Check Valve - MapleSim Help

All Products Maple MapleSim

Home : Support : Online Help : MapleSim : MapleSim Component Library : Hydraulics : Valves : Check Valve

Check Valve

Spring-Loaded check valve

Description

The Check Valve component allows fluid flow in one direction, from port A to port B. The flow is controlled by an adjustable orifice whose area is controlled by the pressure difference from port A to port B.

The area increases linearly from $A_{close}$ to $A_{open}$ as the pressure increases from $p_{close}$ to $p_{open}$ .

The pressure drop vs flow rate, for the computed area, comes from the Orifice model.

	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

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

$Orifice Fluid Equations$

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

$Orifice Area Equations$

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

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

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

$Optional Volume Equations$

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

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

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

Variables

Name	Units	Description	Modelica ID
$A_{cs}$	$m^{2}$	Cross-sectional area of orifice	Acs
$A_{i}$	$m^{2}$	Filtered interpolated area	At
$A_{t}$	$m^{2}$	Interpolated area	At
$q_{V_{X}}$	$\frac{m^{3}}{s}$	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

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
$Exact$	$false$		When false (not checked) first-order dynamics are used for the valve area	Exact
$t_{c}$	$0.1$	$s$	Time constant of dynamics equation used when Exact is false	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

Maple

Maple Add-Ons

MapleSim

MapleSim Add-Ons

Systems Engineering

Consulting Services

Maple T.A. and Möbius

Education

Industries

Automotive and Aerospace

Robotics

Machine Design & Industrial Automation

Other

Application Areas

Product Pricing

Purchasing

Institutional Student Licensing

Maplesoft Elite Maintenance (EMP)

Support

Product Training

Online Product Help

Webinars & Events

Publications

Content Hubs

Examples & Applications

Community

About Maplesoft

Media Center

User Community

Contact

Online Help

All Products Maple MapleSim

Maple

Powerful math software that is easy to use

Maple Add-Ons

MapleSim

Advanced System Level Modeling

MapleSim Add-Ons

Systems Engineering

Consulting Services

Maple T.A. and Möbius

Education

Industries

Automotive and Aerospace

Robotics

Machine Design & Industrial Automation

Other

Application Areas

Product Pricing

Purchasing

Institutional Student Licensing

Maplesoft Elite Maintenance (EMP)

Support

Product Training

Online Product Help

Webinars & Events

Publications

Content Hubs

Examples & Applications

Community

About Maplesoft

Media Center

User Community

Contact

Online Help

All Products Maple MapleSim