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MapleSim Hydraulics Library from Modelon

Poppet Lift Conical Sharp Edge  Conical poppet lift with sharp edge seat

This is a template model for a conical poppet lift with sharp edge seat.

 

Flow Area

Hydraulic Diameter

Chamber Volumes

Implementation

Equations

Variables

Connections

Parameters

Flow Area

When the poppet is far from the seat, the flowarea between the two chambers is limited by the area between the seat-side rod and the seat.

As the poppet moves nearer, the flowarea is limited by the seat and the poppet.

The flow area, A, is the area (excluding top and bottom area) of the truncated cone with base radius r, top radius a, and slant height s, as seen in the picture.

A=πa+rs

s=Xcosθ

a=rssinθ

where X is the distance from the seat to the poppet center and r is the seat radius.

Hydraulic Diameter

The hydraulic diameter is D=4AP, where P is the wetted perimeter and A is the flow area. The wetted perimeter for the poppet lift with sharp edge seat is P=2πa+r.

Chamber Volumes

The chamber volumes V1 (poppet side) and V2 (seat side) are calculated using the following quantities:

The initial volume (when the poppet lift is closed) on both poppet side (V01) and seat side (V02) are known.

The seat-side volume is

V2={V02XXminV02XXminArod2+Vcone1+Vcone2Vcone3otherwise

where

cone 1 has base radius r and top radius Rrod2

cone 2 has base radius r and top radius a

cone 3 has base radius a and top radius Rrod2

and XXmin is the distance the poppet has been lifted from its initial position.

The poppet-side volume, V1, is calculated from V1+V2=V01+V02XXminArod2Arod1.

Implementation

This model calculates the volumes on both sides of the poppet lift, the mass flow between the two sides and the force f. Pressure is calculated in volume components connected to connector portA and portA1.

Equations

fflow=2noEvent`Δp`flowareacosalphak2TransitionType=1fflow=2noEvent`Δp`Cdmaxflowareacosalphaotherwise

qunsigned=`Modelica.Fluid.Utilities.regRoot`k12`ν`2`ρ`2+32flowareak2`Δp``ρ``π`k1`ν``ρ`2max0,flowarea`π`16k22`ρ`2,regRoot_qTransitionType=1qunsigned=Cdmax`Modelica.Math.tanh`2λ`λ`cflowarea`Modelica.Fluid.Utilities.regRoot`2`Δp``ρ`,regRoot_prhootherwise

0=fswitch+fA+fB

0=fswitch+fAsupport+fBsupport

ν=νoilpabs=pxabs,T=T,vair=vgasoil,psat=psat

ρ=ρoilpabs=pxabs,T=T,vair=vgasoil,psat=psat

D=4flowareaπ2a+2r

T=T0oil+ΔTsystem

V2=V02XXminV02XXminArod_2+VTruncCone1+VTruncCone2VTruncCone3otherwise

X=minXmax,maxXmin,switchsarel+X_0

a=rX`Modelica.Math.cos`θsinθ

f=πa2+Arod_1p1+πa2+Arod_2p2fflow

λ=D`Modelica.Fluid.Utilities.regRoot`2`Δp``ρ`,regRoot_prho`ν`

lift=max0,switchsarelXmin

p1abs=p1+patmoil

p2abs=p2+patmoil

VA=V1

pxabs=p1absxp+p2abs1xp

qLmin=60000qunsigned

sarel=sAsAsupport

xp=Modelon.Math.Smoothing.cubicStepΔp+12

Δp=p1p2

VTruncCone1=`Hydraulics.Elements.truncConeVolume`_msim_R=r,_msim_r=Rrod_2,_msim_h=rRrod_2`Modelica.Math.tan`θ

VTruncCone2=`Hydraulics.Elements.truncConeVolume`_msim_R=r,_msim_r=a,_msim_h=ra`Modelica.Math.tan`θ

