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Moving boundary problems are often encountered in engineering and science. One of the methods to solve such problems numerically is the volume of fluid (VOF) method. The VOF method uses an additional field variable/to track the interface using the Eulerian fixed grid. In this work, the VOF method is combined with the Continuum surface force model. The governing flow equations for Newtonian fluids in incompressible flow in two dimensions are solved using the pressure-based algorithm. A linear interface reconstruction algorithm is developed and improved by interpolations. In order to validate the code, the problem of the convection of a two-fluid channel flow with a cylindrical interface is given as an example.

In this paper, a compact gas-kinetic scheme (CGKS) for compressible flow is constructed on hybrid unstructured mesh. Based on high-order gas evolution model at cell interfaces both cell-averaged fl...

We develop a new methodology to assess the streamwise inclination angles (SIAs) of the wall-attached eddies populating the logarithmic region with a given wall-normal height. To remove the influences originating from other scales on the SIA estimated via two-point correlation, the footprints of the targeted eddies in the vicinity of the wall and the corresponding streamwise velocity fluctuations carried by them are isolated simultaneously, by coupling the spectral stochastic estimation with the attached-eddy hypothesis. Datasets produced with direct numerical simulations spanning $Re_{\tau} \sim O(10^2)-O(10^3)$ are dissected to study the Reynolds-number effect. The present results show, for the first time, that the SIAs of attached eddies are Reynolds-number dependent in low and medium Reynolds numbers and tend to saturate at $45^{\circ}$ as the Reynolds number increases. The mean SIA reported by vast previous experimental studies are demonstrated to be the outcomes of the additive effect contributed by multi-scale attached eddies. These findings clarify the long-term debate and perfect the picture of the attached-eddy model., Comment: 17 pages, 12 figures, accepted by Journal of Fluid Mechanics

A third-order compact gas-kinetic scheme is proposed for three-dimensional compressible flow computations. The new scheme is based on three key ingredients: the time-accurate gas evolution model fo...

To better understand dragonflies’ remarkable flapping wing aerodynamic performance, we measured the kinematic parameters of the wings in two different flight modes (Normal Flight Mode (NFM) and Escape Flight Mode (EFM)). When the specimens switched from normal to escape mode the flapping frequency was invariant, but the stroke plane of the wings was more horizontally inclined. The flapping of both wings was adjusted to be more ventral with a change of the pitching angle that resulted in a larger angle of attack during downstroke and smaller during upstroke to affect the flow directions and the added mass effect. Noticeably, the phasing between the fore and hind pair of wings varies between two flight modes, which affects the wing-wing interaction as well as body oscillations. It is found that the momentum stream in the wake of EFM is qualitatively different from that in NFM. The change of the stroke plane angle and the varied pitching angle of the wings diverts the momentum downwards, while the smaller flapping amplitude and less phase difference between the wings compresses the momentum stream. It seems that in order to achieve greater flight maneuverability a flight vehicle needs to actively control positional angle as well as the pitching angle of the flapping wings.

In this paper, a compact high-order gas-kinetic scheme (GKS) with spectral resolution will be presented and used in the simulation of acoustic and shock waves. For accurate simulation, the numerical scheme is required to have excellent dissipation-dispersion preserving property, while the wave modes, propagation characteristics, and wave speed of the numerical solution should be kept as close as possible to the exact solution of governing equations. For compressible flow simulation with shocks, the numerical scheme has to be equipped with proper numerical dissipation to make a crispy transition in the shock layer. Based on the high-order gas evolution model, the GKS provides a time accurate solution at a cell interface, from which both time accurate flux function and the time evolving flow variables can be obtained. The GKS updates explicitly both cell-averaged conservative flow variables and the cell-averaged gradients by applying Gauss-theorem along the boundary of the control volume. Based on the cell-averaged flow variables and cell-averaged gradients, a reconstruction with compact stencil can be obtained. With the same stencil of a second-order scheme, a reconstruction up to 8th-order spacial accuracy can be constructed, which include the nonlinear and linear reconstruction for the non-equilibrium and equilibrium states respectively. The GKS unifies the nonlinear and linear reconstruction through a time evolution process at a cell interface from the non-equilibrium state to an equilibrium one. In the region between these two limits, the contribution from nonlinear and linear reconstructions depends on the weighting functions of $\exp(-\Delta t/\tau)$ and $(1-\exp(-\Delta t /\tau))$, where $\Delta t$ is the time step and $\tau$ is the particle collision time, which is enhanced in the shock region. As a result, both shock and acoustic wave can be captured accurately in GKS., Comment: 35 pages, 51 figures

