Piston Gas Accumulator

Hydraulic accumulator with precharged gas chamber

 Description The Piston Gas Accumulator component consists of a precharged gas chamber, a floating piston, and a hydraulic chamber connected to a hydraulic port. When fluid pressure at the port exceeds the precharged gas pressure, fluid flows into the hydraulic chamber, moving the piston and compressing the gas. The amount of fluid stored in the accumulator depends on the size and charge. The stroke of the piston is restricted by end cushion parameters used to set the boundary of the component respectively.
 Equations ${a}_{\mathrm{rel}}=\frac{\mathrm{d}{v}_{\mathrm{rel}}}{\mathrm{d}t}\phantom{\rule[-0.0ex]{0.5ex}{0.0ex}}{v}_{\mathrm{rel}}=\frac{\mathrm{d}{s}_{\mathrm{rel}}}{\mathrm{d}t}$ ${f}_{\mathrm{gas}}=-A{p}_{\mathrm{gas}}$ ${f}_{{c}_{1}}=\left\{\begin{array}{cc}0& {s}_{\mathrm{rel}}<{L}_{\mathrm{max}}\\ {c}_{\mathrm{ES}}\left({s}_{\mathrm{rel}}-{L}_{\mathrm{max}}\right)& \mathrm{otherwise}\end{array}{f}_{{c}_{2}}=\left\{\begin{array}{cc}0& 0\le {s}_{\mathrm{rel}}\\ {c}_{\mathrm{ES}}{s}_{\mathrm{rel}}& \mathrm{otherwise}\end{array}$ ${f}_{{d}_{1}}=\left\{\begin{array}{cc}0& {s}_{\mathrm{rel}}<{L}_{\mathrm{max}}\\ {d}_{\mathrm{ES}}\frac{\mathrm{d}{s}_{\mathrm{rel}}}{\mathrm{d}t}& \mathrm{otherwise}\end{array}{f}_{{d}_{2}}=\left\{\begin{array}{cc}0& 0\le {s}_{\mathrm{rel}}\\ {d}_{\mathrm{ES}}\frac{\mathrm{d}{s}_{\mathrm{rel}}}{\mathrm{d}t}& \mathrm{otherwise}\end{array}$ ${f}_{{e}_{1}}=\left\{\begin{array}{cc}0& {f}_{{c}_{1}}+{f}_{{d}_{1}}\le 0\\ {f}_{{c}_{1}}+\mathrm{min}\left({f}_{{c}_{1}},{f}_{{d}_{1}}\right)& \mathrm{otherwise}\end{array}{f}_{{e}_{2}}=\left\{\begin{array}{cc}0& 0\le {f}_{{c}_{2}}+{f}_{{d}_{2}}\\ {f}_{{c}_{2}}+\mathrm{max}\left({f}_{{c}_{2}},{f}_{{d}_{2}}\right)& \mathrm{otherwise}\end{array}$ $p={p}_{A}$ $q={q}_{A}=A{v}_{\mathrm{rel}}=\frac{\mathrm{d}{s}_{\mathrm{rel}}}{\mathrm{d}t}$ ${f}_{\mathrm{chamber}}=pA$ $m{a}_{\mathrm{rel}}=-d\cdot {v}_{\mathrm{rel}}+{f}_{\mathrm{gas}}-{f}_{{e}_{1}}-{f}_{{e}_{2}}+{f}_{\mathrm{chamber}}$ ${p}_{\mathrm{gas}}{\left(A{L}_{\mathrm{max}}-A{s}_{\mathrm{rel}}+{v}_{\mathrm{Dead}}\right)}^{k}={p}_{\mathrm{preload}}{\left(A{L}_{\mathrm{max}}+{v}_{\mathrm{Dead}}\right)}^{k}$

Variables

 Name Units Description Modelica ID $p$ $\mathrm{Pa}$ Pressure of fluid in component p $q$ $\frac{{m}^{3}}{s}$ Flow rate of fluid into component q ${s}_{\mathrm{rel}}$ $m$ Relative distance of the piston from the initial position s_rel ${v}_{\mathrm{rel}}$ $\frac{m}{s}$ Relative velocity of the piston v_rel ${a}_{\mathrm{rel}}$ $\frac{m}{{s}^{2}}$ Relative acceleration of the piston a_rel

Connections

 Name Description Modelica ID $\mathrm{portA}$ Hydraulic port portA

Parameters

Damper Parameters

 Name Default Units Description Modelica ID $d$ $0$ $N\frac{s}{m}$ Piston viscous friction coefficient d

Geometry

 Name Default Units Description Modelica ID $A$ $0.01$ ${m}^{2}$ Wetted area of piston A $m$ $0.1$ $\mathrm{kg}$ Mass of the piston m ${L}_{\mathrm{max}}$ $0.4$ $m$ Maximum stroke length of the accumulator Lmax

Hard Stop

 Name Default Units Description Modelica ID ${c}_{\mathrm{ES}}$ $1·{10}^{10}$ $\frac{N}{m}$ Hard stop stiffness c_ES ${d}_{\mathrm{ES}}$ $1·{10}^{6}$ $N\frac{s}{m}$ Hard stop damping d_ES

Gas Chamber

 Name Default Units Description Modelica ID ${v}_{\mathrm{dead}}$ $0.001$ ${m}^{3}$ Dead volume inside the gas chamber vDead $k$ $1.4$ $1$ Specific heat ratio of the gas k

 Name Default Units Description Modelica ID ${p}_{\mathrm{preload}}$ $1·{10}^{5}$ $\mathrm{Pa}$ Initial pressure inside the gas chamber p_preload