Modelica.Media.Interfaces.PartialLinearFluid

Information

Linear Compressibility Fluid Model

This linear compressibility fluid model is based on the assumptions that:

• The specific heat capacity at constant pressure (cp) is constant
• The isobaric expansion coefficient (beta) is constant
• The isothermal compressibility (kappa) is constant
• Pressure and temperature are used as states
• The influence of density on specific enthalpy (h), entropy (s), inner energy (u) and heat capacity (cv) at constant volume is neglected.

That means that the density is a linear function in temperature and in pressure. In order to define the complete model, a number of constant reference values are needed which are computed at the reference values of the states pressure p and temperature T. The model can be interprested as a linearization of a full non-linear fluid model (but it is not linear in all thermodynamic coordinates). Reference values are needed for

1. the density (reference_d),
2. the specific enthalpy (reference_h),
3. the specific entropy (reference_s).

Apart from that, a user needs to define the molar mass, MM_const. Note that it is possible to define a fluid by computing the reference values from a full non-linear fluid model by computing the package constants using the standard functions defined in a fluid package (see example in liquids package).

In order to avoid numerical inversion of the temperature in the T_ph and T_ps functions, the density is always taken to be the reference density in the computation of h, s, u and cv. For liquids (and this model is intended only for liquids) the relative error of doing so is 1e-3 to 1e-4 at most. The model would be more "correct" based on the other assumptions, if occurences of reference_d in the computations of h,s,u and cv would be replaced by a call to density(state). That would require a numerical solution for T_ps, while T_ph can be solved symbolicallyfrom a quadratic function. Errors from this approximation are small because liquid density varies little.

Efficiency considerations

One of the main reasons to use a simple, linear fluid model is to achieve high performance in simulations. There are a number of possible compromises and possibilities to improve performance. Some of them can be influenced by a flag. The following rules where used in this model:

• All forward evaluations (using the ThermodynamicState record as input) are exactly following the assumptions above.
• If the flag constantJacobian is set to true in the package, all functions that typically appear in thermodynamic jacobians (specificHeatCapacityCv, density_derp_h, density_derh_p, density_derp_T, density_derT_p) are evaluated at reference conditions (that means using the reference density) instead of the density of the current pressure and temperature. This makes it possible to evaluate the thermodynamic jacobian at compile time.
• For inverse functions using other inputs than the states (e.g pressure p and specific enthalpy h), the inversion is using the reference state whenever that is necessary to achieve a symbolic inversion.
• If constantJacobian is set to false, the above list of functions is computed exactly according to the above list of assumptions

Authors:

Francesco Casella
Dipartimento di Elettronica e Informazione
Politecnico di Milano
Via Ponzio 34/5
I-20133 Milano, Italy
email: casella@elet.polimi.it
and
Hubertus Tummescheit
Modelon AB
Ideon Science Park
SE-22730 Lund, Sweden
email: Hubertus.Tummescheit@Modelon.se

Extends from Interfaces.PartialPureSubstance (base class for pure substances of one chemical substance).

