FCSys.Characteristics.BaseClasses.CharacteristicNASA

Thermodynamic package with diffusive properties based on NASA CEA

Information

The correlations for transport properties are available in [McBride1996, McBride2002]. For more information, please see the Characteristic package.

Extends from Characteristic (Package of thermodynamic and diffusive properties).

Package Content

Name	Description
T_lim_eta_theta={0,Modelica.Constants.inf}	Temperature limits for the rows of bη and bθ (Tlim η θ)
b_eta	Correlation constants for fluidity (bη)
b_theta	Correlation constants for thermal resistivity (bθ)
fromNASAViscosity	Return constants for fluidity given NASA CEA constants for viscosity
fromNASAThermalConductivity	Return constants for thermal resistivity given NASA CEA constants for thermal conductivity
eta	Fluidity (η) as a function of temperature
theta	Thermal resistivity (θ) as a function of temperature
Inherited
formula	Chemical formula
phase	Material phase
m	Specific mass
d	Specific diameter
z=charge(formula)	Charge number
referenceEnthalpy=ReferenceEnthalpy.enthalpyOfFormationAt25degC	Choice of enthalpy reference
Deltah0_f	Enthalpy of formation at 298.15 K, po (Δhof)
Deltah0	ho(298.15 K) - ho(0 K) (Δho)
h_offset=0	Additional enthalpy offset (hoffset)
n_c=-2	Power of T for 1st column of bc (nc)
T_lim_c={0,Modelica.Constants.inf}	Temperature limits for the rows of bc and Bc (Tlim c)
b_c	Coefficients of isobaric specific heat capacity at po as a polynomial in T (bc)
B_c	Integration constants for specific enthalpy and entropy (Bc)
alpha=1.5*U.pi^1.5*d^2*U.q	Scaled specific intercept area
omega	Root mean square of thermal velocity in one dimension as a function of temperature (ω = √ T/m )
c_p	Isobaric specific heat capacity (cp) as a function of temperature and pressure
c_v	Isochoric specific heat capacity (cv) as a function of temperature and pressure
D	Diffusivity as a function of temperature and specific volume
g	Gibbs potential as a function of temperature and pressure
h	Specific enthalpy as a function of temperature and pressure
s	Specific entropy as a function of temperature and pressure
zeta	** (ζ) as a function of temperature
tauprime	Phase change interval (τ′) as a function of temperature and specific volume
mu	Mobility (μ) as a function of temperature and specific volume
nu	Thermal independity (ν) as a function of temperature and specific volume
p0=U.bar	Reference pressure (po)
n_v={-1,0}	Powers of p/T and T for 1st row and column of bv (nv)
b_v=[1]	Coefficients for specific volume as a polynomial in p/T and T (bv)
isCompressible=anyTrue({anyTrue({abs(b_v[i, j]) > Modelica.Constants.small and n_v[1] + i - 1 <> 0 for i in 1:size(b_v, 1)}) for j in 1:size(b_v, 2)})	true, if density depends on pressure
hasThermalExpansion=anyTrue({anyTrue({abs(b_v[i, j]) > Modelica.Constants.small and n_v[2] + j - n_v[1] - i <> 0 for i in 1:size(b_v, 1)}) for j in 1:size(b_v, 2)})	true, if density depends on temperature
n_p={n_v[1] - size(b_v, 1) + 1,n_v[2] + 1}	Powers of v and T for 1st row and column of bp
b_p=if size(b_v, 1) == 1 then b_v .^ (-n_p[1]) else {(if n_v[1] + i == 0 or n_v[1] + i == 1 or size(b_v, 1) == 1 then b_v[i, :] else (if n_v[1] + i == 2 and n_v[1] <= 0 then b_v[i, :] + b_v[i - 1, :] .^ 2 else (if n_v[1] + i == 3 and n_v[1] <= 0 then b_v[i, :] + b_v[i - 2, :] .* (b_v[i - 2, :] .^ 2 + 3*b_v[i - 1, :]) else zeros(size(b_v, 2))))) for i in size(b_v, 1):-1:1}	Coefficients of p as a polynomial in v and T
dp_Tv	Derivative of pressure as defined by pT v()
dv_Tp	Derivative of specific volume as defined by vT p()
p_Tv	Pressure as a function of temperature and specific volume (pT v())
v_Tp	Specific volume as a function of temperature and pressure (vT p())
beta	Isothermal compressibility as a function of temperature and pressure (β)

Types and constants

constant Q.TemperatureAbsolute T_lim_eta_theta[:]={0,Modelica.Constants.inf} 
  "Temperature limits for the rows of bη and bθ (Tlim η θ)";

constant Real b_eta[size(T_lim_eta_theta, 1) - 1, 4] 
  "Correlation constants for fluidity (bη)";

constant Real b_theta[size(T_lim_eta_theta, 1) - 1, 4] 
  "Correlation constants for thermal resistivity (bθ)";

---

FCSys.Characteristics.BaseClasses.CharacteristicNASA.fromNASAViscosity

Return constants for fluidity given NASA CEA constants for viscosity

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Type	Name	Default	Description
Real	b[4]		NASA CEA constants for viscosity

