Note
Go to the end to download the full example code.
Modeling Species Transport and Gaseous Combustion#
Introduction#
This tutorial examines the mixing of chemical species and the combustion of a gaseous fuel.
A cylindrical combustor burning methane (\(CH_4\)) in air is studied using the eddy-dissipation model in PyFluent.
This tutorial demonstrates how to do the following:
Enable physical models, select material properties, and define boundary conditions for a turbulent flow with chemical species mixing and reaction.
Initiate and solve the combustion simulation using the pressure-based solver.
Examine the reacting flow results using graphics.
Problem Description#
The cylindrical combustor considered in this tutorial is shown in the following figure. The flame considered is a turbulent diffusion flame. A small nozzle in the center of the combustor introduces methane at 80 m/s. Ambient air enters the combustor coaxially at 0.5 m/s. The overall equivalence ratio is approximately 0.76 (approximately 28% excess air). The high-speed methane jet initially expands with little interference from the outer wall, and entrains and mixes with the low-speed air. The Reynolds number based on the methane jet diameter is approximately \(5.7 × 10^3\).
Combustion of Methane Gas in a Turbulent Diffusion Flame Furnace#
Background#
In this tutorial, we will use the generalized eddy-dissipation model to analyze the methane-air combustion system. The combustion will be modeled using a global one-step reaction mechanism, assuming complete conversion of the fuel to \(CO_2\) and \(H_2O\). The reaction equation is
\[CH_4 + 2H_2O → CO_2 + 4H_2\]
This reaction will be defined in terms of stoichiometric coefficients, formation enthalpies, and parameters that control the reaction rate. The reaction rate will be determined assuming that turbulent mixing is the rate-limiting process, with the turbulence-chemistry interaction modeled using the eddy-dissipation model.
Setup and Solution#
Preparation#
Launch Fluent 2D in solution mode and print Fluent version.
import ansys.fluent.core as pyfluent
solver = pyfluent.launch_fluent(dimension=2)
print(solver.get_fluent_version())
Fluent version 2025 R1
Import some direct settings classes which will be used in the following sections. These classes allow straightforward access to various settings without the need to navigate through the settings hierarchy.
from pathlib import Path # noqa: E402
from ansys.fluent.core import ( # noqa: E402
Contour,
Energy,
Mesh,
MixtureMaterial,
PressureOutlet,
Species,
Vector,
VelocityInlet,
Viscous,
WallBoundary,
)
from ansys.fluent.core.examples import download_file # noqa: E402
Mesh#
Download the mesh file and read it into the Fluent session.
Reading "gascomb.msh"...
Buffering for file scan...
1705 nodes.
1615 quadrilateral cells, zone 1.
3141 2D interior faces, zone 4.
58 2D symmetry faces, zone 5.
9 2D wall faces, zone 2.
5 2D velocity-inlet faces, zone 6.
58 2D wall faces, zone 7.
20 2D velocity-inlet faces, zone 8.
28 2D pressure-outlet faces, zone 9.
Building...
mesh
materials,
interface,
domains,
zones,
pressure-outlet-9
velocity-inlet-8
wall-7
velocity-inlet-6
wall-2
symmetry-5
interior-4
fluid-1
parallel,
Done.
General Settings#
Check the mesh.
Fluent will perform various checks on the mesh and will report the progress in the console. Ensure that the reported minimum volume reported is a positive number.
solver.settings.mesh.check()
Domain Extents:
x-coordinate: min (m) = 0.000000e+00, max (m) = 1.800000e+03
y-coordinate: min (m) = 0.000000e+00, max (m) = 2.250000e+02
Volume statistics:
minimum volume (m3): 3.333333e+00
maximum volume (m3): 2.498387e+03
total volume (m3): 4.049600e+05
Face area statistics:
minimum face area (m2): 1.000000e+00
maximum face area (m2): 1.096768e+02
Checking mesh............................
Done.
Scale the mesh and check it again.
Since this mesh was created in units of millimeters, we will need to scale the mesh into meters.
Note
We should check the mesh after we manipulate it (scale, convert to polyhedra, merge, separate, fuse, add zones, or smooth and swap). This will ensure that the quality of the mesh has not been compromised.
solver.settings.mesh.scale(x_scale=0.001, y_scale=0.001)
solver.settings.mesh.check()
Domain Extents:
x-coordinate: min (m) = 0.000000e+00, max (m) = 1.800000e+00
y-coordinate: min (m) = 0.000000e+00, max (m) = 2.250000e-01
Volume statistics:
minimum volume (m3): 3.333333e-06
maximum volume (m3): 2.498387e-03
total volume (m3): 4.049600e-01
Face area statistics:
minimum face area (m2): 1.000000e-03
maximum face area (m2): 1.096768e-01
Checking mesh............................
Done.
Display the mesh in Fluent and save the image to a file to examine locally.
mesh = Mesh(solver, new_instance_name="mesh")
mesh.surfaces_list = mesh.surfaces_list.allowed_values()
mesh.display()
graphics = solver.settings.results.graphics
graphics.views.auto_scale()
if graphics.picture.use_window_resolution.is_active():
graphics.picture.use_window_resolution = False
graphics.picture.x_resolution = 3840
graphics.picture.y_resolution = 2880
graphics.picture.save_picture(file_name="mesh.png")
The Quadrilateral Mesh for the Combustor Model#
Inspect the available options for the two-dimensional space setting and set it to axisymmetric.
solver.settings.setup.general.solver.two_dim_space.allowed_values()
['swirl', 'axisymmetric', 'planar']
solver.settings.setup.general.solver.two_dim_space = "axisymmetric"
Models#
Enable heat transfer by enabling the energy model.
Energy(solver).enabled = True
Inspect the default settings for the k-ω SST viscous model.
Viscous(solver).print_state()
model : k-omega
k_omega_model : sst
k_omega_options :
kw_low_re_correction : False
near_wall_treatment :
wall_omega_treatment : correlation
transition_module : none
options :
viscous_heating : False
production_kato_launder_enabled : False
production_limiter :
enabled : True
clip_factor : 10.0
turbulence_expert :
turb_non_newtonian : False
thermal_p_function : True
restore_sst_v61 : False
user_defined :
turb_visc_func : none
energy_prandtl : none
wall_prandtl : none
Inspect the available options for the species model and set it to species transport.
species = Species(solver)
species.model.option.allowed_values()
['off', 'species-transport', 'non-premixed-combustion', 'premixed-combustion', 'partially-premixed-combustion', 'pdf-transport']
species.model.option = "species-transport"
Adjusting the following setting:
Density explicit underrelaxation factor: from: 1 to: 0.25
Inspect the species model settings.
species.print_state()
model :
option : species-transport
material : mixture-template
number_vol_spec : 3
options :
inlet_diffusion : False
thermal_diffusion : False
diffusion_energy_source : True
multi_component_diffusion : False
save_gradients : False
species_transport_expert : False
reactions :
enable_volumetric_reactions : False
species_transport_expert_options :
linearize_convection_source : False
linearize_diffusion_source : False
blending : False
Enable volumetric reactions.
species.reactions.enable_volumetric_reactions = True
Set the material to methane-air.
Note
The available material list contains the set of chemical mixtures that exist in the Ansys Fluent database. We can select one of the predefined mixtures to access a complete description of the reacting system. The chemical species in the system and their physical and thermodynamic properties are defined by our selection of the mixture material. We can alter the mixture material selection or modify the mixture material properties using the material settings (see Materials).
species.model.material = "methane-air"
There are 5 species in the selected mixture
Set the turbulence-chemistry interaction model to eddy-dissipation.
The eddy-dissipation model computes the rate of reaction under the assumption that chemical kinetics are fast compared to the rate at which reactants are mixed by turbulent fluctuations (eddies).
species.turb_chem_interaction_model = "eddy-dissipation"
Material methane-air:
Changing method of "Reaction" to "eddy-dissipation".
Material mixture-template:
Changing method of "Reaction" to "eddy-dissipation".
Inspect the species model settings after the changes.
species.print_state()
model :
option : species-transport
material : methane-air
number_vol_spec : 5
options :
inlet_diffusion : False
thermal_diffusion : False
diffusion_energy_source : True
multi_component_diffusion : False
save_gradients : False
species_transport_expert : False
reactions :
enable_volumetric_reactions : True
enable_electrochemical_surface : False
turb_chem_interaction_model : eddy-dissipation
turb_chem_interaction_model_options :
species_transport_expert_options :
linearize_convection_source : False
linearize_diffusion_source : False
blending : False
chemistry_solver : non-direct-source
Materials#
In this step, we will examine the default settings for the mixture material. This tutorial uses mixture properties copied from the Ansys Fluent database. In general, we can modify these or create our own mixture properties for our specific problem as necessary.
