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Error with Peng-Robinson EoS

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Old   January 24, 2022, 05:03
Default Error with Peng-Robinson EoS
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Nicola Fontana
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Hi everyone. I'm simulating a stage of a turbine to make a comparison between air and carbon dioxide as working fluid. When I run the simulation with air everything is ok and the program reach the last iteration and end with "Exit succes".
For what regards carbon dioxide, I decided to use Peng-Robinson (any suggestions on how to best model carobn dioxide is welcome) and I setted the properties as follows, without changing any other settings:

Code:
% ------------------------------ sCO2 -----------------------------------------%

% Different gas model (STANDARD_AIR, IDEAL_GAS, VW_GAS, PR_GAS)
FLUID_MODEL= PR_GAS

% Ratio of specific heats (1.4 default and the value is hardcoded
%                          for the model STANDARD_AIR)
GAMMA_VALUE= 1.29

% Specific gas constant (287.058 J/kg*K default and this value is hardcoded 
%                        for the model STANDARD_AIR)
GAS_CONSTANT= 188.92

% Critical Temperature (273.15 K by default)
CRITICAL_TEMPERATURE= 304.25

% Critical Pressure (101325.0 N/m^2 by default)
CRITICAL_PRESSURE= 7377300

% Acentri factor (0.035 (air))
ACENTRIC_FACTOR= 0.22394

% --------------------------- VISCOSITY MODEL ---------------------------------%

% Viscosity model (SUTHERLAND, CONSTANT_VISCOSITY).
VISCOSITY_MODEL= CONSTANT_VISCOSITY
%VISCOSITY_MODEL= SUTHERLAND

% Molecular Viscosity that would be constant (1.716E-5 by default)
MU_CONSTANT= 1.3764E-5

% Sutherland Viscosity Ref (1.716E-5 default value for AIR SI)
%MU_REF= 1.376E-5

% Sutherland Temperature Ref (273.15 K default value for AIR SI)
%MU_T_REF= 273.15

% Sutherland constant (110.4 default value for AIR SI)
%SUTHERLAND_CONSTANT= 222

% --------------------------- THERMAL CONDUCTIVITY MODEL ----------------------%

% Conductivity model (CONSTANT_CONDUCTIVITY, CONSTANT_PRANDTL).
CONDUCTIVITY_MODEL= CONSTANT_CONDUCTIVITY

% Molecular Thermal Conductivity that would be constant (0.0257 by default)
THERMAL_CONDUCTIVITY_CONSTANT= 0.028
I commented some option in the viscosity model after discovering that with Peng-Robinson the only option avaiable is CONSTANT_VISCOSITY.
After this change, the program print this message at every step since the first iteration:

Code:
Root must be bracketed for bisection in rtbis
Too many bisections in rtbis
TD consistency not verified in hs call
Changing some option the message about TD consistency disappear, but the other two remains.
With the inelt condition setted, carbon dioxide should be in the supercritical region, could this be the problem, or anyone have any suggestion on why this happens?
The configuration file is the following:

Code:
% SU2 configuration file                                                       %
% Case description: 2D Axial stage                                             %
% Author: N. Fontana                                                           %
% Institution:                                                                 %
% Date: Jan 12th, 2022                                                         %
% File Version 7.2.0 "Blackbird"                                               %
%                                                                              %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Enable multizone mode
MULTIZONE= YES
%
% List of config files
CONFIG_LIST= (zone_1.cfg, zone_2.cfg)
%
% ------------- DIRECT, ADJOINT, AND LINEARIZED PROBLEM DEFINITION ------------%
%
% Physical governing equations (EULER, NAVIER_STOKES,
%                               WAVE_EQUATION, HEAT_EQUATION, LINEAR_ELASTICITY,
%                               POISSON_EQUATION)                         
SOLVER= RANS
%
% Specify turbulent model (NONE, SA, SST)
KIND_TURB_MODEL= SST
%
% Mathematical problem (DIRECT, ADJOINT, LINEARIZED)
MATH_PROBLEM= DIRECT
%
% Restart solution (NO, YES)
RESTART_SOL= NO
%
%
% -------------------- COMPRESSIBLE FREE-STREAM DEFINITION --------------------%
%
% Mach number (non-dimensional, based on the free-stream values)
MACH_NUMBER= 0.3
%
% Angle of attack (degrees, only for compressible flows)
AOA= 0.0
%
% Free-stream pressure (101325.0 N/m^2 by default, only Euler flows)  
FREESTREAM_PRESSURE= 10000000.0
%
% Free-stream temperature (273.15 K by default)
FREESTREAM_TEMPERATURE=  500.0
%
% Free-stream temperature (1.2886 Kg/m3 by default)
FREESTREAM_DENSITY= 2
%
% Free-stream option to choose if you want to use Density (DENSITY_FS) or Temperature (TEMPERATURE_FS) to initialize the solution
FREESTREAM_OPTION= TEMPERATURE_FS
%
% Free-stream Turbulence Intensity
FREESTREAM_TURBULENCEINTENSITY = 0.03
%
% Free-stream Turbulent to Laminar viscosity ratio
FREESTREAM_TURB2LAMVISCRATIO = 100.0
%
%Init option to choose between Reynolds (default) or thermodynamics quantities for initializing the solution (REYNOLDS, TD_CONDITIONS)
INIT_OPTION= TD_CONDITIONS
%
% ---------------------- REFERENCE VALUE DEFINITION ---------------------------%
%
% Reference origin for moment computation
REF_ORIGIN_MOMENT_X = 0.00
REF_ORIGIN_MOMENT_Y = 0.00
REF_ORIGIN_MOMENT_Z = 0.00
%
% Reference length for pitching, rolling, and yawing non-dimensional moment
REF_LENGTH= 1.0
%
% Reference area for force coefficients (0 implies automatic calculation)
REF_AREA= 1.0
%
%
% Flow non-dimensionalization (DIMENSIONAL, FREESTREAM_PRESS_EQ_ONE,
%                              FREESTREAM_VEL_EQ_MACH, FREESTREAM_VEL_EQ_ONE)
REF_DIMENSIONALIZATION= DIMENSIONAL
%
%
%------------------------------------------------------------------------------%
% ------------------------------ sCO2 -----------------------------------------%
%------------------------------------------------------------------------------%

% Different gas model (STANDARD_AIR, IDEAL_GAS, VW_GAS, PR_GAS)
FLUID_MODEL= PR_GAS

% Ratio of specific heats (1.4 default and the value is hardcoded
%                          for the model STANDARD_AIR)
GAMMA_VALUE= 1.29

% Specific gas constant (287.058 J/kg*K default and this value is hardcoded 
%                        for the model STANDARD_AIR)
GAS_CONSTANT= 188.92

% Critical Temperature (273.15 K by default)
CRITICAL_TEMPERATURE= 304.25

% Critical Pressure (101325.0 N/m^2 by default)
CRITICAL_PRESSURE= 7377300

% Acentri factor (0.035 (air))
ACENTRIC_FACTOR= 0.22394

% --------------------------- VISCOSITY MODEL ---------------------------------%

% Viscosity model (SUTHERLAND, CONSTANT_VISCOSITY).
VISCOSITY_MODEL= CONSTANT_VISCOSITY
%VISCOSITY_MODEL= SUTHERLAND

% Molecular Viscosity that would be constant (1.716E-5 by default)
MU_CONSTANT= 1.3764E-5

% Sutherland Viscosity Ref (1.716E-5 default value for AIR SI)
MU_REF= 1.376E-5

% Sutherland Temperature Ref (273.15 K default value for AIR SI)
MU_T_REF= 273.15