Package Content

Name	Description
cp_const	Specific heat capacity at constant pressure
beta_const	Thermal expansion coefficient at constant pressure
kappa_const	Isothermal compressibility
MM_const	Molar mass
reference_d	Density in reference conditions
reference_h	Specific enthalpy in reference conditions
reference_s	Specific enthalpy in reference conditions
constantJacobian	if true, entries in thermodynamic Jacobian are constant, taken at reference conditions
ThermodynamicState	a selection of variables that uniquely defines the thermodynamic state
BaseProperties	Base properties of medium
setState_pTX	set the thermodynamic state record from p and T (X not needed)
setState_phX	set the thermodynamic state record from p and h (X not needed)
setState_psX	set the thermodynamic state record from p and s (X not needed)
setState_dTX	set the thermodynamic state record from d and T (X not needed)
setSmoothState	Return thermodynamic state so that it smoothly approximates: if x > 0 then state_a else state_b
pressure	Return the pressure from the thermodynamic state
temperature	Return the temperature from the thermodynamic state
density	Return the density from the thermodynamic state
specificEnthalpy	Return the specific enthalpy from the thermodynamic state
specificEntropy	Return the specific entropy from the thermodynamic state
specificInternalEnergy	Return the specific internal energy from the thermodynamic state
specificGibbsEnergy	Return specific Gibbs energy from the thermodynamic state
specificHelmholtzEnergy	Return specific Helmholtz energy from the thermodynamic state
velocityOfSound	Return velocity of sound from the thermodynamic state
isentropicExponent	Return isentropic exponent from the thermodynamic state
isentropicEnthalpy	Return isentropic enthalpy
specificHeatCapacityCp	Return specific heat capacity at constant volume
specificHeatCapacityCv	Return specific heat capacity at constant volume from the thermodynamic state
isothermalCompressibility	Return the iso-thermal compressibility kappa
isobaricExpansionCoefficient	Return the iso-baric expansion coefficient
density_derp_h	Return density derivative w.r.t. pressure at const specific enthalpy
density_derh_p	Return density derivative w.r.t. specific enthalpy at constant pressure
density_derp_T	Return density derivative w.r.t. pressure at const temperature
density_derT_p	Return density derivative w.r.t. temperature at constant pressure
density_derX	Returns the partial derivative of density with respect to mass fractions at constant pressure and temperature
molarMass	Return molar mass
T_ph	Return temperature from pressure and specific enthalpy
T_ps	Return temperature from pressure and specific entropy
Inherited
setState_pT	Return thermodynamic state from p and T
setState_ph	Return thermodynamic state from p and h
setState_ps	Return thermodynamic state from p and s
setState_dT	Return thermodynamic state from d and T
density_ph	Return density from p and h
temperature_ph	Return temperature from p and h
pressure_dT	Return pressure from d and T
specificEnthalpy_dT	Return specific enthalpy from d and T
specificEnthalpy_ps	Return specific enthalpy from p and s
temperature_ps	Return temperature from p and s
density_ps	Return density from p and s
specificEnthalpy_pT	Return specific enthalpy from p and T
density_pT	Return density from p and T
ThermoStates	Enumeration type for independent variables
mediumName="unusablePartialMedium"	Name of the medium
substanceNames={mediumName}	Names of the mixture substances. Set substanceNames={mediumName} if only one substance.
extraPropertiesNames=fill("", 0)	Names of the additional (extra) transported properties. Set extraPropertiesNames=fill("",0) if unused
singleState	= true, if u and d are not a function of pressure
reducedX=true	= true if medium contains the equation sum(X) = 1.0; set reducedX=true if only one substance (see docu for details)
fixedX=false	= true if medium contains the equation X = reference_X
reference_p=101325	Reference pressure of Medium: default 1 atmosphere
reference_T=298.15	Reference temperature of Medium: default 25 deg Celsius
