Piloted Relief Valve - MapleSim Help

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Piloted Relief Valve

Piloted spring-loaded relief valve

Description

The Piloted Relief Valve component is a relief 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.

	Formulation Approaches
	One of two approaches can be selected for modeling the flow in the device. When the boolean parameter $Use constant Cd$ is true, a constant coefficient of discharge ( $C_{d}$ ) is used, otherwise a variable coefficient of discharge with maximum value ( $C_{d (\max)}$ ) and a critical flow number ( ${Crit}_{no}$ ) 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

$p = p_{A} - p_{B}$

$Orifice Fluid Equations$

${\begin{array}{c} p = \frac{π}{4} \frac{ρ ν q}{C_{d}^{2} A_{cs} \sqrt{π A_{cs}}} {(\frac{16 q^{4}}{π^{2} A_{cs}^{2} ν^{4}} + {Re}_{Cr}^{4})}^{\frac{1}{4}} & Use constant Cd = true \\ q = C_{d (\max)} \tanh (4 \frac{\sqrt{\frac{A_{cs}}{π} \frac{2 |p|}{ρ}}}{ν {Crit}_{no}}) A_{cs} \sqrt{\frac{2 |p|}{ρ}} sign (p) & otherwise \end{array}$

$Pilot Equations$

${\begin{array}{c} A_{cs} = A_{i} = A_{t} & Exact \\ \{A_{cs} = \min (A_{open}, \max (A_{close}, A_{i})), t_{c} \frac{d A_{i}}{d t} + A_{i} = A_{t}\} & otherwise \end{array}$

$p_{tot} = p + {\begin{array}{c} k_{p} p_{C} & dir = 1 \\ - k_{p} p_{C} & otherwise \end{array}$

$S = {\begin{array}{c} smoothness & smoothTransition \\ 0 & otherwise \end{array}$

$q_{C} = 0$

$A_{t} = {\begin{array}{c} A_{close} & p_{tot} \leq p_{close} \\ A_{close} + (A_{open} - A_{close}) SmoothTrans (S, \frac{p_{tot} - p_{close}}{p_{open} - p_{close}}) & p_{tot} < p_{open} \\ A_{open} & otherwise \end{array}$

$Optional Volume Equations$

$V_{f_{A}} = {\begin{array}{c} Va (1 + \frac{p_{A}}{El}) & Use volume A = true \\ 0 & otherwise \end{array} V_{f_{B}} = {\begin{array}{c} Vb (1 + \frac{p_{B}}{El}) & Use volume B = true \\ 0 & otherwise \end{array}$

$q = q_{A} - q_{V_{A}} = - (q_{B} - q_{V_{B}})$

$q_{V_{A}} = {\begin{array}{c} \frac{d V_{f_{A}}}{d t} & Use volume A = true \\ 0 & otherwise \end{array} q_{V_{B}} = {\begin{array}{c} \frac{d V_{f_{B}}}{d t} & Use volume B = true \\ 0 & otherwise \end{array}$

Variables

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

Connections

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

Parameters

General Parameters

Name	Default	Units	Description	Modelica ID
$p_{close}$	$1.9 \cdot 10^{7}$	$Pa$	Pressure at which valve is fully closed (A = Aclose)	pclose
$p_{open}$	$2.05 \cdot 10^{7}$	$Pa$	Pressure at which valve is fully open (A = Aopen)	popen
$A_{close}$	$1 \cdot 10^{−12}$	$m^{2}$	Valve area when closed (leakage)	Aclose
$A_{open}$	$1 \cdot 10^{−5}$	$m^{2}$	Valve area when fully open	Aopen
Pilot action	$1$		Select whether the pilot operates to open or close the valve	dir
$k_{pilot}$	$3$		Pilot ratio	kp
$Exact$	$false$		When true (checked) first-order dynamics are used for the valve area	Exact
$t_{c}$	$0.1$	$s$	Time constant	tc
$Smooth Transition$	$false$		True (checked) means enable the smoothness factor	smoothTransition
$smoothness$	$0.5$		Smoothness factor (0: sharpest, 1: smoothest); used when $Smooth Transition$ is enabled	smoothness

Orifice

Name	Default	Units	Description	Modelica ID
$Use constant Cd$	$true$		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 $Use constant Cd$ is true	Cd
${Re}_{Cr}$	$12$		Reynolds number at critical flow; used when $Use constant Cd$ is true	ReCr
$C_{d (\max)}$	$0.7$		Maximum flow-discharge coefficient; used when $Use constant Cd$ is false	Cd_max
${Crit}_{no}$	$1000$		Critical flow number; used when $Use constant Cd$ is false	Crit_no

Optional Volumes

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

For more information see Port Volumes.

Fluid Parameters

The following parameters, used in the equations, are properties of the Hydraulic System Properties component used in the model.

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

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