Direct numerical simulation approach

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... 

The emphasis in this chapter is on the fruitful application of Large Eddy Simulations for reproducing the local and transient flow conditions in which these processes are carried out and on which their performance depends. In addition, examples are given of using Direct Numerical Simulations of flow and transport phenomena in small periodic boxes with the view to find out about relevant details of the local processes. Finally, substantial attention is paid throughout this chapter to the attractiveness and success of exploiting lattice-Boltzmann techniques for the more advanced CFD approaches. 

Pressure drop and dispersion were the focus of work by Magnico (2003) who simulated flow at lower Re by direct numerical simulation (DNS) in beds of spheres with an in-house code. Tobis (2000) simulated a small cluster of four spheres with inserts between them to compare to his experimental measurements of pressure drop. Gunjal et al. (2005) also focused on flow and pressure drop through a small cell of spheres, in order to validate the CFD approach by comparison to the MRI measurements in the same geometry made by Suekane... 

To capture the meso-scale structure and/or to predict its effects, various modeling approaches have been proposed. The spatiotemporal resolution of these approaches grows with the development of the computer capacity, including the single-scale approaches, direct numerical simulations, and multi-scale approaches. 

The first approach is the discretization of the convection and the diffusion operators of the PDEs, which gives rise to a large (or very large) system of effective low-dimensional models. The order of these low-dimensional models depend on the minimum mesh size (or discretization interval) required to avoid spurious solutions. For example, the minimum number of mesh points (Nxyz) necessary to perform a direct numerical simulation (DNS) of convective-diffusion equation for non-reacting turbulent flow is given by (Baldyga and Bourne, 1999)... 

The three main numerical approaches used in turbulence combustion modeling are Reynolds averaged Navier Stokes (RANS) where all turbulent scales are modeled, direct numerical simulations (DNS) where all scales are resolved and large eddy simulations (LES) where larger scales are explicitly computed whereas the effects of smaller ones are modeled ... 

Direct numerical simulation, as the name implies, attempts to simulate all the dynamically important scales of turbulent flows, directly. It is based on the hypothesis that direct simulations may be carried out by artificially decreasing the Reynolds number to the point where important scales can be simulated accurately on existing computers. This is probably the most exact approach to turbulence simulation without requiring any additional modeling beyond accepting the Navier-Stokes equations to describe the turbulent flow processes. The result is equivalent to a single realization of a flow or a short duration laboratory experiment. It is also the simplest approach conceptually. In DNS, all the motions contained in the flow are resolved. 

One of the advantages of CFD approaches is that data can be provided at any point within the computational domain, providing a level of detail that cannot currently be approached by sensor networks this of course carries the caveat that CFD models include a number of assumptions in both the physics and the boundary conditions, all of which affect the accuracy of the predicted wind fields. A third CFD approach. Direct Numerical Simulation (DNS), in which the Navier-Stokes equations are solved directly, is presently not feasible due to the excessive computational requirements. At present, all CFD models are too slow for use in emergency operations they are best suited to detailed postevent studies or preparatory studies to understand the character of the local wind field in complex or urban terrain. 

Three different theoretical approaches have been established describing turbulent flows in general, as outlined in sect 1.3. These methods are the direct numerical simulations (DNS), large eddy simulations (LES), and the Reynolds average Navier-Stokes (RANS) approach. 

Agglomerate size distributions can also be calculated by. solving the Smol uchowski equation using an appropriate expression for the collision kernel. There is a fundamental dilfercncc between this approach and direct numerical simulation of the coagulation process. In computer. simulation, the value of Df is determined by the collision algorithm analyses based on the Smoluchowski equation require an assumption in advance of the value of... 

The total number of independent variables appearing in Fq. (4.32) is thus quite large, and in fact too large for practical applications. However, as mentioned earlier, by coupling Eq. (4.32) with the Navier-Stokes equation to find the forces on the particles due to the fluid, the Ap-particle system is completely determined. Although not written out explicitly, the reader should keep in mind that the mesoscale models for the phase-space fluxes and the collision term depend on the complete set of independent variables. For example, the surface terms depend on all of the state variables A[p ( x ", ", j/p" j, V ", j/p" ). The only known way to determine these functions is to perform direct numerical simulations of the microscale fluid-particle system using all possible sets of initial conditions. Obviously, such an approach is intractable. We are thus led to reduce the number of independent variables and to introduce mesoscale models that attempt to capture the average effect of multi-particle interactions. 

M. Giona, A. Adrover, and S. Cerbelli. On the use of the pulsed-convection approach for modelling advection-diffusion in chaotic flows - A prototypical example and direct numerical simulations. Physica A, 349 37-73, 2005. 

The deterministic approach of direct numerical simulation (DNS) and the probabilistic approach of probability density function (PDF) modeling are implemented for prediction of droplet dispersion and polydis-persity in liquid-fuel combustors. For DNS, a multidomain spectral element method was used for the carrier phase while tracking the droplets individually in a Lagrangian frame. The geometry considered here is a backward-facing step flow with and without a countercurrent shear. In PDF modeling, the extension of previous work to the case of evaporating droplets is discussed. 

An alternative approach is to use direct numerical simulation (DNS). Numerical results can offer considerable detail and allow access to the complete fluid flow. For example, how big is the role of disturbances generated in the atomizer Does the Rayleigh-Taylor instability matter in primary atomization Do ijewly formed droplets immediately collide with ligaments and previously formed droplets How useful are small-perturbation analyses for primary atomization The disadvantage is that DNS is capable of simulating only a small part of the spray. 

Current investigations are directed toward full-field measurement techniques and direct numerical simulation (DNS). The numerical approaches are limited by the need for much bigger and better computers. Previously, visual observations were used for qualitative assessment. Hot-wire/film and LDA measurements were used to provide the hard numbers for a few points in space in the time domain. Today, the visual-based techniques are being extended to allow full-field, time-resolved velocity vector information to be obtained. However, the need for full-field and time-resolved measurements put vast restrictions on what can be accomplished. To get time-resolved results, often today, we must sacrifice resolution. To get resolution, we must sacrifice the dynamics. Ultimately we want both. 

In conclusion, we have introduced a -matrix approach to the optical properties of large-scale PC-circuits. In this approach, an individual functional element is characterized by a 5-matrix which allows efficient computation of the entire. We have applied this approach to double bend waveguiding stmctures and have obtained excellent agreement with direct numerical simulations. 

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