Download Particles, bubbles & drops: their motion, heat and mass by Stathis Efstathios E Michaelides PDF

By Stathis Efstathios E Michaelides

The sector of multiphase flows has grown by way of leaps and boundaries within the final thirty years and is now considered as an important self-discipline. Engineering purposes, items and strategies with debris, bubbles and drops have constantly grown in quantity and significance. increasingly more meetings, medical fora and archived journals are devoted to the dissemination of knowledge on move, warmth and mass move of fluids with debris, bubbles and drops. Numerical computations and “thought experiments” have supplemented such a lot actual experiments and loads of the product layout and checking out methods. The literature on computational fluid dynamics with debris, bubbles and drops has grown at an exponential expense, giving upward thrust to new effects, theories and higher realizing of the delivery methods with debris, bubbles and drops. This booklet captures and summarizes these kinds of advances in a unified, succinct and pedagogical means.

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Additional info for Particles, bubbles & drops: their motion, heat and mass transfer

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The term JhkVi denotes the momentum generated by the mass exchange between the material components h and k within the i-th phase. For example, during evaporation in a pipeline carrying a multicomponent mixture, the creation of more vapor results in higher volume to be conveyed through the pipe. This causes an increase of the velocity for both the liquid and the vapor phase and, hence, a momentum change. Usually combustion processes and evaporation processes tend to increase the velocity of the mixture, while condensation has the opposite effect.

This principle yields an inequality instead of an equation and determines the direction of all processes. In this chapter, the fundamental equations for a multiphase and multi-species material continuum will be formulated in integral as well as in differential form in an Eulerian framework. The fundamental equations for a single particle, bubble or drop inside a continuous medium will also be formulated in a Lagrangian way. An underlying premise of 23 24 Particles, bubbles and drops these forms of the equations is that all phases in the system are continua.

3) 42 Particles, bubbles and drops The quantity inside the parenthesis is the relative velocity of the immersed object with respect to the surrounding fluid. For an immersed object subjected to the gravity, the equation of motion reduces to: m - p = - C D p f A cs |u - v|(u - v) + mg . 4) The terminal velocity, vt, of the immersed object is reached when the acceleration vanishes (dv/dt=0) and the right-hand side of Eq. 4) is equal to 0. C. 5) V where the vectors r and v are with respect to the Lagrangian system of coordinates and T represents the total instantaneous torque acting on the surface A.

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