Steady radial LTE Elenbaas-Heller arc column (custom Cantera Domain1D). More...

#include <ThermalPlasmaColumn1D.h>

Inheritance diagram for rizer::ThermalPlasmaColumn1D:

Public Member Functions
	ThermalPlasmaColumn1D (double R, std::size_t npoints, double electric_field, double T_wall, PropertyTable sigma, PropertyTable kappa, PropertyTable p_rad, double T_center_guess, double rho_cp, PropertyTable init_profile=PropertyTable())
	Construct a radial LTE arc-column domain with tabulated property closures.
std::string	domainType () const override
void	eval (std::size_t jg, Cantera::span< const double > xg, Cantera::span< double > rg, Cantera::span< int > maskg, double rdt) override
	Evaluate the residual function at point jg.
std::string	componentName (std::size_t n) const override
std::size_t	componentIndex (const std::string &name, bool checkAlias=true) const override
	Return the index of the named solution component.
bool	hasComponent (const std::string &name, bool checkAlias=true) const override
	Test whether a component name exists in this domain.
void	getValues (const std::string &component, Cantera::span< double > values) const override
	Copy converged temperatures from the shared global solution vector.
double	initialValue (std::size_t n, std::size_t j) override
	Initial guess for component n at grid point j.
void	resetBadValues (Cantera::span< double > xg) override
	Clamp any out-of-bound temperatures after a failed Newton step to keep the solve from wandering into unphysical territory (T < 0 or T > 1e5 K).
void	setElectricField (double E)
	Change the electric field without rebuilding the domain (used by the Python-side secant iteration for current control).
double	electricField () const
double	radius () const
double	sigmaAt (double T) const
	Property look-ups at a given temperature, for post-processing.
double	kappaAt (double T) const
double	pRadAt (double T) const
Public Member Functions inherited from Cantera::Domain1D
size_t	domainIndex ()
virtual bool	isConnector ()
virtual void	setTransportModel (const string &model)
const OneDim &	container () const
void	setContainer (OneDim *c, size_t index)
void	setBandwidth (int bw=-1)
size_t	bandwidth ()
virtual void	init ()
virtual void	resize (size_t nv, size_t np)
Refiner &	refiner ()
size_t	nComponents () const
size_t	nPoints () const
virtual string	componentName (size_t n) const
void	setComponentName (size_t n, const string &name)
virtual size_t	componentIndex (const string &name, bool checkAlias=true) const
virtual bool	hasComponent (const string &name, bool checkAlias=true) const
virtual void	updateState (size_t loc)
void	setBounds (size_t n, double lower, double upper)
void	setTransientTolerances (double rtol, double atol, size_t n=npos)
void	setSteadyTolerances (double rtol, double atol, size_t n=npos)
double	rtol (size_t n)
double	atol (size_t n)
double	steady_rtol (size_t n)
double	steady_atol (size_t n)
double	transient_rtol (size_t n)
double	transient_atol (size_t n)
double	upperBound (size_t n) const
double	lowerBound (size_t n) const
void	setRefineCriteria (double ratio=10.0, double slope=0.8, double curve=0.8, double prune=-0.1)
vector< double >	getRefineCriteria ()
void	initTimeInteg (double dt, span< const double > x0)
void	setSteadyMode ()
bool	steady ()
bool	transient ()
void	needJacUpdate ()
virtual void	eval (size_t j, span< const double > x, span< double > r, span< int > mask, double rdt=0.0)
size_t	index (size_t n, size_t j) const
virtual double	value (const string &component) const
virtual void	setValue (const string &component, double value)
vector< double >	values (const string &component) const
virtual void	getValues (const string &component, span< double > values) const
virtual void	setValues (const string &component, span< const double > values)
vector< double >	residuals (const string &component) const
virtual void	getResiduals (const string &component, span< double > values) const
virtual void	setProfile (const string &component, span< const double > pos, span< const double > values)
virtual void	setFlatProfile (const string &component, double value)
virtual shared_ptr< SolutionArray >	toArray (bool normalize=false)
virtual void	fromArray (const shared_ptr< SolutionArray > &arr)
string	info (const vector< string > &keys, int rows=10, int width=80)
string	_info (int rows=10, int width=80)
shared_ptr< Solution >	phase () const
size_t	size () const
void	locate ()
virtual size_t	loc (size_t j=0) const
size_t	firstPoint () const
size_t	lastPoint () const
void	linkLeft (Domain1D *left)
void	linkRight (Domain1D *right)
void	append (Domain1D *right)
Domain1D *	left () const
Domain1D *	right () const
double	prevSoln (size_t n, size_t j) const
void	setID (const string &s)
string	id () const
virtual void	show (span< const double > x)
double	z (size_t jlocal) const
double	zmin () const
double	zmax () const
span< double >	grid ()
span< const double >	grid () const
virtual void	setupGrid (span< const double > z)
void	setupUniformGrid (size_t points, double length, double start=0.)
virtual void	_getInitialSoln (span< double > x)
virtual double	initialValue (size_t n, size_t j)
virtual void	_finalize (span< const double > x)
void	forceFullUpdate (bool update)
void	setData (shared_ptr< vector< double > > &data)

