Physics of Fluids

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Table of Contents for Physics of Fluids. List of articles from both the latest and ahead of print issues.
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Pore network model of drying with Kelvin effect

Fri, 02/19/2021 - 03:03
Physics of Fluids, Volume 33, Issue 2, February 2021.
A pore network model of isothermal drying is presented. The model takes into account the capillary effects, the transport of vapor by diffusion, including Knudsen effect, in the gas phase, and the Kelvin effect. The model is seen as a first step toward the simulation of drying in mesoscopic porous materials involving pore sizes between 4 nm and 50 nm. The major issue addressed with the present model is the computation of the menisci mean curvature radius at the boundary of each liquid cluster in conjunction with the Kelvin effect. The impact of Kelvin effect on the drying process is investigated, varying the relative humidity in the ambient air outside the medium. The simulations indicate that the Kelvin effect has a significant impact on the liquid distribution during drying. The evaporation rate is found to fluctuate due to the menisci curvature variations during drying. The simulations also highlight a noticeable non-local equilibrium effect.

Direct numerical simulation of bidisperse inertial particles settling in turbulent channel flow

Fri, 02/19/2021 - 03:03
Physics of Fluids, Volume 33, Issue 2, February 2021.
The behavior of settling velocity and clustering of bidisperse inertial particles in a turbulent channel flow is investigated through direct numerical simulation. The particle-laden planar channel flow has a friction Reynolds number at Reτ = 180. Eulerian–Lagrangian method is used to study the dynamic properties of bidisperse and monodisperse inertial particles with 16 different simulation sets, which are distinguished by Stokes numbers ranging from St+ = 1.31 to 52.58 and particle number ratio from 1:1 to 1:8. Momentum exchange between fluid and particle phases is considered in the simulation as the chosen initial volume fraction at 5 × 10−5 is in the two-way coupling regime. The gravity is set at the direction normal to both the wall normal direction and the streamwise direction. We observe that in the bidisperse cases the turbophoresis effect of inertial particles with the smaller diameter is significant even though it is very weak in the corresponding monodisperse cases. We use radial distribution function (RDF) to investigate the degree of clustering and turbophoresis. The results indicate that RDF is larger in the bidisperse cases for both large and small particles and it is greatly affected by the bulk particle number ratio and the Stokes number ratio. Unlike clustering, the terminal settling velocities of inertial particles in the bidisperse cases are affected by the final volume fraction at the dynamic equilibrium state. When their final volume fractions are lower than those in the corresponding monodisperse cases, the settling velocity of either particle becomes reduced from the monodisperse value. We also investigate the relationship between settling velocity and vortex strength. The results show that the preferential sweeping mechanism is strengthened with Stokes number decreasing and the mechanism can be quantified by the slope of the curve of settling velocity variation with vortex strength.

On the H-type transition to turbulence—Laboratory experiments and reduced-order modeling

Fri, 02/19/2021 - 03:03
Physics of Fluids, Volume 33, Issue 2, February 2021.
A series of experiments were conducted to understand the sources of local, high-amplitude velocity fluctuations produced at the late stages of boundary-layer flow transition to turbulence. The laboratory experiments considered the controlled injection of Tollmien–Schlichting (TS) waves into a nearly zero pressure gradient, laminar boundary layer, resulting in H-type transition to turbulence. Proper orthogonal decomposition (POD) was used to extract the energetic coherent structures within the transitional flow field obtained with particle image velocimetry. The first three modes were observed to feature spatial mode shapes consistent with a cross-section of a canonical hairpin vortex structure and were associated with time-dependent amplitudes having consistent peak frequencies with the fundamental TS wave frequency. Higher-order modes exhibited a combination of sub- and super-harmonics of the TS wave frequency and were attributed to flow interactions produced by a hairpin packet. A conditional averaging method was used to establish a reduced-order model for the overshoot phenomena in Reynolds shear stress and turbulence kinetic energy observed at the late transition stage. The lower portion of the large-scale hairpin vortex structure was observed to be primarily responsible for the overshoot mechanisms, which was well captured in a reduced-order model of the velocity field. The first four POD modes were used to create this reduced-order model, which, while only consisting of ≈15% of the total turbulence kinetic energy of the original velocity field, was able to capture ≈85% of the peak Reynolds stress amplitude across the overshoot region.

