Ind. Eng. Chem. Res. 2005, 44, 2301-2315
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Dilute Gas-Solid Flows in Horizontal and Vertical Bends Tai Yong Quek, Chi-Hwa Wang, and Madhumita B. Ray* Department of Chemical and Biomolecular Engineering, National University of Singapore, 4 Engineering Drive 4, Singapore 117576, Singapore
Simulations of dilute-phase gas-solid flow in pipe bends of different radii of curvature were conducted using computational fluid dynamics (CFD). The renormalization group k- turbulence model was used for the flow calculations of the continuous phase while the Lagrangian approach was used for calculating the discrete-phase trajectory. The model predictions were first validated with particle concentration and velocity measurements adopted from the literature. Subsequently, the deposition pattern of fine particles in horizontal bends was compared with the model predictions. Other flow quantities such as secondary flow intensity and residence time distribution of the particles in the bend were also investigated. Simulation indicates that the rope formation in vertical bend is stronger for the longer bend radius than that in the shorter radius and inlet turbulence intensity (1500 kg/m3). The particle distribution with varying sizes can also be seen in Figures 20a-c, where monodispersed particle sizes flow through each horizontal bend r/D ) 2. The large particles (Figure 20a) were thrown to the outer wall due to the centrifugal force in the bend, while the small particles (Figure 20c) were more evenly spread, with only small qualitative and quantitative changes in the concentration profiles before and after the bend. There were also differences in the roping phenomena with varying particle diameters. The largest and smallest particles did not form a concentrated rope for more than three diameters distance after bend. The largest (200 µm) settled to the lower half of the pipe due to gravity, while the smallest (2.3 µm) particles dispersed through the cross section. Size differences, therefore, affect the particle distribution as they go through a bend, and roping is a more extreme case of such uneven distribution. Conclusion The model presented could be used to simulate two-phase gas-solid flows, which incorporates a RNG k- turbulence to model gas-phase turbulence, the Lagrangian frame of reference for solid-phase trajectory calculations, and an interphase momentum coupling equation to couple the two phases. Despite the existing limitations such as absence of particle-particle interac-
Ind. Eng. Chem. Res., Vol. 44, No. 7, 2005 2315
tions and cohesive forces, the model can capture basic features of dilute two-phase flow. The model was successfully validated for the roping phenomenon of Yilmaz and Levy,5 which showed both qualitative and quantitative agreements with the experimental results. Particle concentration and velocities correlate well because simulated particle ropes exhibited similar concentrations and thicknesses to those of the experimental rope after negotiating the bends. The rope formation in the vertical bend is stronger for the longer bend than that for the shorter bend. The solid deposition patterns of Ruevekamp et al.8 were correlated qualitatively with the simulation results obtained using the present model. Areas of low velocity before and after the bends in the simulations correlate well with the actual areas of deposition found in the experiments. Simulations conducted in this study indicate the following observations hitherto unquantified for pneumatic conveying in bends: (i) secondary velocity near the inner wall after a smooth horizontal bend, which assists in resuspension of the deposited dust, decreases with the increasing radius of curvature of the bend; (ii) the simulated mean residence time of the particles, which can influence the exposure time of the particles to the inertial forces in the bend, increases with the increasing radius of curvature; (iii) effects of inlet turbulence parameters are negligible on the particle dispersion after the bend; (iv) particle diameter is found to have the greatest effect on the flow dispersion after the bend. Nomenclature D ) inner diameter of the pipe, m I ) turbulent intensity, ratio of root-mean-square (rms) fluctuating velocity to rms velocity Dp ) diameter of the particle, µm Fp ) density of the particle, kg m-3 m ˘ p ) solid mass flow rate, kg s-1 x ) distance measured from the pipe wall, m (shown in Figures 1 and 2) ∆tj ) time step, s r ) radius of curvature of pipe bend, m Up ) mean velocity of the fluid at point P, m s-1 kp ) turbulent kinetic energy at point P, m2 s-2 ) dissipation of kinetic energy, m2 s-3 yp ) distance from point P to the wall, m µl ) laminar viscosity of the fluid, kg m-1 s-1 µt ) turbulent viscosity of the fluid, kg m-1 s-1 τw ) wall shear stress, N m-2 ug ) gas-phase rms velocity, m s-1 ugi ) gas-phase local velocity in the ith direction, m s-1 up ) solid particle rms velocity, m s-1 Cp ) solid particle concentration, kg m-3 z ) distance from the exit of bend, position in straight section after the bend, m
µg ) viscosity of the fluid, kg m-1 s-1 φ ) shape factor, φ ) s/S, where s is the surface area of a sphere having the same volume as the particle and S is the actual surface area of the particle
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Received for review April 20, 2004 Revised manuscript received January 7, 2005 Accepted January 19, 2005 IE040123I
