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Modern shock-capturing schemes often suffer from numerical shock instabilities when simulating strong shocks, limiting their application in supersonic or hypersonic flow simulations. In the current study, we devote our efforts to investigating the shock instability problem for second-order schemes, which has not gotten enough attention in previous research but is crucial to address. To this end, we develop the matrix stability analysis method for the finite-volume Monotone Upstream-centered Schemes for Conservation Laws (MUSCL) approach, taking into account the influence of reconstruction. With the help of this newly developed method, the shock instability of second-order schemes is investigated quantitatively and efficiently. The results demonstrate that when second-order schemes are employed, whether shock instabilities will occur is closely related to the property of Riemann solvers, just like the first-order case. However, enhancing spatial accuracy still impacts the shock instability problem, and the impact can be categorized into two types depending on the dissipation of Riemann solvers. Furthermore, the research emphasizes the impact of the numerical shock structure, highlighting both its role as the source of instability and the influence of its state on the occurrence of instability. One of the most significant contributions of this study is the confirmation of the multidimensional coupled nature of shock instability. Both one-dimensional and multidimensional instabilities are proven to influence the instability problem, and they have different properties. Moreover, this paper reveals that increasing the aspect ratio and distortion angle of the computational grid can help mitigate shock instabilities. The current work provides an effective tool for quantitatively investigating the shock instabilities for second-order schemes, revealing the inherent mechanism and thereby contributing to the elimination of shock instability. [ABSTRACT FROM AUTHOR]

In this paper, the cavitation and flow characteristics of the unsteady liquid nitrogen (LN2) cavitating flow in a submersible pump are investigated through both experimental and numerical approaches. The performance curve of the LN2 submersible pump is obtained via experimental measurement. Numerical simulations are performed using a modified shear stress transport k–ω turbulence model, incorporating corrections for rotation and thermal effects as per the Schnerr–Sauer cavitation model. The numerical framework is verified by comparing the cavitation morphology features with previously reported visual data of the LN2 inducer and aligning pump performance data with those obtained from experimental tests of the LN2 submersible pump. The results indicate that cavitation at the designed flow rate predominantly manifests as tip clearance vortex cavitation in the inducer. Increased flow rates exacerbate cavitation, potentially obstructing the flow passage of the impeller. The vortex identification method and the vorticity transport equation are employed to identify the vortex structures and analyze the interaction between cavitation and vortices in the unsteady LN2 cavitating flow. The vortex structures primarily concentrate at the outlet of the impeller flow passage, largely attributed to the vortex dilation term and baroclinic torque. The influence of thermal effects on the cavitation flow of submersible pumps is analyzed. An entropy production analysis model, comprehensively involving various contributing factors, is proposed and utilized to accurately predict the entropy production rate within the pump. This study not only offers an effective numerical approach but also provides valuable insight into the cavitation flow characteristics of the LN2 submersible pump. [ABSTRACT FROM AUTHOR]

Cavitation-induced vortex and energy loss are critical topics in the field of hydraulic machinery. Through a combination of experimental and numerical analysis, this paper investigates how blade loading affects vortical structures and energy loss during cavitation in a waterjet pump. The flow rate and cavitation conditions changed blade tip pressure loading, which significantly affected the trajectories of the primary tip leakage vortex cavitation and secondary tip leakage vortex cavitation. A considerable pressure gradient at the attached cavity closure region leads to a wall reentrant jet and a side-entrant jet, resulting in an attached vortex under the cavitation developing stage and severe stage. The development of the attached vortex leads to the shedding of attached cavities. Furthermore, the blade tip pressure difference loading significantly alters the distribution of tip leakage vortex and gives rise to a perpendicular leakage vortex (PLV). The PLV entrains the shedding cavities and forms a perpendicular cavitation vortex. These complex vortical structures induced by cavitation inevitably enhance enstrophy and lead to entropy production in the pump. The entropy production terms of viscous dissipation, turbulent dissipation, and the wall effect react differently to the development of cavitation. As the cavitation stages developed and became more severe, wall entropy production (S3) decreased. While turbulent dissipative entropy production S2 due to mixing losses occurring in the tip region increased sharply, which dominates the total entropy production S and results in an increase in S. [ABSTRACT FROM AUTHOR]

This paper analyzes the liquid atomization mechanisms of an N-heptane spray jet emerging from a swirl simplex atomizer using numerical and experimental techniques. In particular, a direct seamless coupled Volume of Fluid and Lagrangian Particle Tracking approach together with adaptive mesh refinement within the Large Eddy Simulation framework offers a suitable way to accurately simulate the complex behavior of spray atomization, spray evolution, and droplet dispersion as a whole while using manageable computational cost. The achieved simulation results are first presented in terms of qualitative properties, characteristics of liquid sheet, air core generation, flow recirculation zones, and vortex patterns. For validation purposes, the numerical results are then compared with detailed experimental data obtained by a two-component Phase Doppler Anemometry technique. The assessment includes especially droplet statistics which strongly determine subsequent possible spray combustion process and related product and species emissions. The overall reported agreement demonstrates the capability of the adopted methodology in predicting and comprehensively investigating the complex phenomena associated with a pressure swirl fuel atomizer. In particular, it is found out that the normalized number-based probability density function of droplet size fits well with a lognormal distribution. [ABSTRACT FROM AUTHOR]

In response to the need for efficient, small-scale power sources for applications such as ocean observation and navigation, this paper presents the design, modeling, fabrication, testing, and analysis of a compact point-absorber wave energy converter (PAWEC) equipped with a mechanical direct-drive power takeoff (PTO) mechanism. The motivation is to address the mismatch between the natural frequencies of conventional PAWECs and dominant ocean wave frequencies, which limits energy capture. The primary objective is to enhance the efficiency of small-scale wave energy converters (WEC) without increasing the buoy size. To achieve this, we introduce a novel design element: an added mass plate (AMP) attached to the buoy. The AMP is devised to increase the WEC added mass and natural period, thereby aligning its natural frequency with dominant ocean wave frequencies. In our case study of a scaled model (1:2.2), the AMP effectively doubled the added mass of the WEC and increased its natural period by 32%. The WEC incorporates a rack and pinion mechanical motion rectifier-type PTO to convert the heave oscillations of the buoy into unidirectional rotation. The scaled model was tested in a wave basin facility with regular waves at zero angle of incidence. The WEC with AMP achieved a maximum root mean square power of 9.34 W, a nearly 30% increase compared to the conventional configuration without AMP, which produced 7.12 W under similar wave conditions. Numerical analysis using the boundary element method in the frequency domain for regular waves confirmed these findings. Finally, it has been derived that the proposed WEC, equipped with an AMP, offers enhanced efficiency in longer wave periods without the need for a larger buoy, establishing its viability as a power source for navigational buoys. This paper also offers a comprehensive guide to experimental techniques for characterizing a PAWEC in a laboratory setting, contributing valuable insights into the wave energy community. [ABSTRACT FROM AUTHOR]

