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MapleSim Hydraulics Library from Modelon

Oil  Oil with pressure dependent bulk modulus (Hoffmann model)

A hydraulic oil with pressure dependent bulk modulus (Hoffmann model).

 

Equations

Parameters

Constants

Equations

Density

ρmix=vgaslimρgasref+1vgaslimρhydref1vgaslimρhydrefρhyd+vgaslimTprefyTrefplim

ρhyd=max0.1ρ0,ρ0ⅇxppabspatmlogmax1.10-12,1ⅇxppβ2pabs+pβ11ⅇxppβ2patm+pβ1pβ2βpmax

ρhydref=ρ0

Bulk Modulus

βmix=C1ρhyd+C2yplimC1ρhydβhyd+C2yplimpyplim

βhyd=maxβpmax1ⅇxppβ1+pβ2pabspatm,1.105

C1=ρhyd1vgaslim

C2=vgaslimTprefTref

Dynamic Viscosity

The dynamic viscosity is η=νρ.

Kinematic Viscosity

νmix=νgasVgasFreenom+νhydVhydnomVtotnom

Vtotnom=VgasFreenom+Vhydnom

Vhydnom=ρhydref1vgaslimρhyd

VgasFreenom=vgaslimTprefyTrefplim

νhyd=νTwp

νT=10TA10B6.7

wp=ⅇxpαpabspatm105

Miscellaneous

plim=maxpabs,pabsmin

pabsmin=0.001

psat=vgasprefav

vgaslim=minmax0.000001,vgas,1

y=1z570z4+35z3+15z2+5z+1

z&equals;&lcub;&lcub;1psat<pabs0pabs<pvapmax0&comma;pabspvappsatpvapotherwisepvap<psat&lcub;1psat<pabsmax0&comma;pabsmax0.0001&comma;psatotherwiseotherwise

The variables y and z are, respectively, the fractions of undissolved and dissolved gas in the mixture.

Parameters

General Parameters

Name

Default

Units

Description

Modelica ID

T0

293.15

K

Working temperature

T0

p0

1·107

Pa

Reference pressure

p0

pvapour

100

Pa

Absolute vapour pressure

p_vapour

patm

1·105

Pa

Atmospheric pressure: in case change is wanted for high altitudes

p_atm

display labels

false

 

Display labels

display_labels

ρ0

865

kgm3

Oil density at atmospheric pressure

rho_0

βpmax

1.8·109

Pa

Bulk modulus at maximum pressure

betapmax

p&beta;1

25

 

Parameter

pbeta1

p&beta;2

-2·10-7

1Pa

Parameter

pbeta2

Gas Parameters

Name

Default

Units

Description

Modelica ID

vgas

1·10-6

1

Gas/(hydraulic medium) volume fraction at atmospheric pressure and 0 degC

v_gas

av

6.8

 

Bunsen coefficient

av

ρgas0

1.18

kgm3

Gas density at atmospheric pressure and 0 degC

rho_gas_0

νgas

1.5·10-5

m2s

Gas kinematic viscosity

nu_gas

Viscosity Parameters

Name

Default

Units

Description

Modelica ID

A

3.36858

 

Coefficient for temperature dependent viscosity

A

B

8.6289

 

Coefficient for temperature dependent viscosity

B

α

0.0017

 

Coefficient for pressure dependent viscosity

alpha

Constants

Name

Value

Units

Description

Modelica ID

Tref

273.15

K

Reference temperature for v_air

T_ref

pref

1·105

Pa

Reference pressure for v_air

p_ref

See Also

Fluids

MapleSim Hydraulics Library from Modelon Overview

 


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