**6. Acknowledgement**

This work is supported by RFBR (10-05-00339, 10-05-91177, 09-05-00779, 11-05-00455, 10-01- 00435).

### **7. References**

116 Computational Simulations and Applications

circular, turbulent jet flow with a Gaussian profile of the mean streamwise velocity component in a fluid with stable, linear density stratification is considered which models the flow created in the far wake of a sphere towed in a stratified fluid at large Froude and Reynolds numbers. The DNS results show that at early times ( *Nt* 30 , where *N* is the buoyancy frequency) there occurs a collapse of the vertical velocity fluctuations which brings about the radiation of internal waves (IW). The characteristic spatial period of these waves is found to be close to the wavelength of the spiral instability mode of a non-stratified jet flow. The IW amplitude decreases with increasing the flow global Richardson number

becomes quasi-two-dimensional and is dominated by large-scale pancake vortices. At that stage, internal waves are superseded by non-propagating, columnar, small-amplitude buoyancy oscillations confined to a central vertical layer with a thickness of the order of the jet width. A linear model is proposed where the jet turbulence collapsing under the stabilizing effect of the buoyancy forces, is regarded as an impulsive source of IW radiation. The kinematics and dynamics of the internal waves observed in DNS are found to be in

Note that a relatively narrow IW frequency range ( 0 0 40 arccos / 60 *N* ), similar to the one observed in our DNS, has been also observed in mixing-box experiments (Dohan & Sutherland 2003), in a flow over a vertical obstacle (Sutherland & Linden 1998), during the collapse of a mixed patch (Sutherland et al. 2007) and in LES of a density-stratified boundary layer (Taylor & Sarkar 2007). In these works, several models were proposed to explain the observed IW frequency range, and among them, perhaps, two pertain to the considered case of IW radiation by a temporally developing turbulent jet flow. Dohan and Sutherland (2003) employed stability criteria derived by Sutherland (2001) for low- and high-frequency waves which show that the largest critical IW amplitude corresponds to the

> Ri = 1 Ri = 3

> > <QIW>2 1/2

0

Fig. 14. Temporal development of the volume-averaged dispersion of the IW source function normalized by its initial value for different Richardson numbers. Note that the graph on the

4

8

12

0 20 40 60

Nt

*iw* . At late times (*Nt* > 60) the jet flow

and is well described by the asymptotics 5.0 ~ *Ri*

0 10 20 30

t

<QIW> <sup>16</sup>

1/2

2

right is scaled with the buoyancy frequency.

good agreement with the model prediction.

waves propagating at <sup>0</sup> 45 .

0

4

8

12

16


**6** 

Mitsuru Tanaka

*Japan* 

*Kyoto Institute of Technology* 

**Numerical Study on Flow Structures and Heat** 

**Transfer Characteristics of Turbulent Bubbly** 

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

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

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

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

bubble-turbulence interaction (Tryggvason et al., 2011).

fully clarified especially in turbulent flows.

enhancement is discussed based on the numerical results.

**1. Introduction** 

clarified yet.

**Upflow in a Vertical Channel** 

