Piloted Reducing Valve - MapleSim Help

Piloted Reducing Valve

Reducing valve with opening area linearly dependent on pressure difference

Description

The Piloted Reducing Valve component is a reducing 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 using the formulation in the Orifice component.

 Formulation Approaches One of two approaches can be selected for modeling the flow in the device. When the boolean parameter $\mathrm{Use constant Cd}$ is true, a constant coefficient of discharge (${C}_{d}$) is used, otherwise a variable coefficient of discharge with maximum value (${C}_{d\left(\mathrm{max}\right)}$) and a critical flow number (${\mathrm{Crit}}_{\mathrm{no}}$) are used.
 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 stiffness of the system and improves the solvability.
 Equations $p={p}_{A}-{p}_{B}$ $\mathbf{Orifice Fluid Equations}$ $\left\{\begin{array}{cc}p=\frac{\mathrm{\pi }}{4}\frac{\mathrm{\rho }\mathrm{\nu }q}{{C}_{d}^{2}{A}_{\mathrm{cs}}\sqrt{\mathrm{\pi }{A}_{\mathrm{cs}}}}{\left(\frac{16{q}^{4}}{{\mathrm{\pi }}^{2}{A}_{\mathrm{cs}}^{2}{\mathrm{\nu }}^{4}}+{\mathrm{Re}}_{\mathrm{Cr}}^{4}\right)}^{\frac{1}{4}}& \mathrm{Use constant Cd}=\mathrm{true}\\ q={C}_{d\left(\mathrm{max}\right)}\mathrm{tanh}\left(4\frac{\sqrt{\frac{{A}_{\mathrm{cs}}}{\mathrm{\pi }}\frac{2\left|p\right|}{\mathrm{\rho }}}}{\mathrm{\nu }{\mathrm{Crit}}_{\mathrm{no}}}\right){A}_{\mathrm{cs}}\sqrt{\frac{2\left|p\right|}{\mathrm{\rho }}}\mathrm{sign}\left(p\right)& \mathrm{otherwise}\end{array}$ $\mathbf{Pilot Equations}$ $\left\{\begin{array}{cc}{A}_{\mathrm{cs}}={A}_{i}={A}_{t}& \mathrm{Exact}\\ \left\{{A}_{\mathrm{cs}}=\mathrm{min}\left({A}_{\mathrm{open}},\mathrm{max}\left({A}_{\mathrm{close}},{A}_{i}\right)\right),{t}_{c}\frac{\mathrm{d}{A}_{i}}{\mathrm{d}t}+{A}_{i}={A}_{t}\right\}& \mathrm{otherwise}\end{array}$ ${A}_{t}=\left\{\begin{array}{cc}{A}_{\mathrm{open}}& {p}_{\mathrm{tot}}<{p}_{\mathrm{open}}\\ {A}_{\mathrm{open}}-\left({A}_{\mathrm{open}}-{A}_{\mathrm{close}}\right)\mathrm{SmoothTrans}\left(S,\frac{{p}_{\mathrm{tot}}-{p}_{\mathrm{open}}}{{p}_{\mathrm{close}}-{p}_{\mathrm{open}}}\right)& {p}_{\mathrm{tot}}<{p}_{\mathrm{close}}\\ {A}_{\mathrm{close}}& \mathrm{otherwise}\end{array}$ $S=\left\{\begin{array}{cc}\mathrm{smoothness}& \mathrm{smoothTransition}\\ 0& \mathrm{otherwise}\end{array}$ ${p}_{\mathrm{tot}}={p}_{B}+{k}_{\mathrm{pilot}}{p}_{C}$ ${q}_{C}=0$ $\mathbf{Optional Volume Equations}$ ${V}_{{f}_{A}}=\left\{\begin{array}{cc}\mathrm{Va}\left(1+\frac{{p}_{A}}{\mathrm{El}}\right)& \mathrm{Use volume A}=\mathrm{true}\\ 0& \mathrm{otherwise}\end{array}\phantom{\rule[-0.0ex]{5.0ex}{0.0ex}}{V}_{{f}_{B}}=\left\{\begin{array}{cc}\mathrm{Vb}\left(1+\frac{{p}_{B}}{\mathrm{El}}\right)& \mathrm{Use volume B}=\mathrm{true}\\ 0& \mathrm{otherwise}\end{array}$ $q={q}_{A}-{q}_{{V}_{A}}=-\left({q}_{B}-{q}_{{V}_{B}}\right)$ ${q}_{{V}_{A}}=\left\{\begin{array}{cc}\frac{\mathrm{d}{V}_{{f}_{A}}}{\mathrm{d}t}& \mathrm{Use volume A}=\mathrm{true}\\ 0& \mathrm{otherwise}\end{array}\phantom{\rule[-0.0ex]{4.0ex}{0.0ex}}{q}_{{V}_{B}}=\left\{\begin{array}{cc}\frac{\mathrm{d}{V}_{{f}_{B}}}{\mathrm{d}t}& \mathrm{Use volume B}=\mathrm{true}\\ 0& \mathrm{otherwise}\end{array}$

