Appendix C
Direct Numerical Simulations

Direct numerical simulation (DNS) is a computational approach specifically designed to capture key turbulence-chemistry interactions underlying the operation of modern combustors and, in particular, an approach that can discriminate the effects of differences in fuel properties. In DNS, all of the relevant turbulence and flame scales are resolved numerically using high-order, accurate numerical algorithms. Three-dimensional simulations with complex chemistry, and turbulence parameters within the realm of moderate Reynolds number flames, are of significant interest to the combustion-modeling community (academia, industry, and national laboratories) to provide data for the validation of key turbulence modeling concepts.

Many of the existing combustion models rely on conditioning variables, and it is feasible to assess the magnitude of the conditional fluctuations, leading to an understanding of the extent to which the thermochemical state can be parameterized by a reduced set of variables. Furthermore, it will be possible to assess the degree to which these variables can be predicted from the resolved or mean flow—for example, using presumed forms of the probability density function. For flamelet and transported probability density function models, Lagrangian tracking of fluid particles and flame elements in situ can be used to identify and understand the influence of unsteadiness, differential diffusion of species, and temperature on limit phenomena, including extinction and ignition phenomena. The particle-tracking statistics are also useful for understanding reactive scalar mixing rates and their departure from passive scalar mixing rates.



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Appendix C Direct Numerical Simulations Direct numerical simulation (DNS) is a computational approach spe - cifically designed to capture key turbulence-chemistry interactions under- lying the operation of modern combustors and, in particular, an approach that can discriminate the effects of differences in fuel properties. In DNS, all of the relevant turbulence and flame scales are resolved numerically using high-order, accurate numerical algorithms. Three-dimensional sim - ulations with complex chemistry, and turbulence parameters within the realm of moderate Reynolds number flames, are of significant interest to the combustion-modeling community (academia, industry, and national laboratories) to provide data for the validation of key turbulence model - ing concepts. Many of the existing combustion models rely on conditioning vari - ables, and it is feasible to assess the magnitude of the conditional fluctua - tions, leading to an understanding of the extent to which the thermochem- ical state can be parameterized by a reduced set of variables. Furthermore, it will be possible to assess the degree to which these variables can be predicted from the resolved or mean flow—for example, using presumed forms of the probability density function. For flamelet and transported probability density function models, Lagrangian tracking of fluid particles and flame elements in situ can be used to identify and understand the influence of unsteadiness, differential diffusion of species, and tempera- ture on limit phenomena, including extinction and ignition phenomena. The particle-tracking statistics are also useful for understanding reactive scalar mixing rates and their departure from passive scalar mixing rates. 86

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87 APPENDIX C Once validated, the models can be used in engineering large-eddy simu - lation or Reynolds-averaged Navier-Stokes simulations to optimize the design of future devices. As direct numerical simulations begin to move into the realm of laboratory-scale flames, DNS data can also provide valuable insights to the turbulent-flame experimental community. Experimentalists investi - gating turbulent-flame phenomena not only are limited by the scarcity of the data they are able to measure, but also often need to appeal to simplified theories to interpret measurements. For example, in turbulent premixed flame experiments, researchers typically assume that the flame locally propagates with the laminar-flame speed so that the turbulent- flame speed can be determined by measuring the wrinkling of the flame. This is an accurate approximation for natural gas flames but can lead to significant errors in regimes such as lean hydrogen flames. Simulation data from direct numerical simulations can be used to augment standard experimental diagnostics to obtain a more complete picture of turbulent- flame experiments. A key issue in working with direct numerical simulations is the huge volume of data they generate—as much as 1/3 petabyte of data per realiza- tion on a 1 petaflop machine. Petascale computers are enabling DNS of tur- bulent reactive flows with approximately four decades of spatial scales and the incorporation of realistic chemical kinetics of small, single-component hydrocarbon fuels in three-dimensional turbulent simulations. The advent of exascale computing and beyond in the future will enable an even wider range of turbulence scales and the representation of more complex fuels at thermochemical conditions relevant to practical combustion systems, and the data volume and complexity will continue to increase. However, such large and complex time-varying data sets—typically several hundred terabytes of raw data per simulation on today’s 1 peta- flop machines—pose serious challenges to gleaning physical insight from them and to sharing the data with the broader modeling community. Data-mining and database technology are needed to automate ways to identify patterns, to come up with reduced-order descriptions, to develop machine learning, and to visualize salient features in the data in order to reduce the sheer volume of data to be processed and transmitted. Although only a few combustion researchers have the facilities, including access to high-performance computers, to carry out these enor- mous computations, access by the larger combustion community to the computed results, stored in a consistent and common format, is another important benefit that would be provided by a combustion cyberinfra- structure. These computed results represent a valuable resource that should be exploited by multiple researchers, but there is currently no clear way for such activities to be organized.