The wing aspect ratio (AR), that is, the ratio of the wingspan to the mean wing chord, is the most important geometrical parameter describing an insect wing. While studies have shown that a change in AR affects the flow structure as well as the aerodynamic force components on wings, the reasons behind the wide variety of aspect ratios observed in nature remain underexplored. Further to this, motivated by the developments in micro-air vehicles (MAVs), determining an optimum AR is important for their efficient operation. While the effects on flow structure appear to be, at least superficially, broadly consistent across different studies, the effects on aerodynamic forces have been more strongly debated. Indeed, the considerable variation of force coefficients with AR in different studies suggests different optimal ARs. To help explain this, recent studies have pointed out the coupled effects of AR with other parameters. Specifically, the use of Reynolds and Rossby numbers based on alternative scalings helps to at least partially decouple the effects of AR and also to reconcile previous conflicting trends. This brief review presents an overview of previous studies on aspect-ratio effects of insectlike wings summarizing the main findings. The suggested alternative scalings of Reynolds and Rossby numbers, using the wingspan as the characteristic length, may be useful in aiding the selection of the optimal aspect ratios for MAVs in the future.

A small amount of polymer additives can cause substantial reduction in the energy dissipation and friction loss of turbulent flow. The problem of polymer-induced drag reduction has attracted continuous attention over the seven decades since its discovery. However, changes in research paradigm and perspectives have triggered a wave of new advancements in the past decade. This review attempts to bring researchers of all levels, from beginners to experts, to the forefront of this area. It starts with a comprehensive coverage of fundamental knowledge and classical findings and theories. It then highlights several recent developments that bring fresh insights into long-standing problems. Open questions and ongoing debates are also discussed.

A newly proposed vortex identification method, namely, Rortex, is used to visualize the vortex structures around an in-stream deflector with a large eddy simulation. A comparison with the well-known vortex identification method, the Q criterion, indicates that the Q criterion and Rortex can both capture the main vortex structures in the flow field. However, both the modified Q criterion and the wavelet analysis reveal that Rortex excludes the shear information on the deposited sand surface, while the Q criterion cannot. As a result, Rortex is more suitable for vortex identification.

Experiments are carried out to study the breakup of moving fluid threads tightly confined in circular microchannels. A configuration with two flow-focusing channel junctions is used to control lengths and deformations of fluid threads at the first and second junctions, respectively. As fluid threads move and deform simultaneously at the second junction, the final outcomes (nonbreakup, single breakup, and double breakup) depend on the combination of three flow rates. The regime diagram for different outcomes is obtained, and the critical geometrical condition for the transition between nonbreakup and breakup is then identified from the deformation dynamics of the neck section. A theoretical analysis is then carried out to predict critical values of characteristic geometries for the transition between nonbreakup and breakup. The predictions of the critical initial thread length and the length of the first thread after breakup show good agreement with experimental measurements.

The present study aims to develop a fundamental understanding of the complex nature of fluid flow and particle transport dynamics in the alveolar region of the lungs. The acinus has a fine-scaled structure which allows for gas exchange in the blood. We model the transport characteristics of a single alveolar duct, which represents a single unit of the fine-scale acinar structure. A straight duct, with an expanding/contracting hemispherical bulb at one end, is used as a simplified approximation of a breathing alveolus. The diffusion of respiratory gases is considered across the boundary of the hemispherical bulb in order to account for the gas exchange. The transport equations are solved numerically using an Eulerian-Eulerian approach. The transport of aerosol particles could be demarcated into transient and time-periodic regimes, each with significantly different characteristics. While diffusion is observed to be the main cause of particle transport in the transient regime, the periodic nature of advective particle motion dominates in the time-periodic regime. Surprisingly, particle transport toward the acinus is observed even in a time-periodic breathing flow due to the nonlinear advective acceleration. A reduction in the particle size is observed to substantially aid the transport of aerosols. While gas exchange and increase in breathing frequency aid aerosol transport, the increase in the rate of aerosol transfer is observed to merely lower the aerosol concentration within the duct.

In recent years, microfluidic channels with narrow constrictions are extensively proposed as a new but excellent possibility for advanced delivery technologies based on either natural or artificial capsules. To better design and optimize these technologies, it is essential and helpful to fully understand the releasing behavior of the encapsulated solute from capsules under various flow conditions which, however, remains an unsolved fundamental problem due to its complexity. To facilitate studies in this area, we develop a numerical methodology for the simulation of solute release from an elastic capsule flowing through a microfluidic channel constriction, in which the tension-dependent permeability of the membrane is appropriately modeled. Using this model, we find that the release of the encapsulated solute during the capsule’s passage through the constriction is enhanced with the increase in the capillary number and constriction length or the decrease in the constriction width. On the other hand, a large variation in the channel height, which is generally larger than the capsule diameter, generates little effect on the released amount of the solute. We reveal that the effects of the capillary number and constriction geometry on the solute release are generally attributed to their influence on the capsule deformation. Our numerical results provide a reasonable explanation for previous experimental observations on the effects of constriction geometry and flow rate on the delivery efficiency of cell-squeezing delivery systems. Therefore, we believe these new insights and our numerical methodology could be useful for the design and optimization of microfluidic devices for capsule-squeezing delivery technologies.

We numerically investigate spatial and temporal evolution of multiple three-dimensional vortex pairs in a curved artery model under a fully developed pulsatile inflow of a Newtonian blood-analog fluid. We discuss the connection along the axial direction between regions of organized vorticity observed at various cross sections of the model, extending previous two-dimensional analysis. We model a human artery with a simple, rigid 180° curved pipe with circular cross section and constant curvature, neglecting effects of taper, torsion, and elasticity. Numerical results are computed from a discontinuous high-order spectral element flow solver using the flux reconstruction scheme and compared to experimental results obtained using particle image velocimetry. The flow rate used in both the simulation and the experiment is physiological. Vortical structures resulting from secondary flow are observed in various cross sections of the curved pipe, in particular, during the deceleration phase of the physiological waveform. We provide side-by-side comparisons of the numerical and experimental velocity and vorticity fields during acceleration and deceleration, the latter during which multiple vortical structures of both Dean-type and Lyne-type coexist. Correlations and quantitative comparisons of the data at these cross sections are computed along with trajectories of Dean-type vortices. Comparing cross-sectional flow fields and vortices provides a means to validate wall shear stress values computed from these numerical simulations, since the evolution of interior flow structures is heavily dependent upon geometry curvature and inflow and boundary conditions.

We present a technique for mixing the fluids in a microchannel using ultrasonic waves. Acoustic mixing is driven by the acoustic body force, which depends on the density gradient and speed of the sound gradient of the inhomogeneous fluid domain. In this work, mixing of fluids in a microchannel is achieved via an alternating multinode mixing method, which employs acoustic multinode standing waves of time-varying wavelengths at regular time intervals. The proposed technique is rapid, efficient, and found to enhance the mixing of fluids significantly. It is shown that the mixing time due to acoustic mixing (2–3 s) is reduced by two orders of magnitude compared to the mixing time only due to diffusion (400 s). Furthermore, we investigate the effects of the acoustic mixing on different fluid flow configurations and sound wave propagation directions as they have a direct influence on mixing time and have rarely been addressed previously. Remarkably, it is found that mixing performance is strongly dependent on the direction of the acoustic wave propagation. The acoustic field propagated parallel to the fluid-fluid interface mixes fluids rapidly (2–3 s) as compared to the acoustic field propagated perpendicular to the fluid-fluid interface (40 s).