Wavelet analysis of shearless turbulent mixing layer

Thu, 02/18/2021 - 05:41
Physics of Fluids, Volume 33, Issue 2, February 2021.
The intermittency and scaling exponents of structure functions are experimentally studied in a shearless turbulent mixing layer. Motivated by previous studies on the anomalous scaling in homogeneous/inhomogeneous turbulent flows, this study aims to investigate the effect of strong intermittency caused by turbulent kinetic energy diffusion without energy production by mean shear. We applied an orthonormal wavelet transformation to time series data of streamwise velocity fluctuations measured by hot-wire anemometry. Intermittent fluctuations are extracted by a conditional method with the local intermittency measure, and the scaling exponents of strong and weak intermittent fluctuations are calculated based on the extended self-similarity. The results show that the intermittency is stronger in the mixing layer region than in the quasi-homogeneous isotropic turbulent regions, especially at small scales. The deviation of higher-order scaling exponents from Kolmogorov's self-similarity hypothesis is significant in the mixing layer region, and the large deviation is caused by strong, intermittent fluctuations even without mean shear. The total intermittent energy ratio is also different in the mixing layer region, suggesting that the total intermittent energy ratio is not universal but depends on turbulent flows. The scaling exponents of weak fluctuations with a wavelet coefficient flatness corresponding to the Gaussian distribution value of 3 follow the Kolmogorov theory up to fifth order. However, the sixth order scaling exponent is still affected by these weak fluctuations.

The dynamics of parallel-plate and cone–plate flows

Thu, 02/18/2021 - 05:41
Physics of Fluids, Volume 33, Issue 2, February 2021.
Rotational rheometers are the most commonly used devices to investigate the rheological behavior of liquids in shear flows. These devices are used to measure rheological properties of both Newtonian and non-Newtonian, or complex, fluids. Two of the most widely used geometries are flow between parallel plates and flow between a cone and a plate. A time-dependent rotation of the plate or cone is often used to study the time-dependent response of the fluid. In practice, the time dependence of the flow field is ignored, that is, a steady-state velocity field is assumed to exist throughout the measurement. In this study, we examine the dynamics of the velocity field for parallel-plate and cone–plate flows of Newtonian fluids by finding analytical solutions of the Navier–Stokes equation in the creeping flow limit. The time-dependent solution for parallel-plate flow is relatively simple as it requires the velocity to have a linear dependence on radial position. Interestingly, the time-dependent solution for cone–plate flow does not allow the velocity to have a linear dependence on radial position, which it must have at the steady state. Here, we examine the time-dependent velocity fields for these two flows, and we present results showing the time dependence of the torque exerted on both the stationary and rotating fixtures. We also examine the time dependence of spatial non-homogeneities of the strain rate. Finally, we speculate on the possible implications of our results in the context of shear banding, which is often observed in parallel-plate and cone–plate flows of complex fluids.

Referee acknowledgment for 2020

Wed, 02/17/2021 - 01:21
Physics of Fluids, Volume 33, Issue 2, February 2021.

