**1. Introduction**

118 Computational Simulations and Applications

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Turbulent bubbly flows have attracted a lot of attention because of their importance for many practical applications such as flows in chemical plants and nuclear power plants. Enhancement of heat transfer by bubble-induced turbulence also attracts a lot of attention from the view point of energy saving. Many studies have been conducted for the motion of bubbles and the characteristics of heat-transfer in turbulent bubbly flows. It is expected that the research on turbulent bubbly flows is accelerated by fully resolved simulations of bubble-turbulence interaction (Tryggvason et al., 2011).

The characteristics of bubbly upflow strongly depend on the motions of bubbles and resulting void fraction distribution in the flow. Serizawa et al. (1975) found that the local void fraction is high near the walls and is lower in the core region of upflow in a pipe. Liu (1993) also found in the experiments of turbulent bubbly upflow in a vertical channel that the void fraction has peaks near the walls for the bubbles smaller than 5-6mm, while it has a peak in the core of the channel for the bubbles larger than 5-6mm. Lu & Tryggvason (2008) also showed in their direct numerical simulations of turbulent bubbly upflow in a vertical channel that nearly spherical bubbles tend to concentrate on the near-wall regions, while strongly deformable bubbles tend to be expelled from the near-wall regions. They also showed that the turbulence structures are changed by the motions of bubbles. The detailed mechanism of turbulence modulation due to the bubbles, however, has not been fully clarified yet.

Some experimental studies have been conducted for heat-transfer enhancement by the injection of bubbles. Tamari & Nishikawa (1976) showed in their experiments of laminar natural convection heat transfer in water from a vertical plate that the heat transfer is enhanced by the injection of air bubbles. The enhancement of heat transfer by bubble injection was studied further in detail by Tokuhiro & Lykoudis (1994) and Kitagawa et al. (2008, 2010). However, the mechanism of the heat-transfer enhancement has not yet been fully clarified especially in turbulent flows.

In the present study, direct numerical simulations have been conducted for turbulent bubbly upflow between two parallel heating walls in order to clarify its heat transfer characteristics. The mechanism of the heat-transfer enhancement is examined by performing simulations with different values of control parameters. The performance of the heat-transfer enhancement is discussed based on the numerical results.

Numerical Study on Flow Structures and

is the viscous stress. Here,

and the harmonic average,

For stationary turbulence, the temporal average of

for (or energy equation) is described by

respectively. Here, *CP* denotes specific heat.

the wall shear stress and denotes the channel half width.

vertical direction.

where

and

where

supplemented with the continuity equation

Heat Transfer Characteristics of Turbulent Bubbly Upflow in a Vertical Channel 121

0, *<sup>k</sup> k u x*

*ij*

 

total driving force exerted on the fluids flowing through the channel, and

values for each grid cell are respectively given by the simple average,

 and  *j i*

 

*i j u u x x*

(1 ) ,

 

> 

**f** represents the volume force associated with the interfacial surface

 *F F* 

11 1 (1 ) , *d c F F*

of the two fluids. The subscripts *d* and *c* denote the dispersed and continuous phases, respectively. *p* is the pressure and *P* denotes the mean pressure linearly decreasing in the

tension of the bubbles, and *g* denotes the gravitational acceleration. represents the spatial average over the whole computational domain. The last term in Eq.(2) represents the

Since the mean temperature increases linearly downstream, the temperature *T* is decomposed as *T Gx* , where *G* denotes the mean temperature gradient in the streamwise direction and represents the temperature variance. The governing equation

<sup>1</sup> , *P k*

*C FC F C P d Pd*

11 1 (1 ) *d c F F kk k*

represent the volume-averaged heat capacity (per unit volume) and heat conductivity,

*t x xx*

(1 )

 

*C u Gu k*

. *dP <sup>g</sup> dx*

 

*k jj*

 

equals to

(3)

denote the density and viscosity of the fluid. Their

(6)

(7)

*c Pc* (9)

(10)

*<sup>W</sup>* represents

(8)

 *W* , where

*d c* (5)

(4)