Magnetization relaxation equation (MRE) plays a primary role in numerous phenomena and applications involving ferrofluid dynamics. However, as yet there exist no MREs derived from first principles and applicable to concentrated and strongly interacting ferrofluids. In this paper, we derive a novel MRE based on the projection operator technique. It sufficiently accounts for interparticle correlations beyond the scope of previous models. The MREs by Martsenyuk, Raikher, and Shliomis and by Zubarev and Yushkov (ZY), respectively, for ideal and weakly nonideal (WNI) ferrofluids, are recovered as low-order approximations. We also investigate the magnetoviscous effects. For the first time, we unveil qualitatively the different roles played by short- and long-range interparticle correlations. The long-range correlation effect dominates in a WNI ferrofluid, and both our MRE and the ZY model are in quantitative agreement with simulations on field-dependent rotational viscosity. However, for strongly nonideal ferrofluids, short-range correlations can become substantial and compete with long-range correlations to reduce rotational viscosities. Our MRE is the first dynamic model faithfully capturing both short- and long-range correlations, thereby applicable to ferrofluids characterized by a broad range of concentrations and interacting strengths. It is expected to be a cornerstone for quantitative modeling of the dynamic response of ferrofluids to external fields or flow deformations. Because most commercial ferrofluids are designed to be strongly nonideal to enhance magnetic response, our theory may provide fresh insights for applications of realistic ferrofluids in industry and biomedicine.

We investigate analytically the thruster performances and power consumption rates of a two-liquid electroosmotic thruster based on slit microchannels with hydrodynamic slip walls. The two electrolytes are considered to have different material properties and are arranged in the configuration of a core liquid layer surrounded by immiscible outer liquid layers with the outer layers in contact with the microchannel solid walls, thus forming electrical double layers at the solid-liquid interface. Interfacial potential jumps and surface charge densities are included to model the liquid-liquid interfacial double layers. Results reveal that, with the properties of both liquids being identical, nonzero liquid-liquid interfacial electrostatics only slightly increase the thrust but noticeably reduce the thruster efficiency and thrust-to-power ratio due to the enhanced Joule heating and viscous dissipation caused by the increased charge distributions and distorted velocity profiles. Moreover, the thrust and efficiency can be substantially increased as the dynamic viscosity ratio is decreased with the density ratio fixed at one, whereas the thrust, efficiency, and thrust-to-power ratio are all significantly enhanced by increasing the dynamic viscosity ratio when the kinematic viscosity ratio equals to one. The bulk electrolyte concentration/conductivity ratio is identified as a key parameter capable of simultaneously maximizing one or more thruster performances. While improving upon the performances of the single-liquid electroosmotic thruster previously reported, the two-liquid results and modeling presented herein may likely relax the limitations on the choice of electroosmotic propellants, increase the operational flexibility of electrokinetic thrusters, and be further applied in space or underwater micropropulsion applications.

As stated by the classical Thomson equation, the pore scale thermodynamics of a solvent is different from bulk conditions, being critically controlled by capillary characteristics. This equation shows that the boiling point temperatures decrease remarkably as the pore size becomes smaller, after a threshold value. This paper experimentally investigates this phenomenon for hydrocarbon solvents and compares the results with the values, obtained from the Thomson equation, to test its applicability in modeling heavy-oil recovery by solvents under nonisothermal conditions. As an initial step, the boiling point temperatures of two single-component solvents (heptane and decane) were measured by saturating Hele-Shaw type cells with variable apertures (ranging from 0.04 mm to 5 mm) and monitoring the boiling process. One experiment was run with a thickness of 12 mm to represent the bulk case. As the aperture (pore size) became smaller, the boiling point temperature decreased. For example, the measured boiling temperatures of heptane and decane were approximately 58 °C and 107 °C for the aperture values less than 0.15 mm, which were considerably lower than the “bulk” values (around 40%). In the next step, the same experiments were repeated using micromodels, representing porous media. Using the Thomson equation, the boiling points of the selected liquids were mathematically computed and compared with the experimental results from Hele-Shaw and micromodel experiments. Finally, modifications to the Thomson equation and alternative formulations were suggested.

The central premise of porous electrodes is to make more surface area available for reactions. However, the convoluted pore network of such reactors exacerbates the transport of reacting species. Tortuosity is a measure of such transport distortion and is conventionally expressed in terms of porosity (the fraction of electrode volume occupied by liquid-filled pores). Such an approach is overly simplistic and falls short of accounting for spatial variabilities characteristic of electrode samples. These networks are defined by multiple features such as size distribution, connectivity, and pore morphology, none of which are explicitly considered in a porosity based interpretation, thus limiting predictability. We propose a recourse using a two-point correlation function that deconstructs the pore network into its essential attributes. Such a quantitative representation is mapped to the transport response of these networks. Given the explicit treatment of pore network geometry, this approach provides a consistent treatment of three-dimensionalities such as inhomogeneity and anisotropy. Three-dimensional (3D) tomograms of Li-ion battery electrodes are studied to characterize the efficacy of the proposed approach. The proposed approach is applicable to abstracting effective properties related to different transport modes in porous fluid networks.

The instabilities of thermocapillary–buoyancy convection in droplet migration are examined by linear stability analysis. The droplet is flattened by gravity and placed on a unidirectional heated solid surface. The velocity and temperature distributions of basic flow are derived as a function of the migration velocity and the Bond number. The critical Marangoni number is obtained, which depends on the Prandtl number (Pr), the Bond number, and the migration velocity. The preferred modes at small and moderate Pr are oblique waves, which travel either upstream or downstream. For high Pr, the preferred modes include oblique and streamwise waves, while the amplitude of temperature on the surface is much smaller than that of the hot spot in the flow region. The instability mechanism is discussed and comparisons are made with liquid layers.

In this paper, an interface-compressed diffuse interface method is proposed for simulating multiphase flow with a large density ratio. In this method, an interface-compression term is introduced into the Cahn-Hilliard equation to suppress the interface dispersion caused by the numerical and modeling diffusion. The additional term only takes effect in the region of phase interface and works normal to the interface. The compression rate can be adjusted synchronously according to the local gradient of normal velocity at the interface. Numerical validations of the proposed method are implemented by simulating Rayleigh-Taylor instability, bubble deformation in shear flow, bubble merging, and bubble rising with a density ratio of 1000 and a viscosity ratio of 100. Good agreement of interface shapes and flow properties has been achieved as compared with both analytical solutions and published data in the literature. The obtained results also show that the present method makes great improvement of interface sharpness and avoids the occurrence of unphysical phenomenon. Meanwhile, the tiny interfacial structures can be captured effectively.

The gravity-driven spreading of one fluid in contact with another fluid is of key importance to a range of topics. These phenomena are commonly described by the two-layer shallow-water equations (SWE). When one layer is significantly deeper than the other, it is common to approximate the system with the much simpler one-layer SWE. It has been assumed that this approximation is invalid near shocks, and one has applied additional front conditions to correct the shock speed. In this paper, we prove mathematically that an effective one-layer model can be derived from the two-layer equations that correctly capture the behavior of shocks and contact discontinuities without additional closure relations. The result shows that simplification to an effective one-layer model is justified mathematically and can be made without additional knowledge of the shock behavior. The shock speed in the proposed model is consistent with empirical models and identical to front conditions that have been found theoretically by von Kármán and Benjamin. This suggests that the breakdown of the SWE in the vicinity of shocks is less severe than previously thought. We further investigate the applicability of the SW framework to shocks by studying one-dimensional lock-exchange/-release. We derive expressions for the Froude number that are in good agreement with the widely employed expression by Benjamin. The equations are solved numerically to illustrate how quickly the proposed model converges to solutions of the full two-layer SWE. We also compare numerical results from the model with results from experiments and find good agreement.

Gravity-driven film flow through an inclined corrugated pipe is experimentally investigated following field observations of unsteady, periodic flow patterns. Initial experiments confirmed surging flow at the pipe outlet as originally observed in the field. Fluorescence imaging of the film flow inside the pipe was then applied to examine the traveling wave behavior that leads to surging flow at the outlet. To our knowledge, this is the first investigation of traveling wave behavior in film flow in a corrugated pipe. The effect of flow rate and angle of inclination was studied in both experiments, with the characteristics of the traveling waves becoming the focus of the investigation. Similar to film flows over two-dimensional periodic topography, a statically deformed free surface with a wavelength approximately equivalent to the corrugations developed at all flow rates and angles examined with an amplitude that increased with angle of inclination. In contrast to film flows over two-dimensional periodic topography, the statically deformed free-surface amplitude was independent of the flow rate. Comparative to some two-dimensional studies, traveling waves developed from ambient noise through a strongly selective process. Traveling waves were observed to be approximately nondispersive and having nearly constant frequency and wavelength regardless of the flow rate or angle of inclination. The consistency in traveling wave character with changes in the angle and flow rate seems stronger than that seen for two-dimensional flows. Comparisons with large-scale flow applications, such as stepped spillways, indicate similarities in flow behavior that should be studied further.