In this Brief Communication, we examine in detail the motion of light particles—or dense gas bubbles—rising under gravity in a cellular flow. We follow the methodology of Maxey [Phys. Fluids 30, 1915 (1987)], and we examine a range of parameters not fully discussed in the past, corresponding to particles lighter and yet more inertial than the surrounding fluid if the added mass effect is considered. We observe a nonmonotonic behavior of the particle rise velocity, which exhibits a maximum for density of the particles only slightly smaller than the density of the fluid. The maximum value of the average rise velocity corresponding to the “optimum” density is several times (more than 40) higher than those obtained for small density changes around the optimum. The occurrence of this maximum is due to the combined effects of particle inertia and fluid added mass, which segregate the rising particles into specific, fast pathlines where the local fluid velocity adds to the particle gravitational velocity. A plot covering particle rise velocity for this range—not covered by the analysis of Maxey—is provided. [ABSTRACT FROM AUTHOR]

This paper's goal is to investigate if a gob-side entry retention technique combined with a surrounding rock support system is feasible in three soft coal seams. Field engineering confirmed the results of numerical simulation tests and similar simulation tests, which were conducted in accordance with the actual geological conditions of Zhaojiazhai Mine. The following conclusions are reached after studying the technology and process parameter of the gob-side entry retaining in three soft coal seams in conjunction with theoretical calculations: the coal seam of Zhaojiazhai Coal Mine's 12 209 working face is a part of the soft coal seam, and its loose circle is approximately 1.8 m. The expansion roadway size is 3.5 m, and the potential loose circle range is 1.32 m, according to the same model and numerical simulation test. The support scheme after the expansion of the road working face is determined to be the "anchor rod + anchor cable + hydraulic lifting shed" support method. Furthermore, this article suggests a building method for the reinforcement and enlargement of gob-side entry retaining in three-soft thick coal seam by theoretical analysis and numerical simulation. Roadway shotcrete, advance grouting, building of a large deformation anchor cable and continuous resistance, single column lifting shed, hydraulic lifting shed, and roadway enlargement in advance are all steps in the procedure. Furthermore, an analysis is conducted on the deformation features of the surrounding rock in gob-side entry retention. The study highlights the significance of actively supporting the surrounding rock, fortifying the roof support, guaranteeing the stiffness compatibility between the shoulder filling body and the surrounding rock on the roof, boosting the wall's strength and stability, and enhancing the roadway's stability. [ABSTRACT FROM AUTHOR]

The development of hydrodynamic instabilities has a significant impact on the operation of laser fusion systems. During radiation compression, the shells of a target are accelerated, resulting in the growth of perturbations at their interfaces. In this paper, we study the influence of density perturbations on the stability of the contact boundary during accelerated motion. The analysis is performed in a two-dimensional planar formulation using the linear approximation and assuming a weak spatial dependence on the temperature near the contact boundary. Due to the consideration of small time intervals, the phenomenon of heat conduction is not taken into account. The cases of acceleration of a medium described by the Mie–Grüneisen equation of state (EoS) into a vacuum and of acceleration of two contacting media, each described by the ideal plasma EoS, are considered. The time dependence of the amplitude of the boundary perturbation on time is obtained. The obtained values are in agreement with the results of numerical analysis. It is shown that the boundary curvature occurs independently of the acceleration direction. The theoretical results are compared with numerical results for laser fusion systems. [ABSTRACT FROM AUTHOR]

This paper investigated the differences for the hydraulic characteristics in a single fracture between using the Navier–Stokes (N–S) equation and Darcy's law, which would be benefit to understand the seepage mechanism in the fracture. A numerical model of the radial flow was established considering the aperture size and water injection flow rate. Some conclusion could be given. First, the Darcy's law only described the seepage characteristics when the flow rate was small when the flow rate and pressure response have a linear relationship. While the N–S equation could describe the linear and nonlinear seepage characteristics, resulting in a better model of the actual fracture seepage flow. Second, the aperture size had a limited influence on the water pressure and seepage velocity inside the fracture when the flow rate was small. It began to have a significant impact influence on the seepage characteristics inside the fracture with the aperture increased. Third, the flow–pressure response conformed to the Forchheimer equation in the fracture. The critical Reynold number would decrease from 1.2 to 0.0116 when fracture aperture decreased from 3 to 0.5 mm using the N–S equation. The degree of nonlinearity of the fluid flow increases with fracture roughness increasing. This work gave a guidance to the difference in the two seepage theories and correction for the result by Darcy law, which was widely used in the engineering calculation. [ABSTRACT FROM AUTHOR]

The potential-based multiphase lattice Boltzmann models are widely used because they root in thermodynamics and evade the interface tracking or integrating. This paper investigates several potential-based models with the common equations of state (EOS) by the theoretical analyses and numerical computations of the thermodynamic consistency and spurious currents. Surprisingly, the Shan–Chen model presents a superior accuracy compared to the Zhang–Chen models, although they are mathematically equivalent. We find that the great improvement is attributed to the square root form of the pseudopotential model, which significantly lessens the error of numerical gradient calculation. Inspired by the improvement, a general formula φ ′ = n − 1 φ 1 − n ∂ x (φ n) is introduced for calculating the gradient, and the coefficient n = 0.1 yields better results than n = 0.5 , which is equal to the pseudopotential model. This scheme is further applied to optimize the evaluation of the chemical potential model. The improved chemical potential model displays lower numerical errors in the liquid–gas transition region and smaller spurious currents near the curved phase interface than the pseudopotential model. Additionally, the improved model is confirmed to meet the Young–Laplace law and Galilean invariance. [ABSTRACT FROM AUTHOR]

In this paper, the process of encapsulating solid particle(s) into liquid droplets in a high-throughput flow-focusing microchannel is investigated numerically. Open source software is used, which computes fluid flow in an Eulerian framework and particle dynamics with a Lagrangian approach. Previous studies have demonstrated that if no action is taken, particles suspended in a liquid passing through a flow-focusing microchannel will be encapsulated at random. This is perhaps unsurprising, but in one such study, less than 35% of droplets were found to contain exactly one particle. The two aims of this study are (i) to explore the flow patterns arising in a microfluidic channel and (ii) to elucidate the effect of salient governing parameters on encapsulation efficiency (i.e., the fraction of droplets encapsulating one particle) by focusing on ordering the particles before reaching the droplet generation section. Following validation against experimental reference data, the capillary number is varied across the three droplet generation regimes: squeezing, dripping, and jetting. We demonstrate that under certain conditions, an encapsulation frequency of 100% can be achieved with ordered particles, but in most cases, this is significantly lower. We examine the flow field to help understand how this non-uniform distribution of particles occurs. Notably, we find the dripping to be the best option for particle encapsulation and in this case extend the study to explore the effect of junction angle, finding that an angle of 60 ° is the most favorable. Improved understanding of the encapsulation process derived from this study can help to improve design of high-throughput droplet generation microfluidic systems. [ABSTRACT FROM AUTHOR]

Different compact upwind schemes have been developed and used to numerically approximate a convection term in the Navier–Stokes equation. With different point stencils, the compact upwind schemes are mainly classified as the central, the function-biased, and the derivative-biased compact upwind schemes. They have different numerical characteristics. In this paper, by using Fourier analysis and numerical test, it is found that the function-biased compact upwind schemes have better resolution properties than the derivative-biased compact upwind schemes. Furthermore, an optimization method named dispersion-dissipation-balancing (DDB) optimization is proposed, by which better spectral resolution of these schemes is obtained by optimizing coefficients of these schemes based on the balance between a dispersion error and a dissipation error. Compared with the popular dispersion-relation-preserving (DRP) optimization method, the schemes optimized by the DDB method have proper dispersion and dissipation errors. They eliminate both the nonphysical oscillations and spurious vortices in the numerical case of the double shear layers flow. In addition, the central compact upwind scheme optimized by the DDB method (OCCUS_DDB) has the best performance among the schemes studied in this paper. [ABSTRACT FROM AUTHOR]

