Time-averaged hydrodynamic equations of fluidization

Conference · Fri Jan 01 04:00:00 EST 1993

OSTI ID:6483904

O'Brien, T J ^[1]; Syamlal, M; Nicoletti, P ^[2]; Celik, I ^[3]

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1. USDOE Morgantown Energy Technology Center, WV (United States)
2. EG and G Washington Analytical Services Center, Inc., Morgantown, WV (United States)
3. West Virginia Univ., Morgantown, WV (United States). Dept. of Mechanical and Aerospace Engineering

A set of hydrodynamic equations proposed by Jackson described fluidized beds as interacting continua. Using either the theory of statistical mechanics or continuum mechanics, the granular material was represented as a continuum (or as many continua) which interacted with the interpenetrating fluidizing medium. The equations for each phase are formally similar to the familiar Navier-Stokes equations for a single fluid, except that there are interaction terms between the phases and the density of each phase is replaced by an effective density, the product of its intrinsic density and the volume fraction occupied by that phase. These equations have formed the basis of a hydrodynamic theory of fluidization. Since these equations are a coupled set of transient, multidimensional, partial differential equations, their solution requires extensive computational effort simplifying assumptions are made. The dimensionality of the equations is reduced to 1-D and/or the transient terms are dropped. In the former case, recirculation, which is an essential feature of the granular motion, can not be described. In the latter case, the fluctuating behavior. The purpose of this paper is to present time-steady hydrodynamic equations which still capture the effects of this essential aspect of fluidized-bed behavior. The obvious advantage is that the solution of time-steady equations is computationally more efficient than the calculation of a long time record, by solving the transient equations, and then calculating its time average. The disadvantage is that the effect of fluctuations must be accounted for by additional terms in the time-steady equations, which must be determined a priori. Time-steady equations, derived by merely dropping the transient term, neglect all (nonlinear) effects of bed fluctuations, which are a salient feature of the bed dynamics.

• Research Organization: USDOE Morgantown Energy Technology Center, WV (United States)
• Sponsoring Organization: DOE; USDOE, Washington, DC (United States)
• OSTI ID: 6483904
• Report Number(s): DOE/METC/C-93/7067; CONF-930830--18; ON: DE93013483
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
420400* -- Engineering-- Heat Transfer & Fluid Flow
DIFFERENTIAL EQUATIONS
EQUATIONS
FLUID MECHANICS
FLUIDIZED BEDS
MATHEMATICAL MODELS
MECHANICS
NAVIER-STOKES EQUATIONS
PARTIAL DIFFERENTIAL EQUATIONS