Solids flux profile

The thickness, 8, was found to be insensitive to particle concentration, gas velocity and height within the furnace. That suggests that the thickness results from a balance of solids internal circulation which is generally much higher than netthroughflow. If the local solids flux profile,... 

The reduced solids flux profile, JVI/JV, can be empirically correlated by [Rhodes et al., 1992]... 

Figure 4.40 Solid flux profiles of (A) the reference case (without permeation) with staggered arrangement of 61 membranes of 9.6 mm presented as a vector fieid and (B) iaterai profiles of the axial solid flux for the reference case without permeation and with a permeation ratio of 40% extraction and addition with constant inflow (100% —40% and 100%-f40%, respectively) and constant outflow (140%-40% and 60%+40%, respectively) at seven different vertical positions (100, 200, 300, 400, 500, 600, and 700 mm). Reprinted from De Jong et al. (2013) with permission from Eisevier.

For aU cases, the results for the 100% —40% extraction case, the reference case without permeation and the 100%+ 40% addition case are illustrated in Fig. 4.43. The membrane tubes are depicted in the graphs to highlight the differences between these cases. Please note that the arrangement with fewer membrane tubes (Fig. 4.43B) is not symmetric on a certain axial position, which is reflected in an asymmetric solid flux profiles. Furthermore, the inline arrangement has 10 rows of membrane tubes (compared to 11 rows of membrane tubes in the staggered arrangement) to keep the number of the membranes about the same (60 vs. 61). 

Radial profiles of upward particle momentum tend to be similar in shape to the solids flux profiles (e.g., Azzi et al., 1991). 

Couturier et al., 1991 3.15x3.15x23.8 Pressure profile, solids flux profile... 

Lafranechere Jestin, 1995 9.65 eq. dia. x 36.9 Pressure profiles, solids flux profiles, wall layer thickness... 

Issangya AS, Bai DR, Grace JR, Zhu JX. Solids flux profiles in a high density circulating fluidized bed riser. In Fan LS, Knowlton TM, eds. Fluidization IX. New York Engineering Foundation, 1998, pp 197-204. 

The design and development of a novel vibrating reed technique for on-line measurement of the sedimentation kinetics of two-phase dispersions is described. The technique has been tested in conjunction with a variety of solid/liquid and liquid/liquid dispersions with dense phase concentrations in the range 0-50 % v/v. Typical output include settling velocities, solids flux profiles as well as solids throughputs. Additionally, the performance of a number of sedimentation kinetics models proposed for dilute systems (0 - 2.81 % v/v) are evaluated by comparison with data obtained using the device. 

We make use of the fact that in the case of a settling dispersion, the hydrodynamic head decreases with time as the denser phase settles. Settling velocities and solids flux profiles may in turn be easily obtained by continuous monitoring of the resonant firequencies of a number of reeds positioned at set levels along the settling zone. 

Figure 20 Predicted flow regime diagram of the industrial MIP reactor, with solids flux as a function of the imposed total pressure drop at fixed gas flow rate. The snapshots of voidage profile refer to the transition, from left to right, the dilute transport, choking transition in between with different solids inventory, to the dense fluidization (Lu et al., 2007).

Equations 9.3-22 and 9.3-26 are the basic equations of the melting model. We note that the solid-bed profile in both cases is a function of one dimensionless group ijj, which in physical terms expresses the ratio of the local rate of melting per unit solid-melt interface JX /X to the local solid mass flux into the interface Vszps, where ps is the local mean solid bed density. The solid-bed velocity at the beginning of melting is obtained from the mass-flow rate... 

The required initial conditions for the dynamic model are the temperature and flux profiles of the gas and the solids streams down the entire length of the gasifier at time zero. 

Karri, S.B.R. Knowlton, T.M. A comparison of annulus solids flow direction and radial solids mass flux profiles at low and high mass fluxes in a riser. In Circulating Fluidized Bed Technology VI Werther, J., Ed. Dechema Frankfurt, Germany, 1999 71-76. 

In solid-liquid mixing design problems, the main features to be determined are the flow patterns in the vessel, the impeller power draw, and the solid concentration profile versus the solid concentration. In principle, they could be readily obtained by resorting to the CFD (computational fluid dynamics) resolution of the appropriate multiphase fluid mechanics equations. Historically, simplified methods have first been proposed in the literature, which do not use numerical intensive computation. The most common approach is the dispersion-sedimentation phenomenological model. It postulates equilibrium between the particle flux due to sedimentation and the particle flux resuspended by the turbulent diffusion created by the rotating impeller. 

Figure 10.7 (a) Symmetry and channel wall temperature profiles along the reactor length. Solid lines, without radiation dashed lines, with radiation, (b) Heat flux profile alongthe upperchannel wall when accounting for radiation. Heat flux into the channel is positive heat flux out of the channel is negative. 

Iso-kinetic sampling generally is used to measure solids mass flux profiles. The sampling probe is a thin tube inserted through the vessel wall. The tip of the tube is bent at a 90° angle so that it is parallel to the flow stream. The tube velocity is adjusted to match the surrounding velocity so as not to disturb the main flow. Solids enter the tube then are separated from the gas with a cyclone. 

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