Strouhal Number Research Articles

Aerodynamic efficiency explains flapping strategies used by birds

A faster cruising speed increases drag and thereby the thrust (T) needed to fly, while weight and lift (L) requirement remains constant. Birds can adjust their wingbeat in multiple ways to accommodate this change in aerodynamic force, but the relative costs of different strategies remain largely unknown. To evaluate the efficiency of several kinematic strategies, I used a robotic wing [E. Ajanic, A. Paolini, C. Coster, D. Floreano, C. Johansson, Adv. Intell. Syst. 5, 2200148 (2023)] and quantitative flow measurements. I found that, among the tested strategies, changing the mean wingbeat elevation provides the most efficient solution to changing thrust-to-lift ratio (T/L), offering insight into why birds tend to beat their wings with a greater ventral than dorsal excursion. I also found that although propulsive efficiency (ηp) may peak at a Strouhal number (St, measure of relative flapping speed) near 0.3, the overall efficiency of generating force decreases with St. This challenges the expectance of a specific optimal St for flapping flight and instead suggest the chosen St depends on T/L. This may explain variation in preferred St among birds and why bats prefer flying at higher St than birds [G. K. Taylor, R. L. Nudds, A. L. Thomas, Nature 425, 707-711 (2003)], since their body shape imposes relatively higher thrust requirements [F. T. Muijres, L. C. Johansson, M. S. Bowlin, Y. Winter, A. Hedenström, PLoS One 7, e37335 (2012)]. In addition to explaining flapping strategies used by birds, my results suggest alternative, efficient, flapping motions for drones to explore aiming to extend their flight range.

Hydrodynamics investigation of a three-dimensional fish swimming in oblique flows by a ghost cell method

Fish in nature can encounter various flow environments. This paper numerically simulated a 3D (three-dimensional) carangiform fish swimming in oblique flow. The numerical model adopts a robust ghost cell method with graphics processing unit acceleration. The dynamic performance and the 3D wake evolutions are discussed under different Strouhal numbers and attack angles. It is found that the thrust along the swimming direction would get enhanced with more energy consumption as the Strouhal number (St) rises. The attack angle can get the similar but less significant effect. Also, the stall angle of θ = 40° is approximately determined, which is independent of the Strouhal number. However, the flexible deformation can reduce the adverse effects of the stall. In terms of the wake structures, they are transitioned from the two rows of vortex streets at St = 0.2 to the three rows at St = 0.6, and even to the four rows at St = 1. The connected oblique vortex ring rows induced by the undulating caudal fin contributes to the thrust and lateral forces dominantly. As the St rises, the vortex ring rows is transformed from the typical von Karman vortex streets to the reverse one, indicating the generation of thrust. The slender, parallel vortex contrails are caused by the detachment of leading-edge vortices (LEVs), and they induce the high-order harmonic components in force coefficients. The oblique angle of the vortex rings grows with the Strouhal number, while it is hardly affected by the attack angle. As the attack angle grows, the wake is turned from the disconnected hairpin vortices to the intertwined vortex rings and losses the spanwise symmetry. Moreover, the reattachment of the LEV is not observed after the stall angle.

Monitoring the Wake of Low Reynolds Number Airfoils for Their Aerodynamic Loads Assessment

Experimental investigations are carried out to explore the aerodynamic performance and vortex shedding characteristics of S5010 and E214 airfoil-based wings to provide guidance for the design of MAVs and other low-speed vehicles. Force and wake shedding frequency measurements are carried out in a subsonic wind tunnel in the Reynolds number (Re) range of 4 × 104 - 1 × 105. The measurements with increasing Re show that the slope of the lift curve in the linear region increases by 14% for S5010, while this increment is 11% for E214. The peak lift coefficient of both airfoils reduces with reducing Re. For lower pitch angles, the influence of Re on drag coefficients is less significant, but at higher angles, the drag increases as the Re drops. Unlike pre-stall mountings, the pitch-down propensity of the airfoil enhances in the post-stall region for high Re flows. Moreover, the frequency of shed vortices reduces with rising angle of attack at a given Re. In contrast, the Strouhal number almost remains constant with varying Re at a fixed angle of attack. For S5010 and E214 airfoils, the Strouhal number is noticed to vary between 0.68 - 0.36 and 0.58 - 0.36, respectively, for pitch angle variation of 12°- 28°. The airfoils show a higher Strouhal number than the bluff body wakes, but this difference decreases for high angles of attack mountings. This finding reveals that the wake structure of the airfoil at a high post-stall angle behaves as bluff body wakes.

