AixLib.Fluid.Actuators.Valves.ExpansionValves.UsersGuide.Approaches.PolynomialApproach

# .AixLib.Fluid.Actuators.Valves.ExpansionValves.UsersGuide.Approaches.PolynomialApproach

Polynomial Aprroaches

## Information

A generic polynomial approach is presented below:
`C = corFact * sum(a[i]*P[i]^b[i] for i in 1:nT)`
All flow coefficient models presented in this library are based on a literature review. Therefore, the variable `corFact` allows a correction of the flow coefficient if the general modelling approach presented in the litarature differs from `ṁ = C*Avalve*sqrt(2*ρinlet*dp).`

#### Common model variables

Calculation procedures presented in the litarture have some variables in commen and these variables are presented below:

"Commen variables" border="1" cellspacing="0" cellpadding="2" style="border-collapse:collapse;">

Variable | Comment
--- | ---
`A` | Cross-sectional flow area
`dinlet` | Diameter of the pipe at valve's inlet
`pinlet` | Pressure at valve's inlet
`poutlet` | Pressure at valve's outlet
`ρinlet` | Density at valve's inlet
`ρoutlet` | Density at valve's outlet
`Tinlet` | Temperature at valve's inlet
`μinlet` | Dynamic viscosity at valve's inlet
`σinlet` | Surface tension at valve's inlet
`Coutlet` | Specific heat capacity at valve's outlet
`hfg` | Heat of vaparisation

#### Polynomial flow coefficient models

Actually, two polynomial approaches are implemented in this package. To add further calculation procedures, just add its name in AixLib.Fluid.Actuators.Valves.ExpansionValves.Utilities.Choices and expand the `if-structure` defined in AixLib.Fluid.Actuators.Valves.ExpansionValves.Utilities.FlowCoefficient.PolynomialFlowCoefficient.

"Polynomial approaches" border="1" cellspacing="0" cellpadding="2" style="border-collapse:collapse;">

Reference | Formula | Refrigerants | Validity `Tcondensing` | Validity `Tevaporating` | Validity `Tsubcooling`
--- | --- | --- | --- | --- | ---
ShanweiEtAl2005 | `C = a1*A + a2*ρinlet + a3*ρoutlet + a4*Tsubcooling + a5*dclearance + a6*(pinlet- poutlet)` | `R22, R407C, R410A` | `40 - 50 °C` | `0 - 10 °C` | `1.5 - 10 °C`
Li2013 | `C = a1 + a2*opening + a3*opening^2 + a4*opening*(Tsubcooling/Tcrit) + a5*(Tsubcooling/Tcrit) + a6*(Tsubcooling/Tcrit)^2` | `R22, R407C, R410A` | `30 - 50 °C` | `0 - 30 °C` | `1.5 - 15 °C`

## Revisions

- October 19, 2017, by Mirko Engelpracht, Christian Vering:
  First implementation (see issue 457).

Generated at 2026-05-12T20:19:03Z by OpenModelicaOpenModelica 1.26.7 using GenerateDoc.mos