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Register a new userA fast, low-memory, and stable algorithm for implementing multicomponent transport in direct numerical simulations
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Implementing multicomponent diffusion models in reacting-flow simulations is computationally expensive due to the challenges involved in calculating diffusion coefficients. Instead, mixture-averaged diffusion treatments are typically used to avoid these costs. However, to our knowledge, the accuracy and appropriateness of the mixture-averaged diffusion models has not been verified for three-dimensional turbulent premixed flames. In this study we propose a fast,efficient, low-memory algorithm and use that to evaluate the role of multicomponent mass diffusion in reacting-flow simulations. Direct numerical simulation of these flames is performed by implementing the Stefan-Maxwell equations in NGA. A semi-implicit algorithm decreases the computational expense of inverting the full multicomponent ordinary diffusion array while maintaining accuracy and fidelity. We first verify the method by performing one-dimensional simulations of premixed hydrogen flames and compare with matching cases in Cantera. We demonstrate the algorithm to be stable, and its performance scales approximately with the number of species squared. Then, as an initial study of multicomponent diffusion, we simulate premixed, three-dimensional turbulent hydrogen flames, neglecting secondary Soret and Dufour effects. Simulation conditions are carefully selected to match previously published results and ensure valid comparison. Our results show that using the mixture-averaged diffusion assumption leads to a 15% under-prediction of the normalized turbulent flame speed for a premixed hydrogen-air flame. This difference in the turbulent flame speed motivates further study into using the mixture-averaged diffusion assumption for DNS of moderate-to-high Karlovitz number flames.
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Implementing multicomponent diffusion models in numerical combustion studies is computationally expensive; to reduce cost, numerical simulations commonly use mixture-averaged diffusion treatments or simpler models. However, the accuracy and appropriateness of mixture-averaged diffusion has not been verified for three-dimensional, turbulent, premixed flames. In this study we evaluated the role of multicomponent mass diffusion in premixed, three-dimensional high Karlovitz-number hydrogen, n-heptane, and toluene flames, representing a range of fuel Lewis numbers. We also studied a premixed, unstable two-dimensional hydrogen flame due to the importance of diffusion effects in such cases. Our comparison of diffusion flux vectors revealed differences of 10-20% on average between the mixture-averaged and multicomponent diffusion models, and greater than 40% in regions of high flame curvature. Overall, however, the mixture-averaged model produces small differences in diffusion flux compared with global turbulent flame statistics. To evaluate the impact of these differences between the two models, we compared normalized turbulent flame speeds and conditional means of species mass fraction and source term. We found differences of 5-20% in the mean normalized turbulent flame speeds, which seem to correspond to differences of 5-10% in the peak fuel source terms. Our results motivate further study into whether the mixture-averaged diffusion model is always appropriate for DNS of premixed turbulent flames.
We report results on the explicit parameterisation of discrete Rossby-wave resonant triads of the Charney-Hasegawa-Mima equation in the small-scale limit (i.e. large Rossby deformation radius), following up from our previous solution in terms of elliptic curves (Bustamante and Hayat, 2013). We find an explicit parameterisation of the discrete resonant wavevectors in terms of two rational variables. We show that these new variables are restricted to a bounded region and find this region explicitly. We argue that this can be used to reduce the complexity of a direct numerical search for discrete triad resonances. Also, we introduce a new direct numerical method to search for discrete resonances. This numerical method has complexity ${mathcal{O}}(N^3)$, where $N$ is the largest wavenumber in the search. We apply this new method to find all discrete irreducible resonant triads in the wavevector box of size $5000$, in a calculation that took about $10.5$ days on a $16$-core machine. Finally, based on our method of mapping to elliptic curves, we discuss some dynamical implications regarding the spread of quadratic invariants across scales via resonant triad interactions, in the form of sharp bounds on the size of the interacting wavevectors.
We analyze time series stemming from experiments and direct numerical simulations of hydrodynamic and magnetohydrodynamic turbulence. Simulations are done in periodic boxes, but with a volumetric forcing chosen to mimic the geometry of the flow in the experiments, the von Karman swirling flow between two counter-rotating impellers. Parameters in the simulations are chosen to (within computational limitations) allow comparisons between the experiments and the numerical results. Conducting fluids are considered in all cases. Two different configurations are considered: a case with a weak externally imposed magnetic field, and a case with self-sustained magnetic fields. Evidence of long-term memory and $1/f$ noise is observed in experiments and simulations, in the case with weak magnetic field associated with the hydrodynamic behavior of the shear layer in the von Karman flow, and in the dynamo case associated with slow magnetohydrodynamic behavior of the large scale magnetic field.
To investigate the formation mechanism of energy spectra of internal waves in the oceans, direct numerical simulations are performed. The simulations are based on the reduced dynamical equations of rotating stratified turbulence. In the reduced dynamical equations only wave modes are retained, and vortices and horizontally uniform vertical shears are excluded. Despite the simplifications, our simulations reproduce some key features of oceanic internal-wave spectra: accumulation of energy at near-inertial waves and realistic frequency and horizontal wavenumber dependencies. Furthermore, we provide evidence that formation of the energy spectra in the inertial subrange is dominated by scale-separated interactions with the near-inertial waves. These findings support oceanographers intuition that spectral energy density of internal waves is the result of predominantly wave-wave interactions.
Turbulent flows under transcritical conditions are present in regenerative cooling systems of rocker engines and extraction processes in chemical engineering. The turbulent flows and the corresponding heat transfer phenomena in these complex processes are still not well understood experimentally and numerically. The objective of this work is to investigate the turbulent flows under transcritical conditions using DNS of turbulent channel flows. A fully compressible solver is used in conjunction with a Peng-Robinson real-fluid equation of state to describe the transcritical flows. A channel flow with two isothermal walls is simulated with one heated and one cooled boundary layers. The grid resolution adopted in this study is slightly finer than that required for DNS of incompressible channel flows. The simulations are conducted using both fully (FC) and quasi-conservative (QC) schemes to assess their performance for transcritical wall-bounded flows. The instantaneous flows and the statistics are analyzed and compared with the canonical theories. It is found that results from both FC and QC schemes qualitatively agree well with noticeable difference near the top heated wall, where spurious oscillations in velocity can be observed. Using the DNS data, we then examine the usefulness of Townsend attached eddy hypothesis in the context of flows at transcritical conditions. It is shown that the streamwise energy spectrum exhibits the inverse wavenumber scaling and that the streamwise velocity structure function follows a logarithmic scaling, thus providing support to the attached eddy model at transcritical conditions.
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