Advantages of a Biomimetic Stiffness Profile in Pitching Flexible Fin Propulsion

The use of oscillating flexible fins in propulsion has been the subject of several studies in recent years, but attention israrely paid to the specific role of stiffness profile in thrust production.Stiffness profile is defined as the variation in localchordwise bending stiffness (EI) of a fin, from leading to trailing edge.In this study, flexible fins with a standard NACA0012shape were tested alongside fins with a stiffness profile mimicking that of a Pumpkinseed Sunfish (Lepomis gibbosus).The finswere oscillated with a pitching sinusoidal motion over a range of frequencies and amplitudes, while torque, lateral force andstatic thrust were measured.Over the range of oscillation parameters tested, it was shown that the fin with a biomimetic stiffness profile offered a significantimprovement in static thrust, compared to a fin of similar dimensions with a standard NACA0012 aerofoil profile.Thebiomimetic fin also produced thrust more consistently over each oscillation cycle.A comparison of fin materials of different stiffness showed that the improvement was due to the stiffness profile itself, andwas not simply an effect of altering the overall stiffness of the fin.Fins of the same stiffness profile were observed to follow thesame thrust-power curve, independent of the stiffness of the moulding material.Biomimetic fins were shown to produce up to26% greater thrust per watt of input power, within the experimental range.

The Effect of Body Pitching on Leg-Spring Behavior in Quadruped Running

In this paper we investigated how the running speed would affect the dynamics of body pitching, and whether body inertiais important for animals. Passive trotting of spring-mass model and passive bounding of spring-beam model were studied atdifferent speeds for different sets of body parameters respectively. Furthermore, different body inertias were used in bounding.We found that running speed exerts effect on leg performance by means of centrifugal force. The centrifugal force can be understoodas an enhancement to the natural frequency of the spring-mass system. The disadvantage of body pitching may beoffset by the great increase in centrifugal force at high speed. The results also reveal that body mass distribution might not be themain reason for the difference in maximal running speeds of different animals.

Lagrangian-based investigation of the transient flow structures around a pitching hydrofoil

The objective of this paper is to address the transient flow structures around a pitching hydrofoil by com- bining physical and numerical studies. In order to predict the dynamic behavior of the flow structure effectively, the Lagrangian coherent structures （LCS） defined by the ridges of the finite-time Lyapunov exponent （FTLE） are utilized under the framework of Navier-Stokes flow computations. In the numerical simulations, the k-w shear stress trans- port （SST） turbulence model, coupled with a two-equation F-Reo transition model, is used for the turbulence closure. Results are presented for a NACA66 hydrofoil undergoing slowly and rapidly pitching motions from 0° to 15° then back to 0° at a moderate Reynolds number Re = 7.5 × 105. The results reveal that the transient flow structures can be observed by the LCS method. For the slowly pitching case, it consists of five stages： quasi-steady and laminar, transition from laminar to turbulent, vortex development, large-scale vortex shedding, and reverting to laminar. The observation of LCS and Lagrangian particle tracers elucidates that the trailing edge vortex is nearly attached and stable during the vortex development stage and the interaction between the leading and trailing edge vortex caused by the adverse pres- sure gradient forces the vortexes to shed downstream during the large-scale vortex shedding stage, which corresponds to obvious fluctuations of the hydrodynamic response. For the rapidly pitching case, the inflection is hardly to be observed and the stall is delayed. The vortex formation, interaction, and shedding occurred once instead of being repeated three times, which is responsible for just one fluctuation in the hydrody- namic characteristics. The numerical results also show that the FTLE field has the potential to identify the transient flows, and the LCS can represent the divergence extent of infinite neighboring particles and capture the interface of the vortex region.

