Effect of nozzle diameter and its orientation on the flow pattern and plume dimensions in...

Chemical Engineering Science 62 (2007) 7471–7483www.elsevier.com/locate/ces

Effect of nozzle diameter and its orientation on the flow pattern and plumedimensions in gas–liquid jet reactors

Sachin K. Dahikara, Sagar S. Gulawania, Jyeshtharaj B. Joshia,∗, Manish S. Shahb,Chaganti S. Rama Prasadb, Daya S. Shuklab

aInstitute of Chemical Technology, Matunga, Mumbai 400 019, IndiabChemical Engineering and Technology Group, Bhabha Atomic Research Center, Trombay, Mumbai 400 085, India

Received 24 July 2007; accepted 8 August 2007Available online 22 August 2007

Abstract

Gas–liquid jet reactors are widely used in chemical industries in various applications such as feed-water heaters, metal processing, andthermal energy sources, etc. In all these applications, the principal requirement for the design is a prior knowledge of jet shape and dimensions,which primarily depend upon the nozzle type, size, submergence and its orientation. In the present study, CFD simulations of non-reacting(steam-water) and reacting (SF6-Li) jets have been carried out to understand the variation in plume dimensions of gas–liquid jet reactors. Forcondensation jet and reaction jet, the criteria have been developed to identify the plume boundary based on the hold-up profile of steam/SF6 gasand the evaporated fuel. The effect of nozzle diameter and its orientation, nozzle gas velocity and bath temperature on the plume dimensionshave been studied for both the types of jets. It was observed that the extent of increase in the plume length is always higher in the case ofreaction jet as compared to the condensation jet for all the cases. The analyses also proved that, the availability of reactant is much better withthe horizontal orientation which leads to stable plume length. The CFD model has been extended for the prediction of the flow pattern and itseffect on the rate of condensation/reaction and plume dimensions for both the jet systems.� 2007 Elsevier Ltd. All rights reserved.

Keywords: Gas–liquid jet reactor; CFD; Hydrodynamics; Multiphase reaction; Phase change; Plume dimensions

1. Introduction

The injection of condensing/reacting gas into a liquid is oneof the most common industrial processes. Some important ap-plication include direct contact feedwater heaters, jet pumps,the blowdown of primary nuclear boiler system into water bathwithout releasing the fissionable materials to the atmosphere,metal processing, thermal energy sources, etc. Typically theseprocesses involve condensation of a pure component (steam-water) (Kerney et al., 1972; Weimer et al., 1973; Chen andFaeth, 1982; Chun et al., 1996; Kim et al., 2001), physical dis-solution of a gas into a bulk liquid phase (ammonia into wa-ter), or absorption accompanied by an instantaneous chemicalreaction (SF6-molten Li, HCl-aq.NH3 solution, H2O/LiH-Al,O2/Al-Mg, F2/ molten Li/Al-KClO4, etc.) (Parnell et al., 1989;

∗ Corresponding author. Tel.: +91 22 2414 0865; fax: +91 22 2414 5614.E-mail address: [email protected] (J.B. Joshi).

0009-2509/$ - see front matter � 2007 Elsevier Ltd. All rights reserved.doi:10.1016/j.ces.2007.08.035

(Chan et al., 1990; Chan and Abou-Ellail, 1991; Chan, 1993;Zhang et al., 2002). In thermal energy processes, an oxidizergas is injected into a bath of molten metal. The energy producedis transferred to the water via the heat transfer area for gener-ating a superheated steam. The steam exit from the reactor isused to power a prime mover. In the case of condensation jet,when the vapor is injected it forms a flame like shape, calledas a plume, just next to the nozzle exit. The temperature dif-ference between the injected vapor and the surrounding liquidbath is very high, which leads to fast condensation of the vaporat the nozzle exit. Under transient conditions, the temperatureof the bath increases gradually, decreasing the temperature dif-ference and thus the rate of condensation, leading to the plumeexpansion. In the case of reaction jet, the injected gas reactswith the surrounding reactive species in solutions or moltenbaths. A large amount of heat is produced due to the reac-tion, which evaporates the local liquid. The vapors generateddue to heat of reaction penetrate further inside the bulk liquid

http://www.elsevier.com/locate/ces

mailto:[email protected]

7472 S.K. Dahikar et al. / Chemical Engineering Science 62 (2007) 7471–7483

increasing the overall plume length for the case of reactionjet. However, these vapors of liquid loose heat away from thenozzle tip and get condensed. One of the unique features ofthese two systems is the faster renewal of gas–liquid interfacedue to entrainment of surrounding liquid inside the plume,which enhances the rate of reaction/condensation. Therefore,such types of jets are employed in industry for their efficientheat and mass transfer characteristics. The behavior of plumelength for reaction jet shows similarity with plume behavior ofcondensation jet in terms of phenomena such as heat transferacross gas–liquid interface, condensation at gas–liquid interfaceand the overall plume length consisting of pure vapor phaseand condensate phase. Thus a prior knowledge of jet shape anddimensions, which primarily depend upon various operatingparameter (nozzle diameter, nozzle orientation, mass flowrate and bath temperature) is the principal requirement forthe design of reactor. The development of local turbulencearound the nozzle exit plays a vital role in determining theoverall rates of mass transfer, heat transfer and the chemicalreaction. In view of these important considerations, computa-tional fluid dynamics (CFD) has been employed to study thehydrodynamics of gas–liquid jet reactor.

Over the past four decades the investigations carried out forgas–liquid jet reactors can be classified into experimental fluiddynamics (EFD) and computational fluid dynamics (CFD). Theaim of the EFD analysis was to study the plume dimensions,temperature variation and product distribution (reaction jet) inthe reactor. The gas–liquid jet reactors are broadly classifiedinto condensation and reaction jets. In the condensation jet(non-reacting), studies have been carried out on steam-watersystem. In the case of reaction jets, various systems have beenstudied such as HCl-aq. NH3, H2O-molten Li, H2O-molten Na,Cl2-molten Na, F2-molten Li and SF6-molten Li. Experimen-tal measurements were carried out using various techniquessuch as X-ray radiography, and high speed photography for themeasurements of plume dimensions and product distribution(reaction jet) in the reactor. The thermocouples were used tomeasure the temperature variation in the reactor (Cho et al.,1990; Parnell et al., 1989). Cho et al. (1990) used a special mo-bile thermocouple which measures the temperature along thecenterline of jet axis. Further, the pressure measurements werealso carried out to study the plume stability. CFD studies havebeen performed by developing various turbulence models forthe simulation of condensation/reactionjets viz. locally homo-geneous formulation (LHF), two fluid model (TFM), and multifluid model (MFM) (Chan, 1993). These models along with theapproach of equilibrium state relationship, probability densityfunction (PDF), and k.�.g turbulence model were used to in-vestigate the plume dimensions and the flow pattern in the jetsystems. A complete review of the work till date for the flowprediction and plume dimensions of condensation and reactionjets by using EFD and CFD with their details of modeling pa-rameters and limitations have been discussed in Gulawani et al.(2007).

