Strouhal Number St Research Articles

Hydrodynamic performance of slender swimmer: effect of travelling wavelength

The impact of Strouhal number St (= 0.1–1.0), Reynolds number Re (= 50–2000) and dimensionless wavelength λ (= 0.5–2.0) on the hydrodynamic performance of a travelling wavy foil of a constant length is extensively investigated. The relationship of time-mean thrust with St, Re and λ is presented, suggesting that the propulsive force increases with increasing St, Re and λ. As such, the drag–thrust boundary advances as these parameters increase. A shorter λ makes the thrust steadier while a longer λ enhances the maximum instantaneous thrust. The latter is beneficial for prey to escape from a predator. The fluid added mass caused by the foil oscillation increases with St and λ but declines with Re (<500). Seven types of wake structures produced by the foil are identified, discussed and connected to thrust generation, showing how St, Re and λ affect the fluid dynamics, wake transition, vortex strength, wake jet, velocity, added mass, added damping, power input, efficiency and pressure profiles. The outcome of this work renders a physical basis for understanding the swimming of aquatic animals.

Effects of streamwise gust amplitude on the flow around and forces on two tandem circular cylinders

Three-dimensional large eddy simulations are carried out to investigate the effect of streamwise gust amplitude ratio AR on the flow structure around and dynamic forces on two tandem circular cylinders at a subcritical Reynolds number of Re = 1 × 103. The center-to-center space L between the two cylinders is fixed at 3.5D, where D is the cylinder diameter. The velocity U of sinusoidal streamwise gust is set as U = U0 (1+ARsin2πfut), where the velocity amplitude ratio AR is varied from 0 to 0.25, U0 is the mean velocity, fu is the frequency of the sinusoidal streamwise gust, and t is the time. In order to enhance the understanding of the streamwise gust effect on the physical properties of the flow around the two tandem cylinders, the shear-layer reattachment, flow separation, wake recirculation, Strouhal number (St), unsteady forces, and phase lag (φ) between the fluctuating lift forces of the two cylinders are explicated. The results show that the flow structure around the cylinders is sensitive to AR. A change in AR thus leads to modification of reattaching flow (AR ≤ 0.15) to co-shedding flow (AR ≥ 0.20). The St, fluctuating forces and φ thus jumps at the boundary between the reattaching and co-shedding regimes. A stronger gust effect appears on the fluctuating drag of the upstream cylinder than that of the downstream cylinder. Besides the dominant component of the fluctuating lift induced by the vortex shedding, two other components are observed with the frequencies equaling to the superposition and subtraction of the gust and vortex-shedding frequencies, respectively. In addition, two more cases with L/D = 1.5 and 6.0 are conducted for deeper understanding of AR effects.

Vortex evolution of flow past the near-wall circular cylinder immersed in a flat-plate turbulent boundary layer

The vortex evolutions and the turbulent characteristics in flow past the near-wall circular cylinder immersed in a flat-plate turbulent boundary layer are investigated with particle image velocimetry (PIV), with the objective of clarifying the interaction between the turbulent boundary layer flow and the near-wall cylinder wake. The Reynolds number based on the cylinder diameter D is 1.0×103, and three gap ratios (i.e., G/D=0.5, 1 and 2) are chosen for comparison at δ/D=6.7 where G is the gap size and δ is turbulent boundary layer thickness without the presence of cylinder. The proper orthogonal decomposition (POD) analysis is used to obtain phase-averaged flow fields, combining with the vortex identification method λci, which can capture effectively the evolution process of vortex. For three gap ratios, the cylinder is placed at the logarithmic-law layer of incoming flow, and the Karman-vortex sheets can be generated from the curling of the cylinder shear layers. At G/D=0.5 and G/D=1, the secondary vortex can be formed periodically in the wall due to the induction of the lower wake vortex. The vortex evolutions and turbulent characteristics are significantly affected by incoming turbulent boundary layer flow. The swirling strength of the wake vortices shed from the cylinder is enhanced with increasing G/D, and the swirling strength of the upper wake vortex is slightly bigger than that of the lower wake vortex due to velocity differences of incoming flow. The variation of the Strouhal number (St) is dependent on the gap ratio, and there is nearly 10.4% increase from St=0.211 at G/D=2 to St=0.233 at G/D=0.5, which is caused by the combined effects of the deflected gap flow and the velocity gradient. At large gap ratios, especially at G/D=2, the upstream high-velocity fluids interact with the cylinder wake, leading to strong velocity fluctuations behind the cylinder, and the magnitudes of production and turbulent diffusion in turbulent kinetic energy are increased, which also enhances turbulent transports behind the cylinder.

