The classical energy cascade in turbulence as described by Richardson and Kolmogorov is predominantly a conjecture relying on the locality of interactions between scales of turbulence. This picture is generally accepted and assumes that energy and enstrophy transfers occur between neighbouring scales of turbulence and that vortex stretching plays a major role in the dynamics of this energy cascade. Direct numerical simulation data for Re λ ranging from 37 to 1131 is used to gather evidence for the cascade by investigating the energy and enstrophy fluxes between scales and the interplay between vorticity at one scale and strain at an adjacent scale. This is achieved by using a bandpass filter to educe the turbulent structures at various length scales allowing one to determine the fluxes between these scales and to interrogate the role of non-local (in physical-space) vortex stretching. It is shown that the structures of a length scale L mostly transfer their energy to structures of size 0.3L and that most of the enstrophy flux goes from structures of scale L to 0.3L. Furthermore, vortical structures of a length scale L ω are stretched mostly by straining structures of size 3 to 5L ω and the stretching by eddies of sizes larger than 10L ω is negligible. The stretching is dominated by the most extensive principal strain rate of the straining structures. These observations are found to be independent of Re λ for the range investigated in this study. These results provide strong evidence for the classical view of an energy cascade transferring energy from large to small scales through a hierarchy of steps, each step consisting of the stretching of vortices by somewhat larger structures.
A simple model based on a Perfectly Stirred Reactor (PSR) is proposed for moderate or intense low-oxygen dilution (MILD) combustion. The PSR calculation is performed covering the entire flammability range and the tabulated chemistry approach is used with a presumed joint probability density function (PDF). The jet, in hot and diluted coflow experimental setup under MILD conditions, is simulated using this reactor model for two oxygen dilution levels. The computed results for mean temperature, major and minor species mass fractions are compared with the experimental data and simulation results obtained recently using a multi-environment transported PDF approach. Overall, a good agreement is observed at three different axial locations for these comparisons despite the overpredicted peak value of CO formation. This suggests that MILD combustion can be effectively modelled by the proposed PSR model with lower computational
We propose a physics-informed Echo State Network (ESN) to predict the evolution of chaotic systems. Compared to conventional ESNs, the physics-informed ESNs are trained to solve supervised learning tasks while ensuring that their predictions do not violate physical laws. This is achieved by introducing an additional loss function during the training of the ESNs, which penalizes non-physical predictions without the need of any additional training data. This approach is demonstrated on a chaotic Lorenz system, where the physics-informed ESNs improve the predictability horizon by about two Lyapunov times as compared to conventional ESNs. The proposed framework shows the potential of using machine learning combined with prior physical knowledge to improve the time-accurate prediction of chaotic dynamical systems.
Multiscale analysis of wall-bounded turbulent premixed flames is performed using three-dimensional direct numerical simulation (DNS) data of flame-wall interaction (FWI). The chosen configuration represents head-on quenching of a turbulent statistically planar stoichiometric methane-air flame by an isothermal inert wall. Different turbulence intensities and chemical mechanism have been analysed. A bandpass filtering technique is utilised to analyse the influence of turbulent eddies of varying size and the statistics of vorticity and strain rate fields associated with them. It is found that the presence of the flame does not alter the mechanism of vortex stretching in turbulent flows when the flame is away from the wall, but in the case of FWI, the mechanism of vortex stretching is altered due to a reduction in the contribution from non-local strain, and the small scales of turbulence start to contribute to flame straining process. The results indicate that small scale eddies do not contribute to the tangential strain rate when the flames are away from the walls, whereas the contribution from the small scales to the tangential strain rate increases when the flame is in the vicinity of the wall. It is also found that the choice of chemical mechanism does not influence the underlying fluid mechanical processes involved in flame-wall interaction.
Dunaliella is currently drawing worldwide attention as an alternative source of nutraceuticals. Commercially, β-carotene making up over 10% of Dunaliella biomass is generating the most interest. These compounds, because of their non-toxic properties, have found applications in the food, drug and cosmetic industry. The β-carotene content of Dunaliella cells, however, depends heavily on the growth conditions and especially on the availability of nutrients, salinity, irradiance and temperature in the growth medium. A chemically well defined medium is usually required, which significantly contributes to the cost of pigment production; hence a desire for low cost marine media. The present study aimed at evaluating the suitability of six different media, especially exploiting local potential resources, for the mass production of Dunaliella salina DCCBC15 as functional food and medicine. The efficacy of a new selected low-cost enriched natural seawater medium (MD4), supplemented with industrial N-P-K fertilizer, was investigated with respect to biomass production, chlorophyll, antioxidant capacity, and total carotene by Dunaliella though culture conditions were not optimized yet. This new medium (MD4) appears extremely promising, since it affords a higher production of Dunaliella biomass and pigments compared with the control, a common artificial medium (MD1), while allowing a substantial reduction in the production costs. The medium is also recommended for culturing other marine algae.
We propose a physics-informed Echo State Network (ESN) to predict the evolution of chaotic systems. Compared to conventional ESNs, the physics-informed ESNs are trained to solve supervised learning tasks while ensuring that their predictions do not violate physical laws. This is achieved by introducing an additional loss function during the training, which is based on the system's governing equations. The additional loss function penalizes non-physical predictions without the need of any additional training data. This approach is demonstrated on a chaotic Lorenz system and a truncation of the Charney-DeVore system. Compared to the conventional ESNs, the physics-informed ESNs improve the predictability horizon by about two Lyapunov times. This approach is also shown to be robust with regard to noise. The proposed framework shows the potential of using machine learning combined with prior physical knowledge to improve the time-accurate prediction of chaotic dynamical systems.
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