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Spool Valve

Spool valve with an input signal that controls the orifice area

Description

The Spool Valve component models a spool valve controlled by a signal that sets the orifice area.

The pressure-flow characteristic is based on the equations of 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

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

$Orifice Fluid Equations$

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

$A_{cs} = \max (\frac{Area}{A_{unit}}, A_{\min})$

$Optional Volume Equations$

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

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

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

Variables

Name	Units	Description	Modelica ID
$A_{cs}$	$m^{2}$	Cross-sectional area of orifice	Acs
$q_{V_{X}}$	$\frac{m^{3}}{s}$	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
$portA$	Upstream hydraulic port	portA
$portB$	Downstream hydraulic port	portB
$Area$	Real input; area of orifice in selected units	Area

Parameters

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

General

Name	Default	Units	Description	Modelica ID
Area unit	$1$	${mm}^{2}$	Unit of area used in input signal	areaUnit

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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