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MapleSim Hydraulics Library from Modelon

Line Middle  Line element between entrance and exit

The LineMiddle component contains the equations for an element between the entrance and the exit element. The connectors are used to connect this element to another middle element of long line.

 

Equations

Variables

Connections

Parameters

Constants

Equations

β=11β0+1KpipeelasticWallβ=β0otherwise,ν=ν0,ρ=ρ0constantPropertiesβ=11`oil.bulkModulus`p=pk+`oil.p_atm`,T=T,vair=`oil.v_gas`,psat=psat+1KpipeelasticWallβ=`oil.bulkModulus`p=pk+`oil.p_atm`,T=Totherwise,ν=`oil.kinematicViscosity`p=pk+`oil.p_atm`,T=T,vair=`oil.v_gas`,psat=psat,ρ=`oil.density`p=pk+`oil.p_atm`,T=T,vair=`oil.v_gas`,psat=psatotherwise

dx=noEvent0Refriction<Re1orRe2<RefrictionlnRefrictionRe1ln10otherwise&comma;λ=noEvent1Refriction<64λ2Refriction2otherwise&comma;λ2=noEvent64RefrictionRefrictionRe1Refriction2ln1024ln10Δrel37+28750Refriction9102Re2Refriction64Re1RefrictionRe11+dxc2+dxc3otherwiseotherwisefrictionType=`Hydraulics.Lines.FrictionTypes.LaminarTurbulent`dx=0&comma;λ=1&comma;λ2=64Refrictionotherwise

&Delta;pdynfriction=128k1τ1+128k2τ2+128k3τ3νq`k&plus;`d4π+32wk1+32wk2+32wk3νd2ρasoundelementρ&comma;twk1=αk1Zcq`k&plus;`τ12αwk1τ1&comma;twk2=αk2Zcq`k&plus;`τ22αwk2τ2&comma;twk3=αk3Zcq`k&plus;`τ32αwk3τ3dynFriction=truewk1=0&comma;wk2=0&comma;wk3=0&comma;&Delta;pdynfriction=0otherwise

α&equals;32νd2

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

Zc&equals;4asoundρd2π

pk&equals;pA

friction=noEvent4q`k&plus;``&pi;`d`&nu;`

asound&equals;βρ

pk&plus;&equals;pB

qk&plus;&equals;mflowBρ

qk&minus;&equals;mflowAρ

&Delta;pfriction&equals;noEvent12elementlambda2ν2ρ10q`k&plus;`−1otherwised3

&Delta;pstatichead&equals;981100ρ&Delta;h

ρelementtqk&plus;&equals;14d2πpkpk&plus;&Delta;pfriction&plus;&Delta;pdynfriction&plus;&Delta;pstatichead

tpk&equals;asoundZcqk&minus;qk&plus;element

Variables

Name

Value

Units

Description

Modelica ID

α

 

 

 

alpha

Zc

 

 

 

Zc

wk1

 

 

 

wk1

wk2

 

 

 

wk2

wk3

 

 

 

wk3

pk

 

Pa

 

pk

pk&plus;

 

Pa

 

pkplus

qk&minus;

 

m3s

 

qkminus

qk&plus;

 

m3s

 

qkplus

psat

[1]

Pa

Gas saturation pressure

p_sat

friction

 

1

Dummy or Reynolds number of flow, if frictionType = DetailedFriction

Re_friction

λ

 

 

Dummy or friction coefficient, if frictionType = DetailedFriction

lambda

λ2

 

 

Dummy or non-standard friction coefficient, if frictionType = DetailedFriction (= lambdaRe^2)

lambda2

&Delta;pfriction

 

 

Stationary friction loss

dp_friction

&Delta;pdynfriction

 

 

Dynamic friction term

dp_dynfriction

&Delta;pstatichead

 

 

Static head

dp_statichead

asound

 

ms

Speed of sound in oil

aSound

ν

 

m2s

Viscosity, if constantProperties is false

nu

ρ

 

kgm3

Density  if constantProperties is false

rho

β

 

Pa

Bulk modulus if constantProperties is false

beta

T

 

K

Local temperature

T

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

Connections

Name

Description

Modelica ID

oil

 

oil

portA

Port A, where oil flows into the component (0<q, pB<pA means 0<&Delta;p)

port_A

portB

Port A, where oil leaves the component (q<0, pB<pA means 0<&Delta;p)

port_B

Parameters

General Parameters

Name

Default

Units

Description

Modelica ID

steady-state init

false

 

If true, initialize in steady state

steadyStateInit

constant properties

true

 

If true, properties are treated as constant over time

constantProperties

elastic wall

false

 

If true, pipe properties affect speed of sound in oil

elasticWall

dynamic friction

false

 

If true, dynamic friction

dynFriction

element

 

m

Length of one element

ElementLength

d

 

m

Line diameter

diameter

&Delta;h

0

m

Height difference

heightDiff

friction type

[1]

 

Type of flow model

frictionType

Kpipe

 

 

Pipe bulk modulus of elasticity

bulkModPipe

roughness

0

m

Roughness of pipe

roughness

ρ0

 

kgm3

Constant density, if constantProperties is true

rho0

ν0

 

m2s

Constant viscosity, if constantProperties is true

nu0

β0

 

Pa

Bulk Modulus

beta0

&Delta;Tsystem

0

K

Temperature offset from system temperature

dT_system

[1] Hydraulics.Lines.FrictionTypes.Laminar

Constant Parameters

Name

Default

Units

Description

Modelica ID

Δrel

roughnessd

 

Relative roughness

Delta

Constants

Name

Value

Units

Description

Modelica ID

k1

0.192

 

 

k1

k2

0.0948

 

 

k2

k3

0.0407

 

 

k3

τ1

0.25

 

 

tau1

τ2

0.0352

 

 

tau2

τ3

0.0024

 

 

tau3

See Also

Lines

MapleSim Hydraulics Library from Modelon Overview

 


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