reference_X=fill(1/nX, nX)	Default mass fractions of medium
p_default=101325	Default value for pressure of medium (for initialization)
T_default=Modelica.SIunits.Conversions.from_degC(20)	Default value for temperature of medium (for initialization)
h_default=specificEnthalpy_pTX(p_default, T_default, X_default)	Default value for specific enthalpy of medium (for initialization)
X_default=reference_X	Default value for mass fractions of medium (for initialization)
nS=size(substanceNames, 1)	Number of substances
nX=nS	Number of mass fractions
nXi=if fixedX then 0 else if reducedX then nS - 1 else nS	Number of structurally independent mass fractions (see docu for details)
nC=size(extraPropertiesNames, 1)	Number of extra (outside of standard mass-balance) transported properties
C_nominal=1.0e-6*ones(nC)	Default for the nominal values for the extra properties
FluidConstants	critical, triple, molecular and other standard data of fluid
dynamicViscosity	Return dynamic viscosity
thermalConductivity	Return thermal conductivity
prandtlNumber	Return the Prandtl number
heatCapacity_cp	alias for deprecated name
heatCapacity_cv	alias for deprecated name
beta	alias for isobaricExpansionCoefficient for user convenience
kappa	alias of isothermalCompressibility for user convenience
specificEnthalpy_pTX	Return specific enthalpy from p, T, and X or Xi
specificEntropy_pTX	Return specific enthalpy from p, T, and X or Xi
density_pTX	Return density from p, T, and X or Xi
temperature_phX	Return temperature from p, h, and X or Xi
density_phX	Return density from p, h, and X or Xi
temperature_psX	Return temperature from p,s, and X or Xi
density_psX	Return density from p, s, and X or Xi
specificEnthalpy_psX	Return specific enthalpy from p, s, and X or Xi
AbsolutePressure	Type for absolute pressure with medium specific attributes
Density	Type for density with medium specific attributes
DynamicViscosity	Type for dynamic viscosity with medium specific attributes
EnthalpyFlowRate	Type for enthalpy flow rate with medium specific attributes
MassFlowRate	Type for mass flow rate with medium specific attributes
MassFraction	Type for mass fraction with medium specific attributes
MoleFraction	Type for mole fraction with medium specific attributes
MolarMass	Type for molar mass with medium specific attributes
MolarVolume	Type for molar volume with medium specific attributes
IsentropicExponent	Type for isentropic exponent with medium specific attributes
SpecificEnergy	Type for specific energy with medium specific attributes
SpecificInternalEnergy	Type for specific internal energy with medium specific attributes
SpecificEnthalpy	Type for specific enthalpy with medium specific attributes
SpecificEntropy	Type for specific entropy with medium specific attributes
SpecificHeatCapacity	Type for specific heat capacity with medium specific attributes
SurfaceTension	Type for surface tension with medium specific attributes
Temperature	Type for temperature with medium specific attributes
ThermalConductivity	Type for thermal conductivity with medium specific attributes
PrandtlNumber	Type for Prandtl number with medium specific attributes
VelocityOfSound	Type for velocity of sound with medium specific attributes
ExtraProperty	Type for unspecified, mass-specific property transported by flow
CumulativeExtraProperty	Type for conserved integral of unspecified, mass specific property
ExtraPropertyFlowRate	Type for flow rate of unspecified, mass-specific property
IsobaricExpansionCoefficient	Type for isobaric expansion coefficient with medium specific attributes
DipoleMoment	Type for dipole moment with medium specific attributes
DerDensityByPressure	Type for partial derivative of density with resect to pressure with medium specific attributes
DerDensityByEnthalpy	Type for partial derivative of density with resect to enthalpy with medium specific attributes
DerEnthalpyByPressure	Type for partial derivative of enthalpy with resect to pressure with medium specific attributes
DerDensityByTemperature	Type for partial derivative of density with resect to temperature with medium specific attributes
Choices	Types, constants to define menu choices