Though the attempts have been made to address the phe-nomena of condensation and reaction jets using LHF, TFMand MFM models with PDF formulation; the prediction of the

correct equilibrium state relationship for the species at specificoperating condition is still a major limitation. The determinationof the mass averaged quantities experimentally is one of thedifficulties, which makes PDF approach difficult for conden-sation/reaction modeling. Most of the modeling has been doneby using adiabatic condition. Though there is an attempt to in-corporate the radiation losses term in the governing equationsof energy balance, the modeling efforts have not been validatedcompletely for all the cases of condensation and reaction jets. Inthe case of condensation jet, the phase change is accompaniedby heat transfer. However, the models using LHF/TFM/MFMwith PDF involves species determination based on mixture frac-tion which are calculated based on the averaged mass fractionvalues. In the case of reaction jet, the rate of reaction is instan-taneous and the overall rate is mass transfer controlled. Thusthere is a need to incorporate the simultaneous processes ofphase change, mass transfer, heat transfer, liquid phase reac-tion and the gas phase reaction. The present work addressesthese issues and includes the CFD simulations of non-reacting(steam-water) and reacting (SF6-molten Li) jets. The study hasbeen carried out to understand the flow pattern and its effecton plume dimensions with various nozzle diameters and itsorientations (horizontal and vertically upward). In addition toplume dimensions, a detailed analysis of the liquid phase flowpattern for both types of jet system with horizontal and verti-cally upward insertion has been carried out. A discussion hasbeen presented on the flow pattern and its effect on the plumedimensions. The effect flow pattern on the rate of condensa-tion/reaction and plume dimensions has been discussed for boththe jet systems.

2. Mathematical model

2.1. Condensation jet modeling

A two phase model has been formulated in the Euler–Eulerframework using the method of inter-penetrating continua. Wa-ter has been considered as the primary phase, with the steam asthe secondary phase. Inter-phase mass transfer has been mod-eled by using the thermal phase-change model. For turbulenceclosure, k.� turbulence model has been incorporated. The de-tails of the governing equations for the case of condensationjet have been given by Gulawani et al. (2006).

2.1.1. Thermal phase change modelA thermal phase change model has been used to simulate

evaporation and condensation phenomena, which describes thephase change induced by interphase heat transfer of intrinsicflows. It is only applicable to a change of phase in pure sub-stances and considers the heat transfer processes on each sideof the phase interface. However, it was assumed that the re-sistance to the heat transfer is provided by the liquid phaseand the rate was estimated using the procedure of Gulawaniet al. (2006). In this model, it is assumed that the amount ofheat generated is completely transferred across the interface.An interfacial temperature is determined from the considera-tion of thermodynamic equilibrium and it is assumed to be the

S.K. Dahikar et al. / Chemical Engineering Science 62 (2007) 7471–7483 7473

same (saturation temperature, Ts) for both the phases. The masstransfer flux was determined from the following heat balance.

mgf = qf + qg

Hgs − Hf s

. (1)

2.2. Reaction jet modeling

A two phase model has been formulated in the Euler–Lagran-gian framework. 3D simulations have been carried out for re-active flows where oxidiser gas (SF6) act as a particle whilefuel baths (molten lithium) have been considered as the pri-mary phase. Multi-species transport model has been appliedfor reaction mechanism. For turbulence closure, k.� turbulencemodel has been incorporated. Since the reaction is instanta-neous, the overall rate becomes mass transfer controlled. Thevalue of mass transfer coefficient has been estimated using thelocal values of turbulent kinetic energy (k) and the turbulentenergy dissipation rate (�). The governing equations for thethree-dimensional jet flow are as follows:

2.2.1. Species transportThe conservation of species i can be given as

�(�Yi)

�t+ �(�ujYi)

�xj

= �

�xj

(�ieff

�Yi

�xj

)+ Si . (2)

Yi is the local mass fraction of the species and Si is the sourceterm due to chemical reaction of component i.

The effective diffusion coefficient, �ieff is given by

�ieff = �i + �t

Sct

, (3)

where �i is the molecular diffusion coefficient and (�t /Sct ) isthe eddy diffusion coefficient. The value of Schmidt numbershas been taken as 0.9.

The rate of production/consumption, Si , for component i canbe computed as sum of the rate of progress of all the elementary(N) reactions that component i participates in:

Si =∑

(�′′i − �′

i )R, (4)

where R is the rate of reaction of species i.

2.2.2. Particle trackingIn the CFD model, oxidizer gas has been treated as a discrete

particle. The forces acting on the particle which affect the par-ticle acceleration are due to the difference in velocity betweenthe particle and fluid and due to the displacement of the fluidby the particle. The equation of motion for such a particle canbe given as

mp

dvp

dt= 1

8��f d2CD|vf − vp|(vf − vp) + �d3�f

6

dvf

dt

+ 1

6�d3(�p − �f )g. (5)

The term on the left-hand side is a summation of all of theforces acting on the particle expressed in terms of the particle

acceleration. The first term on the right-hand side is the dragforce acting on the particle. The second term on the right-handside is the force applied on the particle due to the pressuregradient in the fluid surrounding the particle caused by fluidacceleration. It is only significant when the fluid density iscomparable to or greater than the particle density. The thirdterm is the buoyancy force due to the gravity.

2.2.3. Reaction modelingThe reactions under consideration are instantaneous and

highly exothermic. When the oxidizer vapor is injected intothe pool of fuel bath, a large amount of heat is generated,which evaporates the surrounding liquid. The fraction of evap-orated vapor again reacts with the oxidizer vapor, while otherpenetrates into the liquid bath and condenses downstream dueto the entrainment of liquid bath inside the plume. Thus threephenomena have been modeled here: (1) reaction between oxi-dizer gas and the liquid fuel, (2) reaction between oxidizer gasand the evaporated fuel, and (3) condensation of evaporatedfuel. The overall reaction under consideration is as follows:

SF6 + 8Li −→ Li2S(l) + 6LiF(l),

�Hr = −19.267 kJ/g of SF6. (6)

A reaction mixture has been created which includes the reac-tants and products species of respective reactive jet system. Inthe case of SF6-molten Li system, reaction mixture consists ofLi, Li vapor, Li2S and LiF. The proper stoichiometric coeffi-cients have been substituted for all the reactions in order topredict the mole formation of each species after the reaction.Since all the reactions are instantaneous, the specific rate ofreaction is given by (Danckwerts, 1970):

R = kL[A∗]{

1 + [B0]Z[A∗]

√DB

DA

}, (7)

where [B0] is the concentration of liquid phase reactant, Z isthe stoichiometric coefficient, [A∗] and DA is the saturationconcentration and diffusivity of the solute gas in the liquidphase and DB is the diffusivity of liquid phase reacting species.The value of

√DB/DA was assumed to one. Further value of

second term in the bracket of Eq. (7) is much higher than thefirst term, equation simplifies to

R = kL

[B0]Z

. (8)

To estimate the mass transfer coefficient, various models of heatand mass transfer have been proposed in the literature such aslarge eddy model by Fortescue and Pearson (1967), small eddymodel by Lamont and Scott (1970), and single eddy model byLuk and Lee (1986), etc. In the present work, the small eddymodel proposed by Lamont and Scott (1970) has been usedwhere the mass transfer coefficient is given by the followingequation:

kL = 1.44

√DABk

�. (9)

It may be pointed out that the values of kLwere estimated atseveral locations on the interface by using local values of k


and �. Further, a binary homogeneous mixture has been createdwhich consists of liquid and vapor phase of same species (Li andLi vapor). An antoine equation has been specified for the phasechange between the two phases of the same species. Thus withthe help of binary mixture and Antoine equation, condensationand vaporization phenomena have been modeled.

