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MapleSim Hydraulics Library from Modelon

Spool Valve  Spool valve

This is a model of a spool valve.

 

Equations

Variables

Connections

Parameters

Equations

ds_max=2flowareamaxπ&comma;θ=noEvent`Modelica.Math.acos`12s_rel_aswitch2x_minds_max2s_rel_aswitch2x_minds_max<0<22s_rel_aswitch2x_minds_max0s_rel_aswitchx_minπotherwiseotherwiseorificeType=3ds_max=x_maxx_min&comma;θ=0otherwise

fflow=2noEvent&Delta;pflowareacosalphak2TransitionType=1fflow=2noEvent&Delta;pCdmaxflowareacosalphaotherwise

qunsigned=max0&comma;k12ν2ρ2+32flowareak2&Delta;p2ρπk1νρmax0&comma;flowareaπ4k2ρTransitionType=1qunsigned=Cdmax`Modelica.Math.tanh`2λλcflowarea2&Delta;p2ρotherwise

perimeter=ds_maxθ+sinθorificeType=3perimeter=`Modelon.Math.Interpolation.tableInterpolate1b`diam_tab&comma;s_rel_aswitchorificeType=4perimeter=πflowareaπotherwise

flowarea_nom=flowareamaxs_rel_aswitchx_minx_maxx_minorificeType=1flowarea_nom=flowareamaxs_rel_aswitchx_min2x_maxx_min2orificeType=2flowarea_nom=ds_max2θsin2θ24orificeType=3flowarea_nom=`Modelon.Math.Interpolation.tableInterpolate1b`area_tab&comma;s_rel_aswitchotherwise

0&equals;fswitch&plus;fA&plus;fB

0&equals;fswitch&plus;fAsupport&plus;fBsupport

&equals;V0AA_rod&plus;sarelswitch

ν&equals;νoilpabs&equals;pabs&comma;T&equals;T&comma;vair&equals;vgasoil&comma;psat&equals;psat

ρ&equals;ρoilpabs&equals;pabs&comma;T&equals;T&comma;vair&equals;vgasoil&comma;psat&equals;psat

D&equals;2Modelica.Fluid.Utilities.regRootflowareamax11000000000&comma;perimeter

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

V&equals;V0&plus;AA_rodsarelswitch

f&equals;A&plus;A_rodpfflow

λ=D`Modelica.Fluid.Utilities.regRoot`2`&Delta;p``&rho;``&nu;`

p&equals;pA

VA&equals;V

qLmin&equals;60000qunsigned

sarel&equals;sAsAsupport

&Delta;p&equals;pAportA1.p

cosalpha&equals;159100269100+s_rel_aswitchx_mindeltaR+17500<s_rel_aswitchx_min467500otherwise

flowarea&equals;noEventmax0&comma;flowareamaxx_min+ds_max<s_rel_aswitchflowarea_nomx_min<s_rel_aswitch<x_min+ds_max0otherwiseotherwise

portA.m_flow&equals;noEventρqunsigned0&Delta;pρqunsignedotherwise

sabrel&equals;L

sabrel&equals;switchsBsA

sBsupport&equals;Lswitch&plus;sAsupport

pabs&equals;p&plus;patmoil

mflowA1&plus;mflowA&equals;0

Variables

Name

Value

Units

Description

Modelica ID

srela

 

m

Relative position of flange_a wrt support_a

s_rel_a

srelab

 

m

Relative position of flange_b wrt flange_a

s_rel_ab

f

 

N

Force acting in positive direction of flange_a

f

psat

[1]

Pa

Gas saturation pressure

p_sat

λ

 

 

Flow coefficient

lambda

qunsigned

 

 

Absolute value of volume flowrate

qunsigned

qLmin

 

 

Volume flowrate in l/min

qLmin

cosalpha

 

 

Defines direction of flow forces

cosalpha

fflow

 

N

Static flow forces

fflow

flowarea

 

m2

Effective orifice area

flowarea

flowareanom

 

m2

Orifice area (no saturation)

flowarea_nom

dsmax

 

m

Displacement to move from A=0+ to A=Amax

ds_max

 

m

Chamber length

length

D

 

m

Hydraulic diameter

D

perimeter

 

m

Wetted perimeter

perimeter

V

 

m3

Chamber volume

V

T

 

K

Temperature

T

&Delta;p

 

Pa

Pressure difference over the valve

dp

p

 

Pa

Gauge pressure in the chamber

p

pabs

 

Pa

Absolute pressure, used for all property calls

p_abs

ρ

 

kgm3

Fluid density in the chamber

rho

ν

 

m2s

Fluid viscosity in the chamber

nu

qout

[2]

 

 

qout

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

[2] portA&period;m_flowoil&period;densitypabs&equals;pabs&comma;T&equals;T&comma;vair&equals;oil.v_gas&comma;psat&equals;psat

Connections

Name

Description

Modelica ID

supportA

 

supportA

supportB

 

supportB

flangeA

 

flangeA

flangeB

 

flangeB

oil

 

oil

portA

 

portA

portA1

 

portA1

Parameters

General Parameters

Name

Default

Units

Description

Modelica ID

L

 

m

Element length

L

reverse

false

 

Reverse the sign convention, see documentation for details

reverse

V0

0

m3

Dead volume

V0

A

 

m2

Spool area

A

Arod

 

m2

Rod area

A_rod

deltaR

10-5

m

Radial clearance > 0

deltaR

TransitionType

1

 

Type of transition

TransitionType

k1

10

 

Laminar part of flow model

k1

k2

2.04

 

Turbulent part of flow model

k2

Cdmax

0.7

 

Discharge coefficient

Cdmax

λc

14

 

Critical flow number

lambdac

&Delta;Tsystem

0

K

Temperature offset from system temperature

dT_system

Orifice Parameters

Name

Default

Units

Description

Modelica ID

orificeType

1

 

 

orificeType

flowareamax

 

m2

Maximum flow area

flowareamax

xmin

 

m

Position>x_min => valve opens

x_min

xmax

 

m

Position>x_max => valve fully open

x_max

areatab

0&comma;0.1&comma;0.2&comma;0.3

 

Table for orifice area

area_tab

diamtab

0&comma;0.1&comma;0.2&comma;0.3

 

Table for orifice hydraulic diameter

diam_tab

See Also

Elements

MapleSim Hydraulics Library from Modelon Overview

 


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