Particle dispersion in a turbulent natural convection channel flow

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Abstract

Direct numerical simulations of particle dispersion in the turbulent natural convection flow between two vertical walls kept at constant but different temperatures are reported. It is assumed that the particles do not affect the flow (i.e. the dilute phase approximation is adopted). Particles with different levels of inertia, or Stokes numbers (0.843≤St≤17.45), are tracked according to the drag force imposed by the fluid. The gravity force is included for two cases, St=0.843 and St=17.45. The different levels of turbulence near the wall and near the center of the channel produce, as in isothermal turbulent channel or pipe flow, a larger concentration of particles near the wall. This effect becomes more important, and the deposition velocity of particles on the wall increases, as the particle inertia is increased. The simulations at St=8.38 and St=17.45 predict similar concentration profiles and deposition velocities according to the large inertia of these particles. The deposition velocities, obtained when the gravity force is ignored in the particle equations, follow the trend observed and measured for isothermal turbulent channel flows in the diffusion impaction regime. For the conditions considered, the gravity vector imposes a strong descending motion on the particles and this produces the increase of the particle concentration near the wall and a reduction of the deposition velocities in comparison with the results without the gravity force.

Highlights

► Particle dispersion in turbulent natural convection channel flow has been simulated. ► Turbulence produces a larger concentration of particles near the walls. ► Predictions of the deposition velocities are in the diffusion impaction regime. ► These predictions follow the same trend as in isothermal turbulent channel flow. ► Gravity reduces the deposition velocities and the particle velocity fluctuations.

Introduction

Flows that transport small particles, bubbles or drops can be found in many engineering, industrial and environmental situations. The determination of the rates and the mechanisms responsible for the dispersion and the deposition on solid surfaces of the dispersed phase has been the topic of many studies because they have important implications in practical problems. Examples of such problems are the fouling of heat transfer equipment, aerosol deposition on surfaces or the transport and fallout of airborne pollutants. A considerable fraction of these numerical, theoretical and experimental studies have been devoted to the analysis of the particle dispersion in forced convection flows in pipes and channels. Excellent and extensive reviews of the topic can be found in Michaelides (2006) and Guha (2008).

The analyses of particulate flows in natural convection are scarce in the literature. The deposition of aerosol particles in laminar natural convection boundary layer was considered by Nazaroff and Cass (1987), Tsai (2001) and Akbar et al. (2009) in laminar free convection in a square enclosure. The dispersion and the deposition of aerosol and small particles in turbulent natural convection flows are, to our knowledge, not available in the open literature. However these processes have implications, for example, in the air indoor quality and in the fouling of art pieces in museums and exhibitions (Nazaroff & Cass, 1987). The analysis of the behavior of small particles in canonical turbulent natural convection flows has also a fundamental interest because it can help to determine the relative importance of the mechanisms responsible for the particle fluxes and the deposition rates on the walls.

In this study we analyze by direct numerical simulation (DNS) the particle dispersion and wall deposition produced by the turbulent natural convection flow at low Rayleigh numbers between two vertical walls kept at different temperatures (Versteegh and Nieuwstadt, 1998, Versteegh and Nieuwstadt, 1999, Pallares et al., 2010). The simulations were carried out using a Lagrangian particle tracking technique. As a first step and to determine the separated influence of the different forces that may act in the particles, we performed simulations with the aerodynamic drag force and simulations with the drag force and the gravitational force.

The paper is organized as follows. In 2 Physical model, 3 Mathematical model, respectively, the physical and the mathematical models are described. Section 4 discusses the results focusing on the time-averaged particle distribution, the deposition velocities and the analysis of the velocity fluctuations perpendicular to the walls. Finally, the main conclusions are summarized in Section 5.

Section snippets

Physical model

Fig. 1 shows the coordinate system and the computational domain, which models an infinite channel in the x and the z directions. The natural convection flow, driven by the temperature difference imposed at the walls of the channel, is assumed to be hydrodynamically and thermally fully developed. The two walls of the channel located at y=−H/2 and y=H/2 are rigid, smooth and they are kept at constant but different temperatures. All physical properties of the fluid, with a Prandtl number (Pr=ν/α)

Mathematical model

The non-dimensional continuity, Navier–Stokes and thermal energy equations that govern the momentum and thermal energy of the fluid areuixi=0uit+uiujxj=pxi+Pr2uixj2+δi1RaPrTandTt+uiTxi=2Txi2respectively.

The scales used to obtain the non-dimensional variables are the channel width (H) and the thermal diffusion time (H2/α). The non-dimensional temperature is defined as T=(TTo)/(ThTc) where Th and Tc are the temperatures of the hot and the cold walls,

Results and discussion

Table 1 shows the different sizes of the particles and the non-dimensional parameters considered for the simulations. The value of the non-dimensional friction velocity, uτ=uτH/α=(Pr·dU/dy|w), which is used to compute the Stokes number and the non-dimensional deposition velocity is included in Table 1. It can be seen that two simulations considering the gravitational force [Ar≠0] are reported and they correspond to the smallest and to the largest particles for Ar=0.

A possible set of

Conclusions

The preferential concentration and wall-deposition rates of particles in a turbulent natural convection vertical channel flow have been analyzed. Particles with different inertia, or Stokes number, are accumulated differently in the near wall regions of the flow. It has been found that, for the conditions considered, as the Stokes number increases in the range 0.843≤St≤17.45 there is a progressive increase of the concentration of particles in the near wall regions of the channel as well as of

Acknowledgements

This study was financially supported by the Spanish Ministry of Science of Technology and FEDER under project DPI2010-17212.

References (14)

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