[blais.bruno]

Hello everyone,

I am currently trying to simulate supersonic and transonic nozzle (simple, like de Laval nozzle) using SU2. My final goal is to simulate the nozzle as well as the nozzle exit and the gas impacting a subtrate. The idea is to obtain the diamond shock profiles that are formed at the exit.
I have had a great degree of success simulation simple nozzle with inlet and outlet boundary conditions and I verified SU2 using the simple CD nozzle from Nasa (https://www.grc.nasa.gov/WWW/wind/valid/cdv/cdv.html). Picture one shows the results for the sonic case (Ma Vs X) with a shock within the nozzle. This part I am super happy with.

My issue comes when I try to simulate the nozzle with the outside domain. For example Figure 2. This case is also axi-symmetric. The thing, I am not sure of what boundary conditions I should put on the air (top, right and left over the nozzle). Right now I use outlet BC, but this leads to divergence and my simulation explodes. I have tried without multigrid and at low CFL (0.5) and I have tried near-field and far-field BCs, but I am afraid I do not really understand enough the meaning of this type of boundary conditions and when they should be applied (I am not that used to compressible CFD). I used to do similar simulations using OpenFOAM, then I would use non-reflecting boundary conditions. I see similar BC exist in SU2 as I saw in the general config file :

  % Non Reflecting boundary conditions marker(s) (NONE = no marker)
% Format: (marker, data kind flag, list of data)
MARKER_NRBC= ( AIRLIBRE )

but I am afraid I do not know how to use them (what is data kind flag? what is the list of data I should put?

Anyway, so my core question are :
- Are such simulations doable in SU2 (with the outside region of the nozzle)
- If so, what type of boundary condition should I apply on the air? Should I extend my domain or my mesh? Is there something I should be really careful about?

If you feel you can give me a hand, I can also share the full case with the cgns mesh and the .cfg input file by e-mail.
Thanks!

EDIT
So using RIEMANN boundary conditions (with MARKER_RIEMANN= ( AIRLIBRE, STATIC_PRESSURE, 100000.0, 0.0, 0.0, 0.0, 0.0) ) I have been able to get much better results. Still, I cannot get pure Euler results, I can only get some with RANS Navier-Stokes using Spallart-Allmaras, which, if I recall, is actually a very poor turbulence model for internal flow...

[blais.bruno]

This is the input script : (also joined script as file, rename to .cfg if needed)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                                              %
% SU2 configuration file                                                       %
% Case description: Nozzle flow                                                %
% Author: B. Blais                                                             %
% Institution:                                                                 %
% Date: 2017.05                                                                %
% File Version 4.0.2 "Cardinal"                                                %
%                                                                              %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% ------------- DIRECT, ADJOINT, AND LINEARIZED PROBLEM DEFINITION ------------%
%
% Physical governing equations (EULER, NAVIER_STOKES, NS_PLASMA)
%                               
PHYSICAL_PROBLEM= EULER
%PHYSICAL_PROBLEM= NAVIER_STOKES
%Specify turbulence model (NONE, SA, SA_NEG, SST)
KIND_TURB_MODEL= NONE
%KIND_TURB_MODEL= SST     
%KIND_TURB_MODEL= SA     
%
% Mathematical problem (DIRECT, CONTINUOUS_ADJOINT)
MATH_PROBLEM= DIRECT
%
% Restart solution (NO, YES)
RESTART_SOL= NO

% Regime type (COMPRESSIBLE, INCOMPRESSIBLE)
REGIME_TYPE= COMPRESSIBLE

% -------------------- COMPRESSIBLE FREE-STREAM DEFINITION --------------------%
%
% Mach number (non-dimensional, based on the free-stream values)
MACH_NUMBER= 0.2
%
% Angle of attack (degrees, only for compressible flows)
AOA= 0.0
%
% Side-slip angle (degrees, only for compressible flows)
SIDESLIP_ANGLE= 0.0
%
% Free-stream pressure (101325.0 N/m^2 by default)  
FREESTREAM_PRESSURE= 100000.0
%
% Free-stream temperature (288.15 K by default)
FREESTREAM_TEMPERATURE= 288.15

% Init option to choose between Reynolds (default) or thermodynamics quantities
% for initializing the solution (REYNOLDS, TD_CONDITIONS)
INIT_OPTION= TD_CONDITIONS
%
% Free-stream option to choose between density and temperature (default) for
% initializing the solution (TEMPERATURE_FS, DENSITY_FS)
FREESTREAM_OPTION= TEMPERATURE_FS

