Pressure Reducing Valve - MapleSim Help

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Pressure Reducing Valve

Reducing valve with opening area linearly dependent on pressure difference

Description

The Pressure Reducing Valve component models a hydraulic reducing valve as a sharp-edge orifice with the orifice area dependent on the pressure across the valve.

The area varies linearly from $A_{open}$ to $A_{close}$ as the pressure varies from $p_{contract}$ to $p_{close}$ , and remains at the endpoints for pressures outside this range.

Based on the orifice area, the pressure vs flow rate relationships are derived by the formulation used in the Orifice component.

	Formulation Approaches
	Two approaches were taken for formulation of the flow equation inside 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

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

$Orifice Fluid Equations$

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

$Orifice Area Equations$

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

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

$Optional Volume Equations$

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

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

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

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
$A_{cs}$	$m^{2}$	Cross-sectional area of orifice	Acs
$A_{i}$	$m^{2}$	Filtered interpolated area	At
$A_{t}$	$m^{2}$	Interpolated area	At
$q_{VX}$	$\frac{m^{3}}{s}$	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
$portA$	Upstream hydraulic port	portA
$portB$	Downstream hydraulic port	portB

Parameters

General

Name	Default	Units	Description	Modelica ID
$p_{close}$	$2.1 \cdot 10^{7}$	$Pa$	Pressure at which valve is fully closed (A = Aclose)	pclose
$p_{contract}$	$1.9 \cdot 10^{7}$	$Pa$	Pressure till which the valve is fully open (A = Aopen)	pcontract
$A_{close}$	$1 \cdot 10^{−12}$	$m^{2}$	Valve area when closed (leakage)	Aclose
$A_{open}$	$1 \cdot 10^{−5}$	$m^{2}$	Valve area when fully open	Aopen
$Exact$	$false$		When true (checked) a first-order dynamics is used for the valve area	Exact
$t_{c}$	$0.1$	$s$	Time constant used in first-order dynamics; used when $Exact = true$	tc

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 calculation	UseConstantCd
$C_{d}$	$0.7$		Flow-discharge coefficient; used when $Use constant Cd$ is true	Cd
$ℜ_{Cr}$	$12$		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.

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