A comparison of bioinspired slippery and superhydrophobic surfaces: Micro-droplet impact

Wed, 02/17/2021 - 01:21
Physics of Fluids, Volume 33, Issue 2, February 2021.
Slippery lubricant impregnated surfaces (SLIPSs/LISs) exhibit remarkable features of repellency and droplet mobility to a broad range of complex fluids. Their performance in micro-droplet repellency has received less attention. In this study, the anti-wetting performance of SLIPSs in comparison to superhydrophobic surfaces (SHSs) is investigated for the micro-droplet impact on different textured surfaces. Different series of square-pillar arrays are modeled to consider the effect of surface morphology on droplet hydrodynamics. A multiphase numerical model in conjunction with an accurate contact angle method has been implemented to analyze details of three immiscible phases during the droplet impact on the SLIPS. Our findings revealed that on the SLIPS with a low-density micro-textured surface where the effect of lubricant is more significant, droplet repellency and mobility are improved compared to SHSs. It was illustrated that on the SLIPS, droplet pinning decreased significantly and in low Weber number cases where the effect of lubricant is more noticeable, partial bouncing occurred. It was also observed that slippery surfaces with a low-density of micro-pillars exhibit bouncing behavior, which indicated the repellency effect of lubricant in droplet hydrodynamics. Although micro-droplets failed to recoil at a higher Weber number ([math]) on both the SHS and the SLIPS, droplet penetration within the micro-structured surface was considerably smaller on the SLIPS.

Flow and thermal characteristics of three-dimensional turbulent wall jet

Tue, 02/16/2021 - 12:50
Physics of Fluids, Volume 33, Issue 2, February 2021.
In the present work, a three-dimensional turbulent wall jet is simulated using large-eddy simulation to characterize its flow and thermal characteristics. The solver is first validated for streamwise velocity decay, wall-normal and spanwise spread rates, and mean and second-order flow statistics using reference experimental data from the literature. The mean vorticity transport equation for the streamwise component is analyzed to identify the dominant terms that contribute to the large spanwise spread of the jet. The terms that contain Reynolds normal stresses are identified as major contributors to a large mean streamwise component of vorticity. The mean streamwise and wall-normal components of vorticity are studied for their evolution and contribution to the spanwise spread. It was found that both these components together aid in the large spanwise spread of the jet. The heat transfer characteristics are studied for the jet flow on a heated isothermal wall. The profiles of mean and fluctuating temperatures, the evolution of the Nusselt number, and turbulent heat flux characteristics are studied. The streamwise evolution of Nusselt number behavior is explained using instantaneous vortical structures. A significant drop in heat transfer is observed in the potential core region. Further, the turbulent heat flux contours show that the transport of heat in the streamwise direction is different from that of the plane wall jet. A peculiar turbulent heat transport was found in the analysis of the spanwise heat flux. The heat transfer characteristics noted for the three-dimensional wall jet may help in the design and analysis of film-cooling applications.

The continuous eddy simulation capability of velocity and scalar probability density function equations for turbulent flows

Fri, 02/12/2021 - 10:57
Physics of Fluids, Volume 33, Issue 2, February 2021.
There is a well developed spectrum of computational methods for turbulent flows: modeling methods such as Reynolds-averaged Navier–Stokes (RANS) and probability density function (PDF) methods, and resolving methods such as large eddy simulation (LES) and filtered density function (FDF) methods. However, the applicability of RANS/PDF methods is limited to flows that do not essentially require the inclusion of resolved motion, and LES/FDF methods are well applicable if resolution criteria can be satisfied [which is often infeasible for very high Reynolds number (Re) wall-bounded turbulent flows]. A highly attractive approach to overcome these problems is the design of hybrid RANS–LES methods, which can be used with varying amounts of resolved and modeled motions. However, this approach faces the problem to ensure communication and balancing of resolved and modeled motions. A well working solution to this problem was presented recently for non-homogeneous flows with respect to velocity two-equation eddy viscosity turbulence models. Exact analytical results regarding the extension of these methods to velocity and passive scalar PDF/FDF methods and their implied RANS/LES equations are presented here. The latter matters with respect to the justification of the theoretical basis of new hybrid methods (realizability) and the availability of a hierarchy of simple and advanced simulation methods (including passive scalar transport). Based on the continuous mode redistribution mechanism, the new simulation methods are capable of providing reliable predictions of very high Re turbulent flows, which cannot be accomplished by using existing techniques.