Print some specific properties of the mixture material (methane-air). We avoid printing the entire state of the mixture material to keep the output concise.
mixture_material = MixtureMaterial(solver, name="methane-air")
print(f"Species list: {mixture_material.species.volumetric_species.get_object_names()}")
print(f"Reactions option: {mixture_material.reactions.option()}")
print(f"Density option: {mixture_material.density.option()}")
print(f"Cp (specific heat) option: {mixture_material.specific_heat.option()}")
print(f"Thermal conductivity value: {mixture_material.thermal_conductivity.value()}")
print(f"Viscosity value: {mixture_material.viscosity.value()}")
print(f"Mass diffusivity value: {mixture_material.mass_diffusivity.value()}")
Species list: ['ch4', 'o2', 'co2', 'h2o', 'n2']
Reactions option: eddy-dissipation
Density option: incompressible-ideal-gas
Cp (specific heat) option: mixing-law
Thermal conductivity value: 0.0454
Viscosity value: 1.72e-05
Mass diffusivity value: 2.88e-05
Boundary Conditions#
Convert the symmetry zone to the axis type.
The symmetry zone must be converted to an axis to prevent numerical difficulties where the radius reduces to zero.
solver.settings.setup.boundary_conditions.set_zone_type(
zone_list=["symmetry-5"], new_type="axis"
)
Set the boundary conditions for the air inlet (velocity-inlet-8).
Set the zone name to air-inlet.
This name is more descriptive for the zone than velocity-inlet-8.
solver.settings.setup.boundary_conditions.set_zone_name(
zonename="velocity-inlet-8", newname="air-inlet"
)
Set the following boundary conditions for the air-inlet:
Velocity magnitude: 0.5 m/s
Turbulent intensity: 10%
Hydraulic diameter: 0.44 m
Temperature: 300 K
Species mass fraction for o2: 0.23
air_inlet = VelocityInlet(solver, name="air-inlet")
air_inlet.momentum.velocity_magnitude = 0.5
air_inlet.turbulence.turbulence_specification = "Intensity and Hydraulic Diameter"
air_inlet.turbulence.turbulent_intensity = 0.1
air_inlet.turbulence.hydraulic_diameter = 0.44
air_inlet.thermal.temperature = 300
air_inlet.species.species_mass_fraction["o2"] = 0.23
Verify the state of the air-inlet boundary condition after the changes.
air_inlet.print_state()
name : air-inlet
momentum :
velocity_specification_method : Magnitude, Normal to Boundary
reference_frame : Absolute
velocity_magnitude :
option : value
value : 0.5
initial_gauge_pressure :
option : value
value : 0
turbulence :
turbulence_specification : Intensity and Hydraulic Diameter
turbulent_intensity : 0.1
hydraulic_diameter : 0.44
thermal :
temperature :
option : value
value : 300
species :
specify_species_in_mole_fractions : False
species_mass_fraction :
ch4 :
option : value
value : 0
co2 :
option : value
value : 0
h2o :
option : value
value : 0
o2 :
option : value
value : 0.23
Set the boundary conditions for the fuel inlet (velocity-inlet-6).
Set the zone name to fuel-inlet.
This name is more descriptive for the zone than velocity-inlet-6.
solver.settings.setup.boundary_conditions.set_zone_name(
zonename="velocity-inlet-6", newname="fuel-inlet"
)
Set the following boundary conditions for the fuel-inlet:
Velocity magnitude: 80 m/s
Turbulent intensity: 10%
Hydraulic diameter: 0.01 m
Temperature: 300 K
Species mass fraction for ch4: 1
fuel_inlet = VelocityInlet(solver, name="fuel-inlet")
fuel_inlet.momentum.velocity_magnitude = 80
fuel_inlet.turbulence.turbulence_specification = "Intensity and Hydraulic Diameter"
fuel_inlet.turbulence.turbulent_intensity = 0.1
fuel_inlet.turbulence.hydraulic_diameter = 0.01
fuel_inlet.thermal.temperature = 300
fuel_inlet.species.species_mass_fraction["ch4"] = 1
Verify the state of the fuel-inlet boundary condition after the changes.
fuel_inlet.print_state()
name : fuel-inlet
momentum :
velocity_specification_method : Magnitude, Normal to Boundary
reference_frame : Absolute
velocity_magnitude :
option : value
value : 80
initial_gauge_pressure :
option : value
value : 0
turbulence :
turbulence_specification : Intensity and Hydraulic Diameter
turbulent_intensity : 0.1
hydraulic_diameter : 0.01
thermal :
temperature :
option : value
value : 300
species :
specify_species_in_mole_fractions : False
species_mass_fraction :
ch4 :
option : value
value : 1
co2 :
option : value
value : 0
h2o :
option : value
value : 0
o2 :
option : value
value : 0
Set the following boundary conditions for the exit boundary (pressure-outlet-9):
Gauge pressure: 0 Pa
Backflow turbulence intensity: 10%
Backflow Hydraulic diameter: 0.45 m
Backflow total temperature: 300 K
Backflow species mass fraction for o2: 0.23
The Backflow values in the pressure outlet boundary condition are utilized only when backflow occurs at the pressure outlet. Always assign reasonable values because backflow may occur during intermediate iterations and could affect the solution stability.
pressure_outlet = PressureOutlet(solver, name="pressure-outlet-9")
pressure_outlet.momentum.gauge_pressure = 0
pressure_outlet.turbulence.turbulence_specification = "Intensity and Hydraulic Diameter"
pressure_outlet.turbulence.backflow_turbulent_intensity = 0.1
pressure_outlet.turbulence.backflow_hydraulic_diameter = 0.45
pressure_outlet.thermal.backflow_total_temperature = 300
pressure_outlet.species.backflow_species_mass_fraction["o2"] = 0.23
Verify the state of the pressure-outlet boundary condition after the changes.
pressure_outlet.print_state()
name : pressure-outlet-9
momentum :
backflow_reference_frame : Absolute
gauge_pressure :
option : value
value : 0
pressure_profile_multiplier : 1.0
backflow_dir_spec_method : Normal to Boundary
backflow_pressure_spec : Total Pressure
prevent_reverse_flow : False
avg_pressure_spec : False
target_mass_flow_rate : False
turbulence :
turbulence_specification : Intensity and Hydraulic Diameter
backflow_turbulent_intensity : 0.1
backflow_hydraulic_diameter : 0.45
thermal :
backflow_total_temperature :
option : value
value : 300
species :
specify_species_in_mole_fractions : False
backflow_species_mass_fraction :
ch4 :
option : value
value : 0
co2 :
option : value
value : 0
h2o :
option : value
value : 0
o2 :
option : value
value : 0.23
Set the boundary conditions for the outer wall (wall-7).
Set the zone name to outer-wall.
This name is more descriptive for the zone than wall-7.
solver.settings.setup.boundary_conditions.set_zone_name(
zonename="wall-7", newname="outer-wall"
)
Set the following boundary conditions for the outer-wall:
Temperature: 300 K
outer_wall = WallBoundary(solver, name="outer-wall")
outer_wall.thermal.thermal_condition = "Temperature"
outer_wall.thermal.temperature = 300
Verify the state of thermal properties of the outer-wall boundary condition after the changes.
outer_wall.thermal.print_state()
thermal_condition : Temperature
material : aluminum
temperature :
option : value
value : 300
wall_thickness :
option : value
value : 0
heat_generation_rate :
option : value
value : 0
caf :
option : value
value : 1
Set the boundary conditions for the fuel inlet nozzle (wall-2).
Set the zone name to nozzle.
This name is more descriptive for the zone than wall-2.
solver.settings.setup.boundary_conditions.set_zone_name(
zonename="wall-2", newname="nozzle"
)
Set the following boundary conditions for the nozzle for adiabatic wall conditions:
Heat flux: 0 \(W/m^2\)
nozzle = WallBoundary(solver, name="nozzle")
nozzle.thermal.thermal_condition = "Heat Flux"
nozzle.thermal.heat_flux = 0
Verify the state of thermal properties of the nozzle boundary condition after the changes.
nozzle.thermal.print_state()
thermal_condition : Heat Flux
material : aluminum
heat_flux :
option : value
value : 0
wall_thickness :
option : value
value : 0
heat_generation_rate :
option : value
value : 0
caf :
option : value
value : 1
Reaction Solution#
We will calculate a solution for the reacting flow.
