R. T. Lahey Jr., D. A. Drew (auth.), Jeffery Lewins, Martin's Advances in Nuclear Science and Technology PDF

By R. T. Lahey Jr., D. A. Drew (auth.), Jeffery Lewins, Martin Becker (eds.)

ISBN-10: 1461399254

ISBN-13: 9781461399254

ISBN-10: 1461399270

ISBN-13: 9781461399278

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L nd d + ~k. + ~k l nd d + ~k + ~k w i (147 ) w The momentum equation of interest in one-dimensional analysis is normally the linear momentum equation in the axial direction. This equation can be derived from Equation (147) by taking the dot product of each term in that equation with the unit vector, ~z. The resultant axial momentum equation is 1 +-A x-s <">p l + n • --z • T =k. l S'" -k. • n S"'· n k. -k. -z 1 8 + -- A l -z l x-s 8z • n [A Ct k (T x-s nd -z + ~k. l nd + ~k w d • ~ + ~k w ZZk n --z • n -z + T ~ ZZk) 1 n --z (148) In Equation (148) we have used the fact that - gk sine (149) where e is the angle made between the flow direction (n ) and the horizontal.

J(~,t) /:, 1 V Sf 1- a. (x,t) 1- If a. (x,t) ~k /:,~d k. 1 (m" /:'~k. ::'k dS, (65d) 1 ~k W (65c) dS, ~k 1- V a. (x,t) ~k (65b) dS, . q" V a. (x,t) ~k If 1 -1 ff 1 /:, 1 d /:, r\ -k. v. 1 w . ,9;"k dS ' . i . ::'k dS k/P k ) dS (65e) (65f) (65g) THREE-DIMENSIONAL CONSERVATION EQUATION 21 The conservation equations tabulated in Equations (36), (52) and (64) are instantaneous volume-averaged equations. It is well known that, even for single-phase turbulent flows, one must time-average these equations to achieve a tractable set.

I l Thus, i f . r ~k. l d (119a) ~k. k is a b. nd T vd • (119b) = v U. k -l ~k. -k. -k. k . Qi b. n ~l + (l-n) ~2 ' . 5 (13) (for both evaporation and condensation). As can be noted in Figure 4, for the case of ideal annular flow the parameter n represents the weighting relationship between the spatially averaged phasic velocities, ~k' and the interfacial velocity, U .. For highly turbulent flows, in which the velocity pr6file of phase-2 is fairly flat, we might expect n to be close to unity, for both evaporation and condensation.

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Advances in Nuclear Science and Technology by R. T. Lahey Jr., D. A. Drew (auth.), Jeffery Lewins, Martin Becker (eds.)

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