Effects of chamfering and spacing on aerodynamics of two tandem cylinders

The flow over two tandem cylinders is investigated with five different spacing ratios L/D = 1.25, 2.0, 3.5, 4.0, and 6.0 and four chamfered-corner ratios ξ = B/D = 0%, 5%, 10%, and 15% at a Reynolds number Re = 5300, where L, B, and D are the distance between cylinders, chamfered corner dimension, and cylinder width, respectively. This work aims to assimilate the effects of ξ and L/D on flow structures, vortex shedding, aerodynamic forces, Strouhal number, and their relationships. We identified three different flow patterns depending on ξ and L/D: overshoot flow (L/D = 1.25, ξ = 0%), reattachment flow (1.25–2.0 ≤ L/D ≤ 2.0–3.5, ξ = 0%–15%), and coshedding flow (L/D ≤ 2.0–3.5, ξ = 0%–15%). The ξ and L/D play a similar role in the qualitative change of the flow structures, albeit with different degrees. As such, when L/D or ξ is increased, an overshoot/reattachment flow may change to a reattachment/coshedding flow. With the same flow pattern, ξ has a greater influence on the aerodynamic facets than L/D. This study establishes a framework for understanding how ξ and L/D influence flow topology and aerodynamic parameters.

Flow of ferrofluid within a channel driven by a rotating magnetic field: Implications of surface magnetic stresses and magnetic body couples

This research presents a discussion of the flow of a ferrofluid in a square cross-sectional area channel driven by a rotating magnetic field. The objective was to evaluate the coupled effect of surface magnetic stresses and diffusion of the internal angular momentum as potential mechanisms for generating flow. In many analyses of flow induced by time-dependent magnetic fields, the effect of the diffusion of the internal angular momentum has been dismissed, based on the negligible value of the spin viscosity coefficient estimated from order-of-magnitude analyses. In light of these considerations, we conducted a review of the existing analyses and put forward a new approach of the order-of-magnitude analysis of the spin viscosity coefficient. The paper presents a detailed description of the solution procedure for the flow field, with and without the inclusion of the diffusion of the internal angular momentum. To justify the assumptions involved in the analytical solution of the flow, we expanded a previous scale analysis to define Reynolds and Strouhal numbers in the linear and internal angular momentum balance equations. It was proven that the maximum surface velocity predicted at the ferrofluid–air boundary closely aligns with the reported experimental data for moderate amplitudes of the magnetic field.

Aerodynamic investigation of an S-shaped intake employing sweeping jet actuators based on proper orthogonal decomposition

The central curvature change of the S-shaped intake exacerbates the three-dimensional flow separation, resulting in total pressure and swirl distortions at the outlet. In this paper, an efficient active flow control technique, the sweeping jet actuator, was applied to control flow separation. The instantaneous characteristics of the flow field inside and outside the actuator were revealed by using validated numerical simulation methods. In addition, the effect of the sweeping jet on the aerodynamic performance of the S-shaped intake was investigated. Proper orthogonal decomposition (POD), an analysis method used to extract the main feature components of data, was applied to decompose the flow field structure at the S-shaped intake outlet in this study. The results highlight the external flow field characteristics of the actuator, with a jet sweeping range of up to ±40° and a sweeping frequency of 1 500 Hz, corresponding to a Strouhal number of 0.018. When the jet momentum coefficient is only 0.116%, the total pressure loss coefficient and pressure distortion index are reduced by 5.6% and 24.76%, respectively. This study demonstrates the critical role of momentum injection and discretization in inhibiting flow separation in the channel. The POD-based analysis indicates that a sweeping jet with high momentum can significantly enhance the energy in the flow passage and reduce the vorticity intensity of the first three modes. The stable mode structures exist near the outlet, exhibiting excitation frequency and frequency-doubling properties. The findings of this research provide essential input conditions for subsequent distortion studies.

