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 interpreted as a linearization of a full non-linear fluid model (but it is not linear in all thermodynamic coordinates). Reference values are needed for

- the density (reference_d),
- the specific enthalpy (reference_h),
- 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 occurrences 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 symbolically from a quadratic function. Errors from this approximation are small because liquid density varies little.

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

Name | Description |
---|---|

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 isothermal compressibility kappa |

isobaricExpansionCoefficient | Return the isobaric 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 |

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