report on evaporation model - forum.ansys.com

© 2006 ANSYS, Inc. All rights reserved. 1 ANSYS, Inc. Proprietary

Report on evaporation

model

Andrey Troshko

Application Specialist


Problem formulation

• Interfacial mass transfer rate per unit of

volume

LiquidVapor

+

Gas

sati TT

sec

3iivlm

kgS Am

Mass flux vector, kg/(m2 sec)

Interfacial are density, 1/m

in


Problem formulation

• Calculation of evaporation mass flux

LiquidVapor

+

Gas

vi TT

law sDalton'

pressure partial gas

pressure partial vapor

gvtot

totgg

totvv

PPP

PXP

PXP

Schrage’s[1] mass flux

equation:

]//[22

2 2

2/12/1

2/1

smkgT

P

T

P

R

M

v

v

i

i

m

[1] Schrage R.W. A theoretical study of interphase mass transfer,

Columbia University Press, New York 1953

waterairforyefficientcnevaporatio 09.0) (


Problem formulation

• Interfacial area density Ai is defined by topology

of interface:

Euler (Mixture),

i.e., particles of

diameter d

VOF, i.e., exact

expression

0

iAd

6A

p

i

Phase 1 Phase 2

0

0 d

Volume

Interface area

pp AN

V

Area density

dV

A

V

VN

V

V

V

AN

p

ppp

p

ppp

6


UDF implementation

• Phases

– Gas=H2O(vapor)+air

– Liquid=H2O(liquid)

• Mass transfer source is calculated in ADJUST and transferred to

DEFINE_MASS_TRANSFER via UDMI-0

• Mass source has several limiters and different form for

evaporation and condensation

– Evaporation, i.e.,

vap

OHabscellsat

cell

vapvl XPTPRT

MS

2)(

22

22/1

vap

OHabscellsat XPTP2

)(

1.0 if ,0

),(

vapvl

liqliq

vlvl

S

tSMINS


Problem formulation

• Cont.

– Condensation, i.e., vap

OHabscellsat XPTP2

)(

vap

OHabscellsat

cell

vapvl XPTPRT

MS

2)(

22

22/1

1.0 if ,0

),(

liqvl

vapvap

vlvl

S

tSMINS


Results

• Scenario of the trial 2d simulation

– Initiate 2d bubble of pure air in water at temperature 42 C

– Run simulation till equilibrium (zero net mass exchange)

– Expected result – initial air bubble will quickly saturate with

vapor. From steam table the saturation pressure for 42 C is

~0.08 bar, so by Dalton’ law (see slide 3) we expect final

molar fraction of vapor inside air-vapor mixture in the bubble

to be 0.08

– After equilibrium is reached, a heating power source 1014liq

is imposed imitating heating of liquid only by laser

– We expect that bubble starts to expand again

– Add-ons

• Expecting sonic flows density of liquid is prescribed to Tait law

and density of gas is ideal gas mixture


Results

• Equilibrium simulation - initialization

Initial temperature

Initial bubble

10m

Outlet temperature 315 K


Results

• Equilibrium state

Equilibrium temperature – unchanged as expected

Equilibrium

vapor mole

fraction

314.986 K

Saturation vapor mole

fraction at 514 K


Results

• Equilibrium state

10m

Evaporation rate

Bubble VOF

Equilibrium is

reached at ~1 msec


Results

• Equilibrium


Results

• Ablation simulation – 1 msec of heating of liquid at 1e14 W/m3

Evaporation rate Bubble VOF

Heating start

Heating start


Results


After 1 msec of heatingEquilibrium

Temperature

314.986 K


Results



Pressure


Results



Vapor mole fraction

Current vapor

mole fraction

Saturation vapor mole

fraction


Results



Velocity field

report on evaporation model - forum.ansys.com

Documents