Flow and Turbulence

The experimental and mathematical perception of flow conditions in a stirred tank are of great importance for a deeper understanding of mixing processes in different mixing operations and thereby for well-founded scale-up. 

The three dimensional flow field in a tank characterized by secondary flow patterns was long inaccessible to theoretical treatment. It is therefore not surprising that it was first tackled by the statistical theory of turbulence [20, 57, 209, 289]. 

Later numerical methods were applied, which are based on the laws of conservation of mass and momentum, and are restricted to stationary, isothermal and 

The stirrer is thereby approximated for the calculation of turbulent flow by a tangential jet [288, 441], and for laminar flow by a cylinder [46-48, 50, 98J. The stirred tank is split up into a number of zones, to which one can assign characteristic flow patterns and analytically describable velocity profiles. Models with up to 8 zones have been developed, but only two models (for stream ejected by the stirrer and for circulation flow) have been able to explain the experimental results satisfactorily [440]. 

Currently a wide range of calculation methods and powerful computers are available. In the EU, 13 research groups have joined forces to tackle the numerical and experimental investigation of flow conditions in stirred tanks [122]. Both commercially obtainable CFD codes and those further developed in the universities are available (CFD - Computational Fluid Dynamics). Simple k-s and advanced turbulence models are utilized and compared with one another k - kinetic energy per mass s - stirrer power per mass). The flow produced by the stirrer is described by approximate calculations of the 3-dimensional (3D), non-steady state circulation of the stirrer paddles. 

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Corrosion involving nonoxidizing acids can be highly sensitive to flow. Thus regions of high flow and turbulence are often more severely attacked than more quiescent regions. Weirs, lips, and other flow obstructions increase turbulence and thus corrosion. Pipe elbows, tees, and joints are frequently attacked. Outer curves at pipe bends often are more severely wasted than inner bends. 

GASFLOW models geometrically complex containments, buildings, and ventilation systems with multiple compartments and internal structures. It calculates gas and aerosol behavior of low-speed buoyancy driven flows, diffusion-dominated flows, and turbulent flows dunng deflagrations. It models condensation in the bulk fluid regions heat transfer to wall and internal stmetures by convection, radiation, and condensation chemical kinetics of combustion of hydrogen or hydrocarbon.s fluid turbulence and the transport, deposition, and entrainment of discrete particles. 

Note Equation (4.241) characterizes diffusion when the mixture element is in steady state with no turbulence. Diffusion in a pipe can be represented by Eq. (4.241) in convective mass transfer the flow and turbulence are important. 

Figures 4.34 and 4.35 represent two extreme cases. Drying processes represent the case shown in Fig. 4.34 and distillation processes represent Fig. 4.35. Neither case represents a convective mass transfer case while the gas flow is in the boundary layer, other flows are Stefan flow and turbulence. Thus Eqs. (4.243) and (4.244) can seldom be used in practice, but their forms are used in determining the mass transfer factor for different cases.

This equation, which is called the Deutsch equation, has been shown to be a useful tool for estimating the performance of electrostatic precipitators. An interesting detail in the Deutsch equation is the exponent, which is equal to the collection efficiency of a laminar flow system. The equations based on laminar flow and turbulent flow can be assumed to be the extreme conditions, and the true situation is somewhere in between these two cases (see Fig. 13.1,5). 

The major mechanism of a vapor cloud explosion, the feedback in the interaction of combustion, flow, and turbulence, can be readily found in this mathematical model. The combustion rate, which is primarily determined by the turbulence properties, is a source term in the conservation equation for the fuel-mass fraction. The attendant energy release results in a distribution of internal energy which is described by the equation for conservation of energy. This internal energy distribution is translated into a pressure field which drives the flow field through momentum equations. The flow field acts as source term in the turbulence model, which results in a turbulent-flow structure. Finally, the turbulence properties, together with the composition, determine the rate of combustion. This completes the circle, the feedback in the process of turbulent, premixed combustion in gas explosions. The set of equations has been solved with various numerical methods e.g., SIMPLE (Patankar 1980) SOLA-ICE (Cloutman et al. 1976). 

Expected Proportions of Flow and Turbulence in a Mixing System... 

CFD might provide a way of elucidating all these spatial variations in flow conditions, in species concentrations, in bubble drop and particle sizes, and in chemical reaction rates, provided that such computational simulations are already capable of reliably reproducing the details of turbulent flows and their dynamic effects on the processes of interest. This Chapter reviews the state of the art in simulating the details of turbulent flows and turbulent mixing processes, mainly in stirred vessels. To this end, the topics of turbulence and CFD both need a separate introduction. 