Increasing the power density and prolonging the cycle life are effective to reduce the capital cost of the vanadium redox flow battery (VRFB), and thus is crucial to enable its widespread adoption for large-scale energy storage. In this work, we analyze the source of voltage losses and tailor the design of the battery to simultaneously minimize the ohmic resistance, maximize the transport of electrolytes, and boost the surface area and activity of electrodes. These strategies collectively result in an unprecedented improvement in the performance of VRFBs. At the current densities of 200, 400 and 600 mA cm−2, the battery achieves the energy efficiencies of 91.98%, 86.45% and 80.83%, as well as the electrolyte utilizations of 87.97%, 85.21% and 76.98%, respectively. Even at an ultra-high current density of 1000 mA cm−2, the battery is still able to maintain an energy efficiency of as high as 70.40%. It is also demonstrated that the battery can deliver a high peak power density of 2.78 W cm−2 and a high limiting current density of ~7 A cm−2 at room temperature. Moreover, the battery is stably cycled for more than 20,000 cycles at a high current density of 600 mA cm−2. The data reported in this work represent the best charge-discharge performance, the highest peak power density, and the longest cycle life of flow batteries reported in the literature.

A general framework for the development of high-order compact schemes has been proposed recently. The core steps of the schemes are composed of the following. 1). Based on a kinetic model equation, from a generalized initial distribution of flow variables construct a timeaccurate evolution solution of gas distribution function at a cell interface ; 2). Introduce the WENO-type weighting functions into the timederivative of the cell interface flux function in the multistage multiderivative time stepping scheme to cope with the possible impingement of a shock wave on a cell interface within a time step; 3). Take moments of interface gas distribution function to obtain the time-accurate flow variables and the corresponding fluxes at the cell interface, and update the cell-averaged flow variables and their gradients inside each control volume; 4). Within the physical domain of dependence of the reconstructed cell, based on the cell-averaged flow variables and their gradients develop compact initial data reconstruction to get initial flow distributions at the beginning of next time step. A compact gas-kinetic scheme (GKS) up to sixth-order accuracy in space and fourth-order in time has been constructed on 2D unstructured mesh before. In this paper, the compact GKS up to fourth-order accuracy on 3D tetrahedral mesh will be further constructed with the focus on the WENO-type initial data reconstruction. Nonlinear weights are designed to achieve high-order accuracy for the smooth Navier-Stokes solution and keep super robustness in 3D computation with strong shock interactions. The fourth-order compact GKS can use a large time step with CFL number 0.6 in the simulations from subsonic to hypersonic flow. A series of test cases are used to validate the scheme. The high-order compact GKS is ready for 3D applications with complex geometry.

In this paper, a unified framework for particulate two-phase flow will be presented with a wide range of solid-particle concentration from dilute to dense limit. The two phase flow is simulated by two coupled flow solvers, i.e., the gas-kinetic scheme (GKS) for the gas phase and unified gas-kinetic wave-particle method (UGKWP) for the particle phase. The GKS is a second-order Navier-Stokes flow solver for the continuum flow. The UGKWP is a multiscale method for all flow regimes. The wave and particle decomposition in UGKWP depends on the cell's Knudsen number (Kn). At a small Kn number, the high concentrated solid particle phase will be modeled by the Eulerian hydrodynamic wave due to the intensive particle-particle collisions. At a large Kn number, the dilute solid particle will be sampled and followed by the Lagrangian particle formulation to capture the non-equilibrium transport. In the transition regime, the distribution and evolution of particle and wave in UGKWP are controlled by the local Kn number with a smooth transition between the above limits. In the current scheme, the two phase model improves the previous one in all following aspects: drag force model for different solid particle concentrations; the frictional pressure in inter-particle contacts at high solid-particle concentration; a flux limiting model to avoid solid particles' over-packing; additional non-conservative nozzle and work terms for the gas phase. Besides, the inter-particle collisions have been refined numerically for the dense particle flow through the discretization of the collision term and numerical flux function. The numerical scheme is tested in a series of typical gas-particle problems. The results validate the accuracy and reliability of the proposed method for gas-particle flow., arXiv admin note: text overlap with arXiv:2107.05075

