Onedimensional Reacting Flows¶
Composite Domains¶
FreeFlame¶

class
cantera.
FreeFlame
(gas, grid=None, width=None)¶ Bases:
cantera.onedim.FlameBase
A freelypropagating flat flame.
A domain of type FreeFlow named ‘flame’ will be created to represent the flame. The three domains comprising the stack are stored as
self.inlet
,self.flame
, andself.outlet
.Parameters:  grid – A list of points to be used as the initial grid. Not recommended
unless solving only on a fixed grid; Use the
width
parameter instead.  width – Defines a grid on the interval [0, width] with internal points determined automatically by the solver.

flame
¶

get_flame_speed_reaction_sensitivities
()¶ Compute the normalized sensitivities of the laminar flame speed \(S_u\) with respect to the reaction rate constants \(k_i\):
\[s_i = \frac{k_i}{S_u} \frac{dS_u}{dk_i}\]

inlet
¶

outlet
¶

set_initial_guess
()¶ Set the initial guess for the solution. The adiabatic flame temperature and equilibrium composition are computed for the inlet gas composition. The temperature profile rises linearly over 20% of the domain width to Tad, then is flat. The mass fraction profiles are set similarly.
 grid – A list of points to be used as the initial grid. Not recommended
unless solving only on a fixed grid; Use the
BurnerFlame¶

class
cantera.
BurnerFlame
(gas, grid=None, width=None)¶ Bases:
cantera.onedim.FlameBase
A burnerstabilized flat flame.
Parameters:  gas –
Solution
(using the IdealGas thermodynamic model) used to evaluate all gas properties and reaction rates.  grid – A list of points to be used as the initial grid. Not recommended
unless solving only on a fixed grid; Use the
width
parameter instead.  width – Defines a grid on the interval [0, width] with internal points determined automatically by the solver.
A domain of class
AxisymmetricStagnationFlow
namedflame
will be created to represent the flame. The three domains comprising the stack are stored asself.burner
,self.flame
, andself.outlet
.
burner
¶

flame
¶

outlet
¶

set_initial_guess
()¶ Set the initial guess for the solution. The adiabatic flame temperature and equilibrium composition are computed for the burner gas composition. The temperature profile rises linearly in the first 20% of the flame to Tad, then is flat. The mass fraction profiles are set similarly.
 gas –
CounterflowDiffusionFlame¶

class
cantera.
CounterflowDiffusionFlame
(gas, grid=None, width=None)¶ Bases:
cantera.onedim.FlameBase
A counterflow diffusion flame
Parameters:  gas –
Solution
(using the IdealGas thermodynamic model) used to evaluate all gas properties and reaction rates.  grid – A list of points to be used as the initial grid. Not recommended
unless solving only on a fixed grid; Use the
width
parameter instead.  width – Defines a grid on the interval [0, width] with internal points determined automatically by the solver.
A domain of class
AxisymmetricStagnationFlow
namedflame
will be created to represent the flame. The three domains comprising the stack are stored asself.fuel_inlet
,self.flame
, andself.oxidizer_inlet
.
extinct
()¶

flame
¶

fuel_inlet
¶

mixture_fraction
(m)¶ Compute the mixture fraction based on element m
The mixture fraction is computed from the elemental mass fraction of element m, normalized by its values on the fuel and oxidizer inlets:
\[Z = \frac{Z_{\mathrm{mass},m}(z)  Z_{\mathrm{mass},m}(z_\mathrm{oxidizer})} {Z_{\mathrm{mass},m}(z_\mathrm{fuel})  Z_{\mathrm{mass},m}(z_\mathrm{oxidizer})}\]Parameters: m – The element based on which the mixture fraction is computed, may be specified by name or by index >>> f.mixture_fraction('H')

oxidizer_inlet
¶

set_initial_guess
(fuel=None, oxidizer=None, stoich=None)¶ Set the initial guess for the solution. The initial guess is generated by assuming infinitelyfast chemistry.

solve
(loglevel=1, refine_grid=True, auto=False)¶ Solve the problem.
Parameters:  loglevel – integer flag controlling the amount of diagnostic output. Zero suppresses all output, and 5 produces very verbose output.
 refine_grid – if True, enable grid refinement.
 auto – if True, sequentially execute the different solution stages and attempt to automatically recover from errors. Attempts to first solve on the initial grid with energy enabled. If that does not succeed, a fixedtemperature solution will be tried followed by enabling the energy equation, and then with grid refinement enabled. If nondefault tolerances have been specified or multicomponent transport is enabled, an additional solution using these options will be calculated.

strain_rate
(definition, fuel=None, oxidizer='O2', stoich=None)¶ Return the axial strain rate of the counterflow diffusion flame in 1/s.
Parameters:  definition – The definition of the strain rate to be calculated. Options are:
mean
,max
,stoichiometric
,potential_flow_fuel
, andpotential_flow_oxidizer
.  fuel – The fuel species. Used only if definition is
stoichiometric
.  oxidizer – The oxidizer species, default
O2
. Used only if definition isstoichiometric
.  stoich – The molar stoichiometric oxidizertofuel ratio.
Can be omitted if the oxidizer is
O2
. Used only if definition isstoichiometric
.
The parameter definition sets the method to compute the strain rate. Possible options are:
mean
: The mean axial velocity gradient in the entire domain\[a_{mean} = \left \frac{\Delta u}{\Delta z} \right\]
max
:The maximum axial velocity gradient
\[a_{max} = \max \left( \left \frac{du}{dz} \right \right)\]stoichiometric
:The axial velocity gradient at the stoichiometric surface.
\[a_{stoichiometric} = \left \left. \frac{du}{dz} \right_{\phi=1} \right\]This method uses the additional keyword arguments fuel, oxidizer, and stoich.
>>> f.strain_rate('stoichiometric', fuel='H2', oxidizer='O2', stoich=0.5)
potential_flow_fuel
:The corresponding axial strain rate for a potential flow boundary condition at the fuel inlet.
\[a_{f} = \sqrt{\frac{\Lambda}{\rho_{f}}}\]potential_flow_oxidizer
:The corresponding axial strain rate for a potential flow boundary condition at the oxidizer inlet.
\[a_{o} = \sqrt{\frac{\Lambda}{\rho_{o}}}\]
 definition – The definition of the strain rate to be calculated. Options are:
 gas –
CounterflowPremixedFlame¶

