Ind. Eng. Chem. Res. 2003, 42, 3845-3850
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Steady-State Simulations of Liquid-Particle Food Flow in a Vertical Pipe Sevcan Kucuk Unluturk and Hamid Arastoopour* Department of Chemical and Environmental Engineering, Illinois Institute of Technology, 10 West 33rd Street, Chicago, Illinois 60616
Steady-state two-dimensional flow of food containing a liquid and particle mixture in a vertical pipe was simulated using the Lagrangian approach. The Fluent 5.4 computational fluid dynamic program was modified for liquid-particle food flow with the aid of user-defined subroutines and used in this simulation. The particle velocity profile and particle residence time were calculated at the outlet of the vertical pipe. The calculated results were compared with the experimental data of Lareo et al. (Powder Technol. 1997, 93, 23). Good agreement between calculation and experimental data indicates that numerical modeling has a good potential to predict the particle residence time and particle velocity profile, and, in turn, results in the potential reduction of costly experimentation in the food industry. 1. Introduction Particle-liquid flow plays an important role in transport processes in chemical and food processing engineering. In this study, we focused on the application of solid-liquid flow in food processing. There is an increasing demand in the food industry to transport food particles in the processing plants in order to increase the throughput of the plant.2 One of the applications of transport of food particles is the hydraulic transport of cut food pieces. Another application is the new sterilization process called ohmic heating, in which the liquid food mixture containing large particles is transported and electrically heated in the vertical pipe. The food processing industry relies heavily on experimentation due to public safety concerns and, as a result of this focus, has not taken full advantage of the advances in the fluid dynamics of multiphase flow systems and the numerical tools available in this area. Particle residence time and particle velocity are the key factors in designing food processing systems. However, today, most of the food processes including liquid flows containing large particles are designed based on the uniform laminar flow of particles. The objective of this paper is to introduce the computational fluid dynamic (CFD) concept and to use the multiphase flow approach to predict the particle residence time and particle and fluid velocity profiles. There are two modeling approaches in the literature for simulating a fluid-particle flow system: a two-fluid model (Arastoopour3), which considers particles as a separate phase similar to fluid, with a defined constitutive relation (e.g., kinetic theory), and a dispersed-phase model (DPM), which considers force balance for individual particles (Asakura et al.4). In this work, because of the importance of the individual particle residence time for food processes such as pasteurization, the DPM model is the most suitable approach. To achieve our goal, we used a commercially available CFD program * To whom correspondence should be addressed. Tel.: 312567-3041. Fax: 312-567-8874. E-mail:
[email protected].
(Fluent) as the computational tool and then we added the proper and needed forces acting on the particles and boundary conditions for our specific cases to the Fluent program with the aid of user-defined subroutines. 2. Governing Equations To predict the particle trajectories in the liquid phase, the Lagrangian approach was used. In this approach, the motion of each particle is governed by the individual particle dynamic equation. The influence of particles on the flow field of the continuous phase is considered by the momentum transfer of each particle. The momentum transfer from the dispersed phase to the continuous phase is obtained by computing the change in the momentum when an individual particle passes through each control volume. 2.1. Particle Phase. Equations 1 and 2 represent the Lagrangian form of the particle momentum equation. Equation 1 expresses the equilibrium between inertia, drag, gravity, and other forces exerted on the particle per unit mass of particle.
du bp ) dt
∑FB
∑FB ) FBA + FBB + FBD + FBG + FBP + FBS + FBM
(1)
dx b )b up dt
(2)
where F B A, F BB, F BD, F BG, F BP, FS, and F BM are the added (virtual) mass force, Basset history force, drag force, gravity, force due to the pressure gradient, Saffman lift force, and Magnus lift force, respectively. In a two-dimensional steady-state simulation of the vertical pipe (riser), the unsteady forces such as virtual mass, Basset force, and force due to pressure drop were neglected. Therefore, the Saffman lift force, Magnus lift force, drag force, and buoyancy force were the only forces that were considered in this study. The Saffman lift force is due to the pressure distribution developed on a
10.1021/ie0301076 CCC: $25.00 © 2003 American Chemical Society Published on Web 07/12/2003
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Ind. Eng. Chem. Res., Vol. 42, No. 16, 2003
sphere with uniform angular velocity in a fluid at rest and derived the following torque equation:
Table 1. Constants (a’s) for Equation 7 Rep
a1