Inspect the solution methods settings.
solver.settings.solution.methods.print_state()
p_v_coupling :
flow_scheme : Coupled
flux_type :
pbns_cases :
flux_auto_select : True
flux_type : Rhie-Chow: momentum based
spatial_discretization :
gradient_scheme : least-square-cell-based
discretization_scheme :
k : second-order-upwind
mom : second-order-upwind
omega : second-order-upwind
pressure : second-order
species-0 : second-order-upwind
species-1 : second-order-upwind
species-2 : second-order-upwind
species-3 : second-order-upwind
temperature : second-order-upwind
pseudo_time_method :
formulation :
coupled_solver : global-time-step
expert :
reactions : True
reaction_source_term_relaxation_factor : 1.0
numerics_pbns :
implicit_bodyforce_treatment : False
velocity_formulation : absolute
physical_velocity_formulation : False
disable_rhie_chow_flux : False
presto_pressure_scheme : False
first_to_second_order_blending : 1.0
high_order_term_relaxation :
enable : False
warped_face_gradient_correction :
enable : False
species_disc_together : False
Ensure that plot is enabled in residual monitor options.
solver.settings.solution.monitor.residual.options.plot()
True
Initialize the field variables.
solver.settings.solution.initialization.hybrid_initialize()
Initialize using the hybrid initialization method.
Checking case topology...
-This case has both inlets & outlets
-Pressure information is not available at the boundaries.
Case will be initialized with constant pressure
iter scalar-0
1 1.000000e+00
2 3.835177e-06
3 3.116578e-07
4 2.563081e-08
5 2.109805e-09
6 1.736817e-10
7 1.429777e-11
8 1.171677e-12
9 1.023421e-13
10 1.000789e-14
Hybrid initialization is done.
Initializing mass fractions of
ch4 o2 co2 h2o
to 0.01 for Eddy-Dissipation ignition.
Save the case file (gascomb1.cas.h5).
solver.settings.file.write_case(file_name="gascomb1.cas.h5")
Fast-loading "/ansys_inc/v251/fluent/fluent25.1.0/addons/afd/lib/hdfio.bin"
Done.
Writing to 30b945f663a6:"/mnt/pyfluent/gascomb1.cas.h5" in NODE0 mode and compression level 1 ...
Grouping cells for Laplace smoothing ...
1615 cells, 1 zone ...
3319 faces, 7 zones ...
1705 nodes, 1 zone ...
Done.
Done.
Run the calculation for 200 iterations.
solver.settings.solution.run_calculation.iterate(iter_count=200)
iter continuity x-velocity y-velocity energy k omega ch4 o2 co2 h2o time/iter
temperature limited to 5.000000e+03 in 36 cells on zone 1 in domain 1
1 1.0000e+00 2.8826e-02 1.9174e-02 4.6440e-02 2.6366e-01 6.7015e-01 3.9592e-02 1.4869e-01 3.4007e-02 2.9870e-02 0:00:10 199
2 1.0000e+00 3.5666e-02 2.1722e-02 7.1504e-03 4.9893e-02 1.2118e-01 6.2070e-02 4.5739e-02 5.5486e-03 5.5019e-03 0:00:12 198
3 1.0000e+00 3.3955e-02 1.3257e-02 7.6401e-03 5.4174e-02 8.5282e-02 4.0745e-02 1.8683e-02 8.0401e-03 8.0555e-03 0:00:13 197
4 1.0000e+00 4.4596e-02 1.0069e-02 7.8902e-03 7.5493e-02 7.2995e-02 1.8150e-02 1.4173e-02 9.0270e-03 9.1146e-03 0:00:13 196
5 1.0000e+00 4.1067e-02 7.7328e-03 5.5725e-03 6.5997e-02 6.9267e-02 1.0832e-02 1.1928e-02 8.1723e-03 7.8901e-03 0:00:13 195
6 1.0692e+00 3.4400e-02 5.6051e-03 4.6318e-03 4.3506e-02 5.3967e-02 7.1736e-03 1.0468e-02 6.7089e-03 6.5196e-03 0:00:13 194
7 1.1962e+00 2.8974e-02 4.5099e-03 4.2423e-03 2.8360e-02 3.9524e-02 5.7701e-03 9.2417e-03 5.5549e-03 5.4469e-03 0:00:14 193
8 1.3274e+00 2.5402e-02 3.5631e-03 4.0078e-03 2.0264e-02 2.9132e-02 4.8462e-03 8.3787e-03 4.9930e-03 4.9204e-03 0:00:14 192
9 1.3793e+00 2.2675e-02 2.9011e-03 3.7286e-03 1.6773e-02 2.2117e-02 4.2519e-03 7.6729e-03 4.6888e-03 4.6607e-03 0:00:14 191
10 1.3590e+00 2.0183e-02 2.4325e-03 3.4266e-03 1.3579e-02 1.6561e-02 3.6275e-03 6.7757e-03 4.4830e-03 4.4618e-03 0:00:14 190
11 1.3243e+00 1.8005e-02 2.0881e-03 3.2174e-03 1.1109e-02 1.2503e-02 3.0570e-03 5.6272e-03 4.0900e-03 4.0646e-03 0:00:22 189
iter continuity x-velocity y-velocity energy k omega ch4 o2 co2 h2o time/iter
12 1.2981e+00 1.6015e-02 1.8316e-03 2.9872e-03 8.9633e-03 1.0166e-02 2.5681e-03 4.7761e-03 3.7870e-03 3.7814e-03 0:00:21 188
13 1.2708e+00 1.4127e-02 1.6151e-03 2.7627e-03 7.2213e-03 8.0496e-03 2.2394e-03 3.9926e-03 3.2169e-03 3.2124e-03 0:00:19 187
14 1.2320e+00 1.2421e-02 1.4198e-03 2.3752e-03 5.7441e-03 6.4755e-03 1.9033e-03 3.2345e-03 2.6924e-03 2.6901e-03 0:00:18 186
15 1.1727e+00 1.0900e-02 1.2516e-03 1.9646e-03 4.8136e-03 5.4285e-03 1.5791e-03 2.6997e-03 2.2201e-03 2.2170e-03 0:00:18 185
16 1.0887e+00 9.5701e-03 1.1065e-03 1.6440e-03 4.1961e-03 4.6501e-03 1.2966e-03 2.2128e-03 1.8121e-03 1.8123e-03 0:00:17 184
17 9.8844e-01 8.3037e-03 9.7512e-04 1.3204e-03 3.6089e-03 4.0329e-03 1.0885e-03 1.8326e-03 1.4521e-03 1.4518e-03 0:00:16 183
18 8.7814e-01 7.3899e-03 8.3648e-04 1.0900e-03 3.0962e-03 3.3631e-03 9.0410e-04 1.5487e-03 1.1798e-03 1.1801e-03 0:00:16 182
19 7.7585e-01 6.4605e-03 7.2467e-04 9.2991e-04 2.7398e-03 2.9672e-03 7.5231e-04 1.3186e-03 9.5184e-04 9.5107e-04 0:00:15 181
20 6.7820e-01 5.6455e-03 6.3492e-04 7.7791e-04 2.4474e-03 2.5511e-03 6.3057e-04 1.1063e-03 7.8948e-04 7.8898e-04 0:00:15 180
21 5.8514e-01 4.9102e-03 5.6112e-04 6.5067e-04 2.2931e-03 2.2844e-03 5.1742e-04 9.7742e-04 7.0009e-04 6.9959e-04 0:00:15 179
22 5.1597e-01 4.2773e-03 5.1700e-04 5.4157e-04 2.0893e-03 2.0184e-03 4.3349e-04 8.6540e-04 5.8095e-04 5.8049e-04 0:00:15 178
