Lagrangian turbulence

Chaiken, J., Chevray, R., Tabor, M., and Tan, Q. M., Experimental study of Lagrangian turbulence in Stokes flow, Proc. Roy. Soc. Lond. A408, 165-174 (1986). 

Fig. 7.10 Poincare sections of viscous Newtonian flow in alternately turning eccentric cylinders. The inner cylinder turned counterclockwise for a given time, and then the outer cylinder was turned clockwise for 800 periods. There were 11 initial particles. [Reprinted by permission from J. Chaiken, R. Chevray, M. Tabor, and Q. M. Tan, Experimental Study of Lagrangian Turbulence in Stokes Flow, Proc. R. Soc. London A, 408, 165-174 (1986).]...

J. Chaiken, R. Chevray, M. Tabor, and Q. M. Tan, Experimental study of Lagrangian Turbulence in Stokes Flow, Proc. Royal Soc. London A 408 165-174 (1986). 

Although it is possible to derive a PDF transport equation for >(x, t) as described in Section 6.2, this is not usually done. Instead, a stochastic model for the Lagrangian turbulence frequency a> (t) is developed along the lines of those discussed in Section 6.7. The goal of these models is to reproduce as many of the relevant one-point, two-time statistics of the Lagrangian fluid-particle turbulence frequency, co1 (f), as possible. Examples of two such models (log-normal model (Jayesh and Pope 1995) and gamma-distribution model (Pope and Chen 1990 Pope 1991a Pope 1992)) can be found in Pope (2000). Here we will... 

P. Goix, P. Paranthoen, and M. Trinite 1990, A tomographic study of measurements in a V-shaped H2-air flame and a Lagrangian interpretation of the turbulent flame brush evolution. Combust. Flame 81 229-241. 

For simulating computationally the spatial and temporal evolution of both physical and chemical processes in mixing devices operated in a turbulent singlephase mode, two essentially different approaches are available the Lagrangian approach and the Eulerian technique. These will be explained briefly. 

In the Lagrangian approach, individual parcels or blobs of (miscible) fluid added via some feed pipe or otherwise are tracked, while they may exhibit properties (density, viscosity, concentrations, color, temperature, but also vorti-city) that distinguish them from the ambient fluid. Their path through the turbulent-flow field in response to the local advection and further local forces if applicable) is calculated by means of Newton s law, usually under the assumption of one-way coupling that these parcels do not affect the flow field. On their way through the tank, these parcels or blobs may mix or exchange mass and/or temperature with the ambient fluid or may adapt shape or internal velocity distributions in response to events in the surrounding fluid. 

In addition, it is dubious whether this new correlation due to Brucato et al. (1998) should be used in any Euler-Lagrangian approach and in LES which take at least part of the effect of the turbulence on the particle motion into account in a different way. So far, the LES due to Derksen (2003, 2006a) did not need a modified particle drag coefficient to attain agreement with experimental data. Anyhow, the need of modifying particle drag coefficient in some way illustrates the shortcomings of the current RANS-based two-fluid approach of two-phase flow in stirred vessels. 

Aerosol production and transport over the oceans are of interest in studies concerning cloud physics, air pollution, atmospheric optics, and air-sea interactions. However, the contribution of sea spray droplets to the transfer of moisture and latent heat from the sea to the atmosphere is not well known. In an effort to investigate these phenomena, Edson et al.[12l used an interactive Eulerian-Lagrangian approach to simulate the generation, turbulent transport and evaporation of droplets. The k-e turbulence closure model was incorporated in the Eulerian-Lagrangian model to accurately simulate... 

For canonical turbulent flows (Pope 2000), the flow parameters required to complete the CRE models are readily available. However, for the complex flow fields present in most chemical reactors, the flow parameters must be found either empirically or by solving a CFD turbulence model. If the latter course is taken, the next logical step would be to attempt to reformulate the CRE model in terms of a set of transport equations that can be added to the CFD model. The principal complication encountered when following this path is the fact that the CRE models are expressed in a Lagrangian framework, whilst the CFD models are expressed in an Eulerian framework. One of the main goals of this book... 

Figure 2.3. Three components of the Lagrangian velocity U+(t) as a function of t. The velocity was extracted from DNS of isotropic turbulence (Rk = 140) with (U) = 0. (Courtesy of P. K. Yeung.)...

One of the principal difficulties faced when employing Lagrangian micromixing models is the determination of tm based on properties of the turbulent flow fields. Researchers have thus attempted to use the universal nature of high-Reynolds-number isotropic turbulence to link tm to the turbulence time scales. For example, in the E-model (Baldyga and Bourne 1989) the engulfment rate essentially controls the rate of micromixing and is defined by... 

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