a quasi-discrete model for droplet heating and evaporation ... · ahmed elwardany supervised by:...

The Sir Harry Ricardo Laboratories-Centre for Automotive Engineering,

University of Brighton, UK.

Research workshop: Droplets and Sprays: modelling and experimentation 13th January 2012

A quasi-discrete model for droplet heating and evaporation: application to

Diesel and gasoline fuels Presented by:

Ahmed Elwardany Supervised by: Prof. Sergei Sazhin Prof. Morgan Heikal

Ø  Introduction

Ø Concept of quasi-component

Ø  Thermophysical properties of n-alkanes

Ø Preliminary results for Diesel fuel

Ø Advanced results for Diesel and gasoline fuels

Ø Conclusions

Plan

Multi-component Models

Models applicable for Small number of components

(DCM)

Models applicable for Large number of components

(CT or Distillation Curve)

Introduction Ø Models for multi-component droplets can be subdivided

into two groups:

Ø Most of these models assume that the species diffusivity

within the droplet is assumed to be infinitely large or small

while each component has its own volatility.

Concept of quasi-discrete model

Ø  The model is based on the assumption that the

components can be described as CnH2n+2 (n-alkanes).

Ø  The model is based on replacing a large number of actual

components with a small number of quasi-components.

Ø  These quasi-components are then treated as actual

components, taking into account the diffusion of quasi-

components in droplets.



0

0.04

0.08

0.12

0.16

0.2

5 10 15 20 25

diesel

gasoline

n

f m(n

)

Diesel gasoline

n1 n2 n3 n4


Ø  The initial mole fraction of each quasi-component is

calculated as:

Ø where are the molecular weights, ,

, is Gamma function, and α, β, γ are

parameters that determine the shape of the distribution and

the original shift.


Ø  Following Arias-Zugasti and Rosner (2003), we

assumed that: , and (Diesel Fuel)

and (gasoline fuel)

Ø  The choice of assures that:

Ø Each quasi-component carbon atoms estimated as:


Thermophysical properties of n-alkanes

11

•  Critical and Boiling Temperatures

Following Poling et al (2000), the dependence of critical and

boiling temperatures on number of carbon atoms n:

where the constants are:

Coef%icient a b c d

Critical 242.3059898052 55.9186659144 - 2.1883720897 0.0353374481

Boiling 118.3723701848 44.9138126355 - 1.4047483216 0.0201382787

Poling B.E., Prausnitz J.M. and O’Connell J., (2000), The Properties of Gases and Liquids, New York: McGraw-Hill.

12

•  Critical and Boiling Temperatures

300

400

500

600

700

800

5 10 15 20 25

Tcr (K)

check_Tcr

Tb (K)

check Tb

T (K

)

values of Tcr approximation for Tcr values of Tb approximation for Tb

n

13

•  Saturation pressure and Latent heat of vaporization

Following Arias-Zugasti and Rosner (2003) the saturation

pressure of n-alkanes (n = 4-17).

where , and

Latent heat:

where

,

Arias-Zugasti M, Rosner DE. Multicomponent fuel droplet vaporization and combustion using spectral theory for a continuous mixture. Combustion and Flame 2003;135:271-284.

14

•  Liquid Density

Following Yaws (2008), the dependence of liquid density on

number of carbon atoms n and temperature (n = 5-25):

The values of , and are approximated as follows:

Yaws C.L., (2008), Thermophysical properties of chemicals and hydrocarbons, William Andrew.

15

•  Liquid Density

300

400

500

600

700

800

900

5 10 15 20 25

T = 300 K

approximation - T = 300 K

T = 450 K

approximation - T = 450 K

n

dens

ity (k

g/m

3 )

16

•  Liquid Viscosity

Following Mehrotra (1994), the dependence of liquid viscosity

on number of carbon atoms n and temperature (n = 4-44):

where

Mehrotra A.K. (1994), Correlation and prediction of the viscosity of pure hydrocarbon, The Canadian Journal of Chemical Engineering, (72) 554-557.