How does vortex dynamics help undulating bodies spread odor?

In this paper, we examine the coupling between odor dynamics and vortex dynamics around undulating bodies, with a focus on bio-inspired propulsion mechanisms. Utilizing computational fluid dynamics simulations with an in-house immersed boundary method solver, we investigate how different waveform patterns, specifically carangiform and anguilliform, influence the dispersion of chemical cues in both water and air environments. Our findings reveal that vortex dynamics significantly impact the overall trajectory of odor spots, although the alignment between odor spots and coherent flow structures is not always precise. We also evaluate the relative contributions of diffusion and convection in odor transport, showing that convection dominates in water, driven by higher Schmidt numbers, while diffusion plays a more prominent role alongside convection in air. Additionally, the anguilliform waveform generally produces stronger and farther-reaching chemical cues compared to carangiform swimmers. The critical roles of Strouhal number and Reynolds number in determining the efficiency of odor dispersion are also explained, offering insights that could enhance the design of more efficient, adaptive, and intelligent autonomous underwater vehicles by integrating sensory and hydrodynamic principles inspired by fish locomotion.

Effects of surface roughness on the drag coefficient of finite-span cylinders freely rolling on an inclined plane

We present an experimental investigation aimed at understanding the effects of surface roughness on the time-mean drag coefficient ( $\bar {C}_{D}$ ) of finite-span cylinders ( $\text {span/diameter} = \text {aspect ratio}$ , $0.51 \le AR \le 6.02$ ) freely rolling without slip on an inclined plane. While lubrication theory predicts an infinite drag force for ideally smooth cylinders in contact with a smooth surface, experiments yield finite drag coefficients. We propose that surface roughness introduces an effective gap ( $G_{eff}$ ) resulting in a finite drag force while allowing physical contact between the cylinder and the plane. This study combines measurements of surface roughness for both the cylinder and the plane panel to determine a total relative roughness ( $\xi$ ) that can effectively describe $G_{eff}$ at the point of contact. It is observed that the measured $\bar {C}_{D}$ increases as $\xi$ decreases, aligning with predictions of lubrication theory. Furthermore, the measured $\bar {C}_{D}$ approximately matches combined analytical and numerical predictions for a smooth cylinder and plane when the imposed gap is approximately equal to the mean peak roughness ( $R_p$ ) for rough cylinders, and one standard deviation peak roughness ( $R_{p, 1\sigma }$ ) for relatively smooth cylinders. As the time-mean Reynolds number ( $\overline {Re}$ ) increases, the influence of surface roughness on $\bar {C}_{D}$ decreases, indicating that wake drag becomes dominant at higher $\overline {Re}$ . The cylinder aspect ratio ( $AR$ ) is found to have only a minor effect on $\bar {C}_{D}$ . Flow visualisations are also conducted to identify critical flow transitions and these are compared with visualisations previously obtained numerically. Variations in $\xi$ have little effect on the cylinder wake. Instead, $AR$ was observed to have a more pronounced effect on the flow structures observed. The Strouhal number ( $St$ ) associated with the cylinder wake shedding was observed to increase with $\overline {Re}$ , while demonstrating little dependence on $AR$ .

