Turbulence parameters

Turbulent Flow in Stirred Vessels Turbulence parameters such as intensity and scale of turbulence, correlation coefficients, and... 

Such spatial variations in, e.g., mixing rate, bubble size, drop size, or crystal size usually are the direct or indirect result of spatial variations in the turbulence parameters across the flow domain. Stirred vessels are notorious indeed, due to the wide spread in turbulence intensity as a result of the action of the revolving impeller. Scale-up is still an important issue in the field of mixing, for at least two good reasons first, usually it is not just a single nondimensional number that should be kept constant, and, secondly, average values for specific parameters such as the specific power input do not reflect the wide spread in turbulent conditions within the vessel and the nonlinear interactions between flow and process. Colenbrander (2000) reported experimental data on the steady drop size distributions of liquid-liquid dispersions in stirred vessels of different sizes and on the response of the drop size distribution to a sudden change in stirred speed. 

In addition, constant turbulent parameters and constant mixture com-... 

Solntsev, V. P. 1961. Influence of turbulence parameters on the combustion process of homogeneous gasoline-air mixture behind a stabilizer under conditions of confined flow. In Flame stabilization and the development of combustion in turbulent How. Ed. G. N. Gorbunov. Moscow Oborongiz. 75. 

Campbell and Hanratty (1982) used Lau s (1980) measurements with some special optics on a laser Doppler velocimetry system to calculate /3(f) near a fixed interface, in this case, the inside of a clear pipe. They determined w(z,t) from equation (8.52), and solved equations (8.49) and (8.50) numerically for / l(0- Finally, they applied equation (8.51) to determine Kl, which has been the goal all along. The end results (Kl) may then be related to the other, independent parameters that are important to the transfer process, such as diffusivity, viscosity, and turbulence parameters. Campbell and Hanratty performed this operation and found the following correlation ... 

The increase in vertical turbulence intensity caused by cooling tower plumes can be estimated for each temperature gradient and increment of distance from the tower. This can be represented by well-known turbulence parameters developed for Gaussian plume models ... 

In addition to these macromixing characteristics, many authors have determined turbulence parameters and their spatial distribution within the tank volume by measuring velocity and concentration fluctuations(144-147, 19, 158). In a typical investigation (19) concerning a semi-industrial tank (0.15 m2) and aqueous medium, the following spatial variations were found uf =5 to 30 % of jTNd, Lf = 4 to 150 mm, Af = 1 to 5 mm, e/e 0.2 to 2.5, c /C = 2 to 10 x 10 4 (for eddies > 100 pm). This shows that a stirred tank is far from being the homogeneous and uniform system assumed in many academic papers. 

Despite its great potential, in the near future CFD will not completely replace experimental work or standard approaches currently used by the chemical engineering community. In this connection it is even not sure that CFD is guaranteed to succeed or even be an approach that will lead to improved results in comparison with standard approaches. For single-phase turbulent flows and especially for multiphase flows, it is imperative that the results of CFD analysis somehow be compared with experimental data in order to assess the validity of the physical models and the computational algorithms. In this connection we should mention that only computational results that possess invariance with respect to spatial and temporal discretization should be confronted with experimental data. A CFD model usually gives very detailed information on the temporal and spatial variation of many key quantities (i.e., velocity components, phase volume fractions, temperatures, species concentrations, turbulence parameters), which leads to in-... 

T irbulent Flow in Stirred Vessels Turbulence parameters such as intensity and scale of turbulence, correlation coefficients, and energy spectra nave been measured in stirred vessels. However, these characteristics are not used directly in the design of stirred vessels. 

The more usual approach to speeding up FCM methods for multi-body flow / dispersion calculations such as this is to use the continuum approach. This requires some estimates of turbulence parameters such as mixing lengths or eddy diffusivities for the canopy (on the neighbourhood scale), but these characteristics cannot be deduced from turbulence closure models, although they may be estimated from detailed calculations of flow/dispersion around a few typical obstacles - not a straightforward or accurate process (see Moulinec et al., 2003 [436]). 