Types and constants

      constant SpecificHeatCapacity cp_const 
  "Specific heat capacity at constant pressure";

      constant IsobaricExpansionCoefficient beta_const 
  "Thermal expansion coefficient at constant pressure";

      constant SI.IsothermalCompressibility kappa_const 
  "Isothermal compressibility";

      constant MolarMass MM_const "Molar mass";

      constant Density reference_d "Density in reference conditions";

      constant SpecificEnthalpy reference_h 
  "Specific enthalpy in reference conditions";

      constant SpecificEntropy reference_s 
  "Specific enthalpy in reference conditions";

      constant Boolean constantJacobian 
  "if true, entries in thermodynamic Jacobian are constant, taken at reference conditions";

Modelica.Media.Interfaces.PartialLinearFluid.ThermodynamicState

Modelica definition

redeclare record ThermodynamicState 
  "a selection of variables that uniquely defines the thermodynamic state"
  AbsolutePressure p "Absolute pressure of medium";
  Temperature T "Temperature of medium";
end ThermodynamicState;

Modelica.Media.Interfaces.PartialLinearFluid.BaseProperties

Information

Parameters

Type	Name	Default	Description
Advanced
Boolean	preferredMediumStates	false	= true if StateSelect.prefer shall be used for the independent property variables of the medium

Modelica definition

redeclare model extends BaseProperties(
  T(stateSelect=if preferredMediumStates then StateSelect.prefer else 
                     StateSelect.default),
  p(stateSelect=if preferredMediumStates then StateSelect.prefer else 
                     StateSelect.default)) 
  "Base properties of medium"
equation 
  d = (1 + (p-reference_p)*kappa_const - (T-reference_T)*beta_const)*reference_d;
  h = reference_h +
      (T-reference_T)*cp_const +
      (p-reference_p)*(1-beta_const*reference_T)/reference_d;
  u = h - p/d;
  p = state.p;
  T = state.T;
  MM = MM_const;
  R  = 8.3144/MM;
end BaseProperties;

Modelica.Media.Interfaces.PartialLinearFluid.setState_pTX

Information

Inputs

Type	Name	Default	Description
AbsolutePressure	p		Pressure [Pa]
Temperature	T		Temperature [K]
MassFraction	X[:]	reference_X	Mass fractions [kg/kg]

Outputs

Type	Name	Description
ThermodynamicState	state	thermodynamic state record

Modelica definition

redeclare function extends setState_pTX 
  "set the thermodynamic state record from p and T (X not needed)"
algorithm 
  state := ThermodynamicState(p=p,T=T);
end setState_pTX;

Modelica.Media.Interfaces.PartialLinearFluid.setState_phX

Information

Inputs

Type	Name	Default	Description
AbsolutePressure	p		Pressure [Pa]
SpecificEnthalpy	h		Specific enthalpy [J/kg]
MassFraction	X[:]	reference_X	Mass fractions [kg/kg]

Outputs

Type	Name	Description
ThermodynamicState	state	thermodynamic state record

Modelica definition

redeclare function extends setState_phX 
  "set the thermodynamic state record from p and h (X not needed)"
algorithm 
  state := ThermodynamicState(p=p,
                              T=(h - reference_h - (p - reference_p)*((1 - beta_const*reference_T)
                                /reference_d))/cp_const + reference_T);
end setState_phX;

Modelica.Media.Interfaces.PartialLinearFluid.setState_psX

Information

Inputs

Type	Name	Default	Description
AbsolutePressure	p		Pressure [Pa]
SpecificEntropy	s		Specific entropy [J/(kg.K)]
MassFraction	X[:]	reference_X	Mass fractions [kg/kg]

Outputs

Type	Name	Description
ThermodynamicState	state	thermodynamic state record

Modelica definition

redeclare function extends setState_psX 
  "set the thermodynamic state record from p and s (X not needed)"
algorithm 
  state := ThermodynamicState(p=p,
                              T=reference_T*cp_const/(cp_const - s+reference_s +(p-reference_p)*
                                (-beta_const/reference_d)));
end setState_psX;

Modelica.Media.Interfaces.PartialLinearFluid.setState_dTX

Information

Inputs

Type	Name	Default	Description
Density	d		density [kg/m3]
Temperature	T		Temperature [K]
MassFraction	X[:]	reference_X	Mass fractions [kg/kg]

Outputs

Type	Name	Description
ThermodynamicState	state	thermodynamic state record

Modelica definition

redeclare function extends setState_dTX 
  "set the thermodynamic state record from d and T (X not needed)"
algorithm 
  state := ThermodynamicState(p=((d-reference_d) + (state.T-reference_T)*beta_const*reference_d)
                                /(reference_d*kappa_const) + reference_p,
                              T=T);
end setState_dTX;