In this work, a bottom-to-up strategy is adopted to design, fabricate and test a uniformly distributed bismuth nanoparticle-modified carbon cloth electrode for vanadium redox flow batteries (VRFBs). The first-principles study reveals that increasing the number of oxygen-functional groups on the surface of carbon fibers can promote the uniform distribution of electrodeposited bismuth nanoparticles, which increases the effective surface areas and active sites. Results also show that the oxygen-functional groups and bismuth exhibit a synergistically catalytic effect, which enhances the kinetics of redox reactions. Therefore, carbon cloth substrate with a high content of oxygen-functional groups is fabricated and tested. The material and electrochemical characterizations, including scanning electron microscope (SEM), cyclic voltammetry (CV) and electrochemical impedance spectroscopy (EIS), verify the predictions of the first-principles study. Battery tests show that the VRFBs with the prepared electrode enables an energy efficiency of 88.4% at 160 mA cm−2, 19.6% higher than that with the original electrode. Additionally, the battery is capable of delivering an energy efficiency of 80.1% at a high current density of 320 mA cm−2, which are among the highest performances in the open literature. Finally, it is also proved that the prepared bismuth nanoparticle-modified carbon cloth electrode outperforms the bismuth nanoparticle-modified carbon paper electrode, ascribed to the excellent ion/mass transport properties of carbon cloth.

We propose a novel concept of energy storage that incorporates electrically rechargeable liquid fuels made of electroactive species, known as e-fuels, as the storage medium. This e-fuel energy storage system comprises an e-fuel charger and an e-fuel cell. The e-fuel charger electrically charges e-fuels, while the e-fuel cell subsequently generates electricity using charged e-fuels whenever and wherever on demand. The e-fuel energy storage system possesses all the advantages of conventional hydrogen storage systems, but unlike hydrogen, liquid e-fuels are as easy and safe to store and transport as gasoline. The potential e-fuel candidates have been identified to include inorganic electroactive materials, organic electroactive materials, and suspension of solid electroactive materials. In this work, we demonstrate an example e-fuel energy storage system for large-scale energy storage using inorganic e-fuels composed of V2+/V3+ and VO2+/VO2+ redox couples, and compare the performance of the e-fuel energy storage system with that of existing technologies. Results show that our e-fuel charger achieves a charge efficiency of as high as ∼94%, while the e-fuel cell is capable of delivering a peak power density of 3.4 W cm−2, which is 1.7 times higher than that of hydrogen fuel cells. More excitingly, the e-fuel energy storage system exhibits a round-trip efficiency of 80.0% and an electrolyte utilization of 83.0% at an ultra-high discharge current density of 1,000 mA cm−2, which are 19.9% and 67.3% higher than those of conventional vanadium redox flow batteries. This unprecedented performance allows a 27.0% reduction in the capital cost of the e-fuel energy storage system compared with that of vanadium redox flow batteries.