We investigate the effect of continuous-wave laser irradiation on the cavity evolution behind a sphere in water entry. By tuning the irradiation time, the surface temperature (Ts) of the sphere before the impact varies in 105–355 °C. We change the radius and impact velocity of the sphere, by which both the shallow and deep seals are considered. Compared to the reference case (the sphere was roughened to have a cavity initially), we find that the cavity expands or shrinks depending on Ts. Overall, for all cases, the cavity bubble expands to the maximum size and shrinks steeply with increasing Ts. At higher Ts, the cavity is destroyed significantly, even smaller than the reference case. However, the detailed interaction between the cavity and laser-induced cavitation bubbles is quite different. In a shallow-seal case, nucleate boiling occurs on the sphere surface and vapor bubbles merge into the cavity, resulting in the expansion of the cavity. At a highly subcooled condition, on the other hand, the vapor bubble collapses into microbubbles as soon as it contacts water, resulting in the cavity reduction. As the impact speed increases (for a deep-seal condition), the flux of entrained air becomes dominant and the stage of cavity expansion is quite narrow. As Ts increases, the heated cavity collapses into microbubbles and almost 90% is destroyed. Finally, we investigate the effects of modified cavity on hydrodynamic forces on the sphere. While the temporal variation of hydrodynamic forces is complex, the drag reduction over 40% is achieved.

A computational study of thin liquid films over a solid surface is reported. The lubrication equation is numerically solved using an in-house code, which implements the finite volume method. Small slope approximation is abandoned, and a more accurate model for capillary pressure estimation is presented, allowing us to correctly investigate higher contact angles, when compared to the maximum value allowed by small slope approximation. Disjoining pressure is used for modeling substrate wettability. The in-house solver is first validated: a 1D flowing film driven by gravity is simulated and the disjoining pressure model is verified for contact angles up to 60°; replicating literature experimental investigations, a uniform film covering an inclined plate is perturbed, inducing the generation of a large dry patch; rivulet buildup is simulated; and the numerical results are compared with fully 3D computations found in the literature and verified with analytical evidences. Then, a film flowing over an inclined plate bounded by lateral walls, which is a complex configuration commonly used for studying liquid behavior in structured packing, is investigated and relevant parameters are reported.

An experimental study was performed to investigate the dynamics of droplet shedding under the effect of various shear flow speeds on a laser micromachined surface with superhydrophobic properties. To account for the effect of liquid properties on droplet shedding, four different liquids were used in these sets of experiments, namely, distilled water, ethylene glycol, propylene glycol, and glycerol. The wetting length of the liquid droplets was measured based on the air shear speed, and three different regimes were observed based on the critical Weber and Ohnesorge numbers. In the first regime, where the Weber and Ohnesorge numbers are low, droplets deform with slight movement or rotation without detachment from the surface. Under the second regime, where the Weber number is relatively high and the Ohnesorge number is low, droplets deform and detach from the surface, and then subsequent breakup may occur. The variation of droplet detachment time with the Weber and Ohnesorge numbers is further discussed in this paper. In the third regime, where the Ohnesorge number is high, there is no droplet detachment nor are rivulets formed. Finally, empirical correlations are developed to predict the droplet behavior on laser-patterned surfaces under the effect of shear flow. This work can be used as a baseline to study the droplet dynamics on a superhydrophobic surface in cases where temperature changes the liquid properties.

The coalescence-induced self-propelled droplet jumping on superhydrophobic surfaces has a large number of potential applications such as enhancement of condensation heat transfer, self-cleaning, and anti-icing, which becomes a current hotspot. At present, most of the research studies focus on the self-propelled jumping of two identical droplets; however, the jumping induced by unequal-sized droplets is much closer to actuality. In this paper, the coalescence-induced self-propelled jumping of binary unequal-sized droplets is simulated and all energy terms are studied. The normalized liquid bridge width induced by unequal-sized droplets is a function of the square root of the normalized time, and the maximum jumping velocity is a function of the radius ratio as well. The maximum jumping velocity descends with the decrease in the radius ratio and contact angle, and the critical radius ratio shows an upward trend with the decrease in the contact angle. Furthermore, all energy terms decline with the decrease in the radius ratio. The effective energy conversion rate of binary equal-sized jumping is very low, less than 3% in our results. This rate of binary unequal-sized jumping further reduces due to the existence of asymmetric flow. This work helps for a better understanding of the characteristics of coalescence-induced self-propelled droplet jumping.

In this paper, we investigate the nonlinear interaction of two primary progressive waves traveling in the same/opposite direction. Without loss of generality, two cases are considered: waves traveling in the same direction and waves traveling in the opposite direction. There exist an infinite number of resonant wave components in each case, corresponding to an infinite number of singularities in mathematical terms. Resonant wave systems with an infinite number of singularities are rather difficult to solve by means of traditional analytic approaches such as perturbation methods. However, this mathematical obstacle is easily cleared by means of the homotopy analysis method (HAM): the infinite number of singularities can be completely avoided by choosing an appropriate auxiliary linear operator in the frame of the HAM. In this way, we successfully gain steady-state systems with an infinite number of resonant components, consisting of the nonlinear interaction of the two primary waves traveling in the same/opposite direction. In physics, this indicates the general existence of so-called steady-state resonant waves, even in the case of an infinite number of resonant components. In mathematics, it illustrates the validity and potential of the HAM to be applied to rather complicated nonlinear problems that may have an infinite number of singularities.

In the present study, the oscillatory flow of a Maxwell fluid in a long tube of isosceles right triangular cross section is considered. The analytical expressions for the velocity and phase difference for the flow driven by the periodic pressure gradient are obtained explicitly. The numerical solutions are calculated by using a high-order compact finite difference method. The effects of relaxation time and the Deborah number on the velocity and phase difference are discussed numerically and graphically.

The mechanical and thermal behavior of nonisothermal fiber-filled composites in a three-dimensional printing process is studied numerically with a smoothed particle hydrodynamics method. A classical microstructure-based fiber suspension model with a temperature-dependent power-law viscosity model and a microstructure constitutive model is implemented to model a fiber-filled system. The fiber microstructure is described by a second-order tensor A2 which describes the spatially averaged orientation of the fibers. Two benchmark cases are presented to validate the reliability of the present implementation. Three typical printing modes are tested to assess the characteristics of printed layers. The results show that the printed layer becomes thicker, and the fiber alignment in the printing direction is enhanced in the bottom half of the layer and reduced in the top half due to the existence of nonisothermal effects in the process. The variation in fiber orientation becomes larger with increasing fiber concentration. By increasing the Peclet number, the deposited layer thickness reduces and the fiber alignment in the printing direction is enhanced in the top half and reduced in the bottom half. The evolution of the orientation and the velocity gradient tensors projected along several streamlines are discussed to illustrate the effects of the temperature and different printing modes on the deposited layer.

We investigate the capillary driven collapse of a small contracting cavity or hole in a shear-thinning fluid. We find that shear-thinning effects accelerate the collapse of the cavity by decreasing the apparent liquid viscosity near the cavity’s moving front. Scaling arguments are used to derive a power-law relationship between the size of the cavity and the rate of collapse. The scaling predictions are then corroborated and fully characterized using high-fidelity simulations. The new findings have implications for natural and technological systems including neck collapse during microbubble pinch-off, the integrity of perforated films and biological membranes, the stability of bubbles and foams in the food industry, and the fabrication of nanopore based biosensors.

