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Research Papers: Jets, Wakes, and Impingement Cooling

# Film-Cooling Enhancement of the Mist Vertical Wall Jet on the Cylindrical Channel Surface With Heat Transfer

[+] Author and Article Information
V. I. Terekhov

Kutateladze Institute of Thermophysics, Russian Academy of Sciences, Siberian Branch, 1 Academician Lavrent'ev Avenue, Novosibirsk 630090, Russiaterekhov@itp.nsc.ru

M. A. Pakhomov

Kutateladze Institute of Thermophysics, Russian Academy of Sciences, Siberian Branch, 1 Academician Lavrent'ev Avenue, Novosibirsk 630090, Russia

J. Heat Transfer 131(6), 062201 (Mar 30, 2009) (10 pages) doi:10.1115/1.3082404 History: Received March 25, 2007; Revised October 10, 2008; Published March 30, 2009

## Abstract

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.

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Copyright © 2009 by American Society of Mechanical Engineers
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## Figures

Figure 1

Schematic of the gas-droplet wall jet propagating along the wall in the presence of heat flux: (1) air and water droplets and (2) main air flow

Figure 2

Variation in momentum thickness at the injection of a single-phase jet; solid curve—calculation by formula 11, dashed line—calculation by this numerical model, and points—experimental data: (1) Ref. 33, (2) Ref. 34, and (3) Ref. 35

Figure 3

Heat transfer in the cooling region: (1) calculation by the numerical model and (2) as predicted by Eq. 14

Figure 4

Profiles of gaseous phase velocity at the injection of the gas-droplet wall jet: (1) x/S=0, (2) 25, (3) 50, (4) 100, (5) 150, and (6) 200 (qW=5 kW/m2, T1=373 K, TS=TLS=293 K, U1=50 m/s, dS=30 μm, m=0.8, MVS=0.014, MLS=0.05)

Figure 5

Variation in droplet velocity in the two-phase jet over the channel length: (1) x/S=0, (2) 25, and (3) 50. Conditions adopted in the calculations are the same as in Fig. 4.

Figure 6

Effect of droplet concentration MLS (a) and droplet diameter (b) on the gas-flow turbulence in the wall jet: (1) dS=10 μm, (2) 30 μm, (3) 50 μm, and (4) 100 μm(qW=5 kW/m2, T1=373 K, TS=TLS=293 K, U1=50 m/s, m=0.8, MVS=0.014, x/S=50)

Figure 7

Distribution of flow quantities in the two-phase film flow over the channel cross section: (1) ML/MLS, (2) d/dS, (3) Θ, (4) ΘH, (5) U/U1, (6) (MVW−MV)/(MVW−M0), and (7) profile of Θ=U/U0=(y/δt)1/7(qW=5 kW/m2, T1=373 K, TS=TLS=293 K,U1=50 m/s, m=0.8, MVS=0.014, MLS=0.05, dS=30 μm, x/S=50)

Figure 8

Profiles of the mass concentration of steam over the transverse coordinate: (1) x/S=25, (2) 50, (3) 100, (4) 150, and (5) 200. Conditions adopted in the calculations are the same as in Fig. 4.

Figure 9

Wall surface temperature versus the droplet concentration in the two-phase jet: (1) MLS=0, (2) 0.005, (3) 0.01, (4) 0.025, (5) 0.05, (6) TS=TLS=293 K, and (7) T1=373 K(qW=5 kW/m2, T1=373 K, TS=TLS=293 K, U1=50 m/s, m=0.8, MVS=0.014, dS=30 μm)

Figure 10

Heat transfer intensification ratio versus axial coordinate for air main-flow temperature: (1) T1=323 K, (2) 373 K, (3) 423 K, and (4) 473 K (qW=5 kW/m2, TS=TLS=293 K, U1=50 m/s, m=0.8, dS=30 μm, MVS=0.014, MLS=0.05)

Figure 11

Heat transfer in the gas-droplet flow for various values of the relative heat flux q¯×103: (1) 1.4, (2) 2, (3) 2.8, and (4) 5.5 (T1=373 K, TS=TLS=293 K, U1=50 m/s, m=0.8, MVS=0.014, MLS=0.05)

Figure 12

Effect of blowing ratio m on heat transfer augmentation: (1) x/S=25, (2) 50, (3) 100, and (4) 200 (qW=5 kW/m2, T1=373 K, TS=TLS=293 K, U1=50 m/s, MVS=0.014, MLS=0.05, x/S=50)

Figure 13

Heat transfer in gas-droplet jets with different initial droplet diameters: dS=10 μm, (2) 30 μm, (3) 50 μm, and (4) 100 μm

Figure 14

Variation in the droplet size over the cylindrical channel length: (a) for various particle sizes: (1) dS=10 μm, (2) 30 μm, (3) 50 μm, and (4) 100 μm(MLS=0.05); (b) for various dispersed-phase mass concentrations: (1) MLS=0.005, (2) 0.01, (3) 0.025, and (4) 0.05 (dS=30 μm); (c) cross-section profiles of droplet diameter: (1) x/S=0, (2) 25, (3) 50, (4) 100, and (5) 200 (qW=5 kW/m2, T1=373 K, TS=TLS=293 K, U1=50 m/s, m=0.8, MVS=0.014, MLS=0.05)

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