Additional Inherited Members
Protected Member Functions inherited from Cantera::Domain1D
	Domain1D (size_t nv=1, size_t points=1, double time=0.0)
virtual void	_setKinetics (shared_ptr< Kinetics > kin)
virtual void	_setTransport (shared_ptr< Transport > trans)
virtual AnyMap	getMeta () const
virtual void	setMeta (const AnyMap &meta)
Protected Attributes inherited from Cantera::Domain1D
double	m_press
shared_ptr< vector< double > >	m_state
double	m_rdt
size_t	m_nv
size_t	m_points
vector< double >	m_slast
vector< double >	m_max
vector< double >	m_min
vector< double >	m_rtol_ss
vector< double >	m_rtol_ts
vector< double >	m_atol_ss
vector< double >	m_atol_ts
vector< double >	m_z
OneDim *	m_container
size_t	m_index
size_t	m_iloc
size_t	m_jstart
Domain1D *	m_left
Domain1D *	m_right
string	m_id
unique_ptr< Refiner >	m_refiner
vector< string >	m_name
int	m_bw
bool	m_force_full_update
shared_ptr< Solution >	m_solution

Detailed Description

Steady radial LTE Elenbaas-Heller arc column (custom Cantera Domain1D).

ThermalPlasmaColumn1D: a custom Cantera Domain1D solving the steady radial Elenbaas-Heller arc equation in cylindrical coordinates:

\[ \frac{1}{r}\frac{d}{dr}\!\left(r \kappa(T) \frac{dT}{dr}\right) + \sigma(T) E^2 - P_\text{rad}(T) = 0 \]

State: one component (temperature T) per grid point; the grid coordinate is the radius r in [0, R]. Boundary conditions are handled inside eval():

\( r = 0 \): symmetry (natural zero-flux finite-volume face)
\( r = R \): Dirichlet \( T = T_\text{wall} \) The domain is bracketed by Empty1D terminators in PlasmaColumnSolver.

ASSUMPTIONS AND DOMAIN OF VALIDITY (mirrored in the Python wrapper ThermalPlasmaColumn, which is what Sphinx renders – keep the two in sync):

Steady state (no d/dt): the equilibrium arc column, not a transient. For transient/non-equilibrium plasmas use PlasmaChannel1D.
Local Thermodynamic Equilibrium (LTE): a SINGLE temperature T (Te=T_heavy); sigma(T), kappa(T), composition from tabulated LTE data. Valid at high pressure / high collisionality; NOT valid for non-equilibrium plasmas.
1D radial, cylindrical, axisymmetric, infinitely long: no axial gradients, NO convection – a pure radial conduction balance.
Energy: radial conduction + ohmic sigma*E^2 - optional radiation \( P_\text{rad} = 4\pi\,\mathrm{NEC}(T) \) (off by default), treated OPTICALLY THIN (no reabsorption).
Numerics: nonlinear FV solved with Cantera damped-Newton + adaptive grid refinement; current control = secant iteration on E; hot branch is stiff, so it is seeded with the analytical EH profile (seed affects only convergence).

