Results of a numerical study of heat and mass transfer in a gas-droplet wall jet developing over a surface with supplied heat flux are reported. The calculation model is based on an Eulerian/Eulerian approach using a turbulence model that allows for the dynamic and thermal interactions between the phases. This approach is based on using the kinetic equation of probability density function for the coordinates, velocities, and temperatures of droplets in the turbulent flow (Derevich, I. V., “The Hydrodynamics and Heat Transfer and Mass Transfer of Particles Under Conditions of Turbulent Flow of Gas Suspension in a Pipe and in an Axisymmetric Jet,” 2002, High Temp., 40, pp. 78–91). The effects due to many factors are traced, including the dispersed-phase concentration in the wall jet, the droplet diameter, the blowing ratio m=ρSUS/ρ1U1⁠, the main-flow temperature, and the wall heat flux. A considerable enhancement of heat transfer at relatively low mass concentrations of droplets MLS in the jet (more than twofold at MLS≤0.05⁠) has been revealed.

Issue Section:
Jets, Wakes, and Impingement Cooling
Keywords:
gas-droplet wall jet, two-fluid model, droplet evaporation, nonadiabatic cylindrical channel wall, channel flow, computational fluid dynamics, cooling, drops, external flows, jets, mass transfer, multiphase flow, turbulence
Topics:
Drops, Flow (Dynamics), Heat transfer, Turbulence, Evaporation, Temperature, Mass transfer, Heat
1.
Kutateladze
,
S. S.
, and
Leontiev
,
A. I.
, 1989,
Heat Transfer, Mass Transfer and Friction in Turbulent Boundary Layer
,
Hemisphere
,
New York
, p.
305
.
2.
Goldstein
,
R. J.
, 1971, “
Film Cooling
,”
Advance in Heat Transfer
, Vol.
7
,
T. F.
Irvine
 and
J. P.
Hartnett
, eds.,
Academic
,
New York
, pp.
321
–
379
.
3.
Volchkov
,
E. P.
, 1983,
Film Cooling
,
Nauka
,
Novosibirsk
, p.
259
, in Russian.
4.
Leontiev
,
A. I.
, 1999, “
Heat and Mass Transfer Problems in Film Cooling
,”
ASME J. Heat Transfer
0022-1481,
121
, pp.
509
–
527
.
Crossref
Search ADS
 
5.
Repukhov
,
V. M.
, 1980,
The Theory of Thermal Shielding of a Wall by Gas Injection
,
Naukova Dumka
,
Kiev
, p.
295
(in Russian).
6.
Ligrani
,
P. M.
,
Wigle
,
J. M.
, and
Jackson
,
S. W.
, 1994, “
Film-Cooling From Holes With Compared Angle Orientations
,”
ASME J. Heat Transfer
0022-1481,
116
, pp.
353
–
362
.
Crossref
Search ADS
 
7.
Vasiliev
,
A. A.
, 1988, “
The Effectiveness of Gas-Steam and Liquid Thermal Screen Behind a Tangential Slot
,”
Promyshlennya Teplotechnika
,
10
, pp.
36
–
38
(in Russian).
8.
Repukhov
,
V. M.
, and
Neduzhko
,
A. I.
, 1989, “
The Effectiveness of Gas-Steam and Liquid Thermal Screen Behind a Tangential and Inclined Slots
,”
Promyshlennya Teplotechnika
,
11
, pp.
31
–
37
(in Russian).
9.
Terekhov
,
V. I.
, and
Pakhomov
,
M. A.
, 2004, “
The Study of Structure, Heat and Mass Transfer in the Gas-Droplet Near-Wall Jet in a Tube
,”
Proceedings of the Third International Symposium on Two-Phase Flow Modelling and Experimentation
, Pisa, Italy, CD-ROM, Paper No. VEN 11.
10.
Terekhov
,
V. I.
, and
Pakhomov
,
M. A.
, 2004, “
The Modeling of a Tube Flow With Injection of Near-Wall Non-Isothermal Turbulent Gas-Droplets Jet
,”
Proceedings of the Fifth International Conference on Multiphase Flow ISMF-2004
, Yokohama, Japan, CD-ROM, Paper No. 135.
11.
Terekhov
,
V. I.
, and
Pakhomov
,
M. A.
, 2005, “
The Thermal Efficiency of Near-Wall Gas-Droplets Screens. I. Numerical Modeling
,”
Int. J. Heat Mass Transfer
,
48
, pp.
1747
–
1759
. 0017-9310
Crossref
Search ADS
 
