Transfer Phenomena in Turbulent Flow

Velocity distributions in turbulent flowthrough a straight, round tube vary with the flow rate or the Reynolds number. With increasing flow rates the velocity distribution becomes flatter and the laminar sublayer thinner. Dimensionless empirical equations involving viscosity and density are available that correlate the local fluid velocities in the turbulent core, buffer layer, and the laminar sublayer as functions of the distance from the tube axis. The ratio of the average velocity over the entire tube cross section to the maximum local velocity at the tube axis is approximately 0.7-0.85, and increases with the Reynolds number. 

The pressure drop AP (Pa) in turbulent flow of an incompressible fluid with density p (kg m ) through a tube of length L (m) and diameter d (m) at an average velocity of v (m s ) is given by Equation 2.10, namely, the Fanning equation  

Correlations are available for pressure drops in flowthrough pipe fittings, such as elbows, bends, and valves, and for sudden contractions and enlargements of the pipe diameter as the ratio of equivalent length of straight pipe to its diameter. 

When representing rates of transfer of heat, mass, and momentum by eddy activity, the concepts of eddy thermal conductivity, eddy diffusivity, and eddy viscosity are sometimes useful. Extending the concepts of heat conduction, molecular diffusion, and molecular viscosity to include the transfer mechanisms by eddy activity, one can use Equations 2.13-2.15, which correspond to Equations 2.2,2.3, and 2.5, respectively. 

In the above equations, H, fit, and fcv are eddy thermal diffusivity, eddy dif-fusivity, and eddy kinematic viscosity, respectively, all having the same dimensions (L2T ). It should be noted that these are not properties of fluid or system, because their values vary with the intensity of turbulence which depends on flow velocity, geometry of flow channel, and other factors. 

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While the stress tensor component tfor purely viscous fluids can be determined from the instantaneous values of the rate of deformation tensor 4, the past history of deformation together with the current value of 4, may become an important factor in determining t, for viscoelastic fluids. Constitutive equations to describe stress relaxation and normal stress phenomena are also needed. Unusual effects exhibited by viscoelastic fluids include rod climbing (Weis-senberg effect), die swell, recoil, tubeless siphon, drag, and heat transfer reduction in turbulent flow. 

We now take up the problem of estimating the heat transfer coefficients and the energy flux E in turbulent flow in a tube. As in our analysis of the corresponding mass transfer problem (Chapter 10), we consider the transfer processes between a cylindrical wall and a turbulently flowing n-component fluid mixture. We examine the phenomena occurring at any axial position in the tube, assuming that fully developed flow conditions are attained. For steady-state conditions, the differential energy balance (Eqs. 11.1.1 and 11.1.2) takes the form... 

Kostic M (1994) On turbulent drag and heat transfer reduction phenomena and laminar heat transfer enhancement in non-circular duct flow of certain non-Newtonian fluid. Int J Heat Mass Transfer 37 133-147... 

In system 1, the 3-D dynamic bubbling phenomena in a gas liquid bubble column and a gas liquid solid fluidized bed are simulated using the level-set method coupled with an SGS model for liquid turbulence. The computational scheme in this study captures the complex topological changes related to the bubble deformation, coalescence, and breakup in bubbling flows. In system 2, the hydrodynamics and heat-transfer phenomena of liquid droplets impacting upon a hot flat surface and particle are analyzed based on 3-D level-set method and IBM with consideration of the film-boiling behavior. The heat transfers in... 

As discussed in Section 2.1, in high-Reynolds-number turbulent flows the scalar dissipation rate is equal to the rate of energy transfer through the inertial range of the turbulence energy spectrum. The usual modeling approach is thus to use a transport equation for the transfer rate instead of the detailed balance equation for the dissipation rate derived from (1.27). Nevertheless, in order to understand better the small-scale physical phenomena that determine e, we will derive its transport equation starting from (2.99). 

Models may be one-, two-, or three-dimensional Of course, more advanced models describe the flow in the channels more accurately, but this is not required in all types of investigations. Section 2 in Chapter 8 provides an in-depth discussion of relevant flow phenomena that have to be taken into account when modeling monoliths. One-dimensional models can provide interesting information on mass and heat transfer effects in the washcoat [54]. However, if the development of a laminar flow in the monolith channels IS to be simulated, a two-dimensional model is needed. This is the case if multimonolith combustors are investigated [67]. This specific design, discussed in detail in Section IV.A, has a number of monoliths in senes, which enables vanation of monolith materials and cell density. Moreover, it leads to improved mass transfer by induced turbulence at the entrance of each monolith segment. 