Effect of the asymmetric geometry on the wake structures of a pitching foil

The two-dimensional wake produced by a time-periodic pitching foil with the asymmetric geometry is investigated in the present work. Through numerically solving nonlinear Navier–Stokes equations, we discuss the relationship among the kinematics of the prescribed motion, the asymmetric parameter K ranged as-1 ≤ K ≤ 1, and the types of the wakes including the mP＋nS wake, the B′enard–von K′arm′an wake, the reverse B′enard–von K′arm′an wake, and the deviated wake.Compared with previous studies, we reveal that the asymmetric geometry of a pitching foil directly affects the foil＇s wake structures. The numerical results show that the reverse B′enard–von K′arm′an wake is easily deviated at K 〈 0, while the symmetry-breaking of the reverse B′enard–von K′arm′an wake is delayed at K 〉 0. Through the vortex dynamic method,we understand that the initial velocity of the vortex affected by the foil＇s asymmetry plays a key role in the deviation of the reverse B′enard–von K′arm′an wake. Moreover, we provide a theoretical model to predict the wake deviation of the asymmetric foil.

Liquefied Natural Gas Tanks for Suppressing Pitching Motions of FLNG Facility

Floating liquefied natural gas (FLNG) facility using partially filled tanks for control of pitch motion response to wave-exciting forces is investigated in this paper. The governing equations for sloshing analysis of rectangular tanks under pitch motion excitation are first established, then the spatial (boundary- value) partial derivatives are approximated by finite differences. The uncoupled pitch equation of FLNG is derived by assuming that pitch is uncoupled from other modes of vibration. By using state-space model to represent fluid-memory effect, the pitch equation can be transformed to first- order ordinary differential equations which can be solved with sloshing equations simultaneously with the given initial conditions. By using the proposed coupling model for FLNG facility and the liquefied natural gas (LNG) tanks, the performance of partially filled tanks for suppressing pitching motions of FLNG facility is numerically assessed. The parametric studies on the example FLNG show that there is a beneficial filling level by which the pitch motion of FLNG can be considerably reduced.

Pitching for Success

Tsinghua University's Schwarzman College buzzed with academics, professionals, entrepreneurs and investors on May 26 this year. They were all there for the final of Rente & Silk Africa Week: African Startup Pitch Competition, where business solution ideas with impact on China-Africa development were on show.

Dynamic response of liquid-filled rectangular tank with elastic appendages under pitching excitation

Nonlinear dynamics of liquid-filled rectangular tank with elastic appendages are studied. Based on the assumption of ideal fluid, the coupling dynamic equations of rigid tank, elastic appendages and liquid fuel are derived using H-O principle. In the case of pitch excitation, the modified potential function and wave height function are introduced to describe the moving boundary of fluid, then Galerkin＇s method is used to discretize the dynamic equations into ordinary differential equations. The natural frequencics of the coupling system are formulated in liquid depth, the length of the tank, etc. The formulae are confirmed by numerical simulations, which also show that the effects of liquid and elastic appendages on the attitude angular of rigid.

ANALYSIS OF DYNAMIC FLOW BEHAVIOR IN PITCHING MANEUVER

The dynamic flow behavior during pitching maneuver is related to the dynamic wash effect induced by the motion of the object. The dynamic hysteresis effect dueto the pivot position moving back is similar to that due to the increase in pitching rate.During the aircraft pitching up, a strong dynamic hysteresis appears on the canard but another dynamic 'advanced' effect occurs on the horizontal tail. So the stall on the canardwould occur at a higher angle of attack but the stall on the tail would appear at a lower an, gle of attack. The dynamic hysteresis is also affected by the 'heredity' effect relating tothe initial conditions besides the dynamic wash effect.

Effect of the vortical structures on the hydrodynamic performance of a pitching hydrofoil

The objective is to study the vortical structural behaviors of a transient pitching hydrofoil and their effects on the hydrodynamic performance. The pitching motion of the hydrofoil is set to pitch up with an almost constant rate from 5° to 15° and then back to 5°, with the Reynolds number 4.4×10^(5) and the frequency 2 Hz. The results show that the main coherent structures around the pitching hydrofoil include small-scale laminar separation bubble (LSB), large-scale second vortex (SV) and trailing edge vortex (TEV) which are all vortical. The relationship between the vortical structure and the lift is investigated with the finite-domain impulse theory. It indicates that the major part of the lift is contributed by the LSB, whereas the shedding and the formation of the SV and TEV cause the fluctuation of the lift. The proper orthogonal decomposition (POD) method is applied to capture the most energetic modes, revealing that the LSB mode occupies a large amount of energy in the flow field. The dynamic mode decomposition (DMD) method accurately extracts the dominant frequency and modal characteristics, with the first mode corresponding to the mean flow, the second mode corresponding to the LSB structure and the third and fourth modes corresponding to the vortex shedding.

