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MapleSim Hydraulics Library from Modelon

Long Line  Long line with laminar and turbulent flow

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

element<110aSoundfmax

Variables used in the above equations

length

length of the Long Line component 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 exit elements (in order 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

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

[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

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

roughness

0

m

Roughness of pipe

roughness

&Delta;h

0

m

Height difference, if positive then portA higher than portB

heightDiff

friction type

[4]

 

Type of flow model

frictionType

dynamic friction

true

 

If true, dynamic friction

dynFriction

steady-state init

false

 

If true, initialize in steady state

steadyStateInit

[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

elastic wall

false

 

If true, pipe properties affect speed of sound in oil

elasticWall

A

[1]

m2

Line cross-section area

A

element

linen

m

Length of one segment of line

ElementLength

[1] 14πd2

See Also

Lines

LongLine_u_air

RigidLine

MapleSim Hydraulics Library from Modelon Overview

 


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