Computational Methods for Two-Phase Flow and Particle by Wen Ho Lee

By Wen Ho Lee

This e-book describes mathematical formulations and computational equipment for fixing two-phase move issues of a working laptop or computer code that calculates thermal hydraulic difficulties with regards to gentle water and quickly breeder reactors. The actual version additionally handles the particle and gasoline stream difficulties that come up from coal gasification and fluidized beds. the second one a part of this publication bargains with the computational tools for particle shipping.

Readership: Undergraduate and graduate scholars learning mechanical engineering; pros facing fluid mechanics, nuclear physics, and plasma physics of their day by day encounters -- quite using two-phase flows, and particle shipping.

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For example, if one is solving the gas momentum equations, the liquid phase velocity can be used for the interfacial velocity. For separated or counter-current flow, the interfacial velocity should be calculated differently. The interfacial temperature used for computing the energy transfer between the phases can be chosen with the same fashion as the interfacial momentum transfer. Therefore, one will choose liquid temperature as the interfacial temperature to obtain the interfacial energy transfer for solving the gas energy equation.

The finite difference approximation of Eq. 136) is n (αg ρg Ig )n+1 i,j,k = (αg ρg Ig )i,j,k + Δt [ αg ρg ug Ig Δx n i− 12 ,j,k − αg ρg ug Ig + Δt [ αg ρg vg Ig Δy n i,j− 12 ,k + Δt [ αg ρg wg Ig Δz n i,j,k− 12 + n+1 n (αg )i,j,k pi,j,k Δt (ρg )i,j,k − (ρg )i,j,k (ρg )i,j,k Δt − αg ρg vg Ig n i,j+ 12 ,k ] − αg ρg wg Ig n i,j,k+ 12 ] n i+ 12 ,j,k ] March 4, 2013 13:42 52 World Scientific Book - 9in x 6in ws-book9x6 Computational methods for two-phase flow and particle transport 1 ( ρg u g Δx 1 ( ρg vg + Δy n i+ 12 ,j,k − ρg u g n i− 12 ,j,k ) n i,j+ 12 ,k − ρg vg n i,j− 12 ,k ) + 1 ( ρg wg ni,j,k+ 1 − ρg wg ni,j,k− 1 ) 2 2 Δz n n (ug )i+ 1 ,j,k − (ug )i− 1 ,j,k 2 2 − (ρg )ni,j,k Δx + + (vg )ni,j+ 1 ,k − (vg )ni,j− 1 ,k 2 2 Δy + (wg )ni,j,k+ 1 − (wg )ni,j,k− 1 2 2 Δz + Δt[(Sg )ni,j,k + (Λg )ni,j,k ] + (Δt)Ri,j,k [(T )i,j,k − (Tg )i,j,k ] Δt n n [ kg αg ni+ 1 ,j,k (Tg,i+1,j,k − Tg,i,j,k ) 2 Δx2 n n − Tg,i−1,j,k )] − kg αg ni− 1 ,j,k (Tg,i,j,k + 2 + Δt [ kg αg Δy 2 − kg αg n n i,j+ 12 ,k (Tg,i,j+1,k n n i,j− 12 ,k (Tg,i,j,k n − Tg,i,j,k ) n − Tg,i,j−1,k )] Δt n n [ kg αg ni,j,k+ 1 (Tg,i,j,k+1 − Tg,i,j,k ) 2 Δz 2 n n − Tg,i,j,k−1 )] .

The drag functions for chunk flow, plug flow, and counter current flow are more complicated and will not be addressed in this book. The viscous stresses appeared in Eqs. 80) for the gas phase. 83) for the liquid phase. The mean resistive velocity u for a phase and the effective drag function for that phase K are defined in terms of the interaction between phases Kn K ≡ K n with K n > 0. 85) K2 = K21 + K22 = K21 , since K22 = 0 . 86) Also Ku ≡ K n un . 88) K2 u2 = K21 u1 . 89) For the condition of momentum conservation, it is necessary K n = Kn ⇒ K12 = K21 etc.

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