Turbulence, direct numerical simulations

Givi, P. and P. A. McMurtry (1988). Nonpremixed reaction in homogeneous turbulence Direct numerical simulations. AIChE Journal 34, 1039-1042. 

Lu et al. (2009) identified QSS-species and pre-equilibrium reactions on the fly, based on the investigation of system timescales. This information was used to convert the original system of differential equations to a less stiff system of differential algebraic equations. This dynamic stiffness removal method for accelerating simirlations was successfully applied for predictions using an n-heptane oxidatirm mechanism in ID and 2D turbulent direct numerical simulations. 

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-... 

L. Vervisch and T. Poinsot, Direct numerical simulation of non-premixed turbulent flames, Annu. Rev. Fluid Mech. 30 655-691,1998. 

The spectral method is used for direct numerical simulation (DNS) of turbulence. The Fourier transform is taken of the differential equation, and the resulting equation is solved. Then the inverse transformation gives the solution. When there are nonlinear terms, they are calculated at each node in physical space, and the Fourier transform is taken of the result. This technique is especially suited to time-dependent problems, and the major computational effort is in the fast Fourier transform. 

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. 

Direct numerical simulation studies of turbulent mixing (e.g., Ashurst et al. 1987) have shown that the fluctuating scalar gradient is nearly always aligned with the eigenvector of the most compressive strain rate. For a fully developed scalar spectrum, the vortexstretching term can be expressed as... 

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). 

The reduction of the turbulent-reacting-flow problem to a turbulent-scalar-mixing problem represents a significant computational simplification. However, at high Reynolds numbers, the direct numerical simulation (DNS) of (5.100) is still intractable.86 Instead, for most practical applications, the Reynolds-averaged transport equation developed in... 

Bogucki, D., J. A. Domaradzki, and P. K. Yeung (1997). Direct numerical simulations of passive scalars with Pr > 1 advected by turbulent flow. Journal of Fluid Mechanics 343, 111-130. 

Direct numerical simulation of a turbulent reactive plume on a parallel computer. 

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

Eswaran, V. and S. B. Pope (1988). Direct numerical simulations of the turbulent mixing of a passive scalar. The Physics of Fluids 31, 506-520. 

Jou, W. H. and J. J. Riley (1989). Progress in direct numerical simulation of turbulent reacting flows. AAIA Journal 27, 1543-1557. 

Leonard, A. D. and J. C. Hill (1988). Direct numerical simulation of turbulent flows with chemical reaction. Journal of Scientific Computing 3, 25 -3. 

Moin, P. and K. Mahesh (1998). Direct numerical simulation A tool for turbulence research. 

Swaminathan, N. and R. W. Bilger (1997). Direct numerical simulation of turbulent nonpremixed hydrocarbon reaction zones using a two-step reduced mechanism. Combustion Science and Technology 127, 167-196. 

Vedula, P. (2001). Study of Scalar Transport in Turbulent Flows Using Direct Numerical Simulations. Ph. D. thesis, Georgia Institute of Technology, Atlanta. 

Lagrangian characteristics of turbulence and scalar transport in direct numerical simulations. Journal of Fluid Mechanics 427, 241-274. 

Yeung, P. K. and S. B. Pope (1989). Lagrangian statistics from direct numerical simulations of isotropic turbulence. Journal of Fluid Mechanics 207, 531-586. 

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. 

Poinsot, T. 1996. Using direct numerical simulations to understand premixed turbulent combustion. 26th Symposium (International) on Combustion Proceedings. Pittsburgh, PA The Combustion Institute. 219-32. 

Mercier P, Tochon P. Analysis of turbulent flow and heat transfer in compact heat exchangers by a pseudo-direct numerical simulation. In Shah RK, ed. Compact Heat Exchanger for the Process Industry. Begell House, 1997 223-230. 

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