class
cantera.
CounterflowPremixedFlame
(gas, grid=None, width=None)¶ Bases:
cantera.onedim.FlameBase
A premixed counterflow flame
Parameters:  gas –
Solution
(using the IdealGas thermodynamic model) used to evaluate all gas properties and reaction rates.  grid – Array of initial grid points. Not recommended unless solving only on
a fixed grid; Use the
width
parameter instead.  width – Defines a grid on the interval [0, width] with internal points determined automatically by the solver.
A domain of class
AxisymmetricStagnationFlow
namedflame
will be created to represent the flame. The three domains comprising the stack are stored asself.reactants
,self.flame
, andself.products
.
flame
¶

products
¶

reactants
¶

set_initial_guess
(equilibrate=True)¶ Set the initial guess for the solution.
If
equilibrate
is True, then the products composition and temperature will be set to the equilibrium state of the reactants mixture.
 gas –
ImpingingJet¶

class
cantera.
ImpingingJet
(gas, grid=None, width=None)¶ Bases:
cantera.onedim.FlameBase
An axisymmetric flow impinging on a surface at normal incidence.
Parameters:  gas –
Solution
(using the IdealGas thermodynamic model) used to evaluate all gas properties and reaction rates.  grid – A list of points to be used as the initial grid. Not recommended
unless solving only on the initial grid; Use the
width
parameter instead.  width – Defines a grid on the interval [0, width] with internal points determined automatically by the solver.
 surface – A Kinetics object used to compute any surface reactions.
A domain of class
AxisymmetricStagnationFlow
namedflame
will be created to represent the flow. The three domains comprising the stack are stored asself.inlet
,self.flame
, andself.surface
.
flame
¶

inlet
¶

set_initial_guess
(products='inlet')¶ Set the initial guess for the solution. If products = ‘equil’, then the equilibrium composition at the adiabatic flame temperature will be used to form the initial guess. Otherwise the inlet composition will be used.

surface
¶
 gas –
Flow Domains¶
FreeFlow¶

class
cantera.
FreeFlow
(thermo)¶ Bases:
cantera._cantera._FlowBase

P
¶ Pressure [Pa]

bounds
(self, component)¶ Return the (lower, upper) bounds for a solution component.
>>> d.bounds('T') (200.0, 5000.0)

component_index
(self, str name)¶ Index of the component with name ‘name’

component_name
(self, int n)¶ Name of the nth component.

component_names
¶ List of the names of all components of this domain.

description
¶ A description of this domain

energy_enabled
¶ Determines whether or not to solve the energy equation.

grid
¶ The grid for this domain

have_user_tolerances
¶ have_user_tolerances: __builtin__.bool

index
¶ Index of this domain in a stack. Returns 1 if this domain is not part of a stack.

n_components
¶ Number of solution components at each grid point.

n_points
¶ Number of grid points belonging to this domain.

name
¶ The name / id of this domain

radiation_enabled
¶ Determines whether or not to include radiative heat transfer

set_boundary_emissivities
(self, e_left, e_right)¶

set_bounds
(self, *, default=None, Y=None, **kwargs)¶ Set the lower and upper bounds on the solution.
The argument list should consist of keyword/value pairs, with component names as keywords and (lower_bound, upper_bound) tuples as the values. The keyword default may be used to specify default bounds for all unspecified components. The keyword Y can be used to stand for all species mass fractions in flow domains.
>>> d.set_bounds(default=(0, 1), Y=(1.0e5, 2.0))

set_fixed_temp_profile
(self, pos, T)¶ Set the fixed temperature profile. This profile is used whenever the energy equation is disabled.
Parameters:  pos – arrray of relative positions from 0 to 1
 temp – array of temperature values
>>> d.set_fixed_temp_profile(array([0.0, 0.5, 1.0]), ... array([500.0, 1500.0, 2000.0])

set_steady_tolerances
(self, *, default=None, Y=None, abs=None, rel=None, **kwargs)¶ Set the error tolerances for the steadystate problem.
The argument list should consist of keyword/value pairs, with component names as keywords and (rtol, atol) tuples as the values. The keyword default may be used to specify default bounds for all unspecified components. The keyword Y can be used to stand for all species mass fractions in flow domains. Alternatively, the keywords abs and rel can be used to specify arrays for the absolute and relative tolerances for each solution component.

set_transient_tolerances
(self, *, default=None, Y=None, abs=None, rel=None, **kwargs)¶ Set the error tolerances for the steadystate problem.
The argument list should consist of keyword/value pairs, with component names as keywords and (rtol, atol) tuples as the values. The keyword default may be used to specify default bounds for all unspecified components. The keyword Y can be used to stand for all species mass fractions in flow domains. Alternatively, the keywords abs and rel can be used to specify arrays for the absolute and relative tolerances for each solution component.

