Publications

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Formulas for incremental or parallel computation of second order central moments have long been known, and recent extensions of these formulas to univariate and multivariate moments of arbitrary order have been developed. Such formulas are of key importance in scenarios where incremental results are required and in parallel and distributed systems where communication costs are high. We survey these recent results, and recall the first generalizations which we had obtained in [P$\acute0$8]. We then improve these arbitrary-order, numerically stable one-pass formulas to arbitrary-variate formulas which we further extend to arbitrary weights and compound variants. We also develop a generalized correction factor for standard two-pass algorithms that enables the maintenance of accuracy over nearly the full representable range of the input, avoiding the need for extended-precision arithmetic.

The topology of turbulent premixed flames is analysed using data from Direct Numerical Simulation (DNS), with emphasis on the statistical geometry of flame-flame interaction. A general method for obtaining the critical points of line, surface and volume fields is outlined, and the method is applied to isosurfaces of reaction progress variable in a DNS configuration involving a pair of freely-propagating hydrogen-air flames in a field of intense shear-generated turbulence. A complete set of possible flame-interaction topologies is derived using the eigenvalues of the scalar Hessian, and the topologies are parametrised using a pair of shape factors. The frequency of occurrence of each type of topology is evaluated from the DNS dataset for two different Damköhler numbers. Different types of flame-interaction topology are found to be favoured in various regions of the turbulent flame, and the physical significance of each interaction is discussed.

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Extreme-scale computing will bring significant changes to high performance computing system architectures. In particular, the increased number of system components is creating a need for software to demonstrate 'pervasive parallelism' and resiliency. Asynchronous, many-task programming models show promise in addressing both the scalability and resiliency challenges, however, they introduce an enormously challenging distributed, resilient consistency problem. In this work, we explore the viability of resilient collective communication in task scheduling and work stealing and, through simulation with SST/macro, the performance of these collectives on speculative extreme-scale architectures.

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This paper reports the results of a joint experimental and numerical study of the ow characteristics and flame stabilization of a hydrogen rich jet injected normal to a turbulent, vitiated cross ow of lean methane combustion products. Simultaneous high-speed stereoscopic PIV and OH PLIF measurements were obtained and analyzed alongside three-dimensional direct numerical simulations of inert and reacting JICF with detailed H₂/CO chemistry. Both the experiment and the simulation reveal that, contrary to most previous studies of reacting JICF stabilized in low-to-moderate temperature air cross ow, the present conditions lead to an autoigniting, burner-attached flame that initiates uniformly around the burner edge. Significant asymmetry is observed, however, between the reaction zones located on the windward and leeward sides of the jet, due to the substantially different scalar dissipation rates. The windward reaction zone is much thinner in the near field, while also exhibiting significantly higher local and global heat release than the much broader reaction zone found on the leeward side of the jet. The unsteady dynamics of the windward shear layer, which largely control the important jet/cross flow mixing processes in that region, are explored in order to elucidate the important flow stability implications arising in the reacting JICF. Vorticity spectra extracted from the windward shear layer reveal that the reacting jet is globally unstable and features two high frequency peaks, including a fundamental mode whose Strouhal number of ~0.7 agrees well with previous non-reacting JICF stability studies. The paper concludes with an analysis of the ignition, ame stabilization, and global structure of the burner-attached flame. Chemical explosive mode analysis (CEMA) shows that the entire windward shear layer, and a large region on the leeward side of the jet, are highly explosive prior to ignition and are dominated by non-premixed flame structures after ignition. The predominantly mixing limited nature of the flow after ignition is confirmed by computing the Takeno flame index, which shows that ~70% of the heat release occurs in non-premixed regions.

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In the design of high-hydrogen content gas turbines for power generation, ashback of the turbulent ame by propagation through the low velocity boundary layers in the premix- ing region is an operationally dangerous event. Predictive models that could capture the onset of ashback would be indispensable in gas turbine design. For this purpose, modeling of the ashback process using the large eddy simulation (LES) approach is considered here. In particular, the goal is to understand the modeling requirements for predicting ashback in confined goemetries. The ow configuration considered is a turbulent channel ow, for which high-fidelity direct numerical simulation (DNS) data already exists. A suite of LES calculations with different model formulations and filterwidths is considered. It is shown that LES predicts certain statistical properties of the ame front reasonably well, but fails to capture the propagation velocity accurately. It is found that the ashback process is invariant to changes in the initial conditions and additional near-wall grid refinement but the LES filterwidth as well as the subfilter models are found to be important even when the turbulence is almost fully resolved. From the computations, it is shown that for an LES model to predict ashback, suffcient resolution of the near-wall region, proper represen- tation of the centerline acceleration caused by ame blockage, and appropriate modeling of the propagation of a wrinkled ame front near the center of the channel are considered the critical requirements.

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