Piston Gas Accumulator $—$ A gas filled piston accumulator

The gas model in the accumulator is based on the model from:

Span, R., Lemmon, E.W., Jacobsen, R.T, Wagner, W., and Yokozeki, A. "A Reference Equation of State for the Thermodynamic Properties of Nitrogen for Temperatures from 63.151 to 1000 K and Pressures to 2200 MPa," J. Phys. Chem. Ref. Data, 29(6):1361-1433, 2000.

The equation of state (EOS) has been compared to the implementation of REFPROP and gives the same results. This implementation covers only the 1-phase region. It is possible to choose a version that uses the corresponding ideal part only, but this is not recommended.

Variables

 Name Value Units Description Modelica ID $\mathrm{pistonCylinder}$ pistonCylinder $\mathrm{housing}$ housing $\mathrm{friction}$ friction $\mathrm{fixed}$ fixed $\mathrm{chamber}$ chamber $\mathrm{spring}$ Gas or mechanical spring spring $\mathrm{Environment}$ Environment ${p}_{A\left(\mathrm{summary}\right)}$ $\mathrm{chamber.p}$ $\mathrm{Pa}$ Pressure at port A summary_pA ${q}_{\mathrm{cham}\left(\mathrm{summary}\right)}$ $\mathrm{chamber.qcham}$ $\frac{{m}^{3}}{s}$ Flow rate flowing into Chamber summary_qCham ${P}_{\mathrm{hyd}\left(\mathrm{summary}\right)}$ $\mathrm{chamber.summary_HP}$ $W$ Hydraulic Power in chamber summary_HP

Connections

 Name Description Modelica ID ${\mathrm{port}}_{A}$ port_A

Parameters

General Parameters

 Name Default Units Description Modelica ID ${n}_{\mathrm{ports}}$ $0$ Number of ports nPorts ${d}_{i}$ $m$ Inner diameter of cylinder d_i ${V}_{\mathrm{dead}}$ ${10}^{-6}$ ${m}^{3}$ Minimum oil volume dead_volume $m$ $\frac{1}{10}$ $\mathrm{kg}$ Mass of piston m ${s}_{\mathrm{max}}$ $\frac{1}{2}$ $m$ Piston maximum stroke (between stiff, compliant cylinder walls) s_max ${\ell }_{\mathrm{piston}}$ $0.02$ $m$ Length of piston piston_length ${s}_{\mathrm{start}}$ $\frac{1}{2}{s}_{\mathrm{max}}$ $m$ Cylinder initial stroke: default is half full s_start ${p}_{\mathrm{preload}}$ $4.·{10}^{7}$ $\mathrm{Pa}$ Preload pressure for empty accumulator p_preload ${\mathrm{ΔT}}_{\mathrm{system}}$ $0$ $K$ Temperature offset from system temperature dT_system ${T}_{\mathrm{start}}$ $300$ $K$ Initial gas Temperature T_start use time constant $\mathrm{true}$ If true, a time constant is used for the thermal behavior, otherwise a heat transfer law use_time_constant ${t}_{\mathrm{thermal}}$ $60$ $s$ Thermal time constant t_thermal $\mathrm{\alpha }$ $150$ $\frac{W}{{m}^{2}K}$ Heat transfer coefficient alpha ${T}_{\mathrm{env}}$ $298.15$ $K$ Fixed environment temperature T_env initial filling $1$ Initial filling of gas cylinder as fraction of total initialFilling

Friction Parameters

 Name Default Units Description Modelica ID ${d}_{\mathrm{viscous}}$ $4.·{10}^{3}$ $\frac{Ns}{m}$ viscous_damping

Constant Parameters

 Name Default Units Description Modelica ID ${A}_{\mathrm{piston}}$ [1] ${m}^{2}$ Piston area piston_area ${V}_{\mathrm{start}}$ ${s}_{\mathrm{start}}{A}_{\mathrm{piston}}$ ${m}^{3}$ Oil volume at initialization V_start

[1] $\frac{1}{4}{d}_{i}^{2}\mathrm{\pi }$