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Original techniques were proposed for calculating and optimizing double cascades (DC) built of square cascades and a square cascade with an additional product flow (SCAP). Both cascade schemes (DC and SCAP) were tested in solving a task of simultaneous enrichment of three components of a model mixture to a pre-defined level. A comparison of the DC and SCAP efficiency was made according to the minimum of total cascade flow. The results have shown that the double cascade is more efficient in terms of the chosen criterion.

One of the important ways of improving axial compressor performance is to control the tip leakage flow near the endwall region. Numerical computations were conducted to investigate the impact of blade tip suction on the axial compressor cascade performance in current paper. Three suction schemes located on the blade tip with different chordwise coverage were investigated in total. The results show that the cascade overall performance can be effectively enhanced by the proper suction scheme on the blade tip and the best scheme should be arranged at slightly downstream of the onset point of the tip leakage vortex (TLV). The control effectiveness and mechanisms are different for the different suction schemes. For the suction scheme covering the starting point of TLV, the onset point of TLV is shifted downstream, while an additional induced leakage flow near the blade leading edge is generated resulting in the increase of mixing loss. It is more effective when the structure of the main TLV is destroyed and divided into different parts by applying the blade tip suction arranged slightly behind the onset point of TLV. In addition, the blade loading is redistributed near the blade tip after the blade tip suction and the total pressure loss caused by the suction slots should also be considered in the design process.

Two- and three-dimensional direct numerical simulation (DNS) of turbine cascade flow at low Reynolds number with heat transfer are performed using high-order finite difference method. Two-dimensional laminar computation which is used to construct the initial flow of three-dimensional DNS fails to predict Stanton number on the second half of suction side where the flow is turbulent in experiment. In three-dimensional DNS, transition is triggered by periodic blow-and-suction disturbances. Numerical experiments show that phase randomness of the disturbance is not necessary to trigger the transition which can be induced by disturbances with fixed phases. In a range of time fundamental frequency of disturbance, when increasing the frequency, transition moves downstream. When time fundamental frequency is big enough, transition disappears. With fixed space phases, time phases and selected time fundamental frequency, time averaged pressure and Stanton number distributions of three-dimensional DNS coincide with the experimental datum. Averaged velocity and temperature, Root-Mean-squares (RMS) of velocity pulse，temperature pulse, Reynolds shear stress and heat flux are extracted from the DNS database. All statistics agree well with experimental and theoretical results which verify the accuracy of present database.

A continuous flow cascade of multi-step catalytic reactions is a cutting-edge concept to revolutionize stepwise catalytic synthesis yet is still challenging in practical applications. Herein, a method for practical one-pot cascade catalysis is developed by combining Pickering emulsions with continuous flow. Our method involves co-localization of different catalytically active sub-compartments within droplets of a Pickering emulsion yielding cell-like microreactors, which can be packed in a column reactor for continuous flow cascade catalysis. As exemplified by two chemo-enzymatic cascade reactions for the synthesis of chiral cyanohydrins and chiral ester, 5 − 420 fold enhancement in the catalysis efficiency and as high as 99% enantioselectivity were obtained even over a period of 80 − 240 h. The compartmentalization effect and enriching-reactant properties arising from the biomimetic microreactor are theoretically and experimentally identified as the key factors for boosting the catalysis efficiency and for regulating the kinetics of cascade catalysis. A continuous flow cascade of multi-step catalytic reactions would provide significant advantages in faster reaction times, waste reduction, and lowered step-count of syntheses, yet this ideal remains challenging in practical applications. Here the authors describe continuous flow cascade catalysis through co-localization of two catalytically active subcompartments within Pickering emulsion droplets.

Sometimes a power failure can be fairly local, but other times, a seemingly identical initial failure can cascade to cause a massive and costly breakdown in the system. Yang et al. built a model for the North American power grid network based on samples of data covering the years 2008 to 2013 (see the Perspective by D'Souza). Although the observed cascades were widespread, a small fraction of all network components, particularly the ones that were most cohesive within the network, were vulnerable to cascading failures. Larger cascades were associated with concurrent triggering events that were geographically closer to each other and closer to the set of vulnerable components. Science , this issue p. eaan3184 ; see also p. 860 Cascading failures in the U.S. power grid are most likely to occur within cohesive parts of the grid. The understanding of cascading failures in complex systems has been hindered by the lack of realistic large-scale modeling and analysis that can account for variable system conditions. Using the North American power grid, we identified, quantified, and analyzed the set of network components that are vulnerable to cascading failures under any out of multiple conditions. We show that the vulnerable set consists of a small but topologically central portion of the network and that large cascades are disproportionately more likely to be triggered by initial failures close to this set. These results elucidate aspects of the origins and causes of cascading failures relevant for grid design and operation and demonstrate vulnerability analysis methods that are applicable to a wider class of cascade-prone networks.

