Gas Cylinder $—$ Gas volume in a gas-filled piston accumulator

The Gas Cylinder component describes a high-pressure gas volume in a cylinder. For initializing the amount of gas in the cylinder, it is assumed that the preload pressure, p_preload, and the initial temperature, T_start, completely fill the cylinder to initialFilling $\cdot$ s_max, where s_max is the maximum position of the cylinder.

 Equations $\left\{\begin{array}{cc}\mathrm{environment.Q_flow}=\frac{{M}_{\mathrm{gas}}\mathrm{cp}\left(\mathrm{environment.T}-T\right)}{{t}_{\mathrm{thermal}}}& \mathrm{use_time_constant}\\ \mathrm{environment.Q_flow}=\mathrm{\alpha }{A}_{\mathrm{heat}}\left(\mathrm{environment.T}-T\right)& \mathrm{otherwise}\end{array}\right\$ $\mathrm{\rho }=\frac{{M}_{\mathrm{gas}}}{V}$ $V=\left\{\begin{array}{cc}\left|{s}_{\mathrm{rel}}\right|\mathrm{PistonArea}& {s}_{\mathrm{rel}}<{s}_{\mathrm{max}}\\ \left|{s}_{\mathrm{max}}\right|\mathrm{PistonArea}& \mathrm{otherwise}\end{array}\right\$ $\mathrm{cp}=\mathrm{Medium.specificHeatCapacityCp_pT}\left(p,T\right)$ $\mathrm{dU}={M}_{\mathrm{gas}}\left(\mathrm{duTp}{\partial }_{t}\left(T\right)+\mathrm{dupT}{\partial }_{t}\left(p\right)\right)$ $\mathrm{dU}=-p{\partial }_{t}\left(V\right)+\mathrm{environment.Q_flow}$ $\mathrm{duTp}=\mathrm{Medium.specificEnergy_derT_p_pT}\left(p,T\right)$ $\mathrm{dupT}=\mathrm{Medium.specificEnergy_derp_T_pT}\left(p,T\right)$ $p=\mathrm{Medium.pressure_dT}\left(\frac{{M}_{\mathrm{gas}}}{V},T\right)$ $\mathrm{flange_a.f}=p\mathrm{PistonArea}$ $\mathrm{flange_b.f}=f$ ${A}_{\mathrm{heat}}=2\mathrm{PistonArea}+\mathrm{\pi }{d}_{i}\left|{s}_{\mathrm{max}}-{s}_{\mathrm{rel}}\right|$ ${M}_{\mathrm{gas}}=\mathrm{Medium.density_pT}\left({p}_{\mathrm{preload}},{T}_{\mathrm{start}}\right)\mathrm{PistonArea}\mathrm{initialFilling}{s}_{\mathrm{max}}$ ${s}_{\mathrm{rel}}=\mathrm{flange_b.s}-\mathrm{flange_a.s}$ $\mathrm{flange_a.f}+\mathrm{flange_b.f}=0$

Variables

 Name Value Units Description Modelica ID ${s}_{\mathrm{rel}}$ $m$ Relative position s_rel $f$ $N$ Force between flanges f ${A}_{\mathrm{heat}}$ ${m}^{2}$ Heat transfer area A_heat ${M}_{\mathrm{gas}}$ $\mathrm{kg}$ Gas mass filling M_gas $V$ ${m}^{3}$ Gas Volume of cylinder V $p$ $\mathrm{Pa}$ Gas pressure p $T$ $K$ Gas Temperature T $\mathrm{cp}$ $\frac{J}{\mathrm{kg}K}$ Heat capacity of gas cp $\mathrm{\rho }$ $\frac{\mathrm{kg}}{{m}^{3}}$ Density rho $\mathrm{duTp}$ $\frac{J}{\mathrm{kg}K}$ Partial derivative of inner energy wrt T at constant p duTp $\mathrm{dupT}$ $\frac{Jm{s}^{2}}{{\mathrm{kg}}^{2}}$ Partial derivative of inner energy wrt p at constant T dupT $\mathrm{dU}$ $W$ Energy transfer term dU

Connections

 Name Description Modelica ID ${\mathrm{flange}}_{a}$ flange_a ${\mathrm{flange}}_{b}$ flange_b $\mathrm{environment}$ Port for environment temperature environment

Parameters

General Parameters

 Name Default Units Description Modelica ID ${V}_{\mathrm{start}}$ $\mathrm{PistonArea}{s}_{\mathrm{max}}$ ${m}^{3}$ Initial Volume V_start ${T}_{\mathrm{start}}$ $300$ $K$ Initial gas Temperature T_start ${t}_{\mathrm{thermal}}$ $s$ Thermal time constant t_thermal use time constant $\mathrm{true}$ use_time_constant $\mathrm{\alpha }$ $150$ $\frac{W}{{m}^{2}K}$ Heat transfer coefficient alpha ${p}_{\mathrm{preload}}$ $\mathrm{Pa}$ Gas preload pressure p_preload ${V}_{\mathrm{max}}$ $1$ ${m}^{3}$ Maximum volume V_max ${d}_{i}$ $m$ Inner diameter of cylinder d_i ${s}_{\mathrm{max}}$ $m$ Maximum position of cylinder s_max initial filling $1$ Initial filling of cylinder as fraction of total initialFilling

Constant Parameters

 Name Default Units Description Modelica ID $\mathrm{PistonArea}$ [1] ${m}^{2}$ Cross section area PistonArea

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