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DROPLET EVAPORATION
BHANU PRATAP
ME13M010
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Applications
Spray Combustion systemsSpray drying systems
Spray cooling systems
Spray dispersion systems
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Assumptions for Evaporation
1. Quasi-steady process.
2. Quiescent and infinite medium.
3. Single component with zero solubility.
4. Binary diffusion with unity Lewis number ( Zeldovich
energy eqn).
5. Constant thermo-physical properties.
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STAGES DURING EVAPORATION
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Evaporation Rate - Procedure
Step 1
Gas phase mass conservation equation.
Gas phase energy equation.
Droplet gas-phase interface energy balance.
Droplet liquid mass conservation equation.
Step 2 Gas phase energy equation gives Temperature distribution in gas
phase.
Step 3
Temperature distribution with surface energy balance yields theevaporation rate.
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Basic Equations
Species Conservation
Energy Conservation
Liquid Vapor Equilibrium
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AlgorithmEvaporation at atm.
Assume
Drop radius Rs.
Drop surface Temperature Ts (All possible values273
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Tvs Tsfor same m.
As Tincreases the
value of Tsincreases
and reaches a fairly
constant value.
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M vs Ts
As Tsincreases
the value of
Mass flow
increases.
0.00E+00
1.00E-07
2.00E-07
3.00E-07
4.00E-07
5.00E-07
6.00E-07
7.00E-07
8.00E-07
9.00E-07
250 270 290 310 330 350 370
Massflowi
nkg/s
Ts in K
M Vs TS
M Vs TS
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Evaporation Time vs Ts
250
270
290
310
330
350
370
390
0 2000 4000 6000 8000 10000 12000 14000 16000 18000
TsinK
Time in S
Td Vs Ts
Time Vs Ts 1 Bar
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AlgorithmVariation in pressure
Assume
Drop radius Rs
Drop surface Temperature Ts& P (All possible values273
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TinfVs Ts
250
270
290
310
330
350
370
390
0 100 200 300 400 500 600 700 800 900
TsinK
Tinf in K
Tinf Vs Ts
Tinf Vs T 0.5 Bar
Tinf Vs Ts 1 Bar
Tinf Vs Ts 1.5 Bar
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M.Vs Ts
250
270
290
310
330
350
370
390
0 0.00000010.00000020.00000030.00000040.00000050.00000060.00000070.00000080.0000009 0.000001
TsinK
Mass flow in Kg/s
M Vs Ts
M Vs T 0.5 Bar
M Vs Ts 1 Bar
M Vs Ts 1.5 Bar
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Time for evaporation Vs Ts
250
270
290
310
330
350
370
390
0 5000 10000 15000 20000 25000
TsinK
Time in S
Td Vs Ts
Time Vs T 0.5 Bar
Time Vs Ts 1 Bar
Time Vs Ts 1.5 Bar
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Inference
The droplet does not reach its saturation temperature, even it itsambient temperature is too high. It evaporates fully before
reaching saturation.
Evaporation time increases with increase in pressure
For 50 % decrease in pressure it reduces by 50.07% For 50 % increase in pressure it increases by 47.34%
Property Reference (liq. -> water)
1. Perrys Chemical Engg. Handbook
2. Properties of Gases and Liquids by Reid
3. An Introduction to CombustionConcepts and Applications by Stephen
R Turns
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ASSUMPTIONS:
Spherically symmetric droplet.
Spherical cap geometry in case of sessile drop. Single component droplet.
Transient processes are ignored.
- droplet heating.
- variable transport properties.
Recirculation within drops, time dependence of gas temperature andthe convection heat transfer coefficient are not taken into account.
SETTLED SCIENCE:
D2 law.
Ficks law of diffusion.
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Research Proposal
To develop a model of evaporation of a drop in quiescent ambientincorporating the effects of internal flow, transient and variable
transport properties separately.
Two aspects of this theory which have received considerableattention for research are :
validity of the quasi-steady assumption and
accounting for variable transport properties.
Approach
Effects of internal flows due to temperature and pressure will have tobe looked upon and incorporated in the governing equations of
droplet evaporation.
Transient & variable properties can be incorporated by integrating the
mass, species and energy equations governing droplet evaporation.
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References
Hubbard, G.L., Denny, V.E., and Mills, A.F., Droplet Evaporation: Effectsof Transient and Variable properties, International journal of Heat and
Mass Transfer, 18:1003-1008(1975).
S. Kotake and T. Okazaki, Evaporation and combustion of fuel droplet.
Inc. J. Weir! Mass Transfer 12. 595-610 (1969).
The Evaporation of Water Droplets. A Single Droplet Drying Experiment,D.E. Walton, Drying Technology: An international journal, 22:3, pp. 431-
456, 2004.
Turns, Stephen R., An introduction to Combustion: Concepts and
Applications, Tata McGraw Hill Education Private Limited, Third Edition.
Williams, F.A., Combustion Theory, 2
nd
Ed., Addison-Wesley, RedwoodCity, CA, 1985.
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Thank You