Non-linear ultrasonic and viscoelastic properties of gelatine investigated in the temperature range of 30 °C–60 °C

Fri, 02/12/2021 - 10:57
Physics of Fluids, Volume 33, Issue 2, February 2021.
Analysis based on the determination of the multifactorial non-linearity parameter (β) is a promising non-destructive investigation and testing technique. The contribution of temperature variations on the non-linear coefficient is known to be lower than that of hydrostatic pressure changes. We investigated the effect of temperature on the non-linearity parameter in the range 30 °C–60 °C for a viscous, gelatinous compound, resulting from controlled hydrolysis of the collagen protein. Considerable thermal effects are realized and are related to changes in viscous and elastic properties. Remarkable changes in the non-linearity coefficient at temperatures corresponding to the transition temperature of gelatine of 60 °C indicate a signature while no outspoken hysteresis effects were realized with cyclic temperature sweeps. Despite the non-Newtonian nature of the gel, our experiments show comparability to water within the examined range of temperature, which corresponds to a wavelength shift of about 40 μm.

Solute induced jittery motion of self-propelled droplets

Thu, 02/11/2021 - 02:11
Physics of Fluids, Volume 33, Issue 2, February 2021.
The intriguing role of the presence of solutes in the activity of a self-propelling droplet is investigated. A system of self-propelling micrometer-sized 4-Cyano-4′-pentylbiphenyl (5CB) droplets in an aqueous solution of tetradecyltrimethylammonium bromide (TTAB) as the surfactant is considered. It is shown that the addition of glycerol causes the active 5CB droplet to exhibit a transition from smooth to jittery motion. The motion is found to be independent of the droplet size and the nematic state of 5CB. Analogous experiments with Polyacrylamide (PAAm), Polyvinylpyrrolidone (PVP), and Polyvinyl Alcohol (PVA), as solutes, confirm that such a transition cannot merely be explained solely based on the viscosity or Peclet number of the system. We propose that the specific nature of physicochemical interactions between the solute and the droplet interface is at the root of this transition. The experiments show that the timescales associated with the influx and redistribution of surfactants at the interface are altered in the presence of solutes. Glycerol and PVP significantly enhance the rate of solubilization of the 5CB droplets resulting in a quicker re-distribution of the adsorbed TTAB molecules on the interface, causing the droplet to momentarily stop and then restart in an independent direction. On the other hand, low solubilization rates in the presence of PAAm and PVA lead to smooth trajectories. Our hypothesis is supported by the time evolution of droplet size and interfacial velocity measurements in the presence and absence of solute. Overall, our results provide fundamental insights into the complex interactions emerging due to the presence of solutes.

A K–L model with improved realizability for turbulent mixing

Thu, 02/11/2021 - 02:11
Physics of Fluids, Volume 33, Issue 2, February 2021.
Turbulent mixing, induced by Rayleigh–Taylor (RT), Richtmyer–Meshkov (RM), and Kelvin–Helmholtz (KH) instabilities, broadly occurs in both practical astrophysics and inertial confined fusion problems. The Reynolds-averaged Navier–Stokes models remain the most viable approach for the solution of these practical flows. The commonly used mixing models based on the standard eddy viscosity formulation are shown to be capable of accurately predicting the global mixing zone width. However, we find that this approach will become non-realizable for local flow characteristics in the case of a large mean strain rate, including yielding the negative normal stress and the unphysically large turbulence kinetic energy (TKE) in the presence of shocks. This can affect the numerical robustness in calculating turbulent statistics and give rise to highly inaccurate predictions for complex mixings. To overcome this problem, a realizable K–L mixing model is developed, extended from the standard K–L model given by our recent works. A new eddy viscosity formulation is used and modified from the work by Shih et al. to reproduce the growth rate of the KH mixing. This new model yields similar results as the standard model for canonical RT, RM, and KH mixings. However, for complex mixing problems, the present model gives a significant improvement in physically capturing the turbulence characteristics, e.g., predicting the non-negative normal stress for RT mixing with the initial tilted interface and the appropriate TKE when shock interacts with the mixing zone for spherical implosion.