Outputs

Type	Name	Description
Real	b_eta[4]	Constants for fluidity

Modelica definition

function fromNASAViscosity 
  "Return constants for fluidity given NASA CEA constants for viscosity"
  extends Modelica.Icons.Function;

  input Real b[4] "NASA CEA constants for viscosity";
  output Real b_eta[4] "Constants for fluidity";

algorithm 
  b_eta := {-b[1],-b[2]*U.K,-b[3]*U.K^2,-b[4] + b[1]*log(U.K) + log(1e4*U.m*U.s/
    U.g)};
end fromNASAViscosity;

---

FCSys.Characteristics.BaseClasses.CharacteristicNASA.fromNASAThermalConductivity

Return constants for thermal resistivity given NASA CEA constants for thermal conductivity

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Type	Name	Default	Description
Real	b[4]		NASA CEA constants for thermal conductivity

Outputs

Type	Name	Description
Real	b_theta[4]	Constants for thermal resistivity

Modelica definition

function fromNASAThermalConductivity 
  "Return constants for thermal resistivity given NASA CEA constants for thermal conductivity"
  extends Modelica.Icons.Function;

  input Real b[4] "NASA CEA constants for thermal conductivity";
  output Real b_theta[4] "Constants for thermal resistivity";

algorithm 
  b_theta := {-b[1],-b[2]*U.K,-b[3]*U.K^2,-b[4] + b[1]*log(U.K) + log(1e4*U.m*U.K
    /U.W)};
end fromNASAThermalConductivity;

---

FCSys.Characteristics.BaseClasses.CharacteristicNASA.eta

Fluidity (η) as a function of temperature

Information

This function is based on based on NASA CEA [McBride1996, Svehla1995]

Although specific volume is an input to this function, the result is independent of specific volume.

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Type	Name	Default	Description
TemperatureAbsolute	T	298.15*U.K	Temperature [L2.M/(N.T2)]
VolumeSpecific	v	298.15*U.K/U.atm	Specific volume [L3/N]

Outputs

Type	Name	Description
Resistivity	eta	Fluidity [L.T/N]

Modelica definition

redeclare function eta 
  "Fluidity (η) as a function of temperature"

  extends Modelica.Icons.Function;
  input Q.TemperatureAbsolute T=298.15*U.K "Temperature";
  input Q.VolumeSpecific v=298.15*U.K/U.atm "Specific volume";
  // Note:  Specific volume isn't used here but is included for generality.
  output Q.Resistivity eta "Fluidity";

algorithm 
  /*
    assert(T_lim_eta_theta[1] <= T and T <= T_lim_eta_theta[end], "Temperature "
     + String(T/(U.K)) + " K is out of range for the resistivities ([" +
    String(T_lim_eta_theta[1]/U.K) + ", " + String(T_lim_eta_theta[end]
    /U.K) + "] K).");
  */
  // Note:  This is commented out so that the function can be inlined.
  eta := smooth(0, exp(sum(if (T_lim_eta_theta[i] <= T or i == 1) and (T <
    T_lim_eta_theta[i + 1] or i == size(T_lim_eta_theta, 1) - 1) then b_eta[i, 1]
    *log(T) + (b_eta[i, 2] + b_eta[i, 3]/T)/T + b_eta[i, 4] else 0 for i in 1:
    size(T_lim_eta_theta, 1) - 1)));
end eta;

---

FCSys.Characteristics.BaseClasses.CharacteristicNASA.theta

Thermal resistivity (θ) as a function of temperature

Information

This function is based on based on NASA CEA [McBride1996, Svehla1995]

Although specific volume is an input to this function, the result is independent of specific volume.

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Type	Name	Default	Description
TemperatureAbsolute	T	298.15*U.K	Temperature [L2.M/(N.T2)]
VolumeSpecific	v	298.15*U.K/U.atm	Specific volume [L3/N]

Outputs

Type	Name	Description
ResistivityThermal	theta	Thermal resistivity [L.T/N]

Modelica definition

redeclare function theta 
  "Thermal resistivity (θ) as a function of temperature"

  extends Modelica.Icons.Function;
  input Q.TemperatureAbsolute T=298.15*U.K "Temperature";
  input Q.VolumeSpecific v=298.15*U.K/U.atm "Specific volume";
  // Note:  Specific volume isn't used here but is included for generality.
  output Q.ResistivityThermal theta "Thermal resistivity";

algorithm 
  /*
    assert(T_lim_eta_theta[1] <= T and T <= T_lim_eta_theta[end], "Temperature "
     + String(T/(U.K)) + " K is out of range for the resistivities ([" +
    String(T_lim_eta_theta[1]/U.K) + ", " + String(T_lim_eta_theta[end]
    /U.K) + "] K).");
  */
  // Note:  This is commented out so that the function can be inlined.
  theta := smooth(0, exp(sum(if (T_lim_eta_theta[i] <= T or i == 1) and (T <
    T_lim_eta_theta[i + 1] or i == size(T_lim_eta_theta, 1) - 1) then b_theta[i,
    1]*log(T) + (b_theta[i, 2] + b_theta[i, 3]/T)/T + b_theta[i, 4] else 0 for 
    i in 1:size(T_lim_eta_theta, 1) - 1)));
end theta;