Characteristics of vortex formation and thrust performance in drag-based paddling propulsion

Propulsive capability of manta rays' flapping pectoral fins has inspired many to incorporate these fins as propulsive mechanisms for autonomous underwater vehicles. In particular, geometrical factors such as sweep angle have been postulated as being influential to these fins' propulsive capability, specifically their thrust generation. Although effects of sweep angle on static/flapping wings of aircrafts/drones have been widely studied, little has been done for underwater conditions. Furthermore, the findings from air studies may not be relatable to the underwater studies on pectoral fins because of the different Reynolds number (compared to the flapping wings) and force generation mechanism (compared to the static wings). This paper aims to establish a relationship between the sweep angle and thrust generation. An experiment was conducted to measure the thrust generated by 40 fins in a water channel under freestream and still water conditions for chord Reynolds number between 2.2 × 104 and 8.2 × 104. The fins were of five different sweep angles (0 deg, 10 deg, 20 deg, 30 deg, and 40 deg) that were incorporated into eight base designs of different flexibility characteristics. The results showed that the sweep angle (within the range considered) may have no significant influence on these fins' thrust generation, implying no significant effects on thrust under uniform flow condition and on the maximum possible thrust under still water. Overall, it can be concluded that sweep angle may not be a determinant of thrust generation for flapping pectoral fins. This knowledge can ease the decision-making process of design of robots propeled by these fins.

This paper investigates the unsteady flowfield characteristics around three-dimensional insect flapping motion under forward flight conditions. A realistic wing trajectory, called the figure-of-eight motion, is extracted from a blowfly's (phormia regina) tethered flight experiment under a freestream velocity of 2.75 m/s. In the authors' preliminary research [Lee, J., Kim, J., and Kim, C., Numerical Study on the Unsteady-Force-Generation Mechanism of Insect Flapping Motion, AIAA Journal, Vol. 46, No. 7, 2008, pp. 1835―1848. doi:10.2514/1.35646], the two-dimensional blowfly's wing motion was computationally investigated, and the results revealed very interesting and distinctive vortical flowfields, which provide a decisive clue in understanding the rapid maneuverability of insects' flight. On the line of continuous efforts, the present work investigates the role of three-dimensional vortical structure in unsteady aerodynamic force generation. Detailed numerical simulation and analysis on three-dimensional flapping motion are conducted, and interesting flow features of insects' flapping flight are observed, such as the existence of a spanwise flow component, leading-edge vortex, wing tip vortex, trailing-edge vortex, and various forms of vortex tubes and vortex rings. It turns out that vortical structures play a crucial role in determining unsteady characteristics of lift and thrust generation. In particular, the vortex pairing and vortex staying phenomena, which have been observed in two-dimensional flapping motion, are also observed but with a more complicated pattern. On top of that, distinctive lift and thrust generation is observed owing to three-dimensional wing shape, trajectory, and vortex structure. Consequently, the results of the present work provide an important clue in understanding generation of aerodynamic force for rapid maneuverability in insects' flight.

Part 1에서 수행된 검정금파리의 “8자 운동”에 대한 해석결과는 와류들이 양력과 추력발생에 중요한 역할을 하는 것으로 나타났다. 곤충날개에서 발생되는 공기역학적 힘은 레이놀즈수와 같은 공기역학적 요소와 더불어 진동수, 운동진폭, 운동성분 등과 같은 운동학적적 요소들 또 날개의 형태 및 개수등과 같은 형태학적 요소들에 따를 것으로 생각된다. 본 연구에서는 레이놀즈수, 진동수 그리고 운동성분에 따른 양력과 추력발생을 고찰함으로써 이들이 공기역학적으로 어떤 영향을 미치는가를 조사하였다. 이로써 part 1의 결과를 물리적으로 좀 더 상세하게 설명할 수 있는 근거를 찾고자 하였다. 해석결과 “8자 운동”을 구성하는 운동성분 중 회전운동이 추력발생에 지배적인 역할을 하고 있었으며, 또한 추력발생은 반시계 방향의 회전순환과 깊은 관련이 있었다. Numerical results from the "figure-of-eight" motion of Phormia-Regina in Part 1 indicate that vortical structure and vortex dynamics do play a critical role in lift and thrust generation. The aerodynamic force generation of insects' wing could be governed by aerodynamic parameters such as Reynolds number; kinematic parameters such as frequency, amplitude, and component of the figure of eight motion; and morphological parameters such as wing shape and the number of wing. In the present work, the effects of Reynolds number, reduced frequency and motion component are investigated in detail to clarify aerodynamic characteristics of insect wing. Through numerical results and their physical interpretation, the mechanism of aerodynamic force generation is presented more clearly. Rotation turns out to be the most important component in thrust generation and subsequent counterclockwise rotational circulation is closely related with thrust generation.

