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MapleSim Hydraulics Library from Modelon

Flexible Line  Flexible line with laminar and turbulent flow

The Flexible Line component describes the dynamics of a long line with compressibility, inductance and frequency dependent viscosity. This model uses n elements for the line, therefore:

element=linen

The oil in flexible lines is compressible, has a mass, and a resistance. The model includes the frequency dependent friction, compressibility, and inductance. The dynamic response of flexible lines is a function of time and the spatial coordinate (that is, described by partial differential equations). For the library, a lumped parameter model is used that breaks the whole line into n short elements. Flexible Line uses an entrance and exit elements that have only half the length of the n1 middle elements, leading to an effective element length of 1n of the whole line length. The model is adequate if:

element<110aSoundfmax

Variables used in the above equations

length

length of line segment m

aSound

speed of sound in fluid ms

fmax

highest frequency of interest Hz

The steady state flow rate q is positive if oil enters the line at port_A; the pressure drop (port_A.p - port_B.p) is then positive.

The model is valid if the flow is laminar. There is no warning if this condition is not met. The Reynolds number is computed for the entrance and the exit elements (to reduce the necessary computations).

Related Components

RigidLine

Losses of a rigid line as a function of Reynolds number

 

Equations

Variables

Connections

Parameters

Equations

msim/FORmsim/INi#1&comma;1..n2&comma;msim/CONNECTLMiddle[i#1].port_B&comma;LMiddle[i#1 + 1].port_A

Variables

Name

Value

Units

Description

Modelica ID

psat

[1]

Pa

Gas saturation pressure

p_sat

T

[2]

K

Local temperature

T

ρ

[3]

kgm3

Density of oil

rho

pAsummary

pA

Pa

Pressure at port A

summary_pA

pBsummary

pB

Pa

Pressure at port B

summary_pB

&Delta;psummary

pApB

Pa

Pressure drop

summary_dp

qsummary

port_A.m_flowρ

m3s

Flow rate flowing into port_A

summary_q

Phydsummary

[4]

W

Hydraulic Power

summary_HP

LMiddle

 

 

 

LMiddle

LEntrance

 

 

 

LEntrance

LExit

 

 

 

LExit

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

[2] oil.T0&plus;&Delta;Tsystem

[3] Modelica.Media.Air.MoistAir.Utilities.spliceFunctionx&equals;&Delta;psummary&comma;pos&equals;oil.densityp&equals;pA&plus;oil.p_atm&comma;T&equals;T&comma;vair&equals;oil.v_gas&comma;psat&equals;psat&comma;neg&equals;oil.densityp&equals;pB&plus;oil.p_atm&comma;T&equals;T&comma;vair&equals;oil.v_gas&comma;psat&equals;psat&comma;&Delta;x&equals;100

[4] &Delta;psummaryqsummary

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

Parameters

General Parameters

Name

Default

Units

Description

Modelica ID

&Delta;Tsystem

0

K

Temperature offset from system temperature

dT_system

line

1

m

Total length of line

LineLength

d

0.01

m

Line diameter

diameter

constant properties

true

 

If true, properties are treated as constant over time

constantProperties

elastic wall

true

 

If true, pipe properties affect speed of sound in oil

elasticWall

β0

[1]

Pa

Bulk modulus (for non-elastic line)

beta0

ρ0

[2]

kgm3

Density of oil

rho0

a0

β0ρ0

ms

Speed of sound in oil (for non-elastic line)

a0

ν0

[3]

m2s

Kinematic viscosity

nu0

n

10

 

Number of line segments

n

&Delta;h

0

m

Height difference, if positive then portA higher than portB

heightDiff

friction type

[4]

 

Type of flow model

frictionType

steady-state init

false

 

If true, initialize in steady state

steadyStateInit

dynamic friction

true

 

If true, dynamic friction

dynFriction

ν

310

 

Poisson ratio

nu

roughness

0

m

Roughness of line material

roughness

thickness

0.003

m

Line wall thickness

thickness

E

2.·1011

Pa

Modulus of elasticiy of the wall

E

[1] oil.bulkModulusoil.p0&comma;oil.T0&plus;&Delta;Tsystem

[2] oil.densityoil.p0&comma;oil.T0&plus;&Delta;Tsystem

[3] oil.kinematicViscosityoil.p0&comma;oil.T0&plus;&Delta;Tsystem

[4] Hydraulics.Lines.FrictionTypes.Laminar

Constant Parameters

Name

Default

Units

Description

Modelica ID

A

[1]

m2

Line cross-section area

A

element

linen

m

Length of one segment of line

ElementLength

Kpipe

[2]

 

 

bulkModPipe

[1] 14πd2

[2] if elasticWall then Ethickness2d&plus;2thickness1&plus;νd&plus;2thickness2&plus;1νd2 else 10^15

See Also

Lines

LongLine_u_air

RigidLine

MapleSim Hydraulics Library from Modelon Overview

 


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