Turbulence mesoscale

All these findings of disappointing quantitative agreement with experimental data stem from the inherent drawback of the RANS-approach that there is no clear distinction between the turbulent fluctuations modeled by the Reynolds stresses and (mesoscale) fluctuations. In LES, however, the distinction between resolved and unresolved turbulence is clear and relates to the cell size of the computational grid chosen. 

The use of local theories, incorporating parameters such as the eddy viscosity Km and eddy thermal conductivity Ke, has given reasonable descriptions of numerous important flow phenomena, notably large scale atmospheric circulations with small variations in topography and slowly varying surface temperatures. The main reason for this success is that the system dynamics are dominated primarily by inertial effects. In these circumstances it is not necessary that the model precisely describe the role of turbulent momentum and heat transport. By comparison, problems concerned with urban meso-meteorology will be much more sensitive to the assumed mode of the turbulent transport mechanism. The main features of interest for mesoscale calculations involve abrupt... 

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. 

As explained in Table 2.4, these mesoscale models take many hours to compute a single meteorological situation. Nevertheless, they are sufficiently reliable that they are used operationally in the USA for short term forecasts and for computing the future scenarios of air quality in large urban areas. For complex dispersion e.g. from a localised source, stochastic simulations are sometimes used, (e.g. NAME model of UK Met Office, Maryon and Buckland [396] (1995)). Even then their predictions have to be supplemented with more detailed input on the properties of the turbulence. 

ADAPT-LODI, developed at Lawrence Livermore National Laboratory. The ADAPT model assimilates meteorological data provided by observations and models (in particular, by Coupled Ocean/Atmosphere Mesoscale Prediction System [COAMPS ]) to construct the wind and turbulence fields. Particle positions are updated using a Lagrangian particle approach that uses a skewed (non-Gaussian) probability density function (Nasstrom et al. 1999 Ermak and Nasstrom 2000). 

The horizontal airflow in the BL often consists of synoptic-scale (> 1000 km) and mesoscale (10-1000 km) circulations, and microscale ( 1 km) turbulence. Their time scales are days, 1 to 24 h, and less than 1 h, respectively. The impact of toxic dispersion on a synoptic scale or large mesoscale is generally not threatening to health, while for small mesoscale (< 100 km) and microscale, the impact can be life threatening because of accumulated doses over a relatively small area. Small-scale... 

The validation of mesoscale models can be carried out using the numerical solutions to microscale models (Tenneti et al, 2010), in much the same way as that in which DNS is used for model validation in turbulent single-phase flows. A typical mesoscale modeling strategy consists of four steps. 

The remaining chapters in this book are organized as follows. Chapter 2 provides a brief introduction to the mesoscale description of polydisperse systems. There, the mathematical definition of a number-density function (NDF) formulated in terms of different choices for the internal coordinates is described, followed by an introduction to population-balance equations (PBE) in their various forms. Chapter 2 concludes with a short discussion on the differences between the moment-transport equations associated with the PBE and those arising due to ensemble averaging in turbulence theory. This difference is very important, and the reader should keep in mind that at the mesoscale level the microscale turbulence appears in the form of correlations for fluid drag, mass transfer, etc., and thus the mesoscale models can have non-turbulent solutions even when the microscale flow is turbulent (i.e. turbulent wakes behind individual particles). Thus, when dealing with turbulence models for mesoscale flows, a separate ensemble-averaging procedure must be applied to the moment-transport equations of the PBE (or to the PBE itself). In this book, we are primarily... 

In the mesoscale model, setting Tf = 0 forces the fluid velocity seen by the particles to be equal to the mass-average fluid velocity. This would be appropriate, for example, for one-way coupling wherein the particles do not disturb the fluid. In general, fluctuations in the fluid generated by the presence of other particles or microscale turbulence could be modeled by adding a phase-space diffusion term for Vf, similar to those used for macroscale turbulence (Minier Peirano, 2001). The time scale Tf would then correspond to the dissipation time scale of the microscale turbulence. 

Microscale fluid turbulence is, by deflnition, present only when the continuous fluid phase is present. The coefficients Bpv describe the interaction of the particle phase with the continuous phase. In contrast, Bpvf models rapid fluctuations in the fluid velocity seen by the particle that are not included in the mesoscale drag term Ap. In the mesoscale particle momentum balance, the term that generates Bpv will depend on the fluid-phase mass density and, hence, will be null when the fluid material density (pf) is null. In any case, Bpv models momentum transfer to/from the particle phase in fluid-particle systems for which the total momentum is conserved (see discussion leading to Eq. (5.17)). 

It is important to remind the reader that U is the velocity of the fluid phase seen by the particle, U - U is the slip velocity, dp is the particle diameter, and Vf is the kinematic viscosity of the fluid phase. Note that Eq. (5.33) depends on the particle velocity U and is valid in the zero-Stokes-number limit where U = U so that particles follow the fluid. The correlation in Eq. (5.31) is valid only for RCp < 1 and Sc > 200. For larger particle Reynolds numbers the following correlations can be used Sh = 2 -i- 0.724Rep Sc, which is valid for 100 < RCp < 2000, and Sh = 2 -i- 0.425RCp Sc, which is valid for 2000 < RCp <10. Among the other correlations available, it is important to cite the one proposed by Ranz Marshall (1952) for macroparticles Sh = 2.0 -i- O.bReJ Sc. These expressions assume that the fluid velocity U is known. For micron-sized (or smaller) particles moving in turbulent fluids for which only the ensemble-mean fluid velocity (Uf) is known, it is instead better to employ the mesoscale model derived by Armenante Kirwan (1989) Sh = 2.0 -i- 0.52(Re ) Sc, where Re = is the modi-... 

These relationships are valid for isolated bubbles moving under laminar flow conditions. In the case of turbulent flow, the effect of turbulent eddies impinging on the bubble surface is to increase the drag forces. This is typically accounted for by introducing an effective fluid viscosity (rather than the molecular viscosity of the continuous phase, yUf) defined as pi.eff = Pi + C pts, where ef is the turbulence-dissipation rate in the fluid phase and Cl is a constant that is usually taken equal to 0.02. This effective viscosity, which is used for the calculation of the bubble/particle Reynolds number (Bakker van den Akker, 1994), accounts for the turbulent reduction of slip due to the increased momentum transport around the bubble, which is in turn related to the ratio of bubble size and turbulence length scale. However, the reader is reminded that the mesoscale model does not include macroscale turbulence and, hence, using an effective viscosity that is based on the macroscale turbulence is not appropriate. 

Chapter 2 provides a brief introduction to the mesoscale description of polydisperse systems. In this chapter the many possible number-density functions (NDF), formulated with different choices for the internal coordinates, are presented, followed by an introduction to the PBE in their various forms. The chapter concludes with a short discussion on the differences between the moment-transport equations associated with the PBE, and those arising due to ensemble averaging in turbulence theory. 

The numerics in Table 16.2 make two points. One is that turbulence is difficult to achieve at the mesoscale and nearly impossible to achieve in micro- and nanoscale devices. The other point is that diffusion becomes so fast at the microscale that cross-channel (e.g., radial) mixing is essentially instantaneous for all but the very fastest reactions. Thus composition and temperature will be approximately uniform in the cross-channel direction. The solutions to the convective diffusion equations in... 

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