% -------------------- BOUNDARY CONDITION DEFINITION --------------------------%
%
% Euler wall boundary marker(s) (NONE = no marker)
MARKER_EULER= ( METAL )
%MARKER_EULER= ( METAL, SUBSTRATE )
%MARKER_EULER= ( METAL, SUBSTRATE, SYMETRIE )

% Internal boundary marker(s) e.g. no boundary condition (NONE = no marker)
MARKER_INTERNAL= ( EFFACER )

% Symmetry boundary marker(s) (NONE = no marker)
MARKER_SYM= ( SYMETRIE)

% Navier-Stokes (no-slip), isothermal wall marker(s) (NONE = no marker)
% Format: ( marker name, constant wall temperature (K), ... )
%MARKER_ISOTHERMAL= ( METAL, 288.15, SUBSTRATE, 288.15  )

% Navier-Stokes (no-slip), constant heat flux wall  marker(s) (NONE = no marker)
% Format: ( marker name, constant heat flux (J/m^2), ... )
%MARKER_HEATFLUX= ( METAL, 0, SUBSTRATE, 0 )

%
% Inlet boundary marker(s) (NONE = no marker) 
% Format: ( inlet marker, total temperature, total pressure, flow_direction_x, 
%           flow_direction_y, flow_direction_z, ... ) where flow_direction is
%           a unit vector.
% Default: Mach ~ 0.1
%MARKER_INLET= ( inlet, 288.6, 102010.0, 1.0, 0.0, 0.0 )
MARKER_INLET= ( ENTREE, 788.15, 1000000.0, 1.0, 0.0, 0.0 )
%
% Outlet boundary marker(s) (NONE = no marker)
% Format: ( outlet marker, back pressure (static), ... )
%MARKER_OUTLET= ( outlet, 101300.0 )
MARKER_OUTLET= ( AIRLIBRE, 100000, SUBSTRATE, 100000 )
%MARKER_OUTLET= ( outlet, 16000 )

% Near-Field boundary marker(s) (NONE = no marker)
%MARKER_NEARFIELD= ( AIRLIBRE )

% Far-field boundary marker(s) (NONE = no marker)
%MARKER_FAR= ( AIR_LIBRE )

% Non Reflecting boundary conditions marker(s) (NONE = no marker)
% Format: (marker, data kind flag, list of data)
%MARKER_NRBC= ( AIRLIBRE )

% ------------- COMMON PARAMETERS DEFINING THE NUMERICAL METHOD ---------------%
%
% Numerical method for spatial gradients (GREEN_GAUSS, WEIGHTED_LEAST_SQUARES)
NUM_METHOD_GRAD= GREEN_GAUSS
%
% Courant-Friedrichs-Lewy condition of the finest grid
CFL_NUMBER= 6.0
%
% Adaptive CFL number (NO, YES)
CFL_ADAPT= NO
%
% Parameters of the adaptive CFL number (factor down, factor up, CFL min value,
%                                        CFL max value )
CFL_ADAPT_PARAM= ( 1.5, 0.5, 0.1, 1.0 )
%
% Runge-Kutta alpha coefficients
RK_ALPHA_COEFF= ( 0.66667, 0.66667, 1.000000 )
%
% Number of total iterations
EXT_ITER= 10000000

% ------------------------ LINEAR SOLVER DEFINITION ---------------------------%
%
% Linear solver for implicit formulations (BCGSTAB, FGMRES)
%LINEAR_SOLVER= BCGSTAB
LINEAR_SOLVER= FGMRES
%
% Preconditioner of the Krylov linear solver (JACOBI, LINELET, LU_SGS)
LINEAR_SOLVER_PREC= LU_SGS
%
% Minimum error of the linear solver for implicit formulations
LINEAR_SOLVER_ERROR= 1E-4
%
% Max number of iterations of the linear solver for the implicit formulation
LINEAR_SOLVER_ITER= 50

% -------------------------- MULTIGRID PARAMETERS -----------------------------%
%
% Multi-Grid Levels (0 = no multi-grid)
MGLEVEL= 0
%
% Multi-grid cycle (V_CYCLE, W_CYCLE, FULLMG_CYCLE)
MGCYCLE= V_CYCLE
%
% Multi-grid pre-smoothing level
MG_PRE_SMOOTH= ( 1, 2, 3, 3 )
%
% Multi-grid post-smoothing level
MG_POST_SMOOTH= ( 0, 0, 0, 0 )
%
% Jacobi implicit smoothing of the correction
MG_CORRECTION_SMOOTH= ( 0, 0, 0, 0 )
%
% Damping factor for the residual restriction
MG_DAMP_RESTRICTION= 0.9
%
% Damping factor for the correction prolongation
MG_DAMP_PROLONGATION= 0.95

