Download e-book for iPad: Computational Methods for Two-Phase Flow and Particle by Wen Ho Lee

By Wen Ho Lee

ISBN-10: 9814460273

ISBN-13: 9789814460279

This ebook describes mathematical formulations and computational equipment for fixing two-phase movement issues of a working laptop or computer code that calculates thermal hydraulic difficulties regarding mild water and quickly breeder reactors. The actual version additionally handles the particle and fuel move difficulties that come up from coal gasification and fluidized beds. the second one a part of this booklet offers with the computational tools for particle delivery.

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

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Additional info for Computational Methods for Two-Phase Flow and Particle Transport

Example text

126), the old time level n is used for αg ρg which is an explicit scheme. The viscous stress in the y-direction is Vτ y ≈ νs ∂ 2 (αg ρg vg ) ∂ 2 (αg ρg vg ) ∂ 2 (αg ρg vg ) . 127) ∂ 2 vg ∂ 2 vg ∂x2 , ∂y 2 and in Eq. 127). The finite difference of Eq. 127) is (Vτ y )ni,j+ 1 ,k = 2 νs {(αg ρg )ni+ 1 ,j+ 1 ,k [(vg )ni+1,j+ 1 ,k − (vg )ni,j+ 1 ,k ] 2 2 2 2 Δx2 − (αg ρg )ni− 1 ,j+ 1 ,k [(vg )ni,j+ 1 ,k − (vg )ni−1,j+ 1 ,k ]} 2 2 2 2 νs {(αg ρg )ni,j+1,k [(vg )ni,j+ 3 ,k − (vg )ni,j+ 1 ,k ] + 2 2 Δy 2 − (αg ρg )ni,j,k [(vg )ni,j+ 1 ,k − (vg )ni,j− 1 ,k ]} 2 2 νs {(αg ρg )ni,j+ 1 ,k+ 1 [(vg )ni,j+ 1 ,k+1 − (vg )ni,j+ 1 ,k ] + 2 2 2 2 Δz 2 − (αg ρg )ni,j+ 1 ,k− 1 [(vg )ni,j+ 1 ,k − (vg )ni,j+ 1 ,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.

4 World Scientific Book - 9in x 6in Computational methods for two-phase flow and particle transport The location of grid (i, j + 12 ) and its neighboring cells in 2D x–y coordinate. 130) 2 1 1 [(αg ρg )ni,j,k + (αg ρg )ni,j,k−1 ] 2 2 + 1 [(αg ρg )ni,j+1,k + (αg ρg )ni,j+1,k−1 ] . 131) 2 ws-book9x6 March 4, 2013 13:42 World Scientific Book - 9in x 6in ws-book9x6 Finite Differences of the Governing Equations Fig. 5 The grid index (i, k + coordinate. 1 ) 2 49 for plane j = j with its neighboring cells in x–z The viscous stress in the z-direction is Vτ z ≈ νs ∂ 2 (αg ρg wg ) ∂ 2 (αg ρg wg ) ∂ 2 (αg ρg wg ) .

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

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