Modelica.Media.Interfaces.PartialLinearFluid.setSmoothState

Information

Inputs

Type	Name	Default	Description
Real	x		m_flow or dp
ThermodynamicState	state_a		Thermodynamic state if x > 0
ThermodynamicState	state_b		Thermodynamic state if x < 0
Real	x_small		Smooth transition in the region -x_small < x < x_small

Outputs

Type	Name	Description
ThermodynamicState	state	Smooth thermodynamic state for all x (continuous and differentiable)

Modelica definition

redeclare function extends setSmoothState 
  "Return thermodynamic state so that it smoothly approximates: if x > 0 then state_a else state_b"
algorithm 
  state := ThermodynamicState(p= Media.Common.smoothStep(x, state_a.p, state_b.p, x_small),
                              T= Media.Common.smoothStep(x, state_a.T, state_b.T, x_small));
end setSmoothState;

Modelica.Media.Interfaces.PartialLinearFluid.pressure

Information

Inputs

Type	Name	Default	Description
ThermodynamicState	state		thermodynamic state record

Outputs

Type	Name	Description
AbsolutePressure	p	Pressure [Pa]

Modelica definition

redeclare function extends pressure 
  "Return the pressure from the thermodynamic state"
algorithm 
  p :=state.p;
end pressure;

Modelica.Media.Interfaces.PartialLinearFluid.temperature

Information

Inputs

Type	Name	Default	Description
ThermodynamicState	state		thermodynamic state record

Outputs

Type	Name	Description
Temperature	T	Temperature [K]

Modelica definition

redeclare function extends temperature 
  "Return the temperature from the thermodynamic state"
algorithm 
  T :=state.T;
end temperature;

Modelica.Media.Interfaces.PartialLinearFluid.density

Information

Inputs

Type	Name	Default	Description
ThermodynamicState	state		thermodynamic state record

Outputs

Type	Name	Description
Density	d	Density [kg/m3]

Modelica definition

redeclare function extends density 
  "Return the density from the thermodynamic state"
algorithm 
  d := (1 + (state.p-reference_p)*kappa_const - (state.T-reference_T)*beta_const)*reference_d;
end density;

Modelica.Media.Interfaces.PartialLinearFluid.specificEnthalpy

Information

Inputs

Type	Name	Default	Description
ThermodynamicState	state		thermodynamic state record

Outputs

Type	Name	Description
SpecificEnthalpy	h	Specific enthalpy [J/kg]

Modelica definition

redeclare function extends specificEnthalpy 
  "Return the specific enthalpy from the thermodynamic state"
algorithm 
h := reference_h +
    (state.T-reference_T)*cp_const +
    (state.p-reference_p)*(1-beta_const*reference_T)/reference_d;
end specificEnthalpy;

Modelica.Media.Interfaces.PartialLinearFluid.specificEntropy

Information

Inputs

Type	Name	Default	Description
ThermodynamicState	state		thermodynamic state record

Outputs

Type	Name	Description
SpecificEntropy	s	Specific entropy [J/(kg.K)]

Modelica definition

redeclare function extends specificEntropy 
  "Return the specific entropy from the thermodynamic state"
algorithm 
s := reference_s +
    (state.T-reference_T)*cp_const/state.T +
    (state.p-reference_p)*(-beta_const/reference_d);
end specificEntropy;

Modelica.Media.Interfaces.PartialLinearFluid.specificInternalEnergy

Information

Inputs

Type	Name	Default	Description
ThermodynamicState	state		thermodynamic state record

Outputs

Type	Name	Description
SpecificEnergy	u	Specific internal energy [J/kg]

Modelica definition

redeclare function extends specificInternalEnergy 
  "Return the specific internal energy from the thermodynamic state"
algorithm 
  u := specificEnthalpy(state)-state.p/reference_d;
end specificInternalEnergy;