iter continuity x-velocity y-velocity energy k omega ch4 o2 co2 h2o time/iter
23 4.3739e-01 3.8274e-03 4.6114e-04 4.6371e-04 1.9375e-03 1.8473e-03 3.7154e-04 7.8419e-04 5.2614e-04 5.2581e-04 0:00:15 177
24 3.7846e-01 3.4272e-03 4.1923e-04 4.1347e-04 1.8026e-03 1.6797e-03 3.2042e-04 7.3926e-04 4.7990e-04 4.7969e-04 0:00:14 176
25 3.3461e-01 3.0316e-03 3.9318e-04 3.7164e-04 1.6594e-03 1.5339e-03 2.8099e-04 6.9245e-04 4.3380e-04 4.3376e-04 0:00:14 175
26 2.9432e-01 2.7206e-03 3.6132e-04 3.3364e-04 1.5196e-03 1.4159e-03 2.5137e-04 6.4412e-04 3.9751e-04 3.9731e-04 0:00:14 174
27 2.6659e-01 2.4575e-03 3.2995e-04 3.0740e-04 1.3848e-03 1.2880e-03 2.2506e-04 5.9354e-04 3.4979e-04 3.4955e-04 0:00:14 173
28 2.4375e-01 2.2219e-03 3.0093e-04 2.8031e-04 1.2680e-03 1.1752e-03 1.9718e-04 5.4710e-04 3.0998e-04 3.0977e-04 0:00:14 172
29 2.2321e-01 2.0166e-03 2.7590e-04 2.5177e-04 1.1671e-03 1.0690e-03 1.6966e-04 4.9919e-04 2.8066e-04 2.8043e-04 0:00:14 171
30 2.0585e-01 1.8317e-03 2.5567e-04 2.2253e-04 1.0746e-03 9.7939e-04 1.4552e-04 4.4839e-04 2.4943e-04 2.4922e-04 0:00:14 170
31 1.9161e-01 1.6690e-03 2.3487e-04 1.9304e-04 9.9016e-04 8.9977e-04 1.2177e-04 4.0343e-04 2.1764e-04 2.1798e-04 0:00:13 169
32 1.7906e-01 1.5244e-03 2.1818e-04 1.6581e-04 9.1151e-04 8.2861e-04 1.0002e-04 3.5773e-04 1.8865e-04 1.8849e-04 0:00:13 168
33 1.6774e-01 1.3970e-03 2.0101e-04 1.4223e-04 8.3596e-04 7.6454e-04 8.2743e-05 3.1144e-04 1.6237e-04 1.6230e-04 0:00:13 167
iter continuity x-velocity y-velocity energy k omega ch4 o2 co2 h2o time/iter
34 1.5696e-01 1.2827e-03 1.8649e-04 1.2108e-04 7.6381e-04 7.0321e-04 6.9354e-05 2.6707e-04 1.3894e-04 1.3891e-04 0:00:13 166
35 1.4685e-01 1.1831e-03 1.7234e-04 1.0285e-04 6.8665e-04 6.4380e-04 5.8720e-05 2.3069e-04 1.2022e-04 1.2019e-04 0:00:13 165
36 1.3481e-01 1.1053e-03 1.5621e-04 9.1006e-05 6.2932e-04 5.9405e-04 4.9125e-05 2.0291e-04 1.0577e-04 1.0574e-04 0:00:12 164
37 1.2848e-01 1.0212e-03 1.4754e-04 7.6609e-05 5.6345e-04 5.4414e-04 4.2682e-05 1.7779e-04 8.9794e-05 8.9761e-05 0:00:12 163
38 1.1801e-01 9.5762e-04 1.3535e-04 6.9377e-05 5.1517e-04 5.0438e-04 3.7616e-05 1.6185e-04 8.2473e-05 8.2447e-05 0:00:12 162
39 1.1189e-01 8.9111e-04 1.2779e-04 5.9480e-05 4.6108e-04 4.6376e-04 3.3398e-05 1.5008e-04 7.4284e-05 7.4243e-05 0:00:12 161
40 1.0253e-01 8.3804e-04 1.1812e-04 5.6994e-05 4.2107e-04 4.2955e-04 2.9508e-05 1.4180e-04 7.0888e-05 7.0857e-05 0:00:12 160
41 9.7426e-02 7.8236e-04 1.1056e-04 5.1328e-05 3.7829e-04 3.9470e-04 2.6283e-05 1.3571e-04 6.6004e-05 6.5973e-05 0:00:12 159
42 8.9433e-02 7.3868e-04 1.0341e-04 4.9780e-05 3.4256e-04 3.6341e-04 2.3534e-05 1.2766e-04 6.2693e-05 6.2663e-05 0:00:12 158
43 8.4454e-02 6.9708e-04 9.6564e-05 4.7888e-05 3.1432e-04 3.3621e-04 2.1388e-05 1.2082e-04 6.0040e-05 6.0015e-05 0:00:12 157
44 8.1112e-02 6.5333e-04 9.0611e-05 4.3112e-05 2.8558e-04 3.1075e-04 1.9854e-05 1.1758e-04 5.6158e-05 5.6127e-05 0:00:12 156
iter continuity x-velocity y-velocity energy k omega ch4 o2 co2 h2o time/iter
45 7.5241e-02 6.1671e-04 8.4945e-05 4.2296e-05 2.6121e-04 2.8969e-04 1.8218e-05 1.1142e-04 5.4231e-05 5.4212e-05 0:00:12 155
46 7.1387e-02 5.8324e-04 7.9330e-05 3.9057e-05 2.3949e-04 2.7075e-04 1.6700e-05 1.0586e-04 5.2007e-05 5.1992e-05 0:00:12 154
47 6.7955e-02 5.5112e-04 7.3988e-05 3.6401e-05 2.2042e-04 2.5412e-04 1.5422e-05 1.0083e-04 4.8040e-05 4.8014e-05 0:00:12 153
48 6.4660e-02 5.2060e-04 6.9366e-05 3.4344e-05 2.0350e-04 2.3914e-04 1.4296e-05 9.5725e-05 4.6186e-05 4.6152e-05 0:00:11 152
49 6.1716e-02 4.9168e-04 6.5292e-05 3.2262e-05 1.8837e-04 2.2570e-04 1.3283e-05 9.0859e-05 4.3880e-05 4.3851e-05 0:00:11 151
50 5.8634e-02 4.6459e-04 6.1491e-05 3.0277e-05 1.7488e-04 2.1347e-04 1.2389e-05 8.6169e-05 4.1648e-05 4.1622e-05 0:00:12 150
51 5.5787e-02 4.3916e-04 5.7824e-05 2.8217e-05 1.6264e-04 2.0251e-04 1.1546e-05 8.1563e-05 3.8070e-05 3.8045e-05 0:00:12 149
52 5.3308e-02 4.1496e-04 5.4360e-05 2.6565e-05 1.5146e-04 1.9263e-04 1.0823e-05 7.7485e-05 3.6448e-05 3.6421e-05 0:00:11 148
53 5.0855e-02 3.9229e-04 5.1090e-05 2.4733e-05 1.4121e-04 1.8350e-04 1.0064e-05 7.3572e-05 3.3658e-05 3.3633e-05 0:00:11 147
54 4.8466e-02 3.7111e-04 4.8094e-05 2.3349e-05 1.3184e-04 1.7515e-04 9.4115e-06 6.9827e-05 3.2351e-05 3.2324e-05 0:00:11 146
55 4.6268e-02 3.5145e-04 4.5166e-05 2.1844e-05 1.2319e-04 1.6740e-04 8.7746e-06 6.6321e-05 2.9971e-05 2.9949e-05 0:00:11 145
iter continuity x-velocity y-velocity energy k omega ch4 o2 co2 h2o time/iter
56 4.4294e-02 3.3299e-04 4.2264e-05 2.0589e-05 1.1520e-04 1.6034e-04 8.2535e-06 6.2972e-05 2.8229e-05 2.8210e-05 0:00:11 144
57 4.2414e-02 3.1564e-04 3.9532e-05 1.9548e-05 1.0780e-04 1.5378e-04 7.8192e-06 5.9928e-05 2.6782e-05 2.6763e-05 0:00:11 143
58 4.0635e-02 2.9932e-04 3.7148e-05 1.8612e-05 1.0088e-04 1.4767e-04 7.5744e-06 5.4996e-05 2.5448e-05 2.5430e-05 0:00:10 142
59 3.8749e-02 2.8394e-04 3.4999e-05 1.7739e-05 9.4508e-05 1.4195e-04 7.1892e-06 5.1412e-05 2.4190e-05 2.4172e-05 0:00:10 141
60 3.7243e-02 2.6946e-04 3.3135e-05 1.6929e-05 8.8618e-05 1.3652e-04 6.7893e-06 4.8515e-05 2.3052e-05 2.3040e-05 0:00:10 140
61 3.5756e-02 2.5579e-04 3.1405e-05 1.6156e-05 8.3137e-05 1.3140e-04 6.4319e-06 4.6048e-05 2.1980e-05 2.1968e-05 0:00:10 139