Numerical validation of simple non-stationary models for self-propelled pitching foils

High-resolution numerical simulations of the self propelled locomotion of two-dimensional pitching foils are used to assess simplified models based on linear potential theory for the fluid-foil interaction. These models are very useful because they provide simple analytical estimations of the swimming velocity, among other relevant features of the aquatic locomotion of fishes and underwater robotic devices propelled by flapping foils. In particular, we consider a pitching foil self-propelled from two different models of the unsteady thrust force based on linear potential theory, both complemented with a new simple model for the unsteady viscous friction obtained from the present full-numerical simulations, valid in a wide range of Reynolds numbers (103≲Re≲104) of interest for many natural and robotic swimmers. The resulting ordinary differential equation for the swimming velocity is easily integrated numerically, comparing favorably with the full-numerical simulations for small pitch amplitudes (Strouhal numbers St≲0.25) and the above range of Reynolds numbers. Further, when the swimming velocity is small, simple approximate solutions of the dynamic model equation are obtained, whose pitch amplitude validity range is more limited than the numerical solution of the model as the Reynolds number and the foil mass ratio increase, becoming negligibly small when the frequency-based Reynolds number is well over 104. Although both thrust models yield similar quantitative results, they predict qualitatively different dependencies of the swimming velocity on the different non-dimensional parameters.

Effects Of Driving Signal Waveshape On The Velocity Field And Heat Transfer Of Impinging Synthetic Jets

The present work reports on the measurements of the velocity fields and the heat transfer of impinging synthetic jets driven by different waveshapes. The actuator consists of a loudspeaker oscillating inside a cavity provided with a circular nozzle. Sinusoidal input voltage signals with variable ejection duty cycle d (ratio of the duration of the positive part of the signal to the total period) are applied to investigate the influence of the waveshape on the jet dynamics and the thermal performance. A parametric study is carried by varying both d (0.3, 0.4, 0.5, 0.6, 0.7) and the Strouhal number St (0.062, 0.12, 0.19) at constant value of the Reynolds number (3,000) and fixed nozzle-to-plate distance (equal to 2 nozzle exit diameters). The phase and time-average evolution of the synthetic jets is characterized by means of planar Particle Image Velocimetry; simultaneous measurements of the heat transfer coefficients are carried out via infrared thermography using a heated thin foil as heat flux sensor. The present results show that d plays only a minor influence on the time-averaged velocity structure for all the values of the Strouhal number investigated. Nevertheless, for the highest value of St increasing d has a detrimental effect on the heat transfer. The phase-averaged velocity measurements reveal that this behaviour is essentially related to the reduced strength of the synthetic jet vortices formed during the ejection phase, which in fact dominate the heat transfer in such a configuration.

Heat transfer enhancement by pulsating flow of a viscoelastic fluid in a microchannel with a rib plate

ABSTRACT In order to improve the heat transfer performance of the microchannel heat exchanger, a composite heat transfer enhancement method was proposed. Viscoelastic fluid was used as working fluid in pulsating flow condition, and rib plates were added to the microchannel to bring extra disturbance to the flow. The Oldroyd-B constitutive model of the viscoelastic fluid was used in the numerical simulation, and the flow field, temperature field, Nusselt number (Nu), and pressure drop were analyzed when the average Reynolds number (Re) is 10. Both Strouhal number (St) and amplitude are important factors affecting heat transfer, but they have an insignificant influence on pressure drop at low Reynolds number. The St = 0.125 and amplitude A = 0.8 are better parameters. The increase of Weissenberg number (Wi) will cause the vortex to split into several subsidiary vortexes during its development, which will also develop to various positions in the channel, thus further enhancing the heat transfer. When the Wi is in the range of 1 ~ 5, the performance evaluation criteria rises at a relatively fast rate, from 1 to 1.404.

