Gas Volume $—$ Gas Volume

The Gas Volume component describes the behavior of the charge gas in an accumulator as an ideal gas.

 Equations $\mathrm{\kappa }={\mathrm{gas}}_{2}{p}_{\mathrm{\kappa }}^{2}+{\mathrm{gas}}_{1}{p}_{\mathrm{\kappa }}+{\mathrm{gas}}_{0}$ $\mathrm{\rho }={\mathrm{\rho }}_{\mathrm{oil}}\left(p={p}_{\mathrm{abs}},T={T}_{\mathrm{oil}},{v}_{\mathrm{air}}={v}_{\mathrm{gas}\left(\mathrm{oil}\right)},{p}_{\mathrm{sat}}={p}_{\mathrm{sat}}\right)$ $\mathrm{pgas}={p}_{\mathrm{abs}}$ $\mathrm{qaccu}=\frac{{m}_{\mathrm{flow}\left(A\right)}}{\mathrm{\rho }}$ ${T}_{\mathrm{oil}}={T}_{0\left(\mathrm{oil}\right)}+{\mathrm{ΔT}}_{\mathrm{system}}$ ${p}_{\mathrm{\kappa }}=\mathrm{max}\left(5000000,\mathrm{min}\left(40000000,\mathrm{pgas}\right)\right)$ ${p}_{\mathrm{abs}}={p}_{A}+{p}_{\mathrm{atm}\left(\mathrm{oil}\right)}$ ${\partial }_{t}\left(\mathrm{pgas}\right)=\frac{\mathrm{qaccu}\mathrm{\kappa }{\mathrm{pgas}}^{1+\frac{1}{\mathrm{\kappa }}}}{{p}_{\mathrm{precharge}}^{\left(\frac{1}{\mathrm{\kappa }}\right)}{V}_{0}}$

Variables

 Name Value Units Description Modelica ID ${p}_{\mathrm{abs}}$ $\mathrm{Pa}$ Absolute pressure p_abs $\mathrm{\rho }$ $\frac{\mathrm{kg}}{{m}^{3}}$ Gas Density rho ${T}_{\mathrm{oil}}$ $K$ Local temperature of oil T_oil ${p}_{\mathrm{sat}}$ [1] $\mathrm{Pa}$ Gas saturation pressure p_sat $\mathrm{\kappa }$ kappa $\mathrm{pgas}$ $\mathrm{Pa}$ Gas pressure in accumulator, at t = 0 pgas >= pprecharge pgas ${p}_{\mathrm{\kappa }}$ pkappa $\mathrm{qaccu}$ $\frac{{m}^{3}}{s}$ qaccu

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

Connections

 Name Description Modelica ID ${\mathrm{port}}_{A}$ Hydraulic port where oil enters the component port_A $\mathrm{oil}$ oil

Parameters

 Name Default Units Description Modelica ID ${\mathrm{ΔT}}_{\mathrm{system}}$ $0$ $K$ Temperature offset from system temperature dT_system ${V}_{0}$ $0.001$ ${m}^{3}$ Nominal volume V0 ${p}_{\mathrm{precharge}}$ $5.·{10}^{6}$ $\mathrm{Pa}$ Gas pre-charge pressure pprecharge ${p}_{\mathrm{gas}\left(\mathrm{t0}\right)}$ $6.·{10}^{6}$ $\mathrm{Pa}$ Initial gas pressure (at t = 0) pgasstart

Constants

 Name Value Units Description Modelica ID ${\mathrm{gas}}_{0}$ $1.399353688$ gas0 ${\mathrm{gas}}_{1}$ $1.9·{10}^{-8}$ gas1 ${\mathrm{gas}}_{2}$ $-2.86·{10}^{-16}$ gas2