Lagrangian properties particle models

Two model approaches are compared by simulating reactive transport of acenaphthene in a heterogeneous porous medium. In a Monte Carlo approach a Lagrangian onedimensional streamtube model is used to assess the transport behaviour at field scale for distances of up to 800 m. Aquifer properties are taken from results of field experiments characterising a test site in a shallow quaternary sand and gravel aquifer. The results of the streamtube model are compared to model results of a two-dimensional Eulerian model. Both models account for kinetic sorption, described as diffusive transport in intra-particle pores. 

Suppose, in the preceding problems, that the linear cores are characterized by two different porosities as well. What issues are important to effective properties when modeling production rate is important When modeling tracer arrival times What is the difference between the Eulerian velocity at a point versus the Lagrangian velocity following a particle ... 

The approach described above is by no means complete or exclusive. For example, Lamb et al. (1975) have proposed an alternative route to assess the adequacy of the atmospheric diffusion equation. Their approach is based on the Lagrangian description of the statistical properties of nonreacting particles released in a turbulent atmosphere. By employing the boundary layer model of Deardorff (1970), the transition probability density p x, y, z, t x, y, z, t ) is determined from the statistics of particles released into the computed flow field. Once p has been obtained, Eq. (3.1) can then be used to derive an estimate of the mean concentration field. Finally, the validity of the atmospheric diffusion equation is assessed by determining the profile of vertical dififiisivity that produced the best fit of the predicted mean concentration field. 

In order to obtain a correlation, the outflow of the effervescent spray was simulated by a numerical model based on the Navier-Stokes equations and the particle tracking method. The external gas flow was considered turbulent. In droplet phase modeling, Lagrangian approach was followed. Droplet primary and secondary breakup were considered in their model. Secondary breakup consisted of cascade atomization, droplet collision, and coalescence. The droplet mean diameter under different operating conditions and liquid properties were calculated for the spray SMD using the curve fitting technique [43] ... 

Whatever the approach (Eulerian or Lagrangian) for the prediction of particle dispersion, the turbulence field in which the particles disperse must be known. To test the dispersion model itself, this knowledge can be acquired through accurate experiments. However, for practical purposes, another option is to predict the turbulence properties in a first module of the computational codes. This provides the user with a complete computational package, but it is clear that any inaccuracy of the turbulence model and predictions will then be echoed to the dispersion predictions. 

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