12.
Li
,
X.
, and
Wang
,
T.
, 2006, “
Simulation of Film Cooling Enhancement With Mist Injection
,”
ASME J. Heat Transfer
0022-1481,
128
, pp.
509
–
519
.
Crossref
Search ADS
 
13.
Terekhov
,
V. I.
,
Sharov
,
K. A.
, and
Shishkin
,
N. E.
, 1999, “
An Experimental Study of Gas-Steam Mixing With a Near-Wall Gas-Drop Jet
,”
Thermophys. Aeromechanics
0869-8643,
6
, pp.
331
–
339
.
14.
Terekhov
,
V. I.
,
Sharov
,
K. A.
, and
Shishkin
,
N. E.
, 2003, “
Heat Shielding Characteristics of Gas-Droplets Screens in a Vertical Channel
,”
Izvestia Rossiyskoy Akademii Nauk., Ser. Energetika
, pp.
111
–
119
(in Russian).
15.
Terekhov
,
V. I.
,
Pakhomov
,
M. A.
,
Sharov
,
K. A.
, and
Shishkin
,
N. E.
, 2005, “
The Thermal Efficiency of Near-Wall Gas-Droplets Screens. II. Experimental Study and Comparison With Numerical Results
,”
Int. J. Heat Mass Transfer
,
48
, pp.
1760
–
1771
. 0017-9310
Crossref
Search ADS
 
16.
Talmor
,
E.
, and
Weber
,
N.
, 1970, “
Foreign-Gas Film Cooling Along Nonconverging and Converging Walls at Various Free-Stream Turbulence Levels
,”
Proceedings of the Fourth International Heat Transfer Conference IHTC-4
, Paris, France, Paper No. FC-8.7, pp.
1
–
11
.
17.
Li
,
X.
, and
Wang
,
T.
, 2007, “
Effects of Various Modeling Schemes on Mist Film Cooling Simulation
,”
ASME J. Heat Transfer
0022-1481,
129
, pp.
472
–
482
.
Crossref
Search ADS
 
18.
Li
,
X.
, and
Wang
,
T.
, 2006, “
Two Phase Flow Simulation of Mist Film Cooling With Different Wall Heating Conditions
,”
Proceedings of the 13th International Heat Transfer Conference
, Sydney, Australia, Aug. 13–18, Paper No. MPH-46, p.
12
.
19.
Ishii
,
M.
, 1975,
Thermo-Fluid Theory of Two-Phase Flows
,
Eyrolles
,
Paris
.
20.
Drew
,
D. A.
, 1983, “
Mathematical Modeling of Two-Phase Flow
,”
Annu. Rev. Fluid Mech.
,
15
, pp.
261
–
291
. 0066-4189
Crossref
Search ADS
 
21.
Shraiber
,
A. A.
,
Gavin
,
L. B.
,
Naumov
,
V. A.
, and
Yatsenko
,
V. P.
, 1990,
Turbulent Flows of Gas Suspensions
,
Hemisphere
,
New York
.
22.
Volkov
,
E. P.
,
Zaichik
,
L. I.
, and
Pershukov
,
V. A.
, 1994,
Numerical Modeling of Combustion of Solid Fuels
,
Nauka
,
Moscow
(in Russian).
23.
Crowe
,
C. T.
,
Sommerfeld
,
M.
, and
Tsuji
,
T.
,
Fundamentals of Gas-Particle and Gas-Droplet Flows
,
CRC
,
Boca Raton, FL
.
24.
Derevich
,
I. V.
, 2002, “
The Hydrodynamics and Heat Transfer and Mass Transfer of Particles Under Conditions of Turbulent Flow of Gas Suspension in a Pipe and in an Axisymmetric Jet
,”
High Temp.
,
40
, pp.
78
–
91
. 0018-151X
Crossref
Search ADS
 