Thrust generation and scaling parameters for flapping flexible wings are investigated using an integrated framework of computational fluid dynamics and structural dynamics solvers. To explore the influences of the density ratio and the effective stiffness on the thrust generation, surrogate models have been generated for a flapping thin isotropic flat Zimmerman wing in still air at = 1.5×10 3 . Time averaged thrust, bending angle, and twist show qualitatively similar behavior and increased with higher ratio between the density ratio and effective stiffness. Flexibility-induced twisting in the wing promotes the thrust generation. To further investigate the flexibility-induced thrust enhancement, plunging chordwise flexible airfoils in forward flight at = 9.0×10 3 in water are considered. Time averaged thrust increases with larger airfoil thickness, however the thinnest airfoil responded with degradation in performance when motion frequency becomes high. Finally, unified scaling parameters are proposed based on properly normalized governing equations and give a priori order of magnitude estimation of the time averaged thrust and the degree of fluid-structure coupling. The results show that these scaling parameters, given as combinations of the wing geometry, structural properties, and the motion amplitude and frequency, can be applied for both cases with different motion type, Reynolds number, and the fluid medium.

On the thrust generation and wake structures of two travelling-wavy foils

Direct numerical simulations (DNS) of flow over an NACA-0012 airfoil are performed at a low and a moderate Reynolds numbers of Re(sub c)=50 times10(exp 3) and 1times 10(exp 6). The angles of attack are 5 and 15 degrees at the low and the moderate Reynolds number cases respectively. The three-dimensional unsteady compressible Navier-Stokes equations are solved using higher order compact schemes. The flow field in the low Reynolds number case consists of a long separation bubble near the leading-edge region and an attached boundary layer on the aft part of the airfoil. The shear layer that formed in the separated region persisted up to the end of the airfoil. The roles of the turbulent diffusion, advection, and dissipation terms in the turbulent kinetic-energy balance equation change as the boundary layer evolves over the airfoil. In the higher Reynolds number case, the leading-edge separation bubble is very small in length and in height. A fully developed turbulent boundary layer is observed in a short distance downstream of the reattachment point. The boundary layer velocity near the wall gradually decreases along the airfoil. Eventually, the boundary layer separates near the trailing edge. The Reynolds stresses peak in the outer part of the boundary layer and the maximum amplitude also gradually increases along the chord.

The aerodynamic forces and flow structures of a wing of relatively small aspect ratio in some unsteady rotational motions at low Reynolds number (Re=100) are studied by numerically solving the Navier-Stokes equations. These motions include a wing in constant-speed rotation after a fast start, wing accelerating and decelerating from one rotational speed to another, and wing rapidly pitching-up in constant speed rotation. When a wing performs a constant-speed rotation at small Reynolds number after started from rest at large angle of attack (α=35°), a large lift coefficient can be maintained. The mechanism for the large lift coefficient is that for a rotating wing: the variation of the relative velocity along the wing-span causes a pressure gradient and hence a spanwise flow which can prevent the dynamic stall vortex from shedding. When a wing is rapidly accelerating or decelerating from one rotational speed to another, or rapidly pitching-up during constant speed rotation, even if the aspect ratio of the wing is small and the flow Reynolds number is low, a large aerodynamic force can be obtained. During these rapid unsteady motions, new layers of strong vorticity are formed near the wing surfaces in very short time, resulting in a large time rate of change of the fluid impulse which is responsible for the generation of the large aerodynamic force.