This paper presents a numerical analysis of the melting dynamics of n-octadecane in microgravity. The phase change material (PCM) is held in a rectangular container of aspect ratio Γ = L / H = 1.5 , and the upper boundary is open to a layer of air, which both exchanges heat with the PCM and generates thermocapillary convection in the liquid phase via the Marangoni effect. This study extends the analysis conducted by Martinez et al. ["Effect of surface heat exchange on phase change materials melting with thermocapillary flow in microgravity," Phys. Fluids 33, 083611 (2021)] in which the air temperature was assumed to vary linearly between the temperatures applied at the lateral walls. Two different scenarios are analyzed here. In the first case, the air temperature is assumed to be homogeneous and equal to the mean value of the temperatures applied at the lateral walls throughout the melting process. In the second case, the air temperature is similarly taken to be constant but with a value of 23 °C, which is representative of a laboratory environment, including many microgravity platforms. The investigation reveals the effect of key dimensionless parameters, including the Marangoni number (Ma), which quantifies the heat transport due to the thermocapillary flow, and the Biot number (Bi), which characterizes the heat exchanged across the PCM/air interface. In contrast to previous analyses of pattern selection, only oscillatory standing (pulsating) waves are observed under these boundary conditions. The results in each case are presented via stability maps in terms of Bi and Ma. [ABSTRACT FROM AUTHOR]

Reverse wake-induced vibration (RWIV) of two tandem cylinders with the downstream one fixed is numerically studied in this paper; Reynolds number is set as 150 (Re = 150). The effect of different spacing ratios (α) ranging from 3 to 6 with a gap of 0.5 is simulated to investigate the vibration characteristics of RWIV, where the spacing ratio (α) is defined as the nondimensional ratio of the center-to-center separation between the cylinders. As the spacing ratio increases from 3 to 6, RWIV shows a transition from galloping to vortex-induced vibration (VIV), which is also a reverse phenomenon compared to wake-induced vibration (WIV). As to the wake mode, two different types of vortex motion (2S - 2P - 2S and 2S - 2P) are observed within the given range of spacing ratio. Empirical modal decomposition is also applied to further analyze the vibration characteristics of galloping and VIV in RWIV. When the system shows galloping, the number of decomposed modes is larger with the increasing reduced velocity, and different vibration modes show evident mutual anisotropy. In addition, the vortex line diagram is used to analyze the wake vortex characteristics of the RWIV and to supplement the above findings. [ABSTRACT FROM AUTHOR]

Liquid viscosity has a potential effect on bubble dynamics. This paper is concerned with bubble dynamics in a compressible viscous liquid near the free surface. The liquid–gas flow is modeled using the Eulerian finite element method coupled with the volume of fluid method. The numerical results have been shown to be in excellent agreement with those from the spherical bubble theory and experiment. Parametric studies are carried out regarding the Reynolds number Re and the stand-off parameter γd. It clearly demonstrated that the liquid viscosity inhibits bubble pulsation, jet flow, free surface jet, and bubble splitting. Quantitatively, as Reynolds number Re decreases, the maximum bubble volume, jet tip velocity, free surface spike, and crown height decrease, and the toroidal bubble splitting weakens. As the stand-off parameter γd increases, the maximum bubble volume, jet velocity, and bubble average pressure peak increase while the height of the free surface spike decreases. Close observation reveals that the free surface crown tends to disappear at small Re or large γd, further indicating the complex mechanism behind the crown spike evolution. [ABSTRACT FROM AUTHOR]

Water entry is a fluid–structure interaction process closely related to the ocean environment. Repeated water entries take place when ships are sailing in an ocean environment, e.g., ocean currents, which greatly affect the ship's safety and stability in navigation. In this paper, we adopt a smoothed particle hydrodynamics method to numerically study the water entry of a bow-flare ship body section under ocean currents. We simulate the process of water entry under different current velocities and analyze in detail the fluid field regarding the free surface evolution, the velocity and pressure distributions, and the body's forces and motions. It is revealed that the ocean current can induce multidirectional fluid impacts, and a stagnation point with zero velocity occurs at the upstream side. Asymmetric fluid fields including the evolution of the free surface and the velocity and pressure distributions around the body can also be found. In addition, discrepancies are caused in the formation time and the range of the high-pressure region. These fluid field changes greatly affect the ship body's dynamic responses. However, the effects of the ocean current are mainly reflected in the direction of the current flow and are relatively small in the direction perpendicular to the flow. [ABSTRACT FROM AUTHOR]

In this paper, we investigated the effectiveness of the strength of axial flow and suction/injection for the viscous mode (type II) instability within the boundary layer of a rotating disk. To investigate the lower branch, we scaled the viscous mode by using a familiar triple-deck structure analogous to that which was found for Blasius flow over a flat plate. We also analyzed the linear stability behavior of high-Reynolds laminar-turbulent transition. To describe the stationary type II wavenumber and waveangle, we conducted an asymptotic analysis followed by a comparison with the type I mode. We found that a positive axial flow had a stabilizing effect and vice versa a negative axial flow exhibited a destabilizing effect. The results were consistent with previous studies in the literature for positive axial flow, as disturbances were advected downstream in the radial direction. Regarding the suction/injection study, we found suction to be stabilizing, which aligns with previous results in the literature although, conversely, the injection was found to be destabilizing. For the numerical analysis, we found that parameters which result in an increase or decrease of the critical Reynolds number led to a stabilization or destabilization of the flow, respectively. Finally, we compared the asymptotic and numerical stability results for both types I and II followed by the critical Reynolds numbers comparisons, which were found to be consistent in general with results in the literature. [ABSTRACT FROM AUTHOR]

Offshore wind turbines will be developed from shallow water to deep water to meet the rapid growth of wind power generation. Floating offshore wind turbine (FOWT) faces complex load challenges, which endanger its safety and service life. Hence, it is urgent to develop a novel damping device to improve the stability of FOWT. In this paper, a novel extended tuned mass damper (ETMD) is proposed. On this basis, a linear quadratic regulator is added to realize the design and simulation of the extended active tuned mass damper (EATMD) control system to reduce the surge response of FOWT. Numerical analysis shows that under the control of ETMD, the surge response of the tower is reduced by 73%, and the frequency modulation width is increased by 55%. Here, under the control of EATMD, the displacement, velocity, and acceleration of the surge response of the tower are decreased by 47.0%, 30.7%, and 24.2%, respectively. [ABSTRACT FROM AUTHOR]

Understanding the pileup formation process of sequentially deposited droplets is vital in advancing droplet-based printing technologies. While pileups of simple droplets have been extensively studied, knowledge of the hollow pileup formation is inadequate. This paper presents a fully resolved numerical analysis of the pileup formed by successively depositing incoming hollow droplets on a pre-solidified (or base) droplet on a supercool surface. An axisymmetric front-tracking method is used to handle the simulations. The pileup height increases as the incoming droplets coalesce, while the hollow cores may or may not merge. The pileup shape and its hollow configuration depend on parameters such as the Stefan number, Peclet number, Weber number, Fourier number, and the size and number of hollow cores. Varying these parameters does not affect the peak formation at the top of the pile caused by volume expansion during phase change, although the Fourier number has a strong influence on the mean aspect ratio and solidification time of the pileup. Increasing the deposition rate enhances the coalescence of hollow cores and reduces the mean aspect ratio of the pileup. Reducing the Stefan number also promotes hollow core coalescence, which decreases the mean aspect ratio. However, the size of the hollow core and the Peclet and Weber numbers have almost no influence on the outer shape of the hollow pileup. The effect of the number of incoming droplets on the pileup formation is also revealed. [ABSTRACT FROM AUTHOR]