OpenSBLI v3.0: High-fidelity multi-block transonic aerofoil CFD simulations using domain specific languages on GPUs

OpenSBLI is an automatic code-generation framework for compressible Computational Fluid Dynamics (CFD) simulations on heterogeneous computing architectures (previous release: Lusher et al. (2021) [4]). OpenSBLI is coupled to the Oxford Parallel Structured (OPS) Domain Specific Language (DSL), which uses source-to-source translation to enable parallel execution of the code on large-scale supercomputers, including multi-GPU clusters. To date, OpenSBLI has largely been applied to compressible turbulence and shock-wave/boundary-layer interactions on very simple geometries comprised of single mesh blocks with essentially orthogonal grid lines. OpenSBLI has been extended in this new release to target strongly curvilinear cases, including transonic aerofoils using multi-block grids. In addition to multi-block mesh support, more efficient numerical shock-capturing methods and filters have been added to the codebase. Improvements to post-processing, reduced-dimension data output, and coupling to a modal decomposition library are also included. A set of validation cases are presented to showcase the new code features. Furthermore, state-of-the-art wide-span transonic aerofoil simulations on up to N=2.5×109 grid points demonstrate that wider aspect ratios can alter buffet predictions and increase the regularity of the low-frequency shock oscillations by accommodating fully-developed trailing edge flow separation. Spectral Proper Orthogonal Decomposition (SPOD) analysis showed that overly-narrow aerofoil simulations contain additional domain-dependent energy content at a Strouhal number of St≈3 associated with wake modes.

Computational Analysis of Flow Around Two Wall-Mounted Trapezoidal Bluff Bodies Arranged in Tandem Position

Abstract Flow around two identical wall-mounted trapezoidal bluff bodies, arranged in tandem, is numerically investigated at a Reynolds number of 750,000. The investigation employs Reynolds-averaged Navier–Stokes (RANS) equations and the k–ω SST turbulence model. The effect due to the change of the angular orientation of the inclined faces (α) of this bluff body and the pitch distance (L/D) on hydrodynamic quantities and turbulence quantities is investigated. Furthermore, the drag coefficient and Strouhal number have also been evaluated to understand the vortex shedding and flow pattern-related phenomena. For d and intermediate types of bluff bodies, the streamwise mean velocity, cross-stream mean velocity, turbulence kinetic energy, and recirculation length decrease with the increase of α or L/D. Significant changes are also observed in the case of Strouhal number. Reduction in drag coefficient and recirculation length is observed with increased L/D at a constant α for d-type bluff bodies. The change of α and L/D also creates the formation of a periodic von Kármán vortex street at downstream of the second bluff body in the case of L/D = 7, making the flows more complex and unstable. The maximum size of the recirculation bubble occurs in the case of L/D = 10 at α = 30 deg. The investigation provides valuable insight into the complex dynamics of tandem configurations of wall-mounted bluff bodies.

Computational analysis of unsteady oscillatory flow of nanofluid with variable electric conductivity: gear-generalized differential quadrature approach

Abstract This study numerically investigated the entropy production in nanofluids’ dissipative unsteady oscillatory flow characterized by variable electric conductivity and magnetic heating effects. The imposition of the non-isothermal boundary condition on the oscillatory stretching sheet plays a crucial role in establishing the self-similar solution in the presence of viscous heating. An external magnetic field (uniform in space and time) is imposed perpendicular to the plane of the oscillating stretched boundary. The energy equation, incorporating viscous dissipation effects and momentum equation, is reduced to nonlinear coupled partial differential equations and numerically solved using the Gear-generalized differential quadrature scheme.Additionally, to ensure the precision and reliability of the outcomes, the numerical code undergoes a thorough validation process that involves comparing its outputs to the findings of previous available studies. The Corcione model is implemented to describe the nanofluid’s effective viscosity and thermal conductivity. Furthermore, expressions for entropy production and relative irreversibility parameter (Bejan number), considering variable electric conductivity, are derived and computed based on solutions obtained from momentum and energy equations. The impacts of parameters such as magnetic parameter, variable electric conductivity parameter, Eckert number, Strouhal number, Prandtl number and temperature difference parameters on flow, heat transfer, entropy generation, and Bejan number are systematically illustrated and examined. We observed that increasing the variable electric conductivity parameters reduces the velocity profiles while improving the thermal fields. Similar behavior is found when the strength of a magnetic field is increased. The skin friction coefficient exhibits an augmentation in response to the Eckert number, dimensionless time, Strouhal number, nanoparticle volume fraction, magnetic parameter, and variable thermal conductivity parameter. Conversely, the Nusselt number increases concerning the Strouhal number and nanoparticle volume fraction. At the same time, it declines in association with the magnetic parameter, dimensionless time, Eckert number, and variable electric conductivity parameter.This comprehensive investigation enhances our understanding of nanofluid dynamics and provides valuable insights for optimizing thermal management systems across various engineering disciplines.

Agile robotic fish based on direct drive of continuum body

Fish-like agile movements, such as fast swimming and rapid turning, are essential for biomimetic underwater robots but challenging to achieve simultaneously. We present a self-contained robotic fish capable of swimming at a speed of 6.3 body length per second and pivot turning at an angular speed of 1450° per second. These fast motions, comparable to real fish, are realized by directly oscillating a flexible body using an electromagnetic motor, eliminating the need for transmission parts and simplifying the structure. This direct-drive (DD) method improves mechanical robustness and generates fish-like deformations and subsequent rapid swimming. The Strouhal and swimming numbers of the robot match typical values observed in nature. Moreover, the observed frequency peaks in swimming are similar to computed values using a model, which guides the design of the robot. These results illustrate the DD method as a promising framework for the creation of highly versatile biomimetic underwater robots.

Collective swimming pattern and synchronization of fish pairs (Gobiocypris rarus) in response to flow with different velocities.

Collective behaviors in moving fish originate from social interactions, which are thought to be driven by beneficial factors, such as predator avoidance and reduced energy expenditure. Despite numerical simulations and physical experiments aiming at the hydrodynamic mechanisms and interaction rules, how shoaling is influenced by flow velocity and group size is still only partially understood. In this study, spatial distributions, kinematics, and synchronization states between pairs (smallest subsystem of a shoal) of Gobiocypris rarus were investigated in a recirculating swim tunnel with increasing flow velocities from 0.1 to 0.5 m/s (Ucrit = 0.6 m/s). Tests of single fish were also conducted as the control group. The results of spatial distributions showed that fish pairs preferred to swim in the side-by-side configuration under high flows, while under low flows the neighboring fish's positions were more uniformly distributed around the focal fish in the transverse direction. Kinematic analysis revealed that fish pairs adopted similar tail beats (i.e., frequency and Strouhal number) as single fish in low flows, while in high flows both the frequency and Strouhal number of fish pairs were slightly lower. Moreover, the synchronization rates of fish pairs were found to increase with flow velocities, suggesting that synchronized swimming may be beneficial, especially in high flows.

Turbulent flow around convex curved tandem cylinders

Turbulent flow around curved tandem cylinders has been studied for the first time, by means of direct numerical simulation. The convex configuration was used, with a nominal gap ratio of $L/D = 3$ and a Reynolds number of 3900. Along the span, the flow regimes vary from alternating overshoot/reattachment to co-shedding. Three distinct Strouhal numbers coexist in the flow that are tied directly to different tandem cylinder flow regimes. This result differs substantially from convex curved tandem cylinders at a transitional Reynolds number, where only a single dominant frequency is found. All regimes exhibit some degree of instability, so that the flow can be considered multistable. A mode switch from alternating overshoot/reattachment to symmetric reattachment is found. Complex interactions are observed between the primary instability, the shear layer instability and the flow mode alterations. As opposed to previous investigations with single and tandem straight cylinders in the subcritical flow regime, our results indicate that there may be direct feedback from the primary instability to the shear layer instability. The downdraft region in the gap exhibits slow meandering, and may travel upstream and amplify the shear layer instability, causing early transition in the gap shear layer. This downdraft is governed by the slow modulations of the vortex formation region in the lower gap, meaning that the vortex dynamics of this region may indirectly influence the shear layer instability higher up in the gap.

