Direct numerical simulation , drag

Multiscale modeling is an approach to minimize system-dependent empirical correlations for drag, particle-particle, and particle-fluid interactions [19]. This approach is visualized in Eigure 15.6. A detailed model is developed on the smallest scale. Direct numerical simulation (DNS) is done on a system containing a few hundred particles. This system is sufficient for developing models for particle-particle and particle-fluid interactions. Here, the grid is much smaller... 

Beris, A.N. Dimitropoulos, C.D. Sureshkumar, R. Handler, R.D. Direct numerical simulations of polymer-induced drag reduction in viscoelastic turbulent channel flows. Proceedings of the International Congress on Rheology, Cambridge, U.K., Aug 20-25 British Society of Rheology Glasgow, 2000 Vol. 2, 190-192. 

A. N. Direct numerical simulation of viscoelastic turbulent channel flow exhibiting drag reduction effect of the variation of rheological parameters. J. Non-Newton. Fluid 1998, 79 (2-3), 433-468. 

B. J. Direct numerical simulations of maximum drag reduction by polymers, 12th European Drag Reduction Meeting, Herning, Denmark, Apr 18-20, 2002. 

The process of formulating mesoscale models from the microscale equations is widely used in transport phenomena (Ferziger Kaper, 1972). For example, heat transfer between the disperse phase and the fluid depends on the Nusselt number, and mass transfer depends on the Sherwood number. Correlations for how the Nusselt and Sherwood numbers depend on the mesoscale variables and the moments of the NDF (e.g. mean particle temperature and mean particle concentration) are available in the literature. As microscale simulations become more and more sophisticated, modified correlations that are based on the microscale results will become more and more common (Beetstra et al, 2007 Holloway et al, 2010 Tenneti et al, 2010). Note that, because the kinetic equation requires mesoscale models that are valid locally in phase space (i.e. for a particular set of mesoscale variables) as opposed to averaged correlations found from macroscale variables, direct numerical simulation of the microscale model is perhaps the only way to obtain the data necessary in order for such models to be thoroughly validated. For example, a macroscale model will depend on the average drag, which is denoted by... 

It is important to note that the fluid-solid drag coefficients discussed above are valid only for monodisperse particles (i.e. particles with equal diameters and material densities). Using direct numerical simulations (DNS) of the microscale equations for fluid-particle flows, several authors (Beetstra et al, 2007 Buhrer-Skinner et al, 2009 Holloway et al, 2010 Tenneti et al, 2010, 2012 Yin Sundaresan, 2009) have proposed improved drag coefficients to account for polydisperse particles. 

The motion and sedimentation of particles in non-Newtonian fluids was considered by direct numerical simulation in [129, 130,193, 194, 207,484], The books [92, 112, 272] present a detailed review of investigations related to the motion of particles, drops, and bubbles in a non-Newtonian fluid, as well as numerous formulas and curves determining the drag force. 

With the recent advance in computational technology, efforts have also been devoted to numerical simulations of drag reduction, such as for viscoelastic polymers via constitutive equations and finite element methods [Dimitropoulos et al., 1998 Fullerton and McComb, 1999 Mitsoulis, 1999 Beris et al., 2000 Yu and Kawaguchi, 2004] and for DR flow with surfactant additives via second-order finite-difference direct numerical simulation (DNS) studies [Yu and Kawaguchi, 2003, 2006]. 

Turbulent drag reduction in homogeneous flows by polymer or surfactant additives is a striking phenomenon with both theoretical and practical implications. On the theoretical side, it remains a challenge to fully understand the drag reduction mechanism and the interaction details between DRAs and the turbulent flow field. New methods, especially computational ones, have been developed to solve this problem, such as direct numerical simulations and stochastic simulations. On the application... 

Yu, B., and Kawaguchi, Y, Direct numerical simulation of viscoelastic drag-reducing flow a faithful finite difference method, J. Non-Newtonian Fluid Meek, 116, 431-466 (2004). 

Den Toonder and co-workers (64,86), and Massah and Hanratty (87) examined the role of viscoelasticity, extensional viscosity, and stress anisotropy in drag reduction. Direct numerical simulation (DNS) investigation of Den Toonder and co-workers (86) points out that drag increases rather than decreases when the elastic contributions are taken into account. 

Direct numerical simulations (DNS) At the most detailed level of description, the gas flow field is modeled at scales smaller than the size of the solid particles. The interaction of the gas phase with the solid phase is incorporated by imposing no-slip boundary conditions at the surface of the solid particles. This model thus allows one to measure the effective momentum exchange between the two phases, which is a key input in aU the higher scale models. Many different types of DNS models exist, such as the lattice Boltzmann model (Ladd, 1994 Ladd and Verberg, 2001) or immersed boundary techniques (Peskin (2002), UMmann (2005)). The goal of these simulations is to construct drag laws for dense gas—solid systems, which are used in the discrete particle type models. 

Dimitropoulos, C.D., Dubief, Y., Shaqfeh, E.S.G., and Moin, P. (2006) Direct numerical simulations of polymer-induced drag reduction in turbulent boimdary layer flow of inhomogeneous polymer solutions. /. Fluid Mech., 566, 153-166. 

Housiadas, K.D. and Beris, A.N. (2005) Direct Numerical Simulations of viscoelastic turbulent channel flows at high drag reduction. Korea-Aust. RheoLj, 17 (3), 131-140. 

Tenneti S, Garg R, Subramaniam S Drag law for monodisperse gas-solid systems using particle-resolved direct numerical simulation of flow past fixed assemblies of spheres, Int J Multiphase FW 37 1072-1092, 2011. 

As mentioned earlier the trajectory of the liquid jet before and after the CBL is of importance for design purposes. As we will see, it is also a critical piece of information needed by some empirical-numerical models to simulate the atomization process. A considerable number of research studies have been merely focused on measurements and predictions of the jet trajectory and its variation with change in different parameters such as the pressure and the temperature. To develop a simple model for predicting the jet trajectory, we can think of the jet as a stack of thin cylindrical elements piled on top of each other to form a jet. One such element with infinitesimal thickness h is shown in Fig. 29.1b. Then, one can treat the motion of the element like that of a projectile moving up with initial y-direction velocity j and zero x-direction velocity. In the simplest approximation, the only force acting on the element is the aerodynamic drag force... 

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