data ******************$ $---------------- Geometric Model type -------------------------------$ TWOD                        (twod, axisym, threed) $---------------- Grid File Data -------------------------------------$ GRID FORMAT             3.0 (1=sb fmt, 2=sb unf, 3=mb fmt, 4=mb unf) GRID                    0.0 (0=plot3d->3D ; plot2d->2D/axi, 1=plot3d->all) spltr_2d_cmb.grd GRID SCALING FACTOR     1.0 (mult. factor to convert grid units to meters) $---------------- Restart File Data ----------------------------------$ RESTART OUT            50.0 (output restart file name to follow) spltr_2d_cmb.rsrt $---------------- Post-Processing Control ----------------------------$ PLOT ON                 3.0 (1=sb fmt, 2=sb unf, 3=mb fmt, 4=mb unf) PLOT NODES                  (create PLOT3D files using data averaged to nodes) PLOT FUNCTION           6.0 (create PLOT3D function file with these variables)   DENSITY   VELOCITY   PRESSURE   TEMPERATURE   MACH NO.   MASS FRACTION   5   H2   H2O   N2   OH   O2   $---------------- Equation Set, Gas, and Reaction Model Control ------$ GAS/THERMO MODEL        1.0 (0=calorically perfect, 1=thermally perfect) CHEMISTRY MODEL         1.0 (0=frozen, 1=finite rate, 2=n/a) IMPLICIT CHEMISTRY      0.0 (0 or 1=analytical jacobian, 2=numerical jacobian) GLOBAL VISCOUS          0.0 (solve Navier-Stokes equation set) VISCOSITY MODEL         1.0 (n/a=power law, 1=Sutherlands law) CONDUCTIVITY MODEL      0.0 (0=Prandtl no., 1=Wassilej's law) UNIV. GAS CONST.        8314.34 NO. OF CHEMICAL SPECIES     7.0 ~your_login/Vulcan/Ver_6.1.0/Data_base/gas_mod.Lewis_1     N2    O    OH      O2    H    H2    H2O  0.7686  0.0  0.0   0.2314  0.0  0.0    0.0 NO. OF CHEMICAL REACTIONS   7.0 ~your_login/Vulcan/Ver_6.1.0/Data_base/reac_mod.Larc_7x7 $---------------- Reference Condition Data ---------------------------$ NONDIM                  1.0 (1=static conditions, 2=total conditions) MACH NO.                1.93e+00 STATIC TEMP.            1.00e+03 STATIC RHO              3.52e-01 LAM. PRANDTL NO.        0.72 LAM. SCHMIDT NO.        0.22 TURB. PRANDTL NO.       0.90 TURB. SCHMIDT NO.       0.90 $---------------- Turbulence Model Data ------------------------------$ TURB. MODEL                   MENTER   TURB. INTENSITY       0.01   TURB. VISC. RATIO     0.10   BOUSSINESQ REY. STRESS      0.0   NO 2/3 RHOK IN REY. STRESS  0.0 $---------------- Runge-Kutta Scheme Control -------------------------$ NSTAGE                  3.0 (no. of Runge-Kutta stages)  0.33333333333333 0.5 1.0 RESMTYP                 0.0 (res. smoothing: 0=none, 1=fix coef. 2=var coef.) $---------------- Boundary and Cut Control ---------------------------$ BLOCKS                  3.0 (no. of blocks) FLOWBCS                 9.0 (no. of boundary conditions) CUTBCS                  2.0 (no. of C(0) cut connectivity conditions) BLOCK CONFIG.           1.0 (no. of lines of block configuration input) BLK I-STRESS J-STRESS K-STRESS TURB  REAC  PLOT  REGION 0       T        T       N        Y    Y    Y       1 '$********* Region 1 Control ******************************************$' 0.0 SOLVER  HLLC  KAPPA  LIMITER   LIM-COEF.   ENTROPY [U]  ENTROPY [U+a]   E/A         3 3 3  2  2  2  2.0 2.0 2.0  0.0 0.0 0.0   0.0 0.0 0.0 FMG-LVLS  NITSCG1  NITSCG2  NITSFG  1ST-ORDER  REL-RES  ABS-RES    3         25       25      200       -2       -4.0     -5.0 MG-CYCLE  COARSE GRIDS  DQ-SMOOTH  DQ-COEF.  DAMP-MEAN  DAMP-TURB      V           2          0.1       0.25       0.5        0.5 TURB CONVECTION  DT RATIO  NON-EQUIL  POINT-IMP  COMP MODEL  CG WALL BC       2ND           1.0       25.0        Y           Y          STW SCHEME TIME STEP IT-STATS CFL-MIN ADP-CFL #CFL-VAL VISC-DT IMP-BC REG-REST   DAF    GLOBAL     10      0.5      Y        3       Y       N      N    1       50      500   0.5     2.5      5.0 '!******************* End of general control data *********************!' 0.0 BC  NAME BLK  FACE  PLACE DIR1 BEG  END  DIR2 BEG  END IN-ORDER  BC TYPE AIR-IN    1     I    MIN   J   MIN  MAX   K   MIN  MAX     1     FIXED  N2   O   OH  O2   H   H2 H2O   Rho  U-Vel V-Vel W-Vel    Pres   T-int Mut/Mu 0.77 0.0 0.0 0.23 0.0 0.0 0.0 0.3516 1.2E3   0.0   0.0 -101325.0  0.01   1.0 BOTTOM    1     J    MIN   I   MIN  MAX   K   MIN  MAX     0     EXTRAP WALL      1     J    MAX   I   MIN  MAX   K   MIN  MAX     0     AWALLM H2-IN     2     I    MIN   J   MIN  MAX   K   MIN  MAX     2     FIXED  N2   O   OH  O2   H   H2 H2O   Rho  U-Vel V-Vel W-Vel   Temp  T-int Mut/Mu 0.0  0.0 0.0 0.0  0.0 1.0 0.0 0.0246 3.8E3   0.0   0.0  1000.0  0.01   1.0 WALL      2     J    MIN   I   MIN  MAX   K   MIN  MAX     0     AWALLM TOP       2     J    MAX   I   MIN  MAX   K   MIN  MAX     0     EXTRAP PROFILE   3     I    MAX   J   MIN  MAX   K   MIN  MAX     0     EXTRAP difflame.prof BOTTOM    3     J    MIN   I   MIN  MAX   K   MIN  MAX     0     EXTRAP TOP       3     J    MAX   I   MIN  MAX   K   MIN  MAX     0     EXTRAP CUT NAME BLK  FACE  PLACE DIR1 BEG  END  DIR2 BEG  END IN-ORDER 1-3       1     I    MAX   J   MIN  MAX   K   MIN  MAX     0 1-3       3     I    MIN   J   MIN  MAX   K   MIN  MAX     3 2-3       1     I    MAX   J   MIN  MAX   K   MIN  MAX     0 2-3       3     I    MIN   J    65  MAX   K   MIN  MAX     4