2.2.4. Turbulence equationsThe standard k.� model (Launder and Spalding, 1972) has

been used to model turbulence in the liquid phase. The con-servation equations for the turbulent kinetic energy kand thedissipation rate � for each phase are

�

�t(�f ∈f kf ) + �

�xj

(�f ∈f uf,j kf )

− �

�xj

(∈f

(� + �t

�k

)�kf

�xj

)= −∈f (Gf − �f �f ), (10)

�

�t(�f ∈f �f ) + �

�xj

(�f ∈f uf,j �f )

− �

�xj

(∈f

(� + �t

��

)��f�xj

)

= −∈f

�fkf

(c�1Gf − c�2�f �f ). (11)

The term Gf is the production term of turbulent kinetic energy.The turbulent viscosity of the continuous phase is calculated as

�t = C��f

k2

�. (12)

The values of various constants such as C�,,c�1, c�2, �k , �� are0.09, 1.44, 1.92, 1.0, 1.3, respectively.

2.3. Boundary conditions

In the case of condensation and reaction jet, at the noz-zle inlet, total pressure/mass flow rate/velocity has been set asthe boundary condition. Based on the nozzle inlet mass flowrate/velocities, the values for k and � were initialized as follows:

k = 0.03

(m0

�0

)2

and � = k1.5

0.3d0. (13)

At the outlet, ambient conditions have been set for the atmo-spheric pressure. The reactor wall is considered to be adiabatic;with no slip conditions imposed at all the walls.

2.4. Method of solution

In the case of condensation jet, CFD simulations have beencarried out with the experimental data of Kerney et al. (1972)with horizontal insertion. An unstructured tetrahedral grid of35,000 nodes has been employed for the data set of Kerney et al.(1972). Herein 5800 nodes are used along the axis of the jet. Inthe case of reaction jet, CFD simulations have been carried outwith the experimental data of Parnell et al. (1989) and Zhanget al. (2002) with horizontal insertion and Chan et al. (1990) forvertically upward insertion. 3D simulations have been carried

out for the experimental data of Parnell et al. (1989) in rectan-gular geometry (0.07 × 0.12 × 0.32 m) with nozzle diameterof 2 mm. For Chan et al. (1990) experimental data, simulationshave been carried out in cylindrical geometry (ID = 0.154 mand H = 0.122 m) with nozzle diameter of 0.79 mm. The sim-ulations for Zhang et al. (2002) have been carried out using thegeometry of Parnell et al. (1989) with nozzle diameter of 1 mm.An unstructured tetrahedral grid of 85,250 and 79,580 nodeshave been employed for the geometry of Parnell et al. (1989)and Chan et al. (1990), respectively. The grids are made finerin the nozzle region, while these gradually become coarser to-wards the wall. Steady state simulations have been carried outwith convergence criteria that the residue falls below 10−4. Acommercial software package CFX 10.0 from ANSYS Tech-nology has been used. High resolution discretization schemehas been applied for mass and momentum equations, while up-wind discretization scheme has been employed for turbulentkinetic energy, turbulent dissipation rate and volume fractionequations.

3. Results and discussion

In the case of condensation jet, the present CFD model hasbeen validated by Gulawani et al. (2006), by comparing theCFD predictions with the experimental values of axial and ra-dial temperature profiles reported by Kim et al. (2001). Thepresent work pertains to the validation of CFD simulation forthe reaction jets. The CFD predictions of plume dimensionshave been compared with the experimental values reported byParnell et al. (1989), Chan et al. (1990) and Zhang et al. (2002)for SF6-molten Li system.

3.1. Plume shape and size

CFD simulations have been performed for condensation andreaction jet systems over a wide range of jet velocity, pooltemperature and nozzle diameter. Further, the effect of reactordeclination has also been investigated. The plume length hasbeen estimated under two conditions: (a) considering only ox-idation region and (b) oxidation as well as fuel vapor region.Further, for the identification of plume length, two criteria havebeen considered, based on the hold-up profile of gas/vapor. Forcondensation jet, a criterion has been developed to identify theplume boundary based on the hold-up profile of the steam. Inthe first criterion, for only steam region, volume fraction ofsteam was assumed to be 99%, while in the second criterion,a boundary has been identified where a sharp change in thehold-up profile of steam occurs. In the second criterion, thevolume fraction of steam is in the range of 92.55% to 95.5%.The results of these two criteria have been shown in Figs. 1Aand 1B, respectively. Thus the hold-up of 99% assures com-plete vapor phase while the hold-up in the range of 92–95%includes the corresponding condensation zone. In the case ofreaction jet, since there is complete consumption of SF6 gasdue to reaction, the hold-up profile of SF6 gas gives directlya reaction plume length (Fig. 1C). Further, the overall plumelength has been identified from the hold-up profile of lithium


Fig. 1. Prediction of plume length for condensation jet and reaction jet. (A) Hold-up profile of steam showing plume length with only steam zone, (B) hold-upprofile of steam showing complete plume length along with condensation zone, (C) hold-up profile of SF6 gas showing reaction plume length, and (D) hold-upprofile of lithium vapor showing complete plume length.

vapor. A point hasbeen identified where complete condensationof lithium vapor occurs [i.e., hold-up of lithium vapor equalsto 10−4 (Fig. 1D)]. In all the cases of condensation (Kerneyet al., 1972; Chun et al., 1996; Kim et al., 2001) and reac-tion jets (Parnell et al., 1989; Chan et al., 1990; Zhang et al.,2002) the nozzle diameter has been covered in the range of0.4–9.5 mm and 0.79–2 mm, respectively. The nozzle velocitywas in the range 203–333 m/s and 120–325 m/s, respectively.An elliptical plume shape has been observed for all the simu-lations. Table 1 gives a summary of the published experimen-tal work which includes reactor dimensions, nozzle diameters,bath temperatures, and nozzle velocities. Table 1 also showsthe experimental and predicted values of plume dimensions forboth jet systems. Fig. 2 shows a good agreement between theCFD predictions and the experimental values of plume lengthwhichvalidates the proposed CFD model for the case of reac-tion jet as well. As stated earlier, Gulawani et al. (2006) havevalidated the CFD model for the case of condensation jet.