In this article, we have investigated, via numerical simulation, the interaction of two identical balls settling in a vertical square tube filled with a viscoelastic fluid. For two balls released in Oldroyd-B fluids, one on top of the other initially, we have observed two possible scenarios, among others: either the trailing ball catches up the leading one to form a doublet (dipole) or the balls separate with a stable final distance. If the ball density is slightly larger than the fluid density, the two balls form a doublet, either vertical or tilted. If one further increases the ball density, the two balls still form a doublet if the initial distance is small enough, but for larger initial distances at higher elasticity numbers, the balls move away from each other and their distance reaches a stable constant. Factors influencing doublet formation are (possibly among others) the ball density, the ball initial distance, and the fluid elasticity number. When settling in finite extendable nonlinear elastic–Chilcott and Rallison fluids, low values of the coil maximal extension limit enhance ball separation.

To predict fiber orientation for injection molded parts, it is important to use a slow-kinetics orientation model and pay careful attention to the role of flow kinematics on orientation evolution speed. A model incorporating the impact of flow type on the fiber reorientation rate was tested by comparing with experimental data measured in an injection molded center-gated disk for both short and long glass fiber thermoplastics. Unlike the existing orientation models using a constant factor, a variable strain reduction factor (SRF) is expressed as a function of an objective flow-type parameter reflecting local flow kinematics. The use of this model improved the fiber orientation predictions at locations where the constant SRF, obtained from simple shear flow, deviated significantly from that based on the local flow kinematics.

Elastic turbulence, which is sensitive to geometry and polymer rheology, has shown great potential for improving the performance of mixing, heat transfer, and even oil recovery. Recent studies showed the importance of the rheological properties of polymer solutions on the onset of elastic turbulence. However, variations of rheological properties based on polymer sensitivities such as salinity and its corresponding effects on the elastic turbulence have not been revealed. This work investigated systematically the effects of salinity on the onset of elastic turbulence in both swirling flow and curvilinear microchannels. The variations of statistical properties, such as probability distribution functions (PDFs) and power spectral density of injected power (PSD), were analyzed for characterization. The onset conditions of elastic turbulence are postponed by high salinity, which is consistent with the mixing performance in a curvilinear microchannel. A salinity independent power-law exponent at a value of −4.3 is observed in a fully developed elastic regime for all polymer solutions. Particularly, the diffusion of fluorescein at a low flow rate in the microchannel is possible due to the existence of a steady secondary flow before the onset of elastic instability.

This paper theoretically examines the spatial linear instability of viscoelastic jets subjected to unrelaxed axial stress tension and moving within an inviscid stationary gas medium. Unlike the constant value assumption of previous studies, the effects of spatial decaying of the unrelaxed stress tension are included here. The Oldroyd-B constitutive equation has been adopted to model fluid viscoelasticity. Results indicated that the effects of unrelaxed stress tension were complicated and mainly dependent on stress relaxation time. When stress relaxation time was short, the maximum growth rates along the jet decreased to the constant value of the completely relaxed case; increasing unrelaxed tension slightly decreased the breakup length. When the stress relaxation time increased to exceed the critical value, the maximum growth rates continued to increase along the jet and larger unrelaxed tensions caused longer breakup lengths. This twofold effect can be explained by the competition between the stabilizing effects of the unrelaxed tension itself and the destabilizing effects of the spatial decay. Moreover, the fluid elasticity suppressed instability when the unrelaxed tension was great. Responses to the spatial decaying unrelaxed tension of the axisymmetric and nonaxisymmetric disturbances for high-speed viscoelastic jets were similar to those of the capillary case. Generally, the complex effects of the interplay between fluid elasticity and the spatially decaying unrelaxed tension may qualitatively explain the breakup behaviors of viscoelastic jets in experiments.

Exact up-down asymmetric solutions to the Navier-Stokes equations for a viscous and incompressible fluid with time-dependent viscosity ν(t) are derived. Transformations of the exact solutions are defined that produce an infinite sequence of new solutions from each known one. The solutions are presented in terms of elementary functions and have no singularities. Three infinite-dimensional families of new exact axisymmetric unsteady solutions to the viscous magnetohydrodynamics equations are derived. Dynamics of vortex rings and vortex blobs is studied for some exact up-down asymmetric incompressible viscous fluid flows and viscous plasma flows.

The drop impact on a solid surface is studied in the context of complex fluids that exhibit viscoplastic, viscoelastic, and thixotropic behavior. The effects of rheology and surface tension are investigated for a range of corresponding dimensionless numbers associated with each phenomenon. Two usual quantities are employed to understand the drop dynamics, namely, the maximum spreading diameter and the time the drop remains in contact with the solid. Another result is the drop shape evolution, captured by displaying selected instants. The first part of the work is dedicated to examine the influence of capillary effects for more real fluids, in the present case, solutions of Carbopol, kaolin, and bentonite whose mechanical properties are taken from experimental measurements reported in the literature. In the second part, we conduct parametric studies varying the dimensionless numbers that govern the problem. We have shown that the influence of surface tension in yield stress materials is less significant and can be negligible when real parameters are input in the model. On the other hand, Newtonian and viscoelastic fluids are more susceptible to surface tension effects. This quantity tends to decrease maximum spreading diameter and decrease contact time due to its resistance in the spreading stage. While inertia, elasticity, and plastic effects favor the drop to spread and to increase its contact time with the solid substrate, a more thixotropic behavior leads to the opposite trend.

Dynamics of a single porous, rigid, two-dimensional (2D) elliptic particle settling in a narrow vertical channel filled with a Newtonian fluid is numerically studied using the lattice-Boltzmann method. The main objective of the work is to investigate the role played by the particle’s permeability on its trajectory, orientation, and terminal velocity when released from the rest state with prescribed initial conditions. Assuming that the flow induced in the fluid surrounding the particle is laminar, incompressible, isothermal, and two-dimensional, numerical results could be obtained over a wide range of parameter settings suggesting that permeability can strongly affect the modes of sedimentation reported in the literature for impermeable elliptic particles provided that the particle’s permeability is larger than a threshold. Above this threshold, permeability is predicted to increase the terminal velocity of the particle with its severity depending on the blockage ratio. It is also predicted that a permeable particle is less sensitive to initial orientation and position as compared with an impermeable particle.

The present study concerns Lagrangian transport and (chaotic) advection in three-dimensional (3D) flows in cavities under steady and laminar conditions. The main goal is to investigate topological equivalences between flow classes driven by different forcing; streamline patterns and their response to nonlinear effects are examined. To this end, we consider two prototypical systems that are important in both natural and industrial applications: a buoyancy-driven flow (differentially heated configuration with two vertical isothermal walls) and a lid-driven flow governed by the Grashof (Gr) and the Reynolds (Re) numbers, respectively. Symmetries imply fundamental similarities between the streamline topologies of these flows. Moreover, nonlinearities induced by fluid inertia and buoyancy (increasing Gr) in the buoyancy-driven flow vs fluid inertia (increasing Re) and single- or double-wall motion in the lid-driven flow cause similar bifurcations of the Lagrangian flow topology. These analogies imply that Lagrangian transport is governed by universal mechanisms, and differences are restricted to the manner in which these phenomena are triggered. Experimental validation of key aspects of the Lagrangian dynamics is carried out by particle image velocimetry and 3D particle-tracking velocimetry.