17

•  Liquid Viscosity

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

5 10 15 20 25

T =300 K approximation - T = 300 K T= 450 K approximation - T = 450 K

n

visc

osity

(Pa.

s)

The approximations are reproduced using the equation suggested by Mehrotra (1994). The symbols are reproduced from http://webbook.nist.gov/chemistry/

18

•  Liquid Heat Capacity

Following van Miltenburg (2000), the dependence of liquid

heat capacity on number of carbon atoms n and temperature

(n = 2-26):

van Miltenburg J.C.(2000), Fitting the heat capacity of liquid n-alkanes: new measurements of n-heptadecane and n-octadecane, Thermochimica Acta (343) 57-62.

19

•  Liquid Heat Capacity

2000

2200

2400

2600

2800

5 7 9 11 13 15 17 19 21 23 25

T =300 K approximation - T = 300 K approximation - T = 450 K

n

heat

cap

acity

(J/k

g.K

)

The data of n-heptadecane and n-octadecane (triangles) reproduced from van Miltenburg (2000), the other data (squares) reproduced from http://webbook.nist.gov/chemistry/.

20

•  Liquid Thermal Conductivity

Following Yaws (1995), the dependence of liquid thermal

conductivity on number of carbon atoms n and temperature (n

= 5-20):

where

Yaws C.L., (1995), Handbook of thermal conductivity, Vol (2): Organic compounds, C5 to C7 and Vol (3): Organic compounds, C8 to C28. Gulf Publishing Company, Houston, Texas, USA.

21

•  Liquid Thermal Conductivity

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

5 10 15 20 25

T = 300 K approximation - T = 300 K T = 450 K approximation - T = 450 K

n

ther

mal

con

duct

ivity

(W/m

.K)

Hollow symbols are reproduced from http://webbook.nist.gov/chemistry/. Solid Symbols are reproduced form Yaws (1995) using the corresponding values of the constants.

Preliminary results

Diesel Results

Pg =3 Mpa, Rd =10 µm, Ud =1 m/s,Tg = 880 K, Td,initial = 300 K

0

2

4

6

8

10

12

300

400

500

600

700

800

0 0.25 0.5 0.75 1 1.25 1.5

Ts_n=1 Ts_n=10 Ts-n=20,ITC

Time (ms)

T s (K

) Rd (µm

)

One quasi-component-ETC/ED Twenty quasi-components-ETC/ED Twenty quasi-components-ITC/ID

Diesel Results

450

460

470

480

0 5 10 15 20

Ts-ETC-ED Ts-ITC_ID ETC/ED model ITC/ID model

Time = 0.25 ms

Number of quasi-components

T s (K

)

(a)

9.925

9.95

9.975

10

0 5 10 15 20

Rd-ETC-ED Rd-ITC_ID ETC/ED model ITC/ID model

Time = 0.25 ms


Rd (µm

)

(b)

Diesel Results

605

610

615

620

625

0 5 10 15 20

Ts-ETC-ED

ETC/ED model ITC/ID model

Time = 1 ms

T s (K

)


(a)

6.8

7

7.2

7.4

7.6

0 5 10 15 20

Rd-ETC-ED Rd-ITC_ID ETC/ED model ITC/ID model

Time = 1 ms

Rd (µ

m)


(b)

Advanced results

Diesel Results

0

2

4

6

8

10

12

300

400

500

600

700

800

0 0.4 0.8 1.2 1.6

Ts_n=1 Ts_n=10 Ts-n=20,ITC Ts_old

Time (ms)

T s (K

) Rd (µm

)

One quasi-component-ETC/ED Twenty quasi-components-ETC/ED Twenty quasi-components-ITC/ID Twenty quasi-components-ETC/ED (n-dodecane)

Diesel fuel

Pg =3 Mpa, Rd =10 µm, Ud =1 m/s,Tg = 880 K, Td,initial = 300 K

Diesel Results

537

539

541

543

0 4 8 12 16 20

ETC, ED models ITC, ID models

Time =0.5 ms


T s (K

)

