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MapleSim Hydraulics Library from Modelon

Orifice N  Orifice with laminar/turbulent flow without cavitation

The Orifice N component describes the laminar/turbulent flow through an orifice if no cavitation occurs. The flow rate of the orifice is given by:

Δp=12Kρq2A2

K=k1+k2

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

k1

parameter of the orifice, describes laminar flow

k2

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

Reynolds number

The equations are set up such that the pressure drop (Δp) will be calculated if the flow rate q is known. This approach can help with HWIL-simulations because no volumes are needed. 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.

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.

Restrictions[Basic]

Differences between basic models are shown by a figure.

 

Equations

Variables

Connections

Parameters

Equations

ν=Modelica.Media.Air.MoistAir.Utilities.spliceFunctionx=Δp,pos=νoilp=pAabs,T=T,vair=vgasoil,psat=psat,neg=νoilp=pBabs,T=T,vair=vgasoil,psat=psat,Δx=100

ρ=Modelica.Media.Air.MoistAir.Utilities.spliceFunctionx=Δp,pos=ρoilp=pAabs,T=T,vair=vgasoil,psat=psat,neg=ρoilp=pBabs,T=T,vair=vgasoil,psat=psat,Δx=100

T=T0oil+ΔTsystem

q=mflowAρ

Δp=pAlimitedpBlimited

&Delta;p&equals;dpunsignednoEvent0<qdpunsignedotherwise

dpunsigned&equals;8k2q2&plus;2dk1νπnoEventqρd4π2

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

dpunsigned

 

Pa

 

dpunsigned

[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

0.001

m

Orifice diameter

diameter

k1

10

 

Laminar part of orifice model

k1

k2

2

 

Turbulent part of orifice model, k2&equals;1Cd2

k2

See Also

Lam Res No States

Metering Ori 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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