Stable Vertical Takeoff of an Insect-Mimicking Flapping-Wing System Without Guide Implementing Inherent Pitching Stability

We briefly summarized how to design and fabricate an insect-mimicking flapping-wing system and demonstrate how to implement inherent pitching stability for stable vertical takeoff. The effect of relative locations of the Center of Gravity （CG） and the mean Aerodynamic Center （AC） on vertical flight was theoretically examined through static force balance considera- tion. We conducted a series of vertical takeoff tests in which the location of the mean AC was determined using an unsteady Blade Element Theory （BET） previously developed by the authors. Sequential images were captured during the takeoff tests using a high-speed camera. The results demonstrated that inherent pitching stability for vertical takeoff can be achieved by controlling the relative position between the CG and the mean AC of the flapping system.

Physical analysis and numerical simulation for the dynamic behaviour of vehicles in pitching oscillations or rocking motions

Analytical methods of nonlinear dynamics and numerical simulations for the cou-pling equations of Navier-Stokes and flight mechanics are used to study the dynamic behaviour of pitching motions of reentry capsules with the variation of Mach number, and rocking motions of swept wings with the variation of angle of attack. Conditions under which the dynamic instability, Hopf bifurcation and saddle-node bifurcation occur are obtained. The node-saddle-node topological structure in the phase portrait, i.e. the state of bi-attractors (attracting basins) is described. The evolving process of dynamic behaviour and flow fields are given. The theories are compared with some numerical simulations conducted by the authors. Besides, some verifiable experi-mental results are cited. The agreement between them is very well.

NUMERICAL STUDY OF THE PITCHING MOTIONS OF SUPERCAVITA-TING VEHICLES

The pitching motions of supercavitating vehicles could not be avoided due to the lost water buoyancy. In order to have some insight for the design of the supercavitating vehicles, the fixed frequency and free pitching motions are investigated. A numerical predicting method based on the relative motion principle and the non-inertia coordinate system is proposed to simulate the free pitching motions of supercavitating vehicles in the longitudinal plane. Homogeneous and two fluid multiphase models are used to predict the natural and the ventilated supercavitating flows. In the fixed frequency pitching motions, a variety of working conditions are considered, including the pitching angular velocities and the supercavity scales and the results are found to be consistent with the available experimental results in literature. The mesh deformation technology controlled by the moment of momentum equation is adopted to study the free pitching motions and finally to obtain the planing states proposed by Savchenko. The numerical method is validated for predicting the pitching motions of supercavitating vehicles and is found to enjoy better calculation efficiency as comparing with the mesh regeneration technology.

EXPERIMENTAL STUDY OF VENTILATED SUPERCAVITIES WITH A DYNAMIC PITCHING MODEL

An investigation of the ventilated supercavitation for a supercavitating vehicle pitching up and down in the supercavity was carded out in a high-speed water tunnel. The emphasis is laid on the understanding of the interaction of the vehicle aft body with the cavity boundary. The flow characteristics were measured and the stability of supercaviting flow with different pitching frequencies and amplitudes was analyzed. In particular, the objectives of this study are to understand the effect of the impact upon the cavity distortion, and to quantify the impact process by investigating the evolution of the pressure inside the cavity and then the loads on the vehicle during the pitching motion. It is also shown that the evolution of the pressure detected in different,as inside the supercavity, is coherent and uniform during the periods of the pitching motion. This study is of direct relevance to reliable and accurate prediction of hydrodynamic loads associated with the slamming and impact on supercavitating vehicles.

