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Axial flow pumps often experience uneven distribution of axial force on the blades when deviating from design conditions, which can easily lead to local damage to the pump blades. In response to this issue, this article conducts a detailed study on the hydraulic and axial force characteristics of large vertical axial flow pumping stations in China based on constant and non-constant numerical simulation research methods. Research has found that under biased operating conditions, due to the angle between the water flow direction inside the impeller and the impeller blades, the water body collides with the blades, resulting in concentrated pressure distribution on both sides of the inlet side of the impeller blades. Under low flow conditions, the high axial force area of the impeller blade is concentrated in the middle and rear position of the suction surface, while under high flow conditions, the high axial force area is widely distributed. Under the conditions of 0.8 Q to 1.4 Q , the fluctuation of axial force on the impeller blades is mainly affected by the rotation of the impeller blades. However, under low flow conditions, due to the turbulence of the flow state, there is no obvious pattern of axial force variation on the impeller blades. In addition, under different flow conditions, there is no obvious pattern in the fluctuation of axial force on the guide vanes. This also proves that there are problems such as uneven axial force distribution and no periodic changes in the impeller blades under low flow conditions, which can easily lead to damage to the impeller blades. The above analysis can provide some reference for the design of impeller blades.

We propose a linear electrolyzer model for steady-state load flow analysis of multi-carrier energy networks, where the electrolyzer is capable of producing hydrogen gas and heat. For our electrolyzer model, we show that there are boundary conditions that lead to a well-posed problem. We derive these conditions for two cases, namely with a known and unknown heat efficiency parameter. Furthermore, the derived conditions are validated numerically. Moreover, we investigate the extensibility of our model by including nonlinear models from electricity, gas, and heat. In this setting, we derived boundary conditions based on our previous findings. Due to the involvement of nonlinearity, it is a challenge to prove that the boundary conditions lead to a well-posed problem. Therefore, we simulated the electrolyzer connected with an electricity, gas, and heat system. Additionally, we considered a known and unknown heat efficiency parameter. The numerical results support that the linear electrolyzer model is solvable in a multi-carrier energy network.

Au confluent de la comptabilité, de la finance, de la stratégie et de l’analyse sociale, l’analyse financière permet de pénétrer le fonctionnement financier de l’entreprise, de ses équilibres et déséquilibres, de saisir la portée financière des stratégies mises en œuvre mais également d’analyser les mécanismes de création et de répartition de la valeur. Dérangeante dans sa capacité à révéler les enjeux de pouvoir, elle intègre une puissante dimension normative, rarement explicitée. Cet article propose d’en interroger les objectifs et les enjeux à travers l’histoire de l’un de ses dispositifs, le tableau de financement sur la période 60s-80s. L’analyse des différents modèles permet de mettre en lumière, à travers les controverses et les conflits, les préoccupations des acteurs et des institutions économiques qui ont pesé sur les choix réalisés, d’interroger le rôle de l’analyse financière sur sa représentation des rapports sociaux et de lever les ombres sur certains de ses impensés. At the intersection between accounting, finance, strategy and social analysis, financial analysis enables us to penetrate the financial operation of a business with its balances and imbalances, grasp the financial reach of the strategies implemented, and analyze the value creation and distribution mechanisms. Its ability to reveal the stakes of power is disturbing and it incorporates a powerful normative dimension that is rarely explicit. This article seeks to explore the objectives and stakes of financial analysis through the history of one of its devices, the cash flow statement, from the 1960s to the 1980s. Analysis of its various forms and the related controversies and conflicts highlights the concerns of the actors and economic institutions that influenced the choices made, questions the role of financial analysis and examines how the role of financial analysis affects its representations of social relationships and bring some of its impensés out of the shadows.

Droplet dynamics in microfluidic applications is significantly influenced by surfactants. It remains a research challenge to model and simulate droplet behaviour including deformation, breakup and coalescence, especially in the confined microfluidic environment. Here, we propose a hybrid method to simulate interfacial flows with insoluble surfactants. The immiscible two-phase flow is solved by an improved lattice Boltzmann colour-gradient model which incorporates a Marangoni stress resulting from non-uniform interfacial tension, while the convection–diffusion equation which describes the evolution of surfactant concentration in the entire fluid domain is solved by a finite difference method. The lattice Boltzmann and finite difference simulations are coupled through an equation of state, which describes how surfactant concentration influences interfacial tension. Our method is first validated for the surfactant-laden droplet deformation in a three-dimensional (3D) extensional flow and a 2D shear flow, and then applied to investigate the effect of surfactants on droplet dynamics in a 3D shear flow. Numerical results show that, at low capillary numbers, surfactants increase droplet deformation, due to reduced interfacial tension by the average surfactant concentration, and non-uniform effects from non-uniform capillary pressure and Marangoni stresses. The role of surfactants on the critical capillary number ( $Ca_{cr}$ ) of droplet breakup is investigated for various confinements (defined as the ratio of droplet diameter to wall separation) and Reynolds numbers. For clean droplets, $Ca_{cr}$ first decreases and then increases with confinement, and the minimum value of $Ca_{cr}$ is reached at a confinement of 0.5; for surfactant-laden droplets, $Ca_{cr}$ exhibits the same variation in trend for confinements lower than 0.7, but, for higher confinements, $Ca_{cr}$ is almost a constant. The presence of surfactants decreases $Ca_{cr}$ for each confinement, and the decrease is also attributed to the reduction in average interfacial tension and non-uniform effects, which are found to prevent droplet breakup at low confinements but promote breakup at high confinements. In either clean or surfactant-laden cases, $Ca_{cr}$ first remains almost unchanged and then decreases with increasing Reynolds number, and a higher confinement or Reynolds number favours ternary breakup. Finally, we study the collision of two equal-sized droplets in a shear flow in both surfactant-free and surfactant-contaminated systems with the same effective capillary numbers. It is identified that the non-uniform effects in the near-contact interfacial region immobilize the interfaces when two droplets are approaching each other and thus inhibit their coalescence.