Benchmark experimental study on cavitating flow around Clark-Y 11.7 % hydrofoil at various angles of attack under controlled levels of dissolved air

The present research aims to study cavitating flow around a CLARK-Y 11.7 % hydrofoil with variable angles of attack (α) while maintaining controlled levels of dissolved air in the operating fluid, which is water. A series of experiments were conducted using a water tunnel facility, where the cavitation characteristics were measured and observed using sensors and high-speed imaging techniques. The variables studied in the present work are cavitation number (1 ≤ σ ≤ 2.2) and angle of attack (α = 4°, 6°, 8°, 10°, and 12°), with dissolved air levels (DAL) in the range of 9.3 ppm to 13.1 ppm. The dimensionless cavity length decreases significantly with increasing values of σ/α, indicating an inverse relationship where higher cavitation numbers or lower angles of attack result in shorter cavities. The cavity length follows a power-law scaling relationship, with the empirical equation Lmax/C=4.78×σ/α−0.76.Increasing the angle of attack transitions the cavitation nature from stable (Mode I) to dynamic (Mode II) and highly oscillating (Mode III). Larger cavities result in lower Strouhal numbers, which indicates reduced vortex shedding activity. The relationship between the Strouhal number and the normalized cavitation number σ/α is characterized by the power-law equation St=0.041×σ/α0.3. The pressure coefficient at the leading-edge increases with the angle of attack at low cavitation numbers, while higher cavitation numbers lead to greater pressure coefficient differences between the leading and trailing edges.The present study offers an extensive dataset and empirical correlations that may serve as a benchmark framework, which facilitates the validation of computational and experimental models of cavitating flow under similar conditions.

Periodic morphing of a NACA6409 aerofoil in ground effect, its wake mechanisms and thrust generation

Abstract The camber morphing of an aerofoil in ground effect was investigated using the FishBAC method and Detached Eddy Simulations with the k-omega SST turbulence model at a Reynolds number of 320,000. The aerofoil was periodically morphed at a start location of 25% chord from the leading edge with a trailing edge deflection range of 0.1% to 3% and morphing frequencies between a Strouhal number of 0.45 to 4 at a constant ground clearance of 10%. Periodically morphing the aerofoil using a sinusoidal function showed that lift and drag increased on the downstroke and decreased on the upstroke in the cycle, resulting in periodic values of lift and drag throughout the cycle. The amplitude of lift and drag increased as the morphing frequency and/or trailing edge deflection increased. It was found that the wake characteristics varied as a function of trailing edge deflection and morphing frequency. For small trailing edge deflections below 0.4% and frequencies below a 2.2 Strouhal number, Kelvin Helmholtz shedding was observed, and above this the wake became chaotic. Large trailing edge deflections showed Von-Karman shedding, where the interaction between the lower counter-clockwise vortex and the ground plane resulted in a jet-like flow that caused forward thrust. For the maximum deflection and morphing frequency tested in this study, reversed Von-Karman shedding was observed, which caused forward thrust from the interaction of the two-shedding counter-rotating vortices. Von-Karman or reversed Von-Karman shedding shows positive thrust generation, however, chaotic shedding should be avoided due to large drag gains. Varying the Reynolds number caused the Strouhal number to change as they depend on the same variables. It was found that the Strouhal number variation had a large effect on the wake, however, the Reynolds number had a minimal effect.

Analysis of the impact of key similarity criteria numbers of TBCC inlet during the mode transition

Abstract A simplified configuration was developed to facilitate the mode transition process within an over-under Turbine-Based Combined Cycle (TBCC) inlet. Leveraging dynamic mesh technology, an unsteady numerical simulation of the mode transition was conducted, emphasising the flow characteristics of the mode transition and the impact of key similarity criteria numbers. The findings indicate that at an incoming Mach number of 2.0, the mode transition is paired with a continuous alteration in the capture mass flow of the high-speed duct. This continual change instigates the inlet unstarting, with subsequent flow characteristics being contingent on the historical effect, exhibiting a degree of hysteresis characteristics. When the scale effect is considered, it is observed that a larger model scale results in higher Reynolds (Re) and Strouhal (St) numbers. This directly contributes to a notable delay in the unstart moment, a decrease in the unstart interval, and an enlargement of the hysteresis loop. An examination of control variables reveals that the Re number marginally influences mode transition characteristics, while the St number’s effect constitutes approximately 90% of the scale effect. This conclusively demonstrates that the St number is the predominant similarity criterion number in the mode transition process.