Effect of pivot location on the semi-active flapping hydrofoil propulsion for wave glider from wave energy extraction

This paper experimentally investigates the propulsion of semi-active hydrofoils from wave energy. For the case of NACA 0012 foil section, heave amplitude h0 = 1.0 chord, Reynolds number Re=2×104, a series of flapping experiments were carried out. We examine the effects of the pivot location xp = 0.09c, 0.16c, 0.25c, and 0.33c on the propulsion and efficiency of the semi-active flapping hydrofoils. Combined with numerical simulation and Theodorsen's theory, some conclusions are given. The results demonstrate that for the pivot location xp=0.33c, the semi-active flapping hydrofoil might fall into a pitch unstable state at a low oscillating frequency, which leads to low efficiency (<20%). For the semi-active hydrofoil, a pivot location xp≤0.25c is favored. Additionally, for the pivot location xp=0.09c with non-dimensional stiffness K∗=1.69, we find that an energy conversion efficiency of more than 40% is achievable at nearly all Strouhal numbers St = 0.2–0.77. Meanwhile, for the pivot location xp close to 0.25c, a smaller torsion stiffness should be implemented to achieve better efficiency, and a bigger torsion stiffness for xp close to the leading edge. These results have significant references to the semi-active hydrofoil design of wave gliders.

Hydrodynamic Interaction of Two Self-Propelled Fish Swimming in a Tandem Arrangement

Collective locomotion in biological systems is ubiquitous and attracts much attention, and there are complex hydrodynamics involved. The hydrodynamic interaction for fish schooling is examined using two-dimensional numerical simulations of a pair of self-propelled swimming fish in this paper. The effects of different parameters on swimming speed gain and energy-saving efficiency are investigated by adjusting swimming parameters (initial separation distance d0, tail beat amplitude A, body wavelength λ, and period of oscillation T) at different phase difference δϕ between two fish. The hydrodynamic interaction performance of fish swimming in a tandem arrangement is analyzed with the help of the instantaneous vorticity contours, pressure contours, and mean work done. Using elementary hydrodynamic arguments, a unifying mechanistic principle, which characterizes the fish locomotion by deriving a scaling relation that links swimming speed u to body kinematics (A, T, and λ), arrangement of formation (d0), and fluid properties (kinematic viscosity ν), is revealed. It is shown that there are some certain scaling laws between similarity criterion number (Reynolds number (Re) and Strouhal number (St)) and energy-consuming coefficient (CE) under different parameters (Δ). In particular, a generality in the relationships of St–Re and CE–(Re ·Δ) can emerge despite significant disparities in locomotory performance.

A Numerical Investigation of the Dominant Characteristics of A Transonic Flow Over A Hemispherical Turret

The transonic characteristics of a flow over a hemispherical turret with a freestream Mach number M∞ of 0.8 are numerically studied. The flow field is simulated using the improved delayed detached eddy simulation (IDDES) with a modified sub-grid scale. The results using the adopted medium and fine grids, including for the mean pressure coefficients and the incoming boundary layer, match experimental data very well. It is observed that the wake fluctuates periodically as the shock moves upstream and downstream. The dominant flow characteristics are identified along with their frequencies. The first two proper orthogonal decomposition (POD) modes show a lateral shift of the wake, fluctuating at a Strouhal number (St) of 0.15–0.2. Modes 3 and 4 show a wall-normal fluctuation of the wake with St of 0.35. A dynamic mode decomposition (DMD) gives St values of the lateral shift and wall-normal fluctuation of 0.1813 and 0.3467, respectively.

Genesis of Antibiotic Resistance (AR) LXXXII: Turbulence Modeling(TM) of Hemodynamics in Simplified Severe Sepsis Protocol‐2 (SSSP‐2)‐NCT01663701: The “Von Kármán Vortex Street” (Vasospasm probability index(VPI)) Fillip Zone of Obstruction Consequent Comatose to ihm