% -------------------- FLOW NUMERICAL METHOD DEFINITION -----------------------%
%
% Convective numerical method (JST, LAX-FRIEDRICH, CUSP, ROE, AUSM, HLLC,
%                              TURKEL_PREC, MSW)
CONV_NUM_METHOD_FLOW= ROE
%
% Spatial numerical order integration (1ST_ORDER, 2ND_ORDER, 2ND_ORDER_LIMITER)
%
%SPATIAL_ORDER_FLOW= 1ST_ORDER
SPATIAL_ORDER_FLOW= 2ND_ORDER_LIMITER
%
% Slope limiter (VENKATAKRISHNAN, MINMOD)
SLOPE_LIMITER_FLOW= VENKATAKRISHNAN
%
% Coefficient for the limiter (smooth regions)
LIMITER_COEFF= 0.3
%
% 1st, 2nd and 4th order artificial dissipation coefficients
AD_COEFF_FLOW= ( 0.15, 0.5, 0.02 )
%
% Time discretization (RUNGE-KUTTA_EXPLICIT, EULER_IMPLICIT, EULER_EXPLICIT)
TIME_DISCRE_FLOW= EULER_IMPLICIT

% Relaxation coefficient
RELAXATION_FACTOR_FLOW= 0.95

% -------------------- TURBULENT NUMERICAL METHOD DEFINITION ------------------%
%
% Convective numerical method (SCALAR_UPWIND)
CONV_NUM_METHOD_TURB= SCALAR_UPWIND
%
% Spatial numerical order integration (1ST_ORDER, 2ND_ORDER, 2ND_ORDER_LIMITER)
SPATIAL_ORDER_TURB= 1ST_ORDER
%
% Slope limiter (VENKATAKRISHNAN)
SLOPE_LIMITER_TURB= VENKATAKRISHNAN
%
% Viscous limiter (NO, YES)
VISCOUS_LIMITER_TURB= YES
%
% Time discretization (EULER_IMPLICIT)
TIME_DISCRE_TURB= EULER_IMPLICIT
%
% Reduction factor of the CFL coefficient in the turbulence problem
CFL_REDUCTION_TURB= 1.0
%
% Relaxation coefficient
RELAXATION_FACTOR_TURB= 0.95

% --------------------------- CONVERGENCE PARAMETERS --------------------------%
%
% Convergence criteria (CAUCHY, RESIDUAL)
%
CONV_CRITERIA= RESIDUAL
%
% Residual reduction (order of magnitude with respect to the initial value)
RESIDUAL_REDUCTION= 3
%
% Min value of the residual (log10 of the residual)
RESIDUAL_MINVAL= -7
%
% Start convergence criteria at iteration number
STARTCONV_ITER= 100
%
% Number of elements to apply the criteria
CAUCHY_ELEMS= 100
%
% Epsilon to control the series convergence
CAUCHY_EPS= 1E-10

% ------------------------- INPUT/OUTPUT INFORMATION --------------------------%
%
% Mesh input file
MESH_FILENAME= nozzleMeshExtMax2.cgns
%
% Mesh input file format (SU2, CGNS, NETCDF_ASCII)
MESH_FORMAT= CGNS
%
% Mesh output file
MESH_OUT_FILENAME= mesh_out.su2
%
% Restart flow input file
SOLUTION_FLOW_FILENAME= restart_flow.dat
%
% Restart adjoint input file
SOLUTION_ADJ_FILENAME= solution_adj.dat
%
% Output file format (PARAVIEW, TECPLOT, STL)
OUTPUT_FORMAT= PARAVIEW
%
% Output file convergence history (w/o extension) 
CONV_FILENAME= history
%
% Output file restart flow
RESTART_FLOW_FILENAME= restart_flow.dat
%
%
% Output file flow (w/o extension) variables
VOLUME_FLOW_FILENAME= flow
%
% Writing solution file frequency
WRT_SOL_FREQ= 250
%
% Writing convergence history frequency
WRT_CON_FREQ= 10


%----------------------------------------------------------
AXISYMMETRIC= YES

[amitavamandal]

I am new to CFD. Can you please guide regarding grid fineness near nozzle throat and wall for viscous flow simulation of a CD nozzle.

[PENGGEGE777]

Hi sir, do you have any idea about the boundary condition? is so, could you please share it here, thank you so much.

[hconel]

I'm also interested in this kind of simulation. So far, I've tried:

• MARKER_RIEMANN and MARKER_OUTLET types
• Putting the farfield boundary far away from the nozzle, extending 100 times the nozzle length, in different configurations as such:
  

but none of these setups converged. I've also imposed sensible inlet conditions based on theoretical solutions. Any ideas?