The two-dimensional flow around a rotating circular cylinder is studied at Re = 100. The instability mechanisms for the first and second shedding modes are analysed. The region in the flow with a role of ‘wavemaker’ in the excitation of the global instability is identified by considering the structural sensitivity of the unstable mode. This approach is compared with the analysis of the perturbation kinetic energy production, a classic approach in linear stability analysis. Multiple steady-state solutions are found at high rotation rates, explaining the quenching of the second shedding mode. Turning points in phase space are associated with the movement of the flow stagnation point. In addition, a method to examine which structural variation of the base flow has the largest impact on the instability features is proposed. This has relevant implications for the passive control of instabilities. Finally, numerical simulations of the flow are performed to verify that the structural sensitivity analysis is able to provide correct indications on where to position passive control devices, e.g. small obstacles, in order to suppress the shedding modes.

The stability characteristics of compressible spanwise-periodic open-cavity flows are investigated with direct numerical simulation (DNS) and biglobal stability analysis for rectangular cavities with aspect ratios of $L/D=2$ and 6. This study examines the behaviour of instabilities with respect to stable and unstable steady states in the laminar regime for subsonic as well as transonic conditions where compressibility plays an important role. It is observed that an increase in Mach number destabilizes the flow in the subsonic regime and stabilizes the flow in the transonic regime. Biglobal stability analysis for spanwise-periodic flows over rectangular cavities with large aspect ratio is closely examined in this study due to its importance in aerodynamic applications. Moreover, biglobal stability analysis is conducted to extract two-dimensional (2-D) and 3-D eigenmodes for prescribed spanwise wavelengths $\\unicode[STIX]{x1D706}/D$ about the 2-D steady state. The properties of 2-D eigenmodes agree well with those observed in the 2-D nonlinear simulations. In the analysis of 3-D eigenmodes, it is found that an increase of Mach number stabilizes dominant 3-D eigenmodes. For a short cavity with $L/D=2$ , the 3-D eigenmodes primarily stem from centrifugal instabilities. For a long cavity with $L/D=6$ , other types of eigenmodes appear whose structures extend from the aft-region to the mid-region of the cavity, in addition to the centrifugal instability mode located in the rear part of the cavity. A selected number of 3-D DNS are performed at $M_{\\infty }=0.6$ for cavities with $L/D=2$ and 6. For $L/D=2$ , the properties of 3-D structures present in the 3-D nonlinear flow correspond closely to those obtained from linear stability analysis. However, for $L/D=6$ , the 3-D eigenmodes cannot be clearly observed in the 3-D DNS due to the strong nonlinearity that develops over the length of the cavity. In addition, it is noted that three-dimensionality in the flow helps alleviate violent oscillations for the long cavity. The analysis performed in this paper can provide valuable insights for designing effective flow control strategies to suppress undesirable aerodynamic and pressure fluctuations in compressible open-cavity flows.

Runoff‐generated debris flows are a potentially destructive and deadly response to wildfire until sufficient vegetation and soil‐hydraulic recovery have reduced susceptibility to the hazard. Elevated debris‐flow susceptibility may persist for several years, but the controls on the timespan of the susceptible period are poorly understood. To evaluate the connection between vegetation recovery and debris‐flow occurrence, we calculated recovery for 25 fires in the western United States using satellite‐derived leaf area index (LAI) and compared recovery estimates to the timing of 536 debris flows from the same fires. We found that the majority (>98%) of flows occurred when LAI was less than 2/3 of typical prefire values. Our results show that total vegetation recovery is not necessary to inhibit runoff‐generated flows in a wide variety of regions in the western United States. Satellite‐derived vegetation data show promise for estimating the timespan of debris‐flow susceptibility. Plain Language Summary Debris flows caused by excessive surface‐water runoff during intense rainfall can be a deadly and destructive hazard in mountainous areas after wildfire. In some cases, debris flows have only occurred in the burned area in the weeks to months after the fire, while, in other cases, debris flows occurred over several years. Though the recovery of vegetation is important for stabilizing sediment and reducing debris‐flow likelihood, uncertainty remains about how much recovery is needed to inhibit debris flows and about how much time is needed to reach this level of recovery. Knowing for how long debris flows are likely to be a hazard is important for managing risks to residents and infrastructure. To investigate this issue, we assembled a data set of 536 debris flows from the western United States and used satellite‐derived vegetation data to calculate the recovery condition of the burned area when each debris flow occurred. We found that the vast majority of the debris flows initiated when the burned area had not yet reached two‐thirds of its prefire vegetation condition. Burned areas that were slower to recover tended to experience debris flows over more protracted timescales. Key Points Majority (>98%) of western United States postfire debris flows occurred when leaf area index was less than 2/3 of typical prefire values Total recovery of vegetation not necessary to inhibit debris flows Remotely sensed postfire vegetation state useful to evaluate elevated debris‐flow susceptibility with time

