$$$$ XBIF NOTICE CHAT 11/09/12 21:18:35 7124 DATE 11/09/12 Procedure XBIF Voir aussi : -------------- DESCRIPTION : ------------- This procedure solves the equations of a two-fluid model. Two phases coexist: a gas which is the carrier fluid and particles which are considered as a (particulate) gas. The main assumptions follow: - the particles are monodisperse, homogeneous and spherical - the particulate fluid is very diluated: its volumetric fraction is much less than one and one apprximates the carrier fluid volumetric fraction by one - the carrier fluid is incompressible - the pressure gradient exerted on each of the phases is the same, except a proportionality factor: the ratio of the carrier fluid and solid densities - the both phases coupling appears in their momentum equations through an interfacial transfer term which is more or less the Stokes drag or a formula with a drag coefficient; the coupling term is +/-K*(U-V) where U and V are respectively the carrier gas and particles velocities The dynamic problem is composed of two conservation equations (mass and momentum) for each of both phases. So, there are four equations and four unknowns: carrier gas and particulate gas velocities, total pressure and particles volumetric fraction. The equations to solve are listed bellow: | alphf = 1 ; div(U) = 0 | | dU/dt + (U.div)U = -grad(P)/rof + nuf*lapl(U) - Kf*(U-V) | | dV/dt + (V.div)V = -grad(P)/rop + nup*lapl(U) + Kp*(U-V) | + (1-rof/rop)*g | | d(alphp)/dt + div(alphp*V) = 0 with: rof carrier gas density rop solid density nuf carrier gas kinematic viscosity nup particles kinematic viscosity (those four physical properties are supposed to be constant) Kf carrier gas coupling coefficient Kp particles coupling coefficient alphf carrier gas volumetric fraction alphp particulate gas volumetric fraction U carrier gas velocity V particulate gas velocity P total pressure 1/ One solves the coupled momentum equations system (they are Navier-Stokes equations) with the semi-implicit algorithms of the both NS operators associated to the equations. The carrier gas is uncompressible. This is the way one gets the common to the both phases pressure. The coupling between the momentum equations of the carrier gas and the particles is treated explicitely. This is a numerical limit of the model: the coupling cannot be extremely strong (very small particles). If it were the case, one must conclude there is no-slip betwenn the gas and the particles. There vaelocities are equal. The informations are given in an EQEX type table (created by EQEX). This table has to have a 'PRESSION' input containing an EQPR type table (created by EQPR) where the informations relative to the pressure equation and its resolution are placed. Finally the table must have a 'KIZT' input, table created by the user and containing the CHAMPOINT-TRIO. 2/ One solves the mass conservation equation of the particles with the KONV operator following the informations given in an EQEX type table (created by EQEX). For more details, see the EQEX, EQPR, NS and KONV operators. SYNTAX : -------- XBIF Tab1 Tab2 Tab3 Flo1 Flo2 ; Tab1 is an EQEX type table (2 momentum equations) quantite de mouvement) Tab2 is an EQPR type table (pressure) Tab3 is an EQEX type table (particles continuity) Flo1 is a real (carrier gas coupling coefficient) Flo2 is a real (particulate gas coupling coefficient) REMARKS : --------- 1/ The user can find an example of data with a call to the XBIF procedure. It is xbif.dtc. 2/ Notice that in the present state of the modeling, there are no terms relative to the turbulence.
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