% Sutherland constant (110.4 default value for AIR SI)
SUTHERLAND_CONSTANT= 222

% --------------------------- THERMAL CONDUCTIVITY MODEL ----------------------%

% Conductivity model (CONSTANT_CONDUCTIVITY, CONSTANT_PRANDTL).
CONDUCTIVITY_MODEL= CONSTANT_CONDUCTIVITY

% Molecular Thermal Conductivity that would be constant (0.0257 by default)
THERMAL_CONDUCTIVITY_CONSTANT= 0.028
%
% -------------------- BOUNDARY CONDITION DEFINITION --------------------------%
%
% Navier-Stokes wall boundary marker(s) (NONE = no marker)
MARKER_HEATFLUX= ( wall1, 0.0, wall2, 0.0)
%
% Periodic boundary marker(s) (NONE = no marker)
% Format: ( periodic marker, donor marker, rot_cen_x, rot_cen_y, rot_cen_z, rot_angle_x-axis, rot_angle_y-axis, rot_angle_z-axis, translation_x, translation_y, translation_z)
MARKER_PERIODIC= ( periodic1, periodic2, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.04463756775, 0.0, periodic3, periodic4, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.04463756775, 0.0)
%
%
%-------- INFLOW/OUTFLOW BOUNDARY CONDITION SPECIFIC FOR TURBOMACHINERY --------%
%
% Inflow and Outflow markers must be specified, for each blade (zone), following the natural groth of the machine (i.e, from the first blade to the last)
MARKER_TURBOMACHINERY= (inflow, outmix, inmix, outflow)
%
% Mixing-plane interface markers must be specified to activate the transfer of information between zones
MARKER_MIXINGPLANE_INTERFACE= (outmix, inmix)
%
% Giles boundary condition for inflow, outfolw and mixing-plane
% Format inlet:  ( marker, TOTAL_CONDITIONS_PT, Total Pressure , Total Temperature, Flow dir-norm, Flow dir-tang, Flow dir-span, under-relax-avg, under-relax-fourier)
% Format outlet: ( marker, STATIC_PRESSURE, Static Pressure value, -, -, -, -, under-relax-avg, under-relax-fourier)
% Format mixing-plane in and out: ( marker, MIXING_IN or MIXING_OUT, -, -, -, -, -, -, under-relax-avg, under-relax-fourier)
MARKER_GILES= (inflow, TOTAL_CONDITIONS_PT, 22000000, 800, 1.0, 0.0, 0.0,1.0,1.0, outmix, MIXING_OUT, 0.0, 0.0, 0.0, 0.0, 0.0,1.0,1.0, inmix, MIXING_IN, 0.0, 0.0, 0.0, 0.0, 0.0,1.0, 1.0 outflow, STATIC_PRESSURE, 8000000.00, 0.0, 0.0, 0.0, 0.0,1.0,1.0)
%
%YES Non reflectivity activated, NO the Giles BC behaves as a normal 1D characteristic-based BC
SPATIAL_FOURIER= NO
%
%
%---------------------------- TURBOMACHINERY SIMULATION -----------------------------%
%
% Specify kind of architecture (AXIAL, CENTRIPETAL, CENTRIFUGAL, CENTRIPETAL_AXIAL)
TURBOMACHINERY_KIND= AXIAL AXIAL
%
% Specify option for turbulent mixing-plane (YES, NO) default NO
TURBULENT_MIXINGPLANE= YES
%
% Specify ramp option for Outlet pressure (YES, NO) default NO
RAMP_OUTLET_PRESSURE= NO
%
% Parameters of the outlet pressure ramp (starting outlet pressure, updating-iteration-frequency, total number of iteration for the ramp)
RAMP_OUTLET_PRESSURE_COEFF= (140000.0, 10.0, 2000)
%
% Specify Kind of average process for linearizing the Navier-Stokes equation at inflow and outflow BC included mixing-plane
% (ALGEBRAIC, AREA, MASSSFLUX, MIXEDOUT) default AREA 
AVERAGE_PROCESS_KIND= MIXEDOUT
%
% Specify Kind of average process for computing turbomachienry performance parameters
% (ALGEBRAIC, AREA, MASSSFLUX, MIXEDOUT) default AREA
PERFORMANCE_AVERAGE_PROCESS_KIND= MIXEDOUT
%
%Parameters of the Newton method for the MIXEDOUT average algorithm (under relaxation factor, tollerance, max number of iterations) 
MIXEDOUT_COEFF= (1.0, 1.0E-05, 15)
%
% Limit of Mach number below which the mixedout algorithm is substituted with a AREA average algorithm
AVERAGE_MACH_LIMIT= 0.05
%
%
% ------------------------ SURFACES IDENTIFICATION ----------------------------%
%
% Marker(s) of the surface in the surface flow solution file
MARKER_PLOTTING= (wall1, wall2)
%
% ------------- COMMON PARAMETERS DEFINING THE NUMERICAL METHOD ---------------%
%
% Numerical method for spatial gradients (GREEN_GAUSS, WEIGHTED_LEAST_SQUARES)
NUM_METHOD_GRAD= WEIGHTED_LEAST_SQUARES
%
% Courant-Friedrichs-Lewy condition of the finest grid
CFL_NUMBER= 10.0
%
% 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= ( 1.3, 1.2, 1.0, 10.0)
%