Oscillatory Couette flow of rarefied binary gas mixtures

Thu, 02/11/2021 - 02:10
Physics of Fluids, Volume 33, Issue 2, February 2021.
The oscillatory Couette flow of binary gas mixtures is numerically investigated on the basis of the McCormack model. The dependence of the velocity and shear stress amplitudes and the penetration depth on the gas rarefaction and the oscillation parameters is studied numerically. Two typical mixtures of noble gases, i.e., a neon–argon (Ne–Ar) mixture with a molecular mass ratio less than 2 and a helium–xeon (He–Xe) mixture with a molecular mass ratio of about 32, are considered to explore the influences of the molecular mass ratio and molar concentration. It is found that the Ne–Ar mixture exhibits similar behavior with a single gas, while significant deviations can be observed between a single gas and the He–Xe mixture. Particularly when the gases are in the transitional and near-continuum regimes and the oscillation frequency is high, the amplitudes of velocity and shear stress for the He–Xe mixture vary non-monotonically between the plates as the molar concentration of the light species He exceeds 50% due to the oscillation superposition of the two species. These findings are helpful to design the structure of micro-electromechanical devices.

Marangoni-driven instability patterns of an N-hexadecane drop triggered by assistant solvent

Wed, 02/10/2021 - 03:33
Physics of Fluids, Volume 33, Issue 2, February 2021.
Flows of thin fluid layers spreading, which have a distinguished history, have been studied since the days of Reynolds, who was among the early researchers to examine flows. Different from surfactant-driven spreading, which is currently the most common subject of study, we observe the spreading process of n-hexadecane driven by volatile silicone oil at the surface of the aqueous substrates and explore the influence of Marangoni flow caused by surface tension gradient on liquid-driven spreading. We find that on different substrates, the initial state of n-hexadecane is different, and there are two instability patterns during the spreading, subsequently, which are analyzed theoretically. While the n-hexadecane drop stationed on the liquid surface is small, it is driven to form a rim and then breaks up into beads, which shows the Rayleigh–Plateau instability patterns. When we put the n-hexadecane drop on the surface of the saturated sodium chloride solution, which spreads out more, it is driven to form a circular belt first and fingering instability subsequently occurs at the inner edge of the circular belt.

A conservative and consistent scalar filtered mass density function method for supersonic flows

Wed, 02/10/2021 - 03:33
Physics of Fluids, Volume 33, Issue 2, February 2021.
A novel scalar filtered mass density function (SFMDF) method is developed for high-speed flows, especially for supersonic reactive flows. The total energy is proposed as the energy form for SFMDF, instead of the commonly used enthalpy or sensible enthalpy. Such an energy form is entirely consistent with the one typically used in large eddy simulation (LES) for fully compressible flows, so that the exact/modeled energy equations in both LES and SFMDF are readily identical. Moreover, the total energy can formulate the SFMDF energy transport equation in such a way that the high-speed source term is strictly conservative. Following the conservative formulation, numerically robust conservative schemes are readily available for flows with discontinuities. Tests in one-dimensional Euler equations show that the temperature redundantly obtained based on the total energy (with conservative high-speed source terms) shows better agreement with the analytical result than the one based on the enthalpy. The proposed LES-SFMDF method is further tested in a shock tube interacting with an isotropic turbulent flow, a compressible two-dimensional non-reactive temporally developing mixing layer, and a supersonic three-dimensional reactive temporally developing mixing layer. Results show that SFMDF with the total energy can considerably improve the temperature distribution in both non-reactive and reactive flows. The proposed LES-SFMDF method with the total energy predicts the turbulence–chemistry interaction better than LES-SFMDF with the enthalpy as well as LES with the well-stirred reactor model in supersonic combustion. This conservative and consistent SFMDF method can be readily extended to more sophisticated probability density function methods in high-speed flows.

