functions for kinetics calculations More...

Functions
double	LliqMax (double &)
	maximum allowable amount of liquid blowing agent (n-pentane) in liquid More...

double	ddT_LliqMax (double &)
	derivative of LliqMax with respect to temperature More...

double	arrhenius (double &, double &, double &)
	Arrhenius function. More...

double	BAdilution (double &, double &, double &)
	dilution term for the blowing agent (n-pentane) More...

double	QKinW (double &, double &, double &, double &, double &, double &, double &)

double	henryCoefficient (double &T)
	Henry coefficient for CO2. More...

double	bubbleRadius (const double m0, const double m1)

double	partialPressureCO2 (double &M_CO2, double &M_B, double &surfaceTension, double &wCO2_g, double &wBA_g, double &p, double &R)
	partial pressure of CO2 More...

double	partialPressureBA (double &M_B, double &M_CO2, double &surfaceTension, double &wBA_g_val, double &wCO2_g_val, double &prsr, double &bubble_radius)
	partial pressure of blowing agent More...

double	wCO2Max (double &M_CO2, double &M_liq, double &pCO2, double &henryCoeff)
	dissolved amount of CO2 in liquid More...

double	xBL (double &T, double &dxdT)
	mole fraction of blowing agent (R-11) in liquid polymer More...

double	wBL_D (double &xBL, double &M_B, double &M_NCO, double &L0)
	weight fraction of maximum allowable blowing agent (R-11) in liquid More...

double	LmaxR11 (double &tmptr)

double	creamTemperature (double &xBL0, double &dxdT)
	criticall temperature that foaming process starts More...

double	dTdtFirstOrder (double &Tc, double &To, double &timeStep)
	first order accurate dTdt More...

double	dTdtSecondOrder (double &Tc, double &To, double &Too, double &timeStep)
	second order accurate dTdt More...

double	thermalDiffusivityGas (double &T)
	thermal diffusivity of gas as a function of temperature More...

double	nodeRadius (const double &v)

double	QKinW (double &AW, double &EW, double &tempi, double &Lliq, double &rhoPoly, double &rhoBL)
	arrhenius term times by dilution term More...

Detailed Description

functions for kinetics calculations

Definition in file KineticsFunctions.H.

Function Documentation

◆ arrhenius()

double arrhenius	(	double &	AOH,
		double &	EOH,
		double &	tempt
	)

Arrhenius function.

Parameters

AOH	pre-exponential factor
EOH	activation energy
tempt	temperature

Returns: arrhenius value

Definition at line 164 of file KineticsFunctions.H.

◆ BAdilution()

double BAdilution	(	double &	L_l,
		double &	rhoPoly,
		double &	rhoBL
	)

dilution term for the blowing agent (n-pentane)

Parameters

L_l	weight fraction of liquid blowing agent
rhoPoly	density of liquid mixture (polymer)
rhoBL	density of blowing agent

Returns: dilution term

Definition at line 170 of file KineticsFunctions.H.

References QKinW().

◆ creamTemperature()

double creamTemperature	(	double &	xBL0,
		double &	dxdT
	)

criticall temperature that foaming process starts

Parameters

xBL0	initial mole fraction of the blowing agent (R-11)
dxdT	constant

Returns: cream temperature

Definition at line 323 of file KineticsFunctions.H.

◆ ddT_LliqMax()

double ddT_LliqMax ( double & tmptr )

derivative of LliqMax with respect to temperature

Parameters

tmptr input temperature

Returns: value of derivative for input temperature

Definition at line 156 of file KineticsFunctions.H.

◆ dTdtFirstOrder()

double dTdtFirstOrder	(	double &	Tc,
		double &	To,
		double &	timeStep
	)

first order accurate dTdt

Parameters

Tc	current value of temperature
To	old value of temperature
timeStep	time step

Returns: first order derivative

Definition at line 328 of file KineticsFunctions.H.

◆ dTdtSecondOrder()

double dTdtSecondOrder	(	double &	Tc,
		double &	To,
		double &	Too,
		double &	timeStep
	)

second order accurate dTdt

Parameters

Tc	current value of temperature
To	old value of temperature
Too	old-old value of temperature
timeStep	time step

Returns: second order derivative

Definition at line 332 of file KineticsFunctions.H.