Modelica.Media.Interfaces.PartialLinearFluid.specificGibbsEnergy

Information

Inputs

Type	Name	Default	Description
ThermodynamicState	state		thermodynamic state record

Outputs

Type	Name	Description
SpecificEnergy	g	Specific Gibbs energy [J/kg]

Modelica definition

redeclare function extends specificGibbsEnergy 
  "Return specific Gibbs energy from the thermodynamic state"
  extends Modelica.Icons.Function;
algorithm 
  g := specificEnthalpy(state) - state.T*specificEntropy(state);
end specificGibbsEnergy;

Modelica.Media.Interfaces.PartialLinearFluid.specificHelmholtzEnergy

Information

Inputs

Type	Name	Default	Description
ThermodynamicState	state		thermodynamic state record

Outputs

Type	Name	Description
SpecificEnergy	f	Specific Helmholtz energy [J/kg]

Modelica definition

redeclare function extends specificHelmholtzEnergy 
  "Return specific Helmholtz energy from the thermodynamic state"
  extends Modelica.Icons.Function;
algorithm 
  f := specificInternalEnergy(state) - state.T*specificEntropy(state);
end specificHelmholtzEnergy;

Modelica.Media.Interfaces.PartialLinearFluid.velocityOfSound

Information

Inputs

Type	Name	Default	Description
ThermodynamicState	state		thermodynamic state record

Outputs

Type	Name	Description
VelocityOfSound	a	Velocity of sound [m/s]

Modelica definition

redeclare function extends velocityOfSound 
  "Return velocity of sound from the thermodynamic state"
  extends Modelica.Icons.Function;
algorithm 
  a := sqrt(max(0,1/(kappa_const*density(state) -beta_const*beta_const*state.T/cp_const)));
end velocityOfSound;

Modelica.Media.Interfaces.PartialLinearFluid.isentropicExponent

Information

Inputs

Type	Name	Default	Description
ThermodynamicState	state		thermodynamic state record

Outputs

Type	Name	Description
IsentropicExponent	gamma	Isentropic exponent [1]

Modelica definition

redeclare function extends isentropicExponent 
  "Return isentropic exponent from the thermodynamic state"
  extends Modelica.Icons.Function;
algorithm 
 gamma := 1/(state.p*kappa_const)*cp_const/specificHeatCapacityCv(state);
end isentropicExponent;

Modelica.Media.Interfaces.PartialLinearFluid.isentropicEnthalpy

Information

A minor approximation is used: the reference density is used instead of the real one, which would require a numeric solution.

Extends from (Return isentropic enthalpy).

Inputs

Type	Name	Default	Description
AbsolutePressure	p_downstream		downstream pressure [Pa]
ThermodynamicState	refState		reference state for entropy

Outputs

Type	Name	Description
SpecificEnthalpy	h_is	Isentropic enthalpy [J/kg]

Modelica definition

redeclare function extends isentropicEnthalpy 
  "Return isentropic enthalpy"

/* Previous wrong equation:

protected
  SpecificEntropy s_upstream = specificEntropy(refState)
    "specific entropy at component inlet";
  ThermodynamicState downstreamState "state at downstream location";
algorithm
  downstreamState.p := p_downstream;
  downstreamState.T := reference_T*cp_const/
    (s_upstream -reference_s -(p_downstream-reference_p)*(-beta_const/reference_d) - cp_const);
  h_is := specificEnthalpy(downstreamState);
*/
algorithm 
  /* s := reference_s + (refState.T-reference_T)*cp_const/refState.T +
                        (refState.p-reference_p)*(-beta_const/reference_d)
        = reference_s + (state.T-reference_T)*cp_const/state.T +
                        (p_downstream-reference_p)*(-beta_const/reference_d);

      (state.T-reference_T)*cp_const/state.T
     = (refState.T-reference_T)*cp_const/refState.T + (refState.p-reference_p)*(-beta_const/reference_d)
       - (p_downstream-reference_p)*(-beta_const/reference_d)
     = (refState.T-reference_T)*cp_const/refState.T + (refState.p-p_downstream)*(-beta_const/reference_d)

