Turbulence properties

In homogeneous turbulence, turbulence properties are independent of spatial position. The kinetic energy of turbulence k is given by... 

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). 

Another family of feedbacks involving biota arise via the process of evapotranspiration in which the rate of water vapor is transferred from the land surface to the atmosphere is mediated by plants. Several consequences have been proposed that include influences of biota on the greenhouse effect of water vapor as well as relative humidity and clouds. Lovelock (1988) suggested that tropical forests might be kept cool by increasing cloud cover in response to higher relative humidity released through enhanced evapotranspiration (via the clouds influences on albedo). Yet another connection arises because tree-covered land has different turbulence properties above it than bare soil, which also influences the cloud cover above. 

PIV has become the most popular technique to measure velocity and turbulent properties (Figure 15.1). The movement of seed particles in a millimeter-thick laser sheet is measured by correlating two photos taken a few milliseconds apart. With two cameras, it is also possible to obtain a 3D vector of the velocity in that plane. The method gives, in general, very good resolution of the flow, but it requires optical access. Also, measurement close to walls can be problematic due to light reflections that disturb the measurements. One extension of PIV is the micro-PIV that uses fluorescent tracer particles, which allows all direct light, for example, reflections at the walls, to be filtered out [1]. 

LDV is the traditional method using tracer particles to measure velocity and one-point statistics of turbulent properties [2]. It is still a very useful technique and has the advantage that it can measure closer to walls compared to PIV. An inherent problem with LDV is that it does not measure at a specific point but rather at places... 

Velocity measurement of the dispersed phase in multiphase flow is possible using both PIV and LDV. In PIV, the particles can be masked according to size, and the velocity for each size fraction can be estimated [7]. The turbulent properties, for example, granular temperature, are more difficult to measure because of the low number of particles in the measured volume. With LDV it is also possible to obtain the velocity and size for the dispersed phase, but the turbulent properties for the dispersed phase are still difficult to measure accurately, owing to the low number of particles and also because the position of the particles is not exactly the same aU the time. 

Almost all flows in chemical reactors are turbulent and traditionally turbulence is seen as random fluctuations in velocity. A better view is to recognize the structure of turbulence. The large turbulent eddies are about the size of the width of the impeller blades in a stirred tank reactor and about 1/10 of the pipe diameter in pipe flows. These large turbulent eddies have a lifetime of some tens of milliseconds. Use of averaged turbulent properties is only valid for linear processes while all nonlinear phenomena are sensitive to the details in the process. Mixing coupled with fast chemical reactions, coalescence and breakup of bubbles and drops, and nucleation in crystallization is a phenomenon that is affected by the turbulent structure. Either a resolution of the turbulent fluctuations or some measure of the distribution of the turbulent properties is required in order to obtain accurate predictions. 

Chemical engineers, however, have to find practical ways for dealing with turbulent flows in flow devices of complex geometry. It is their job to exploit practical tools and find practical solutions, as spatial variations in turbulence properties usually are highly relevant to the operations carried out in their process equipment. Very often, the effects of turbulent fluctuations and their spatial variations on these operations are even crucial. The classical toolbox of chemical engineers falls short in dealing with these fluctuations and its effects. Computational Fluid Dynamics (CFD) techniques offer a promising alternative approach. 

This review paper is restricted to stirred vessels operated in the turbulent-flow regime and exploited for various physical operations and chemical processes. The developments in the field of computational simulations of stirred vessels, however, are not separated from similar developments in the fields of, e.g., turbulent combustion, flames, jets and sprays, tubular reactors, and multiphase reactors and separators. Fortunately, there is a strong degree of synergy and mutual cross-fertilization between these various fields. This review paper focuses on aspects specific to stirred vessels (such as the revolving impeller, the resulting strong spatial variations in turbulence properties, and the macroinstabilities) and on the processes carried out in them. 