set_transport
(self, _SolutionBase phase)¶ Set the
Solution
object used for calculating transport properties.

soret_enabled
¶ Determines whether or not to include diffusive mass fluxes due to the Soret effect. Enabling this option works only when using the multicomponent transport model.

steady_abstol
(self, component=None)¶ Return the absolute error tolerance for the steady state problem for a specified solution component, or all components if none is specified.

steady_reltol
(self, component=None)¶ Return the relative error tolerance for the steady state problem for a specified solution component, or all components if none is specified.

tolerances
(self, component)¶ Return the (relative, absolute) error tolerances for a solution component.
>>> rtol, atol = d.tolerances('u')

transient_abstol
(self, component=None)¶ Return the absolute error tolerance for the transient problem for a specified solution component, or all components if none is specified.

transient_reltol
(self, component=None)¶ Return the relative error tolerance for the transient problem for a specified solution component, or all components if none is specified.

AxisymmetricStagnationFlow¶

class
cantera.
AxisymmetricStagnationFlow
(thermo)¶ Bases:
cantera._cantera._FlowBase
An axisymmetric flow domain.
In an axisymmetric flow domain, the equations solved are the similarity equations for the flow in a finiteheight gap of infinite radial extent. The solution variables are:
 u
 axial velocity
 V
 radial velocity divided by radius
 T
 temperature
 lambda
 (1/r)(dP/dr)
 Y_k
 species mass fractions
It may be shown that if the boundary conditions on these variables are independent of radius, then a similarity solution to the exact governing equations exists in which these variables are all independent of radius. This solution holds only in in lowMachnumber limit, in which case (dP/dz) = 0, and lambda is a constant. (Lambda is treated as a spatially varying solution variable for numerical reasons, but in the final solution it is always independent of z.) As implemented here, the governing equations assume an ideal gas mixture. Arbitrary chemistry is allowed, as well as arbitrary variation of the transport properties.

P
¶ Pressure [Pa]

bounds
(self, component)¶ Return the (lower, upper) bounds for a solution component.
>>> d.bounds('T') (200.0, 5000.0)

component_index
(self, str name)¶ Index of the component with name ‘name’

component_name
(self, int n)¶ Name of the nth component.

component_names
¶ List of the names of all components of this domain.

description
¶ A description of this domain

energy_enabled
¶ Determines whether or not to solve the energy equation.

grid
¶ The grid for this domain

have_user_tolerances
¶ have_user_tolerances: __builtin__.bool

index
¶ Index of this domain in a stack. Returns 1 if this domain is not part of a stack.

n_components
¶ Number of solution components at each grid point.

n_points
¶ Number of grid points belonging to this domain.

name
¶ The name / id of this domain

radiation_enabled
¶ Determines whether or not to include radiative heat transfer

set_boundary_emissivities
(self, e_left, e_right)¶

set_bounds
(self, *, default=None, Y=None, **kwargs)¶ Set the lower and upper bounds on the solution.
The argument list should consist of keyword/value pairs, with component names as keywords and (lower_bound, upper_bound) tuples as the values. The keyword default may be used to specify default bounds for all unspecified components. The keyword Y can be used to stand for all species mass fractions in flow domains.
>>> d.set_bounds(default=(0, 1), Y=(1.0e5, 2.0))

set_fixed_temp_profile
(self, pos, T)¶ Set the fixed temperature profile. This profile is used whenever the energy equation is disabled.
Parameters:  pos – arrray of relative positions from 0 to 1
 temp – array of temperature values
>>> d.set_fixed_temp_profile(array([0.0, 0.5, 1.0]), ... array([500.0, 1500.0, 2000.0])

set_steady_tolerances
(self, *, default=None, Y=None, abs=None, rel=None, **kwargs)¶ Set the error tolerances for the steadystate problem.
The argument list should consist of keyword/value pairs, with component names as keywords and (rtol, atol) tuples as the values. The keyword default may be used to specify default bounds for all unspecified components. The keyword Y can be used to stand for all species mass fractions in flow domains. Alternatively, the keywords abs and rel can be used to specify arrays for the absolute and relative tolerances for each solution component.

set_transient_tolerances
(self, *, default=None, Y=None, abs=None, rel=None, **kwargs)¶ Set the error tolerances for the steadystate problem.
The argument list should consist of keyword/value pairs, with component names as keywords and (rtol, atol) tuples as the values. The keyword default may be used to specify default bounds for all unspecified components. The keyword Y can be used to stand for all species mass fractions in flow domains. Alternatively, the keywords abs and rel can be used to specify arrays for the absolute and relative tolerances for each solution component.

set_transport
(self, _SolutionBase phase)¶ Set the
Solution
object used for calculating transport properties.

soret_enabled
¶ Determines whether or not to include diffusive mass fluxes due to the Soret effect. Enabling this option works only when using the multicomponent transport model.

steady_abstol
(self, component=None)¶ Return the absolute error tolerance for the steady state problem for a specified solution component, or all components if none is specified.

steady_reltol
(self, component=None)¶ Return the relative error tolerance for the steady state problem for a specified solution component, or all components if none is specified.

tolerances
(self, component)¶ Return the (relative, absolute) error tolerances for a solution component.
>>> rtol, atol = d.tolerances('u')

transient_abstol
(self, component=None)¶ Return the absolute error tolerance for the transient problem for a specified solution component, or all components if none is specified.

