.AixLib.Media.Refrigerants.UsersGuide.Approaches.HybridApproach .AixLib.Media.Refrigerants.UsersGuide.Approaches.HybridApproachThe hybrid approach is developed by Sangi et al. and consists of both the Helmholtz equation of state and fitted formula for thermodynamic state properties at bubble or dew line (e.g. psat or hl,sat) and thermodynamic state properties depending on two independent state properties (e.g. T_ph or T_ps). In the following, the basic formulas of the hybrid approach are given.
The Helmholtz equation of state
The Helmholtz equation of state (EoS) allows the accurate description of fluids' thermodynamic behaviour and uses the Helmholtz energy as fundamental thermodynamic relation with temperature and density as independent variables. Furthermore, the EoS allows determining all thermodynamic state properties from its partial derivatives and its general formula is given below:
As it can be seen, the general formula of the EoS can be divided in two part: The ideal gas part (left summand) and the residual part (right summand). Both parts' formulas are given below:
Both, the ideal gas part and the residual part can be divided in three subparts (i.e. the summations) that contain different coefficients (e.g. nL, li, pi or ei). These coefficients are fitting coefficients and must be obtained during a fitting procedure. While the fitting procedure, the general formula of the EoS is fitted to external data (e.g. obtained from measurements or external media libraries) and the fitting coefficients are determined. Finally, the formulas obtained during the fitting procedure are implemented in an explicit form.
For further information of the EoS and its partial derivatives, please read the paper " HelmholtzMedia - A fluid properties library" by Thorade and Saadat as well as the paper " Partial derivatives of thermodynamic state properties for dynamic simulation" by Thorade and Saadat.
Fitted formulas
Fitted formulas allow to reduce the overall computing time of the
refrigerant model. Therefore, both thermodynamic state properties at
bubble and dew line and thermodynamic state properties depending on
two independent state properties are expresses as fitted formulas.
The fitted formulas' approaches implemented in this package are
developed by Sangi et al. within their "Fast_Propane" model and given
below:
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Saturation pressure |
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Saturation temperature |
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Bubble density |
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Dew density |
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Bubble Enthalpy |
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Dew Enthalpy |
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Bubble Entropy |
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Dew Entropy |
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Temperature_ph |
First Input |
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Second Input |
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Temperature_ps |
First Input |
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Second Input |
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Density_pT |
First Input |
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Second Input |
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Functional approach |
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As it can be seen, the fitted formulas consist basically of the coefficients ei, ci as well as of the parameters Meani and Stdi. These coefficients are the fitting coefficients and must be obtained during a fitting procedure. While the fitting procedure, the formulas presented above are fitted to external data (e.g. obtained from measurements or external media libraries) and the fitting coefficients are determined. Finally, the formulas obtained during the fitting procedure are implemented in an explicit form.
For further information of the hybrid approach, please read the paper "A Medium Model for the Refrigerant Propane for Fast and Accurate Dynamic Simulations" by Sangi et al..
Smooth transition
To ensure a smooth transition between different regions (e.g.
from supercooled region to two-phase region) and, therefore,
to avoid discontinuities as far as possible, Sangi et al.
implemented functions for a smooth transition between the
regions. An example (i.e. specificEnthalpy_ps) of these
functions is given below:
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From supercooled region to bubble line and vice versa |
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From dew line to superheated region and vice versa |
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From bubble or dew line to two-phase region and vice versa |
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Two limitations are known for this package:
