Effects of anisotropy on the geometry of tracer particle trajectories in turbulent flows

Using curvature and torsion to describe Lagrangian trajectories gives a full description of these as well as an insight into small and large time scales as temporal derivatives up to order 3 are involved. One might expect that the statistics of these properties depend on the geometry of the flow. Therefore, we calculated curvature and torsion probability density functions (PDFs) of experimental Lagrangian trajectories processed using the Shake-the-Box algorithm of turbulent von K\'arm\'an flow, Rayleigh-B\'enard convection and a zero-pressure-gradient turbulent boundary layer over a flat plate. The results for the von K\'arm\'an flow compare well with previous experimental results for the curvature PDF and numerical simulation of homogeneous and isotropic turbulence for the torsion PDF. Results for Rayleigh-B\'enard convection agree with those obtained for K\'arm\'an flow, while results for the logarithmic layer within the boundary layer differ slightly, and we provide a potential explanation. To detect and quantify the effect of anisotropy either resulting from a mean flow or large-scale coherent motions on the geometry or tracer particle trajectories, we introduce the curvature vector. We connect its statistics with those of velocity fluctuations and demonstrate that strong large-scale motion in a given spatial direction results in meandering rather than helical trajectories

Effects of anisotropy on the geometry of tracer particle trajectories in turbulent flows

Using curvature and torsion to describe Lagrangian trajectories gives a full description of these as well as an insight into small and large time scales as temporal derivatives up to order 3 are involved. One might expect that the statistics of these properties depend on the geometry of the flow. Therefore, we calculated curvature and torsion probability density functions (PDFs) of experimental Lagrangian trajectories processed using the Shake-the-Box algorithm of turbulent von Kármán flow, Rayleigh-Bénard convection and a zero-pressuregradient boundary layer over a flat plate. The results for the von-Kármán flow compare well with experimental results for the curvature PDF and numerical simulation of homogeneous and isotropic turbulence for the torsion PDF. For the experimental Rayleigh-Bénard convection, the power law tails found agree with those measured for von-Kármán flow. Results for the logarithmic layer within the boundary layer differ slightly, we give some potential explanation below. To detect and quantify the effect of anisotropy either resulting from a mean flow or large-scale coherent motions on the geometry or tracer particle trajectories, we introduce the curvature vector. We connect its statistics with those of velocity fluctuations and demonstrate that strong large-scale motion in a given spatial direction results in meandering rather than helical trajectories

Production and Demand Management

This Chapter ranges through a wide variety of production and demand management problems related to energy commodities systems. The Oil and Gas production enhancement is discussed via oil wells optimal placement as well as water and gas optimal injection, namely waterflooding and gas lift. Further is analyzed the optimal schedule and design of commodities generation in energy hubs and combined cooling, heat and power systems, reaching finally the chemical processes where the specification of the products is taken into account, with mixing tanks, pools, and blending points. Overall, each of these problems is qualitatively discussed identifying the typical objective functions, variables and constraints generalizing its structure, the problem typology is identified as well as the most common methods to solve it

Production and Demand Management

This Chapter ranges through a wide variety of production and demand management problems related to energy commodities systems. The Oil and Gas production enhancement is discussed via oil wells optimal placement as well as water and gas optimal injection, namely waterflooding and gas lift. Further is analyzed the optimal schedule and design of commodities generation in energy hubs and combined cooling, heat and power systems, reaching finally the chemical processes where the specification of the products is taken into account, with mixing tanks, pools, and blending points. Overall, each of these problems is qualitatively discussed identifying the typical objective functions, variables and constraints generalizing its structure, the problem typology is identified as well as the most common methods to solve it.Numerical Analysi