transient_reltol
(self, component=None)¶ Return the relative error tolerance for the transient problem for a specified solution component, or all components if none is specified.
Boundaries¶
Outlet1D¶

class
cantera.
Outlet1D
(phase, name=None)¶ Bases:
cantera._cantera.Boundary1D
A onedimensional outlet. An outlet imposes a zerogradient boundary condition on the flow.
OutletReservoir1D¶

class
cantera.
OutletReservoir1D
(phase, name=None)¶ Bases:
cantera._cantera.Boundary1D
A onedimensional outlet into a reservoir.
SymmetryPlane1D¶

class
cantera.
SymmetryPlane1D
(phase, name=None)¶ Bases:
cantera._cantera.Boundary1D
A symmetry plane.
Surface1D¶

class
cantera.
Surface1D
(phase, name=None)¶ Bases:
cantera._cantera.Boundary1D
A solid surface.
Base Classes¶
Domain1D¶

class
cantera.
Domain1D
(name=None)¶ Bases:
object
Domain1D(_SolutionBase phase, name=None, *args, **kwargs)

bounds
(self, component)¶ Return the (lower, upper) bounds for a solution component.
>>> d.bounds('T') (200.0, 5000.0)

component_index
(self, str name)¶ Index of the component with name ‘name’

component_name
(self, int n)¶ Name of the nth component.

component_names
¶ List of the names of all components of this domain.

description
¶ A description of this domain

grid
¶ The grid for this domain

have_user_tolerances
¶ have_user_tolerances: __builtin__.bool

index
¶ Index of this domain in a stack. Returns 1 if this domain is not part of a stack.

n_components
¶ Number of solution components at each grid point.

n_points
¶ Number of grid points belonging to this domain.

name
¶ The name / id of this domain

set_bounds
(self, *, default=None, Y=None, **kwargs)¶ Set the lower and upper bounds on the solution.
The argument list should consist of keyword/value pairs, with component names as keywords and (lower_bound, upper_bound) tuples as the values. The keyword default may be used to specify default bounds for all unspecified components. The keyword Y can be used to stand for all species mass fractions in flow domains.
>>> d.set_bounds(default=(0, 1), Y=(1.0e5, 2.0))

set_steady_tolerances
(self, *, default=None, Y=None, abs=None, rel=None, **kwargs)¶ Set the error tolerances for the steadystate problem.
The argument list should consist of keyword/value pairs, with component names as keywords and (rtol, atol) tuples as the values. The keyword default may be used to specify default bounds for all unspecified components. The keyword Y can be used to stand for all species mass fractions in flow domains. Alternatively, the keywords abs and rel can be used to specify arrays for the absolute and relative tolerances for each solution component.

set_transient_tolerances
(self, *, default=None, Y=None, abs=None, rel=None, **kwargs)¶ Set the error tolerances for the steadystate problem.
The argument list should consist of keyword/value pairs, with component names as keywords and (rtol, atol) tuples as the values. The keyword default may be used to specify default bounds for all unspecified components. The keyword Y can be used to stand for all species mass fractions in flow domains. Alternatively, the keywords abs and rel can be used to specify arrays for the absolute and relative tolerances for each solution component.

steady_abstol
(self, component=None)¶ Return the absolute error tolerance for the steady state problem for a specified solution component, or all components if none is specified.

steady_reltol
(self, component=None)¶ Return the relative error tolerance for the steady state problem for a specified solution component, or all components if none is specified.

tolerances
(self, component)¶ Return the (relative, absolute) error tolerances for a solution component.
>>> rtol, atol = d.tolerances('u')

transient_abstol
(self, component=None)¶ Return the absolute error tolerance for the transient problem for a specified solution component, or all components if none is specified.

transient_reltol
(self, component=None)¶ Return the relative error tolerance for the transient problem for a specified solution component, or all components if none is specified.

Boundary1D¶

class
cantera.
Boundary1D
(phase, name=None)¶ Bases:
cantera._cantera.Domain1D
Base class for boundary domains.
Parameters: phase – The (gas) phase corresponding to the adjacent flow domain 
T
¶ The temperature [K] at this boundary.

X
¶ Species mole fractions at this boundary. May be set as either a string or as an array.

Y
¶ Species mass fractions at this boundary. May be set as either a string or as an array.

mdot
¶ The mass flow rate per unit area [kg/m^2]

Sim1D¶

class
cantera.
Sim1D
(domains)¶ Bases:
object
Sim1D(domains, *args, **kwargs)
Class Sim1D is a container for onedimensional domains. It also holds the multidomain solution vector, and controls the process of finding the solution.
Domains are ordered lefttoright, with domain number 0 at the left.

clear_stats
(self)¶ Clear solver statistics.

domain_index
(self, dom)¶ Get the index of a domain, specified either by name or as a Domain1D object.

domains
¶

eval_count_stats
¶ Return number of nonJacobian function evaluations made in each call to solve()

eval_time_stats
¶ Return CPU time spent on nonJacobian function evaluations in each call to solve()

extinct
(self)¶ Method overloaded for some flame types to indicate if the flame has been extinguished. Base class method always returns ‘False’

get_max_grid_points
(self, domain)¶ Get the maximum number of grid points in the specified domain.