An experimental investigation of the viscosity behavior of solutions of nanoparticles, surfactants, and electrolytes

Wed, 02/10/2021 - 03:33
Physics of Fluids, Volume 33, Issue 2, February 2021.
Several studies have reported that the viscosity profile of nanofluids has a similar trend to electrolytes. This behavior is attributed to the complex interactions of the ions of nanoparticles (NPs) with the ions of aqueous solutions. Recently, laboratory experiments have shown that nanofluids are suitable candidates for enhanced oil recovery in different reservoirs. The improvement in oil recovery during nanofluid injection is attributed to the wettability alteration, interfacial tension reduction, and viscosity modification. Low salinity water and surfactants are used to stabilize and prevent the aggregation of NPs, which are injected into the reservoir. However, the interactions between the reservoir/injected fluids with NPs alter the properties of the fluid. The complex interactions among the ions present in the solutions of NPs, surfactants, and electrolytes (NSE) that result in the viscosity modification are not completely understood. Therefore, this work presents a detailed study on the complex interactions existing between the ions of NPs and other ions of aqueous solution present in the reservoir fluid using the dynamic light scattering, transmission electron microscopy, and Fourier transform infrared spectroscopy techniques to understand the viscosity behavior of NSE solutions. The viscosity profile of NSE solutions with increasing concentration of NPs has the same trend as aqueous solutions, while that with increasing concentration of the sodium dodecyl sulfate surfactant behaves like spherical particles. The explained mechanisms behind the viscosity behavior of NSE solutions in this study can improve the optimization design for nanofluid injection into the reservoir.

Simulation-based study of COVID-19 outbreak associated with air-conditioning in a restaurant

Tue, 02/09/2021 - 03:45
Physics of Fluids, Volume 33, Issue 2, February 2021.
COVID-19 has shown a high potential of transmission via virus-carrying aerosols as supported by growing evidence. However, detailed investigations that draw direct links between aerosol transport and virus infection are still lacking. To fill in the gap, we conducted a systematic computational fluid dynamics (CFD)-based investigation of indoor airflow and the associated aerosol transport in a restaurant setting, where likely cases of airflow-induced infection of COVID-19 caused by asymptomatic individuals were widely reported by the media. We employed an advanced in-house large eddy simulation solver and other cutting-edge numerical methods to resolve complex indoor processes simultaneously, including turbulence, flow–aerosol interplay, thermal effect, and the filtration effect by air conditioners. Using the aerosol exposure index derived from the simulation, we are able to provide a spatial map of the airborne infection risk under different settings. Our results have shown a remarkable direct linkage between regions of high aerosol exposure index and the reported infection patterns in the restaurant, providing strong support to the airborne transmission occurring in this widely reported incident. Using flow structure analysis and reverse-time tracing of aerosol trajectories, we are able to further pinpoint the influence of environmental parameters on the infection risks and highlight the need for more effective preventive measures, e.g., placement of shielding according to the local flow patterns. Our research, thus, has demonstrated the capability and value of high-fidelity CFD tools for airborne infection risk assessment and the development of effective preventive measures.

