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MapleSim Hydraulics Library from Modelon

Metering Ori No States  Metering orifice with variable area and laminar/turbulent flow without cavitation

The Metering Ori No States component describes the laminar/turbulent flow through an orifice if no cavitation occurs.

Pressure drop/flow rate

The pressure drop across the orifice may be described in two different ways:

1. 

By means of the loss coefficient K:

Δp=12Kρq2A2

where K is given by:

K=k1+k2

2. 

By means of the discharge coefficient cd:

Q=cdA2Δpρ

where cd is given by

cd=Cdtanh2λλc

λ=D2Δpρν

Note that when

k2=1Cd2

and

k1=12λcCd

both descriptions are equivalent at high and low Reynolds numbers (Re).

Orifice dimension

The dimension of the orifice is given by the input signal (u) at the connector. The dimension of the input signal may be

1. 

An area

2. 

A diameter

3. 

A relative area, the maximal area being defined by a nominal point (pnom, qnom, ρnom) at turbulent conditions

4. 

A relative diameter, the maximal diameter being defined by a nominal point (pnom, qnom, ρnom) at turbulent conditions

Δpnom=12k2ρnomqnom2Aeq2

Variables used in the above equations

Δp

pressure drop across orifice Pa

K

loss coefficient

ρ

mass density, from FluidProp kgm3

q

flow rate m3s

A

area of the orifice m2; A=14πdiameter2; diameter is input at the signal connector m

k1

parameter of the orifice, describes laminar flow

k2

parameter of the orifice, describes turbulent flow k2 = 1Cd2

Reynolds number

The mass and flow forces are not included.

Related Components

Name

Description

Lam Res No States

Resistance with laminar flow.

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.

Two Orifices

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

Restrictions[Basic]

Differences between basic models are shown by a figure.

 

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

Aeq=πDeq24&comma;Deq=command0<command0otherwiseorif=`Hydraulics.Restrictions.Basic.PressureDrop.orifinput.D`Aeq=smooth0&comma;command0<command0otherwise&comma;Deq=2Aeqπorif=`Hydraulics.Restrictions.Basic.PressureDrop.orifinput.A`Aeq=πDeq24&comma;Deq=smooth0&comma;commandDmax0<command0otherwiseorif=`Hydraulics.Restrictions.Basic.PressureDrop.orifinput.Dr`Aeq=smooth0&comma;commandAmax0<command0otherwise&comma;Deq=2Aeqπotherwise

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

Aeq

m2

Orifice area

A

D

Deq

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

0

m3sPa

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

G

λ

 

 

Flow coefficient

lambda

command

u

 

 

command

Deq

 

 

Equivalent diameter

Deq

Aeq

 

 

Equivalent area

Aeq

[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

u

Command

u

Parameters

General Parameters

Name

Default

Units

Description

Modelica ID

&Delta;Tsystem

0

K

Temperature offset from system temperature

dT_system

orif

[1]

 

Orifice dimension

orif

Transition

1

 

Transition model

Transition

k1

10

 

Laminar part

k1

k2

2

 

k2&equals;1Cd2

k2

Cd

1k2

 

Max discharge coefficient

C_d

λc

2k1k2

 

Critical flow number

lambdac

pnom

106

Pa

Nominal pressure drop

pnom

qnom

1.89·10-5

m3s

Nominal volume flow rate

qnom

ρnom

865

kgm3

Nominal density

rhonom

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

Constant Parameters

Name

Default

Units

Description

Modelica ID

flowcond

1

 

Flow condition

flowcond

reg type

0

 

Regularization type

regtype

reg param

0

 

Regularization parameter

regparam

cavitation

false

 

Cavitation

cavitation

checkvalve

false

 

 

checkvalve

0

m

Orifice length; 1<d

length

trans

0

 

Transition Reynolds number

Re_trans

ptrans

0

Pa

Transition pressure

p_trans

pclosed

0

Pa

Cracking pressure

p_closed

Gleak

0

m3sPa

Leakage conductance

G_Leak

Cd

Cd_eq

 

 

Cd

Constants

Name

Value

Units

Description

Modelica ID

&alpha;[k]

0.649

 

 

alpha_k

See Also

Lam Res No States

Ori Cav No States

Ori Poly No States

Orifice No States

Restrictions

Restrictions[Basic]

Sim Ori No States

Two Orifices

Var Lam Res No States

MapleSim Hydraulics Library from Modelon Overview

 


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