grid_size_stats
¶ Return total grid size in each call to solve()

jacobian_count_stats
¶ Return number of Jacobian evaluations made in each call to solve()

jacobian_time_stats
¶ Return CPU time spent evaluating Jacobians in each call to solve()

max_time_step_count
¶ Get/Set the maximum number of time steps allowed before reaching the steadystate solution

profile
(self, domain, component)¶ Spatial profile of one component in one domain.
Parameters:  domain – Domain1D object, name, or index
 component – component name or index
>>> T = s.profile(flow, 'T')

refine
(self, loglevel=1)¶ Refine the grid, adding points where solution is not adequately resolved.

restore
(self, filename='soln.xml', name='solution', loglevel=2)¶ Set the solution vector to a previouslysaved solution.
Parameters:  filename – solution file
 name – solution name within the file
 loglevel – Amount of logging information to display while restoring, from 0 (disabled) to 2 (most verbose).
>>> s.restore(filename='save.xml', name='energy_off')

restore_steady_solution
(self)¶ Set the current solution vector to the last successful steadystate solution. This can be used to examine the solver progress after a failure during grid refinement.

restore_time_stepping_solution
(self)¶ Set the current solution vector to the last successful timestepping solution. This can be used to examine the solver progress after a failed integration.

save
(self, filename='soln.xml', name='solution', description='none', loglevel=1)¶ Save the solution in XML format.
Parameters:  filename – solution file
 name – solution name within the file
 description – custom description text
>>> s.save(filename='save.xml', name='energy_off', ... description='solution with energy eqn. disabled')

set_fixed_temperature
(self, T)¶ Set the temperature used to fix the spatial location of a freely propagating flame.

set_flat_profile
(self, domain, component, value)¶ Set a flat profile for one component in one domain.
Parameters:  domain – Domain1D object, name, or index
 component – component name or index
 v – value
>>> s.set_flat_profile(d, 'u', 3.0)

set_grid_min
(self, dz, domain=None)¶ Set the minimum grid spacing on domain. If domain is None, then set the grid spacing for all domains.

set_initial_guess
(self, *args, **kwargs)¶ Set the initial guess for the solution. Derived classes extend this function to set approximations for the temperature and composition profiles.

set_interrupt
(self, f)¶ Set an interrupt function to be called each time that OneDim::eval is called. The signature of f is
float f(float)
. The default interrupt function is used to trap KeyboardInterrupt exceptions so thatctrlc
can be used to break out of the C++ solver loop.

set_max_grid_points
(self, domain, npmax)¶ Set the maximum number of grid points in the specified domain.

set_max_jac_age
(self, ss_age, ts_age)¶ Set the maximum number of times the Jacobian will be used before it must be reevaluated.
Parameters:  ss_age – age criterion during steadystate mode
 ts_age – age criterion during timestepping mode

set_max_time_step
(self, tsmax)¶ Set the maximum time step.

set_min_time_step
(self, tsmin)¶ Set the minimum time step.

set_profile
(self, domain, component, positions, values)¶ Set an initial estimate for a profile of one component in one domain.
Parameters:  domain – Domain1D object, name, or index
 component – component name or index
 positions – sequence of relative positions, from 0 on the left to 1 on the right
 values – sequence of values at the relative positions specified in positions
>>> s.set_profile(d, 'T', [0.0, 0.2, 1.0], [400.0, 800.0, 1500.0])

set_refine_criteria
(self, domain, ratio=10.0, slope=0.8, curve=0.8, prune=0.05)¶ Set the criteria used to refine one domain.
Parameters:  domain – domain object, index, or name
 ratio – additional points will be added if the ratio of the spacing on either side of a grid point exceeds this value
 slope – maximum difference in value between two adjacent points, scaled by the maximum difference in the profile (0.0 < slope < 1.0). Adds points in regions of high slope.
 curve – maximum difference in slope between two adjacent intervals, scaled by the maximum difference in the profile (0.0 < curve < 1.0). Adds points in regions of high curvature.
 prune – if the slope or curve criteria are satisfied to the level of ‘prune’, the grid point is assumed not to be needed and is removed. Set prune significantly smaller than ‘slope’ and ‘curve’. Set to zero to disable pruning the grid.
>>> s.set_refine_criteria(d, ratio=5.0, slope=0.2, curve=0.3, prune=0.03)

set_steady_callback
(self, f)¶ Set a callback function to be called after each successful steadystate solve, before regridding. The signature of f is
float f(float)
. The argument passed to f is “0” and the output is ignored.

set_time_step
(self, stepsize, n_steps)¶ Set the sequence of time steps to try when Newton fails.
Parameters:  stepsize – initial time step size [s]
 n_steps – sequence of integer step numbers
>>> s.set_time_step(1.0e5, [1, 2, 5, 10])

set_time_step_callback
(self, f)¶ Set a callback function to be called after each successful timestep. The signature of f is
float f(float)
. The argument passed to f is the size of the timestep. The output is ignored.

set_time_step_factor
(self, tfactor)¶ Set the factor by which the time step will be increased after a successful step, or decreased after an unsuccessful one.

set_value
(self, domain, component, point, value)¶ Set the value of one component in one domain at one point to ‘value’.
Parameters:  domain – Domain1D object, name, or index
 component – component name or index
 point – grid point number within domain starting with 0 on the left
 value – numerical value
>>> s.set(d, 3, 5, 6.7) >>> s.set(1, 0, 5, 6.7) >>> s.set('flow', 'T', 5, 500)

show_solution
(self)¶ print the current solution.

show_stats
(self, print_time=True)¶ Show the statistics for the last solution.
If invoked with no arguments or with a nonzero argument, the timing statistics will be printed. Otherwise, the timing will not be printed.