Since the CFD model has been validated for condensation aswell as reaction jet over a wide range of design and operatingconditions, it was thought desirable to undertake a systematicinvestigation of parametric sensitivity of nozzle diameter andits orientation.

3.2. Effect of nozzle diameter

The effect of nozzle diameter on the plume length has beenstudied by performing the CFD simulations at different nozzle

diameters for condensation (d0=0.4, 0.79, 1.58, 3.76, 6.35, and9.5 mm) and reaction jets (d0=0.79, 1, 2, 3.76, and 6.35 mm) byvarying nozzle gas velocities and bath temperatures. Tables 2Aand 2B summarize the operating conditions (nozzle diameterand its orientation, gas velocity, and the bath temperature) usedfor the simulation of condensation and reaction jet systems,respectively. Tables also provide the values of plume lengthpredicted from the simulations. Figs. 3 and 4 show results forcondensation jets (Figs. 3A–D) and reaction jets (Figs. 4A–D)with respect to nozzle diameters, gas velocities and bath tem-peratures. From the figures following observations can be made:(i) the plume length of a reaction jet is relatively much largerthan the plume length of a condensation jet under otherwiseidentical conditions. (ii) The plume length increases with anincrease in the nozzle diameter for both the types of jets. How-ever, the extent of increase was found to be different inthe con-densation and the reaction jet systems. For instance, an increasein the nozzle diameter by a factor of 8 (d0 = 0.79.6.35 mm),resulted in an increase in the plume length by a factor of 5.6(L = 10.25.57.66 mm) for condensation jet and by a factor of6.5 (L = 11.54.75.35 mm) for reaction jet. In the case of re-action jet, higher nozzle diameter leads to higher availabilityof SF6 gas for reaction with the surrounding liquid bath. Thisresults into high generation of heat which leads to higher pene-tration of plume to dissipate the heat to the surrounding liquid.The generation of heat is very high as compared to the latentheat of the steam. Thus higher plume length is observed for thereaction jet as compared to condensation jet. Thus the nozzle


Tabl

e1

Sum

mar

yof

the

publ

ishe

dw

ork:

reac

tor

dim

ensi

ons

and

oper

atin

gco

nditi

ons

for

(A)

cond

ensa

tion

and

(B)

reac

tion

jets

Syst

emA

utho

rR

eact

ordi

men

sion

s(m

)N

ozzl

eor

ient

atio

nN

ozzl

edi

amet

er(m

m)

Vel

ocity

(m/s

)B

ath

tem

pera

ture

(K)

Dim

ensi

onle

sspl

umle

ngth

Plum

esh

ape

(L/d

0)

Exp

erim

ent

Pred

ictio

n

(A)

Con

dens

atio

nje

tK

erne

yet

al.

(197

2)R

ecta

ngul

arst

eel

tank

(LR

=1.

52;H

R=

0.76

;W

R=

0.36

)

Hor

izon

tal

subm

erge

d0.

420

5.20

340.

0022

.00

22.8

0E

llipt

ical

332.

2234

2.80

18.0

019

.08

0.79

254.

9332

7.60

10.0

009

.85

Elli

ptic

al25

4.57

349.

0015

.00

16.2

01.

5824

8.42

324.

1005

.00

05.7

5E

llipt

ical

332.

7634

0.10

11.5

012

.73

6.35

256.

5733

9.40

09.5

009

.63

Elli

ptic

al25

9.35

351.

0033

.50

35.2

89.

523

4.38

327.

0016

.30

16.7

4E

llipt

ical

228.

6134

0.20

22.6

023

.10

(B)

Rea

ctio

nje

tPa

rnel

let

al.

(198

9)R

ecta

ngul

arst

eel

tank

(LR

=0.

32;H

R=

0.12

;W

R=

0.07

)

Hor

izon

tal

( =

0◦;

=

30◦ ;

=

45◦ )

232

5.0

1273

50(a

vera

ge)

53.5

1E

llipt

ical

1273

62.5

(ave

rage

)54

.25

1273

46.9

(ave

rage

)48

.15

Cha

net

al.

(199

0)C

ylin

dric

al(I

D=

0.15

4;L

R=

1.22

0)V

ertic

alup

war

d0.

7920

3.4

1130

5.66

07.1

0E

llipt

ical

1358

11.6

513

.24

1415

36.4

437

.64

1586

132.

4213

3.54

Zha

nget

al.

(200

2)R

ecta

ngul

arst

eel

tank

(LR

=0.

32;H

R=

0.12

;W

R=

0.07

)

Hor

izon

tal

112

0.0

1130

–08

.84

Elli

ptic

al13

5815

16.4

514

15–

42.1

5


0

30

60

90

120

150

0 30 60 90 120 150

PR

ED

ICT

ED

PL

UM

E L

EN

GT

H, L

(m

m)

EXPERIMENTAL PLUME LENGTH, L (mm)

Fig. 2. Parity plot between the predicted and experimental values of theplume length for reaction jet systems. Parnell et al. (1989), �; Chan et al.(1990), �; Zhang et al. (2002), ◦.

diameter has a relatively greater influence when reaction occursin the jet.

Figs. 3 and 4 also show the effect of nozzle velocity onthe plume length for both the jet systems. An increase in thenozzle velocity from 203.4 to 325 m/s, for same nozzle diameter(d0=0.79 mm), the plume length for condensation jet increasesby a factor of 1.4 (L=10.25.14.1 mm) while the plume lengthfor reaction jet increases by a factor of 3 (L=11.54.34.4 mm).The injection of high velocity of SF6 leads to the availabilityof higher amount of SF6 for the reaction which liberates higherheat in the surrounding molten lithium. This subsequently leadsto high rate of evaporation of lithium leading to longer plumelength.

Figs. 3 and 4 show the variation in the plume length for boththe jet systems with respect to bath temperature. An increasein the bath temperature by a factor of 1.2 [for condensation(300–350 K), and for reaction jet (1130–1358 K)], for nozzlediameter of 0.79 mm and the gas velocity of 203.4 m/s, theplume length for condensation jet increases by a factor of 1.5(L = 10.25.15.05 mm) while the plume length for reactionjet increases by a factor of 2.5 (L = 11.54.34.4 mm). As thebath temperature increases, the rate of subcooling (saturationtemperature minus the bath temperature) decreases. Thus thegas travels a longer distance or the plume length is longer. Thusthe higher the bath temperature, the higher is the plume length.Since the density of SF6 gas is higher than the steam, the higherpenetration of plume is observed in the case of reaction jet thanthe condensation jet with increase in bath temperature.

