Reynolds-number scaling analysis on lift generation of a flapping and passive rotating wing with an inhomogeneous mass distribution

Insects usually fly by passively rotating wings,which has been applied to the design of flapping-wing Micro-Air Vehicles(MAVs)to reduce mechanical complexity.In this paper,a robotic passive rotating-wing model is designed to investigate wing kinematics and lift generation,which are measured by a high-speed camera and a force transducer,respectively.In addition,flow fields are measured using the Particle Image Velocimetry(PIV).Experimental results demonstrate that passive rotating motion has a coordinative relationship with actively stroking motion.As the stroke amplitude or frequency increases,the rotating amplitude is enlarged.To characterize the active stroking motion,a driving Reynolds number Redrivingis defined,which varies from 68 to 366 in this study.Moving the gravity center of the wing towards trailing ed ge induces the increase of additional torque M,which decreases the wing rotating amplitude and promotes the advance of wing rotation.We find that the timing of wing rotation is gradually delayed and the mean lift coefficient C^(-)_(L)monotonously decreases as Redrivingincreases.By increasing the additional torque M,C^(-)_(L)is slightly improved and approaches to the lift coefficient of a real fruit fly at driving Re approximately equal to 230.The instantaneous lifts combined with the vortical structures further demonstrate that the lift generation associated with wing rotation is mainly attributed to the growth of the LeadingEdge Vortex(LEV)and the passive wake capture mechanism.Passive wake capture is influenced by LEV,reversal stroke motion and wing additional torque together,which can only maintain the lift at a high level for a considerable period.The high-lift generation mechanisms of flapping and passive rotating flight could shed light on the simplified design of MAVs and the improvement of their aerodynamic performance.

Passive scalar mixing induced by the formation of compressible vortex rings

This study aims to determine the relationship between the physical features of a compressible vortex and the mixing process.Such relationship is of significant importance to design combustors that can achieve optimal or most effective mixing.The passive scalar mixing induced by the formation of a canonical compressible vortex ring(CVR)generated at the end of a shock tube is investigated by using numerical simulation.In addition,the method of finite-time Lyapunov exponent(FTLE)field are detected to identify the region of CVR,as well as to analyze the passive scalar mixing during the CVR formation.As the CVR rolls up,the ambient fluid outside the shock tube is entrained into the ring.The entrainment fraction(the mass of entrained fluid to the total mass of CVR)is found to strongly depend on two features of CVRs.One is the compressibility of CVRs,which is characterized by the Mach number of the incident shock denoted by Mach number(Ma).The other is pinch-off of CVRs,which happens at a certain timescale with narrow range of 2–4.As Ma increases,the entrainment fraction of the leading CVR decreases linearly due to smaller vortex core and weaker radial diffusion of vorticity generated by larger compressibility.After CVRs pinch off,trailing vortices appear and show less effective at entrainment than the leading CVRs do.Moreover,the tendency of the rate of entrainment is examined.The results indicate that increasing compressibility and total fluid flux are in favor of the rate of entrainment but restrain the entrainment fraction of total jet.

Scaling analysis of the circulation growth of leading-edge vortex in flapping flight

In this paper,an experiment of a robotic model at Reynolds number of approximately 240 is performed with the aim of establishing a scaling law for describing the circulation growth of the leading-edge vortex(LEV)on a flapping wing.Three typical modes of wing rotation,i.e.,advanced,symmetric,and delayed modes,are considered to examine the effects of wing rotation on the scaling formation of LEV.The streamwise velocity fields of the LEV along the span of the wing are measured by particle image velocimetry technique.Experimental results demonstrated that a spirally three dimensional(3D)LEV with spanwise distribution of circulation rolls up on the upper surface of wing and the circulation of LEV usually obtains the peak before the end of wing stroke.Based on the concept of vortex formation time,the formation time of the 3D LEV are defined in two distinct manners.One(denoted by T∗LEV)is defined based on the LEV circulation,and the other(denoted by T∗∗LEV)is defined based on the wing kinematics.It is found that T∗∗LEV increases monotonously during the upstroke and downstroke,whereas T∗LEV generally arrives peaks and then decreases.The peak value of T∗LEV indicates the formation number of LEV,which stays in the range of 2.5–5.5,agrees with the scaling formation number predicted by other vortices.Moreover,the mode of wing rotation plays a controllable role in the formation number of LEV by modulating the characteristic length scale that feeds the formation of LEV.After reaching the formation number,the LEVs stably remain attached on the flapping wing and even further grow at some spanwise locations because of vorticity transport.Furthermore,the linear relationship between T∗LEV and T∗∗LEV before reaching the formation number can suggest a potential model for predicting the circulation growth of LEV based on wing kinematics.

雷诺数和施密特数对激波-气泡相互作用中变密度混合的影响

惯性约束聚变、水动力空化侵蚀和微观尺度激波加速流动中的激波-气泡相互作用(SBI)构型处于高黏度(低雷诺数)或低扩散率(高施密特数)环境中,其混合性能尚不清楚.通过测定宽范围内的粘度和扩散系数,采用高分辨率数值模拟研究了雷诺数Re和施密特数Sc对SBI流动结构和混合行为的影响.次级斜压涡度(SBV)增长明显受雷诺数的影响,表现为斜压涡和黏性耗散之间的生长抑制涡度动力学平衡.混合速率受施密特数的影响,标度为χ^(∗)=β·Sc^(−α),其中系数β∼Re−0.2和标度指数α∼Re−0.385.混合标度表明,较高雷诺数下的SBV拉伸增强导致混合速率对施密特数的依赖性减弱,这可能为实际应用中的混合增强设计开辟新的途径.

Lagrangian analysis of the fluid transport induced by the interaction of two co-axial co-rotating vortex rings

In this paper,the fluid transport in the interaction of two co-axial co-rotating vortex rings are investigated.Vortex rings are generated using the piston-cylinder apparatus,and the resulting velocity fields are measured using digital particle image velocimetry.The interaction process is analysed by means of vorticity contour,as well by investigation of the Lagrangian coherent structures(LCSs)defined by the ridges of the finite-time Lyapunov exponent(FTLE).Experimental results demonstrate that two types of vortex interaction are identified,namely strong and weak interactions,respectively.For the strong interaction,the Lagrangian boundaries of the two vortex rings are merged together and form a flux window for fluid transport.For weak interaction,only the Lagrangian drift induced by the motion of the front vortex ring is observed and affects the Lagrangian boundary of the rear vortex ring.Moreover,the fluids transported in the strong interaction carry considerable momentum but no circulation.By contrast,there are nearly no fluxes occurring in the weak interaction.By tracking the variations of circulation and impulse occupied by the separated regions distinguished by the LCSs,it is found that the circulation nearly has no change,but the impulse occupied by vortex core region has significant change.In the strong interaction,the impulse of rear vortex ring decreases but the impulse of the front vortex ring increases.Based on the impulse law,it is speculated that the fluid force generated by the formation of the rear vortex rings can be enhanced.Therefore,the strong interaction between wake vortices can actually improve the propulsive efficiency of the biological systems by operating the formation of large-scale vortices.