62 3.4323e-02 2.4294e-04 2.9727e-05 1.5412e-05 7.7998e-05 1.2656e-04 6.1118e-06 4.3819e-05 2.0969e-05 2.0956e-05 0:00:10 138
63 3.2946e-02 2.3087e-04 2.8166e-05 1.4723e-05 7.3190e-05 1.2203e-04 5.8132e-06 4.1772e-05 2.0045e-05 2.0032e-05 0:00:10 137
64 3.1627e-02 2.1948e-04 2.6727e-05 1.4090e-05 6.8718e-05 1.1771e-04 5.5377e-06 3.9924e-05 1.9174e-05 1.9163e-05 0:00:10 136
65 3.0348e-02 2.0872e-04 2.5407e-05 1.3493e-05 6.4544e-05 1.1361e-04 5.2690e-06 3.8199e-05 1.8372e-05 1.8361e-05 0:00:10 135
66 2.9134e-02 1.9855e-04 2.4126e-05 1.2939e-05 6.0673e-05 1.0967e-04 5.0201e-06 3.6583e-05 1.7515e-05 1.7505e-05 0:00:10 134
iter continuity x-velocity y-velocity energy k omega ch4 o2 co2 h2o time/iter
67 2.8014e-02 1.8897e-04 2.2985e-05 1.2370e-05 5.7080e-05 1.0586e-04 4.6967e-06 3.6143e-05 1.6945e-05 1.6935e-05 0:00:10 133
68 2.6943e-02 1.8001e-04 2.1882e-05 1.1941e-05 5.3725e-05 1.0220e-04 4.6181e-06 3.4254e-05 1.6232e-05 1.6223e-05 0:00:10 132
69 2.5993e-02 1.7151e-04 2.0848e-05 1.1425e-05 5.0595e-05 9.8642e-05 4.3559e-06 3.3679e-05 1.5701e-05 1.5693e-05 0:00:10 131
70 2.5064e-02 1.6348e-04 1.9960e-05 1.1051e-05 4.7684e-05 9.5158e-05 4.2438e-06 3.1751e-05 1.5060e-05 1.5052e-05 0:00:10 130
71 2.4170e-02 1.5588e-04 1.9139e-05 1.0585e-05 4.4971e-05 9.1793e-05 4.0001e-06 3.1202e-05 1.4493e-05 1.4486e-05 0:00:10 129
72 2.3308e-02 1.4868e-04 1.8376e-05 1.0200e-05 4.2457e-05 8.8545e-05 3.8224e-06 3.0490e-05 1.3974e-05 1.3967e-05 0:00:10 128
73 2.2514e-02 1.4186e-04 1.7650e-05 9.8330e-06 4.0150e-05 8.5443e-05 3.6664e-06 2.9621e-05 1.3476e-05 1.3470e-05 0:00:10 127
74 2.1766e-02 1.3539e-04 1.6944e-05 9.4719e-06 3.7991e-05 8.2503e-05 3.5223e-06 2.8676e-05 1.3048e-05 1.3041e-05 0:00:10 126
75 2.1066e-02 1.2938e-04 1.6239e-05 9.1722e-06 3.5934e-05 7.9689e-05 3.4357e-06 2.6570e-05 1.2509e-05 1.2503e-05 0:00:09 125
76 2.0409e-02 1.2371e-04 1.5568e-05 8.8832e-06 3.4005e-05 7.6993e-05 3.2375e-06 2.6144e-05 1.2247e-05 1.2242e-05 0:00:09 124
77 1.9743e-02 1.1833e-04 1.4966e-05 8.6415e-06 3.2184e-05 7.4404e-05 3.1473e-06 2.4718e-05 1.1785e-05 1.1779e-05 0:00:09 123
iter continuity x-velocity y-velocity energy k omega ch4 o2 co2 h2o time/iter
78 1.9127e-02 1.1321e-04 1.4459e-05 8.3960e-06 3.0440e-05 7.1893e-05 2.9754e-06 2.4585e-05 1.1548e-05 1.1543e-05 0:00:09 122
79 1.8521e-02 1.0840e-04 1.3967e-05 8.1497e-06 2.8859e-05 6.9464e-05 2.8616e-06 2.4195e-05 1.1292e-05 1.1287e-05 0:00:09 121
80 1.7957e-02 1.0372e-04 1.3495e-05 7.9559e-06 2.7417e-05 6.7095e-05 2.8000e-06 2.2834e-05 1.0892e-05 1.0888e-05 0:00:09 120
81 1.7398e-02 9.9230e-05 1.3020e-05 7.6374e-06 2.6060e-05 6.4741e-05 2.6544e-06 2.2496e-05 1.0640e-05 1.0636e-05 0:00:21 119
82 1.6856e-02 9.4956e-05 1.2565e-05 7.5445e-06 2.4766e-05 6.2393e-05 2.5282e-06 2.1360e-05 1.0255e-05 1.0251e-05 0:00:19 118
83 1.6359e-02 9.0889e-05 1.2120e-05 7.2050e-06 2.3548e-05 6.0008e-05 2.4060e-06 2.1135e-05 1.0054e-05 1.0051e-05 0:00:17 117
84 1.5913e-02 8.7028e-05 1.1687e-05 7.0878e-06 2.2418e-05 5.7612e-05 2.3175e-06 2.0096e-05 9.6488e-06 9.6452e-06 0:00:15 116
85 1.5480e-02 8.3462e-05 1.1286e-05 6.7487e-06 2.1371e-05 5.5216e-05 2.2086e-06 1.9844e-05 9.4419e-06 9.4385e-06 0:00:14 115
86 1.5022e-02 8.0066e-05 1.0924e-05 6.6343e-06 2.0401e-05 5.3119e-05 2.1452e-06 1.8842e-05 9.1088e-06 9.1053e-06 0:00:12 114
87 1.4559e-02 7.6819e-05 1.0582e-05 6.3621e-06 1.9499e-05 5.1395e-05 2.0949e-06 1.8005e-05 8.8298e-06 8.8267e-06 0:00:12 113
88 1.4097e-02 7.3696e-05 1.0222e-05 6.2676e-06 1.8669e-05 4.9734e-05 1.9927e-06 1.7553e-05 8.6541e-06 8.6512e-06 0:00:11 112
iter continuity x-velocity y-velocity energy k omega ch4 o2 co2 h2o time/iter
89 1.3657e-02 7.0742e-05 9.9061e-06 6.1148e-06 1.7896e-05 4.8112e-05 1.9064e-06 1.7160e-05 8.4810e-06 8.4785e-06 0:00:10 111
90 1.3272e-02 6.7928e-05 9.6165e-06 5.9648e-06 1.7169e-05 4.6706e-05 1.8306e-06 1.6810e-05 8.3202e-06 8.3178e-06 0:00:10 110
91 1.2905e-02 6.5235e-05 9.3382e-06 5.8493e-06 1.6484e-05 4.5335e-05 1.7626e-06 1.6510e-05 8.1767e-06 8.1742e-06 0:00:10 109
92 1.2556e-02 6.2659e-05 9.0707e-06 5.7382e-06 1.5836e-05 4.4164e-05 1.7005e-06 1.6228e-05 8.0303e-06 8.0279e-06 0:00:10 108
93 1.2245e-02 6.0198e-05 8.8095e-06 5.6355e-06 1.5225e-05 4.3355e-05 1.6429e-06 1.5958e-05 7.8448e-06 7.8423e-06 0:00:09 107
94 1.1924e-02 5.7873e-05 8.5394e-06 5.4970e-06 1.4656e-05 4.2491e-05 1.5626e-06 1.6182e-05 7.7398e-06 7.7376e-06 0:00:09 106
95 1.1591e-02 5.5669e-05 8.2713e-06 5.4138e-06 1.4118e-05 4.1578e-05 1.5133e-06 1.6332e-05 7.6708e-06 7.6687e-06 0:00:09 105
96 1.1292e-02 5.3568e-05 8.0336e-06 5.3367e-06 1.3606e-05 4.0617e-05 1.4829e-06 1.6382e-05 7.6022e-06 7.5999e-06 0:00:08 104
97 1.1019e-02 5.1562e-05 7.8210e-06 5.2787e-06 1.3104e-05 3.9643e-05 1.4376e-06 1.6297e-05 7.5364e-06 7.5340e-06 0:00:08 103
98 1.0753e-02 4.9718e-05 7.6236e-06 5.2790e-06 1.2619e-05 3.8643e-05 1.3955e-06 1.6055e-05 7.4551e-06 7.4528e-06 0:00:08 102
99 1.0548e-02 4.7976e-05 7.4451e-06 5.2328e-06 1.2172e-05 3.7636e-05 1.3550e-06 1.5833e-05 7.3827e-06 7.3807e-06 0:00:08 101
iter continuity x-velocity y-velocity energy k omega ch4 o2 co2 h2o time/iter
100 1.0303e-02 4.6318e-05 7.2496e-06 5.1768e-06 1.1756e-05 3.6628e-05 1.3243e-06 1.5636e-05 7.3152e-06 7.3133e-06 0:00:08 100
101 1.0042e-02 4.4734e-05 7.0575e-06 5.1297e-06 1.1368e-05 3.5618e-05 1.3011e-06 1.5488e-05 7.2509e-06 7.2489e-06 0:00:08 99