25.
Terekhov
,
V. I.
, and
Pakhomov
,
M. A.
, 2004, “
The Numerical Modeling of the Tube Turbulent Gas-Drop Flow With Phase Changes
,”
Int. J. Therm. Sci.
,
43
, pp.
595
–
610
. 1290-0729
Crossref
Search ADS
 
26.
Terekhov
,
V. I.
, and
Pakhomov
,
M. A.
, 2006, “
Numerical Study of the Near-Wall Droplet Jet in a Tube With Heat Flux on the Surface
,”
J. Appl. Mech. Tech. Phys.
,
47
, pp.
1
–
11
. 0021-8944
Crossref
Search ADS
 
27.
Abramovich
,
G. N.
,
Girshovich
,
T. A.
,
Krasheninnikov
,
S. Yu.
,
Sekundov
,
A. N.
, and
Smirnova
,
I. P.
, 1984,
The Theory of Turbulent Jets
,
Nauka
,
Moscow
(in Russian).
28.
Mastanaiah
,
K.
, and
Ganic
,
E. N.
, 1981, “
Heat Transfer in Two-Component Dispersed Flow
,”
ASME J. Heat Transfer
,
103
, pp.
300
–
306
. 0022-1481
Crossref
Search ADS
 
29.
Hwang
,
C. B.
, and
Lin
,
C. A.
, 1998, “
Improved Low-Reynolds-Number k-ε̃ Model Based on Direct Simulation Data
,”
AIAA J.
,
36
, pp.
38
–
43
. 0001-1452
Crossref
Search ADS
 
30.
Haywood
,
R. J.
,
Nafziger
,
R.
, and
Renksizbulut
,
M.
, 1989, “
A Detailed Examination of Gas and Liquid Phase Transient Processes in Convective Droplet Evaporation
,”
ASME J. Heat Transfer
,
111
, pp.
495
–
502
. 0022-1481
Crossref
Search ADS
 
31.
Brailovskaya
,
I. Yu.
, and
Chudov
,
L. A.
, 1962, “
Solving the Boundary Layer Equations With Using Finite-Difference Technique
,”
Vychislitelnye Metody i Programmirovanie
, pp.
167
–
182
(in Russian).
32.
Fletcher
,
C. A. J.
, 1988,
Computational Techniques for Fluid Dynamics
, Vol.
2
,
Springer
,
Berlin
.
33.
Lebedev
,
A. V.
, and
Shvaikovsky
,
Yu. V.
, 1965, “
Experimental Study Velocity Distribution and Turbulence Characteristics in the Gas Screen
,”
High Temp.
,
3
, pp.
569
–
576
. 0018-151X
34.
Hartnett
,
J. P.
,
Eckert
,
E. R. G.
, and
Birkebak
,
R. C.
, 1961, “
Velocity Distribution, Temperature Distributions, Effectiveness, and Heat Transfer for Air Injected Through Tangential Slot Into a Turbulent Boundary Layer
,”
ASME J. Heat Transfer
,
83
, pp.
293
–
306
. 0022-1481
Crossref
Search ADS
 
35.
Seban
,
R. A.
, and
Back
,
L. H.
, 1962, “
Velocity and Temperature Profiles in Turbulent Boundary Layers With Tangential Injection
,”
ASME J. Heat Transfer
,
84
, pp.
255
–
265
. 0022-1481
Copyright © 2009
 by American Society of Mechanical Engineers
You do not currently have access to this content.