In the remainder of this chapter, an overview of the CRE and FM approaches to turbulent reacting flows is provided. Because the description of turbulent flows and turbulent mixing makes liberal use of ideas from probability and statistical theory, the reader may wish to review the appropriate appendices in Pope (2000) before starting on Chapter 2. Further guidance on how to navigate the material in Chapters 2-7 is provided in Section 1.5. 

Figure 7.2 Plot of rate constants for the uptake of HOCs by SPMDs and fish, relative to compound hydrophobicity. Also, potential rate-limiting steps/factors are illustrated as related to compound hydrophobicity. Low to moderate flow and turbulence were assumed.

As with the flow regimes in fluid dynamic theory, that is, the stagnation, laminar flow and turbulent flow, it is obvious that a solid phase can exhibit the corresponding flow pattern regimes, which herein are referred to as fixed, moving and mixed, respectively. The terms fixed, moving and mixed are defined as the relative motion of the particle phase with respect to a fixed coordinate system (see Figure 26). Examples of commercial PBC systems with different fuel-bed movement are found in section B.3.4. A comparison between theoretical and practical conversion systems. 

The solid phase of a batch bed can either be fixed, moving or mixed, whereas continuous fuel beds can either be moving or mixed. A successful and comprehensive mathematical model needs to consider these three modes of fuel-bed movement. There is a close analogy between the fluid-solid dynamics, where we have proposed fixed, moving, and mixed, and the fluid dynamics where the corresponding terminology is stagnancy, laminar flow and turbulent flow, respectively. 

The hot-wire anemometer can, with suitable cahbration, accurately measure velocities from about 0.15 m/s (0.5 fl/s) to supersonic velocities and detect velocity fluctuations with frequencies up to 200,000 Hz. Eairly rugged, inexpensive units can be built for the measurement of mean velocities in the range of 0.15 to 30 m/s (about 0.5 to 100 ft/s). More elaborate, compensated units are commercially available for use in unsteady flow and turbulence measurements. In cahbrating a hotwire anemometer, it is preferable to use the same gas, temperature, and pressure as will be encountered in the intended apphcation. In this case the quantity I RJAt can be plotted against /v, where I = hot-wire current, = hot-wire resistance. At = difference between the wire temperature and the gas bulk temperature, and V = mean local velocity. A procedure is given by Wasan and Raid [Am. Inst. Chem. Eng. J., 17, 729-731 (1971)] for use when it is impractical to calibrate with the same gas composition or conditions of temperature and pressure. Andrews, Rradley, and Hundy [Int. J. Heat Mass Transfer, 15, 1765-1786 (1972)] give a cahbration correlation for measurement... 

As mentioned above, two distinct patterns of fluid flow can be identified, namely laminar flow and turbulent flow. Whether a fluid flow becomes laminar or turbulent depends on the value of a dimensionless number called the Reynolds number, (Re). For a flow through a conduit with a circular cross section (i.e., a round tube), (Re) is defined as ... 

Vedernikov (V2), 1946 Theoretical treatment of wavy flow in open channels. Wavy flow and turbulent flow clearly distinguished. 

Fig. I. Constant power, eftect of impeller size, and speed on flow and turbulence...

NMR imaging techniques were applied to the measurements of velocity field in opaque systems such as tomato juice and paper pulp suspensions [58-60]. In both cases, the particle concentrations are sufficiently high that widely applied techniques such as hot film and laser Doppler anemometry could not be used. The velocity profile for a 6 % tomato juice slurry clearly showed a power-law behavior [58, 59]. Row NMR images for a 0.5 % wood pulp suspension provided direct visual of three basic types of shear flow plug flow, mixed flow and turbulent flow as mean flow rate was increased. Detailed analysis of flow NMR image is able to reveal the complex interaction between the microstructure of suspensions and the flow [60]. 

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. 

Few studies have rigorously assessed the roles of flow and turbulence on chemically mediated foraging, so generalization of results obtained using blue crabs is unclear. Experiments designed... 

Distinguish between laminar flow and turbulent flow. (4 marks)... 

Flows are much less well defined than in Laminar flow, and turbulence is an empirically based subject... 

Looney, M. K. and J. J. Walsh, 1984. Mean-flow and Turbulent Characteristics of Free and Impinging Jet Flows. Journal of Fluid Mechanics, 147 397-429. 

Eq (18-28) was tested by Babbitt and Caldwell and found to apply to streamline-flow conditions. Between this type of flow and turbulent flow there is an indeterminate region. The lower and upper limits of this region are given by the following equations ... 

It should be noted, and the point will be discussed further at a later stage, that the equations derived in the present section are applicable to both laminar flow and turbulent flow. In the case of turbulent flow, the mean values of the variables are implied although strictly for turbulent flow, M will be given by... 

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