Accu2 $—$ Hydro-pneumatic accumulator (refined gas model)

The Accu2 component describes a hydro-pneumatic accumulator. The model of the charge gas is more refined than in the Accu1 component. There is a valve at the inlet port. Oil flows into the accumulator if the pressure at port_A is higher than the gas pressure, pgas. A lower limit is given for the gas pressure, pgas, by the precharge pressure. This is calculated from the volume of the accumulator, the temperature of the environment and the gas mass. The gas volume at t = 0 must be less than or equal to the volume of the accumulator. There is a check whether this condition is met. The model uses the Beattie-Bridgeman-equation to calculate the behavior of nitrogen as the charge gas. The following m-files calculate parameters for model Accu2. They can help with the numerical analysis of an accumulator and are to be used with MATLAB(R), not Dymola(R). This model will be replaced by a new model next release.

 Name Description bbp.m Calculates the pressure for given temperature and specific volume. bbvs.m Calculates the specific volume for given temperature and pressure. cvp.m Calculates the specific capacity for constant volume.

Related Components

 Name Description Hydro-pneumatic accumulator with a simple model of the charge gas.

Variables

 Name Value Units Description Modelica ID $\mathrm{GasVolBB}$ GasVolBB $\mathrm{TWV}$ TWV ${\mathrm{PMeas}}_{1}$ PMeas1 ${\mathrm{PMeas}}_{2}$ PMeas2 $\mathrm{ValveLog}$ ValveLog ${p}_{A\left(\mathrm{summary}\right)}$ ${p}_{A}$ $\mathrm{Pa}$ Pressure at port A summary_pA

Connections

 Name Description Modelica ID $\mathrm{oil}$ oil ${\mathrm{port}}_{A}$ Port A, where oil flows into the component ($0, ${p}_{B}<{p}_{A}$ means $0<\mathrm{Δp}$) port_A

Parameters

General Parameters

 Name Default Units Description Modelica ID ${V}_{\mathrm{acc}}$ $0.001$ ${m}^{3}$ Volume of accumulator AccVol ${V}_{\mathrm{gas}\left(\mathrm{T0}\right)}$ $0.001$ ${m}^{3}$ Gas volume at t = 0 GasVol_T0 $\mathrm{\Theta }$ $300$ $K$ Temperature of environment Theta ${\mathrm{Temp}}_{0}$ $300$ $K$ Temperature of charge gas at t = 0 Temp_0 ${m}_{\mathrm{gas}}$ $0.0394$ $\mathrm{kg}$ Gas mass (default is for 1e-3 m3 und 3.5 MPa) gm $\mathrm{Τ}$ $5$ $s$ Thermal time constant Tau $\overline{cv}$ $750$ Mean value of cv CvBar

Oil Parameters

 Name Default Units Description Modelica ID ${V}_{A}$ ${10}^{-6}$ ${m}^{3}$ Geometric volume at port A of TwoWayValve volumeA ${V}_{B}$ ${10}^{-6}$ ${m}^{3}$ Geometric volume at port B of TwoWayValve volumeB

Valve Parameters

 Name Default Units Description Modelica ID $\mathrm{overlap}$ $0.02$ Overlap of valve relative to max. displacement = 1 overlap ${q}_{\mathrm{nom}}$ $8.33·{10}^{-4}$ $\frac{{m}^{3}}{s}$ Nominal flow rate of valve qnom ${\mathrm{Δp}}_{\mathrm{nom}}$ $3.5·{10}^{6}$ $\mathrm{Pa}$ Pressure drop at qnom of valve dpnom ${d}_{\mathrm{leak}}$ $0$ $m$ Diameter of equivalent orifice to model leakage of closed valve dleak ${k}_{1}$ $10$ Laminar part of orifice model k1 ${k}_{2}$ $2$ Turbulent part, ${k}_{2}=\frac{1}{{C}_{d}^{2}}$ k2 ${\mathrm{\omega }}_{0}$ $500$ $\frac{\mathrm{rad}}{s}$ Natural frequency of spool omega0 $\mathrm{damp}$ $1$ Damping coefficient of spool damp

Constant Parameters

 Name Default Units Description Modelica ID $\mathrm{spezVol}$ $\frac{{V}_{\mathrm{acc}}}{{m}_{\mathrm{gas}}}$ computed spezVol ${p}_{\mathrm{precharge}}$ [1] $\mathrm{Pa}$ Gas pre-charge pressure, computed pprecharge

[1] $\frac{100000R\mathrm{\Theta }\left(1-\frac{C}{{\mathrm{\Theta }}^{3}\mathrm{spezVol}}\right)\left(\mathrm{spezVol}+{B}_{0}\left(1-\frac{B}{\mathrm{spezVol}}\right)\right)}{{\mathrm{spezVol}}^{2}}-\frac{100000{A}_{0}\left(1-\frac{\mathrm{AA}}{\mathrm{spezVol}}\right)}{{\mathrm{spezVol}}^{2}}$

Constants

 Name Value Units Description Modelica ID $R$ $0.00297$ R ${A}_{0}$ $0.00174$ A0 ${B}_{0}$ $0.0018$ B0 $\mathrm{AA}$ $9.34·{10}^{-4}$ AA $B$ $-2.47·{10}^{-4}$ B $C$ $5.09·{10}^{-8}$ C