◆ henryCoefficient()

double henryCoefficient ( double & T )

Henry coefficient for CO2.

Parameters

T	temperature

Returns: Henry coefficient

Definition at line 185 of file KineticsFunctions.H.

◆ LliqMax()

double LliqMax ( double & tmptr )

maximum allowable amount of liquid blowing agent (n-pentane) in liquid

Parameters

tmptr input temperature

Returns: equilibrium value of blowing agent in liquid

Definition at line 139 of file KineticsFunctions.H.

◆ partialPressureBA()

double partialPressureBA	(	double &	M_B,
		double &	M_CO2,
		double &	surfaceTension,
		double &	wBA_g_val,
		double &	wCO2_g_val,
		double &	prsr,
		double &	bubble_radius
	)

partial pressure of blowing agent

Parameters

M_B	molecular weight of blowing agent
M_CO2	molecular weight of CO2
surfaceTension	surface tension
wBA_g	weight fraction of blowing agent in gas
wCO2_g	weight fraction of CO2 in gas
p	ambient pressure
R	bubble radius

Returns: partial pressure of blowing agent

Definition at line 239 of file KineticsFunctions.H.

References M_B.

◆ partialPressureCO2()

double partialPressureCO2	(	double &	M_CO2,
		double &	M_B,
		double &	surfaceTension,
		double &	wCO2_g,
		double &	wBA_g,
		double &	p,
		double &	R
	)

partial pressure of CO2

Parameters

M_CO2	molecular weight of CO2
M_B	molecular weight of blowing agent
surfaceTension	surface tension
wCO2_g	weight fraction of CO2 in gas
wBA_g	weight frcation of blowing agent in gas
p	ambient pressure
R	bubble radius

Returns: partial pressure of CO2

Definition at line 218 of file KineticsFunctions.H.

◆ QKinW()

QKinW	(	double &	AW,
		double &	EW,
		double &	tempi,
		double &	Lliq,
		double &	rhoPoly,
		double &	rhoBL
	)

arrhenius term times by dilution term

Parameters

AW	pre-exponential factor
EW	activation energy
tempi	temperature
Lliq	weight fraction of liquid blowing agent
rhoPoly	density of liquid mixture (polymer)
rhoBL	density of blowing agent

Returns: source term

Definition at line 176 of file KineticsFunctions.H.

Referenced by BAdilution().

◆ thermalDiffusivityGas()

double thermalDiffusivityGas ( double & T )

thermal diffusivity of gas as a function of temperature

Parameters

T	temperature

Returns: thermal diffusivity of gas

Definition at line 337 of file KineticsFunctions.H.

References nodeRadius().

◆ wBL_D()

double wBL_D	(	double &	xBL,
		double &	M_B,
		double &	M_NCO,
		double &	L0
	)

weight fraction of maximum allowable blowing agent (R-11) in liquid

Parameters

xBL	mole fraction of blowing agent (R-11)
M_B	molecular weight of blowing agent (R-11)
M_NCO	molecular weight of NCO

Returns: maximum solubility of R-11 in liquid

Definition at line 294 of file KineticsFunctions.H.

References M_NCO, and xBL().

◆ wCO2Max()

double wCO2Max	(	double &	M_CO2,
		double &	M_liq,
		double &	pCO2,
		double &	henryCoeff
	)

dissolved amount of CO2 in liquid

Parameters

M_CO2	molecular weight of CO2
M_liq	molecular weight of liquid mixture
pCO2	partial pressure of CO2
henryCoeff	Henry coefficient

Returns: maximum solubility of CO2 in liquid

Definition at line 260 of file KineticsFunctions.H.

◆ xBL()

double xBL	(	double &	T,
		double &	dxdT
	)

mole fraction of blowing agent (R-11) in liquid polymer

Parameters

T	temperature
dxdT	model constant

Returns: mole fraction of R-11 in liquid

Definition at line 275 of file KineticsFunctions.H.

Referenced by wBL_D().