solve
(self, loglevel=1, refine_grid=True, auto=False)¶ Solve the problem.
Parameters:  loglevel – integer flag controlling the amount of diagnostic output. Zero suppresses all output, and 5 produces very verbose output.
 refine_grid – if True, enable grid refinement.
 auto – if True, sequentially execute the different solution stages and attempt to automatically recover from errors. Attempts to first solve on the initial grid with energy enabled. If that does not succeed, a fixedtemperature solution will be tried followed by enabling the energy equation, and then with grid refinement enabled. If nondefault tolerances have been specified or multicomponent transport is enabled, an additional solution using these options will be calculated.

solve_adjoint
(self, perturb, n_params, dgdx, g=None, dp=1e5)¶ Find the sensitivities of an objective function using an adjoint method.
For an objective function \(g(x, p)\) where \(x\) is the state vector of the system and \(p\) is a vector of parameters, this computes the vector of sensitivities \(dg/dp\). This assumes that the system of equations has already been solved to find \(x\).
Parameters:  perturb –
A function with the signature
perturb(sim, i, dp)
which perturbs parameteri
by a relative factor ofdp
. To perturb a reaction rate constant, this function could be defined as:def perturb(sim, i, dp): sim.gas.set_multiplier(1+dp, i)
Calling
perturb(sim, i, 0)
should restore that parameter to its default value.  n_params – The length of the vector of sensitivity parameters
 dgdx – The vector of partial derivatives of the function \(g(x, p)\) with respect to the system state \(x\).
 g – A function with the signature
value = g(sim)
which computes the value of \(g(x,p)\) at the current system state. This is used to compute \(\partial g/\partial p\). If this is identically zero (i.e. \(g\) is independent of \(p\)) then this argument may be omitted.  dp – A relative value by which to perturb each parameter
 perturb –

time_step_stats
¶ Return number of time steps taken in each call to solve()

value
(self, domain, component, point)¶ Solution value at one point
Parameters:  domain – Domain1D object, name, or index
 component – component name or index
 point – grid point number within domain starting with 0 on the left
>>> t = s.value('flow', 'T', 6)

work_value
(self, domain, component, point)¶ Internal work array value at one point. After calling eval, this array contains the values of the residual function.
Parameters:  domain – Domain1D object, name, or index
 component – component name or index
 point – grid point number in the domain, starting with zero at the left
>>> t = s.value(flow, 'T', 6)

FlameBase¶

class
cantera.
FlameBase
(domains, gas, grid=None)¶ Bases:
cantera._cantera.Sim1D
Base class for flames with a single flow domain
Parameters:  gas – object to use to evaluate all gas properties and reaction rates
 grid – array of initial grid points

L
¶ Array containing the radial pressure gradient (1/r)(dP/dr) [N/m^4] at each point. Note: This value is named ‘lambda’ in the C++ code.

P
¶ Get/Set the pressure of the flame [Pa]

T
¶ Array containing the temperature [K] at each grid point.

V
¶ Array containing the tangential velocity gradient [1/s] at each point.

X
¶ Get/Set the species mole fractions. Can be set as an array, as a dictionary, or as a string. Always returns an array:
>>> phase.X = [0.1, 0, 0, 0.4, 0, 0, 0, 0, 0.5] >>> phase.X = {'H2':0.1, 'O2':0.4, 'AR':0.5} >>> phase.X = 'H2:0.1, O2:0.4, AR:0.5' >>> phase.X array([0.1, 0, 0, 0.4, 0, 0, 0, 0, 0.5])
Returns an array of size
n_species
xn_points
.

Y
¶ Get/Set the species mass fractions. Can be set as an array, as a dictionary, or as a string. Always returns an array:
>>> phase.Y = [0.1, 0, 0, 0.4, 0, 0, 0, 0, 0.5] >>> phase.Y = {'H2':0.1, 'O2':0.4, 'AR':0.5} >>> phase.Y = 'H2:0.1, O2:0.4, AR:0.5' >>> phase.Y array([0.1, 0, 0, 0.4, 0, 0, 0, 0, 0.5])
Returns an array of size
n_species
xn_points
.

chemical_potentials
¶ Array of species chemical potentials [J/kmol].
Returns an array of size
n_species
xn_points
.

concentrations
¶ Get/Set the species concentrations [kmol/m^3].
Returns an array of size
n_species
xn_points
.

cp
¶ Heat capacity at constant pressure [J/kg/K or J/kmol/K] depending on
basis
.Returns an array of length
n_points
.

cp_mass
¶ Specific heat capacity at constant pressure [J/kg/K].
Returns an array of length
n_points
.

cp_mole
¶ Molar heat capacity at constant pressure [J/kmol/K].
Returns an array of length
n_points
.

creation_rates
¶ Creation rates for each species. [kmol/m^3/s] for bulk phases or [kmol/m^2/s] for surface phases.
Returns an array of size
n_species
xn_points
.

cv
¶ Heat capacity at constant volume [J/kg/K or J/kmol/K] depending on
basis
.Returns an array of length
n_points
.

cv_mass
¶ Specific heat capacity at constant volume [J/kg/K].
Returns an array of length
n_points
.

cv_mole
¶ Molar heat capacity at constant volume [J/kmol/K].
Returns an array of length
n_points
.

delta_enthalpy
¶ Change in enthalpy for each reaction [J/kmol].
Returns an array of size
n_reactions
xn_points
.

delta_entropy
¶ Change in entropy for each reaction [J/kmol/K].
Returns an array of size
n_reactions
xn_points
.