% ------------------------ LINEAR SOLVER DEFINITION ---------------------------%
%
% Linear solver or smoother for implicit formulations (BCGSTAB, FGMRES, SMOOTHER)
LINEAR_SOLVER= FGMRES
%
% Preconditioner of the Krylov linear solver (ILU, LU_SGS, LINELET, JACOBI)
LINEAR_SOLVER_PREC= LU_SGS
%
% Min error of the linear solver for the implicit formulation
LINEAR_SOLVER_ERROR= 1E-4
%
% Max number of iterations of the linear solver for the implicit formulation
LINEAR_SOLVER_ITER= 10
%
%
% -------------------------- MULTIGRID PARAMETERS -----------------------------%
%
% ----------- NOT WORKING WITH PERIODIC BOUNDARY CONDITIONS !!!!! --------------%
%
%
% ----------------------- SLOPE LIMITER DEFINITION ----------------------------%
%
% Coefficient for the limiter
VENKAT_LIMITER_COEFF= 0.05
%
% Freeze the value of the limiter after a number of iterations
LIMITER_ITER= 999999
%
%
% -------------------- 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)
MUSCL_FLOW= YES
%
% Slope limiter (VENKATAKRISHNAN, VAN_ALBADA_EDGE)
SLOPE_LIMITER_FLOW= VAN_ALBADA_EDGE
%
% Entropy fix coefficient (0.0 implies no entropy fixing, 1.0 implies scalar artificial dissipation, 0.001 default)
ENTROPY_FIX_COEFF= 0.01
%
% 2nd and 4th order artificial dissipation coefficients
JST_SENSOR_COEFF= ( 0.5, 0.02 )
%
% Time discretization (RUNGE-KUTTA_EXPLICIT, EULER_IMPLICIT, EULER_EXPLICIT)
TIME_DISCRE_FLOW= EULER_IMPLICIT

% -------------------- TURBULENT NUMERICAL METHOD DEFINITION ------------------%
%
% Convective numerical method (SCALAR_UPWIND)
CONV_NUM_METHOD_TURB= SCALAR_UPWIND
%
% Monotonic Upwind Scheme for Conservation Laws (TVD) in the turbulence equations.
%           Required for 2nd order upwind schemes (NO, YES)
MUSCL_TURB= NO
%
% Slope limiter (VENKATAKRISHNAN, MINMOD)
SLOPE_LIMITER_TURB= VENKATAKRISHNAN
%
% Time discretization (EULER_IMPLICIT)
TIME_DISCRE_TURB= EULER_IMPLICIT
%
% Reduction factor of the CFL coefficient in the turbulence problem
CFL_REDUCTION_TURB= 1.0
%
%
% --------------------------- CONVERGENCE PARAMETERS --------------------------%

% Number of total iterations
OUTER_ITER= 6000

% Min value of the residual (log10 of the residual)
CONV_RESIDUAL_MINVAL= -12

% Start convergence criteria at iteration number
CONV_STARTITER= 10

% Number of elements to apply the criteria
CONV_CAUCHY_ELEMS= 100

% Epsilon to control the series convergence
CONV_CAUCHY_EPS= 1E-6



% ------------------------- INPUT/OUTPUT INFORMATION --------------------------%

% Mesh input file
MESH_FILENAME= mesh_axial_stage_2d_turb.su2

% Mesh input file format (SU2, CGNS, NETCDF_ASCII)
MESH_FORMAT= SU2

% Mesh output file
MESH_OUT_FILENAME= meshout.su2

% Restart flow input file
SOLUTION_FILENAME= solution_flow.dat

% Restart adjoint input file
SOLUTION_ADJ_FILENAME= solution_adj.dat

% Output file format (PARAVIEW, TECPLOT, STL)
TABULAR_FORMAT= CSV

% Output file convergence history (w/o extension) 
CONV_FILENAME= history

% Output file restart flow
RESTART_FILENAME= restart_flow.dat

% Output file restart adjoint
RESTART_ADJ_FILENAME= restart_adj.dat

% Output file flow (w/o extension) variables
VOLUME_FILENAME= multizone_AIR_changed

% Output file adjoint (w/o extension) variables
VOLUME_ADJ_FILENAME= adjoint

% Output objective function gradient (using continuous adjoint)
GRAD_OBJFUNC_FILENAME= of_grad.dat

% Output file surface flow coefficient (w/o extension)
SURFACE_FILENAME= surface_flow

% Output file surface adjoint coefficient (w/o extension)
SURFACE_ADJ_FILENAME= surface_adjoint

% Writing solution file frequency
OUTPUT_WRT_FREQ= 1000
For completeness, I first run some simulations with the same geometry and same fluid model (CO2), with inlet condition much lower (Tin=305K, Pin=1.96bar, Pout=1 bar) and with this settings everything is ok and the program exit with succes.

Thank you in advance,
Nicola
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