This paper proposes three strong second order cone programming (SOCP) relaxations for the AC optimal power flow (OPF) problem. These three relaxations are incomparable to each other and two of them are incomparable to the standard SDP relaxation of OPF. Extensive computational experiments show that these relaxations have numerous advantages over existing convex relaxations in the literature: (i) their solution quality is extremely close to that of the standard SDP relaxation (the best one is within 99.96% of the SDP relaxation on average for all the IEEE test cases) and consistently outperforms previously proposed convex quadratic relaxations of the OPF problem, (ii) the solutions from the strong SOCP relaxations can be directly used as a warm start in a local solver such as IPOPT to obtain a high quality feasible OPF solution, and (iii) in terms of computation times, the strong SOCP relaxations can be solved an order of magnitude faster than the standard SDP relaxation. For example, one of the proposed SOCP relaxations together with IPOPT produces a feasible solution for the largest instance in the IEEE test cases (the 3375-bus system) and also certifies that this solution is within 0.13% of global optimality, all this computed within 157.20 seconds on a modest personal computer. Overall, the proposed strong SOCP relaxations provide a practical approach to obtain feasible OPF solutions with extremely good quality within a time framework that is compatible with the real-time operation in the current industry practice.

Estimation of the initial state of turbulent channel flow from limited data is investigated using an adjoint-variational approach. The data are generated from a reference direct numerical simulation that is subsampled at different spatiotemporal resolutions. When the velocity data are at 1/4096 the spatiotemporal resolution of the direct numerical simulation, the correlation coefficient between the true and adjoint-variational estimated state exceeds 99 %. The robustness of the algorithm to observation noise is demonstrated. In addition, the impact of the spatiotemporal density of the data on estimation quality is evaluated, and a resolution threshold is established for a successful reconstruction. The critical spanwise data resolution is proportional to the Taylor microscale, which characterizes the domain of dependence of an observation location. Owing to mean advection, either the streamwise or temporal data resolution must satisfy a criterion based on the streamwise Taylor microscale. A second configuration is considered where the subsampled data comprise velocities in the outer layer and wall shear stresses only. The near-wall flow statistics and coherent structures, although not sampled, are accurately reconstructed, which is possible because of the coupling between the outer flow and near-wall motions. Finally, the most challenging configuration is addressed where only the spatiotemporally resolved wall stresses are observed. The estimation remains accurate within the viscous sublayer and deteriorates significantly with distance from the wall. In wall units, this trend is nearly independent of the Reynolds number considered, and is indicative of the fundamental difficulty of reconstructing wall-detached motions from wall data.

Wall-pressure fluctuations are a practically robust input for real-time control systems aimed at modifying wall-bounded turbulence. The scaling behaviour of the wall-pressure–velocity coupling requires investigation to properly design a controller with such input data so that it can actuate upon the desired turbulent structures. A comprehensive database from direct numerical simulations (DNS) of turbulent channel flow is used for this purpose, spanning a Reynolds-number range $Re_\\tau \\approx 550\\unicode{x2013}5200$. Spectral analysis reveals that the streamwise velocity is most strongly coupled to the linear term of the wall pressure, at a Reynolds-number invariant distance-from-the-wall scaling of $\\lambda _x/y \\approx 14$ (and $\\lambda _x/y \\approx 8$ for the wall-normal velocity). When extending the analysis to both homogeneous directions in $x$ and $y$, the peak coherence is centred at $\\lambda _x/\\lambda _z \\approx 2$ and $\\lambda _x/\\lambda _z \\approx 1$ for $p_w$ and $u$, and $p_w$ and $v$, respectively. A stronger coherence is retrieved when the quadratic term of the wall pressure is concerned, but there is only little evidence for a wall-attached-eddy type of scaling. An experimental dataset comprising simultaneous measurements of wall pressure and velocity complements the DNS-based findings at one value of $Re_\\tau \\approx 2$k, with ample evidence that the DNS-inferred correlations can be replicated with experimental pressure data subject to significant levels of (acoustic) facility noise. It is furthermore shown that velocity-state estimations can be achieved with good accuracy by including both the linear and quadratic terms of the wall pressure. An accuracy of up to 72 % in the binary state of the streamwise velocity fluctuations in the logarithmic region is achieved; this corresponds to a correlation coefficient of $\\approx$0.6. This thus demonstrates that wall-pressure sensing for velocity-state estimation – e.g. for use in real-time control of wall-bounded turbulence – has merit in terms of its realization at a range of Reynolds numbers.