Based on Flow‐3DÒ Hydro FD simulation Model 04 (Courtesy: Flow‐3DÒ), clinical data for spontaneous subarachnoid hemorrhage (SAH) and flow gauge, here we present a plausible physiological basis for fluid bolus induced alteration of velocity profile with a fluid volume expansion, that leads to 100% ihm usual care cohort of SSSP‐2 (PMID: 28973227). Subsequent to SAH, an increase in blood flow velocity in cerebral arteries has been observed. The blood flow velocity after SAH was observed to be between 73 and 215 cm/sec (the frequency range of the pure tones: 140 to 820 Hz). The murmurs occurred after SAH has been suggested to be a transitional state between silent flow(laminar) and the phenomenon of bruit (DDx: Carotid Artery Stenosis, carotid cavernous fistula, fibromuscular dysplasia, Takayasu’s arteries, arteriovenous fistula). The cause of the murmur has been suggested to be periodic shedding of vortices in the cerebral arteries, referred to as “a von Kármán vortex street”.Murmurs are an indication of a pathological increase in blood velocities to reflect the degree of spasm(vascular) (PMID: 6689725). VPI, is a combination of transcranial Doppler(TCD) velocities, cerebral blood flow, and clinical risk factors to predict cerebral vasospasm after aneurysmal SAH (PMID: 18077946). Geometry: Lindegaard ratios and spasm indexes (TCD velocities/hemispheric CBF) to evaluate the probability of cerebral vasospasm after aneurysmal SAH. An increase in blood flow velocity (BFV) is the principal criterion for vasospasm. The Middle Cerebral Artery (MCA) /internal carotid artery (ICA) index (Lindegaard Index) is used to distinguish between vasospasm and cerebral hyperperfusion. The intracranial arteriovenous index (AVI) is used to assess vasospasm after SAH. (PMID 29243981). CPP=MAP‐ICP. The blood flow rate in carotid arteries, Table 4.14 p172, ISBN 9780128024089. Governing Equation:Part A: Strouhal number (St): This formula will generally hold true for the range 250 &lt; Red &lt; 200000: St=0.198 (1‐19.7/Red); where St=fd/U, f = vortex shedding frequency, d = diameter of the cylinder, U = flow velocity.Part B: To calculate pressure drop in cylindrical pipe Poiseuille Equation (Hagen‐Poiseuille Eq): Vmax= DPR2 / 4μL, (Eq 1.47, p32) where DP= pressure difference between the two ends, μ = dynamic viscosity, L= length of the pipe, Q= volumetric flow rate, π = 22/7 @3.14, R= pipe radius. For volumetric flow rate (Q) equals cross‐section area multiplied by velocity (Q=ṼA), so DP=8μL/πR4. To represent pressure drop and flow rate in cerebral arteries Poiseuille’s equation is written as Q=DP π R4/ 8ηL where η = viscosity. Derivation and Prospect:Taken together, direct correlation of S&amp;SX of SSSP‐2 (NCT01663701), that subsequent to the fluid bolus, the usual care cohort of SSSP‐2, may have had SAH within 24 to 48 hrs. During that period the LPE aggregates‐toxins of AR‐ClPrs origin forming the ZoO with a concurrent increase ICP, CBF, CBV, PRx, CPPopt, may have caused the cerebral vessel collapse eliciting CCP followed by 100% ihm.

Vortex induced vibration of four cylinders configurations at critical spacing in 0° and 45° flow incidence angle

This work presents a numerical study on vortex-induced vibration of four circular cylinders with one and two degrees of freedom subjected to uniform free-stream velocity U at α=0°and α=45°angle of incidence, Reynolds number of Re=UD/ν=150, center-to-center cylinders distance of L=3.5D and a mass ratio of ρc/ρ=2.5and24/π. The structural damping is set to zero for reduced velocity UR=U/(fnD) from 1 to 14. The high-precision code Incompact3d coupled to a moving immersed boundary method is applied to solve the governing equations. The oscillation amplitudes (Ax, Ay), transverse force frequency ratio f/fn, wake Strouhal number St, vorticity fields, and force coefficients statistics are investigated. A wake-stiffness is inferred by f/fn=2 of the lateral cylinders in the 45°rotated configuration. For the one degree of freedom case, when α changes from 0°to 45°, the overall peaks of the force coefficients statistics and oscillation amplitudes increase. In contrast, for the two degrees of freedom case (2dof), only the |C¯L| and CL′ overall peaks increase about 10%, and the Ax peak decreases around 37%. Besides, when L/D is reduced from 5 to 3.5 in 2dof, the overall maximum Ay is slightly affected. However, for α=0°, the |C¯L| , CD′ and Ax peaks respectively are 106%, 284% and 177% higher at L/D=3.5. For α=45°, the CD′ and Ax peaks increase 42% and 33%, respectively.