102 9.8180e-03 4.3213e-05 6.8667e-06 5.0908e-06 1.1001e-05 3.4630e-05 1.2810e-06 1.5348e-05 7.1837e-06 7.1820e-06 0:00:08 98
103 9.6107e-03 4.1766e-05 6.6786e-06 5.0494e-06 1.0644e-05 3.3660e-05 1.2615e-06 1.5196e-05 7.1114e-06 7.1097e-06 0:00:07 97
104 9.3982e-03 4.0419e-05 6.4997e-06 5.0012e-06 1.0294e-05 3.2715e-05 1.2423e-06 1.5024e-05 7.0311e-06 7.0290e-06 0:00:07 96
105 9.1985e-03 3.9144e-05 6.3237e-06 4.9468e-06 9.9540e-06 3.1781e-05 1.2229e-06 1.4846e-05 6.9457e-06 6.9436e-06 0:00:07 95
106 9.0254e-03 3.7949e-05 6.1599e-06 4.8860e-06 9.6265e-06 3.0860e-05 1.2022e-06 1.4665e-05 6.8588e-06 6.8566e-06 0:00:07 94
107 8.8429e-03 3.6808e-05 6.0141e-06 4.8187e-06 9.3107e-06 2.9948e-05 1.1805e-06 1.4462e-05 6.7584e-06 6.7561e-06 0:00:07 93
108 8.6411e-03 3.5722e-05 5.8510e-06 4.7414e-06 9.0050e-06 2.9045e-05 1.1530e-06 1.4296e-05 6.6595e-06 6.6555e-06 0:00:07 92
109 8.4519e-03 3.4693e-05 5.7074e-06 4.6698e-06 8.7085e-06 2.8146e-05 1.1303e-06 1.4033e-05 6.5976e-06 6.5958e-06 0:00:07 91
110 8.2756e-03 3.3699e-05 5.5682e-06 4.5943e-06 8.4199e-06 2.7252e-05 1.1085e-06 1.3791e-05 6.5288e-06 6.5267e-06 0:00:07 90
iter continuity x-velocity y-velocity energy k omega ch4 o2 co2 h2o time/iter
111 8.1082e-03 3.2737e-05 5.4286e-06 4.5109e-06 8.1398e-06 2.6369e-05 1.0745e-06 1.3561e-05 6.4650e-06 6.4629e-06 0:00:07 89
112 7.9827e-03 3.1824e-05 5.2911e-06 4.4239e-06 7.8760e-06 2.5496e-05 1.0517e-06 1.3305e-05 6.3538e-06 6.3519e-06 0:00:07 88
113 7.8425e-03 3.0977e-05 5.1661e-06 4.3336e-06 7.6227e-06 2.4631e-05 1.0300e-06 1.3036e-05 6.2105e-06 6.2082e-06 0:00:07 87
114 7.7056e-03 3.0159e-05 5.0425e-06 4.2436e-06 7.3775e-06 2.3784e-05 1.0073e-06 1.2753e-05 6.0718e-06 6.0694e-06 0:00:07 86
115 7.5657e-03 2.9363e-05 4.9139e-06 4.1662e-06 7.1352e-06 2.2963e-05 9.8899e-07 1.2462e-05 5.9273e-06 5.9250e-06 0:00:07 85
116 7.4152e-03 2.8594e-05 4.7867e-06 4.0795e-06 6.8976e-06 2.2120e-05 9.6506e-07 1.2177e-05 5.7883e-06 5.7863e-06 0:00:06 84
117 7.2541e-03 2.7840e-05 4.6728e-06 3.9895e-06 6.6617e-06 2.1528e-05 9.4014e-07 1.1872e-05 5.6378e-06 5.6357e-06 0:00:06 83
118 7.1010e-03 2.7103e-05 4.5741e-06 3.8940e-06 6.4441e-06 2.1181e-05 9.1354e-07 1.1562e-05 5.4859e-06 5.4839e-06 0:00:06 82
119 6.9391e-03 2.6385e-05 4.4821e-06 3.8173e-06 6.2472e-06 2.0818e-05 8.8687e-07 1.1280e-05 5.3530e-06 5.3511e-06 0:00:06 81
120 6.7685e-03 2.5687e-05 4.3956e-06 3.7568e-06 6.0809e-06 2.0453e-05 8.6111e-07 1.1066e-05 5.2507e-06 5.2488e-06 0:00:06 80
121 6.5967e-03 2.5008e-05 4.3140e-06 3.6937e-06 5.9296e-06 2.0087e-05 8.3944e-07 1.0815e-05 5.1272e-06 5.1254e-06 0:00:06 79
iter continuity x-velocity y-velocity energy k omega ch4 o2 co2 h2o time/iter
122 6.4224e-03 2.4355e-05 4.2381e-06 3.6110e-06 5.7846e-06 1.9746e-05 8.3949e-07 1.0683e-05 5.0761e-06 5.0743e-06 0:00:06 78
123 6.2457e-03 2.3721e-05 4.1805e-06 3.6092e-06 5.6490e-06 1.9409e-05 8.0496e-07 1.0501e-05 4.9952e-06 4.9933e-06 0:00:06 77
124 6.0855e-03 2.3128e-05 4.1220e-06 3.5407e-06 5.5215e-06 1.9039e-05 7.9982e-07 1.0358e-05 4.9307e-06 4.9292e-06 0:00:09 76
125 5.9503e-03 2.2553e-05 4.0272e-06 3.4976e-06 5.3973e-06 1.8631e-05 7.8606e-07 1.0215e-05 4.8663e-06 4.8649e-06 0:00:08 75
126 5.8422e-03 2.1986e-05 3.9374e-06 3.4550e-06 5.2750e-06 1.8190e-05 7.6658e-07 1.0065e-05 4.7970e-06 4.7957e-06 0:00:08 74
127 5.7252e-03 2.1428e-05 3.8477e-06 3.4063e-06 5.1547e-06 1.7770e-05 7.4456e-07 9.9042e-06 4.7210e-06 4.7197e-06 0:00:07 73
128 5.6035e-03 2.0908e-05 3.7608e-06 3.3515e-06 5.0386e-06 1.7324e-05 7.2166e-07 9.7289e-06 4.6376e-06 4.6364e-06 0:00:07 72
129 5.4814e-03 2.0411e-05 3.6843e-06 3.2910e-06 4.9248e-06 1.6855e-05 6.9991e-07 9.5454e-06 4.5487e-06 4.5476e-06 0:00:06 71
130 5.3586e-03 1.9923e-05 3.6087e-06 3.2256e-06 4.8101e-06 1.6380e-05 6.7951e-07 9.3532e-06 4.4548e-06 4.4539e-06 0:00:06 70
131 5.2363e-03 1.9444e-05 3.5382e-06 3.1562e-06 4.6951e-06 1.5898e-05 6.5961e-07 9.1513e-06 4.3583e-06 4.3573e-06 0:00:06 69
132 5.1124e-03 1.8969e-05 3.4662e-06 3.0834e-06 4.5787e-06 1.5416e-05 6.3987e-07 8.9409e-06 4.2497e-06 4.2487e-06 0:00:06 68
iter continuity x-velocity y-velocity energy k omega ch4 o2 co2 h2o time/iter
133 4.9877e-03 1.8501e-05 3.3936e-06 3.0106e-06 4.4616e-06 1.4938e-05 6.2047e-07 8.7265e-06 4.1450e-06 4.1440e-06 0:00:06 67
134 4.8643e-03 1.8047e-05 3.3241e-06 2.9366e-06 4.3436e-06 1.4466e-05 6.0134e-07 8.5094e-06 4.0414e-06 4.0404e-06 0:00:05 66
135 4.7427e-03 1.7614e-05 3.2543e-06 2.8614e-06 4.2248e-06 1.4003e-05 5.8247e-07 8.2881e-06 3.9363e-06 3.9354e-06 0:00:05 65
136 4.6237e-03 1.7184e-05 3.1828e-06 2.7854e-06 4.1061e-06 1.3548e-05 5.6387e-07 8.0634e-06 3.8293e-06 3.8284e-06 0:00:05 64
137 4.5112e-03 1.6758e-05 3.1130e-06 2.7087e-06 3.9886e-06 1.3104e-05 5.4530e-07 7.8360e-06 3.7208e-06 3.7199e-06 0:00:05 63
138 4.4031e-03 1.6336e-05 3.0433e-06 2.6313e-06 3.8718e-06 1.2670e-05 5.2736e-07 7.6071e-06 3.6119e-06 3.6110e-06 0:00:05 62
139 4.2897e-03 1.5921e-05 2.9750e-06 2.5541e-06 3.7560e-06 1.2244e-05 5.0996e-07 7.3799e-06 3.5033e-06 3.5025e-06 0:00:05 61
140 4.1700e-03 1.5515e-05 2.9059e-06 2.4862e-06 3.6441e-06 1.1831e-05 4.9424e-07 7.1585e-06 3.3971e-06 3.3963e-06 0:00:05 60
141 4.0523e-03 1.5116e-05 2.8402e-06 2.4154e-06 3.5325e-06 1.1425e-05 4.7834e-07 6.9404e-06 3.2928e-06 3.2920e-06 0:00:05 59
