Propulsive performance and flow field characteristics of a 2-D flexible fin with variations in the location of its pitching axis

The thrust coefficients and propulsive efficiency of a two-dimensional flexible fin with heaving and pitching motion were computed using FLUENT. The effect of different locations of the pitching axis on propulsive performance was examined using three deflexion modes which are respectively, modified Bose mode, cantilever beam with uniformly distributed load and cantilever beam with non-uniformly distributed load. The results show that maximum thrust can be achieved with the pitching axis at the trailing edge, but the highest propulsive efficiency can be achieved with the pitching axis either 1/3 of the chord length from the leading edge in modified Bose mode, or 2/3 of the chord length from the leading edge in cantilever beam mode. At the same time, the effects of the Strouhal number and maximal attack angle on the hydrodynamics performance of the flexible fin were analyzed. Parameter interval of the maximum thrust coefficient and the highest propulsive efficiency were gained. If the Strouhal number is low, high propulsive efficiency can be achieved at low αmax , and vice versa.

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.

Baseball pitching kinematics,joint loads,and injury prevention

There is a need for the prevention of upper extremity injuries that affect a large number of competitive baseball players.Currently available evidence alludes to three possible ways to prevent these injuries:1) regulation of unsafe participation factors,2) implementation of exercise intervention to modify suboptimal physical characteristics,and 3) instructional intervention to correct improper pitching techniques.Of these three strategies,instruction of proper pitching technique is under-explored as a method of injury prevention.Therefore,the purpose of this review was to explore the utility of pitching technique instruction in prevention of pitching-related upper extremity injuries by presenting evidence linking pitching technique and pitching-related upper extremity injuries,as well as identifying considerations and potential barriers in pursuing this approach to prevent injuries.Various kinematic parameters measured using laboratory-based motion capture system have been linked to excessive joint loading,and thus pitching-related upper extremity injuries.As we gain more knowledge about the influence of pitching kinematics on joint loading and injury risk,it is important to start exploring ways to modify pitching technique through instruction and feedback while considering the specific skill components to address,mode of instruction,target population,duration of program,and ways to effectively collaborate with coaches and parents.

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.

Forecasting the underground waters regime in the pitching aquifers in Huainan mining area

Huainan area is an important coal base of the east of China. In the early part of the 1980s, the study of the underground waters dynamic state in the area was gradually paid close attention to. This paper introduces the observation system of the groundwater dynamic state in the multilayered pitching aquifer, and expounds the hydrogeologic feature and the waterpower relations among aquifers. Furthermore, based on the analysis of the relations of the groundwater dynamic state to surface water, meteoric water and mining shaft outflow rate, this paper establishes main water filled aquifers of mining shaft (C 3-1 ,C 3-2 ,C 3-3 and O 2).In the light of the actual situation of the greatly changing aquifer occurrence and steep dip angle, the “two layer space curved surface seepage model" and the calculating step are all suggested. Since 1991,the groundwater dynamic state of the next year has been predicted (numerical simulation) every year. Contracting with the measured data, we gain a relatively ideal effect.

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.

The Investigation of the Effect of Heaving and Pitching on Wave-Induced Vertical Hull Vibration of a Container Ship in Regular Waves

The aim of this paper is to investigate the effect of heaving and pitching of ship motion due to springing bending moment. The investigation was conducted both experimentally and validated theoretically. Series of experiment were carried out using a container model-ship of which length was 3 meter, and the possibility of the so-called nth resonant springing vibration is tested by taking n from n = 2 to n = 4. The bending moment due- to vibration is also measured. The following conclusions were obtained： （l） Occurance of the higher order resonant vibration between 2nd-4th is recognized experimentally; （2） The results indicated that heaving and pitching of ship motion influenced the springing bending moment accurately.

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.

Application of the Grey topological method to predict the effects of ship pitching

Ship motion,with six degrees of freedom,is a complex stochastic process.Sea wind and waves are the primary influencing factors.Prediction of ship motion is significant for ship navigation.To eliminate errors,a path prediction model incorporating ship pitching was developed using the Gray topological method,after analyzing ship pitching motions.With the help of simple introduction to Gray system theory,we selected a group of threshold values.Based on an analysis of ship pitch angle sequences over 40 second intervals,a Grey metabolism GM(1,1) model was established according to the time-series which every threshold corresponded to.Forecasting future ship motion with the GM(1,1) model allowed drawing of the forecast curve with effective forecasting points.The precision of the test results show that the model is accurate,and the forecast results are reliable.

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.

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.

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.

Numerical investigation of an advanced aircraft model during pitching motion at high incidence

An unsteady Reynolds averaged Navier–Stokes(URANS) method combined with a rigid dynamic mesh technique was developed to simulate unsteady flows around complex configurations during pitching motion. First, a test case with the NACA0012 airfoil was selected to validate the numerical methods and our in-house codes. Then, we evaluated the unsteady flows around an advanced aircraft model during harmonic pitching motion at high incidence. The effects of pitching motion on the hysteresis of aerodynamic force, the evolution of the leading-edge vortex, and the distribution of pressure on the model's surface were analyzed in detail. The roles of several significant parameters such as the reduced frequency and pitching amplitude were revealed. Several conclusions were found: pitching motion would delay the initiation of the leading-edge vortex, strengthen the vorticity, postpone the occurrence of vortex breakdown, and weaken the massively separated flows, thus causing additional aerodynamic force. Two categories of critical reduced frequency have been found, which divide the influence of reduced frequency on aerodynamic force into three stages, called the linear increasing range, slowly increasing range, and constant range. The first-order phase lag between the aerodynamic force and the incidence is a constant that is independent of the amplitude when the reduced frequency is sufficiently high. A scaled maximum value of C_L is proposed; it depends only on the reduced frequency(instead of the amplitude), and increases linearly when the reduced frequency is sufficiently low.