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MapleSim Hydraulics Library from Modelon

Two Way Valve  Two way valve with second-order spool dynamics

The Two Way Valve component describes a two way valve with second-order spool dynamics. The laminar/turbulent flow through the valve is modeled as flow through an orifice without cavitation. The parameter qnom gives the nominal flow rate of the fully opened valve at the pressure drop dpnom. The parameter dleak gives the equivalent diameter of an orifice to describe the leakage flow if the valve is closed.

Amax=qnom12ρk2Δpnom

Aleak=14πdleak2

The commanded relative opening of the valve is input at command.

command0

Valve closed (only leakage)

1command

Valve completely open

 

The position of the spool is modeled as a second-order system with natural frequency ω0, damping damp, input command, and output position [0...1]. The flow area depends linearly on the spool position.

positionoverlap

Leakage from P  A. Flow area: Aleak.

overlap<position < 1

Flow from P  A. Flow area: positionoverlapAmax1overlap&plus;Aleak

1position

Maximum flow from P  A. Flow area: Amax&plus;Aleak

 

The mass and flow forces are not included. Use the modifier(s)

VolumeA(port_A(p(start=1e5,fixed=true)))

and/or

VolumeB(port_A(p(start=1e5,fixed=true)))

to set the initial condition(s) for the pressure of the lumped volume(s) Pa. Use the modifier(s)

TWVnS(FlA(position(start=0.1,fixed=true)))

or

TWVnS(FlA(velocity(start=0.1,fixed=true)))

or

TWVnS(FlA(velocity(start=0.1,fixed=true),position(start=1,fixed=true)))

to set the initial condition(s) for the position/velocity of the spool.

 

Equations

Variables

Connections

Parameters

Equations

ν&equals;Modelica.Media.Air.MoistAir.Utilities.spliceFunctionx&equals;&Delta;p&comma;pos&equals;νoilp&equals;pAabs&comma;T&equals;T&comma;vair&equals;vgasoil&comma;psat&equals;psat&comma;neg&equals;νoilp&equals;pBabs&comma;T&equals;T&comma;vair&equals;vgasoil&comma;psat&equals;psat&comma;&Delta;x&equals;100

ρ&equals;Modelica.Media.Air.MoistAir.Utilities.spliceFunctionx&equals;&Delta;p&comma;pos&equals;ρoilp&equals;pAabs&comma;T&equals;T&comma;vair&equals;vgasoil&comma;psat&equals;psat&comma;neg&equals;ρoilp&equals;pBabs&comma;T&equals;T&comma;vair&equals;vgasoil&comma;psat&equals;psat&comma;&Delta;x&equals;100

T&equals;T0oil&plus;&Delta;Tsystem

q&equals;mflowAρ

&Delta;p&equals;pAlimitedpBlimited

pAabs&equals;pA&plus;patmoil

pAlimited&equals;maxpA&comma;pvapouroilpatmoil

pBabs&equals;pB&plus;patmoil

pBlimited&equals;maxpB&comma;pvapouroilpatmoil

Variables

Name

Value

Units

Description

Modelica ID

&Delta;p

 

Pa

Pressure drop

dp

q

 

m3s

Flow rate flowing into port_A

q

pAlimited

 

Pa

Limited gauge pressure

pA_limited

pBlimited

 

Pa

Limited gauge pressure

pB_limited

ρ

 

kgm3

Upstream density

rho

ν

 

m2s

Upstream kinematic viscosity

nu

pAabs

 

Pa

Absolute pressure pA

pA_abs

pBabs

 

Pa

Absolute pressure pB

pB_abs

T

 

K

Local temperature

T

pAsummary

pA

Pa

Pressure at port A

summary_pA

pBsummary

pB

Pa

Pressure at port B

summary_pB

&Delta;psummary

&Delta;p

Pa

Pressure drop

summary_dp

qsummary

q

m3s

Flow rate flowing into port_A

summary_q

Phydsummary

&Delta;pq

W

Hydraulic Power

summary_HP

psat

[1]

Pa

Gas saturation pressure

p_sat

VA

 

 

 

VolumeA

VB

 

 

 

VolumeB

TWVnS

 

 

 

TWVnS

[1] oil.gasSaturationPressureT&equals;T&comma;vgas&equals;oil.vgas

Connections

Name

Description

Modelica ID

portA

Layout of port where oil flows into an element (0<mflow, pB<pA means 0<&Delta;p)

port_A

portB

Hydraulic port where oil leaves the component (mflow<0, pB<pA means 0<&Delta;p)

port_B

oil

 

oil

command

Command signal for spool position

command

Parameters

General Parameters

Name

Default

Units

Description

Modelica ID

&Delta;Tsystem

0

K

Temperature offset from system temperature

dT_system

use volume A

true

 

If true, a volume is present at port_A

useVolumeA

use volume B

true

 

If true, a volume is present at port_B

useVolumeB

VA

10-6

m3

Geometric volume at port A

volumeA

VB

10-6

m3

Geometric volume at port B

volumeB

Actuation Parameters

Name

Default

Units

Description

Modelica ID

ω0

500

rads

Natural frequency of spool

omega0

damp

710

 

Damping coefficient of spool

damp

overlap

0.02

 

Overlap relative to max. displacement = 1

overlap

Flow Parameters

Name

Default

Units

Description

Modelica ID

qnom

8.33·10-4

m3s

Nominal flow rate

qnom

&Delta;pnom

3.5·106

Pa

Pressure drop at qnom

dpnom

dleak

1.67·10-5

m

Diameter of equivalent orifice to model leakage of closed valve

dleak

k1

10

 

Laminar part of orifice model

k1

k2

2

 

Turbulent part of orifice model, k2&equals;1Cd2

k2

See Also

Valves

MapleSim Hydraulics Library from Modelon Overview

 


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