Relief Valve - MapleSim Help

All Products Maple MapleSim

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

Relief Valve

Relief valve with opening area linearly dependent on pressure difference

Description

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

The area varies linearly from $A_{closed}$ to $A_{open}$ as the pressure varies from $p_{closed}$ to $p_{open}$ , 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
$A_{cs}$	$m^{2}$	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
$p_{closed}$	$1.9 \cdot 10^{7}$	$Pa$	Pressure at which valve is fully closed ( $A = A_{closed}$ )	pclosed
$p_{open}$	$2.05 \cdot 10^{7}$	$Pa$	Pressure at which valve is fully open ( $A = A_{open}$ )	popen
$A_{open}$	$1 \cdot 10^{−5}$	$m^{2}$	Valve area when fully open	Aopen
$A_{closed}$	$1 \cdot 10^{−12}$	$m^{2}$	Valve area when closed (leakage)	Aclosed
$Use constant Cd$	$true$		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.

Fluid Parameters

The following parameters, used in the equations, are properties of the Hydraulic Fluid 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

What kind of issue would you like to report? (Optional)
Please add your Comment (Optional)
E-mail Address (Optional)
What is ?	This question helps us to combat spam

Maple

Maple 附加模块

MapleSim

MapleSim 附加模块

系统工程

项目服务

Maple T.A. and Möbius

教育

行业

汽车与航空航天

机器人

机器设计和工业自动化

其他

应用领域

产品价格

购买

院系/全校正版授权

Maplesoft精英维护升级计划

支持

产品培训

产品在线帮助

研讨会与活动

出版

资源中心

示例和应用

社区

关于 Maplesoft

媒体中心

用户社区

联系我们

Online Help

All Products Maple MapleSim

Was this information helpful?

Tell us what we can do better:

Thanks for your Comment

Maple

数学软件

Maple 附加模块

MapleSim

多学科系统级建模仿真

MapleSim 附加模块

系统工程

项目服务

Maple T.A. and Möbius

教育

行业

汽车与航空航天

机器人

机器设计和工业自动化

其他

应用领域

产品价格

购买

院系/全校正版授权

Maplesoft精英维护升级计划

支持

产品培训

产品在线帮助

研讨会与活动

出版

资源中心

示例和应用

社区

关于 Maplesoft

媒体中心

用户社区

联系我们

Online Help

All Products Maple MapleSim

Was this information helpful?

Tell us what we can do better:

Thanks for your Comment