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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.

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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