Boundary-layer flow time-dependent

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. 

The operator-splitting approach is likely to be most useful in the treatment of systems having more than one spatial dimension, for example, two-dimensional, time-dependent, boundary layer flow, where the governing equations are of the form... 

Traditionally, an average Sherwood number has been determined for different catalytic fixed-bed reactors assuming constant concentration or constant flux on the catalyst surface. In reality, the boundary condition on the surface has neither a constant concentration nor a constant flux. In addition, the Sh-number will vary locally around the catalyst particles and in time since mass transfer depends on both flow and concentration boundary layers. When external mass transfer becomes important at a high reaction rate, the concentration on the particle surface varies and affects both the reaction rate and selectivity, and consequently, the traditional models fail to predict this outcome. 

Fig. 19. Time-dependent development of structured flows in a dextran/sorbitol system (see legend of (Fig. 18) with blue-labelled dextran initially introduced into the bottom solution. The photograph was taken 2 h after formation of the boundary layer...

The Reynolds number at observed transition location (defined as a location where the intermittency factor is about 0.1 i.e. the flow is 10 % of time turbulent and rest of the time it is laminar) for zero pressure gradient flat plate boundary layer is of the order of 3.5 X 10 . This corresponds to Re = 950. The distance between the point of instability and the point of transition depends on the degree of amplification and the kind of disturbance present with the oncoming flow. This calls for a study of local and total amplification of disturbances. The following description is as developed in Arnal (1984) for two-dimensional incompressible flows. 

Large-eddy simulation output is a three-dimensional, time-dependent flow and scalar field. The results are unique in reproducing most aspects of the turbulent flow field and its interaction with a layer of vegetation. Due to the considerable demand on computational resources, it is not yet reasonable to utilize a grid network that can sufficiently resolve a vegetation canopy and, at the same time, extend both horizontally and vertically to simulate a full atmospheric boundary layer. Nevertheless, even simulations with quite limited vertical extent, as few as three canopy heights, have been successful in accurately reproducing the features described earlier. 

Discrepancies between experimentally obtained and theoretically calculated data for cadmium concentration in the strip phase are 10-150 times at feed or strip flow rate variations. These differences between the experimental and simulated data have the following explanation. According to the model, mass transfer of cadmium from the feed through the carrier to the strip solutions is dependent on the diffusion resistances boundary layer resistances on the feed and strip sides, resistances of the free carrier and cadmium-carrier complex through the carrier solution boundary layers, including those in the pores of the membrane, and resistances due to interfacial reactions at the feed- and strip-side interfaces. In the model equations we took into consideration only mass-transfer relations, motivated by internal driving force (forward... 

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