Stratified double-diffusive layers (DDLs) in fluidic mixtures such as oceans, magma, and latte typically contain alternating low gradient mixing regions separated by high gradient interfaces. The prior knowledge is restricted to the formation of layers, but the existence of DDLs, under prolonged freezing conditions, as well as in multicomponent mixtures, is not yet understood well. In this work, a new observation depicting the existence of a life-cycle for a double-diffusive layer is revealed with the help of real-time observations of unidirectional freezing of multicomponent mixtures. The observations showed a systematic occurrence of the onset, formation, disappearance, and recurrence of the DDLs when freezing conditions prevailed for longer durations of time. The results also include first-ever observations of compositional stratification in a ternary mixture, which depends on the regimes and nature of buoyant convection. The ternary experiments also demonstrated the formation of DDLs much closer to the solidifying mush, which shed light on retaining the stratified layers in the frozen state. Furthermore, the hypothesized life-cycle of the DDL was mapped to the regimes of occurrence and the nonexistence of DDLs in the mixture phase diagrams of binary and ternary systems, with a threshold composition difference and the corresponding critical Rayleigh number. This distinction of the regimes on the phase diagram shows a striking correlation with a reduced ternary phase diagram of igneous rocks, thus providing a suitable basis for explaining the formation of layered rocks.

The two-phase Couette flow with transpiration through both walls is considered, where there is a constant blowing v0 at the lower wall and a corresponding suction at the upper wall. The interface between both fluids is initially flat and, hence, stays flat as it moves upward at the constant speed of the transpiration velocity v0. The corresponding initial value problem is subject to three dimensionless numbers consisting of the Reynolds number Re and the viscosity and density ratios, ϵ and γ. The solution is obtained by the unified transform method (Fokas method) in the form of an integral representation depending on initial and all boundary values including the Dirichlet and Neumann values at the interface. The unknown values at the moving interface are determined by a system of linear Volterra integral equations (VIEs). The VIEs are of the second kind with continuous and bounded kernels. Hence, the entire two-phase spatiotemporal 1 + 1 system has dimensionally reduced. The system of VIEs is solved via a standard marching method. For the numerical computation of the complex integral contours, a parameterized hyperbola is used. The influence of the dimensionless numbers Re, γ, and ϵ is studied exemplarily. The most notable effect results from ϵ that gives rise to a kink in the velocity at the moving interface. Both ratios, ϵ and γ, allow for very different flow regimes in each fluid phase such as nearly pure Couette flows and transpiration dominated flows with strongly curved velocity profiles. Those regimes are mainly determined by the effective Reynolds number in the respective phases.

Laminar flow around and heat transfer from two inline square cylinders under an active flow control (uniform blowing and suction) are numerically investigated at Reynolds numbers of 70–150, a Prandtl number of 0.71, and a cylinder-gap spacing (G) ratio of G/d = 1–5, where d is the cylinder side. A finite-volume code based on a collocated grid arrangement is employed in the two-dimensional numerical simulations. Uniform blowing and suction are applied to the upstream cylinder only (referred to as UFC) or applied to both cylinders (referred to as OFC). The purpose of using these two flow controls is to reduce time-mean and fluctuating forces and to suppress vortex shedding. The noncontrol case is referred to as the reference case where vortex shedding occurs from both cylinders for G/d ≥ 3 and from the downstream cylinder only for G/d < 3. For UFC, vortex shedding from the upstream cylinder is suppressed for G/d = 1–5 examined. A drag reduction of more than 50% occurs for the upstream cylinder with G/d = 1–5, while the downstream cylinder has such a high drag reduction for G/d ≥ 3 only. In the case of OFC, vortex shedding from either cylinder is suppressed while the time-mean and fluctuating forces reduce for the entire G/d range. The maximum reduction in the total drag force (sum of both cylinders) is about 70%. The blowing hinders heat transfer from the cylinders while the suction enhances it.

The cross flow-induced vibrations of a circular cylinder at the Reynolds number of 150 are numerically investigated in a systematic manner in terms of a wide range of reduced velocity. The effect of the mass ratio on the cylinder behavior is studied, with three mass ratios, namely, 2, 10, and 50, being considered particularly in detail. The mass ratio is defined as the mass of the cylinder to the mass of the fluid it displaces. A sudden decrease in the vibration amplitude takes place at a certain value of the reduced velocity, accompanied by an abrupt increase in the lift coefficient and the vortex shedding frequency. The vortex shedding frequency at the upper end of the lock-in region is about 0.14 for all the mass ratios, which may mark the lower limit of the vortex shedding frequency at this Reynolds number. The jump phenomena may be ascribed to this limitation. Moreover, the vortex shedding frequency in the non-lock-in region varies slightly with the reduced velocity but is not approaching the Strouhal number for the stationary cylinder at the same Reynolds number. In fact, the frequency rises with the increasing mass ratio and reaches about 0.2 as the mass ratio is larger than 10. Besides, the vortex shedding mode does not remain “2S” for the mass ratio larger than 14 when the reduced velocity is increased to get into the non-lock-in region since the vortex shedding frequency is separate from the cylinder oscillation frequency.

This experimental study provides striking examples of the complex flow and turbulence structures resulting from blade–wake and wake–wake interactions in a multistage turbomachine. Particle image velocimetry measurements were performed within the second-stage rotors of a two-stage compressor. The first-stage stator wake is distorted and produces a kink structure in the second-stage rotor blades passage. This kink, also called a turbulent hot spot, with concentrated vorticity, high turbulence levels, and high turbulence kinetic energy, is caused by the interaction between the first-stage rotor wake and the stator wake. A high-speed region and a low-speed region are observed around the turbulent hot spot. The perturbation velocity is counterclockwise around the turbulent hot spot, with a magnitude much larger than that in the wake. The turbulent hot spot is more unstable and active than the wake and, thus, might play a pivotal role in the passage flow. The high turbulence and the negative jet behavior of the wake dominate the interaction between the unsteady wake and the separated boundary layer on the suction surface of the blade. When the upstream wake impinges on the blade, the boundary layer thickness first increases owing to the presence of the negative jet, and a thickened boundary layer region in the form of a turbulent spot is formed because of the high turbulence intensity in the wake. Then, the boundary layer gradually becomes thinner because of the presence of a calmed region that follows the thickened boundary layer region. Finally, the boundary layer gradually thickens again and recovers to separation. Thus, the boundary layer thickness is periodic in a wake passing cycle.

This article deals with the dynamics of a cylindrical bluff-body-stabilized M-shaped premixed flame at low flow rates. A comparative analysis with classical conical flames was performed. The velocities and flame front field dynamics were studied with the use of numerical methods. It was shown that the processes under the investigation are similar to those in a conical flame. The flame front is deformed by moving Kelvin–Helmholtz vortices along the front. It was found that M-shaped flame tips perform in-phase low-frequency oscillations in both vertical and horizontal directions as opposed to the conical one. It was also found that fuel enrichment does not affect the frequency of the flicker as compared to the classical conical flame. A number of experiments have shown that vertical displacement amplitude in M-shaped flame is approximately 3.5 times smaller than in a conical one at the same flow rate. An explanation of this phenomenon is the fact that a part of the energy under compression goes to the horizontal displacement of the front.

The stability of the interface formed by fine suspended particles is studied through linear stability analysis. Our derivation using the regular perturbation expansion with respect to the particle’s settling velocity shows that the unstable modes are independent of the gravitational settling of individual particles. These modes can be obtained from the six-order ordinary differential equation obtained from the analysis of zero-order quantities. In addition to the four boundary conditions applied at the interface in the traditional Rayleigh-Taylor problem in the semi-infinite domain, two conditions based on the continuity of the concentration of the background stratification agent and its gradient are introduced. Our stability results show transition of modes from a small value in a regime of Rayleigh-Taylor instability to the large values of double-diffusive convection when the background density stratification becomes increasingly significant. In the latter case, our analysis shows growth of small perturbations with dominant wavelengths scaled by the double-diffusion length scale. The transition of unstable modes depends on the density ratio, the Prandtl number of the stratification agent, and the viscosity ratio between the two fluid layers. The analysis is further confirmed by the results from the direct numerical simulation.

