**5. References**

Aulisa, E.; Manservisi, S.; Scardovelli, R. & Zaleski, S. (2003) A geometrical area-preserving Volume-of-Fluid advection method. *Journal of Computational Physics*, Vol.192, p.355-364

We still have many issues to resolve in order to clarify the heat transfer characteristics of turbulent bubby upflows. Firstly, the size of the computational domain is possibly too small to obtain the correct statistics of the turbulent bubbly flow since we utilized a minimal channel. In addition, statistical errors may be large since the number of bubbles is small and the computational time is relatively short to obtain the turbulence statistics. Larger and longer simulations are required to resolve these problems. Secondly, we set the density ratio at 0.1 and the viscosity ratio at 1.0, which are much higher than the corresponding values in an air-water system. The bubble motions and the generation of vortices due to the bubbles should be examined by changing the values of these two ratios. The continuous-phase Prandtl number of 2.0 employed in the present study is low compared with that of about 7 at room temperature. Simulations at higher Prandtl numbers are desirable. Thirdly, only two flow patterns (the bubbly and the droplet flows) have been simulated in the present study. As was shown in Lu & Tryggvason (2008), the bubble distribution consists of a core where the flow is essentially homogeneous, and a wall layer with a larger number of bubbles sliding along the wall in the case where the buoyancy effect is dominant. This interesting situation should be examined in the future study. The heat transfer

characteristics of bubbly drag-reducing flows is also an interesting topic to explore.

performed. We have obtained the following results.

turbulent channel upflow.

shear near the walls.

bubbles (or droplets).

Direct numerical simulations have been conducted for turbulent bubbly upflow between two parallel heating walls at a constant volume flow rate in order to clarify its heat transfer characteristics. For comparison, simulations for neutrally buoyant droplets have also been

The bubbles accumulate in the vicinity of the wall and slide along the wall in the

The droplets are distributed rather uniformly throughout the channel though some

The turbulence production is enhanced by the bubbles or the droplets in the near-wall

 The wall friction is increased by the injection of bubbles. This is mainly caused by the interfacial surface tension resulting from the deformation of the bubbles due to high

 The heat transfer is enhanced by the injection of bubbles (or droplets). This is because the turbulent heat flux is augmented by the generation of the vortices due to the

 The reduction in the Nusselt number due to the insulating effect of the bubbles is very small, while the low heat capacity of the gas inside the bubbles causes some amount of

 The performance of heat transfer enhancement is not good in the bubbly and droplet turbulent flows. However, the performance is improved in the bubbly flow if the

Aulisa, E.; Manservisi, S.; Scardovelli, R. & Zaleski, S. (2003) A geometrical area-preserving Volume-of-Fluid advection method. *Journal of Computational Physics*, Vol.192, p.355-364

buoyancy force exerted on bubbles is available as a driving force of the upflow.

The heat-transfer enhancement is more noticeable at higher Prandtl numbers.

tendency of accumulation in the vicinity of the walls is observed.

**3.4 Future research** 

**4. Conclusion** 

regions.

reduction.

**5. References** 


**7**

*Estonia* 

**Mathematical Modelling of the Motion of Dust-**

Fluidized beds are the units designed to provide fluid-solid contacting by the fluid flow through a bed of particles (Andrews and Arthur 2007). A number of thermal processes in technology take advantage of the importance of gas-solid interaction in fluidized beds to carry out gas-solid reactions, heterogeneous catalysis and particle drying. The gas-solid fluidization process in circulating fluidized beds is widely applied in many industrial branches. Characterization of the gas-solid particle flow in a circulating fluidized bed (CFB) riser is important for the process optimization. The particle size distribution has significant influence on the dynamics of gas-solid flow (He et al., 2008) along with another important property of the giving system, such as difference in the physical densities of the used materials. The gas-fluidized beds consist of fine granular materials that are subject to the gas flow from below giving the transport velocity that is large enough to overcome the gravity by the viscous drag force and thus the particles can suspend and be fluidized. When in the fluidized state, the moving particles work effectively as a mixer resulting in a uniform temperature distribution and high mass transfer rate, which are beneficial for the efficiency of many physical and chemical processes (Wang et al., 2005). For this reason the gasfluidized beds are widely applied in different industries: thermal, energy, chemical, petrochemical, metallurgical, and environmental industries in large-scale operations involving adhesion optimized coating, granulation, drying, and synthesis of fuels and base chemicals (Kunii & Levenspiel, 1991). In general, the lack of understanding of fundamentals of the dense gas–particle flows has led to severe difficulties in design and scale-up of these industrially important gas-solid contactors (van Swaaij, 1985). In most cases, the design and scale-up of fluidized bed reactors is a fully empirical process based on preliminary tests on pilot-scale model reactors, which is a very time consuming and thus expensive activity. Clearly, computer simulations can be a very useful tool to aid this design and scale-up

In the CFB furnaces the ash solids and inert materials like sand particles are mainly used as a solid heat carrier – separated in a hot cyclone and cooled after that in a heat exchanger

**1. Introduction** 

process.

**Laden Gases in the Freeboard of CFB Using**

**the Two-Fluid Approach** 

*Department of Thermal Engineering, Tallinn,* 

Alexander Kartushinsky1 and Andres Siirde2 *1Tallinn University of Technology, Faculty of Science, Laboratory of Multiphase Media Physics, Tallinn,* 

*2Tallinn University of Technology, Faculty of Mechanical Engineering,* 