This sample case shows how the options in table XI can be used to address the initialization problem. In the boundary condition section of the sample input file, the IN-ORDER column is highlighted. IN-ORDER stands for INitialization ORDER and the integers in the column serve a two-fold purpose. If the integer is zero then the boundary condition will NOT be used during initialization. However, if the integer is greater than zero it WILL be used during initialization. The integer also indicates the relative order the boundary condition, CUT, or PATCH will be used during the initialization process. By relative it is meant that consecutive integers (i.e. 1,2,3,4,...) do not have to be used. Rather the user can use non-consecutive integers with the same relative order and achieve the same result (i.e. 1,3,5,8,...). This allows boundary conditions to be removed without having to renumber the initialization integers. Ignoring the 'BLEND' initialization for the moment the example input file would result in the following initialization sequence.

1) The flow conditions in the I-MIN boundary ghost cells set by the 'AIR IN'... 'FIXED' boundary condition will be propagated from the I-MIN to the I-MAX boundary of block 1.
2) The flow conditions in the I-MIN boundary ghost cells set by the 'H2  IN'... 'FIXED' boundary condition will be propagated from the I-MIN to the I-MAX boundary of block 2.
3) The flow conditions in the I-MIN boundary ghost cells from J=1 to J=65 set by side 2 of 'CUT1-3' (which connects block 3 to block 1) will be propagated from the I-MIN to the I-MAX boundary of block 3.
4) The flow conditions in the I-MIN boundary ghost cells from J=65 to J=J-MAX set by side 2 of 'CUT2-3' (which connects block 3 to block 2) will be propagated from the I-MIN to the I-MAX boundary of block 3.

This initialization process will result in the following initial flow field, providing a much better initial guess for the spatially elliptic flow solver. As shown in figure 10, the N2/O2 mixture and the hydrogen have now been propagated through the entire computational domain.

Figure 10. Sample flow field initialization