This study explores the effects of wear and shaft-shape error defects on the tribo-dynamic responses of water-lubricated bearings under nonlinear propeller disturbance using a numerical model. The model proposed in this paper is verified by comparing the results from experiments and simulations in published studies. Numerical simulation studies reveal the effects of nonlinear propeller disturbance on the dynamic behavior and lubrication performance, such as hydrodynamic force, contact force, and journal trajectory, of the water-lubricated bearings with wear and shaft-shape errors. In addition, the effects of the critical factors for wear and shaft-shape errors, including wear depth, deviation angle, magnitude, and waviness order, on the tribo-dynamic responses of water-lubricated bearings are identified. The results of numerical spectrum analyses show that the nonlinear disturbance significantly affects the dynamic behavior (shown as the fluctuation range of the journal trajectory increases), and reasonable wear parameters can improve the lubrication performance of the water-lubricated bearing. Moreover, the effects of shaft-shape errors on the transient hydrodynamic force, contact force, film thickness, pressure, and journal trajectory are greater than that of wear. [ABSTRACT FROM AUTHOR]

The shear stress of a power-law fluid is exponentially related to the shear rate. Thus, unlike for Newtonian fluids, the Reynolds lubrication equation in the simplified differential form is nonlinear and cannot be solved analytically. This paper investigates the flow of a power-law fluid in comma-roll coating and planar blade coating. We establish an intermediate function F(x), defined as the ratio of the shear force τ(X,0) in the X-direction on the edge of the blade coater to the pressure gradient G(x). Using various flow patterns, the signs of F and G are determined, and expressions for ∂U/∂Y are obtained in terms of F and G. Combined with the velocity boundary condition, ∂U/∂Y is integrated and the explicit relation between the coating thickness H∞ and F is established. The pressure gradient is also obtained. Finally, dP/dX is integrated and combined with the inlet and outlet pressure conditions, and the bisection method is used to determine H∞. The coating thickness and pressure given by the proposed method for both comma-roll coating and flat blade coating are highly consistent with the exact results for n = 1, 1/2, and 1/3 calculated by Dien and Elrod's method. We deduce that the limiting thickness of comma-roll coating is (n + 1)/(2n + 1), and the limit of the pressure gradient is − [ n + 1 / n ] n . Moreover, we construct a phase diagram of the relationship between the shape parameter k of the blade coater and the power-law exponent n. These results have instructive significance and application value for guiding coating operations and applicator design. [ABSTRACT FROM AUTHOR]

A numerical analysis based on detached eddy simulations is conducted to investigate vortex dynamics of a pre-swirl pumpjet propulsor (PJP) in oblique inflow. In this paper, the working conditions of PJP operating in axisymmetric flow and drift with two angles (10° and 20°) are considered. The effects of incidence α and propeller loading on the wake dynamics of PJP as well as the mechanism leading to its destabilization are discussed. The results show that high hydrodynamic efficiency loss is found for PJP operating in drift. In addition, a different "secondary vortex structure" caused by the duct is found for PJP in both axisymmetric and oblique flow conditions. The instability mechanism of tip vortices shows obvious asymmetry. On the leeward side, it is dominated by the interaction caused by the duct-induced vortex, while it is dominated by the secondary vortices on the windward side. Furthermore, the fluctuation frequency of tip vortex for PJP is characterized by the rotor blade-passing frequency and the stator blade-passing frequency. In addition, the hub rotation frequency is important in oblique flow conditions. [ABSTRACT FROM AUTHOR]

This paper through the in-house code numerically examines the cavitation–vortex–turbulence interaction mechanism. The high grid resolution can obtain a more detailed flow field structure, which is helpful to reveal the relationship between cavitation occurrence and development and local turbulent flow field. Results are presented for a three-dimensional NACA66 hydrofoil fixed at an 8° angle of attack under a moderate Reynolds number of 1 × 106 and sheet/cloud cavitating conditions. Numerical simulations are performed via the boundary data immersion method coupled with the artificial compressibility method through a Fortran-based code. The results show that the numerical predictions are capable of capturing the unsteady cavitation characteristics, in accordance with the quantitative features observed in high-speed cavitation tunnel experiments. The evolution of the transient cavitating flow can be divided into three stages: growth of the attached sheet cavity, development of a re-entrant jet, and cloud shedding downstream. The Liutex method is applied to capture the vortex structure. Further analysis of the process of enstrophy transport reveals that cavitation promotes vortex production and increases the enstrophy as the cavity becomes more unstable. Moreover, the structure of the vortex gradually evolves from a vortex tube to a U-type vortex, Ω-type vortex, and streamwise vortex. Finally, the interaction between cavitation and turbulence is expounded using the turbulent energy transport equation, which demonstrates that cavitation promotes the production, diffusion, and dissipation of turbulent kinetic energy, while the viscous transport term only acts during the process of cloud cavity shedding. [ABSTRACT FROM AUTHOR]

The effects of the Coriolis force in inhomogeneous rotating turbulence are studied in the paper. Linear analyses and numerical simulations both reveal that energy is transported to the slowly rotating fields, and the energy distribution is proportional to Ω 3 − 2 (x 3). The scale energy is almost spatially self-similar, and the inverse cascade is reduced by inhomogeneous rotation. The corresponding evolution equation of the scale energy, i.e., the generalized Kolmogorov equation, is calculated to study the scale transport process in the presence of inhomogeneity. The equation is reduced to twice the energy transport equation at sufficiently large scales, which is verified by numerical results. In addition, the results reveal the dominant role of the corresponding pressure of the Coriolis force in the spatial energy transport. An extra turbulent convention effect in r-space solely in slowly rotating fields is also recognized. It can be associated with the small-scale structures with strong negative vorticity, whose formation mechanism is similar to rotating condensates. Finally, by vortex dynamic analyses, we find that the corresponding pressure of the Coriolis force transports energy by vorticity tube shrinking and thickening. The effects of the Coriolis force can be divided into two components: one is related to the gradient of rotation, and the other is associated with the strength of rotation. [ABSTRACT FROM AUTHOR]

Reynolds-averaged Navier–Stokes (RANS) simulations are still the main method to study complex flows in engineering. However, traditional turbulence models cannot accurately predict flow fields with separations. In such a situation, machine learning methods provide an effective way to build new data-driven turbulence closure models. Nevertheless, a bottleneck that the data-driven turbulence models encounter is how to ensure the stability and convergence of the RANS equations in a posterior iteration. This paper studies the effects of different coupling modes on the convergence and stability between the RANS equations and turbulence models. Numerical results demonstrate that the frozen coupling mode, commonly used in machine learning turbulence models, may lead to divergence and instability in a posterior iteration; while the mutual coupling mode can maintain good convergence and stability. This research can provide a new perspective to the coupling mode for machine learning turbulence models with RANS equations in a posterior iteration. [ABSTRACT FROM AUTHOR]