Brodkey [56] stated that only with the advent of the modem turbulence theory a deep understanding of micro-mixing processes and turbulent scalar transfer processes on a microscopic level was possible and that this theory enabled the definition of measurable mixing criteria. Knowledge of the turbulence parameter made it possible to estimate the degree of mixing. The parameters could be estimated from the geometry of the flow system and from simple empirical expressions. The... 

Several studies [23-25] have shown the effect of the combustor inlet conditions on the predicted flame structure, liner temperature, and emissions. These boundary conditions include the axial, tangential, and radial velocities the turbulent kinetic energy and associated length scale. To characterize the flow field at the exit of the TARS, two approaches were adopted. First, advanced diagnostic, such as LDV (discussed above), was used to measure the flow field distribution at the exit of the swirler. The data collected are used for inlet boundary conditions for the LES and database for numerical model validation. Second, a RANS model was used to study mixing and turbulence parameters in the TARS swirler [6]. 

Turbulent Flow in Stirred Vessels Turbulence parameters... 

The effect of turbulence in creating new surface is implicit in the surface renewal time of Eq. (5), but is not easily determined from measurable turbulence parameters. A number of more explicit models have been developed. These differ in how the interaction of turbulent eddies with the interface is parameterized [28,33-36]. 

Discretization Integration of the governing equations for conservation of mass and momentum, and other scalars (e.g., turbulence parameters) on a cell (= control volume) yielding a set of mathematical expressions for the dependent variables, such as velocity, pressure, etc. 

Flow of liquid with viscosity coefficient JIm = 1 mPa-sec and density p = 1000 kg/m was considered. Boundary conditions are the symmetry conditions along z axis and conditions of liquid adhesion to solid surfaces of reaction volume. They set pressure at apparatus output (on CD line) and linear flow speed V = 5 m/sec at input (on AB line) in the line of symmetry axis (Fig. 3.1). The lengths of input and output of reaction zone significantly exceed zone s diameter (L da) that allows exception of influence of input and output turbulence parameters on reagents mixing characteristics. The last ones are the subjects of inquiry. 

Turbulent stresses are determined by standard and modified K-e models of turbulence. For determination of flow field near the wall the method of parietal functions was used. Rates fields and pressures were corrected in the course of calculation according with SIMPLE-C algorithm. Diffusion of indicator was modeled as transmission of scalar introduced in less space of time in comparison with its average residence time in apparatus at fixed rate fields and turbulence parameters. 

The length and time scales of chemical reactions are generally much smaller than the ones of the underlying flow. In fact, with today s computers, CFD computations cannot resolve all the scales in technically relevant combustion problems. Consequently, modeling is required to make meaningful combustion predictions. Since for fuel sprays the gas flow is usually turbulent, the fuel-air mixing process depends on the turbulence parameters from which the chemical reaction rates are determined. 

Liquid-phase surface tension (mN /m or dyn/cm) Turbulent parameters in k-e equations (N/m) Surface tension of tap water (mN/m or dyn/cm) Contact time (s)... 

In this class, the fluctuations in the velocity are truly random such that averaged values of turbulence parameters are independent of the position in space. Thus, the fluctuations do not vary with the axis of translation (Brodkey 1967). This type of turbulence can be generated with a well-defined equipment geometry. However, it can only be sustained over relatively short distances. An important parameter that can be used to represent turbulence is the root-mean-square velocity defined earher. For homogeneous turbulence, the values need not be equal but they should not vary over the field under consideration. 

Effect of Turbulence Parameters as Discerned from the Variation of... 

Levins and Glastonbury (1972a, b, c), Kuboi et al. (1974a), and Lee (1981,1984) refined Harriott s approach subsequently. The importance of turbulence parameters, such as intensity/scale of turbulence, in deciding the mass transfer coefficient was expanded in these studies. Evidently, application of this approach required more elaborate information on the relevant turbulence parameters. Some of the experimental investigations, particularly in stirred vessels, are discussed in the following. The early investigations used equipment with limited capabilities and accuracy. Contemporary techniques such as laser Doppler anemometry/velocimetry have far more sophistication and accuracy. Nonetheless, the initial studies deserve mention because many of them included simultaneous measurements of mass transfer. 

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