Among all aquatic species, mantas and rays swim by oscillating their pectoral fins; this motion is similar to other fishes in term of efficiency, but it gives better agility in turning with respect to fishes moving their caudal fin. The fin motion is featured by a travelling wave going opposite to the forward motion, producing a force thanks to momentum conservation. Another contribution to the generation of thrust is given by the generation of a vortex in correspondence of the leading edge of the fin, which pulls the fish forward thanks to the lower pressure in its centre. In literature these contributions have been highlighted, but it remains to understand which one of these two mechanisms is prevailing according to different conditions of swimming, how they affect each other and what is the influence of the two on energetical efficiency. The object of this activity is to investigate how thrust generation is influenced by geometrical characteristics of the fin, such as size, geometry and flexibility and by parameters of motion, such as speed, amplitude and frequency of fin oscillation and velocity of the travelling wave. A CFD model of the fish has been implemented in OpenFOAM, not only confirming that both upstroke and downstroke contribute positively to the forward movement according to the momentum conservation principle, but also highlighting the formation of a leading-edge vortex enhancing thrust generation. The description of how thrust generation is linked to motion parameters is simulated also coupling the CFD with a multibody to simulate the whole motion in its complexity.

Many numerical and experimental researches have been done for the unsteady flow around a flapping airfoil. The main research topics are vortex shedding, dynamic stall phenomenon, and MAV''s lift and thrust generation for the flow over a flapping airfoil. Although many researches have been studied to analyze the flow for the variation of frequency and amplitude, much research is still needed. In this study, thrust generation, wake structures, and acoustic wave propagation characteristics were studied for a flapping airfoil. The governing equation was the Navier-Stokes equation with LES turbulence model, and the Optimized High-Order Compact (OHOC) scheme and 4th order Runge-Kutta method were used. The Mach number and Reynolds number were 0.3 and 1000, respectively. The analysis of mean lift and drag coefficients showed the thrust generation characteristics according to the phase angle and the reduced frequency. The wake vortex shedding and propagation characteristics of acoustic waves could be simulated using the high order method.

Abstract. The root flow of wind turbine blades is subjected to complex physical mechanisms that influence significantly the rotor aerodynamic performance. Spanwise flows, the Himmelskamp effect, and the formation of the root vortex are examples of interrelated aerodynamic phenomena that take place in the blade root region. In this study we address those phenomena by means of particle image velocimetry (PIV) measurements and Reynolds-averaged Navier–Stokes (RANS) simulations. The numerical results obtained in this study are in very good agreement with the experiments and unveil the details of the intricate root flow. The Himmelskamp effect is shown to delay the stall onset and to enhance the lift force coefficient Cl even at moderate angles of attack. This improvement in the aerodynamic performance occurs in spite of the negative influence of the mentioned effect on the suction peak of the involved blade sections. The results also show that the vortex emanating from the spanwise position of maximum chord length rotates in the opposite direction to the root vortex, which affects the wake evolution. Furthermore, the aerodynamic losses in the root region are demonstrated to take place much more gradually than at the tip.

In this paper, large-eddy simulation of the interaction between a shock wave and the hypersonic turbulent boundary layer in a compression corner with a fixed 34° deflection angle at Ma = 6 for different Reynolds number cases is conducted. For investigating the effects of the Reynolds number for hypersonic cases, three cases where the free-stream Reynolds numbers are 14000, 20000, and 30000/mm are selected. The averaged statistics, such as the mean velocity, the skin friction, the heat flux, and the wall pressure, are used in this paper. The flow structures in the compression ramp including the shock wave and interaction region are discussed. The decomposition of the mean skin-friction drag for the flat flow is extended to be used in the compression corner. In addition, the turbulent kinetic energy is studied through the decomposition of the mean skin-friction drag for the flat-plate region and the corner region. It is found that higher Reynolds numbers would increase the turbulent kinetic energy by turbulent dissipation at the interaction region, while higher Reynolds numbers would decrease the turbulent kinetic energy by turbulent dissipation after reattachment. In addition, it is also found that the turbulent kinetic energy is larger with a higher Reynolds number and higher turbulent kinetic energy inhibits the movement from the separation point to the inflection point (x = 0 mm), which deduces larger separation bubbles.