The gas-side mass-transfer coefficients kefl and ko increase with liquid feed rate or with gas velocity at each given position in the venturi scrubber and decrease at constant liquid rate and gas velocity with increasing distance from the point of liquid injection (J7, VI1). The values ofkifl generally increase with increasing liquid flow rate or gas velocity (often referred to as the velocity at the throat). However, ki,a will sometimes exhibit a maximum when the gas velocity increases the explanation is that, at higher gas velocities, an increase in turbulence in the throat of the venturi results in the formation of droplets smaller than the thin filaments first formed at lower gas velocities. Internal circulation is reduced in these smaller droplets, and there is also a reduction in the size of the zone of intense turbulence. These two phenomena lead to a maximum for the values of/cL. as found experimentally by Kuznetsov and Oratovskii (K15) and Virkar and Sharma (VI1). The values of the effective interfacial area a increase with both gas and liquid flow rates. 

A fundamental shortcoming of the Chilton-Colburn approach for multicomponent mass transfer calculations is that the assumed dependence of [/ ] on [Sc] takes no account of the variations in the level of turbulence, embodied by r turb/, with variations in the flow conditions. The reduced distance y is a function of the Reynolds number y = (y/R )(//8) / Re consequently. Re affects the reduced mixing length defined by Eq. 10.2.21. An increase in the turbulence intensity should be reflected in a relative decrease in the influence of the molecular transport processes. So, for a given multicomponent mixture the increase in the Reynolds number should have the direct effect of reducing the effect of the phenomena of molecular diffusional coupling. That is, the ratios of mass transfer coefficients 21/ 22 should decrease as Re increases. 

The changes in heat transfer coefficient due to vibration are strongly dependent on the initial flow Reynolds number. This means that the effects of vibration are strongly influenced by the initial turbulence level of the liquid. Therefore, subsequent studies of the effects of vibration on convective heat transfer phenomena should give close attention to initial or residual turbulence levels in the fluid. 

Microreactors are developed for a variety of different purposes, specifically for applications that require high heat- and mass-transfer coefficients and well-defined flow patterns. The spectrum of applications includes gas and liquid flow as well as gas/liquid or liquid/liquid multiphase flow. The variety and complexity of flow phenomena clearly poses major challenges to the modeling approaches, especially when additional effects such as mass transfer and chemical kinetics have to be taken into account. However, there is one aspect that makes the modeling of microreactors in some sense much simpler than that of macroscopic equipment the laminarity of the flow. Typically, in macroscopic reactors the conditions are such that a turbulent flow pattern develops, thus making the use of turbulence models [1] necessary. With turbulence models the stochastic velocity fluctuations below the scale of grid resolution are accounted for in an effective manner, without the need to explicitly model the time evolution of these fine details of the flow field. Heat- and mass-transfer processes strongly depend on the turbulent velocity fluctuations, for this reason the accuracy of the turbulence model is of paramount importance for a reliable prediction of reactor performance. However, to the... 

The heat-transfer phenomena for forced convection over exterior surfaces are closely related to the nature of the flow. The heat transfer in flow over tube bundles depends largely on the flow pattern and the degree of turbulence, which in turn are functions of the velocity of the fluid and the size and arrangement of the tubes. The equations available for the calculation of heat transfer coefficients in flow over tube banks are based entirely on experimental data because the flow Is too complex to be treated analytically. Experiments have shown that, in flow over staggered tube banks, the transition from laminar to turbulent flow Is more gradual than in flow through a pipe, whereas for in-line tube bundles the transition phenomena resemble those observed in pipe flow. In either case the transition from laminar to turbulent flow begins at a Reynolds number based on the velocity in the minimum flow area of about 100, and the flow becomes fully turbulent at a Reynolds number of about 3,000. The equation below can be used to predict heat transfer for flow across ideal tube banks. 

Hsing et al. [66] presented simulations of two- and three-dimensional fluid flows, thermal fields, and chemical species concentrations in microreactors for the Pt-catalyzed NH3 oxidation in the T-shaped microreactor. Simulations and experiments showed good agreement and reactions were mass transfer limited. Therefore, it is not possible to obtain kinetic information, that is, details of the kinetic mechanism from the simulation data. Nevertheless, the comparison of predicted and experimental data demonstrates that it is possible to accurately predict and understand transport phenomena in microreactors, which is often difficult to obtain with macroscopic systems because of flow distributors, baffles, and turbulence. 

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