Heat transfer of gas–solid two-phase mixtures flowing through a packed bed

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Abstract

This paper reports an experimental study on both transient and steady-state heat transfer behavior of a gas–solid two-phase mixture flowing through a packed bed under constant wall temperature conditions. A logarithmic mean temperature difference (LMTD) method is used to process the temperature data to obtain the overall heat transfer coefficient. The influences of particle loading and gas flow Reynolds number are investigated. The results show that the introduction of suspended particles greatly enhances heat transfer between the flowing gas–solid two-phase mixture and the packed bed, and the enhancement increases approximately linearly with increasing particle loading. The heat transfer coefficient data are processed to give the Nusselt number, which is found to correlate well to the Reynolds number, the Archimedes number and the suspended particle loading ratio. A comparison of the data of this work with the published data reveals large discrepancy. Possible reasons for the discrepancy are discussed.

Introduction

Gas–solid two-phase mixtures flowing through a packed bed are of relevance to a number of industrial processes. Examples include waste heat recovery, adsorption of gas components from a dust laden gas and pulverized coal gasification and combustion in packed beds. Heat transfer can play a crucial role in determining the performance of these processes. Although there are numerous reports on the heat transfer behavior of single gas phase flowing through packed beds (Kunii and Suzuki, 1967, Gunn and De Souza, 1974, Wakao et al., 1979, Shent et al., 1981, Beasley and Clark, 1984, Ferreira et al., 2002, Collier et al., 2004, Wen and Ding, 2006) and gas–solid two-phase mixtures flowing through empty tubes (Depew and Kramer, 1973, Sun and Chen, 1988, Lu et al., 1994, Shi et al., 2003, Mansoori et al., 2004), very few studies have been found in the literature on the heat transfer between gas–solid two-phase mixtures and packed beds (Royston, 1971, Balakrishnan and Pei, 1978, Balakrishnan and Pei, 1979, Balakrishnan and Pei, 1990), as briefly reviewed below.

Royston (1971) investigated heat transfer between a vertical adiabatic column packed with 6.35 mm stainless steel particles and a downwards flowing gas–solid suspension. The packed bed was made of glass and had a diameter of 76 mm and a height of 178 mm. Zircon, ilmenite, glass ballotini and a catalyst ranging from 68 to 245μm were used as suspended particles. The experiments were performed with different loadings of fine particles in the gas at a Reynolds number ranging from 840 to 1400. The results demonstrated a significant enhancement of heat transfer in comparison with single gas phase cases and the enhancement ratio was shown to relate linearly to the solids loading ratio, Gscs/Ggcg:hmhg=1+0.26GscsGgcg,where hm and hg are, respectively, the heat transfer coefficients of gas–solid two-phase and gas phase flows, Gs is the solids phase mass flux, Gg is the gas phase flux, cs is the solids phase heat capacity and cg is the gas phase heat capacity. The enhancement ratio, however, was found to be insensitive to the gas Reynolds number and other thermal properties of suspended particles such as density and thermal conductivity.

Balakrishnan and Pei, 1978, Balakrishnan and Pei, 1979, Balakrishnan and Pei, 1990 performed experiments in a 50 mm diameter pyrex glass column with packed particles of 48 mm height. Different shapes of iron oxide, nickel oxide and two types of vanadium pentoxide with equivalent diameters between 5 and 13 mm were used as packed particles. Spherical glass beads with 0.1, 0.15 and 0.25 mm diameters were used as suspended particles. A microwave heating method was used to instantaneously heat the bed to a uniform temperature. The use of microwave method eliminated conduction between packed particles, which made possible the evaluation of convective heat transfer coefficient between the packed bed and gas–solid mixtures flowing through the bed. The experiments were carried out at a Reynolds number ranging from 400 to 1400. Again a large increase in the heat transfer coefficient was observed in comparison with the pure gas flow cases. The data of the convective heat transfer coefficient were processed to give the Nusselt number (Num) which was then related to particle Reynolds number (Rep), Archimedes number (Arm), solids loading ratio and the shape factor of the packing materials as follows:Num=0.016Arm0.25Rep0.51+GsGg0.68φs3.76,where Num=hmdp/kg, Rep=ρgvgdp/μg, Arm=dp3gρg(ρp-ρg)(1-ε)2/μg2, ρg and ρp are, respectively, the gas and solids densities, g is the gravitational acceleration, μg is the gas phase viscosity, ε is the voidage, dp is the packed particle diameter, φs is the particle shape factor, kg is the gas conductivity and vg is the superficial gas velocity.

