Turbulent convection

For a chemical reaction such as combustion to proceed, mixing of the reactants on a molecular scale is necessary. However, molecular diffusion is a very slow process. Dilution of a 10-m diameter sphere of pure hydrocarbons, for instance, down to a flammable composition in its center by molecular diffusion alone takes more than a year. On the other hand, only a few seconds are required for a similar dilution by molecular diffusion of a 1-cm sphere. Thus, dilution by molecular diffusion is most effective on small-scale fluctuations in the composition. These fluctuations are continuously generated by turbulent convective motion. 

Separation layer mixers use either a miscible or non-miscible layer between the reacting solutions, in the first case most often identical with the solvent used [48]. By this measure, mixing is postponed to a further stage of process equipment. Accordingly, reactants are only fed to the reaction device, but in a defined, e.g. multi-lamination-pattem like, fluid-compartment architecture. A separation layer technique inevitably demands micro mixers, as it is only feasible in a laminar flow regime, otherwise turbulent convective flow will result in plugging close to the entrance of the mixer chamber. 

The combined effect of turbulent convection from liquid with high subcooling and radiation for film boiling on a flat surface was analyzed by Hamill and Baumeister (1967), resulting in the expression... 

When the concentration profile is fully developed, the mass-transfer rate becomes independent of the transfer length. Spalding (S20a) has given a theory of turbulent convective transfer based on the hypothesis that profiles of velocity, total (molecular plus eddy) viscosity, and total diffusivity possess a universal character. In that case the transfer rate k + can be written in terms of a single universal function of the transfer length L and fluid properties (expressed as a molecular and a turbulent Schmidt number) ... 

This expression applies to the transport of any conserved quantity Q, e.g., mass, energy, momentum, or charge. The rate of transport of Q per unit area normal to the direction of transport is called the flux of Q. This transport equation can be applied on a microscopic or molecular scale to a stationary medium or a fluid in laminar flow, in which the mechanism for the transport of Q is the intermolecular forces of attraction between molecules or groups of molecules. It also applies to fluids in turbulent flow, on a turbulent convective scale, in which the mechanism for transport is the result of the motion of turbulent eddies in the fluid that move in three directions and carry Q with them. 

The general transport models for the turbulent convective transport of heat and mass can be expressed as follows ... 

The three models were calculated with the same chemical and physical inputs with the only exception of convection, for which we adopted the Full Spectrum of Turbulence convective model (FST, Canuto Mazzitelli 1991), and the MLT model (Vitense 1953) with two values of the free parameter connected to the mixing length a = 1.7 (the standard value, used to reproduce the evolution of the Sun) and a = 2.1. 

Turbulent convective burning of vertical plate. An approximate solution matched to data was given by Ahmad and Faeth [11]. The average burning rate mp for a distance x measured from the start of the plate is given by the formula below ... 

In addition, for turbulent convection it is commonly found that the Nusselt number is important, Nu = hcl/k. Since... 

This formulation can be compared with the multi-environment (ME) presumed PDF method discussed in Section 5.10. The principal difference between the two approaches is the treatment of turbulent convection. In the transported PDF simulation, turbulent convection is simulated by a random process. In the ME—PDF approach, it is handled using standard FV/FD discretization. 

Relaxation of initial probability density functions in the turbulent convection of scalar fields. The Physics of Fluids 22, 20-30. 

Image of the Sun taken by the SOHO spacecraft, showing the turbulent convection in the surface layers. Lighter areas are hotter and darker areas are cooler. Image courtesy of SOHO (ESA and NASA). 

The fundamental self-similarity laws of the evolution of freely-ascending laminar and turbulent convective flows have found numerous applications, above all in geophysics. 

It should be mentioned that, as is often the case in a first draft, the author based his treatment of the turbulent convection on certain assumptions which in fact were not necessary, in particular the semi-empirical concept of L. Prandtl. Moreover, even in the analysis of laminar convection, the author [cf., for example the transition from equation (9) to equation (10)], to derive the asymptotic laws, resorts to simplifications of the equations which are really not necessary. Actually, it is possible to manage without these assumptions so that Zeldovich s asymptotic laws (8), (8a), (11), and (11a) may be obtained by simple dimensional analysis under the most general assumptions. 

First, the role of system design on the details of convection and solute segregation in industrial-scale crystal growth systems has not been adequately studied. This deficiency is mostly because numerical simulations of the three-dimensional, weakly turbulent convection present in these systems are at the very limit of what is computationally feasible today. New developments in computational power may lift this limitation. Also, the extensive use of applied magnetic fields to control the intensity of the convection actually makes the calculations much more feasible. 

Diffusion combustion of small samples (<0.2-0.3 m) is mostly laminar, but as the combustion zone and, correspondingly, the flame height, increase the flame may become turbulent. Turbulent convective heat transfer is essential in the case of such flames. And finally, in medium and large-sized samples (>0.2-0.3 m) radiation is the prevailing heat transfer mechanism... 

Equations (45) and (46) are only two of many formulas that have been used to describe erosive burning [8]. Most of the formulas that have been suggested are based on physical concepts of influences of crossflow on propellant burning. Among these concepts is the idea that high external velocities produce a turbulent boundary layer (see Chapter 12) on the propellant surface and thereby effectively increase the thermal diffusivity of the gas, which in turn increases the rate of heat transfer to the propellant and hence the burning rate [99]. The idea that turbulent convective heat transfer from the hot combustion products outside the boundary layer provides an additive contribution to the heat flux reaching the propellant surface and,... 

The heat transfer mechanisms that are active in boiling in micro-channels can be summarized as follows (i) in bubbly flow, nucleate boiling and liquid convection would appear to be dominant, (ii) in slug flow, the thin film evaporation of the liquid film trapped between the bubble and the wall and convection to the liquid and vapor slugs between two successive bubbles are the most important heat transfer mechanisms, also in terms of their relative residence times, (iii) in annular flow, laminar or turbulent convective evaporation across the liquid film should be dominant, and (iv) in mist flow, vapor phase heat transfer with droplet impingement will be the primary mode of heat transfer. For those interested, a large number of two-phase videos for micro-channel flows from numerous laboratories can be seen in the e-book of Thome [22]. 

Adverse hydraulic conditions of settling such as turbulence, convective flows, mixing, etc. represent negative influences on emulsion separation. Significant improvement of separation efficiency for petroleum emulsions is achieved by the use of gravitational settling in combination with thermal, chemical and electrical methods. 

Natural convection and forced convection, depending respectively on the magnitude of buoyancy and the power of the pump or fan, may be laminar or turbulent. As we know from fluid mechanics, the streamlines of a laminar flow behave in an orderly manner, while the streamlines of a turbulent flow fluctuate irregularly about a mean flow. In this chapter, we shall deal with laminar convection. Turbulent convection will be left to Chapter 6. 

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