Theoretical gas dynamics uses the physical Knudsen number $$\mathrm {Kn}_\mathrm{p}$$, which is defined as the ratio of the particle mean free path $$\lambda $$ to the characteristic length scale L, to categorize the flow into different regimes. The Boltzmann equation is the fundamental equation for dilute gases, while the Navier–Stokes (NS) equations are used for the description of continuum flow at $$\mathrm {Kn}_\mathrm{p}\le 10^{-3}$$. For computational fluid dynamics (CFD), the numerical resolution is limited by the discrete cell size and time step. Therefore, we can define a cell Knudsen number $$\mathrm {Kn}_\mathrm{c}$$ as the ratio of the particle mean free path $$\lambda $$ to the cell size $$\Delta x$$. In CFD, the numerical solution and the corresponding numerical flow regime are fully controlled by a numerical Knudsen number $$\mathrm {Kn}_\mathrm{n}$$, which is a function of the physical Knudsen number $$\mathrm {Kn}_\mathrm{p}$$ and the cell Knudsen number $$\mathrm {Kn}_\mathrm{c}$$. The limitation principle relates to the connections between $$\mathrm {Kn}_\mathrm{n}$$, $$\mathrm {Kn}_\mathrm{p}$$, and $$\mathrm {Kn}_\mathrm{c}$$. In this paper, based on the relationship between the modeling equation, cell resolution, and the physical structure thickness, we propose the division of numerical flow regimes. According to the limitation principle, the range of validity of the NS equations is extended to $$\max (\mathrm {Kn}_\mathrm{p},\mathrm {Kn}_\mathrm{c})\le 10^{-3}$$. During a mesh refinement process, in some cases the NS equations alone may not be able to capture the flow physics once the large gradients and high-frequency modes are resolved by numerical mesh size and time step. In order to obtain a physical solution in the corresponding numerical scale efficiently, a multiscale method is preferred to identify the flow physics in the corresponding cell Knudsen number $$\mathrm {Kn}_\mathrm{c}$$, such as capturing hydrodynamic wave propagation in the coarse mesh resolution case and the kinetic particle transport in the fine mesh case. The unified gas-kinetic scheme (UGKS) is such a multiscale method for providing continuum, near-continuum, and non-equilibrium solutions with a variation of cell Knudsen number. Numerical examples with different physical Knudsen numbers are calculated under different cell Knudsen numbers. These results show the mesh size effect on the numerical representation of a physical solution. In comparison with the NS and direct Boltzmann solvers, the multiscale UGKS is able to capture flow physics in different regimes seamlessly with a variation of numerical resolution.

The widespread application of vanadium redox flow batteries (VRFBs) presents an imperative need to mass produce electrodes with simple and cost-effective method. In this work, a novel room-temperature activation method is developed and adopted to fabricate electrodes for VRFBs. The VRFB with the prepared electrodes exhibits an energy efficiency of 84.0% at the current density of 200 mA cm−2, and can be stably cycled for more than 500 cycles with a high capacity retention rate of 99.94% per cycle. In addition, the battery can be operated at the high current densities of 250 and 300 mA cm−2 with energy efficiencies of 80.9% and 77.8%, which is the highest performance for the electrodes activated at room temperature. More remarkably, the room-temperature activated graphite felt electrode outperforms the thermally treated graphite felt electrode. Therefore, compared with the conventional method for thermally treating graphite felts, which requires expensive equipment to withstand high temperatures and consume a large amount of energy, the present room-temperature activation method offers a more promising choice to mass produce high-performance electrodes for VRFBs.

In this work, a bi-porous graphite felt electrode is prepared by a simple yet effective catalytic etching method for vanadium redox reflow batteries (VRFBs). The primary pores, ∼100 μm in size and formed by voids between interconnected carbon fibers, act as the macroscopic pathways for electrolyte flow, while the secondary pores, ∼200 nm in size and formed onto carbon fibers, increase the active surfaces for electrochemical reactions. The Brunauer-Emmett-Teller results show that the specific surface area of bi-porous graphite felt is 17.73 m2 g−1, which is 7 times larger than that of the original graphite felt. The cyclic voltammetry and electrochemical impedance spectroscopy tests demonstrate the higher peak currents, smaller peak potential separations and lower charge transfer resistances of the bi-porous graphite felt than the original graphite felt. Battery tests show that the VRFB with the bi-porous graphite felt electrode achieves an energy efficiency of 87.02% and an electrolyte utilization of 84.07% at the current density of 200 mA cm−2, which are 17.90% and 38.91% higher than that with the original graphite felt electrodes. More importantly, the battery can be operated at the high current densities of 300 and 400 mA cm−2 with the energy efficiencies of 82.47% and 77.69%, among the highest performance in the open literature. All these superior results demonstrate that the bi-porous graphite felt prepared in this work offers a promise to replace conventional mono-scale porous graphite felt electrodes for VRFBs.