All of the chemical species, except one, will be assumed to be completely soluble. The one partially insoluble species will nucleate and grow a solid phase. A typical example is A + B ->P where P is a sparingly soluble compound. The rates of nucleation J and molecular surface growth G can be functions of the local concentration vector c, the particle size l, and the local turbulence properties. Neglecting aggregation and breakage processes, a microscopic PBE for this system can be written as follows ... 

Smaller particles primarily see only the fluctuating velocity component. When the particle size is much less than 100 /zm, the turbulent properties of the fluid become important. This is the definition of the boundary size for microscale mixing. 

Turbulence modeling and time accuracy are closely related. In RANS solvers, turbulence models are used to describe all the turbulent properties of the flow. A range of different models have been... 

The Reynolds number must be checked to determine if the condensate film is laminar or turbulent. Properties are evaluated at the film temperature ... 

An alternative view [36] is that if l/d becomes too small, then extinctions of laminar flamelets are reflected in extinction of the turbulent flame. According to this idea, there is a region to the upper left in Figure 10.5 in which turbulent flame propagation cannot occur. It seems physically that phenomena of this type may pertain to confined turbulent flows in reactors of small volume, where they would reflect influences of turbulence properties... 

Experimental facts which support the recirculation flow and its turbulence properties are given here, mainly in relation to the simplified theory developed in the preceding section. 

III,D,5). In this chapter, the equation is further examined in relation to bed performance, since the turbulence properties of the bed result from interaction between bubbles and the continuous phase. As shown in Fig. 34, the mean slip velocity of bubbles in a fluidized catalyst bed of good fluidity is essentially the same as that for a bubble column when Uq > 20 cm/sec. A criterion under which bubble size approaches a dynamic equilibrium is obviously needed for predicting or evaluating the performance of scaled-up beds. 

It is also worth noting that the early measurements in forests or in agricultural stands were done with the use of mechanical cup-anemometers placed on several levels of high masts, as was mentioned in [186], Because of their inertia, they were adequate for recording the average speeds, but insufficient to reflect the turbulence properties. 

To complete the model specification, boundary conditions have to be specified. These describe the flow conditions at the domain boundaries. At flow inlets one can usually specify the fluid velocity, a mass flow rate, or an inlet pressure. Depending on the problem definition, the inlet temperature, species concentrations, turbulence properties, and volume fractions of any secondary phase must also be supplied. At flow exits, one usually specifies an outlet pressure, and if entrainment through a flow exit is anticipated, the exit... 

The final step in a CFD simulation is to analyze and interpret the results, a step also referred to as postprocessing. Typical CFD results include values for the pressure, the three velocity components, turbulence properties, temperature, and species concentrations at all grid cells in the domain (which is typically on the order of several hundred thousand in today s applications). The total amount of available data is thus extremely large and detailed. To be useful to an engineer the data have to be presented in an understandable way. 

To satisfy the requirement that the turbulent properties of the flow within the eddy will not change significantly as the eddy advects past a sensor, the following criterion should be fulfilled ... 

Moilanen et al [59] did use CFX to simulate two-phase aerated fermenters. A MRRF technique was employed to describe the impeller motion. The results obtained using two different turbulence closures were compared with experimental and visual observations. The two turbulence models tested were the standard k-e and the SST models. R was stated that the k-e model did behave unphysically in the bulk regions of the vessel by generating unreasonable turbulence properties. The SST model gave more reasonable results. 

The dual beam configuration of LDA is most widely used today, where the Doppler difference frequency is directly measured and the receiving optics may be placed at an arbitrary position with respect to the transmitting beams. Laser-Doppler anemometry has been first applied to measurements of mean velocities and turbulence properties in single phase flows. In this case small particles, which follow the flow and the turbulent fluctuations, need to be present in the flow or must be added to it (i.e. seeding the flow with a tracer). The principles of LDA are, for example, described in detail by Durrani and Greated (1977), Durst et al. (1981), and Durst et al. (1987). 

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