Transitional boundary layers over lifting bodies represent an important class of flows in many industrial applications, and accurately capturing the transition is crucial for the prediction of important phenomena such as lift, drag, and trailing-edge noise. In this study, we consider how large eddy simulations (LESs) can be used to capture the natural boundary layer transition and compare the results to fully resolved direct numerical simulations that provide a detailed picture of the transition and trailing edge flow. The ability of LES to capture the transition is considered by looking at different elements of the subfilter scale modeling and discretization. The behavior of the subfilter scale model is shown to be critical, and it must remain inactive during the early stages of transition to avoid erroneous predictions due to excessive dissipation. Dispersion errors, when present, can cause the natural transition mechanism to be bypassed at an earlier stage, which leads to higher levels of turbulent kinetic energy at the trailing edge.

The aim of this paper is to characterize large-scale instabilities during the primary breakup process in liquid centered coaxial air-water jets. The interest here is to investigate the role of annular air swirl on such instabilities. A coaxial airblast atomizer that incorporates an axial swirler is considered for this purpose. The atomizer was operated in a wide range of the Weber number, Weg(80–958), momentum flux ratio, M(1–26), and air swirl strength, S(0–1.6). High-speed shadowgraphic images of the primary jet breakup process were recorded. Proper orthogonal decomposition (POD) analysis of the time-resolved images was performed for each operating condition. The 2nd and 3rd POD modes depicted some universal spatial features which refer to large scale instabilities. Three different dominant large scale instabilities were identified, viz., jet flapping, wavy breakup, and explosive breakup, for the entire range of the injector operating condition either in the presence or absence of air swirl. It was found that jet flapping (referred to as the lateral oscillation of the tail end of the jet) is the dominant mode of jet instability for a lower range of M, while explosive jet breakup (referred to as the radial expansion of the jet) governs jet breakup unsteadiness for a higher range of M. The wavy or sinuous mode of breakup is a secondary mechanism relevant under low M conditions. The mechanisms of large scale instabilities and the role of air swirl in that context are explained based on the Fourier analysis of the temporal coefficients of the corresponding POD modes.

The rolling pad instability is caused by electromagnetic interactions in systems of horizontal layers with strongly different electric conductivities. We analyze the instability for a simplified model of a liquid metal battery, a promising device for large-scale stationary energy storage. Numerical simulations of the flow and the dynamics of electromagnetically coupled interfacial waves are performed using OpenFOAM. This work confirms the earlier conclusions that the instability is a significant factor affecting the battery’s operation. The critical role played by the ratio between the density differences across the two interfaces is elucidated. It is found that the ratio determines the stability characteristics and the type (symmetrically or antisymmetrically coupled) of dominant interfacial waves.

This paper presents a nonlinear time-series analysis of the thermoacoustic instabilities of an experimental slot burner. The main objective was the calculation of indexes capable of detecting in advance the combustion instabilities by gradually increasing the flow Reynolds number of the pilot burner. A chaotic analysis based on diagonalwise measurements of the recurrence plots was performed on the basis of which the following indexes were calculated: the τ-recurrence rate index RRτ, the τ-determinism index DETτ, the τ-average diagonal line length index Lτ, and the τ-entropy index sτ. A quantification carried out by means of the standard deviation σ and mean values μ of the diagonalwise measurements showed that the aforementioned indexes were successfully able to sort all cases under analysis mainly into two groups: the first three cases that correspond to the stable regime named “Combustion Noise” and the remaining cases that were associated with the unstable regime called “Combustion Instability.” Additionally, the particle image velocimetry optical method was applied in order to compute a new index based on the velocity fields. The results showed that the index Vh, based on the local heights of the velocity profiles of the central flame, was also capable of detecting the same two groups previously identified by the nonlinear analysis. Nevertheless, the most sensitive indexes were the indexes RRτμ, DETτσ, and sτσ since these indexes were able to detect the transition between the combustion noise and combustion instability regimes. Therefore, the present results proved that the proposed five indexes were effective precursors in order to detect in advance the combustion instabilities.

Tracking transitional and turbulent flows requires methods other than the classical techniques, which capture coherent structures via locating pressure minima, after the disturbance field has evolved to late-transitional and turbulent flow stages. Keeping it in mind, transition to turbulence of zero pressure gradient flow is studied, following two routes of excitation, by solving the three-dimensional Navier-Stokes equation in derived variable formulation, with vorticity as one of the dependent variables. For such flows, disturbance structures should be traced from the receptivity to the coherent structure stage for the fully developed turbulent flow. The coherent structures in turbulent flows are identified by the Q- and λ2-criteria, based on the occurrence of pressure minima at the vortex cores. In the proposed study here, the zero pressure gradient boundary layer is excited (i) at the wall with a monochromatic source and (ii) causing transition to turbulence, by a convecting vortex in the free stream. The main aim here is to trace the incipient disturbances from the onset to the turbulent state in terms of physical quantities, such as the disturbance mechanical energy introduced by Sengupta et al. [“Vortex-induced instability of an incompressible wall-bounded shear layer,” J. Fluid Mech. 493, 277–286 (2003)] and disturbance enstrophy transport equation, as proposed by Sengupta et al. [“An enstrophy-based linear and nonlinear receptivity theory,” Phys. Fluids 30(5), 054106 (2018)]. Such methods are capable of tracing disturbance structures from the onset to the evolved stage. We compare these methods with Q- and λ2-criteria to trace disturbance evolution.

In this paper, the effect of a special active control on the Blasius boundary layer is investigated with the Orr-Sommerfeld and the Reynolds-Orr energy equations. The control moves the wall in the streamwise direction proportional to the fluctuating wall shear stress which was proposed by Józsa et al. [“Active and passive in-plane wall fluctuations in turbulent channel flows,” J. Fluid Mech. 866, 689–720 (2019)]. Our results showed that the negative proportional parameters destabilize the flow, while the positive values lead to a contradictory outcome. According to the Orr-Sommerfeld equation, with the right choice of the parameter, the critical Reynolds number can be significantly increased. At the same time, the Reynolds-Orr equation predicts that any streamwise movement of the wall proportional to the wall shear stress slightly destabilizes the flow.

We report the statistical properties of temperature and thermal energy dissipation rate in low-Prandtl number turbulent Rayleigh-Bénard convection. High resolution two-dimensional direct numerical simulations were carried out for the Rayleigh number (Ra) of 106 ≤ Ra ≤ 107 and the Prandtl number (Pr) of 0.025. Our results show that the global heat transport and momentum scaling in terms of Nusselt number (Nu) and Reynolds number (Re) are Nu = 0.21Ra0.25 and Re = 6.11Ra0.50, respectively, indicating that scaling exponents are smaller than those for moderate-Prandtl number fluids (such as water or air) in the same convection cell. In the central region of the cell, probability density functions (PDFs) of temperature profiles show stretched exponential peak and the Gaussian tail; in the sidewall region, PDFs of temperature profiles show a multimodal distribution at relatively lower Ra, while they approach the Gaussian profile at relatively higher Ra. We split the energy dissipation rate into contributions from bulk and boundary layers and found the locally averaged thermal energy dissipation rate from the boundary layer region is an order of magnitude larger than that from the bulk region. Even if the much smaller volume occupied by the boundary layer region is considered, the globally averaged thermal energy dissipation rate from the boundary layer region is still larger than that from the bulk region. We further numerically determined the scaling exponents of globally averaged thermal energy dissipation rates as functions of Ra and Re.

The use of parameter extension simulation (PES) as a mathematical method for simulating turbulent flows is proposed in this study. It is defined as the calculation of a turbulent flow with the help of a reference solution. A typical PES calculation includes three steps, as follows: setting up an asymptotic relationship between the exact solution of the Navier–Stokes equations and the reference solution for the initial parameter values, calculating the reference solution and the necessary asymptotic coefficients, and extending the reference solution to the parameter values to produce the exact solution. The method of controlled eddy simulation (CES) has been developed to calculate the reference solution and the asymptotic coefficients. The CES method is a special case of large eddy simulation (LES), in which a weighting coefficient and an artificial force distribution are used to damp part of the turbulent motions. The distribution of artificial force is modeled with the help of eddy viscosity. The reference-weighting coefficient can be determined empirically or in a convergence study. To demonstrate potential uses, the proposed PES method is used to simulate four types of turbulent flows. The flows are decaying homogeneous and isotropic turbulence, smooth-wall channel flows, rough-wall channel flows, and compressor-blade cascade flows. The numerical results show that the PES solution is more accurate than a Reynolds-average Navier–Stokes simulation solution. Unlike a traditional LES method, which uses the Smagorinsky, k-equation-transport, or WALE subgrid model, the PES requires a lower mesh resolution. These characteristics make it a potential method for simulating the engineering of turbulent flows with complex geometry and a high Reynolds number.

