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MapleSim Hydraulics Library from Modelon

Lam Res No States  Resistance with laminar flow

The Lam Res No States component describes the laminar flow through a resistance. The flow rate of the resistance is given by

q=GΔp

Variables used in the above equations

q

flow rate m3s

G

conductance m3sPa

Δp

pressure drop across resistance Pa

Equations to calculate the conductance G are given in the manual for several components. A conductance of G = 4.167e-13 m3sPa leads to a flow rate of 1 lminute at 40 MPa. As the critical Reynolds number depends on the component, there is no check whether the flow is actually laminar or turbulent.

Name

Description

Var Lam Res No States

Resistance with laminar flow and externally commanded conductance.

Orifice No States

The component, based on the loss coefficient K, describes both flow regimes: laminar for very small Reynolds numbers and turbulent for higher Reynolds numbers (default model).

Ori Poly No States

The component describes both flow regimes, using an interpolation polynomial.

Ori Cav No States

Orifice component checking for cavitation.

Sim Ori No States

Simple textbook component, using a constant discharge coefficient. It is valid for turbulent flow only; severe numerical problems for laminar flow.

Metering Ori No States

Metering Orifice (that is, model Orifice No States with variable diameter).

Two Orifices

Two orifices in series, one with variable the other with fixed flow area.

Orifice N

Same as Orifice No States, but with the equations rearranged to compute Δp for given q.

 

Equations

Variables

Connections

Parameters

Constants

Equations

dpeff=dpacting&comma;dpeffu=0&comma;pmax=0&comma;pmin=0&comma;pminab=0&comma;alpha_dmax=0&comma;delta_pk=0checkvalvedpeff=noEventdpeffu0<&Delta;pdpeffuotherwise&comma;dpeffu=noEventpmaxpmin&comma;pmax=maxpAlimited&comma;pBlimited&comma;pmin=pmaxdelta_pkpminab<pmaxdelta_pkpminabotherwise&comma;pminab=minpAlimited&comma;pBlimited&comma;alpha_dmax=8271000172000D&comma;delta_pk=&alpha;[k]2max0&comma;pmaxalpha_dmax+10ν1+94D2&alpha;[k]1ρD2cavitationdpeff=&Delta;p&comma;dpeffu=0&comma;pmax=0&comma;pmin=0&comma;pminab=0&comma;alpha_dmax=0&comma;delta_pk=0otherwiseotherwise