142 3.9366e-03 1.4721e-05 2.7774e-06 2.3431e-06 3.4205e-06 1.1029e-05 4.6168e-07 6.7243e-06 3.1890e-06 3.1882e-06 0:00:05 58
143 3.8238e-03 1.4332e-05 2.7205e-06 2.2709e-06 3.3097e-06 1.0645e-05 4.4469e-07 6.5086e-06 3.0855e-06 3.0848e-06 0:00:05 57
iter continuity x-velocity y-velocity energy k omega ch4 o2 co2 h2o time/iter
144 3.7141e-03 1.3947e-05 2.6692e-06 2.1997e-06 3.2007e-06 1.0273e-05 4.2708e-07 6.2928e-06 2.9823e-06 2.9817e-06 0:00:04 56
145 3.6014e-03 1.3568e-05 2.6170e-06 2.1283e-06 3.0939e-06 9.9152e-06 4.0904e-07 6.0789e-06 2.8808e-06 2.8803e-06 0:00:04 55
146 3.4903e-03 1.3225e-05 2.5635e-06 2.0571e-06 2.9898e-06 9.5627e-06 3.9089e-07 5.8676e-06 2.7810e-06 2.7806e-06 0:00:04 54
147 3.3862e-03 1.2889e-05 2.5089e-06 1.9869e-06 2.8904e-06 9.2201e-06 3.7307e-07 5.6596e-06 2.6829e-06 2.6826e-06 0:00:04 53
148 3.2924e-03 1.2557e-05 2.4546e-06 1.9178e-06 2.7947e-06 8.8876e-06 3.5602e-07 5.4555e-06 2.5872e-06 2.5869e-06 0:00:04 52
149 3.1977e-03 1.2227e-05 2.3996e-06 1.8499e-06 2.7029e-06 8.5626e-06 3.3944e-07 5.2563e-06 2.4939e-06 2.4937e-06 0:00:04 51
150 3.0998e-03 1.1900e-05 2.3436e-06 1.7837e-06 2.6158e-06 8.2465e-06 3.2353e-07 5.0638e-06 2.4032e-06 2.4030e-06 0:00:04 50
151 2.9963e-03 1.1578e-05 2.2891e-06 1.7188e-06 2.5319e-06 7.9377e-06 3.0813e-07 4.8774e-06 2.3154e-06 2.3152e-06 0:00:04 49
152 2.8940e-03 1.1259e-05 2.2364e-06 1.6559e-06 2.4516e-06 7.6355e-06 2.9325e-07 4.6958e-06 2.2299e-06 2.2297e-06 0:00:04 48
153 2.7945e-03 1.0944e-05 2.1828e-06 1.5948e-06 2.3744e-06 7.3401e-06 2.7891e-07 4.5194e-06 2.1468e-06 2.1466e-06 0:00:04 47
154 2.6964e-03 1.0634e-05 2.1362e-06 1.5353e-06 2.3001e-06 7.0519e-06 2.6505e-07 4.3486e-06 2.0663e-06 2.0662e-06 0:00:04 46
iter continuity x-velocity y-velocity energy k omega ch4 o2 co2 h2o time/iter
155 2.5969e-03 1.0327e-05 2.0906e-06 1.4779e-06 2.2285e-06 6.7728e-06 2.5200e-07 4.1832e-06 1.9881e-06 1.9880e-06 0:00:03 45
156 2.4993e-03 1.0023e-05 2.0440e-06 1.4218e-06 2.1610e-06 6.5034e-06 2.3998e-07 4.0236e-06 1.9124e-06 1.9122e-06 0:00:03 44
157 2.4041e-03 9.7244e-06 1.9968e-06 1.3676e-06 2.0951e-06 6.2483e-06 2.2826e-07 3.8691e-06 1.8390e-06 1.8388e-06 0:00:03 43
158 2.3196e-03 9.4314e-06 1.9532e-06 1.3141e-06 2.0294e-06 6.0061e-06 2.1697e-07 3.7166e-06 1.7666e-06 1.7665e-06 0:00:03 42
159 2.2350e-03 9.1409e-06 1.9094e-06 1.2591e-06 1.9679e-06 5.7602e-06 2.0598e-07 3.5574e-06 1.6911e-06 1.6910e-06 0:00:03 41
160 2.1530e-03 8.8706e-06 1.8642e-06 1.2054e-06 1.9086e-06 5.5167e-06 1.9519e-07 3.4005e-06 1.6169e-06 1.6169e-06 0:00:03 40
161 2.0729e-03 8.6113e-06 1.8181e-06 1.1545e-06 1.8502e-06 5.2798e-06 1.8467e-07 3.2488e-06 1.5452e-06 1.5452e-06 0:00:03 39
162 1.9951e-03 8.3540e-06 1.7719e-06 1.1065e-06 1.7926e-06 5.0530e-06 1.7452e-07 3.1090e-06 1.4785e-06 1.4785e-06 0:00:03 38
163 1.9184e-03 8.0999e-06 1.7260e-06 1.0607e-06 1.7362e-06 4.8353e-06 1.6491e-07 2.9756e-06 1.4154e-06 1.4154e-06 0:00:03 37
164 1.8400e-03 7.8499e-06 1.6800e-06 1.0165e-06 1.6809e-06 4.6268e-06 1.5633e-07 2.8474e-06 1.3547e-06 1.3547e-06 0:00:03 36
165 1.7645e-03 7.6026e-06 1.6341e-06 9.7433e-07 1.6264e-06 4.4242e-06 1.4812e-07 2.7245e-06 1.2963e-06 1.2964e-06 0:00:03 35
iter continuity x-velocity y-velocity energy k omega ch4 o2 co2 h2o time/iter
166 1.6913e-03 7.3596e-06 1.5885e-06 9.3390e-07 1.5729e-06 4.2295e-06 1.4029e-07 2.6061e-06 1.2403e-06 1.2403e-06 0:00:03 34
167 1.6225e-03 7.1206e-06 1.5454e-06 8.9451e-07 1.5207e-06 4.0427e-06 1.3275e-07 2.4921e-06 1.1868e-06 1.1868e-06 0:00:03 33
168 1.5571e-03 6.8864e-06 1.5078e-06 8.5647e-07 1.4697e-06 3.8634e-06 1.2552e-07 2.3827e-06 1.1353e-06 1.1354e-06 0:00:02 32
169 1.4934e-03 6.6562e-06 1.4716e-06 8.1987e-07 1.4200e-06 3.6899e-06 1.1851e-07 2.2784e-06 1.0853e-06 1.0855e-06 0:00:02 31
170 1.4322e-03 6.4365e-06 1.4350e-06 7.8430e-07 1.3718e-06 3.5211e-06 1.1176e-07 2.1775e-06 1.0378e-06 1.0380e-06 0:00:02 30
171 1.3752e-03 6.2205e-06 1.3986e-06 7.4989e-07 1.3250e-06 3.3548e-06 1.0528e-07 2.0800e-06 9.9202e-07 9.9220e-07 0:00:02 29
172 1.3177e-03 6.0074e-06 1.3620e-06 7.1640e-07 1.2801e-06 3.1946e-06 9.9040e-08 1.9848e-06 9.4721e-07 9.4738e-07 0:00:02 28
173 1.2619e-03 5.7989e-06 1.3252e-06 6.8425e-07 1.2366e-06 3.0405e-06 9.3117e-08 1.8929e-06 9.0388e-07 9.0407e-07 0:00:05 27
174 1.2088e-03 5.5965e-06 1.2885e-06 6.5329e-07 1.1944e-06 2.8924e-06 8.7649e-08 1.8059e-06 8.6286e-07 8.6305e-07 0:00:04 26
175 1.1654e-03 5.3981e-06 1.2537e-06 6.3672e-07 1.1587e-06 2.7537e-06 8.3151e-08 1.7260e-06 8.3162e-07 8.3188e-07 0:00:04 25
176 1.1405e-03 5.2066e-06 1.2223e-06 5.8504e-07 1.1172e-06 2.6222e-06 7.4876e-08 1.6691e-06 7.9396e-07 7.9393e-07 0:00:03 24
iter continuity x-velocity y-velocity energy k omega ch4 o2 co2 h2o time/iter
177 1.0854e-03 5.0131e-06 1.1938e-06 5.8210e-07 1.0822e-06 2.4963e-06 7.1968e-08 1.5798e-06 7.5219e-07 7.5245e-07 0:00:03 23
178 1.0516e-03 4.8209e-06 1.1607e-06 5.3863e-07 1.0445e-06 2.3787e-06 7.0200e-08 1.5022e-06 7.2523e-07 7.2545e-07 0:00:02 22
179 1.0201e-03 4.6342e-06 1.1302e-06 5.1573e-07 1.0068e-06 2.2649e-06 6.6730e-08 1.4322e-06 6.9447e-07 6.9468e-07 0:00:02 21
180 9.8731e-04 4.4539e-06 1.1000e-06 4.9370e-07 9.7065e-07 2.1552e-06 6.2681e-08 1.3680e-06 6.6391e-07 6.6411e-07 0:00:02 20
! 180 solution is converged
Set time scale factor to 5.