     (x - reference_T)/x = k
     x - reference_T = k*x
     (1-k)*x = reference_T
     x = reference_T/(1-k);

     state.T = reference_T/(1 - ((refState.T-reference_T)*cp_const/refState.T + (refState.p-p_downstream)*(-beta_const/reference_d))/cp_const)
  */

  h_is :=specificEnthalpy(setState_pTX(
    p_downstream,
    reference_T/(1 - ( (refState.T - reference_T)/refState.T +
                       (refState.p - p_downstream)*(-beta_const/(reference_d*cp_const)))),
    reference_X));
end isentropicEnthalpy;

Modelica.Media.Interfaces.PartialLinearFluid.specificHeatCapacityCp

Information

Inputs

Type	Name	Default	Description
ThermodynamicState	state		thermodynamic state record

Outputs

Type	Name	Description
SpecificHeatCapacity	cp	Specific heat capacity at constant pressure [J/(kg.K)]

Modelica definition

redeclare function extends specificHeatCapacityCp 
  "Return specific heat capacity at constant volume"
algorithm 
  cp := cp_const;
end specificHeatCapacityCp;

Modelica.Media.Interfaces.PartialLinearFluid.specificHeatCapacityCv

Information

Inputs

Type	Name	Default	Description
ThermodynamicState	state		thermodynamic state record

Outputs

Type	Name	Description
SpecificHeatCapacity	cv	Specific heat capacity at constant volume [J/(kg.K)]

Modelica definition

redeclare function extends specificHeatCapacityCv 
  "Return specific heat capacity at constant volume from the thermodynamic state"
algorithm 
  cv := if constantJacobian then cp_const - reference_T*beta_const*beta_const/(kappa_const*reference_d) else 
        state.T*beta_const*beta_const/(kappa_const*reference_d);
end specificHeatCapacityCv;

Modelica.Media.Interfaces.PartialLinearFluid.isothermalCompressibility

Information

Inputs

Type	Name	Default	Description
ThermodynamicState	state		thermodynamic state record

Outputs

Type	Name	Description
IsothermalCompressibility	kappa	Isothermal compressibility [1/Pa]

Modelica definition

redeclare function extends isothermalCompressibility 
  "Return the iso-thermal compressibility kappa"
algorithm 
  kappa := kappa_const;
end isothermalCompressibility;

Modelica.Media.Interfaces.PartialLinearFluid.isobaricExpansionCoefficient

Information

Inputs

Type	Name	Default	Description
ThermodynamicState	state		thermodynamic state record

Outputs

Type	Name	Description
IsobaricExpansionCoefficient	beta	Isobaric expansion coefficient [1/K]

Modelica definition

redeclare function extends isobaricExpansionCoefficient 
  "Return the iso-baric expansion coefficient"
algorithm 
  beta := beta_const;
end isobaricExpansionCoefficient;

Modelica.Media.Interfaces.PartialLinearFluid.density_derp_h

Information

Inputs

Type	Name	Default	Description
ThermodynamicState	state		thermodynamic state record

Outputs

Type	Name	Description
DerDensityByPressure	ddph	Density derivative w.r.t. pressure [s2/m2]

Modelica definition

redeclare function extends density_derp_h 
  "Return density derivative w.r.t. pressure at const specific enthalpy"
algorithm 
  ddph := if constantJacobian then kappa_const*reference_d +
    (beta_const*(1-reference_T*beta_const))/cp_const else 
        kappa_const*density(state) +
     (beta_const*(1-temperature(state)*beta_const))/cp_const;
end density_derp_h;

Modelica.Media.Interfaces.PartialLinearFluid.density_derh_p

Information

Inputs

Type	Name	Default	Description
ThermodynamicState	state		thermodynamic state record

