Influence of turbulence on heat and mass transfer

A turbulent flow is characterised by velocity fluctuations which overlap the main flow. The disturbed flow is basically three-dimensional and unsteady. At sufficiently high Reynolds numbers, the boundary layer is also no longer laminar but turbulent, such that the velocities, temperatures and concentrations all vary locally at a fixed position, as Fig. 3.14 shows for a velocity component wt. At every position it can be formed as the sum of a time-mean value (T here is the integration time) 

Only flows steady with respect to the time-mean properties will be considered here. The time-mean value of the fluctuation velocity is, by definition, equal to zero, w = 0. Correspondingly, pressure, temperature and concentration can also be split into mean and fluctuating values 

Incompressible flow will be presumed, so the splitting of the density into these two values is not required. 

Splitting the velocity into a mean value and a fluctuation velocity, w = in the continuity equation (3.93) leads to 

After averaging this over time remains 

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Most theoretical studies of heat or mass transfer in dispersions have been limited to studies of a single spherical bubble moving steadily under the influence of gravity in a clean system. It is clear, however, that swarms of suspended bubbles, usually entrained by turbulent eddies, have local relative velocities with respect to the continuous phase different from that derived for the case of a steady rise of a single bubble. This is mainly due to the fact that in an ensemble of bubbles the distributions of velocities, temperatures, and concentrations in the vicinity of one bubble are influenced by its neighbors. It is therefore logical to assume that in the case of dispersions the relative velocities and transfer rates depend on quantities characterizing an ensemble of bubbles. For the case of uniformly distributed bubbles, the dispersed-phase volume fraction O, particle-size distribution, and residence-time distribution are such quantities. 

Emnlsion polymerisation is influenced by system turbulence due to its heterogeneous nature. System effective agitation is necessary to keep the particles in dispersed phase, to prevent flocculation, to improve mass and heat transfer, phenomena that influence the reaction mechanism and kinetics as well as the final product properties and the properties of the product based on achieved latex. The influence of agitation on properties of the product using the obtained latex is presented, with emphasis on viscosity and rheological behaviour. Also presented is the influence of system initial rheology scaling up. 18 refs. 

Heat transfer and its counterpart diffusion mass transfer are in principle not correlated with a scale or a dimension. On a molecular level, long-range dimensional effects are not effective and will not affect the molecular carriers of heat. One could say that physical processes are dimensionless. This is essentially the background of the so-called Buckingham theorem, also known as the n-theorem. This theorem states that a product of dimensionless numbers can be used to describe a process. The dimensionless numbers can be derived from the dimensional numbers which describe the process (for example, viscosity, density, diameter, rotational speed). The amount of dimensionless numbers is equal to the number of dimensional numbers minus their basic dimensions (mass, length, time and temperature). This procedure is the background for the development of Nusselt correlations in heat transfer problems. It is important to note that in fluid dynamics especially laminar flow and turbulent flow cannot be described by the same set of dimensionless correlations because in laminar flow the density can be neglected whereas in turbulent flow the viscosity has a minor influence [144], This is the most severe problem for the scale-up of laminar micro results to turbulent macro results. 

In commercial manufacture, most batch operations require agitation to obtain optimum results. In many continuous operations, nonhomogeneous reaction masses are passed through tubular reactors under turbulent flow conditions in order to obtain good mixing and efficient heat transfer. In some cases, however, turbulent flow is not required to obtain a satisfactory amination. The continuous amination of chlorobenzene to produce aniline, described in Sec. X, is a case in point. The influence of the speed of stirring on the reaction velocity of a number of unit processes has been worked out by Huber and Reid, who found that three classes existed ... 

Mass transfer processes are complicated, usually involving turbulent flow, heat transfer, multiple phases, chemical reactions, unsteady operation, as well as the influences from internal construction of the equipment and many other factors. To study such complicated system, we propose a novel scientific computing framework in which all the relevant equations on mass transfer, fluid-dynamics, heat transfer, chemical reactions, and all other influencing factors are involved and solved numerically. This is the main task and research methodology of computational mass transfer (CMT). 

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