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Modeling of Humidification in Comsol Multiphysics 4.4

Indrajit Wadgaonkar, Advanced Engineering

Tata Motors Ltd. Pune

Contents:

• Overview of the Physical problem

• Simulation domain

• Governing Equations

• Implementation in Comsol Multiphysics 4.4

• Results

• Conclusions

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What is Humidification???

• Humidification is the process of increasing the moisture content of air and thereby the Relative

Humidity.

• One of the methods to humidify air is evaporation of water droplets suspended in air.

• From the point of view of CFD, this presents a complex problem consisting of multiphase flow,

heat transfer and mass transfer phenomenon all coupled

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Simulation domain

• As a precursor to actual humidifier modeling we conducted a simplified simulation of evaporation

of water droplets in a straight air channel

• Particle Tracing Module was coupled with CFD module in Comsol Multiphysics

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Walls

Velocity Inlet Pressure Outlet

Governing Equations

• The air flow is governed by the Navier Stokes Equations with source terms added to Continuity

and Energy equations to account for the water droplet evaporation.

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m

pTu

t)().(

Body

TFuuPuu

t

u

))(.().(

)(

)))(.()(().().()(

eiwpp

p

HmhMcDTTkTuCt

TC

(Continuity Equation)

(Momentum Equation)

(Energy Equation)

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)(pD

p

vuFt

v

cellepppppp

p

ppVolumeHmTTTATThA

t

TCm

)()()(

)(~ 44

w

p

M

mTcDcu

t

c

)())(.().(

)((Transport Equation for vapor)

(Momentum Equation for particle)

(Energy Equation for particle)

Implementation in Comsol Multiphysics • Comsol Multiphysics 4.4 did not allow the exchange of variables between Lagrangian frame

(particles) and Eulerian frame (air flow).

• Hence a system of PDE’s was defined as:

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2

1.

1

1

1

1

2

2

S

S

v

u

td

v

u

te

aa

Set to zero Source terms from particles

Results:

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Effect of inlet air temperature and velocity on evaporation

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Temperature (K) Evaporation initiation

length (m)

350 0.03

400 0.00115

500 0.001

Evaporation initiation length for various inlet air temperatures:

Conclusions:

•Complex phenomenon of coupled Multiphase flow with heat and mass transfer was modeled with

Comsol Multiphysics 4.4 .

•The contours of vapor concentration depict that the phenomenon has been captured well.

•As expected the evaporation increased with increasing temperature of inlet air and evaporation

initiation length reduced.

• There is an optimum velocity of inlet air for maximum evaporation.

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Thank You

Appendix

• Drag Coefficient and particle Reynold’s number:

• Calculation of heat transfer coefficient ,h for particles:

• Updating the particle diameter:

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pp

d

dd

pp

D

dvuC

dF

||Re;

24

Re18

2

3/12/1PrRe6.00.2

d

air

p

k

hdNu

old

old

pold

p

new

p

m

dmdd

3

• Rate of mass transfer:

cs is concentration of vapor at droplet surface assuming pressure to be equal to saturation

pressure, while kc is calculated as :

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)(, cckNiwheremscVolume

MAN

element

vaporpi

Dd

pc

air

airScwhereSc

D

dkSh

,,Re6.00.2

3/12/1