Insights into vibration-induced softening effect: A thermodynamic approach

This work investigates the wear behavior of nickel-based alloy during ultrasonic vibration-assisted machining (UVAM) by combining molecular dynamics simulation and thermodynamic theory. The research reveals that the tangential force exhibits periodic variations during UVAM, with a period half of the vibration period. Tangential force and total resistance decrease due to the synergistic effect of vibration-induced softening and thermal softening. A deeper understanding of the total resistance variation during the UVAM process can be achieved by the dimensionless resistance coefficient, which is difficult for the traditional friction coefficient (CoF). The Bejan number elucidates the contributions of the thermal softening and vibration-induced softening effects in the wear process. The findings highlight that the vibration-induced softening effect dominates when adjusting the amplitude for the active control of friction. In contrast, when the frequency is modulated, the contributions of vibration-induced softening and thermal softening effects are nearly equivalent. Furthermore, the wear mode transitions with increasing vibration frequency, characterized by the Strouhal number (Srw). The vibration wear mode attains dominance when Srw > 1.88. This work provides essential theoretical guidance to gain insight into the wear behavior in UVAM to optimize the machining performance.

A new approach to account for turbulence distortion effect on Amiet's leading-edge noise prediction

A turbulent inflow distorts as it approaches an airfoil's leading edge (LE), which is an important phenomenon influencing the airfoil LE noise. This mechanism is not yet fully understood and is not accounted for in Amiet's theory for LE noise. Thus, the main contribution of this paper is to discuss a possible new approach to account for turbulence distortion in Amiet's LE noise model. The analysis is based on wind tunnel experiments performed for four NACA airfoil geometries. Hot-wire anemometry and a microphone array were used to evaluate the turbulence in the LE region and the radiated noise, respectively. Turbulent inflow was generated with a rod and a grid. Based on the measured turbulence data, a formulation that describes the turbulence length scale near the airfoil LE is introduced, which yields more accurate noise predictions when used in combination with Amiet's model. The proposed approach to estimate LE noise consists of using an appropriate turbulence spectrum formulation for the distorted turbulence and the proposed expression to determine the turbulence length scale near the airfoil LE, yielding a maximum discrepancy between measured and predicted LE noise of 4dB for a rod Strouhal number from 0.3 to 3.

The mechanism of aerodynamic performance enhancement of flapping wings with spanwise active deformation

The single stiffness makes the micro-air vehicles (MAVs) only to show excellent flight performance in a specific flow field environment. The MAVs should have the ability to actively deform to adapt to different application scenarios. This study investigates the effects of spanwise active deformation amplitude (ψmax), phase difference (φP), and Strouhal number (St) on the aerodynamic loads and vortex of a wing through numerical simulations. Under the condition of Re= 1000, numerical simulations were conducted on a rectangular wing with an aspect ratio of 4 during the flapping process. The study reveals that moderate spanwise deformation can increase the thrust of the wing and improve propulsion efficiency (ηP). Within the study's scope, the thrust coefficient increases monotonically and linearly with the deformation, but the propulsion efficiency improves only within a limited parameter range. By observing the vortex under different spanwise deformations and monitoring the forces at different positions of the wing, it was found that active deformation can enhance the strength of the leading-edge vortex (LEV) and the wingtip vortex (TV), thereby enhancing the generation of thrust. The results also indicate that the enhancement of LEV is achieved through the coupling between LEV and secondary vortex. At different Strouhal numbers, improvements in ηP can only be achieved through the combined effects of increased vortex strength and optimal vortex residence time. Additionally, it was observed that at lower St, TV can switch from contributing thrust to causing drag.