The Time Scale Factor allows us to further manipulate the computed time step size calculated by Fluent. Larger time steps can lead to faster convergence. However, if the time step is too large it can lead to solution instability.
solver.settings.solution.run_calculation.pseudo_time_settings.time_step_method.time_step_size_scale_factor = (
5
)
Run the calculation for 200 iterations.
solver.settings.solution.run_calculation.iterate(iter_count=200)
iter continuity x-velocity y-velocity energy k omega ch4 o2 co2 h2o time/iter
180 9.8731e-04 4.4539e-06 1.1000e-06 4.9370e-07 9.7065e-07 2.1552e-06 6.2681e-08 1.3680e-06 6.6391e-07 6.6411e-07 0:00:20 200
! 180 solution is converged
181 2.4223e-03 4.5361e-06 1.1305e-06 9.6245e-07 1.4112e-06 2.7110e-06 1.2524e-07 2.7120e-06 1.3544e-06 1.3546e-06 0:00:18 199
182 1.9375e-03 4.0183e-06 1.0338e-06 1.2183e-06 1.2315e-06 2.6664e-06 1.5388e-07 3.4098e-06 1.6380e-06 1.6381e-06 0:00:17 198
183 1.7417e-03 3.5345e-06 9.3314e-07 1.1938e-06 1.0766e-06 2.4145e-06 1.5569e-07 3.2712e-06 1.5644e-06 1.5646e-06 0:00:17 197
184 1.6240e-03 3.0544e-06 8.2972e-07 1.1005e-06 9.2646e-07 2.0884e-06 1.4862e-07 2.9967e-06 1.4167e-06 1.4171e-06 0:00:17 196
185 1.5351e-03 2.6011e-06 7.2541e-07 9.6647e-07 7.7628e-07 1.7522e-06 1.3129e-07 2.5867e-06 1.2302e-06 1.2306e-06 0:00:17 195
186 1.4126e-03 2.1942e-06 6.3148e-07 8.2632e-07 6.4811e-07 1.4628e-06 1.1152e-07 2.1964e-06 1.0501e-06 1.0504e-06 0:00:16 194
187 1.3244e-03 1.8488e-06 5.5063e-07 6.9906e-07 5.4825e-07 1.2277e-06 9.4161e-08 1.8297e-06 8.8227e-07 8.8252e-07 0:00:16 193
188 1.2604e-03 1.5605e-06 4.7758e-07 5.7674e-07 4.6165e-07 1.0204e-06 8.3312e-08 1.5060e-06 7.2567e-07 7.2585e-07 0:00:16 192
189 1.1873e-03 1.3348e-06 4.1791e-07 4.8801e-07 3.9820e-07 8.4752e-07 7.2026e-08 1.2107e-06 5.9737e-07 5.9766e-07 0:00:16 191
190 1.1166e-03 1.1344e-06 3.6601e-07 4.0447e-07 3.4083e-07 7.1274e-07 6.1061e-08 9.9514e-07 4.9642e-07 4.9663e-07 0:00:15 190
iter continuity x-velocity y-velocity energy k omega ch4 o2 co2 h2o time/iter
191 1.0304e-03 9.7570e-07 3.2135e-07 3.3209e-07 2.9517e-07 5.9745e-07 5.3908e-08 8.2685e-07 4.0947e-07 4.0963e-07 0:00:15 189
192 9.3448e-04 8.4421e-07 2.8513e-07 2.7217e-07 2.5466e-07 5.0003e-07 4.8290e-08 6.8293e-07 3.3575e-07 3.3588e-07 0:00:15 188
! 192 solution is converged
Save the case and data files (gascomb1.cas.h5 and gascomb1.dat.h5).
solver.settings.file.write_case_data(file_name="gascomb1.cas.h5")
Writing to 30b945f663a6:"/mnt/pyfluent/gascomb1.cas.h5" in NODE0 mode and compression level 1 ...
Grouping cells for Laplace smoothing ...
1615 cells, 1 zone ...
3319 faces, 7 zones ...
1705 nodes, 1 zone ...
Done.
Done.
Writing to 30b945f663a6:"/mnt/pyfluent/gascomb1.dat.h5" in NODE0 mode and compression level 1 ...
Writing results.
Done.
Postprocessing#
Review the solution by examining graphical displays of the results and performing surface integrations at the combustor exit.
Report the total sensible heat flux. We shall use wildcards to specify all zones.
solver.settings.results.report.fluxes.get_heat_transfer_sensible(zones="*")
{'Net': -0.5353470930422191, 'air-inlet': 173.7936396580586, 'fuel-inlet': 16.64962057794938, 'nozzle': -0.0, 'outer-wall': -12842.71004368723, 'pressure-outlet-9': -191740.9839789067}
Display filled contours of temperature and save the image to a file.
contour1 = Contour(solver, new_instance_name="contour-temp")
contour1.field = "temperature"
contour1.surfaces_list = contour1.surfaces_list.allowed_values()
contour1.coloring.option = "banded"
contour1.display()
graphics.views.auto_scale()
# graphics.picture.save_picture(file_name="contour-temp.png")
Contours of Temperature#
The peak temperature is approximately 2300 K.
Display velocity vectors and save the image to a file.
vector1 = Vector(solver, new_instance_name="vector-vel")
vector1.surfaces_list = ["interior-4"]
vector1.scale.scale_f = 0.01
vector1.vector_opt.fixed_length = True
The fixed length option is useful when the vector magnitude varies dramatically. With fixed length vectors, the velocity magnitude is described only by color instead of by both vector length and color.
vector1.vector_opt.scale_head = 0.1
vector1.display()
graphics.views.auto_scale()
graphics.picture.save_picture(file_name="vector-vel.png")
Velocity Vectors#
The entrainment of air into the high-velocity methane jet is clearly visible.
Display filled contours of mass fraction of \(CH_4\) and save the image to a file.
contour2 = Contour(solver, new_instance_name="contour-ch4-mass-fraction")
contour2.field = "ch4"
contour2.surfaces_list = contour2.surfaces_list.allowed_values()
contour2.display()
graphics.views.auto_scale()
graphics.picture.save_picture(file_name="contour-ch4-mass-fraction.png")
Contours of \(CH_4\) Mass Fraction#
Display filled contours of mass fraction of \(O_2\) and save the image to a file.
contour3 = Contour(solver, new_instance_name="contour-o2-mass-fraction")
contour3.field = "o2"
contour3.surfaces_list = contour3.surfaces_list.allowed_values()
contour3.display()
graphics.views.auto_scale()
graphics.picture.save_picture(file_name="contour-o2-mass-fraction.png")
Contours of \(O_2\) Mass Fraction#
Display filled contours of mass fraction of \(CO_2\) and save the image to a file.
contour4 = Contour(solver, new_instance_name="contour-co2-mass-fraction")
contour4.field = "co2"
contour4.surfaces_list = contour4.surfaces_list.allowed_values()
contour4.display()
graphics.views.auto_scale()
graphics.picture.save_picture(file_name="contour-co2-mass-fraction.png")
Contours of \(CO_2\) Mass Fraction#
Display filled contours of mass fraction of \(H_2O\) and save the image to a file.
contour5 = Contour(solver, new_instance_name="contour-h2o-mass-fraction")
contour5.field = "h2o"
contour5.surfaces_list = contour5.surfaces_list.allowed_values()
contour5.display()
graphics.views.auto_scale()
graphics.picture.save_picture(file_name="contour-h2o-mass-fraction.png")
Contours of \(H_2O\) Mass Fraction#
Determine the average exit temperature.
The mass-averaged temperature will be computed as:
\[\bar{T}=\frac{\int T \rho \vec{v} \cdot d \vec{A}}{\int \rho \vec{v} \cdot d \vec{A}}\]
The mass-averaged temperature at the exit is approximately 1840 K.
solver.settings.results.report.surface_integrals.get_mass_weighted_avg(
report_of="temperature", surface_names=["pressure-outlet-9"]
)
{'pressure-outlet-9': 1840.02573809136}
Determine the average exit velocity.
The mass-averaged velocity will be computed as:
\[v=\frac{1}{A} \int v d A\]
The Area-Weighted Average field will show that the exit velocity is approximately 3.37 m/s.
solver.settings.results.report.surface_integrals.get_area_weighted_avg(
report_of="velocity-magnitude", surface_names=["pressure-outlet-9"]
)
{'pressure-outlet-9': 3.305919548597063}
Save the case file (gascomb1.cas.h5).
solver.settings.file.write_case(file_name="gascomb1.cas.h5")
Writing to 30b945f663a6:"/mnt/pyfluent/gascomb1.cas.h5" in NODE0 mode and compression level 1 ...
Grouping cells for Laplace smoothing ...
1615 cells, 1 zone ...
3319 faces, 7 zones ...
1705 nodes, 1 zone ...
Done.
Done.
Close Fluent#
solver.exit()
Summary#
In this tutorial we used PyFluent to model the transport, mixing, and reaction of chemical species. The reaction system was defined by using a mixture-material entry in the Ansys Fluent database. The procedures used here for simulation of hydrocarbon combustion can be applied to other reacting flow systems.
Total running time of the script: (2 minutes 8.811 seconds)