delta_gibbs
¶ Change in Gibbs free energy for each reaction [J/kmol].
Returns an array of size
n_reactions
xn_points
.

delta_standard_enthalpy
¶ Change in standardstate enthalpy (independent of composition) for each reaction [J/kmol].
Returns an array of size
n_reactions
xn_points
.

delta_standard_entropy
¶ Change in standardstate entropy (independent of composition) for each reaction [J/kmol/K].
Returns an array of size
n_reactions
xn_points
.

delta_standard_gibbs
¶ Change in standardstate Gibbs free energy (independent of composition) for each reaction [J/kmol].
Returns an array of size
n_reactions
xn_points
.

density
¶ Density [kg/m^3 or kmol/m^3] depending on
basis
.Returns an array of length
n_points
.

density_mass
¶ (Mass) density [kg/m^3].
Returns an array of length
n_points
.

density_mole
¶ Molar density [kmol/m^3].
Returns an array of length
n_points
.

destruction_rates
¶ Destruction rates for each species. [kmol/m^3/s] for bulk phases or [kmol/m^2/s] for surface phases.
Returns an array of size
n_species
xn_points
.

electrochemical_potentials
¶ Array of species electrochemical potentials [J/kmol].
Returns an array of size
n_species
xn_points
.

elemental_mass_fraction
(m)¶ Get the elemental mass fraction \(Z_{\mathrm{mass},m}\) of element \(m\) at each grid point, which is defined as:
\[Z_{\mathrm{mass},m} = \sum_k \frac{a_{m,k} M_m}{M_k} Y_k\]with \(a_{m,k}\) being the number of atoms of element \(m\) in species \(k\), \(M_m\) the atomic weight of element \(m\), \(M_k\) the molecular weight of species \(k\), and \(Y_k\) the mass fraction of species \(k\).
Parameters: m – Base element, may be specified by name or by index. >>> phase.elemental_mass_fraction('H') [1.0, ..., 0.0]

elemental_mole_fraction
(m)¶ Get the elemental mole fraction \(Z_{\mathrm{mole},m}\) of element \(m\) at each grid point, which is defined as:
\[Z_{\mathrm{mole},m} = \sum_k \frac{a_{m,k}}{\sum_j a_{j,k}} X_k\]with \(a_{m,k}\) being the number of atoms of element \(m\) in species \(k\) and \(X_k\) the mole fraction of species \(k\).
Parameters: m – Base element, may be specified by name or by index. >>> phase.elemental_mole_fraction('H') [1.0, ..., 0.0]

energy_enabled
¶ Get/Set whether or not to solve the energy equation.

enthalpy_mass
¶ Specific enthalpy [J/kg].
Returns an array of length
n_points
.

enthalpy_mole
¶ Molar enthalpy [J/kmol].
Returns an array of length
n_points
.

entropy_mass
¶ Specific entropy [J/kg].
Returns an array of length
n_points
.

entropy_mole
¶ Molar entropy [J/kmol/K].
Returns an array of length
n_points
.

equilibrium_constants
¶ Equilibrium constants in concentration units for all reactions.
Returns an array of size
n_reactions
xn_points
.

forward_rate_constants
¶ Forward rate constants for all reactions. Units are a combination of kmol, m^3 and s, that depend on the rate expression for the reaction.
Returns an array of size
n_reactions
xn_points
.

forward_rates_of_progress
¶ Forward rates of progress for the reactions. [kmol/m^3/s] for bulk phases or [kmol/m^2/s] for surface phases.
Returns an array of size
n_reactions
xn_points
.

g
¶ Gibbs free energy [J/kg or J/kmol] depending on
basis
.Returns an array of length
n_points
.

gas
¶

gibbs_mass
¶ Specific Gibbs free energy [J/kg].
Returns an array of length
n_points
.

gibbs_mole
¶ Molar Gibbs free energy [J/kmol].
Returns an array of length
n_points
.

grid
¶ Array of grid point positions along the flame.

h
¶ Enthalpy [J/kg or J/kmol] depending on
basis
.Returns an array of length
n_points
.

heat_production_rates
¶ Get the volumetric heat production rates [W/m^3] on a perreaction basis. The sum over all reactions results in the total volumetric heat release rate. Example: C. K. Law: Combustion Physics (2006), Fig. 7.8.6
>>> f.heat_production_rates[2] # heat production rate of the 2nd reaction

heat_release_rate
¶ Get the total volumetric heat release rate [W/m^3].

int_energy
¶ Internal energy in [J/kg or J/kmol].
Returns an array of length
n_points
.

int_energy_mass
¶ Specific internal energy [J/kg].
Returns an array of length
n_points
.

int_energy_mole
¶ Molar internal energy [J/kmol].
Returns an array of length
n_points
.

isothermal_compressibility
¶ Isothermal compressibility [1/Pa].
Returns an array of length
n_points
.

max_grid_points
¶ Get/Set the maximum number of grid points used in the solution of this flame.

mix_diff_coeffs
¶ Mixtureaveraged diffusion coefficients [m^2/s] relating the massaveraged diffusive fluxes (with respect to the mass averaged velocity) to gradients in the species mole fractions.
Returns an array of size
n_species
xn_points
.

mix_diff_coeffs_mass
¶ Mixtureaveraged diffusion coefficients [m^2/s] relating the diffusive mass fluxes to gradients in the species mass fractions.
Returns an array of size
n_species
xn_points
.