3.3. Effect of nozzle orientation

In order to study the effect of orientation on the plume length,simulations have been carried out with nozzle diameter of 0.79

and 2 mm with gas velocities of 203.4 and 325 m/s at differentbath temperatures (T =1130, 1273, 1358 and 1415 K). The val-idation of the CFD model for orientation has been done usingexperimental data of plume length by Parnell et al. (1989) for−30◦ and 45◦ orientation (Fig. 2). In the case of reaction jet,the plume region is dominated by the vapors of molten lithium.One of the features of the reaction jet is that the products formed(Li2S and LiF) are denser than the reactant (Li) and accumulateat the bottom of the reactor. Table 3 shows the predicted valuesof plume length, plume width and volume of plume region fordifferent nozzle diameters, nozzle orientations, nozzle veloci-ties and bath temperatures. The largest plume length was ob-served for 90◦ orientation (i.e., vertically upward). Further, theplume length was found to decrease as the angle changes from90◦ to −90◦. However, the width and volume of the plume werefound to follow opposite trend. In the case of 90◦ orientation,the direction of momentum of the plume and the direction ofbuoyancy force acting on the plume are the same. This resultsinto the longer plume length. However, in the case of −90◦orientation, the buoyancy force tends to oppose the verticallydownward motion of the plume. This results into reduction inthe momentum of the plume which leads to escape of lithiumvapors from sideways. Thus, the width of the plume increasesand its length decreases. However, as a design objective, theplume length is more important as it governs the reactor length(Fig. 5).

Along with the net effect of buoyancy force, the concentra-tion of the available reactant also affects the plume dimensionsand its stability. It was found that the availability of reactantis maximum when the reactor and jet orientation are horizon-tal ( = 0◦). As a results, the rate of reaction and hence therate of heat generation increases, and as a consequence, big-ger plumes (by volume) are formed. In addition to the effect oforientation on size, it was observed that the bigger plumes (byvolume) tend to be more stable. This particular observation canbe considered as an important feature of the reaction plumes.

3.4. Centerline axial velocity and temperature

The variation in the centerline axial velocity and temperatureprofiles have been studied for both condensation and reactionjet systems. In the case of condensation jet, simulations havebeen performed to determine the axial and radial temperaturevariation by using experimental data of Kim et al. (2001) withtwo different nozzles (d0 =10.15 and 20 mm). For both axial aswell as radial temperature profiles, CFD simulation shows verygood agreement with the experimental observations (Gulawaniet al., 2006). In the case of reaction jet, simulations have beenperformed for injection of SF6 gas into molten Li with experi-mental conditions of Parnell et al. (1989). However, the experi-mental data for axial velocity and temperature are not available.Thus the comparison for centerline axial velocity and center-line axial temperature has been carried out with the predictionsof LHF and MFM model proposed by Chan (1993). Figs. 6and 7 show the prediction of centerline axial velocity and cen-terline axial temperature from present model and the predictions


Table 2(A) Effect of nozzle diameter and its orientation, steam velocity and bath temperature on the plume dimensions for condensation jet; (B) effect of nozzlediameter and its orientation, SF6 velocity and bath temperature on the plume dimensions for reaction jet

(A)Condensation jet Horizontal insertion Vertically upward insertion

Reactordimensions

Gas velocityu0 (m/s)

Bathtemperature,T (K)

Nozzle diameter, d0 (mm)

0.4 0.79 1.58 3.76 6.35 9.5 0.4 0.79 1.58 3.76 6.35 9.5Plume length, L (mm) Plume length, L (mm)

Rectangular steeltank (LR = 1.52;HR = 0.76;WR = 0.36)

203.4 300.00 6.14 10.25 16.32 38.31 57.66 69.73 6.96 10.77 17.80 39.76 61.30 73.10

320.00 6.84 12.13 20.33 40.27 62.42 77.05 7.48 13.08 21.12 41.09 64.12 78.62330.00 7.56 13.74 21.73 42.11 66.17 83.41 8.20 13.96 22.69 43.83 68.02 86.00340.00 8.38 14.40 23.51 44.78 69.09 85.60 8.92 15.10 24.78 46.66 70.23 87.91350.00 8.95 15.05 24.47 46.55 72.77 92.72 9.87 16.20 26.01 49.50 76.00 97.30

250 300.00 6.85 11.81 18.58 41.59 64.83 77.52 7.60 12.82 19.61 44.00 67.70 80.00320.00 7.49 12.77 22.25 45.53 70.29 83.41 8.81 13.33 23.48 46.81 71.61 85.76330.00 8.27 14.32 24.11 48.80 73.41 87.02 9.46 14.86 24.39 51.40 76.30 90.20340.00 8.82 15.67 26.65 52.15 76.52 93.48 9.98 16.17 27.54 53.14 78.51 95.32350.00 9.67 16.24 27.33 53.09 82.80 99.56 10.80 16.76 30.20 56.60 86.40 102.70

300 300.00 7.46 12.83 21.71 45.68 69.98 90.92 8.42 13.96 22.78 48.40 72.50 93.90320.00 7.96 13.98 24.08 49.18 75.31 95.19 9.32 14.88 25.71 50.32 76.91 96.48330.00 8.79 15.26 26.13 52.23 78.61 100.99 10.20 16.49 27.31 54.50 81.00 103.50340.00 9.38 16.65 27.48 54.93 81.98 107.07 10.99 17.36 28.78 56.39 83.76 109.10350.00 10.76 17.34 28.63 58.24 88.07 113.81 11.92 18.65 31.50 61.80 91.10 116.90

325 300.00 7.87 14.10 22.75 51.85 78.87 104.98 8.72 15.20 23.05 54.00 82.10 108.00320.00 9.06 15.04 24.21 55.50 82.74 112.96 10.02 16.24 25.09 56.75 84.82 114.82330.00 9.99 16.46 25.00 57.68 88.33 120.94 10.91 17.64 28.00 60.00 92.00 124.00340.00 11.05 17.44 27.95 60.27 92.58 125.50 11.34 18.58 28.89 61.71 94.04 128.31350.00 11.66 18.60 31.36 64.48 99.19 134.24 12.87 19.20 34.90 70.30 106.80 137.20

(B)

Reaction jet Horizontal insertion Vertically upward insertion

Reactordimensions

Gas velocityu0 (m/s)

Bathtemp, T (K)

Nozzle diameter, d0 (mm)

0.79 1.00 2.00 3.76 6.35 0.79 1.00 2.00 3.76 6.35Plume length, L (mm) Plume length, L (mm)

Rectangular steeltank (LR = 0.32;HR = 0.12;WR = 0.07)

203.4 1130 11.54 21.78 36.75 48.27 75.35 15.20 29.12 42.2 58.40 83.80

1273 15.56 33.38 51.64 83.52 113.18 18.80 39.08 58.8 92.18 124.271358 20.00 51.05 78.26 108.23 147.17 24.45 62.1 87.5 119.50 157.201415 28.70 68.43 109.67 137.80 175.90 32.80 81.03 113 148.70 192.03