Among the variety of correlated states exhibited by twisted bilayer graphene, cascades in the spectroscopic properties and in the electronic compressibility occur over larger ranges of energy, twist angle and temperature compared to other effects. This suggests a hierarchy of phenomena. Using a combined dynamical mean-field theory and Hartree calculation, we show that the spectral weight reorganisation associated with the formation of local moments and heavy quasiparticles can explain the cascade of electronic resets without invoking symmetry breaking orders. The phenomena reproduced here include the cascade flow of spectral weight, the oscillations of remote band energies, and the asymmetric jumps of the inverse compressibility. We also predict a strong momentum differentiation in the incoherent spectral weight associated with the fragile topology of twisted bilayer graphene. Twisted bilayer graphene hosts a sequence of electronic resets evidenced experimentally by characteristic spectroscopic cascades and sawtooth peaks in the inverse electronic compressibility. Here, the authors use combined dynamical mean-field theory and Hartree calculations to demonstrate that symmetry-breaking transitions are not necessary to observe cascades in twisted bilayer graphene.

The problem of highly concentrated molybdenum isotopes production in multiflow cascades is considered. A method of the cascade with two additional product flows optimization has been developed. Two components intermediate in weight are concentrated simultaneously in those flows. The optimization problem is solved using a variation of the partial flow cuts of the cascade stages with large separation coefficients. The optimization criterion is the minimum of the stage total feed flow while ensuring a given concentration of isotopes. A computational experiment was carried out to separate a mixture of molybdenum hexafluoride. The experiment demonstrated the features of intermediate components concentrating in additional product flows of the cascade.

Research on the flow mechanism and dynamic characteristics of a cascade comprising three NACA hydrofoils was conducted under varying cavitation numbers and angles of attack. This study serves as a theoretical foundation for the high-speed miniaturization of fluid machinery. Drawing upon prior findings on individual hydrofoils, comparisons were made regarding the cavitation characteristics of the cascade versus a single hydrofoil, emphasizing pressure and velocity distributions in the flow field. Results suggest that while the cascade consists of three hydrofoils, their interactions profoundly influence the flow field. The cavitation phenomena in the cascade diverge considerably from that of a single hydrofoil. Multiple hydrofoils cause a low-pressure region to appear in the middle of the cascade, making it more susceptible to cavitation flow compared to a single hydrofoil. However, interactions among the hydrofoils constrain the expansion of this low-pressure zone, rendering the cavitation flow in the cascade’s middle layer more stable. As the angle of attack rises, the cavitation flow around the cascade undergoes notable changes, with varying cavitation flows at different cascade positions. The upper layer experiences cavitation flow akin to that of a single hydrofoil. In contrast, the middle layer sustains a thin, weakly periodic cavitation flow.

Rotating Rayleigh–Bénard convection is investigated numerically with the use of an asymptotic model that captures the rapidly rotating, small Ekman number limit, $Ek \\rightarrow 0$. The Prandtl number ($Pr$) and the asymptotically scaled Rayleigh number ($\\widetilde {Ra} = Ra Ek^{4/3}$, where $Ra$ is the typical Rayleigh number) are varied systematically. For sufficiently vigorous convection, an inverse kinetic energy cascade leads to the formation of a pair of large-scale vortices of opposite polarity, in agreement with previous studies of rapidly rotating convection. With respect to the kinetic energy, we find a transition from convection dominated states to a state dominated by large-scale vortices at an asymptotically reduced (small-scale) Reynolds number of $\\widetilde {Re} \\approx 6$ ($\\widetilde {Re} = Re Ek^{1/3}$, where $Re$ is the Reynolds number associated with vertical flows) for all investigated values of $Pr$. The ratio of the depth-averaged kinetic energy to the kinetic energy of the convection reaches a maximum at $\\widetilde {Re} \\approx 24$, then decreases as $\\widetilde {Ra}$ is increased. This decrease in the relative kinetic energy of the large-scale vortices is associated with a decrease in the convective correlations with increasing Rayleigh number. The scaling behaviour of the convective flow speeds is studied; although a linear scaling of the form $\\widetilde {Re} \\sim \\widetilde {Ra}/Pr$ is observed over a limited range in Rayleigh number and Prandtl number, a clear departure from this scaling is observed at the highest accessible values of $\\widetilde {Ra}$. Calculation of the forces present in the governing equations shows that the ratio of the viscous force to the buoyancy force is an increasing function of $\\widetilde {Ra}$, that approaches unity over the investigated range of parameters.

Unruptured intracranial aneurysms are common in the general population, and many uncertainties remain when predicting rupture risks and treatment outcomes. One of the cutting-edge tools used to investigate this condition is computational fluid dynamics (CFD). However, CFD is not yet mature enough to guide the clinical management of this disease. In addition, recent studies have reported significant flow instabilities when refined numerical methods are used. Questions remain as to how to properly simulate and evaluate this flow, and whether these instabilities are really turbulence. The purpose of the present study is to evaluate the impact of the simulation setup on the results and investigate the occurrence of turbulence in a cerebral artery with an aneurysm. For this purpose, direct numerical simulations were performed with up to 200 cardiac cycles and with data sampling rates of up to 100,000 times per cardiac cycle. Through phase-averaging or triple decomposition, the contributions of turbulence and of laminar pulsatile waves to the velocity, pressure and wall shear stress fluctuations were distinguished. For example, the commonly used oscillatory shear index was found to be closely related to the laminar waves introduced at the inlet, rather than turbulence. The turbulence energy cascade was evaluated through energy spectrum estimates, revealing that, despite the low flow rates and Reynolds number, the flow is turbulent near the aneurysm. Phase-averaging was shown to be an approach that can help researchers better understand this flow, although the results are highly dependent on simulation setup and post-processing choices.