VTruncCone3=`Hydraulics.Elements.truncConeVolume`_msim_R=a,_msim_r=Rrod_2,_msim_h=aRrod_2`Modelica.Math.tan`θ

cosalpha=`Modelica.Math.cos``π`2θ

flowarea=flowarea_nom

flowarea_nom=`Hydraulics.Elements.truncConeArea2`_msim_R=r,_msim_r=a,_msim_s=X`Modelica.Math.cos`θ

portA.m_flow=smooth0,noEvent`ρ`qunsigned0`Δp``ρ`qunsignedotherwise

portA1.V=V2

sabrel=L

sabrel=switchsBsA

sBsupport=Lswitch+sAsupport

p1=pA

p2=portA1.p

V1+V2=V01+V02XXminArod_2Arod_1

mflowA1+mflowA=0

tXmax=0

Variables

Name

Value

Units

Description

Modelica ID

srela

 

m

Relative position of flange_a wrt support_a

s_rel_a

srelab

 

m

Relative position of flange_b wrt flange_a

s_rel_ab

f

 

N

Force acting in positive direction of flange_a

f

λ

 

 

Flow coefficient

lambda

qunsigned

 

 

Absolute value of volume flowrate

qunsigned

qLmin

 

 

Volume flowrate in l/min

qLmin

X

 

m

Distance from poppet center/poppet to seat

X

lift

 

m

Poppet lift

lift

fflow

 

N

Static flow forces

fflow

cosalpha

 

 

Defines direction of flow forces

cosalpha

flowarea

 

m2

Effective orifice area

flowarea

flowareanom

 

m2

Orifice area (no saturation)

flowarea_nom

D

 

m

Hydraulic diameter

D

V1

 

m3

Volume, poppet side

V1

V2

 

m3

Volume, seat side

V2

T

 

K

Temperature

T

Δp

 

Pa

Pressure difference over the valve

dp

p1

 

Pa

Pressure, poppet side

p1

p2

 

Pa

Pressure, seat side

p2

ρ

 

kgm3

Fluid density in the chamber

rho

ν

 

m2s

Fluid viscosity in the chamber

nu

psat

[1]

Pa

Gas saturation pressure

p_sat

p1abs

 

Pa

Absolute pressure, used for all property calls

p1_abs

p2abs

 

Pa

Absolute pressure, used for all property calls

p2_abs

Xmax

 

m

 

Xmax

VTruncCone1

 

m3

Cone 1 used for calculating chamber volumes

VTruncCone1

VTruncCone2

 

m3

Cone 2 used for calculating chamber volumes

VTruncCone2

VTruncCone3

 

m3

Cone 3 used for calculating chamber volumes

VTruncCone3

[1] oil.gasSaturationPressureT=T,vgas=oil.vgas

Connections

Name

Description

Modelica ID

supportA

 

supportA

supportB

 

supportB

flangeA

 

flangeA

flangeB

 

flangeB

oil

Fluid property model

oil

portA

 

portA

portA1

 

portA1

Parameters

General Parameters

Name

Default

Units

Description

Modelica ID

L

 

m

Element length

L

reverse

false

 

Reverse the sign convention, see documentation for details

reverse

R

0.1

m

Poppet radius

R

θ

[1]

rad

Conical seat/poppet angle

theta

r

0.05

m

Throat radius

r

Rrod1

 

m

Rod radius, poppet side

Rrod_1

Rrod2

 

m

Rod radius, seat side

Rrod_2

lift0

0

m

Poppet lift in neutral position

lift_0

piston

L

m

Piston length

l_piston

V1

[2]

m3

Volume, poppet side, when closed valve

V01

V2

[2]

m3

Volume, seat side, when closed valve

V02

Xmin

0

m

minimum distance between poppet center and seat in basic case, otherwise set as 0

Xmin

transition type

1

 

Type of transition

TransitionType

k1

10

 

Laminar part of flow model

k1

k2

2.04

 

Turbulent part of flow model

k2

Cdmax

0.7

 

Discharge coefficient

Cdmax

λc

14

 

Critical flow number

lambdac

Xmaxstart

r

 

 

XmaxStart

Xmaxnom

0.001Xmaxstart

 

 

XmaxNominal

ΔTsystem

0

K

Temperature offset from system temperature

dT_system

[1] 0.333333333333333π

[2] 2.0πLR2

Constant Parameters

Name

Default

Units

Description

Modelica ID

Aflowmax

[1]

m2

Maximum flow area

flowareamax

Arod1

[2]

m2

Rod area, poppet side

Arod_1

Arod2

[3]

m2

Rod area, seat side

Arod_2

X0

lift0+Xmin

m

distance from seat to poppet center

X_0

[1] πr2Arod2_

[2] πRrod12

[3] πRrod22

See Also

Elements

MapleSim Hydraulics Library from Modelon Overview

 


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