Experimental investigation of cavitating flow around chamfered cylinders vertically inserted in a circular pipe

An experimental investigation was conducted to study the cavitating flow around cylinders with different chamfer angles vertically inserted in a circular pipe. The experiments were performed in a variable-pressure closed-loop cavitation rig at a constant Reynolds number of Re=1.2×105 with cavitation numbers corresponding from inception to supercavitation. In practical hydraulic systems, numerous structures can be modeled as vertically inserted chamfered cylinders and the cavitation phenomenon can occur around such structures with serious side effects. This work is an attempt to understand the cavity dynamics and the influence of the chamfer angle θ on the characteristics of cavitating flows, with the aim of providing guidelines for designing relevant structures. The low- and high-speed images of the cavitating flow in different cavitation regimes were analyzed to investigate the dynamics of the cavitating flow around the cylinder with chamfer angle θ=60°. From the space–time diagram obtained from the high-speed series, it is found that for cavitation number σ>0.80, the shedding of the small vapor filaments is induced by interfacial instabilities; for cavitation number σ<0.75, the re-entrant jet accounts for the periodic shedding of the vapor clouds. In the transition region (0.75<σ<0.80), the shedding is caused by a complex combination of both mechanisms. The dominant shedding frequency, expressed as Strouhal number St, drops with the decrease of the cavitation number σ in the regime dominated by interfacial instabilities; while in re-entrant jet regime, it is almost insensitive to the change of the cavitation number σ. In addition, the influences of the chamfer angle θ on the inception condition, cavity length, pressure drop, and pressure fluctuation are also discussed in the present work. With the increase of θ, the cavitation resistance becomes better and the pressure drop through the test section decreases.

Numerical analysis of heat transfer improvement for pulsating flow in a periodic corrugated channel with discrete V-type winglets

In the present study, the effects on the hydraulic and thermal performance of pulsating flow in a periodic corrugated channel with discrete V-type winglets were numerically investigated. Three different channel flows were considered with non-winglet, solid winglet, and perforated winglet configurations. The winglets were placed in the center of the channel in a discrete V-shape downstream. Numerical analyses were carried out with the finite volume approach. The effects of pulsation amplitude (A), Strouhal number (St), and Reynolds number (Re) on the flow and heat transfer were examined. The upper and lower surfaces of the corrugated channel were protected at Tw = 350 K and thermal performance and pressure drop were acquired for a pulsating cycle across the channel. The numerical results were presented in terms of thermal performance (η), dimensionless friction factor (Γ), and thermal performance factor (TPF). To observe the effects of the pulsation parameters and Reynolds number, time-averaged velocity and temperature distributions in the channels were obtained. The findings showed that the flow and heat transfer characteristics were highly affected by the channel and winglet geometry. The pulsation parameters significantly contributed to heat transfer improvement, especially at high Reynolds numbers. Thermal performance increased considerably with increasing pulsation amplitude and frequency with a slight increase in friction factor. Also, it was observed that the perforated winglets reduced the friction factor compared to the solid winglets. The highest TPF values for non-winglet, solid winglet, and perforated winglet configurations were respectively found as 5.71, 4.68, and 5.17 at Re = 1000, A = 1.5, and St = 8.

Experimental and numerical studies on the three-dimensional flow around single and two tandem circular cylinders in a duct

Experimental and numerical investigations are conducted in order to understand the flow around identical tandem circular cylinders confined in a duct (blockage ratio b = 0.1 and aspect ratio a = 5). In this work, the Reynolds number Re ranges from 40 to 200 and the spacing ratio (distance between two centers of tandem circular cylinders to diameter, L/d) from 0 to 8. When fluid flows around a single cylinder placed symmetrically in the duct (L/d=0), it is found that the Strouhal numbers St and mean drag coefficients Cd¯ increase with the increase in Re, although the separation angle θs decreases. For the flows around two tandem circular cylinders, the research is focused on examining the coupling effect of Re and L/d on St, flow structures, θs, Cd¯ and reverse region length Lr. Based on numerical results, the mathematical descriptions are established, Cd¯∼Re−1, θs∼Re−1/2, and St∼Re−1. The dependence of flow structures, drag forces, θs and Lr, on L/d is described in detail with the help of approaching velocity profiles, pressure coefficient Cp, and vorticity ωz* distribution on a cylinder's surface. Through numerical simulations, the detailed mechanisms about influences of these factors on the flow properties are revealed. The experimental results evidence the occurrence of three flow modes, i.e., no vortex shedding mode, single body mode, and reattachment mode, which are determined practically by the Reynolds number and space ratio. Both the measured St based on the dominate frequencies of vortex shedding and the visual flow field match well with numerical simulations.

