Multi Port Oil Volume $—$ Lumped volume with pressure-dependent bulk modulus, with vectorized connector

The Multi Port Oil Volume component describes a lumped volume with pressure-dependent bulk modulus. The pressure in the volume is calculated by:

${\partial }_{t}p=\frac{\mathrm{\beta }q}{\mathrm{volume}\mathrm{\rho }}$

The bulk modulus is given by:

$\mathrm{\beta }=\mathrm{\beta }\left(p\right)$

Variables used in the above equations

 $p$ pressure in the volume $\left[\mathrm{Pa}\right]$ $\mathrm{\beta }$ bulk modulus, pressure-dependent $\left[\mathrm{Pa}\right]$ $\mathrm{volume}$ geometric volume of oil under pressure (parameter) $\left[{m}^{3}\right]$ $q$ port_A.q $\left[\frac{\mathrm{kg}}{s}\right]$

The calculated pressure is not limited to the vapor pressure but can reach unlimited negative values. A limitation is done in TwoPortComp where all pressures used to compute the differential pressure between the ports are limited to the vapor pressure.

Model Oil Volume is the default model for all lumped volumes in the library. The equations are also used in the cylinder models.

Use the modifier

port_A(p(start=2e6,fixed=true))

to set the initial condition for the pressure of the lumped volume in $\mathrm{Pa}$.

The compressibility is an important property of the oil and influences the dynamic behavior of the circuit. Besides the bulk modulus of "pure" (that is, air-free) oil, the amount of undissolved air, the pressure, and the compliance of the component determine the "effective bulk modulus". The default model in the Hydraulics library includes all these effects and describes a typical circuit. However, there are situations when it makes sense to use other models (for example, for a sensitivity analysis to check that the overall dynamic response of the circuit doesn't heavily depend on the oil model).

Figure Bulk modulus of different models as a function of pressure.

 Equations $\mathrm{msim/FOR}\left(\mathrm{msim/IN}\left(\mathrm{i#1},1..{n}_{\mathrm{ports}}\right),p=\mathrm{ports\left[i#1\right].p}\right)$ $\mathrm{\beta }={\mathrm{\beta }}_{\mathrm{oil}}\left(p={p}_{\mathrm{abs}},T=T,{v}_{\mathrm{air}}={v}_{\mathrm{gas}\left(\mathrm{oil}\right)},{p}_{\mathrm{sat}}={p}_{\mathrm{sat}}\right)$ $\mathrm{\rho }={\mathrm{\rho }}_{\mathrm{oil}}\left(p={p}_{\mathrm{abs}},T=T,{v}_{\mathrm{air}}={v}_{\mathrm{gas}\left(\mathrm{oil}\right)},{p}_{\mathrm{sat}}={p}_{\mathrm{sat}}\right)$ $T={T}_{0\left(\mathrm{oil}\right)}+{\mathrm{ΔT}}_{\mathrm{system}}$ ${p}_{\mathrm{abs}}=p+{p}_{\mathrm{atm}\left(\mathrm{oil}\right)}$ ${\partial }_{t}\left(p\right)=\frac{\mathrm{\beta }\left({\sum }\phantom{\rule[-0.0ex]{5.0px}{0.0ex}}\mathrm{ports.m_flow}\right)}{V\mathrm{\rho }}$

Variables

 Name Value Units Description Modelica ID $T$ $K$ Local temperature T $p$ $\mathrm{Pa}$ Pressure in volume p $\mathrm{saturation}$ [1] Saturation value in HSV color space saturation $\mathrm{\beta }$ $\mathrm{Pa}$ Bulk modulus of oil beta ${p}_{\mathrm{abs}}$ $\mathrm{Pa}$ Absolute pressure, used for all property calls p_abs ${p}_{\mathrm{sat}}$ [2] $\mathrm{Pa}$ Gas saturation pressure p_sat ${p}_{A\left(\mathrm{summary}\right)}$ $p$ $\mathrm{Pa}$ Pressure at port A summary_pA ${T}_{\mathrm{summary}}$ $T$ $K$ Local Temperature summary_T ${\mathrm{\beta }}_{\mathrm{summary}}$ $\mathrm{\beta }$ $\mathrm{Pa}$ Bulk modulus of oil summary_beta ${\mathrm{\rho }}_{\mathrm{summary}}$ $\mathrm{\rho }$ $\frac{\mathrm{kg}}{{m}^{3}}$ Density summary_rho $\mathrm{\rho }$ $\frac{\mathrm{kg}}{{m}^{3}}$ Density rho $\mathrm{oilWarnings}$ oilWarnings $\mathrm{pressureSensor}$ pressureSensor

[1] $\frac{\mathrm{max}\left(0,\mathrm{min}\left(p,{p}_{\mathrm{max}\left(\mathrm{color}\right)}\right)-{p}_{\mathrm{min}\left(\mathrm{color}\right)}\right)}{{p}_{\mathrm{max}\left(\mathrm{color}\right)}-{p}_{\mathrm{min}\left(\mathrm{color}\right)}}$

[2] $\mathrm{oil.gasSaturationPressure}\left(T=T,{v}_{\mathrm{gas}}={\mathrm{oil.v}}_{\mathrm{gas}}\right)$

Connections

 Name Description Modelica ID $\mathrm{ports}$ ports $\mathrm{oil}$ oil

Parameters

General Parameters

 Name Default Units Description Modelica ID ${n}_{\mathrm{ports}}$ $0$ Number of ports nPorts ${\mathrm{ΔT}}_{\mathrm{system}}$ $0$ $K$ Temperature offset from system temperature dT_system steady-state init $\mathrm{false}$ Steady state initialization steadyStateInit $\mathrm{volume}$ ${10}^{-6}$ ${m}^{3}$ volume volume