The aim of this work is to contribute to the understanding of sensitivity of boundary layers to the upstream boundary condition and history effects for both laminar and fully turbulent states in equilibrium conditions as well as some nonequilibrium turbulent boundary layers. Solutions of the two-dimensional boundary layer equations are obtained numerically for this study together with the Reynolds-averaged Navier-Stokes approach for turbulence modeling. The external pressure gradient is imposed through an evolution of the external velocity of the form Ue∝(x−x0)m, and boundary layers are initialized from a profile giving a perturbed shape factor. It is found that laminar boundary layers require very long distances for convergence toward the nondisturbed profiles in terms of the initial boundary layer thickness (∼104δin) and that this distance is dependent on m. In turbulent boundary layers, much shorter distances, although still large (∼102δin), are observed and they are also dependent on m. The maximum adverse pressure gradient for which convergence to a reference solution is possible is also studied finding that there is no limit for attached laminar boundary layers, whereas turbulent boundary layers do not converge once they are out of equilibrium. The convergence distances in turbulent boundary layers are also studied in terms of the turnover length (δUe+) because it has been shown to be more appropriate to refer the convergence distance to this length rather than the boundary layer thickness. The values for convergence using this criterion are extended to pressure gradient boundary layers. Moreover, an equivalent criterion is proposed and studied for laminar boundary layers based on the viscous characteristic time.

The nonreacting and reacting jet in crossflow (JICF) is an important flow configuration for effective mixing and combustion in practical applications. Many studies in the literature exist that examine the overall mixing characteristics of an isothermal, unconfined, nonreacting JICF. This experimental study examines the mixing characteristics in the very near field (s/d ≤ 3) of a nonreacting jet in a hot crossflow of combustion products (1500 K), a configuration relevant to gas turbine combustion. A range of jet-to-crossflow momentum flux ratios (5.2 ≤ J ≤ 24.2) and jet-to-crossflow density ratios (3.2 ≤ ρj/ρcf ≤ 7.8) was studied for a round jet with fully developed turbulent pipe flow and 4% mean turbulence intensity at the jet exit. Temperature measurements were made using planar laser Rayleigh scattering. Jet trajectory, jet centerline concentration decay based on adiabatic mixing assumption, Favre-averaged scalar dissipation, and scalar mixing time scales were determined as a function of the above-mentioned jet parameters. The observed center-plane mixing metrics indicated that better near field mixing was exhibited for lower values of the momentum flux ratio and larger values of density ratio in the extreme near field of the jet. As the momentum flux ratio was increased, windward and leeward mixing around the elongated potential core decreased, as indicated by the relative temperatures in these regions. The magnitude of scalar dissipation in the windward region decreased as the jet momentum flux increased, while the leeward dissipation region increased in size and magnitude as the momentum flux ratio increased. When the density ratio was decreased toward unity, both the windward and leeward dissipation regions reduced in size and magnitude.

We develop wall modeling capabilities for large-eddy simulations (LESs) of channel flow subjected to spanwise rotation. The developed models are used for flows at various Reynolds numbers and rotation numbers, with different grid resolutions and in differently sized computational domains. We compare a physics-based approach and a data-based machine learning approach. When pursuing a data-based approach, we use the available direct numerical simulation data as our training data. We highlight the difference between LES wall modeling, where one writes all flow quantities in a coordinate defined by the wall-normal direction and the near-wall flow direction, and Reynolds-averaged Navier-Stokes modeling, where one writes flow quantities in tensor forms. Pursuing a physics-based approach, we account for system rotation by reformulating the eddy viscosity in the wall model. Employing the reformulated eddy viscosity, the wall model is able to predict the mean flow correctly. Pursuing a data-based approach, we train a fully connected feed-forward neural network (FNN). The FNN is informed about our knowledge (although limited) on the mean flow. We then use the trained FNNs as wall models in wall modeled LES (WMLES) and show that it predicts the mean flow correctly. While it is not the focus of this study, special attention is paid to the problem of log-layer mismatch, which is common in WMLES. Our study shows that log-layer mismatch, or rather, linear-layer mismatch in WMLES of spanwise rotating channels, is not present at high rotation numbers, even when the wall-model/LES matching location is at the first grid point.

The basic problems of transition in both incompressible and compressible boundary layers are reviewed. Flow structures in low-speed transitional and developed turbulent boundary layers are presented, together with almost all of the physical mechanisms that have been proposed for their formation. Comparisons of different descriptions of the same flow structures are discussed as objectively as possible. The importance of basic structure such as solitonlike coherent structure is addressed. For compressible flows, the receptivity and instability of boundary layer are reviewed, including the effect of different parameters on the transition. Finally, the principle of aerodynamic heating of hypersonic boundary layer is presented.

We theoretically and experimentally study the quasistatic growth of bubbles in a gelatin gel under dissolved-gas supersaturation in order to examine the role of the gel elasticity in the mass-diffusion-driven process. First, we model the diffusion-driven bubble growth with the classical Epstein-Plesset approach for quasistatic bubble growth, accounting for elasticity of the medium surrounding the bubbles. Next, we devise an experimental technique to visualize the bubble growth in an air-supersaturated gel of different gelatin concentrations and to obtain the growth rate of the bubble. We show, from comparisons between the theory and experiments, that the bubble growth is hindered by the gel elasticity.

The inviscid hydrodynamics of inert compressible media governed by the Euler equations of motion only require knowledge of a caloric equation of state e(p, v) for the material relating the internal energy e to the fluid pressure p and specific volume v (or density). For departures from the ideal gas behavior, simple equations of state such as the stiffened gas, Noble-Abel, or a hybrid recently generalized by Le Métayer and Saurel [“The Noble-Abel stiffened-gas equation of state,” Phys. Fluids 28, 046102 (2016)] can correctly model compressible flows in gases, liquids, and solids. However, reactive and multicomponent descriptions require a formal definition of temperature. In the present note, we formulate a general thermodynamically based method to determine the thermal equation of state T(p, v) compatible with a generic e(p, v) relation. We apply our method to the Noble-Abel Stiffened Gas equation of state and recover the closed form solution of Le Métayer and Saurel. We also show that variations of the model taking its exponent different from the ratio of specific heats do not permit to define a thermodynamic temperature.

In this paper, the typical normal-hovering mode with different surging motions is numerically simulated by solving two-dimensional unsteady Navier-Stokes equations with the aim of investigating the effects of stroke deviation on aerodynamic performance. An elliptic wing model with 2% thickness is employed, conducting a horizontal motion (plunge), a vertical motion (surge), and a rotating motion (pitch). A low Reynolds number of 100 is adopted. The various surging motion in each half-stroke is defined by a half-sine or full-sine waveform, while the pitching and plunging motions are fixed for 16 patterns. The details of the aerodynamic force histories, vortex dynamics, induced jet effects, and time-averaged aerodynamics are systematically analyzed. The results show that for most patterns, stroke deviation plays a negative role in reducing lift and increasing energy consumption, which results in a decline of lifting efficiency. The forward surging motion that commences up the horizontal stroke plane attenuates the wake capture mechanism and reinforces the delayed stall mechanism. Compared to the typical normal-hovering pattern with no deviation, the resulting lift in pattern E decreases at the beginning of stroke and increases at the midstroke. The downward surging motion shows an opposite effect on the aerodynamics. The minimum power (−10.2%) is consumed in pattern F, although the minimum lift is generated in the meantime. In addition, the maximum lift augmentation of 8.7% is produced in pattern I along with the characteristic of power economy. Our study can provide advice on utilizing stroke deviation to increasing lift production and decreasing power consumption.