A numerical study of a lifted hbox {H}_2/hbox {N}_2 flame excited by an axial and flapping forcing

The large eddy simulation method combined with the Eulerian stochastic field approach has been used to study excited lifted hydrogen flames in a stream of hot co-flow in a configuration closely corresponding to the so-called Cabra flame. The excitation is obtained by adding to an inlet velocity profile three types of forcing [(1) axial; (2) flapping; (3) combination of both] with the amplitude of 15% of the fuel jet velocity and the frequency corresponding to the Strouhal numbers St=0.30,, 0.45,, 0.60, ,text {and}, ,0.75. It is shown that such a type of forcing significantly changes the lift-off height (L_h) of the flame and its global shape, resulting in the flame occupying a large volume or the flame, which transforms from the circular one into a quasi-planar one. Both the L_h and size of the flames were found to be a function of the type of forcing and its frequency. The minimum value of L_h has been found for the case when the axial and flapping forcing were combined and acted at the forcing frequency close to the preferred one in the non-excited configuration. The impact of the flapping forcing manifested through a widening of the flame in the flapping direction. It was shown that the excitation increases the level of temperature fluctuations caused by an intensified mixing process. The computational results are validated based on the solutions obtained for the non-excited flame for which experimental data are available.

Numerical simulations of flow around three cylinders using momentum exchange-based immersed boundary-lattice Boltzmann method

Wake flow behind multiple bluff bodies is of critical significance in ocean engineering and has important scientific significance in fluid mechanics and dynamics. Three cylinders arranged in side-by-side, tandem, equilateral-triangular, and staggered arrangements were extensively researched in the previous study. In this study, the flow passing through three cylinders in staggered and equilateral-triangular arrangement were numerical calculated using a momentum exchange-based immersed boundary-lattice Boltzmann method. The numerical investigations for staggered arrangement were carried out by changing the Reynolds number (Re) from 10 to 200 with an increment of 1, and varying the gap ratio (δ = ΔP/D) from 0.1 to 8.0 with an increment of 0.1. The flow patterns of three equilateral-triangular cylinders with different gap ratios at Re = 100 were also numerical studied. The numerical results identified various flow patterns, and the variations of the above two parameters have a decisive influence on the vortex shedding patterns and flow properties. The drag coefficient, lift coefficient, and Strouhal number (St) were also surveyed to demonstrate the relationship among flow pattern, parameters δ and Re. The outcomes in this paper provide a relatively comprehensive understanding to the vortex shedding patterns and flow properties of three circular cylinders with different gap ratios and Reynolds number.

Flow-induced vibration of a cantilevered cylinder in oscillatory flow at high KC

Flow-induced vibrations of a cantilevered circular cylinder are measured in sinusoidal, oscillatory, water flows with amplitude of reduced velocity in the range 1.9≤Ur≤4.4 and Keulegan–Carpenter number in the range 120≤KC≤900 respectively. Flow velocities are measured using laser Doppler anemometry, and forces and moments are measured using a 6-axis load cell; the two-degree-of-freedom (2-DOF) cylinder motions are determined from the measured moments. The dominant type of vibration occurring within the flow half-period is shown to depend mainly on Ur, with predominantly in-line vibration occurring for Ur⪅2.7, figure-8 vibration occurring for 2.7⪅Ur⪅4, and transverse vibration occurring for Ur⪆4. In-line vibration frequency, fx, is close to, or slightly higher than the cylinder’s natural frequency in still-water, while transverse vibration frequency, fy, is generally close to the vortex shedding frequency given by Strouhal number St=0.2. Some unsteadiness is seen in the transverse vibration frequency in that accelerating flow fy is consistently higher than decelerating flow fy for the same instantaneous reduced velocity ur. The most notable unsteady effect is seen in the in-line vibration amplitude, Ax, which is much higher during flow deceleration than during flow acceleration; maximum Ax occurs at decelerating ur≈2 for all three vibration types. Transverse vibration amplitude, Ay, increases with increasing ur and shows only slight asymmetry between accelerating and decelerating flow. Experiments with the cylinder placed within a large array of similar cylinders with a spacing between cylinders of six cylinder diameters, show that cylinder vibrations within the array are more variable than those of the isolated cylinder, but exhibit similar average vibration amplitudes and frequencies as the isolated cylinder. An empirical model for unsteady in-line vibration based on theoretical considerations and the experimental data is presented. Model-predicted and measured in-line vibration amplitudes through the flow half-period show good agreement for in-line, figure-8 and transverse vibrations.