This paper investigates the inception mechanism of propeller wake instability based on an improved detached eddy simulation method at a moderate advance coefficient of J = 0.65. Computational fluid dynamics simulations involving a rotating propeller using a dynamic overset technique are performed at J = 0.38 and J = 0.88 to validate the numerical approach, and these results are compared against experimental data of thrust and torque coefficients and phase-averaged axial velocity from the literature. The results indicate that propeller wake instability results from interactions among vortex structures behind the propeller and the high-speed shear layer. In addition, the diffusion of azimuthal velocity plays an important role in the mutual induction process. Finally, we propose a model that includes the main physical processes leading to tip vortex instability and can predict the time and location of vortex pairing. The present study provides deeper insight into the flow physics driving the tip vortex pairing process. [ABSTRACT FROM AUTHOR]

This study parametrically assessed the stability of the phase-field lattice Boltzmann model (PFLBM) before applying it to analyze the effect of annular piping geometry on the flow of Taylor bubbles. The impacts of both eccentricity and pipe diameter ratio were examined, providing an insight into the behavior of these bubbles as well as the applicability and shortcomings in current prediction methodologies. A recently developed PFLBM was implemented into the open-source simulation framework, waLBerla, for this analysis. The stability properties of the code were investigated in detail by assessing various lattice discretizations and relaxation kernels applied to the Rayleigh–Taylor benchmark problem and a Rayleigh–Taylor instability in a tubular geometry, with gravitational Reynolds numbers of up to 30 000 and 10 000, respectively. This paper makes three contributions relating to the stability and usage of the PFLBM as well as the flow of Taylor bubbles in annular pipes. First, the work numerically explored the stability properties of the velocity-based, PFLBM and concluded the impact of various collision models and lattice discretizations on simulation results. Second, it provided a flexible open-source code that the interested researcher can use interactively for practical flow problems as well as the analysis of numerical properties of various lattice Boltzmann algorithms. Finally, it quantified the effect of pipe eccentricity and diameter ratio on the propagation of a Taylor bubble inside a water-filled annular pipe, concluding that a previously defined closure model captured the diameter ratio for the cases examined. To extend this work, future studies aim to analytically investigate the stability properties parametrically observed in this study and apply the findings to simulate the interaction of multiple Taylor bubbles. [ABSTRACT FROM AUTHOR]

A numerical analysis based on detached eddy simulations is conducted to investigate vortex instabilities in the wake of a preswirl pumpjet propulsor. Three models are established to separate the roles that the rotor, stator, and duct play in the vortex structure of the pumpjet propulsor. In this paper, only the vortex structure of the rotor is considered. The results show that the vortex system of the rotor is mainly composed of the tip vortices, a hub vortex, the trailing tip vortices, and the trailing root vortices. The trailing tip vortices are generated by the premature shedding of the tip vortices in the rotor model compared with a normal single propeller. The existence of trailing root vortices increases the stability of the hub vortex. Furthermore, a unique multi-inductance instability mode of the tip vortex, called the "overlap–forward" phenomenon, is found for low values of the advance coefficient J. It is found that the instability of the tip vortex depends not only on the spiral-to-spiral distance but also on the highest-efficiency point of the propeller. The instability inception point of the tip vortex moves farther downstream with increasing J, whereas when J is greater than the highest-efficiency point of the propeller, the stable length of the tip vortices drops sharply. The energy transfer process from blade harmonics to shaft harmonics of the tip vortices depends on J and is related to the spatial evolution of the tip vortices. [ABSTRACT FROM AUTHOR]

The paper investigates a planar hydraulic jump during a thin film flow over a two-dimensional obstacle spanning the entire width of a horizontal channel. The shallow water analysis supported by numerical simulations identifies a hydraulic drop and simultaneous jump-drop-jump phenomenon under certain flow conditions. A hydraulic drop although observed for flow over obstacles in the macro-domain has never been reported for a thin film flow. The study, thus, establishes the efficacy of shallow water analysis which, with a novel solution methodology, predicts jump and drop characteristics over obstacles with much less computational effort compared to computational fluid dynamics based simulations. In addition, analytical expressions for jump efficiency and head loss across jump along with energy dissipation analysis are provided for a viscous jump. The numerical simulations reveal recirculation zones close to the channel floor and at the free surface, and the energy dissipation analysis provides a quantitative criterion for formation of recirculation zone pair. The observations are consolidated as a phase diagram which characterizes a myriad of free surface profiles based on operating and geometrical parameters. [ABSTRACT FROM AUTHOR]

This paper presents a numerical performance evaluation of the electrostatic rotary bell sprayer (ERBS) with a particular focus on droplet charge, electric field, and ambient conditions through the implementation of a high-voltage control-ring field pattern effect into the fully turbulent airflow and by including the atomized droplets discrete phase. The simulation shows that the inclusion of droplet charging and electric field coupling, with different parametric values, significantly impacts the atomized droplet distribution over the spray plume and the deposition rate. This analysis was conducted using a three-dimensional (3D) Eulerian–Lagrangian model to describe the two-phase spraying flow by extending the base OpenFOAM package. The procedure includes an unsteady compressible Navier–Stokes solver combined with a large Eddy simulation approach to model turbulence effects on the air flowfield. This is coupled to the spray dynamics by including droplet trajectory tracking, wall film dynamics, and electric field charge. The approach is further extended to include the evaporation phenomenon and the transport of its products. Compared to a conventional ERBS, herein, we provide an in-depth analysis of the fluid dynamic characteristics around the ERBS with a control-ring field pattern for vorticity, velocity, and electrical fields. The results indicate that the control-ring operation improves the performance and transfer efficiency of the ERBS, and it also helps to harmonize the direction of the charged paint droplets. For the first time, finding a balance between the effect of the inside bell cup surface and control-ring voltage and charged droplet has been conducted. [ABSTRACT FROM AUTHOR]

This paper presents numerical investigations of the nonlinear interactions between two underwater explosion (UNDEX) bubbles using the compressible Eulerian finite-element method (EFEM). The volume of fluid method is applied to capture the multi-fluid interface. In this model, the high-temperature and high-pressure gaseous products inside the UNDEX bubble are described by the equation of state for Jones–Wilkins–Lee, which allows us to consecutively simulate the propagation of the primary explosion shock wave and multi-period bubble pulsations. To verify the efficiency and accuracy of the present model, comparisons with experimental data are performed, showing that both the dynamic behaviors of oscillating bubbles and the pressure profiles of primary shock waves, bubble pulsations, and jetting loads are highly consistent. In addition, it is found that the EFEM model can satisfactorily reproduce the complex characteristics of interacting bubbles, such as the coalescence and splitting that occur during later pulsating cycles in bubbles. On this basis, the effects of the initial bubble–bubble distance γbb and buoyancy parameter δ on the features of bubble interactions and the corresponding pressure loads in the flow field are analyzed and discussed. In particular, the pressure induced by two identical UNDEX bubbles (each generated by detonation of an explosive with weight W) is compared to that induced by a single bubble generated by an explosive with weight W or 2W to provide the basic technical support and reference for the design of multiple-weapon attacks in military engineering applications. [ABSTRACT FROM AUTHOR]

