Turbulence summary

A summary of the nine batch reactor emulsion polymerizations and fifteen tubular reactor emulsion polymerizations are presented in Tables III IV. Also, many tubular reactor pressure drop measurements were performed at different Reynolds numbers using distilled water to determined the laminar-turbulent transitional flow regime. 

The equations for both laminar and turbulent flows, and the finite volume methods used to solve them, have been presented extensively in the literature (Patankar, 1980 Mathur and Murthy, 1997 Ranade, 2002 Fluent, 2003). The following summary focuses on aspects of particular concern for simulation of packed tubes and also those options chosen for our own work. 

In summary, for a non-stationary turbulent reacting flow wherein all scalars can be assumed to have identical molecular diffusivities and the initial and boundary conditions are uniform/constant, the -component molar concentration vector... 

If AW AW the process of finding a linear-mixture basis can be tedious. Fortunately, however, in practical applications Nm is usually not greater than 2 or 3, and thus it is rarely necessary to search for more than one or two combinations of linearly independent columns for each reference vector. In the rare cases where A m > 3, the linear mixtures are often easy to identify. For example, in a tubular reactor with multiple side-injection streams, the side streams might all have the same inlet concentrations so that c(2) = = c(iVin). The stationary flow calculation would then require only AW = 1 mixture-fraction components to describe mixing between inlet 1 and the Nm — I side streams. In summary, as illustrated in Fig. 5.7, a turbulent reacting flow for which a linear-mixture basis exists can be completely described in terms of a transformed composition vector ipm( defined by... 

In summary, in the equilibrium-chemistry limit, the computational problem associated with turbulent reacting flows is greatly simplified by employing the presumed mixture-fraction PDF method. Indeed, because the chemical source term usually leads to a stiff system of ODEs (see (5.151)) that are solved off-line, the equilibrium-chemistry limit significantly reduces the computational load needed to solve a turbulent-reacting-flow problem. In a CFD code, a second-order transport model for inert scalars such as those discussed in Chapter 3 is utilized to find ( ) and and the equifibrium com-... 

The derivation of the mixture-balance laws has been given by Chapman and Cowling for a binary mixture. Its generalization to multicomponent mixtures, as in Equation 5-1, uses a determination of the invariance of the Boltzmann equation. This development has been detailed by Hirschfelderet These derivations were summarized in the notes of Theodore von Karmin s Sorbonne lectures given in 1951-1952, and the results of his summaries were stated in Pinner s monograph. For turbulent flow, the species-balance equation can be represented in the Boussinesq approximation as ... 

In summary, the calculation of pressure drops by the Lockhart-Marti-nelli method appears to be reasonably useful only for the turbulent-turbulent regions. Although it can be applied to all flow patterns, accuracy of prediction will be poor for other cases. Perhaps it is best considered as a partial correlation which requires modification in individual cases to achieve good accuracy. Certainly there seems to be no clear reason why there should be a simple general relationship between the two-phase frictional pressure-drop and fictitious single-phase drops. As already pointed out, at the same value of X in the same system, it is possible to have two different flow patterns with two-phase pressure-drops which differ by over 100%. The Loekhart-Martinelli correlation is a rather gross smoothing of the actual relationships. 

Summaries of the aerosol carbon data obtained as part of the POLTERCAIST I and II conducted at the National Oceanographic and Atmospheric Administration (NOAA) Atmospheric Turbulence and Diffusion Laboratory (ATDL) Walker Branch site near Oak Ridge, TN, in cooperation with NOAA-ATDL and Oak Ridge National Laboratory (ORNL) staff are reported in Tables I and II. Concentrations of... 

Table 11.1. Summary of turbulent LES runs (fully developed turbulent channel).

In summary, while most studies of atmospheric boundary layer flows have used local theories involving eddy transport coefficients, it is now recognized that turbulent transport coefficients are not strictly a local property of the mean motion but actually depend on the whole flow field and its time history. The importance of this realization in simulating mean properties of atmospheric flows depends on the particular situation. However, for mesoscale phenomena that display abrupt changes in boundary properties, as is often the case in an urban area, local models are not expected to be reliable. 

An appropriately chosen set of surface parameters can be related to specific physical processes. For example, it is not surprising that the area covered by vegetation drives the magnitude of the latent heat flux, or that morphometric parameters help to describe the roughness and turbulence characteristics over a particular urban surface. Therefore, the following three most important characteristics can be outlined (cf. Piringer and Joffre, 2005 [497], for a summary). 

In summary, experimental data indicates that the turbulent boundary layer can be subdivided into an inner constant wall stress layer for the approximate range 0 < < 0.1(5, and an outer non-constant stress layer bounded by... 

Because the upcoming derivations are sometimes long and involved, it is easy to lose sight of the forest for the trees. The following summary gives the steps that will be taken in the subsequent subsects, to develop the governing equations in a form suitable for describing turbulent flows. 

In summary, one of the weakest links in modeling reactive systems operated in bubble columns is the fluid dynamic part considering multi-phase turbulence modeling, interfacial closures, and especially the impact and descriptions of bubble size and shape distributions. For reactive systems the estimates of the contact areas and thus the interfacial mass transfer rates are likely to contain large uncertainties. 

For bare particleboards in suitable test chambers, mass transfer resistances are usually found to lie between 1,500 and 10,000 s/m. When there is no internal circulation or when there is insufficient turbulence, it is not uncommon to find an extra mass transfer resistance for the gas phase of 12,000 s/m at a ventilation rate of 0.75 per hour. A more detailed estimation is given in the summary. 

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