In this work, we designed and characterized a passive structural wing actuation setup that was able to realistically mimic the flapping and pitching kinematics of dragonflies. In this setup, an inelastic string limited the wing pitch that may be sufficiently simple for practical micro air vehicle applications. To further evaluate the dominance of inertial passive and active muscle-controlled pitch actuation in dragonfly flight, the flow fields and pitching angle variations of the naturally actuated wing of a tethered dragonfly were compared with that of the same wing artificially actuated via a proposed passive mechanism. We found that passive rotation characterizes most of the forewing flapping cycle except the upstroke reversal where the dragonfly uses its muscle movement to accelerate its forewing rotation. The measured flow fields show that accelerated wing rotation at the upstroke reversal will result in a stronger leading edge vortex during the downstroke, the additional force from which is estimated to account for 4.3% of the total cycle averaged force generated.

Insect scale flapping-wing flight vehicles can conduct environmental monitoring, disaster assessment, mapping, positioning and security around complex and challenging surroundings. To develop bio-inspired flight vehicles, systematic probing based on the particular category of flight vehicles is needed. This Element addresses the aerodynamics, aeroelasticity, geometry, stability and dynamics of flexible flapping wings in the insect flight regime. We highlight distinct features and issues related to wing-wing interactions, contrast aerodynamic stability between rigid and flexible wings, implications of the wing aspect ratio, using canonical models and dragonflies to elucidate scientific insight as well as technical capabilities of bio-inspired design.

In this paper, the high-order compact gas-kinetic scheme (CGKS) on three-dimensional hybrid unstructured mesh is further developed with the p-multigrid technique for steady-state solution acceleration. The p-multigrid strategy is a two-level algorithm. On the high-order level, the high-order CGKS is used to evolve both cell-averaged conservative flow variables and their gradients under high-order compact initial reconstruction at the beginning of next time step. On the low-order level, starting from the high-order level solution the cell-averaged conservative flow variables is evolved by a first-order scheme, where implicit backward Euler smoother is adopted for accelerating the convergence of steady-state solution. The final iterative updating scheme becomes numerically simple and computationally efficient. The effectiveness of the p-multigrid method is validated in both subsonic and supersonic flow simulations in two- and three-dimensional space with hybrid unstructured mesh. One order of magnitude speedup in the convergence rate has be achieved by the approach in comparison with the explicit counterpart., Comment: arXiv admin note: text overlap with arXiv:2107.05169

Computational fluid dynamics is a direct modeling of physical laws in a discretized space. The basic physical laws include the mass, momentum and energy conservations, physically consistent transport process, and similar domain of dependence and influence between the physical reality and the numerical representation. Therefore, a physically soundable numerical scheme must be a compact one which involves the closest neighboring cells within the domain of dependence for the solution update under a CFL number $(\sim 1 )$. In the construction of explicit high-order compact scheme, subcell flow distributions or the equivalent degree of freedoms beyond the cell averaged flow variables must be evolved and updated, such as the gradients of the flow variables inside each control volume. The direct modeling of flow evolution under generalized initial condition will be developed in this paper. The direct modeling will provide the updates of flow variables differently on both sides of a cell interface and limit high-order time derivatives of the flux function nonlinearly in case of discontinuity in time, such as a shock wave moving across a cell interface within a time step. The direct modeling unifies the nonlinear limiters in both space for the data reconstruction and time for the time-dependent flux transport. Under the direct modeling framework, as an example, the high-order compact gas-kinetic scheme (GKS) will be constructed. The scheme shows significant improvement in terms of robustness, accuracy, and efficiency in comparison with the previous high-order compact GKS., Comment: 30 pages, 30 figures

In this paper, a unified gas-kinetic wave-particle scheme (UGKWP) for the disperse dilute gas-particle multiphase flow is proposed. The gas phase is always in the hydrodynamic regime. However, the particle phase covers different flow regimes from particle trajectory crossing to the hydrodynamic wave interaction with the variation of local particle phase Knudsen number. The UGKWP is an appropriate method for the capturing of the multiscale transport mechanism in the particle phase through its coupled wave-particle formulation. In the regime with intensive particle collision, the evolution of solid particle will be followed by the analytic wave with quasi-equilibrium distribution; while in the rarefied regime the non-equilibrium particle phase will be captured through particle tracking and collision, which plays a decisive role in recovering particle trajectory crossing behavior. The gas-kinetic scheme (GKS) is employed for the simulation of gas flow. In the highly collision regime for the particles, no particles will be sampled in UGKWP and the wave formulation for solid particle with the hydrodynamic gas phase will reduce the system to the two-fluid Eulerian model. On the other hand, in the collisionless regime for the solid particle, the free transport of solid particle will be followed in UGKWP, and coupled system will return to the Eulerian-Lagrangian formulation for the gas and particle. The scheme will be tested for in all flow regimes, which include the non-equilibrium particle trajectory crossing, the particle concentration under different Knudsen number, and the dispersion of particle flow with the variation of Stokes number. A experiment of shock-induced particle bed fluidization is simulated and the results are compared with experimental measurements. These numerical solutions validate suitability of the proposed scheme for the simulation of gas-particle multiphase flow.

