Direct numerical simulation of heat and mass transfer of spheres in a fluidized bed Zhi-Gang Feng ⁎, Samuel Gem Musong Department of Mechanical Engineering, University of Texas at San Antonio, TX, United States abstract article info Article history: Received 6 December 2013 Received in revised form 17 February 2014 Accepted 4 April 2014 Available online 24 April 2014 Keywords: Fluidized bed Heat and mass transfer Forced convection Direct numerical simulation Resolved discrete particle method Immersed boundary method We have developed a direct numerical simulation approach combined with the immersed boundary (DNS–IB) method for studying heat transfer in particulate flows. In this method, fluid velocity and temperature fields are obtained by solving the modified momentum and heat transfer equations, which are due to the presence of heat- ed particles in the fluid; particles are tracked individually and their velocities and positions are solved based on the equations of linear and angular motions; particle temperature is assumed to be constant. The momentum and heat exchanges between a particle and the surrounding fluid at its surface are resolved using the immersed boundary method with the direct forcing scheme. The DNS–IB method has been used to study the heat transfer of 225 heated spheres in a fluidized bed. By exploring the rich data generated from the DNS–IB simulations, we are able to obtain statistically averaged fluid and particle velocities as well as the overall heat transfer rate in the fluidized bed. Good agreement between the current study and the one by Pan et al. (2002) is found for the hydro- dynamic properties of the bed such as pressure gradients within the bed and the relationship between fluidiza- tion velocity and bed solid fraction. The particle-averaged Nusselt number is found to increase as the fluidization velocity increases and the bed height rises; particles at the entrance of the bed tend to have the maximum heat transfer rate because of the higher particle–fluid temperature gradients in this region; as the fluid moves upward in the bed, it gets warmer, which reduces particle–fluid temperature gradients and decreases the transfer rate of particles. Published by Elsevier B.V. 1. Introduction Fluidization involves a fluid flow that is supplied through a bed of solid particles at a sufficient velocity such that the entire suspension of solid particles behaves like a fluid. Because of enhanced particle–fluid heat transfer and chemical reaction rates in fluidized beds, fluidization is used in several industrial applications such as chemical reactors, coal combustion, fluid catalytic cracking, gasification, coating processes, and pyrolysis. Fluidized bed combustion, for example, offers several ad- vantages over conventional combustion technologies such as better heat transfer characteristics due to uniform particle mixing, lower temperature requirements, near isothermal process conditions, and continuous operation ability. To better understand the flow dynamics and heat transfer of particulate flows, numerical simulation could provide an efficient and accurate technique in predicting key operating parameters such as pressure drop, minimum fluidization velocity, solid fraction, and heat transfer coefficient without any prior testing. Most of the early studies on the heat transfer in fluidized beds lead to physical or mechanistic models based on experimental measurements. One of the first studies was done by Mickley and Fairbanks [18], who studied the heat transfer mechanism between fluidized beds and the surfaces they contact. They found the heat transfer coefficient to be pro- portional to the square root of the thermal conductivity of the quiescent beds of different gases for the same particle constituents. Decker and Glicksman [4] proposed a heat transfer model for immersed surfaces in large particle fluidized beds (1 mm or larger), showing an increase in the heat transfer rate by gas convection with increase in the particle size. Arters and Fan [1] studied solid–liquid mass transfer in fluidized beds and proposed an axial dispersion model. They developed a correla- tion which is able to accurately predict the mass transfer in both two- and three-phase fluidized beds. Basu and Nag [3] developed a more realistic hydrodynamic model to predict the heat transfer in a circulating fluidized bed (CFB) by estimating the residence time from Subbarao's [25] cluster theory; the predicted that heat transfer coefficient was expressed in terms of cluster residence time, which agrees well with the previous experimental data of Kiang et al. [15] and Martin [17] for different superficial velocities and solid circulating rates. The heat trans- fer for different geometry immersed in a fluidized bed has also been studied experimentally by Penny et al. [21] and Baskakov et al. [2]. The challenge with the experimental values of the heat transfer co- efficients in general is the low accuracy in-bed temperature measure- ments and oversimplifications in the flow models. In order to find an averaged heat transfer coefficient over the whole bed, one has to Powder Technology 262 (2014) 62–70 ⁎ Corresponding author. Tel.: +1 210 4585737; fax: +1 210 4586504. E-mail address: zhigang.feng@utsa.edu (Z.-G. Feng). http://dx.doi.org/10.1016/j.powtec.2014.04.019 0032-5910/Published by Elsevier B.V. Contents lists available at ScienceDirect Powder Technology journal homepage: www.elsevier.com/locate/powtec