Definition at line 48 of file ThermalPlasmaColumn1D.h.

Constructor & Destructor Documentation

◆ ThermalPlasmaColumn1D()

rizer::ThermalPlasmaColumn1D::ThermalPlasmaColumn1D	(	double	R,
		std::size_t	npoints,
		double	electric_field,
		double	T_wall,
		PropertyTable	sigma,
		PropertyTable	kappa,
		PropertyTable	p_rad,
		double	T_center_guess,
		double	rho_cp,
		PropertyTable	init_profile = PropertyTable() )

Construct a radial LTE arc-column domain with tabulated property closures.

Parameters

R	Outer (wall) radius [m]
npoints	Initial uniform grid point count [-]
electric_field	Axial electric field E [V/m]
T_wall	Wall (r=R) Dirichlet temperature [K]
sigma	Electrical conductivity table sigma(T) [S/m] vs. T [K]
kappa	Thermal conductivity table kappa(T) [W/m/K] vs. T [K]
p_rad	Volumetric radiative loss table P_rad(T) [W/m^3] vs. T [K]; empty -> no radiation term
T_center_guess	Parabolic-seed centerline temperature [K], used when init_profile is empty
rho_cp	rho*cp [J/m^3/K], scales the pseudo-transient Newton-fallback term
init_profile	Optional seed T(r) profile [K] vs. r [m]; empty -> default parabola

Definition at line 10 of file ThermalPlasmaColumn1D.cpp.

Member Function Documentation

◆ componentIndex()

std::size_t rizer::ThermalPlasmaColumn1D::componentIndex	(	const std::string &	name,
		bool	checkAlias = true ) const

override

Return the index of the named solution component.

Parameters

name	Component name; only "T" is valid for this domain
checkAlias	Unused (this domain has no aliases)

Definition at line 44 of file ThermalPlasmaColumn1D.cpp.

◆ componentName()

std::string rizer::ThermalPlasmaColumn1D::componentName ( std::size_t n ) const

inlineoverride

Definition at line 95 of file ThermalPlasmaColumn1D.h.

◆ domainType()

std::string rizer::ThermalPlasmaColumn1D::domainType ( ) const

inlineoverridevirtual

Reimplemented from Cantera::Domain1D.

Definition at line 74 of file ThermalPlasmaColumn1D.h.

◆ electricField()

double rizer::ThermalPlasmaColumn1D::electricField ( ) const

inline

Definition at line 134 of file ThermalPlasmaColumn1D.h.

◆ eval()

void rizer::ThermalPlasmaColumn1D::eval	(	std::size_t	jg,
		Cantera::span< const double >	xg,
		Cantera::span< double >	rg,
		Cantera::span< int >	maskg,
		double	rdt )

override

Evaluate the residual function at point jg.

If jg == npos(=-1), evaluate the residual function at all points.

Parameters

	jg	Grid point to (re)evaluate (0..npts-1), or Cantera::npos for a full residual pass [-]
	xg	Full global state vector (all domains); this domain's slice at loc() is T(r) [K]
[out]	rg	Full global residual vector to write into (dT/dt at each grid point, 0 at steady state), same layout as xg
[out]	maskg	Full global transient/algebraic mask (1 = has dT/dt, 0 = algebraic row) [-]
	rdt	Pseudo-transient reciprocal time step 1/dt [1/s] (0 for a pure steady solve)

Definition at line 100 of file ThermalPlasmaColumn1D.cpp.