In this paper, a comparison of the performance of two high-order finite volume methods based on the gas-kinetic scheme (GKS) and HLLC fluxes is carried out on structured rectangular mesh. For both schemes, the fifth-order WENO-AO reconstruction is adopted to achieve a high-order spatial accuracy. In terms of temporal discretization, a two-stage fourth-order (S2O4) time marching strategy is adopted for WENO5-AO-GKS scheme, and the fourth-order Runge-Kutta (RK4) method is employed for WENO5-AO-HLLC scheme. For the viscous flow computation, the GKS includes both inviscid and viscous fluxes in the evolution of a single cell interface gas distribution function. While for the WENO5-AO-HLLC scheme, the inviscid flux is provided by HLLC Riemann solver, and the viscous flux is discretized by a sixth-order central difference method. Based on the tests of forward Mach step, double Mach reflection, and viscous shock tube, both schemes show outstanding shock capturing property. From the Titarev-Toro and double shear layer tests, WENO5-AO-GKS scheme seems to have a better resolution than WENO5-AO-HLLC scheme. Both schemes show excellent robustness in extreme cases, such as the Le Blanc problem. From the cases of the Noh problem and the compressible isotropic turbulence, WENO5-AO-GKS scheme shows favorite robustness. In the compressible isotropic turbulence and three-dimensional Taylor-Green vortex problems, WENO-AO-GKS can use a CFL number up to 0.5, instead of 0.3 for WENO5-AO-HLLC. In terms of computational efficiency, WENO5-AO-HLLC scheme is about 27% more expensive than WENO5-AO-GKS scheme in the two-dimensional viscous flow problems, but is about 15% faster in the three-dimensional case, because WENO5-AO-GKS scheme needs multidimensional spatial reconstruction for flow variables in both one normal and two tangential directions in the 3D case. Due to the multi-dimensionality, WENO5-AO-GKS scheme shows better resolution than WENO5-AO-HLLC scheme in the laminar boundary layer and the double shear layer test.

In this paper an even higher-order compact GKS up to sixth order of accuracy will be constructed for the shock and acoustic wave computation on unstructured mesh. The compactness is defined by the physical domain of dependence for an unstructured triangular cell, which may involve the closest neighbors of neighboring cells. The compactness and high-order accuracy of the scheme are coming from the consistency between the high-order initial reconstruction and the high-order gas evolution model under GKS framework. The high-order evolution solution at a cell interface provides not only a time-accurate flux function, but also the time-evolving flow variables. Therefore, the cell-averaged flow variables and their gradients can be explicitly updated at the next time level from the moments of the same time-dependent gas distribution function. Based on the cell averages and cell-averaged derivatives, both linear and nonlinear high-order reconstruction can be obtained for macroscopic flow variables in the evaluation of local equilibrium and non-equilibrium states. The current nonlinear reconstruction is a combination of WENO and ENO methodology. The initial piecewise discontinuous reconstruction is used for the determination non-equilibrium state and an evolved smooth reconstruction for the equilibrium state. The evolution model in gas-kinetic scheme is based on a relaxation process from non-equilibrium to equilibrium state. The accuracy, efficiency, and robustness of the scheme have been validated. The main conclusion of the paper is that beyond the first-order Riemann solver, the use of high-order gas evolution model seems necessary in the development of high-order schemes., Comment: 40 pages, 62 figures