λ=0&comma;qunsigned=`Hydraulics.Restrictions.Basic.PressureDrop.lossCoeff`&Delta;p=dpeffpopen&comma;k1=k1&comma;k2=k2&comma;ν=ν&comma;ρ=ρ&comma;A=A&comma;D=D&comma;orif=orifTransition=1qunsigned&comma;λ=`Hydraulics.Restrictions.Basic.PressureDrop.dischargeCoeff`&Delta;p=dpeffpopen&comma;Cd=Cd&comma;λc=λc&comma;ν=ν&comma;ρ=ρ&comma;A=A&comma;D=D&comma;orif=orifotherwise&comma;qnoleak=noEventqunsigned0dpeffpopen0otherwisecheckvalveqnoleak=noEventqunsigned0dpeffpopenqunsignedotherwiseotherwise&comma;q_reg=qnoleak&comma;popen=ptrans&comma;qopen=0flowcond=1λ=0&comma;q_reg=qnoleak&comma;qunsigned=`Hydraulics.Restrictions.Basic.PressureDrop.laminar`&Delta;p=dpeff&comma;G=G&comma;popen=0&comma;qnoleak=qunsigned&comma;qopen=0flowcond=2λ=0&comma;q_reg=qnoleak&comma;qunsigned=`Hydraulics.Restrictions.Basic.PressureDrop.dischargeCoeff`&Delta;p=dpeff&comma;Cd=Cd&comma;flownumber=false&comma;ρ=ρ&comma;A=A&comma;D=D&comma;orif=orif&comma;popen=0&comma;qnoleak=noEventqunsigned0dpeffqunsignedotherwise&comma;qopen=0flowcond=3qnoleak=noEventsmooth0&comma;qunsignedpopen<dpeffq_regotherwise0dpeffpclosed0otherwisecheckvalveqnoleak=noEventsmooth0&comma;qunsignedpopen<dpeffq_regotherwise0dpeffpclosedsmooth0&comma;qunsigneddpeff<popenq_regotherwiseotherwiseotherwise&comma;qopen=1G+1G2+2pclosedρCd2A2Cd2A2ρTransition=2qopen=1Gρk1ν2DA+1G+ρk1ν2DA2+2pclosedρk2A2A2ρk2otherwise&comma;λ=0&comma;popen=pclosed+qopenGregparam=1popen=`Hydraulics.Restrictions.Basic.PressureDrop.inv_lossCoeff`q=qopen&comma;k1=k1&comma;k2=k2&comma;ρ=ρ&comma;ν=ν&comma;D=DTransition=1popen=`Hydraulics.Restrictions.Basic.PressureDrop.inv_dischargeCoeff`q=qopen&comma;Cd=Cd&comma;ρ=ρ&comma;D=Dotherwise&comma;λ=0&comma;qopen=RetransνADregparam=2λ=0&comma;qopen=`Hydraulics.Restrictions.Basic.PressureDrop.lossCoeff`&Delta;p=popen&comma;ρ=ρ&comma;A=A&comma;D=D&comma;k1=k1&comma;k2=k2&comma;ν=ν&comma;orif=orifTransition=1qopen&comma;λ=`Hydraulics.Restrictions.Basic.PressureDrop.dischargeCoeff`&Delta;p=popen&comma;ρ=ρ&comma;A=A&comma;D=D&comma;Cd=Cd&comma;flownumber=false&comma;orif=orifotherwise&comma;popen=ptransotherwise&comma;qunsigned&comma;q_reg=`Hydraulics.Restrictions.Basic.PressureDrop.conditionalFlow`&Delta;p=dpeff&comma;ρ=ρ&comma;A=A&comma;D=D&comma;Transition=Transition&comma;regtype=regtype&comma;ν=ν&comma;pclosed=pclosed&comma;popen=popen&comma;qopen=qopen&comma;k1=k1&comma;k2=k2&comma;Cd=Cdotherwise

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

q&equals;mflowAρ

q&equals;qnoleak&plus;qleak

&Delta;p&equals;pAlimitedpBlimited

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

qleak

Gleak&Delta;p

m3s

Leakage flow

q_leak

qnoleak

 

m3s

Flow rate through component

q_noleak

dpeff

 

Pa

Effective pressure drop

dpeff

A

1

m2

Orifice area

A

D

1

m

Orifice diameter

D

qopen

 

m3s

Flow when fully open orifice

q_open

popen

 

Pa

Pressure when fully open orifice

p_open

dpacting

0

Pa

Acting, i.e. delayed pressure differential

dpacting

G

4.2·10-13

m3sPa

Hydraulic conductance G&equals;&PartialD;q&PartialD;p

G

λ

 

 

Flow coefficient

lambda

[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

General Parameters

Name

Default

Units

Description

Modelica ID

&Delta;Tsystem

0

K

Temperature offset from system temperature

dT_system

Constant Parameters

Name

Default

Units

Description

Modelica ID

orif

[1]

 

Orifice dimension

orif

flowcond

2

 

Flow condition

flowcond

Transition

0

 

Transition model

Transition

reg type

1

 

Regularization type

regtype

reg param

1

 

Regularization parameter

regparam

cavitation

false

 

Cavitation

cavitation

checkvalve

false

 

 

checkvalve

k1

1

 

Laminar part

k1

k2

1

 

k2&equals;1Cd2

k2

Cd

1

 

Max discharge coefficient

C_d

λc

1

 

Critical flow number

lambdac

1

m

Orifice length; 1<d

length

trans

1

 

Transition Reynolds number

Re_trans

ptrans

1

Pa

Transition pressure

p_trans

pclosed

1

Pa

Cracking pressure

p_closed

Gleak

0

m3sPa

Leakage conductance

G_Leak

[1] Hydraulics.Restrictions.Basic.PressureDrop.orifinput.D

Constants

Name

Value

Units

Description

Modelica ID

&alpha;[k]

0.649

 

 

alpha_k

See Also

Metering Ori No States

Ori Cav No States

Ori Poly No States

Orifice N

Orifice No States

Restrictions

Sim Ori No States

Two Orifices

Var Lam Res No States

MapleSim Hydraulics Library from Modelon Overview

 


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