◆ getValues()

void rizer::ThermalPlasmaColumn1D::getValues	(	const std::string &	component,
		Cantera::span< double >	values ) const

override

Copy converged temperatures from the shared global solution vector.

Only "T" is a valid component name; throws otherwise.

Parameters

	component	Component name; only "T" is valid for this domain
[out]	values	T [K] at each radial grid point

Definition at line 60 of file ThermalPlasmaColumn1D.cpp.

◆ hasComponent()

bool rizer::ThermalPlasmaColumn1D::hasComponent	(	const std::string &	name,
		bool	checkAlias = true ) const

override

Test whether a component name exists in this domain.

Parameters

name	Component name to test
checkAlias	Unused (this domain has no aliases)

Definition at line 54 of file ThermalPlasmaColumn1D.cpp.

◆ initialValue()

double rizer::ThermalPlasmaColumn1D::initialValue	(	std::size_t	n,
		std::size_t	j )

override

Initial guess for component n at grid point j.

Uses the seeded profile (interpolated) if one was provided, otherwise falls back to a parabola: \( T(r) = T_\text{wall} + (T_\text{center} - T_\text{wall}) (1 - (r/R)^2) \).

Parameters

n	Component index [-]; always 0 ("T") for this domain
j	Radial grid point index [-]

Definition at line 77 of file ThermalPlasmaColumn1D.cpp.

◆ kappaAt()

double rizer::ThermalPlasmaColumn1D::kappaAt ( double T ) const

inline

Parameters

T	Temperature [K]; returns kappa(T) [W/m/K]

Definition at line 141 of file ThermalPlasmaColumn1D.h.

◆ pRadAt()

double rizer::ThermalPlasmaColumn1D::pRadAt ( double T ) const

inline

Parameters

T	Temperature [K]; returns P_rad(T) [W/m^3]

Definition at line 143 of file ThermalPlasmaColumn1D.h.

◆ radius()

double rizer::ThermalPlasmaColumn1D::radius ( ) const

inline

Definition at line 135 of file ThermalPlasmaColumn1D.h.

◆ resetBadValues()

void rizer::ThermalPlasmaColumn1D::resetBadValues ( Cantera::span< double > xg )

overridevirtual

Clamp any out-of-bound temperatures after a failed Newton step to keep the solve from wandering into unphysical territory (T < 0 or T > 1e5 K).

Parameters

[out] xg Full global state vector (all domains); this domain's slice at loc() is clamped in place, T [K]

Reimplemented from Cantera::Domain1D.

Definition at line 89 of file ThermalPlasmaColumn1D.cpp.

◆ setElectricField()

void rizer::ThermalPlasmaColumn1D::setElectricField ( double E )

inline

Change the electric field without rebuilding the domain (used by the Python-side secant iteration for current control).

Parameters

E	Axial electric field E [V/m]

Definition at line 133 of file ThermalPlasmaColumn1D.h.

◆ sigmaAt()

double rizer::ThermalPlasmaColumn1D::sigmaAt ( double T ) const

inline

Property look-ups at a given temperature, for post-processing.

Parameters

T	Temperature [K]; returns sigma(T) [S/m]

Definition at line 139 of file ThermalPlasmaColumn1D.h.

The documentation for this class was generated from the following files:

/home/runner/work/rizer/rizer/rizer/cantera_ext/src/ThermalPlasmaColumn1D.h
/home/runner/work/rizer/rizer/rizer/cantera_ext/src/ThermalPlasmaColumn1D.cpp

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ ThermalPlasmaColumn1D()

Member Function Documentation

◆ componentIndex()

◆ componentName()

◆ domainType()

◆ electricField()

◆ eval()

◆ getValues()

◆ hasComponent()

◆ initialValue()

◆ kappaAt()

◆ pRadAt()

◆ radius()

◆ resetBadValues()

◆ setElectricField()

◆ sigmaAt()