In this paper, a fourth-order compact gas-kinetic scheme (GKS) is developed for the compressible Euler and Navier–Stokes equations under the framework of two-stage fourth-order temporal discretization and Hermite WENO (HWENO) reconstruction. Due to the high-order gas evolution model, the GKS provides a time dependent gas distribution function at a cell interface. This time evolution solution can be used not only for the flux evaluation across a cell interface and its time derivative, but also time accurate flow variables at a cell interface. As a result, besides updating the conservative flow variables inside each control volume, the cell averaged slopes inside each control volume through the differences of flow variables at the cell interfaces can be updated as well in GKS. So, with the updated flow variables and their slopes inside each cell, the HWENO techniques can be naturally implemented for the compact high-order reconstruction at the beginning of each time step. Therefore, a compact higher-order GKS, such as the two-stage fourth-order compact scheme can be constructed. This fourth-order compact GKS has the same stencil and as robust as the second-order scheme. In comparison with the fourth-order DG method, they have the same stencil. In order to get a fourth-order temporal accuracy, the GKS uses two stages and DG needs four stages in the time stepping methods. The CFL number used in GKS is on the order of 0.5 instead of 0.11 in the DG. This research concludes that beyond the first-order Riemann solver the use of high-order time evolution model at a cell interface is extremely helpful in the design of robust, accurate, and efficient higher-order compact schemes for the compressible flow simulations.

We mimic a flapping wing through a fluid–structure interaction (FSI) framework based upon a generalized lumped-torsional flexibility model. The developed fluid and structural solvers together determine the aerodynamic forces, wing deformation and self-propelled motion. A phenomenological solution to the linear single-spring structural dynamics equation is established to help offer insight and validate the computations under the limit of small deformation. The cruising velocity and power requirements are evaluated by varying the flapping Reynolds number ($20\leqslant Re_{f}\leqslant 100$), stiffness (represented by frequency ratio,$1\lesssim \unicode[STIX]{x1D714}^{\ast }\leqslant 10$) and the ratio of aerodynamic to structural inertia forces (represented by a dimensionless parameter$\unicode[STIX]{x1D713}$($0.1\leqslant \unicode[STIX]{x1D713}\leqslant 3$)). For structural inertia dominated flows ($\unicode[STIX]{x1D713}\ll 1$), pitching and plunging are shown to always remain in phase ($\unicode[STIX]{x1D719}\approx 0$) with the maximum wing deformation occurring at the end of the stroke. When aerodynamics dominates ($\unicode[STIX]{x1D713}>1$), a large phase difference is induced ($\unicode[STIX]{x1D719}\approx \unicode[STIX]{x03C0}/2$) and the maximum deformation occurs at mid-stroke. Lattice Boltzmann simulations show that there is an optimal$\unicode[STIX]{x1D714}^{\ast }$at which cruising velocity is maximized and the location of optimum shifts away from unit frequency ratio ($\unicode[STIX]{x1D714}^{\ast }=1$) as$\unicode[STIX]{x1D713}$increases. Furthermore, aerodynamics administered deformations exhibit better performance than those governed by structural inertia, quantified in terms of distance travelled per unit work input. Closer examination reveals that although maximum thrust transpires at unit frequency ratio, it is not transformed into the highest cruising velocity. Rather, the maximum velocity occurs at the condition when the relative tip displacement${\approx}\,0.3$.

Achieving a uniform distribution of zinc in the negative electrode is crucial to increase the electrode utilization, maximize the discharge capacity, suppress the dendrite formation and enhance the cycling stability for zinc bromine flow batteries (ZBFBs). To promote the uniform distribution of zinc and thus propel the commercial applications for ZBFBs, in this work, a first-principles study is carried out to investigate the zinc adsorption and diffusion on representative carbon surfaces, including a pristine graphite (0 0 0 1) surface, two surfaces with vacancies, and three surfaces with oxygen-functional groups, aiming to unravel the effect of carbon defects on the ion transport inside the porous electrode, clarify the underlying zinc anchoring mechanism and seek effective ways to promote the uniform distribution of zinc. It is found that the zinc distribution and morphology can be varied by adjusting carbon surface properties, especially by increasing the number of single vacancy. A graphite felt negative electrode with a high content of carbon defects is then prepared and tested in ZBFBs. Experimental results reveal that a much more uniform distribution of zinc is achieved in the prepared electrode than the original electrode does after charing, demonstrating the validity of our proposed mechanism and method. The results reported here provide new insights and novel methods to fabricate uniformly distributed zinc negative electrode, which can guide the rational design of electrode and promote the future applications of ZBFBs and other hybrid flow batteries (e.g. Zn-I2, Zn-Ce and all-iron).