Experimental and numerical investigation of threedimensional vortex structures of a pitching airfoil at a transitional Reynolds number

This research examines the vortex behaviors and aerodynamic forces in dynamic stall phenomena at a transitional Reynolds number(Re=90000)using experimental and numerical approaches.Periodic sinusoidal pitching motion at two different reduced frequencies is used to achieve the dynamic stall of a NACA 0012 airfoil.Several leading edge vortices form and detach in the dynamic stall stage.The flow then quickly transitions to a full separation zone in the stall stage when the angle of attack starts to decrease.There is discrepancy between the phaseaveraged and instantaneous flow field in that the small flow structures increased with angle of attack,which is a characteristic of the flow field at the transitional Reynolds number.The interaction between the streamwise vortices in the three-dimensional numerical results and the leading edge vortex are the main contribution to the turbulent flow.In addition,the leading edge vortex that supplies vortex lift is more stable at higher reduced frequency,which decreases the lift fluctuation in the dynamic stall stage.The leading edge vortex at higher reduced frequency is strong enough to stabilize the flow,even when the airfoil is in the down-stroke phase.

Supersonic flow over a pitching delta wing using surface pressure measurements and numerical simulations

Experimental and numerical methods were applied to investigating high subsonic and supersonic flows over a 60°swept delta wing in fixed state and pitching oscillation. Static pressure coefficient distributions over the wing leeward surface and the hysteresis loops of pressure coefficient versus angle of attack at the sensor locations were obtained by wind tunnel tests. Similar results were obtained by numerical simulations which agreed well with the experiments. Flow structure around the wing was also demonstrated by the numerical simulation. Effects of Mach number and angle of attack on pressure distribution curves in static tests were investigated. Effects of various oscillation parameters including Mach number, mean angle of attack, pitching amplitude and frequency on hysteresis loops were investigated in dynamic tests and the associated physical mechanisms were discussed. Vortex breakdown phenomenon over the wing was identified at high angles of attack using the pressure coefficient curves and hysteresis loops, and its effects on the flow features were discussed.

Individual influence of pitching and plunging motions on flow structures over an airfoil during dynamic stall

The individual influence of pitching and plunging motions on flow structures is studied experimentally by changing the phase lag between the geometrical angle of attack and the plunging angle of attack.Five phase lags are chosen as the experimental parameters,while the Strouhal number,the reduced frequency and the Reynolds number are fixed.During the motion of the airfoil,the leading edge vortex,the reattached vortex and the secondary vortex are observed in the flow field.The leading edge vortex is found to be the main flow structure through the proper orthogonal decomposition.The increase of phase lag results in the increase of the leading edge velocity,which strongly influences the leading edge shear layer and the leading edge vortex.The plunging motion contributes to the development of the leading edge shear layer,while the pitching motion is the key reason for instability of the leading edge shear layer.It is also found that a certain increase of phase lag,around 34.15°in this research,can increase the airfoil lift.

Effects of blade aspect ratio and taper ratio on hovering performance of cycloidal rotor with large blade pitching amplitude

In recent years, a lot of research work has been carried out on the cycloidal rotors. However, it lacks thorough understanding about the effects of the blade platform shape on the hover efficiency of the cycloidal rotor, and the knowledge of how to design the platform shape of the blades. This paper presents a numerical simulation model based on Unsteady ReynoldsAveraged Navier–Stokes equations(URANSs), which is further validated by the experimental results. The effects of blade aspect ratio and taper ratio are analyzed, which shows that the cycloidal rotors with the same chord length have quite similar performance even though the blade aspect ratio varies from a very small value to a large one. By comparing the cycloidal rotors with different taper ratios, it is found that the rotors with large blade taper ratio outperform those with small taper ratio. This is due to the fact that the blade with larger taper ratio has longer chord and hence better efficiency. The analysis results show that the unsteady aerodynamic effects due to blade pitching motion play a more important role in the efficiency than the blade platform shape. Therefore we should pay more attention to the blade airfoil and pitching motion than the blade platform shape.The main contributions of this paper include: the analysis of the effects of aspect ratio and taper ratio on the hover efficiency of cycloidal rotor based on both the experimental and numerical simulation results; the finding of the main influencing factors on the hover efficiency; the qualitative guidance on how to design the blade platform shape for cycloidal rotors.