Outputs

Type	Name	Description
DerDensityByEnthalpy	ddhp	Density derivative w.r.t. specific enthalpy [kg.s2/m5]

Modelica definition

redeclare function extends density_derh_p 
  "Return density derivative w.r.t. specific enthalpy at constant pressure"
algorithm 
ddhp := if constantJacobian then -beta_const*reference_d/cp_const else 
        -beta_const*density(state)/cp_const;
end density_derh_p;

Modelica.Media.Interfaces.PartialLinearFluid.density_derp_T

Information

Inputs

Type	Name	Default	Description
ThermodynamicState	state		thermodynamic state record

Outputs

Type	Name	Description
DerDensityByPressure	ddpT	Density derivative w.r.t. pressure [s2/m2]

Modelica definition

redeclare function extends density_derp_T 
  "Return density derivative w.r.t. pressure at const temperature"
algorithm 
  ddpT := if constantJacobian then kappa_const*reference_d else 
        kappa_const*density(state);
end density_derp_T;

Modelica.Media.Interfaces.PartialLinearFluid.density_derT_p

Information

Inputs

Type	Name	Default	Description
ThermodynamicState	state		thermodynamic state record

Outputs

Type	Name	Description
DerDensityByTemperature	ddTp	Density derivative w.r.t. temperature [kg/(m3.K)]

Modelica definition

redeclare function extends density_derT_p 
  "Return density derivative w.r.t. temperature at constant pressure"
algorithm 
  ddTp := if constantJacobian then -beta_const*reference_d else 
       -beta_const*density(state);
end density_derT_p;

Modelica.Media.Interfaces.PartialLinearFluid.density_derX

Information

Inputs

Type	Name	Default	Description
ThermodynamicState	state		thermodynamic state record

Outputs

Type	Name	Description
Density	dddX[nX]	Derivative of density w.r.t. mass fraction [kg/m3]

Modelica definition

redeclare function extends density_derX 
  "Returns the partial derivative of density with respect to mass fractions at constant pressure and temperature"
algorithm 
  dddX := fill(0,nX);
end density_derX;

Modelica.Media.Interfaces.PartialLinearFluid.molarMass

Information

Inputs

Type	Name	Default	Description
ThermodynamicState	state		thermodynamic state record

Outputs

Type	Name	Description
MolarMass	MM	Mixture molar mass [kg/mol]

Modelica definition

redeclare function extends molarMass "Return molar mass"
algorithm 
  MM  := MM_const;
end molarMass;

Modelica.Media.Interfaces.PartialLinearFluid.T_ph

Inputs

Type	Name	Default	Description
SpecificEnthalpy	h		Specific enthalpy [J/kg]
AbsolutePressure	p		pressure [Pa]

Outputs

Type	Name	Description
Temperature	T	Temperature [K]

Modelica definition

function T_ph 
  "Return temperature from pressure and specific enthalpy"
  input SpecificEnthalpy h "Specific enthalpy";
  input AbsolutePressure p "pressure";
  output Temperature T "Temperature";
algorithm 
  T :=(h - reference_h - (p - reference_p)*((1 - beta_const*reference_T)
    /reference_d))/cp_const + reference_T;
end T_ph;

Modelica.Media.Interfaces.PartialLinearFluid.T_ps

Inputs

Type	Name	Default	Description
AbsolutePressure	p		Pressure [Pa]
SpecificEntropy	s		Specific entropy [J/(kg.K)]

Outputs

Type	Name	Description
Temperature	T	Temperature [K]

Modelica definition

function T_ps "Return temperature from pressure and specific entropy"
  input AbsolutePressure p "Pressure";
  input SpecificEntropy s "Specific entropy";
  output Temperature T "Temperature";
algorithm 
  T := reference_T*cp_const/(s-reference_s -(p-reference_p)*(-beta_const/reference_d) - cp_const);
end T_ps;