Lacking effective anchoring materials to suppress the severe shuttle effect is a longstanding issue hindering the development of lithium–sulfur (Li–S) batteries. In this work, a first-principles study is carried out to investigate the potential of borophene and defective borophene, which have high ionic conductivity and adsorbent ability, as anchoring materials for Li–S batteries. Borophene is found to exhibit ultra-high adsorption energies towards lithium polysulfides, but the material facilitates the decomposition of Li–S clusters, leading to an undesirable sulfur loss during battery cycling. For this reason, borophene is not an ideal anchoring material for Li–S batteries. On the contrary, defective borophene is found to show moderate adsorption energies ranging from 1 to 3 eV, which not only effectively anchors lithium polysulfides to suppress the shuttle effect, but also keeps their cyclic structures undecomposed. In addition, defective borophene exhibits a metallic characteristic during the whole reaction process, ensuring the lithium polysulfides be easily charged back and not accumulate on the anchoring materials. Given these advantages, it is expected that defective borophene is a promising anchoring material, leading to a suppressed shuttle effect and enhanced capacity retention for Li–S batteries.

Developing high-performance electrodes with high operating current densities and long-term cycling stability is crucial to the widespread application of vanadium redox flow batteries (VRFBs). In this work, boron-doped graphite felt electrodes are designed, fabricated and tested for VRFBs. The first-principles study first demonstrates that the boron-doped carbon surface possesses highly active and stabilized reaction sites. Based on this finding, boron-doped graphite felt electrodes are fabricated for VRFBs. Testing results show that the batteries with boron-doped graphite felt electrodes achieve energy efficiencies of 87.40% and 82.52% at the current densities of 160 and 240 mA cm−2, which are 15.63% and 19.50% higher than those with the original electrodes. In addition, the batteries can also be operated at high current densities of 320 and 400 mA cm−2 with energy efficiencies of 77.97% and 73.63%, which are among the highest performances in the open literature. More excitingly, the VRFBs with the boron-doped graphite felt electrodes exhibit excellent stability during long-term cycling tests. The batteries can be stably cycled for more than 2000 cycles at 240 mA cm−2 with ultra-low capacity and efficiency decay rates of only 0.028% and 0.0002% per cycle. In addition, after refreshing the electrolytes, the performances of the batteries are nearly recovered regardless of the inevitable decay of the membrane. All these results suggest that highly efficient and ultra-stable boron-doped graphite felts are promising electrodes for VRFBs.

The effects of aspect ratio on the leading-edge vortex, tip vortex, and their interactions under sinusoidal rotating kinematics, simulating a half-stroke of a flapping wing, are investigated using ...

The potential of B 4 C as a metal-free catalyst for vanadium redox reactions is investigated by first-principles calculations. Results show that the central carbon atom of B 4 C can act as a highly active reaction site for redox reactions, due primarily to the abundant unpaired electrons around it. The catalytic effect is then verified experimentally by cyclic voltammetry (CV) and electrochemical impedance spectroscopy (EIS) tests, both of which demonstrate that B 4 C nanoparticles can enhance the kinetics for both V 2+ /V 3+ and VO 2+ /VO 2 + redox reactions, indicating a bi-functional effect. The B 4 C-nanoparticle-modified graphite felt electrodes are finally prepared and tested in vanadium redox flow batteries (VRFBs). It is shown that the batteries with the prepared electrodes exhibit energy efficiencies of 88.9% and 80.0% at the current densities of 80 and 160 mA cm −2 , which are 16.6% and 18.8% higher than those with the original graphite felt electrodes. With a further increase in current densities to 240 and 320 mA cm −2 , the batteries can still maintain energy efficiencies of 72.0% and 63.8%, respectively. All these results show that the B 4 C-nanoparticle-modified graphite felt electrode outperforms existing metal-free catalyst modified electrodes, and thus can be promising electrodes for VRFBs.