Many fish and marine animals swim in a combination of active burst and passive coast phases, which is known as burst-and-coast swimming. The immersed boundary method was used to explore the intermittent locomotion of a three-dimensional self-propelled plate. The degree of intermittent locomotion can be defined in terms of the duty cycle (DC = Tb/Tf), which is the ratio of the interval of the burst phase (Tb) to the total flapping period (Tf = Tb + Tc), where Tc is the interval of the coast phase. The average cruising speed (ŪC), the input power (P¯), and the swimming efficiency (η) were determined as a function of the duty cycle (DC). The maximum ŪC arises for DC = 0.9, whereas the maximum η arises for DC = 0.3. The hydrodynamics of the intermittent locomotion was analyzed by examining the superimposed configurations of the plate and the phase map. The characteristics of the flapping motions in the burst and coast phases are discussed. A modal analysis was performed to examine the role of the flapping motion in the propulsion mechanism. The velocity map and the vortical structures are visualized to characterize qualitatively and quantitatively the influence of intermittent locomotion on propulsion.

Blood is a non-Newtonian suspension of red and white cells, platelets, fibrinogen, and cholesterols in Newtonian plasma. To assess its non-Newtonian behaviors, this work considers a newly proposed blood test, unidirectional large-amplitude oscillatory shear flow (udLAOS). In the laboratory, we generate this experiment by superposing LAOS onto steady shear flow in such a way that the shear rate never changes sign. It is thus intended to best represent the unidirectional pulsatile flow in veins and arteries. To model human blood, we consider the simplest model that can predict infinite-shear viscosity, the corotational Jeffreys fluid. We arrive at an exact analytical expression for the shear stress response of this model fluid. We discover fractional harmonics comprising the transient part of the shear stress response and both integer and fractional harmonics, the alternant part. By fractional, we mean that these occur at frequencies other than integer multiples of the superposed oscillation frequency. We generalize the corotational Jeffreys fluid to multimode to best represent three blood samples from three healthy but different donors. To further improve our model predictions, we consider the multimode Oldroyd 8-constant framework, which contains the corotational Jeffreys fluid as a special case. In other words, by advancing from the multimode corotational Jeffreys fluid to the multimode Oldroyd 8-constant framework, five more model parameters are added, yielding better predictions. We find that the multimode corotational Jeffreys fluid adequately describes the steady shear viscosity functions measured for three different healthy donors. We further find that adding two more specific nonlinear constants to the multimode corotational Jeffreys fluid also adequately describes the behaviors of these same bloods in udLAOS. This new Oldroyd 5-constant model may find usefulness in monitoring health through udLAOS.

With general rigid bead-rod modeling, we recreate shapes of complex macromolecular structures with beads, by rigidly fixing bead positions relative to one another. General rigid-bead rod theory then attributes the elasticity of polymeric liquids to the orientation that their macromolecules develop during flow. For linear viscoelastic behaviors, this theory has been evaluated for just a few very simple structures: rigid rings, the rigid tridumbbell, and three quadrafunctional branched structures. For oscillatory shear flow, the frequency dependencies of both parts of the complex viscosity are, at least qualitatively, predicted correctly. In this paper, we use general rigid-bead rod theory for the most complex macromolecular architectures to date. We thus explore the role of helix geometry on the complex viscosity of a helical polymeric liquid. Specifically, for both singly and doubly helical structures, we investigate the effects of helix radius, flight length, helix length, and the number of beads per flight on the complex viscosity function, the fluid relaxation time, and the zero-shear values of the steady shear viscosity and of the first normal stress coefficient. As a worked example, we examine specifically deoxyribonucleic acid (DNA). Using general rigid bead-rod theory, we dissect the DNA to see how the first helix, second helix, and then the base pairs each contribute to the complex viscosity. We next explore the rheological implications of gene replication to find that the unzipping of DNA into a pair of single strands is viscostatic.

Digestion is the process of breaking down food into smaller nutrient components which can be easily absorbed in the intestinal tract. The aim of this study was to experimentally investigate the influence of bolus (gastric content) viscosity on digestion and nutrient absorption processes, using an in vitro gastrointestinal model, the TIM-1 system. Two types of simple carbohydrates, namely, glucose and maltodextrin, were used as model foods. The initial bolus viscosity was varied (∼1 mPa·s, ∼15 mPa·s, and ∼100 mPa·s) using different glycerol-water proportions. A fluorescent molecular rotor compound (Fast Green For Coloring Food) was used to monitor viscosity changing patterns of the gastrointestinal content during digestion in the in vitro stomach and small intestinal sections. The digested-nutrient absorption data indicated that the initial bolus viscosity did not significantly affect the glucose absorption process in the small intestine. However, an increase in the initial bolus viscosity from ∼1 mPa·s to ∼15 mPa·s reduced the maltodextrin to glucose conversion by 35%. A further increase in the initial bolus viscosity from ∼15 mPa·s to ∼100 mPa·s did not significantly reduce the maltodextrin to glucose conversion.

The effects of flexibility on the wake structures of a foil under a heaving motion in a viscous uniform flow are numerically studied using an immersed boundary method. An inspection of the phase diagram of the wake structures in a map of the chord-length-based dimensionless heaving amplitude (AL) and Strouhal number (StL) shows that the wake transition boundaries of the rigid foil are well predicted by constant amplitude-based Strouhal number (StA) lines, similar to previous studies. However, the wake transition boundaries of the flexible foil are predictable by constant StA lines only for high StL cases. A large deformation angle of a flexible foil by the amplitude difference and phase difference between the leading and trailing edge cross-stream displacements reduces the effective leading edge velocity, with an accompanying decrease in the leading edge circulation. However, the trailing edge circulation for a flexible foil is increased due to increased trailing edge amplitude. The sum of the leading and trailing edge circulations plays an important role in determining the wake pattern behind a rigid and flexible foil, and wake transitions are observed beyond critical circulations. The decrease in the thrust coefficient for large values of StL and AL is closely associated with the generation of a complex wake pattern behind a foil, and the complex wake is a direct consequence of sufficiently large leading edge circulation. A critical effective phase velocity in a vortex dipole model is proposed to predict the maximum thrust coefficient without a complex wake pattern.

Gas transport in micropores/nanopores deviates from classical continuum calculations due to nonequilibrium in gas dynamics. In such a case, transport can be classified by the Knudsen number (Kn) as the ratio of gas mean free path and characteristic flow diameter. The well-known Klinkenberg correction and its successors estimate deviation from existing permeability values as a function of Kn through a vast number of modeling attempts. However, the nonequilibrium in a porous system cannot be simply modeled using the classical definition of the Kn number calculated from Darcy’s definition of the pore size or hydraulic diameter. Instead, a proper flow dimension should consider pore connectivity in order to characterize the rarefaction level. This study performs a wide range of pore-level analysis of gas dynamics with different porosities, pore sizes, and pore throat sizes at different Kn values in the slip flow regime. First, intrinsic permeability values were calculated without any rarefaction effect and an extended Kozeny-Carman model was developed by formulating the Kozeny-Carman constant by porosity and pore to throat size ratio. Permeability increased by increasing the porosity and decreasing the pore to throat size ratio. Next, velocity slip was applied on pore surfaces to calculate apparent permeability values. Permeability increased by increasing Kn at different rates depending on the pore parameters. While the characterization by the Kn value calculated with pore height or hydraulic diameter did not display unified behavior, relating permeability values with the Kn number calculated from the equivalent height definition created a general characterization based on the porosity independent from the pore to throat size ratio. Next, we extended the Klinkenberg equation by calculating unknown Klinkenberg coefficients which were found as a simple first order function of porosity regardless of the corresponding pore connectivity. The extended model as a combination of Kozeny-Carman for intrinsic permeability and Klinkenberg for apparent permeability correction yielded successful results.