The data obtained by Royston (1971) include contributions from both the convection and conduction due to a non-uniform temperature distribution in the packed bed. Balakrishnan and Pei, 1978, Balakrishnan and Pei, 1979, Balakrishnan and Pei, 1990 claimed to have achieved a uniform temperature distribution due to the use of microwaving heating so their data consisted of only the convection contribution. However, the bed height used by Balakrishnan and Pei, 1978, Balakrishnan and Pei, 1979, Balakrishnan and Pei, 1990 was very short due to size limit of the microwave facility. These limited studies used glass columns, which are rarely used in the industrial practice. The studies used an adiabatic boundary condition at the wall and only steady-state heat transfer coefficient was obtained based on temperature measurements at very few points. For example, the heat transfer enhancement ratio from Royston (1971) was only based on a matched pair of thermocouples inside the bed. The transient behavior and temperature distribution in the interior of the packed bed are unknown, where the former has significance to the start-up process of reactors and the latter is crucial for process control and optimization. This work investigates the heat transfer behavior of gas–solid mixture flowing through a packed bed under more industrially relevant conditions. Both transient and steady-state experiments are performed using a long stainless steel packed bed heated externally with electrical heaters. Relatively low Reynolds numbers e.g. <400 are used. The operating conditions are relevant to an on-going study on a new low-temperature hydrogen production process based on adsorption enhanced chemical reaction and solids circulating technologies for which heat supply to the packed bed reactor and heat transfer within the bed are identified as two important challenges (Wang et al., 2004; Ding et al., 2005a, Ding et al., 2005b).

Section snippets

Experiments

The experimental system used in this work is shown schematically in Fig. 1. It consisted of a packed column, a compressed air supply unit, a suspended particle collection tank, a suspended particle dispensing tank, a particle injection unit for introducing suspended particles into the packed bed, two cyclones in series for particle separation and various flow and temperature measurement and control units. The solids flow was controlled by a Venturi type of device; see Wang et al. (2004) and

Transient temperature profiles in the axial directions

Fig. 3, Fig. 4 show the temperature responses at different axial positions of the column center to the introduction of suspended particles under two conditions. In these experiments, the bed was first purged with air at a mass flux of Gg=1.37kg/m2s, which corresponds to a particle Reynolds number of 335. Suspended particles are introduced after a steady state is reached. In the two figures, the axial temperature profiles have been made dimensionless in the form of (Tax-T0)/(Tw-T0), where Tax is

Concluding remarks

An experimental investigation into gas–solid two-phase mixtures flowing through a packed bed has been carried out under constant wall temperature conditions. Both transient and steady-state heat transfer behaviors are investigated and the following conclusions are obtained:

  • When suspended particles are introduced into a steady-state packed bed, a transient process occurs and the length of the transient period depends on the solids loading and the Reynolds number. After the transient period,

Notation

Ahtheat transfer area, m2
ArmArchimedes number defined as Arm=dp3gρg(ρp-ρg)(1-ε)2μg2
cggas specific heat, J/kg K
cssolids phase specific heat, J/kg K
dppacked particle diameter, m
ggravitational acceleration, m/s2
Gggas flow flux, kg/m2s
Gssuspended solids flux, kg/m2s
hgheat transfer coefficient of pure gas flow, W/m2K
hmheat transfer coefficient of gas–solid two-phase flow, W/m2K
kfthermal conductivity, W/m K
mggas flowrate, kg/m2s
mssolids flowrate, kg/m2s
NumNusselt number defined as Num=hmdpkg
Qheat flux, W

Acknowledgments

The authors would like to extend their thanks to EPSRC for financial support under Grants GR/S524985. T.N. Cong would like to acknowledge the Vietnamese government for providing a PhD studentship. H.C. thanks Chinese Academy of Sciences for a visiting fellowship.

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Present address: Department of Engineering, Queen Mary University of London, Mile End Road, London E1 4NS, UK.

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