In this paper, the cross-flow vortex-induced vibration (VIV) response of a top tension riser under different flow fields are comprehensively studied using a numerical simulation model based on time domain analysis. A semi-empirical time-domain analysis model that considers the fluid-structure interaction problem in the riser vibration process is proposed and verified by comparison with the previous experimental results. The influence of the flow velocity, the spanwise length of the flow field, and other factors on the VIV amplitude and frequency characteristics of the riser is analyzed in detail. The results show that the VIV response of the riser exhibits obvious multi-modal characteristics, which are accompanied by modal transition, lock-in vibration, synchronous vibration, etc., and the region where the lock-in or synchronous vibration occurs is exactly the region where the crest of the amplitude curve locates. Besides, the VIV intensity of the riser in the stepped flow and uniform flow fields show a tendency of fluctuating increase with the increase of the flow velocity and spanwise length of the flow field, while the VIV intensity of the riser in shear flow is positively correlated with the flow velocity and spanwise length of the flow field. The present study may provide a reference for the prediction of VIV of marine riser in the complex current environment. [ABSTRACT FROM AUTHOR]

In this paper, the free convective flow around an engineered porous fin with spherical connections is investigated experimentally and numerically. In addition, the effects of different positioning angles for different fin materials on thermal fin performance are analyzed. First, the copper, aluminum, and brass fins are made and their thermal performances under free convective flow are examined experimentally. Then, in order to extend the results, after validation the numerical analysis is carried out in steady and three-dimensional calculations. Then, at different positioning angles, the formed free convective flow around the porous fin is analyzed numerically and compared with the results of a rigid fin. The results show that the efficiency of the copper fins at all positioning angles is maximal. It was also found that the highest amount of Nusselt number occurs at the angle of 45°. In the numerical investigations, it is determined that the maximum increase in the Nusselt number of the engineered porous fins is about two times that of the rigid fin. Moreover, a relationship between the Nusselt number and the Rayleigh number is presented for a horizontal engineered porous fin in laminar free convection flow. [ABSTRACT FROM AUTHOR]

Although the modified Young’s equation is frequently applied to evaluate the line tension of droplets, debate concerning the value and even the sign of the line tension is ongoing. The reason for this is that the line tension defined in the modified Young’s equation is not a pure line tension but an apparent line tension, which includes the effects of the Tolman length and the stiffness coefficients. In this paper, we employ molecular dynamics (MD) to simulate three-dimensional water nanodroplets on platinum surfaces and determine their apparent line tensions by applying a linear fit to the relation of the cosine of the contact angle to the curvature of the contact line. The effects of the Tolman length and the position of the solid-liquid dividing interface on the measured line tension are investigated. On the one hand, our results elucidate the reason why MD results for line tensions are so scattered and also lend numerical support to Schimmele et al.’s theoretical predictions [“Conceptual aspects of line tensions,” J. Chem. Phys. 127, 164715 (2007)]. On the other hand, our MD simulation results demonstrate that the modified Young’s equation is a useful tool to predict the macroscopic contact angle based on a linear fit of the measured contact angles at the nanoscale. The apparent line tension is, however, sensitive to the chosen position of the solid-liquid dividing interface. [ABSTRACT FROM AUTHOR]

Jet injection into a supersonic crossflow is a classical fluid dynamics problem with many engineering applications. Several experimental and numerical studies have been taken up to analyze the interaction of a single jet with the incoming crossflow. However, there is a dearth of the literature on the interaction of multiple jets with one another and with the crossflow. Jets in a supersonic crossflow are known to produce a three-dimensional bow-shock structure due to the blockage of the flow. Multiple jets in a streamwise linear array interact with both one another and the incoming supersonic flow. In this paper, a parametric study is carried out to analyze the effect of microjet (sub-mm diameter) injection in a Mach 1.5 supersonic crossflow using flow visualization and velocity field measurements. The variation of the microjet orifice diameter and spacing within an array is used to study the three-dimensional nature of the flow field around the jets. The strength of the microjet-generated shock, scaling of the shock wave angle with the momentum coefficient, averaged streamwise, spanwise, and cross-stream velocity fields, and microjet array trajectories are detailed in the paper. It was found that shock angles of the microjet-generated shocks scale with the momentum coefficient for the three actuator configurations tested. As the microjets issue in the crossflow, a pair of longitudinal counter-rotating vortices (CVPs) are formed. The vortex pairs remain coherent for arrays with larger spanwise spacing between the micro-orifices and exhibit significant three-dimensionality similar to that of a single jet in crossflow. As the spacing between the jets is reduced, the CVPs merge resulting in a more two-dimensional flow field. The bow shock resulting from microjet injection also becomes nearly two-dimensional as the spacing between the micro-orifices is reduced. Trajectory estimations yield that microjets in an array have similar penetration as single jets. A notional schematic depicting the interaction of the microjet arrays with the supersonic crossflow is presented summarizing the principal features of the interaction. [ABSTRACT FROM AUTHOR]

Two-bubble interaction is the most fundamental problem in multi-bubbles dynamics, which is crucial in many practical applications involving air-gun arrays and underwater explosions. In this paper, we experimentally and numerically investigate coalescence, collapse, and rebound of non-buoyant bubble pairs below a rigid wall. Two oscillating vapor bubbles with similar size are generated simultaneously near a rigid wall in axisymmetric configuration using the underwater electric discharge method, and the physical process is captured by a high-speed camera. Numerical simulations are conducted based on potential flow theory coupled with the boundary integral method. Our numerical results show excellent agreement with the experimental data until the splashing of the jet impact sets in. With different ranges of γbw (the dimensionless distance between the rigid wall and the nearest bubble center), the interaction between the coalesced bubble and the rigid wall is divided into three types, i.e., “weak,” “intermediate,” and “strong.” As γbw decreases, the contact point of the two axial jets migrates toward the wall. In “strong interaction” cases, only an upward jet towards the upper rigid wall forms and a secondary jet with a larger width appears at the base of the first jet. The collapsing coalesced bubble in a toroidal form splits into many smaller bubbles due to the instabilities and presents as bubble clouds during the rebounding phase, which may lead to a weakened pressure wave because the focusing energy associated with the collapsing bubble is disintegrated. [ABSTRACT FROM AUTHOR]

This paper proposes a new non-oscillatory energy-splitting conservative algorithm for computing multi-fluid flows in the Eulerian framework. In comparison with existing multi-fluid algorithms in the literature, it is shown that the mass fraction model with isobaric hypothesis is a plausible choice for designing numerical methods for multi-fluid flows. Then we construct a conservative Godunov-based scheme with the high order accurate extension by using the generalized Riemann problem solver, through the detailed analysis of kinetic energy exchange when fluids are mixed under the hypothesis of isobaric equilibrium. Numerical experiments are carried out for the shock-interface interaction and shock-bubble interaction problems, which display the excellent performance of this type of schemes and demonstrate that nonphysical oscillations are suppressed around material interfaces substantially. [ABSTRACT FROM AUTHOR]

In this paper, we study the swimming of a model organism, the so-called Taylor's swimming sheet, in a viscoelastic fluid close to a solid boundary. This situation comprises natural habitats of many swimming microorganisms, and while previous investigations have considered the effects of both swimming next to a boundary and swimming in a viscoelastic fluid, seldom have both effects been considered simultaneously.We re-visit the small wave amplitude result obtained by Elfring and Lauga ["Theory of locomotion through complex fluids," in Complex Fluids in Biological Systems, Biological and Medical Physics, Biomedical Engineering, edited by S. E. Spagnolie (Springer New York, New York, NY, 2015), pp. 283-317] and give a mechanistic explanation to the decoupling of the effects of viscoelasticity, which tend to slow the sheet, and the presence of the boundary, which tends to speed up the sheet. We also develop a numerical spectral method capable of finding the swimming speed of a waving sheet with an arbitrary amplitude and waveform. We use it to show that the decoupling mentioned earlier does not hold at finite wave amplitudes and that for some parameters the presence of a boundary can cause the viscoelastic effects to increase the swimming speed of microorganisms. [ABSTRACT FROM AUTHOR]

