Oil $—$ Base model for a hydraulic table-based medium

Base model for a hydraulic table-based medium

Required inputs:

 • Bulk modulus data as function of pressure and temperature
 • Viscosity data as function of pressure and temperature.
 • Density data as function of temperature at atmospheric pressure

Data format

The data could either be added to the model in a table-based format or be specified in an external file. The parameter from_file determines which data option to use.

Bulk modulus data

The bulk modulus data should be a function of pressure (bar absolute) and temperature (degC) and should be specified in $\mathrm{bar}$.

Example:

 $\left(0\right)⟦\mathrm{bar}⟧$ $50⟦\mathrm{bar}⟧$ $100⟦\mathrm{bar}⟧$ $\left(0\right)⟦C⟧$ $B\left(0,0\right)$ $B\left(0,50\right)$ $B\left(0,100\right)$ $30⟦C⟧$ $B\left(30,0\right)$ $B\left(30,50\right)$ $B\left(30,100\right)$ $80⟦C⟧$ $B\left(80,0\right)$ $B\left(80,50\right)$ $B\left(80,100\right)$

where $B\left({T}_{i},{p}_{j}\right)$ is the Bulk modulus (in $\mathrm{bar}$) at temperature T in row i and pressure p in column j.

Viscosity data

The viscosity data should be a function of pressure (bar absolute) and temperature (degC). The boolean parameter kinematicViscosityData determines whether the data is provided as kinematic viscosity or as absolute viscosity. If parameter kinematicViscosityData is true, the data should be kinematic viscosity in $\mathrm{cSt}$ (centiStokes), otherwise it should be dynamic viscosity in $\mathrm{cP}$ (centiPoise).

In order to have better interpolation between data points, the values inserted in the table should be the logarithm of the viscosity. The logarithmic base should be equal to the value given in the  parameter log_base.

Example (for kinematicViscosityData false):

 $\left(0\right)⟦\mathrm{bar}⟧$ $50⟦\mathrm{bar}⟧$ $100⟦\mathrm{bar}⟧$ $\left(0\right)⟦C⟧$ $\mathrm{log}\left(\mathrm{\nu }\left(0,0\right)\right)$) $\mathrm{log}\left(\mathrm{\nu }\left(0,50\right)\right)$) $\mathrm{log}\left(\mathrm{\nu }\left(0,100\right)\right)$) $30⟦C⟧$ $\mathrm{log}\left(\mathrm{\nu }\left(30,0\right)\right)$) $\mathrm{log}\left(\mathrm{\nu }\left(30,50\right)\right)$) $\mathrm{log}\left(\mathrm{\nu }\left(30,100\right)\right)$) $80⟦C⟧$ $\mathrm{log}\left(\mathrm{\nu }\left(80,0\right)\right)$) $\mathrm{log}\left(\mathrm{\nu }\left(80,50\right)\right)$) $\mathrm{log}\left(\mathrm{\nu }\left(80,100\right)\right)$)

where $\mathrm{log}\left(\mathrm{\nu }\left({T}_{i},{p}_{j}\right)\right)$ is the logarithmic value of the kinematic viscosity (in $\mathrm{cSt}$) at temperature $T$ in row $i$ and pressure $p$ in column $j$.

Density data

The density data should be a function of temperature (degC) at atmospheric pressure.

Example:

 $\left(0\right)⟦C⟧$ $\mathrm{\rho }\left({T}_{i},{p}_{\mathrm{atm}}\right)$ $30⟦C⟧$ $\mathrm{\rho }\left({T}_{i},{p}_{\mathrm{atm}}\right)$ $80⟦C⟧$ $\mathrm{\rho }\left({T}_{i},{p}_{\mathrm{atm}}\right)$

where $\mathrm{\rho }\left({T}_{i},{p}_{\mathrm{atm}}\right)$ is the density at temperature $T$ in row $i$ at atmospheric pressure

Parameters

General Parameters

 Name Default Units Description Modelica ID ${T}_{0}$ $293.15$ $K$ Working temperature T0 ${p}_{0}$ ${10}^{7}$ $\mathrm{Pa}$ Reference pressure p0 ${p}_{\mathrm{vapour}}$ $100$ $\mathrm{Pa}$ Absolute vapour pressure p_vapour ${p}_{\mathrm{atm}}$ ${10}^{5}$ $\mathrm{Pa}$ Atmospheric pressure: in case change is wanted for high altitudes p_atm display labels $\mathrm{false}$ Display labels display_labels from file $\mathrm{false}$ Read table data from file from_file kinematic viscosity data $\mathrm{true}$ If true, model assumes that viscosity data is kinematic else dynamic kinematicViscosityData file name $"NoName"$ file_name density table name $"NoName"$ Table for density at p = 1 bar abs density_T_table_name viscosity table name $"NoName"$ Table for viscosity viscosity_table_name bulk modulus table name $"NoName"$ Table for bulk modulus bulk_modulus_table_name density table Density tabular data (see above for format), for T at p = 1.0 bar absolute density_T_table viscosity table Dynamic viscosity tabular data (see above for format and units) viscosity_table ${\mathrm{log}}_{\mathrm{base}}$ $10$ Logarithmic base for tabulated viscosity log_base bulk modulus table Bulk modulus tabular data (see above for format and units) bulk_modulus_table density smoothness [1] Smoothness of density table interpolation density_smoothness viscosity smoothness [1] Smoothness of viscosity table interpolation viscosity_smoothness bulk modulus smoothness [1] Smoothness of bulk modulus table interpolation bulk_modulus_smoothness

[1] $\mathrm{Modelica.Blocks.Types.Smoothness.ContinuousDerivative}$

Gas Parameters

 Name Default Units Description Modelica ID ${v}_{\mathrm{gas}}$ ${10}^{-6}$ $1$ Gas/(hydraulic medium) volume fraction  at atmospheric pressure and 0 degC v_gas $\mathrm{av}$ $6.8$ Bunsen coefficient av ${\mathrm{\rho }}_{\mathrm{gas}\left(0\right)}$ $1.28$ $\frac{\mathrm{kg}}{{m}^{3}}$ Gas density at atmospheric pressure and 0 degC rho_gas_0 ${\mathrm{\nu }}_{\mathrm{gas}}$ $1.5·{10}^{-5}$ $\frac{{m}^{2}}{s}$ Gas kinematic viscosity nu_gas

Constant Parameters

 Name Default Units Description Modelica ID $A$ $0$ Coefficient for temperature-dependent viscosity A $B$ $0$ Coefficient for temperature-dependent viscosity B $\mathrm{\alpha }$ $0$ Coefficient for pressure-dependent viscosity alpha

Constants

 Name Value Units Description Modelica ID ${T}_{\mathrm{ref}}$ $273.15$ $K$ Reference temperature for v_air T_ref ${p}_{\mathrm{ref}}$ ${10}^{5}$ $\mathrm{Pa}$ Reference pressure for v_air p_ref