Pitching Moment Generation in an Insect-Mimicking Flapping-Wing System

Unlike birds, insects lack control surfaces at the tail and hence most insects modify their wing kinematics to produce control forces or moments while flapping their wings. Change of the flapping angle range is one of the ways to modify wing kinematics, resulting in relocation of the mean Aerodynamic force Center （mean AC） and finally creating control moments. In an attempt to mimic this feature, we developed a flapping-wing system that generates a desired pitching moment during flap- ping-wing motion. The system comprises a flapping mechanism that creates a large and symmetric flapping motion in a pair of wings, a flapping angle change mechanism that modifies the flapping angle range, artificial wings, and a power source. From the measured wing kinematics, we have found that the flapping-wing system can properly modify the flapping angle ranges. The measured pitching moments show that the flapping-wing system generates a pitching moment in a desired direction by shifting the flapping angle range. We also demonstrated that the system can in practice change the longitudinal attitude by generating a nonzero pitching moment.

Numerical studies of the hysteresis in locomotion of a passively pitching foil

The direct-forcing fictitious domain method is extended to simulate the locomotion of a passively pitching foil. Our study focuses on the hysteresis phenomenon that the critical frequency for the reverse of the locomotion direction of the wing in case of decreasing frequency is smaller than that in case of increasing frequency. In our simulations, the hysteresis phenomenon is produced by imposing different initial conditions at a same frequency. Our results indicate that the ratio of the heaving amplitudes of two foil edges is crucial to the direction of the foil＇s horizontal motion, and the amplitude of the leading edge is generally smaller. The critical frequencies for the reverse of the locomotion direction are increased, when the foil-fluid density ratio is decreased or the spring constant is increased. The critical frequencies in the bi-stability regime also depend on the initial velocity imposed, and the hysteresis loop generally becomes larger if the initial velocities are closer to the terminal locomotion velocities of the foil.

Variable slip window technology in transition detection on pitching airfoil

In the pitching motion,the unsteady transition and relaminarization position plays an important role in the dynamic characteristics of the airfoil.In order to facilitate the computer to automatically and accurately calculate the position of the transition and relaminarization,a Variable Slip Window Technology(VSWT)suitable for airfoil dynamic data processing was developed using the S809 airfoil experimental data in this paper and two calculation strategies,i.e.,global strategy and single point strategy,were proposed:global strategy and single point strategy.The core of the VSWT is the selection of the window function h and the parameters setting in the h function.The effect of the VSWT was evaluated using the dimensionless pulse strength value(INB),which can be used to evaluate the signal characteristics,of the root mean square(RMS)value of the fluctuating pressure.It is found that:the h function characteristics have a significant influence on the VSWT.The suitable functions are Hn function constructed in this paper and step function.For the left boundary of the magnified area,the step function can obtain the largest INB value,but the robustness is not good.The H1 function(Gaussian-like function,n=1)can show higher robustness while ensuring a large INB value.The two computing strategies,which are single point strategy and global strategy,have their own advantages and disadvantages.The former strategy,that is the single point strategy,can achieve a higher INB value,but the RMS magnification at the feature position needs to be known in advance.Although the INB value obtained by the latter strategy,that is the global strategy,is slightly smaller than the calculation results of the former strategy,it is not necessary to know the RMS magnification at the feature position in advance.So the global strategy has better robustness.The experimental data of NACA0012 airfoil was used to further validate the developed VSWT in this paper,and the results show that the VSWT developed in this paper can still double the INB value of the transition/relaminarization position.The VSWT developed in this paper has certain practicability,which is convenient for the computer to automatically determine the transition/relaminarization characteristics.