Results from three-dimensional numerical simulation of laminar, buoyancy assisting, mixed convection airflow adjacent to a backward-facing step in a vertical rectangular duct are presented. The Reynolds number, and duct geometry were kept constant at Re = 200, AR = 8, ER = 2, and S = 1 cm. Heat flux at the wall downstream from the step was kept uniform, but its magnitude was varied to cover a Grashof number (Gr) range between 0.0 to 4000. All the other walls in the duct were kept at adiabatic condition. The flow, upstream of the step, is treated as fully developed and isothermal. The relatively small aspect ratio of the channel is selected specifically to focus on the developments of the three-dimensional mixed convection flow in the separated and reattached flow regions downstream from the step. The presented results focus on the effects of increasing the buoyancy force, by increasing the uniform wall heat flux, on the three-dimensional flow and heat transfer characteristics. The flow and thermal fields are symmetric about the duct’s centerline. Vortex generated near the sidewall, is the major contributor to the three dimensional behavior in the flow domain, and that feature increases as the Grashof number increases. Increasing the Grashof number results in an increase in the Nusselt number, the size of the secondary recirculating flow region, the size of the sidewall vortex, and the spanwise flow from the sidewall toward the center of the channel. On the other hand, the size of the primary reattachment region decreases with increasing the Grashof number. That region lifts away and partially detaches from the downstream wall at high Grashof number flow. The maximum Nusselt number occurs near the sidewalls and not at the center of the channel. The effects of the buoyancy force on the distributions of the three-velocity components, temperature, reattachment region, friction coefficient, and Nusselt number are presented, and compared with 2-D results.

<div class="htmlview paragraph">The typical aeronautical engineering approach to low Reynolds number flight studies has been to start with known high Reynolds number aerodynamic paradigms and attempt to match them by scaling to observations of birds and insects. On the other hand, the typical biological approach to natural flight aerodynamics has been to try to fit the observations of birds and insects into the typical known aerodynamic paradigms. Neither of these approaches has met with much success, and although we know more about the potential processes of natural flight, we have not been able to describe them using the framework of conventional aerodynamics. The investigation of low Reynolds number aerodynamic flows at the University of Dayton has led to a proposed new method of characterizing and describing the aerodynamics of natural flight. Lift in natural flight is theorized to be based in the spanwise flow along the curvature of a flapping wing.</div>

A numerical investigation of unsteady compressible flow in 3D converging-diverging micronozzles has been performed. The baseline model for the study is derived from the NASA / Goddard Space Flight Center MEMS-based hydrogen peroxide micro-thruster prototype. The 3D micronozzles investigated here have depths of 25μm, 50μm, 100μm, and 150μm and employ expanders with a 30 ◦ divergence half-angle. A hyperbolic-tangent function is used to model micro-valve actuation in order to simulate the start-up and shut-down sequence of the thruster. Transient micronozzle performance is characterized based on the peak throat Reynolds number achieved during the duty cycle. In this study, peak Reynolds numbers range from 160−800 and the propulsion scheme employs85% pure hydrogen peroxide as a monopropellant. Unsteady simulation results have been analyzed in order to quantify subsonic layer evolution, thrust production as a function of time, and total impulse delivered for a single micronozzle duty cycle. Micronozzle impulse efficiency has also been determined based on a theoretical maximum impulse achieved by a quasi-1D isentropic flow responding instantaneously to the actuation profile. It is found that both the flow and thrust exhibit a response ‘lag’ to the time-varying inlet pressure profile during start-up. However, residual thrust is not observed during shut-down owing to viscous forces promoting a reduction in mass flow as the valve closes. Simulation results indicate that thrust and total impulse per unit depth increase with Reynolds number and nozzle depth. However, when quantifying total impulse per unit mass of propellant consumed, performance increases are strongly correlated with nozzle depth and are much less senstitive to Reynolds number.

Thrust and total impulse performance of a SparkJet actuator are affected by pressure waves inside the cavity, so it is important to understand these effects. The two objectives of the present study are to characterize the jet performance of a SparkJet actuator and to investigate pressure waves inside the cavity and correlate them with actuator performance. To this end, a SparkJet actuator is solved numerically based on equilibrium gas assumption. Loss of thrust occurs because of the pressure drop caused by the pressure wave, flow separation at the orifice throat, and vortex above the orifice exit. A fast Fourier transform of thrust reveals pressure wave components at two natural frequencies that originate from the pressure waves inside the cavity. The reflected pressure waves inside the cavity affect natural frequencies. The pressure wave reflected in the r-axis direction is affected by the energy deposition aspect ratio which influenced the total impulse by as much as ∼3.21%. The pressure wave reflected in the z-axis direction is affected by the effective height distance. However, this rarely affects the total impulse directly. The use of an appropriate taper angle affects the total impulse by as much as ∼8.49%. Approximately, 11% of the total impulse is originated from oscillations by the reflected wave in the r-axis direction, whereas 4% of it is from the reflected wave in the z-axis direction. This work contributes to improving the design of electrode and cavity configurations for SparkJet actuators and showing the importance of oscillations made by reflected pressure waves.