Wall-resolved Large-Eddy Simulations (LES) are still limited to moderate Reynolds number flows due to the high computational cost required to capture the inner part of the boundary layer. Wall-modeled LES (WMLES) provide more affordable LES by modeling the near-wall layer. Wall function-based WMLES solve LES equations up to the wall, where the coarse mesh resolution essentially renders the calculation under-resolved. This makes the accuracy of WMLES very sensitive to the behavior of the numerical method. Therefore, best practice rules regarding the use and implementation of WMLES cannot be directly transferred from one methodology to another regardless of the type of discretization approach. Whilst numerous studies present guidelines on the use of WMLES, there is a lack of knowledge for discontinuous finite-element-like high-order methods. Incidentally, these methods are increasingly used on the account of their high accuracy on unstructured meshes and their strong computational efficiency. The present paper proposes best practice guidelines for the use of WMLES in these methods. The study is based on sensitivity analyses of turbulent channel flow simulations by means of a Discontinuous Galerkin approach. It appears that good results can be obtained without the use of a spatial or temporal averaging. The study confirms the importance of the wall function input data location and suggests to take it at the bottom of the second off-wall element. These data being available through the ghost element, the suggested method prevents the loss of computational scalability experienced in unstructured WMLES. The study also highlights the influence of the polynomial degree used in the wall-adjacent element. It should preferably be of even degree as using polynomials of degree two in the first off-wall element provides, surprisingly, better results than using polynomials of degree three. [ABSTRACT FROM AUTHOR]

The present paper reports the numerical investigation of thermocoalescence of droplets in a microchannel network consisting of a droplet formation section connecting to a temperature-induced merging chamber. The numerical model is formulated as an incompressible immiscible two-phase flow problem with oil and water as the continuous and dispersed phase, respectively. The governing equations are solved using finite volume method on a staggered mesh. The interface is captured by a narrow-band particle level-set method. The paper examines the droplet formation process and droplet size at 4 different ratios of oil and water flow rate. The motion of the droplets from the formation section into and through the heat-induced merging chamber is analyzed. The numerical method is able to provide a visual presentation of the droplet movement in a heated environment under the influence of thermocapillarity. The relationship between the critical merging temperature and the fluid flow rate is also analyzed and discussed. [ABSTRACT FROM AUTHOR]

This paper numerically investigates the influence of a uniform magnetic field on the droplet formation process at a microfluidic flow focusing configuration. The mathematical model was formulated by considering the balance of forces such as interfacial tension, magnetic force, and viscous stress across the liquid/liquid interface. A linearly magnetizable fluid was assumed. The magnetic force acts as a body force where the magnetic permeability jumps across the interface. The governing equations were solved with finite volume method on a Cartesian fixed staggered grid. The evolution of the interface was captured by the particle level set method. The code was validated with the equilibrium steady state of a ferrofluid droplet exposed to a uniform magnetic field. The evolution of the droplet formation in a flow focusing configuration was discussed. The paper mainly analyzes the effects of magnetic Bond number and the susceptibility on the velocity field and the droplet size. The droplet size increased with increasing magnetic strength and susceptibility. [ABSTRACT FROM AUTHOR]

The Cahn-Hilliard model uses diffusion between fluid components to regularize the stress singularity at a moving contact line. In addition, it represents the dynamics of the near-wall layer by the relaxation of a wall energy. The first part of the paper elucidates the role of the wall relaxation in a flowing system, with two main results. First, we show that wall energy relaxation produces a dynamic contact angle that deviates from the static one, and derive an analytical formula for the deviation. Second, we demonstrate that wall relaxation competes with Cahn-Hilliard diffusion in defining the apparent contact angle, the former tending to 'rotate' the interface at the contact line while the latter to 'bend' it in the bulk. Thus, varying the two in coordination may compensate each other to produce the same macroscopic solution that is insensitive to the microscopic dynamics of the contact line. The second part of the paper exploits this competition to develop a computational strategy for simulating realistic flows with microscopic slip length at a reduced cost. This consists in computing a moving contact line with a diffusion length larger than the real slip length, but using the wall relaxation to correct the solution to that corresponding to the small slip length. We derive an analytical criterion for the required amount of wall relaxation, and validate it by numerical results on dynamic wetting in capillary tubes and drop spreading. [ABSTRACT FROM AUTHOR]

In this paper, we use the numerical and empirical approaches and investigate the flow around a finite size disk in a finite size outer cylindrical casing. The disk is located at the center of the stationary casing and it is supported by a driving shaft through the disk and the casing. The disk rotates with the driving shaft. Five sizes of disks with different thicknesses and radii are used. The main purpose of this paper is to estimate the effect of the radial gaps on the entire flows. The combination of the thickness of the disk with smaller radius and the inner side of the casing with larger radius forms Taylor-Couette-like vortex flow in the radial gap. The supercritical instability makes the unsteady wavy vortex flow around the disk rim. When the axial gap between the disk surface and the end-wall of the casing is wide, the unsteady wavy flow is convected along the end-wall of the casing and it makes spiral rolls with negative front angles. When the axial gap is narrower and the Reynolds number is small, the instabilities are confined in the radial gap, and a beadlike flow appears around the disk rim. At higher Reynolds number, the turbulent spirals and the mixed spirals with positive and negative front angles are predicted. It is also shown that the phase velocity of the spiral is about or above the half of the velocity of the rotating disk. [ABSTRACT FROM AUTHOR]

The full and partial ground effects on the lift generation of a flapping airfoil in normal hovering mode are investigated numerically using the discrete vortex method in two dimensions. To achieve full ground effect, the airfoil of chord c is made to hover above the center of a finite-sized platform of length 10c. We have observed the force-enhancement, force-reduction, and force-recovery regimes at low, medium, and high ground clearances in line with the existing literature. This paper puts special focus on partial ground effect when the airfoil is hovering near the edge of the platform. Lift-modifying mechanisms not previously observed under full ground effect have been discovered. When stroke reversal occurs near the edge of the platform, a relatively stationary strong vortex may form above the platform edge. This strong vortex can either increase or decrease the instantaneous lift force on the airfoil depending on the position of the airfoil relative to the platform edge. Also, the platform edge may lead to the formation of an additional vortex pair which increases the instantaneous lift force as the airfoil sweeps past the edge under suitable conditions. Lastly, the platform edge can lead to the formation of a reverse von Kármán vortex street that extends well below the stroke plane under suitable geometric arrangements. [ABSTRACT FROM AUTHOR]