Variables

 Name Units Description Modelica ID $p$ $\mathrm{Pa}$ Pressure drop from A to B p ${p}_{X}$ $\mathrm{Pa}$ Pressure at port X pX $q$ $\frac{{m}^{3}}{s}$ Flow rate from port A to port B q ${q}_{X}$ $\frac{{m}^{3}}{s}$ Flow rate into port X q ${q}_{{V}_{X}}$ $\frac{{m}^{3}}{s}$ Flow rate into port X's optional volume qVX ${V}_{{f}_{X}}$ ${m}^{3}$ Effective volume at port X VfX

$X,Y\in \left\{A,B,C\right\}$

Connections

 Name Description Modelica ID $\mathrm{portA}$ Upstream hydraulic portA $\mathrm{portB}$ Downstream hydraulic port portB $\mathrm{portC}$ Venting hydraulic port (no volume, used as pilot) portC

Parameters

General

 Name Default Units Description Modelica ID ${p}_{\mathrm{close}}$ $2.1·{10}^{7}$ $\mathrm{Pa}$ Pressure at which valve is fully closed (A = Aclose) pclose ${p}_{\mathrm{open}}$ $1.9·{10}^{7}$ $\mathrm{Pa}$ Pressure at which the 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 $\mathrm{kp}$ $3$ Pilot ratio kp $\mathrm{Exact}$ $\mathrm{false}$ When false (not checked) first-order dynamics are used for the valve area Exact ${t}_{c}$ $0.1$ $s$ Time constant tc $\mathrm{Smooth Transition}$ $\mathrm{false}$ True (checked) means enable the smoothness factor smoothTransition $\mathrm{smoothness}$ $0.5$ Smoothness factor (0: sharpest, 1: smoothest); used when $\mathrm{Smooth Transition}$ is enabled smoothness

Orifice

 Name Default Units Description Modelica ID $\mathrm{Use constant Cd}$ $\mathrm{true}$ True (checked) means a constant coefficient of discharge is implemented, otherwise a variable ${C}_{d}$ is used in flow calculations UseConstantCd ${C}_{d}$ $0.7$ Flow-discharge coefficient; used when $\mathrm{Use constant Cd}$ is true Cd ${\mathrm{Re}}_{\mathrm{Cr}}$ $12$ Reynolds number at critical flow; used when $\mathrm{Use constant Cd}$ is true ReCr ${C}_{d\left(\mathrm{max}\right)}$ $0.7$ Maximum flow-discharge coefficient; used when $\mathrm{Use constant Cd}$ is false Cd_max ${\mathrm{Crit}}_{\mathrm{no}}$ $1000$ Critical flow number; used when $\mathrm{Use constant Cd}$ is false Crit_no

Optional Volumes

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

 Name Units Description Modelica ID $\mathrm{\nu }$ $\frac{{m}^{2}}{s}$ Kinematic viscosity of fluid nu $\mathrm{\rho }$ $\frac{\mathrm{kg}}{{m}^{3}}$ Density of fluid rho $\mathrm{El}$ $\mathrm{Pa}$ Bulk modulus of fluid El