250 1130 19.84 36.59 53.30 73.60 99.20 22.30 47.44 56.90 84.30 110.001273 25.00 52.89 72.81 105.60 140.06 30.50 60.01 79.00 114.70 145.901358 35.20 76.12 101.20 131.90 168.30 40.00 83.31 107.40 138.50 177.001415 44.60 89.07 121.55 154.90 196.24 48.00 97.80 126.70 162.30 201.40

300 1130 26.60 41.84 64.49 99.10 127.40 30.24 49.77 68.90 104.80 135.201273 38.30 59.15 91.08 122.90 156.21 42.60 67.72 93.50 129.40 164.101358 47.30 78.40 117.60 147.72 186.80 53.18 89.21 120.90 155.60 190.301415 57.40 97.14 137.80 169.97 207.20 62.10 111.01 141.78 175.40 214.06

325 1130 34.40 49.11 72.28 111.45 147.90 37.89 53.4 79.89 119.10 154.701273 48.00 64.48 104 139.30 177.91 52.74 72 110.2 144.00 186.301358 62.10 83.68 128.60 167.41 198.08 68.82 89.1 135 172.51 206.421415 80.50 107.55 149.70 186.90 221.80 87.52 116.02 158.16 194.13 228.03

from LHF and MFM model. Fig. 6 indicates that, the LHFmodel overestimate the centerline axialvelocities whereas thepredictions of present model are close to the predictions by

MFM model. Further, Fig. 7 reveals that the LHF model highlyunder-predicts the temperature in the plume zone. The predic-tions of the present model are close to those from MFM model.


0

20

40

60

80

100

120

140

PLU

ME

LE

NG

TH

, L (

mm

)2

1

45

6

321

45

6

3

0

20

40

60

80

100

120

140

0 10

21

45

6

3

PLU

ME

LE

NG

TH

, L (

mm

)

21

45

6

3

2 4 6 8 0 102 4 6 8NOZZLE DIAMETER, d0 (mm) NOZZLE DIAMETER, d0 (mm)

Fig. 3. Effect of nozzle diameter on the plume length for condensation jet at different bath temperatures and gas velocities. (A) u0 = 203.4 m/s; horizontalinsertion; (1) 300 K; (3) 330 K; (5) 350 K, vertically upward insertion; (2) 300 K; (4) 330 K; (6) 350 K (B) u0 = 250 m/s; horizontal insertion; (1) 300 K;(3) 330 K; (5) 350 K, vertically upward insertion; (2) 300 K; (4) 330 K; (6) 350 K (C) u0 = 300 m/s; horizontal insertion; (1) 300 K; (3) 330 K; (5) 350 K,vertically upward insertion; (2) 300 K; (4) 330 K; (6) 350 K (D) u0 =325 m/s; Horizontal insertion; (1) 300 K; (3) 330 K; (5) 350 K, vertically upward insertion;(2) 300 K; (4) 330 K; (6) 350 K.

0

40

80

120

160

200

240

321

67

8

5

PLU

ME

LE

NG

TH

, L (

mm

)

321

67

8

5

4

4

0

40

80

120

160

200

240

0 2 6

32

1

56

78

PLU

ME

LE

NG

TH

, L (

mm

)

321

67

8

5

44

NOZZLE DIAMETER, d0 (mm) NOZZLE DIAMETER, d0 (mm)1 3 4 5 7 0 2 61 3 4 5 7

Fig. 4. Effect of nozzle diameter on the plume length for reaction jet at different bath temperatures and gas velocities. (A) u0 =203.4 m/s; horizontal insertion;(1) 1130 K; (3) 1273 K; (5) 1358 K; (7) 1415 K, vertically upward insertion; (2) 1130 K; (4) 1273 K; (6) 1358 K; (8) 1415 K (B) u0 = 250 m/s; horizontalinsertion; (1) 1130 K; (3) 1273 K; (5) 1358 K; (7) 1415 K, vertically upward insertion; (2) 1130 K; (4) 1273 K; (6) 1358 K; (8) 1415 K (C) u0=300 m/s; horizontalinsertion; (1) 1130 K; (3) 1273 K; (5) 1358 K; (7) 1415 K, vertically upward insertion; (2) 1130 K; (4) 1273 K; (6) 1358 K; (8) 1415 K (D) u0 = 325 m/s;horizontal insertion; (1) 1130 K; (3) 1273 K; (5) 1358 K; (7) 1415 K, vertically upward insertion; (2) 1130 K; (4) 1273 K; (6) 1358 K; (8) 1415 K.


Tabl

e3

Eff

ect

ofor

ient

atio

non

the

plum

edi

men

sion

sat

vari

ous

nozz

ledi

amet

er,

nozz

leve

loci

tyan

dba

thte

mpe

ratu

re

Noz

zle

orie

ntat

ion

angl

eT

=11

30K

T=

1273

KT

=13

58K

T=

1415

K

wrt

.ho

rizo

ntal

L(m

m)

W(m

m)

V(m

m3)

L(m

m)

W(m

m)

V(m

m3)

L(m

m)

W(m

m)

V(m

m3)

L(m

m)

W(m

m)

V(m

m3)

d0

=0.

79m

m;u

0=

203.

4m

/s

90◦

15.2

00.

956.

8818

.80

1.10

11.0

424

.45

1.16

16.1

832

.80

1.23

24.0

760

◦14

.10

1.07

7.90

17.6

21.

1811

.86

22.9

91.

2417

.75

30.9

41.

3025

.47

45◦

12.9

81.

147.

9816

.44

1.25

12.2

621

.83

1.31

18.7

129

.82

1.39

27.3

30◦

11.5

41.

207.

8315

.56

1.33

13.0

020

.00

1.40

19.0

528

.70

1.45

29.6

2−3

0◦13

.91

1.11

8.08

16.7

21.

1911

.56

23.0

11.

2918

.80

29.9

81.

3426

.70

−45◦

10.0

21.

419.

1712

.56

1.48

13.5

218

.04

1.54

21.5

225

.72

1.62

33.3

6−9

0◦8.

831.

499.

6410

.92

1.62

14.1

616

.21

1.74

24.3

623

.54

1.82

37.4

4

d0

=0.

79m

m;u

0=

325

m/s

90◦

37.8

91.

1122

.89

52.7

41.

1936

.79

68.8

21.

2754

.89

87.5

21.

3474

.88

60◦

36.7

71.

2528

.38

50.9

71.

2841

.31

66.8

71.

3659

.49

85.3

81.

4280

.58

45◦

35.6

91.

3230

.57

49.3

31.

3645

.64

64.5

71.

4465

.69

82.7

91.

4986

.51

0◦34

.40

1.65

45.4

548

.00

1.70

71.3

262

.10

1.79

94.8

280

.50

1.89

139.