(a)


9.55

9.6

9.65

9.7

0 4 8 12 16 20


Time =0.5 ms


Rd (µ

m)

(b)


Diesel Results

600

610

620

630

0 4 8 12 16 20


Time =1 ms


T s (K

)

(a)


6.9

7.1

7.3

7.5

7.7

0 4 8 12 16 20

ETC, ED models ITC, ID models Time =1 ms


Rd (µ

m)

(b)


30

Gasoline Results

Pg =3 bar, Rd =10 µm, Ud =10 m/s,Tg = 450 K, Td,initial = 300 K

0

2

4

6

8

10

12

300

350

400

450

500

0 2 4 6 8

Ts_n=1 Ts_n=10 Ts-n=20,ITC

Time (ms)

T s (K

) Rd (µm

)

One quasi-component-ETC/ED Thirteen quasi-components-ETC/ED Thirteen quasi-components-ITC/ID

Gasoline Results

330

335

340

345

350

0 3 6 9 12


Time =0.5 ms


T s (K

)

(a)


9.25

9.3

9.35

9.4

9.45

9.5

0 3 6 9 12


Time =0.5 ms


Rd (µ

m)

(b) ETC/ED model ITC/ID model

Gasoline Results

340

360

380

400

0 3 6 9 12



T s (K

)

(a)


5.6

5.8

6

6.2

6.4

6.6

6.8

7

0 3 6 9 12



Rd (µ

m)

(b)


Suggested composition for Diesel and gasoline fuels

Gasoline Fuel Diesel Fuel 60% C6H14 10% C8H18

30% C9H20 57% C12H26

8% C12H26 29% C16H34

3% C15H32 4% C21H44

Conclusions

Ø  A new quasi-discrete model for multi-component droplets heating and evaporation, applicable for large number of components, has been developed. Ø This model takes into account the effect of heat and mass diffusion within the droplet and it takes into account the dependence of the thermophysical properties of the fuel on the number of carbon atoms and temperature.

Ø  We applied this model for Diesel and gasoline fuels.

Ø Diesel and Gasoline fuels could be presented by a mixture of only four quasi-components.

•  Kristyadi T., Deprédurand V., Castanet G., Lemoine F., Sazhin S.S., Elwardany A., Sazhina E.M. and Heikal M.R. (2010), Monodisperse monocomponent fuel droplet heating and evaporation, Fuel 89 (2010) 3995–4001. •  Sazhin S.S., Elwardany A.E., Krutitskii P.A., Castanet G., Lemoine F., Sazhina E.M. and Heikal M.R. (2010), A simplified model for bi-component droplet heating and evaporation, Int. J. Heat Mass Transfer 53, 4495–4505.

•  Abdelghaffar, W.A., Elwardany, A.E., Sazhin, S.S. (2011), Modelling of the processes in Diesel engine-like conditions: effects of fuel heating and evaporation, Atomization and Sprays, 53(13-14), 2826-2836.

•  Sazhin S.S., Elwardany A.E., Krutitskii P.A., Deprédurand V., Castanet G., Lemoine F., Sazhina E.M., Heikal M.R. (2011), Multi-component droplet heating and evaporation: numerical simulation versus experimental data, Int. J. Thermal Sciences, 50(2011) 1164-1180. • Sazhin S.S., Elwardany A.E., Sazhina E.M., Heikal M.R. (2011), A quasi-discrete model for heating and evaporation of complex multicomponent hydrocarbons fuel droplets, Int. J. Heat Mass Transfer 54, 19-20, 4325-4332.

Publications: International Journals

Thank you

Ahmed Elwardany The Sir Harry Ricardo Laboratories-Centre for Automotive Engineering,

University of Brighton, UK.

Research workshop: Droplets and Sprays: modelling and experimentation 13th January 2012

a quasi-discrete model for droplet heating and evaporation ... · ahmed elwardany supervised by:...

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