Why coronavirus survives longer on impermeable than porous surfaces

Tue, 02/09/2021 - 03:45
Physics of Fluids, Volume 33, Issue 2, February 2021.
Previous studies reported that the drying time of a respiratory droplet on an impermeable surface along with a residual film left on it is correlated with the coronavirus survival time. Notably, earlier virus titer measurements revealed that the survival time is surprisingly less on porous surfaces such as paper and cloth than that on impermeable surfaces. Previous studies could not capture this distinct aspect of the porous media. We demonstrate how the mass loss of a respiratory droplet and the evaporation mechanism of a thin liquid film are modified for the porous media, which leads to a faster decay of the coronavirus on such media. While diffusion-limited evaporation governs the mass loss from the bulk droplet for the impermeable surface, a much faster capillary imbibition process dominates the mass loss for the porous material. After the bulk droplet vanishes, a thin liquid film remaining on the exposed solid area serves as a medium for the virus survival. However, the thin film evaporates much faster on porous surfaces than on impermeable surfaces. The aforesaid faster film evaporation is attributed to droplet spreading due to the capillary action between the contact line and fibers present on the porous surface and the modified effective wetted area due to the voids of porous materials, which leads to an enhanced disjoining pressure within the film, thereby accelerating the film evaporation. Therefore, the porous materials are less susceptible to virus survival. The findings have been compared with the previous virus titer measurements.

Three-dimensional spectral proper orthogonal decomposition analyses of the turbulent flow around a seal-vibrissa-shaped cylinder

Tue, 02/09/2021 - 02:56
Physics of Fluids, Volume 33, Issue 2, February 2021.
The flow around a seal-vibrissa-shaped cylinder (SVSC) is numerically investigated using the large eddy simulation framework at a Reynolds number of 20 000. Compared with a circular cylinder (CC), the wake of the SVSC presents more stable three-dimensional separation, a longer vortex formation length, and a weaker vortex strength. The mean drag and fluctuation of the lift coefficient are 59.5% and 87.7% lower than those of the CC, respectively. Three-dimensional spectral proper orthogonal decomposition (SPOD) is used to investigate the turbulent flow around these two types of cylinders in terms of the spatial modes, mode energy, mode coefficients, and reconstructed flow by a reduced-order modeling. Four typical vortex shedding patterns are first extracted by SPOD for the SVSC, producing crescent-, twist-, branch-, and knot-shaped vortices. A concept model is proposed for the wake dynamics of the SVSC, allowing the formation and transformation of these modes to be elucidated. Detailed analysis of the impact of the flow pattern on the associated forces indicates that the dominant out-phase vortex shedding at the upper and lower saddle planes makes a significant contribution to the reduction in lift fluctuations.

Effects of wing-to-body mass ratio on insect flapping flights

Tue, 02/09/2021 - 02:15
Physics of Fluids, Volume 33, Issue 2, February 2021.
Bio-flyers of insects, birds, and bats are observed to have a broad range of wing-to-body mass ratio (WBMR) from 0.1% to 15%. The WBMR and wing mass distribution can lead to large inertial forces and torques in fast-flapping wings, particularly in insect flights, comparable with or even greater than aerodynamic ones, which may greatly affect the aerodynamic performance, flight stability, and control, but still remain poorly understood. Here, we address a simulation-based study of the WBMR effects on insect flapping flights with a specific focus on unraveling whether some optimal WBMR exists in balancing the flapping aerodynamics and body control in terms of body pitch oscillation and power consumption. A versatile, integrated computational model of hovering flight that couples flapping-wing-and-body aerodynamics and three degree of freedom body dynamics was employed to analyze free-flight body dynamics, flapping aerodynamics, and power cost for three typical insects of a fruit fly, a bumblebee, and a hawkmoth over a wide range of Reynolds numbers (Re) and WBMRs. We found that the realistic WBMRs in the three insect models can suppress the body pitch oscillation to a minimized level at a very low cost of mechanical power. We further derived a scaling law to correlate the WBMR with flapping-wing kinematics of stroke amplitude (Φ), flapping frequency (f), and wing length (R) in terms of [math], which matches well with measurements and, thus, implies that the WBMR-based body pitch minimization may be a universal mechanism in hovering insects. The realistic WBMR likely offers a novel solution to resolve the trade-off between body-dynamics-based aerodynamic performance and power consumption. Our results indicate that the WBMR plays a crucial role in optimization of flapping-wing dynamics, which may be useful as novel morphological intelligence for the biomimetic design of insect- and bird-sized flapping micro-aerial vehicles.

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