Interactions between an internal flow and wall deformation occur in many biological systems. Such interactions can involve a complex and rich dynamical behavior and a number of peculiarities which depend on the flow parameter range. The aim of this paper is to present a variant (obtained via a weighted residual approach) of the averaged one-dimensional model derived by Stewart et al. ["Local and global instabilities of flow in a flexible-walled channel," Eur. J. Mech. B/Fluids 28, 541-557 (2009)]. The asymptotic expansions for small Reynolds numbers of these two models, compared to the exact solution obtained from the lubrication approach, reveal some quantitative difference, even at higher Reynolds numbers. Qualitatively, the two models give similar results at least at a linear level. It is shown that for relatively low membrane tension (T), there are distinct regions in the (T, R) parameter space where steady bifurcating flows may occur. These flows can also be observed at vanishingly small Reynolds numbers combined with relatively high membrane tension. At sufficiently high T and R, the bifurcating flow is rather time periodic. A weakly nonlinear analysis is then performed in both cases leading to the derivation of evolution equations for the amplitudes of the bifurcating flows. The amplitude equations show that the saddle node bifurcation has a transcritical character while the Hopf bifurcation is either subcritical or supercritical, depending both on the mode number and membrane tension. [ABSTRACT FROM AUTHOR]

This paper presents an experimental and numerical investigation of the entry of a rigid square flat plate into pure and aerated water. Attention is focused on the measurement and calculation of the slamming loads on the plate. The experimental study was carried out in the ocean basin at Plymouth University's COAST laboratory. The present numerical approach extends a two-dimensional hydro-code to compute three-dimensional hydrodynamic impact problems. The impact loads on the structure computed by the numerical model compare well with laboratory measurements. It is revealed that the impact loading consists of distinctive features including (1) shock loading with a high pressure peak, (2) fluid expansion loading associated with very low sub-atmospheric pressure close to the saturated vapour pressure, and (3) less severe secondary reloading with super-atmospheric pressure. It is also disclosed that aeration introduced into water can effectively reduce local pressures and total forces on the flat plate. The peak impact loading on the plate can be reduced by half or even more with 1.6% aeration in water. At the same time, the lifespan of shock loading is prolonged by aeration, and the variation of impulse is less sensitive to the change of aeration than the peak loading. [ABSTRACT FROM AUTHOR]

In this paper, we investigate both theoretically and numerically the Forward-In-Time (FIT) and Backward-In-Time (BIT) dispersion of fluid and inertial particle-pairs in isotropic turbulence. Fluid particles are known to separate faster BIT than FIT in threedimensional turbulence, and we find that inertial particles do the same. However, we find that the irreversibility in the inertial particle dispersion is in general much stronger than that for fluid particles. For example, the ratio of the BIT to FIT mean-square separation can be up to an order of magnitude larger for the inertial particles than for the fluid particles. We also find that for both the inertial and fluid particles, the irreversibility becomes stronger as the scale of their separation decreases. Regarding the physical mechanism for the irreversibility, we argue that whereas the irreversibility of fluid particle-pair dispersion can be understood in terms of a directional bias arising from the energy transfer process in turbulence, inertial particles experience an additional source of irreversibility arising from the non-local contribution to their velocity dynamics, a contribution that vanishes in the limit St → 0, where St is the particle Stokes number. For each given initial (final, in the BIT case) separation, r0, there is an optimum value of St for which the dispersion irreversibility is strongest, as such particles are optimally affected by both sources of irreversibility. We derive analytical expressions for the BIT, mean-square separation of inertial particles and compare the predictions with numerical data obtained from a Reλ ≈ 582 (where Reλ is the Taylor Reynolds number) Direct Numerical Simulation (DNS) of particle-laden isotropic turbulent flow. The small-time theory, which in the dissipation range is valid for times ≤ max[Stτη, τη] (where τη is the Kolmogorov time scale), is in excellent agreement with the DNS. The theory for long-times is in good agreement with the DNS provided that St is small enough so that the inertial particle motion at long-times may be considered as a perturbation about the fluid particle motion, a condition that would in fact be satisfied for arbitrary St at sufficiently long-times in the limit Reλ → ∞. [ABSTRACT FROM AUTHOR]

Ribbons are long narrow strips possessing three distinct material length scales (thickness, width, and length) which allow them to produce unique shapes unobtainable by wires or filaments. For example, when a ribbon has half a twist and is bent into a circle it produces a Möbius strip. Significant effort has gone into determining the structural shapes of ribbons but less is know about their behavior in viscous fluids. In this paper, we determine, asymptotically, the leading-order hydrodynamic behavior of a slender ribbon in Stokes flows. The derivation, reminiscent of slender-body theory for filaments, assumes that the length of the ribbon is much larger than its width, which itself is much larger than its thickness. The final result is an integral equation for the force density on a mathematical ruled surface, termed as the ribbon plane, located inside the ribbon. A numerical implementation of our derivation shows good agreement with the known hydrodynamics of long flat ellipsoids and successfully captures the swimming behavior of artificial microscopic swimmers recently explored experimentally. We also study the asymptotic behavior of a ribbon bent into a helix, that of a twisted ellipsoid, and we investigate how accurately the hydrodynamics of a ribbon can be effectively captured by that of a slender filament. Our asymptotic results provide the fundamental framework necessary to predict the behavior of slender ribbons at low Reynolds numbers in a variety of biological and engineering problems. [ABSTRACT FROM AUTHOR]

The immiscible displacement of one viscous liquid by another in a capillary tube is experimentally and numerically analyzed in the low inertia regime with negligible buoyancy effects. The dimensionless numbers that govern the problem are the capillary number Ca and the viscosity ratio of the displaced to the displacing fluids Nμ. In general, there are two output quantities of interest. One is associated to the relation between the front velocity, Ub, and the mean velocity of the displaced fluid,Ū2. The other is the layer thickness of the displaced fluid that remains attached to the wall. We compute these quantities as mass fractions in order to make them able to be compared. In this connection, the efficiency mass fraction, me, is defined as the complement of the mass fraction of the displaced fluid that leaves the tube while the displacing fluid crosses its length. The geometric mass fraction, mg, is defined as the fraction of the volume of the layer that remains attached to the wall. Because in gas-liquid displacement, these two quantities coincide, it is not uncommon in the literature to use mg as a measure of the displacement efficiency for liquid-liquid displacements. However, as is shown in the present paper, these two quantities have opposite tendencies when we increase the viscosity of the displacing fluid, making this distinction a crucial aspect of the problem. Results from a Galerkin finite element approach are also presented in order to make a comparison. Experimental and numerical results show that while the displacement efficiency decreases, the geometrical fraction increases when the viscosity ratio decreases. This fact leads to different decisions depending on the quantity to be optimized. The quantitative agreement between the numerical and experimental results was not completely achieved, especially for intermediate values of Ca. The reasons for that are still under investigation. The experiments conducted were able to achieve a wide range of Ca. We show that in the range 1 < Nμ < 2, wavy shape instabilities appear at the interface and that increasing capillary number the amplitude of those waves increases. A deeper investigation on the operation window where these instabilities occur is in order. [ABSTRACT FROM AUTHOR]

In this paper acoustic agglomeration of aerosols is studied in its simplest form, using a time-averaged form of the coalescence equations. An acoustic coagulation kernel is introduced that neglects all nonlinear effects, as well as particle interactions. Based on this model, it is shown that an acoustic frequency exists that optimizes the coalescence process. This optimum frequency does not have a unique value for all distributions, but for size distributions that are not too wide, it is given by ω[SUBopt] =1/τ*, where τ* is the relaxation time of a particle having a diameter corresponding to the mode count diameter of the initial size distribution function. The paper also includes the result of a numerical integration of the coalescence equations for typical aerosol distributions; which show their evolution under the influence of a sound wave. [ABSTRACT FROM AUTHOR]