mix_diff_coeffs_mole
¶ Mixtureaveraged diffusion coefficients [m^2/s] relating the molar diffusive fluxes to gradients in the species mole fractions.
Returns an array of size
n_species
xn_points
.

net_production_rates
¶ Net production rates for each species. [kmol/m^3/s] for bulk phases or [kmol/m^2/s] for surface phases.
Returns an array of size
n_species
xn_points
.

net_rates_of_progress
¶ Net rates of progress for the reactions. [kmol/m^3/s] for bulk phases or [kmol/m^2/s] for surface phases.
Returns an array of size
n_reactions
xn_points
.

partial_molar_cp
¶ Array of species partial molar specific heat capacities at constant pressure [J/kmol/K].
Returns an array of size
n_species
xn_points
.

partial_molar_enthalpies
¶ Array of species partial molar enthalpies [J/kmol].
Returns an array of size
n_species
xn_points
.

partial_molar_entropies
¶ Array of species partial molar entropies [J/kmol/K].
Returns an array of size
n_species
xn_points
.

partial_molar_int_energies
¶ Array of species partial molar internal energies [J/kmol].
Returns an array of size
n_species
xn_points
.

partial_molar_volumes
¶ Array of species partial molar volumes [m^3/kmol].
Returns an array of size
n_species
xn_points
.

radiation_enabled
¶ Get/Set whether or not to include radiative heat transfer

reverse_rate_constants
¶ Reverse rate constants for all reactions. Units are a combination of kmol, m^3 and s, that depend on the rate expression for the reaction.
Returns an array of size
n_reactions
xn_points
.

reverse_rates_of_progress
¶ Reverse rates of progress for the reactions. [kmol/m^3/s] for bulk phases or [kmol/m^2/s] for surface phases.
Returns an array of size
n_reactions
xn_points
.

s
¶ Entropy [J/kg/K or J/kmol/K] depending on
basis
.Returns an array of length
n_points
.

set_boundary_emissivities
(e_left, e_right)¶

set_gas_state
(point)¶ Set the state of the the Solution object used for calculations,
self.gas
, to the temperature and composition at the point with index point.

set_profile
(component, locations, values)¶ Set an initial estimate for a profile of one component.
Parameters:  component – component name or index
 positions – sequence of relative positions, from 0 on the left to 1 on the right
 values – sequence of values at the relative positions specified in positions
>>> f.set_profile('T', [0.0, 0.2, 1.0], [400.0, 800.0, 1500.0])

set_refine_criteria
(ratio=10.0, slope=0.8, curve=0.8, prune=0.0)¶ Set the criteria used for grid refinement.
Parameters:  ratio – additional points will be added if the ratio of the spacing on either side of a grid point exceeds this value
 slope – maximum difference in value between two adjacent points, scaled by the maximum difference in the profile (0.0 < slope < 1.0). Adds points in regions of high slope.
 curve – maximum difference in slope between two adjacent intervals, scaled by the maximum difference in the profile (0.0 < curve < 1.0). Adds points in regions of high curvature.
 prune – if the slope or curve criteria are satisfied to the level of ‘prune’, the grid point is assumed not to be needed and is removed. Set prune significantly smaller than ‘slope’ and ‘curve’. Set to zero to disable pruning the grid.
>>> f.set_refine_criteria(ratio=3.0, slope=0.1, curve=0.2, prune=0)

solution
(component, point=None)¶ Get the solution at one point or for the full flame domain (if
point=None
) for the specified component. The component can be specified by name or index.

soret_enabled
¶ Get/Set whether or not to include diffusive mass fluxes due to the Soret effect. Enabling this option works only when using the multicomponent transport model.

standard_cp_R
¶ Array of nondimensional species standardstate specific heat capacities at constant pressure at the current temperature and pressure.
Returns an array of size
n_species
xn_points
.

standard_enthalpies_RT
¶ Array of nondimensional species standardstate enthalpies at the current temperature and pressure.
Returns an array of size
n_species
xn_points
.

standard_entropies_R
¶ Array of nondimensional species standardstate entropies at the current temperature and pressure.
Returns an array of size
n_species
xn_points
.

standard_gibbs_RT
¶ Array of nondimensional species standardstate Gibbs free energies at the current temperature and pressure.
Returns an array of size
n_species
xn_points
.

standard_int_energies_RT
¶ Array of nondimensional species standardstate internal energies at the current temperature and pressure.
Returns an array of size
n_species
xn_points
.

thermal_conductivity
¶ Thermal conductivity. [W/m/K].
Returns an array of length
n_points
.

thermal_diff_coeffs
¶ Return a onedimensional array of the species thermal diffusion coefficients [kg/m/s].
Returns an array of size
n_species
xn_points
.

thermal_expansion_coeff
¶ Thermal expansion coefficient [1/K].
Returns an array of length
n_points
.

u
¶ Array containing the velocity [m/s] normal to the flame at each point.

viscosity
¶ Viscosity [Pas].
Returns an array of length
n_points
.

volume
¶ Specific volume [m^3/kg or m^3/kmol] depending on
basis
.Returns an array of length
n_points
.

volume_mass
¶ Specific volume [m^3/kg].
Returns an array of length
n_points
.

volume_mole
¶ Molar volume [m^3/kmol].
Returns an array of length
n_points
.

write_csv
(filename, species='X', quiet=True)¶ Write the velocity, temperature, density, and species profiles to a CSV file.
Parameters:  filename – Output file name
 species – Attribute to use obtaining species profiles, e.g.
X
for mole fractions orY
for mass fractions.