34−3

0◦35

.84

1.42

36.2

249

.79

1.48

52.4

567

.06

1.52

76.8

284

.18

1.58

103.

71−4

5◦29

.18

1.94

55.4

042

.26

1.99

80.9

857

.08

2.10

126.

0974

.67

2.19

174.

58−9

0◦28

.48

2.07

61.7

039

.12

2.15

89.7

954

.27

2.29

141.

1371

.56

2.42

206.

63

d0

=2

mm

;u

0=

203.

4m

/s

90◦

42.2

02.

8016

6.34

58.8

03.

1028

3.32

87.5

03.

2848

0.63

113.

003.

4065

7.48

60◦

40.5

43.

1220

1.23

55.7

93.

3931

7.72

84.7

93.

5052

9.60

112.

313.

6977

2.10

45◦

38.3

63.

4823

2.64

53.1

63.

5633

3.77

81.4

83.

6554

9.41

111.

093.

8483

0.48

0◦36

.75

3.70

239.

8151

.64

3.78

370.

8278

.26

3.89

595.

8510

9.67

4.00

881.

57−3

0◦36

.92

3.16

184.

3954

.87

3.35

314.

5683

.54

3.62

560.

2511

1.03

3.74

780.

16−4

5◦31

.29

3.90

241.

4047

.02

4.10

387.

4171

.11

4.56

743.

2798

.39

4.96

1154

.38

−90◦

27.4

54.

1524

3.24

39.9

14.

3939

4.27

55.1

04.

7575

4.12

89.9

45.

1312

09.7

2

d0

=2

mm

;u

0=

325

m/s

90◦

79.8

93.

2040

6.72

110.

203.

4867

6.35

135.

003.

6189

7.76

158.

163.

8011

41.7

360

◦77

.26

3.49

475.

5410

8.16

3.63

729.

4213

2.98

3.84

1007

.48

155.

323.

9312

13.9

045

◦74

.59

3.83

544.

2010

6.77

3.90

815.

0113

0.16

4.07

1097

.86

152.

254.

2113

75.3

10◦

72.2

84.

6278

2.92

104.

004.

8212

35.6

112

8.60

5.02

1655

.46

149.

705.

2620

64.5

4−3

0◦75

.51

4.00

602.

2410

8.50

4.12

942.

7813

0.91

4.26

1205

.34

156.

044.

4015

34.2

5−4

5◦66

.83

5.52

1019

.35

96.3

05.

6415

32.0

511

8.87

5.89

2095

.86

134.

696.

1024

72.3

6−9

0◦60

.25

5.81

1042

.37

87.5

05.

9415

93.9

310

6.52

6.14

2057

.09

123.

126.

3225

04.3

7


0

200

400

600

800

1000

1200

0

200

400

600

800

1000

1200

1400

1600

1800

0

500

1000

1500

2000

2500

1100 1150 1200 1250 1300 1350 1400 14500

500

1000

1500

2000

2500

3000

1100 1150 1200 1250 1300 1350 1400 1450

PLU

ME

VO

LU

ME

, V (

mm

3 ) 11

62

4

23

6 7

4

3

2

55

76

4

3

2

1

PLU

ME

VO

LU

ME

, V (

mm

3 ) 1

6

4

3

2

575

BATH TEMPERATURE, T (K) BATH TEMPERATURE, T (K)

Fig. 5. Effect of nozzle orientation on plume length for reaction jet at different nozzle diameters, bath temperatures, and gas velocities. (A) d0 = 0.79 mm;u0 = 203 m/s; (1) 90◦; (2) 60◦; (3) 45◦; (4) 0◦; (5) −30◦; (6) −45◦; (7) −90◦, (B) d0 = 0.79 mm; u0 = 325 m/s; (1) 90◦; (2) 60◦; (3) 45◦; (4) 0◦; (5) −30◦;(6) −45◦; (7) −90◦, (C) d0 = 2 mm; u0 = 203 m/s; (1) 90◦; (2) 60◦; (3) 45◦; (4) 0◦; (5) −30◦; (6) −45◦; (7) −90◦, (D) d0 = 2 mm; u0 = 325 m/s; (1) 90◦;(2) 60◦; (3) 45◦; (4) 0◦; (5) −30◦; (6) −45◦; (7) −90◦.

0.01

0.10

1.00

0.1 1.0 10.0 100.0

DIM

EN

SIO

NL

ESS

AX

IAL

VE

LO

CIT

Y, U

/U0

(-)

3

2

1

DIMENSIONLESS AXIAL DISTANCE, x/d0 (-)

Fig. 6. Comparison of centerline axial velocity variation for SF6-molten Lisystem between the predictions of present model and predictions by Chan(1993) using LHF and MFM model. (1) LHF model; (2) MFM model; (3)present model.

These variations in the centerline axial velocity and tempera-ture are attributed to the model development. LHF model ne-glects the buoyancy effect in the source term of the momentumequation. Further, it does not accommodate the effects of inter-facial momentum, or energy and mass exchange between the

0

1000

2000

3000

4000

0.10 1.00 10.00 100.00

3

2

1

BA

TH

TE

MPE

RA

TU

RE

, T (

K)

DIMENSIONLESS AXIAL DISTANCE, x/d0 (-)

Fig. 7. Comparison of centerline axial temperature variation for SF6-moltenLi system between the predictions of present model and predictions by Chan(1993) using LHF and MFM model. (1) LHF model; (2) MFM model; (3)present model.

phases. These drawbacks have been overcome while develop-ing MFM model. However, the prediction of the correct equi-librium state relationship for the species at specific operatingcondition, the determination of the mass averaged quantitiesfor PDF approach and modeling of SF6 gas–Li vapor reaction


results in the difference of the predictions of MFM model andthe present model.

4. Conclusions

(1) CFD simulations for the condensation (steam-water) aswell as the reaction jets have shown a good agreement withthe experimental data on plume length.

(2) The effect of nozzle diameter, nozzle gas velocity and bathtemperature on the plume length has been studied for bothcondensation and reaction jets. It can be observed that,the extent of plume length expansion is always higher forreaction jet than condensation jet in all the cases. In thecase of reaction jet, higher heat generation due to reactionleads to more vapors of liquid bath which increases theoverall plume length.

(3) The effect of nozzle orientations on the plume length hasbeen studied for reaction jet system. The variation in theplume length depends upon the effect of buoyancy forceand the availability of reactant in the plume region. Theplume length decreases with the changes of orientationfrom 90◦ (vertically upward) to −90◦ (vertically down-ward) orientation while the plume width and the volumeof the plume vapor follows the opposite trend.

(4) The analyses of the effect of nozzle diameter, nozzle gasvelocity and bath temperature on the plume length showthat with smaller nozzle diameter (d0 < 2 mm), the extentof increase in the plume length between both the systemis not significant. However, for higher values of all theseoperating parameters, the extent of increase in the plumelength for reaction jet is much higher than the condensa-tion jet. Further, horizontal orientation leads to controlledentrainment and proper distribution of products in the re-actor. Thus it is highly recommended to operate the reactorwith horizontal (0◦) orientation and with smaller nozzlediameter for both the system in order to get stable plume.