Numerical simulation of flow over flapping wings in tandem: Wingspan effects

We report direct numerical simulations of a pair of wings in horizontal tandem configuration to analyze the effect of their aspect ratio on the flow and the aerodynamic performance of the system. The wings are immersed in a uniform free stream at the Reynolds number Re = 1000, and they undergo heaving and pitching oscillation with the Strouhal number St = 0.7. The aspect ratios of forewing and hindwing vary between 2 and 4. The aerodynamic performance of the system is dictated by the interaction between the trailing edge vortex (TEV) shed by the forewing and the induced leading-edge vortex formed on the hindwing. The aerodynamic performance of the forewing is similar to that of an isolated wing irrespective of the aspect ratio of the hindwing, with a small modulating effect produced by the forewing–hindwing interactions. On the other hand, the aerodynamic performance of the hindwing is clearly affected by the interaction with the forewing's TEV. Tandem configurations with a larger aspect ratio on the forewing than on the hindwing result in a quasi-two-dimensional flow structure on the latter. This yields an 8% increase in the time-averaged thrust coefficient of the hindwing, with no change in its propulsive efficiency.

Influences of serrated trailing edge on the aerodynamic and aeroacoustic performance of a flapping wing during hovering flight

The influences of serrated trailing edge on the aerodynamic and aeroacoustic performance of a flapping wing during hovering flight are investigated using a hybrid framework of an immersed boundary Navier–Stokes solver for the flow field and the Ffowcs Williams–Hawkings (FW–H) analogy for the sound field. A rigid rectangular wing with an aspect ratio of 2 undergoes pitching and stroke motions at a Reynolds number (Re) of 310 and a Mach number (M) of 0.012. Simulations are conducted by varying the dimensionless wavenumber k* from 2π to 10π and wave amplitude 2h* from 0.25 to 1.0. We find that at k*=8π and 2h*=1.5 (D4), the average sound power level is reduced by up to 6.8 dB within the Strouhal number (St) between 2.0 and 4.0 compared to that of a plain trailing edge while the lift coefficient is maintained. The directivity at St = 0.2, St = 0.4, St = 2.2, and St = 2.4 is discussed. It is found that the serrations of D4 do not affect the directivity for the first two frequencies and significantly reduce the magnitude of the directivity for the last two frequencies. The serrations of D4 considerably alter the flow field near the wing surface and reduced the surface pressure fluctuations near the wing tip, leading to the noise reduction. The lift coefficient of D4 is not significantly changed, because the reduction in the pressure-contributed lift is compensated by an increase in the shear stress-contributed lift. The serrations with higher 2h* and k* have larger shear stress-contributed lift.

Numerical Analysis of the Effect of Flexibility on the Propulsive Performance of a Heaving Hydrofoil Undergoing Sinusoidal and Non-Sinusoidal Motions

Abstract Numerical simulations of fluid-structure interaction (FSI) on an elastic foil heaving with constant amplitude in freestream flow are carried out at a low Reynolds number of 20,000. The commercial software STAR-CCM+ is employed to solve the flow field and the large-scale passive deformation of the structure. The results show that introducing a certain degree of flexibility significantly improves the thrust and efficiency of the foil. For each Strouhal number St considered, an optimal flexibility exists for thrust; however, the propulsive efficiency keeps increasing with the increase in flexibility. The visualisation of the vorticity fields elucidates the improvement of the propulsive characteristics by flexibility. Furthermore, the mechanism of thrust generation is discussed by comparing the time-varying thrust coefficient and vortex structure in the wake for both rigid and elastic foils. Finally, in addition to sinusoidal motions, we also consider the effect of non-sinusoidal trajectories defined by flattening parameter S on the propulsive characteristics for both rigid and elastic foils. The non-sinusoidal trajectories defined by S=2 are associated with the maximum thrust, and the highest values of propulsive efficiency are obtained with S=0.5 among the cases considered in this work.