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MapleSim Hydraulics Library from Modelon

Rigid Line No States  Losses of a rigid line as a function of Reynolds number

The RigidLineNoStates component describes the laminar/turbulent flow through a circular, smooth rigid line (that is, it calculates the flow rate q as a function of pressure drop dp). There are two flow modes:

0 < Re < ReCrit

laminar (Hagen-Poiseuille)

ReCrit < Re

turbulent (Blasius)

The functions q = q(Re) and q = q(dp) are unique.

 

Equations

Variables

Connections

Parameters

Constants

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

&Delta;pabs&equals;noEvent&Delta;p

&Delta;pturb&equals;max1&comma;&Delta;pabs

laminar&equals;noEvent1&Delta;p<laminarLimit0otherwise

q&equals;mflowAρ

q&equals;Modelica.Media.Air.MoistAir.Utilities.spliceFunctionqturbunsigned&comma;qlam&comma;dp_abslaminarLimit&comma;laminarLimit

qlam&equals;1128&Delta;pd4πνρ

&Delta;p&equals;pAlimitedpBlimited

ReynoldsNumber&equals;4noEventqdπν

laminarLimit&equals;32ν2ReCritρd3

qturbunsigned&equals;11686&sol;7dpturb4&sol;7d19&sol;7πν1&sol;7Blasiusconstantρ4&sol;7

pAabs&equals;pA&plus;patmoil

pAlimited&equals;maxpA&comma;pvapouroilpatmoil

pBabs&equals;pB&plus;patmoil

pBlimited&equals;maxpB&comma;pvapouroilpatmoil

mflowA&plus;mflowB&equals;0

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

laminar

 

 

 

laminar

qlam

 

m3s

 

qlam

qturbunsigned

 

m3s

 

qturbunsigned

dpturb

 

Pa

 

dpturb

ReynoldsNumber

 

1

Reynolds number

ReynoldsNumber

[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

Parameters

Name

Default

Units

Description

Modelica ID

&Delta;Tsystem

0

K

Temperature offset from system temperature

dT_system

d

0.05

m

Line diameter

diameter

10

m

Line length

length

Constants

Name

Value

Units

Description

Modelica ID

Blasiusconstant

0.316

 

Coefficient for blasius

Blasiusconstant

ReCrit

2.32·103

1

Critical Reynolds number

ReCrit

See Also

Lines

MapleSim Hydraulics Library from Modelon Overview

 


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