Particle dispersion in a turbulent natural convection channel flow
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 areandrespectively.
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⁎=(T−To)/(Th−Tc) 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)
- et al.
Particle transport in a small square enclosure in laminar natural convection
Journal of Aerosol Science
(2009) - et al.
Experiments on turbulent natural convection in an enclosed tall cavity
International Journal of Heat and Fluid Flow
(2000) - et al.
Direct numerical simulation of particle wall transfer and deposition in upward turbulent pipe flow
International Journal of Multiphase Flow
(2003) - et al.
Statistics of particle dispersion in direct numerical simulations of wall-bounded turbulence: Results of an international collaborative benchmark test
International Journal of Multiphase Flow
(2008) - et al.
Particle deposition from a natural convection flow onto a vertical isothermal flat plate
Journal of Aerosol Science
(1987) - et al.
Turbulent large-scale structures in natural convection vertical channel flow
International Journal of Heat and Mass Transfer
(2010) Aerosol particle transport in a natural convection flow onto a vertical flat plate
International Journal of Heat and Mass Transfer
(2001)
Cited by (8)
Direct numerical simulation of the fully developed turbulent free convection flow in an asymmetrically heated vertical channel
2023, International Journal of Thermal SciencesDeposition of corrosion products under pressurised water nuclear reactor conditions: The effect of flow velocity and dissolved hydrogen
2019, Corrosion ScienceCitation Excerpt :In these regions, clogging phenomena are frequently associated with a global reduction of the thermohydraulic performance of the heat exchanger [2]. Several investigations on the dependence between the fluid velocity on CRUD build-up are available in the literature [14–23]. Early works on the deposition of magnetite and silica particles on Stainless Steel and Alloy 800 [15–17], although carried out at low temperature, showed that the CRUD deposition process is dependent on flow velocity and pH. However, due to the low experimental temperature (seldom higher than 90 °C) the validity of these observations to PWR conditions is debatable.
Particle dispersion in a double-diffusive turbulent layer
2018, International Journal of Heat and Mass TransferFully resolved numerical simulation of interphase heat transfer in gas–solid turbulent flow
2017, International Journal of Heat and Mass TransferTransport of pollutant particles in a reservoir due to diurnal temperature variation
2014, International Communications in Heat and Mass TransferCitation Excerpt :This is the result of the relatively stronger flow at the higher Grashof numbers, which incurs a larger drag force to carry particles around. This observation is generally consistent with the literature (e.g. [8,10,16]). Here the adjusted R-square instead of the normal R-square is quoted as it is considered to be a better indicator of the quality of curve fitting [17].
Deposition Process and Equivalent Markov Motion of High-Inertia Particles in a Long Straight Pipeline
2021, Journal of Fluids Engineering, Transactions of the ASME