Piloted Check Valve - MapleSim Help

Piloted Check Valve

 Description The Piloted Check Valve component is a check valve with a pilot pressure that can be used to assist in opening or closing the valve. The valve orifice area is assumed to be a piecewise linear function of the pressure difference between port A and port B. Based on the orifice area, the pressure vs. flow rate relationship is calculated by the formulation used in the Orifice component.
 Optional Volumes The boolean parameters Use volume A and Use volume B, when true, add optional volumes ${V}_{A}$  and ${V}_{B}$ to ports A and B, respectively. See Port Volumes for details. If two orifices or valves are connected, enabling a volume at the common port reduces the the stiffness of the system and improves the solvability.
 Equations $\left\{\begin{array}{cc}\left\{{A}_{\mathrm{cs}}={A}_{i},{A}_{i}={A}_{t}\right\}& \mathrm{Exact}\\ \left\{{A}_{\mathrm{cs}}=\mathrm{min}\left({A}_{\mathrm{open}},\mathrm{max}\left({A}_{\mathrm{close}},{A}_{i}\right)\right),{t}_{c}\frac{\mathrm{d}{A}_{i}}{\mathrm{d}t}+{A}_{i}={A}_{t}\right\}& \mathrm{otherwise}\end{array}$ ${A}_{t}=\left\{\begin{array}{cc}{A}_{\mathrm{close}}& {p}_{\mathrm{tot}}\le {p}_{\mathrm{close}}\\ {A}_{\mathrm{close}}+\left({p}_{\mathrm{tot}}-{p}_{\mathrm{close}}\right)\frac{{A}_{\mathrm{open}}-{A}_{\mathrm{close}}}{{p}_{\mathrm{open}}-{p}_{\mathrm{close}}}& {p}_{\mathrm{tot}}<{p}_{\mathrm{open}}\\ {A}_{\mathrm{open}}& \mathrm{otherwise}\end{array}$ ${V}_{{f}_{A}}=\left\{\begin{array}{cc}\mathrm{Va}\left(1+\frac{{p}_{A}}{\mathrm{El}}\right)& \mathrm{useVolumeA}\\ 0& \mathrm{otherwise}\end{array}\phantom{\rule[-0.0ex]{5.0ex}{0.0ex}}{V}_{{f}_{B}}=\left\{\begin{array}{cc}\mathrm{Vb}\left(1+\frac{{p}_{B}}{\mathrm{El}}\right)& \mathrm{useVolumeB}\\ 0& \mathrm{otherwise}\end{array}$ $p={p}_{A}-{p}_{B}$ ${p}_{\mathrm{tot}}=p+\left\{\begin{array}{cc}{k}_{p}{p}_{C}& \mathrm{dir}=1\\ -{k}_{p}{p}_{C}& \mathrm{otherwise}\end{array}$ ${q}_{C}=0$ $q={q}_{A}-{q}_{{V}_{A}}$ ${q}_{{V}_{A}}=\left\{\begin{array}{cc}\frac{\mathrm{d}{V}_{{f}_{A}}}{\mathrm{d}t}& \mathrm{useVolumeA}\\ 0& \mathrm{otherwise}\end{array}\phantom{\rule[-0.0ex]{4.0ex}{0.0ex}}{q}_{{V}_{B}}=\left\{\begin{array}{cc}\frac{\mathrm{d}{V}_{{f}_{B}}}{\mathrm{d}t}& \mathrm{useVolumeB}\\ 0& \mathrm{otherwise}\end{array}$ ${q}_{A}+{q}_{B}-{q}_{{V}_{A}}-{q}_{{V}_{B}}=0$

Variables

 Name Value Units Description Modelica ID $p$ Pressure across component $\mathrm{Pa}$ Pressure drop from A to B p $q$ Flow rate through component $\frac{{m}^{3}}{s}$ Flow rate from port A to port B q ${q}_{\mathrm{summary}}$ $q\mathrm{flowScaleSummary}$ $\frac{{m}^{3}}{s}$ Internal flow sensor q_summary ${\mathrm{dp}}_{\mathrm{summary}}$ $p\mathrm{pressScaleSummary}$ $\mathrm{Pa}$ Internal pressure difference sensor dp_summary

Connections

 Name Description Modelica ID $\mathrm{portA}$ Hydraulic port on left side portA $\mathrm{portB}$ Hydraulic port on right side portB $\mathrm{portC}$ Hydraulic port on the bottom (no volume, used as pilot) portC

Parameters

General Parameters

 Name Default Units Description Modelica ID ${p}_{\mathrm{close}}$ $1.9·{10}^{7}$ $\mathrm{Pa}$ Pressure at which valve is fully closed (A = Aclose) pclose ${p}_{\mathrm{open}}$ $2.05·{10}^{7}$ $\mathrm{Pa}$ Pressure at which valve is fully open (A = Aopen) popen ${A}_{\mathrm{close}}$ $1·{10}^{-12}$ ${m}^{2}$ Valve area when closed (leakage) Aclose ${A}_{\mathrm{open}}$ $1·{10}^{-5}$ ${m}^{2}$ Valve area when fully open Aopen Pilot action $1$ Select whether the pilot operates to open or close the valve dir ${k}_{\mathrm{pilot}}$ $3$ Pilot ratio kp $\mathrm{Exact}$ $\mathrm{false}$ When true (checked) a first-order dynamics is used for the valve area Exact ${t}_{c}$ $\frac{1}{10}$ $s$ Time constant tc ${C}_{d}$ $\frac{7}{10}$ Flow-discharge coefficient Cd ${\mathrm{\Re }}_{\mathrm{Cr}}$ $12$ Reynolds number at critical flow ReCr

Volume Parameters

 Name Default Units Description Modelica ID Use volume A $\mathrm{false}$ When true a hydraulic volume chamber is added to portA useVolumeA ${V}_{A}$ $1·{10}^{-6}$ ${m}^{3}$ Volume of chamber A Va Use volume B $\mathrm{false}$ When true a hydraulic volume chamber is added to portB useVolumeB ${V}_{B}$ $1·{10}^{-6}$ ${m}^{3}$ Volume of chamber B Vb