(5) The variation in the centerline axial velocity and center-line axial temperature profiles have been studied for bothcondensation and reaction jets. In the case of condensa-tion jet, the model shows good agreement with the experi-mental data of axial and radial temperature profiles. In thecase of reaction jet, the predictions from present model forcenterline axial velocity and temperature are close to theMFM model proposed by Chan (1993).

Notation

[A∗] saturation concentration of the solute gas in theliquid phase

B driving potential for condensation, (Cp(Tg −Tf )/(hg − hf )), dimensionless

[B0] concentration of liquid phase reactantc�1 model parameter in the turbulent dissipation,

Eq. (11)c�2 model parameter in the turbulent dissipation,

Eq. (11)

CD drag coefficientCP specific heat of liquid bath, J/kg KC� model parameter in the turbulent kinetic en-

ergyd0 internal nozzle diameter, mmdb bubble diameter, mmDA diffusivity of the solute gas in the liquid phaseDB diffusivity of liquid phase reacting speciesDAB diffusivity of A into B, m2/sg gravitational constant, m/s2

G0 steam mass flux at nozzle injector, kg/m2 sGf production term in kinetic energy equation,

Eq. (10)Gm critical steam mass flux at atmosphere,

kg/m2 sh average heat transfer coefficient, W/m2 KHf s enthalpy transferred from interface to liquidHgs enthalpy transferred from gas to interfaceHR height of reactor, mk turbulent kinetic energy per unit mass, m2/s2

kL mass transfer coefficient, m/sL plume length, mmLR length of reactor, mm0 mass flux at nozzle exit, kg/m2 smgf mass flux into liquid phase from gas phase,

kg/smp mass of particle, kgNp multiple number of phasesP pressure in bath liquid, N/m2

q sensible heat flux, W/m2

R rate of reaction, kmol/m2 sSi source term due to chemical reaction of com-

ponent i

St Stanton number, (h/CpG0), dimensionlesst time, sTf water temperature, KTg temperature of gasphase, KTs saturation temperature, Ku velocity component, m/sv particle velocity, m/sV volume of plume, m3

W width of plume, mWR width of reactor, mx axial direction, mYi local mass fraction of the species i

Z stoichiometric coefficient

Greek letters

� turbulent energy dissipation rate per unitmass, m2/s3

angle of reactor declination, deg� viscosity of bath liquid, kg/m s� density, kg/m3

�k model constant in Eq. (10)�� model constant in Eq. (11)�′ stoichiometric coefficient for reactant in the

reaction


�′′ stoichiometric coefficient for product in thereaction

�i molecular diffusivity, m2/s�ieff effective diffusivity, m2/s�Hr heat of reaction, kJ/kg

Subscripts

0 injector exit conditionf liquid phaseg gas phasei, j co-ordinate system indexp particlet turbulent

Acknowledgement

This work has been a part of the project program supportedby Department of Atomic Energy (DAE), Government of India(Project No. 47.01.01), Sanction No. CHE&TG/03/81, dated28/03/2003.

References

Chan, S.H., 1993. Multiphase turbulent liquid metal fuel combustion. ProgressEnergy Combustion Science 19, 105–143.

Chan, S.H., Tan, C.C., Zhao, Y.G., Janke, P.J., 1990. Li-SF6 combustion instored chemical energy propulsion systems. In: Twenty Third InternationalSymposium of Combustion, pp. 1139–1146.

Chan, S.H., Abou-Ellail, M.M.M., 1991. Multi-fluid model of turbulence forLi-SF6 submerged combustion. In: Proceedings of Third ASME-JSMEThermal Engineering Joint Conference, vol. 5, pp. 95–102.

Chen, L.D., Faeth, G.M., 1982. Condensation of submerged vapor jets insubcooled liquids. Transactions ASME Journal of Heat Transfer 104,774–780.

Cho, D.H., Armstrong, D.R., Bova, L., 1990. Experimental study of reactinggas jets in liquids: heat release effects. Chemical Engineering Science 45(2), 423–440.

Chun, H., Kim, Y.K., Park, J.W., 1996. An investigation of direct condensationof steam jet in subcooled water. International Communication Heat MassTransfer 23 (7), 947–958.

Danckwerts, P.V., 1970. Gas–liquid reactions, vol. 15. McGraw-Hill,New York.

Fortescue, G.E., Pearson, J.R.A., 1967. On gas absorption into a turbulentliquid. Chemical Engineering Science 22, 1163–1176.

Gulawani, S.S., Joshi, J.B., Shah, M.S., Prasad, C.S.R., Shukla, D.S., 2006.CFD analysis of flow pattern and heat transfer in direct contact steamcondensation. Chemical Engineering Science 61, 5204–5220.

Gulawani, S.S., Joshi, J.B., Shah, M.S., Prasad, C.S.R., Shukla, D.S., 2007.Submerged gas jet into a liquid bath: a review. Industrial and EngineeringChemistry Research 46, 3188–3218.

Kerney, P.J., Faeth, G.M., Olson, D.R., 1972. Penetration characteristics ofsubmerged jet. A.I.Ch.E. Journal 18 (3), 548–553.

Kim, H.W., Bael, Y.Y., Song, C.H., Park, J.K., Choi, S.M., 2001.Characterization of direct contact condensation of steam jets discharginginto subcooled water. International Journal of Energy Research 25,239–252.

Launder, B.E., Spalding, D.B., 1972. Mathematical Models of Turbulence.Academic Press, London.

Lamont, J.C., Scott, D.S., 1970. An eddy cell model of mass transfer intothe surface of a turbulent liquid. A.I.Ch.E. Journal 16, 512–519.

Luk, S., Lee, Y.H., 1986. Mass transfer in eddies close to air–water interface.A.I.Ch.E. Journal 32 (9), 1546–1555.

Parnell, L.A., Edmunds, D.G., Rogerson, D.J., 1989. Combustion instabilitiesof submerged oxidizer jets in liquid metal fuel. In: Proceedings of SecondONR Propulsion Meeting on Energy Materials Combust, CombustionDiagnostic Underwater Propulsion, pp. 188–195.

Weimer, J.C., Faeth, G.M., Olson, D.R., 1973. Penetration of vapor jetssubmerged in subcooled liquids. A.I.Ch.E. Journal 19 (3), 552–558.

Zhang, H.Q., Zhou, L.X., Chan, C.K., 2002. A double k–� and multi- pdfmodel for turbulent gas–liquid reacting flows. Fuel 81, 817–827.

Effect of nozzle diameter and its orientation on the flow pattern and plume dimensions in...

Documents

Transcript of Effect of nozzle diameter and its orientation on the flow pattern and plume dimensions in...