Direct numerical simulations model

Wang, G., Mukherjee, P P, and Wang, C. Y. Optimization of polymer electrolyte fuel cell cathode catalyst layers via direct numerical simulation modeling. Electrochimica Acta 2007 52 6367-6377. 

Mukherjee, P.P. and Wang, C.Y. (2007) Direct numerical simulation modeling of bilayer cathode catalyst layers in polymer electrolyte fuel cells. /. Electrochem. Soc., 154(11), B1121-B1131. 

Electrochemistry coupled direct numerical simulation model... 

The engineer is offered a large variety of flow-modeling methods, whose complexity ranges from simple order-of-magnitude analysis to direct numerical simulation. Up to now, the methods of choice have ordinarily been experimental and semi-theoretical, such as cold flow simulations and tracer studies. 

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 term direct in Direct Numerical Simulations indicates that the flow is fully resolved by solving, without any modeling, the classical NS equations... 

The CFD models considered up to this point are, as far as the momentum equation is concerned, designed for single-phase flows. In practice, many of the chemical reactors used in industry are truly multiphase, and must be described in the context of CFD by multiple momentum equations. There are, in fact, several levels of description that might be attempted. At the most detailed level, direct numerical simulation of the transport equations for all phases with fully resolved interfaces between phases is possible for only the simplest systems. For... 

The material covered in the appendices is provided as a supplement for readers interested in more detail than could be provided in the main text. Appendix A discusses the derivation of the spectral relaxation (SR) model starting from the scalar spectral transport equation. The SR model is introduced in Chapter 4 as a non-equilibrium model for the scalar dissipation rate. The material in Appendix A is an attempt to connect the model to a more fundamental description based on two-point spectral transport. This connection can be exploited to extract model parameters from direct-numerical simulation data of homogeneous turbulent scalar mixing (Fox and Yeung 1999). 

As discussed in Chapter 2, a fully developed turbulent flow field contains flow structures with length scales much smaller than the grid cells used in most CFD codes (Daly and Harlow 1970).29 Thus, CFD models based on moment methods do not contain the information needed to predict x, t). Indeed, only the direct numerical simulation (DNS) of (1.27)-(1.29) uses a fine enough grid to resolve completely all flow structures, and thereby avoids the need to predict x, t). In the CFD literature, the small-scale structures that control the chemical source term are called sub-grid-scale (SGS) fields, as illustrated in Fig. 1.7. 

Only direct numerical simulation (DNS) resolves all scales (Moin and Mahesh 1998). However, DNS is com-putationally intractable for chemical reactor modeling. 

This chapter is devoted to methods for describing the turbulent transport of passive scalars. The basic transport equations resulting from Reynolds averaging have been derived in earlier chapters and contain unclosed terms that must be modeled. Thus the available models for these terms are the primary focus of this chapter. However, to begin the discussion, we first review transport models based on the direct numerical simulation of the Navier-Stokes equation, and other models that do not require one-point closures. The presentation of turbulent transport models in this chapter is not intended to be comprehensive. Instead, the emphasis is on the differences between particular classes of models, and how they relate to models for turbulent reacting flow. A more detailed discussion of turbulent-flow models can be found in Pope (2000). For practical advice on choosing appropriate models for particular flows, the reader may wish to consult Wilcox (1993). 

Domingo, P. and T. Benazzouz (2000). Direct numerical simulation and modeling of a nonequilibrium turbulent plasma. AIAA Journal 38, 73-78. 

Direct numerical simulation is expected to play a more dominant role for analytical treatment of turbulent flames. In addition to capturing physical phenomena, the authors feel that a very powerful role of DNS is its capability for model validations. In fact, in most of our modeling activities, DNS has been the primary means of verifying specific assumptions and/or approximations. This is partially due to difficulties in laboratory measurements of some of the correlations and also in setting configurations suitable for model assessments. Of course, the overall evaluation of the final form of the model requires the use of laboratory data for flows in which all of the complexities are present. 

A more detailed study of fuel cloud dispersion, though one lacking direct exptl verification, was made by Rosenblatt et al (Ref 23). The purpose of their study was to develop and use physically based numerical simulation models to examine the cloud dispersion and cloud detonation with fuel mass densities and particle size distributions as well as the induced air pressures and velocities as the principal parameters of interest. A finite difference 2-D Eulerian code was used. We quote The basic numerical code used for the FAE analysis was DICE, a 2-D implicit Eulerian finite difference technique which treats fluid-particle mixtures. DICE treats par-... 

In order to evaluate the effect of pore volume blockage in the presence of liquid water causing hindered oxygen transport to the active reaction sites, the direct numerical simulation (DNS) model, mentioned earlier and detailed in our work,25-27 68 is deployed for the pore-scale description of species and charge transport through the reconstructed CL microstructure. 

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. 

Although direct numerical simulations under limited circumstances have been carried out to determine (unaveraged) fluctuating velocity fields, in general the solution of the equations of motion for turbulent flow is based on the time-averaged equations. This requires semi-empirical models to express the Reynolds stresses in terms of time-averaged velocities. This is the closure problem of turbulence. In all but the simplest geometries, numerical methods are required. 

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