Large amplitude lunate-tail theory of fish locomotion

1976 ◽  
Vol 74 (1) ◽  
pp. 161-182 ◽  
Author(s):  
M. G. Chopra
Keyword(s):  
Angle Of Attack ◽  
Leading Edge ◽  
Finite Amplitude ◽  
Dimensional Theory ◽  
Propulsive Efficiency ◽  
Suction Force ◽  
Fish Locomotion ◽  
Reduced Frequency ◽  
Accurate Comparison ◽  
Arbitrary Amplitude

The two-dimensional theory of lunate-tail propulsion is extended to motions of arbitrary amplitude, regular or irregular, so that an accurate comparison may be made with the actual lunate-tail propulsion of scombroid fishes and cetacean mammals. There is no restriction at all on the amplitude of motion but the tail's angle of attack relative to its instantaneous path through the water is assumed to remain small. The theory is applied to the regular finite amplitude motion of a thin aerofoil with a rounded leading edge to take advantage of the suction force and a sharp trailing edge to ensure smooth tangential flow past the rear tip. This can represent the vertical motions of the horizontal lunate tails of large aspect ratio with which cetacean mammals propel themselves or the horizontal undulations of the vertical lunate tails of certain fast fishes. The dependence of the thrust, the hydromechanical propulsive efficiency and the energy wasted in churning up the eddying wake on the reduced frequency, the angle of attack and the amplitude of motion is exhibited.

Effect of pectoral fin kinematics on manta ray propulsion

2018 ◽  
Vol 32 (12n13) ◽  
pp. 1840025
Author(s):  
Hao Lu ◽  
Khoon Seng Yeo ◽  
Chee-Meng Chew
Keyword(s):  
Leading Edge ◽  
Wave Model ◽  
Pectoral Fin ◽  
Long Distance ◽  
Propulsive Efficiency ◽  
Fish Locomotion ◽  
Pectoral Fins ◽  
Flow Features ◽  
Edge Vortex ◽  
Manta Ray

Recent advancement of bio-inspired underwater vehicles has led to a growing interest in understanding the fluid mechanics of fish locomotion, which involves complex interaction between the deforming structure and its surrounding fluid. Unlike most natural swimmers that undulate their body and caudal fin, manta rays employ an oscillatory mode by flapping their large, flattened pectoral fins to swim forward. Such a lift-based mode can achieve a substantially high propulsive efficiency, which is beneficial to long-distance swimming. In this study, numerical simulations are carried out on a realistic manta ray model to investigate the effect of pectoral fin kinematics on the propulsive performance and flow structure. A traveling wave model, which relates a local deflection angle to radial and azimuthal wavelengths, is applied to generate the motion of the pectoral fins. Hydrodynamic forces and propulsive efficiency are reported for systematically varying kinematic parameters such as wave amplitude and wavelengths. Key flow features, including a leading edge vortex (LEV) that forms close to the tip of each pectoral fin, and a wake consisting of interconnected vortex rings, are identified. In addition, how different fin motions alter the LEV behavior and hence affect the thrust and efficiency is illustrated.

Effect of amplitude and mean angle-of-attack on the boundary layer of an oscillating aerofoil

2008 ◽  
Vol 112 (1138) ◽  
pp. 705-713 ◽  
Author(s):  
M. R. Soltani ◽  
A. Bakhshalipour
Keyword(s):  
Boundary Layer ◽  
Transition Point ◽  
Angle Of Attack ◽  
Wind Tunnel Test ◽  
Leading Edge ◽  
Stream Velocity ◽  
Velocity Amplitude ◽  
Surface Pressure Distribution ◽  
Reduced Frequency ◽  
Hot Film

Abstract Extensive experiments were conducted to study the effect of various parameters on the surface pressure distribution and transition point of an aerofoil section used in a wind turbine blade. In this paper details of the variation of transition point on the aforementioned aerofoil are presented. The aerofoil spanned the wind-tunnel test section and was oscillated sinusoidally in pitch about the quarter chord. The imposed variables of the experiments were free stream velocity, amplitude of motion, mean angle-of-attack, and oscillation frequency. The spatial-temporal progressions of the leading-edge transition point and the state of the unsteady boundary-layer were measured using eight closely-spaced, hot-film sensors (HFS). The measurements show that: (i) Reduced frequency has a pronounced effect on the variations of the transition point. (ii) There exists a hysteresis loop in the dynamic transition location and its shape varies with the reduced frequency and mean angle-of-attack.

Numerical Study on Thrust Generation Performance of Plunging Airfoils

2013 ◽  
Vol 312 ◽  
pp. 235-238
Author(s):  
Ji Gao ◽  
Rui Shan Yuan ◽  
Ming Hui Zhang ◽  
Yong Hui Xie
Keyword(s):  
Viscous Flow ◽  
Numerical Study ◽  
Angle Of Attack ◽  
Leading Edge ◽  
Thrust Coefficient ◽  
Propulsive Efficiency ◽  
Propulsion Performance ◽  
Incompressible Viscous Flow ◽  
Thrust Generation ◽  
The Difference

In this paper, the effects of angle of attack, camber and camber location on propulsion performance of flapping airfoils undergoing plunging motion were numerically studied at Re=20000 and h=0.175. The unsteady incompressible viscous flow around four different airfoil sections was simulated applying the dynamic mesh. The results show that the time averaged thrust coefficient CTmean and propulsive efficiency η of the symmetric airfoil decrease with the increasing angle of attack, and the variation of CTmean is more obvious than that of CPmean. Both CTmean and η for NACA airfoils studied in this paper decrease with the increasing camber and the difference between the propulsion performances of different airfoils is not obvious, and the thrust generation and power of various NACA airfoils gradually increase during the downstroke and decrease during the upstroke. Under the same conditions, the airfoil with a further distance between the maximum camber location and the chord of the leading edge leads to higher propulsive efficiency.

Note on optimum propulsion of heaving and pitching airfoils from linear potential theory

2017 ◽  
Vol 826 ◽  
pp. 781-796 ◽  
Author(s):  
R. Fernandez-Feria
Keyword(s):  
Phase Shift ◽  
Potential Theory ◽  
Linear Theory ◽  
Leading Edge ◽  
Linear Potential ◽  
Thrust Coefficient ◽  
Propulsive Efficiency ◽  
Pitching Motion ◽  
Reduced Frequency ◽  
Linear Potential Theory

The conditions that maximize the propulsive efficiency of a heaving and pitching airfoil are analysed using a novel formulation for the thrust force within the linear potential theory. Stemming from the vortical impulse theory, which correctly predicts the decay of the thrust efficiency as the inverse of reduced frequency$k$for large$k$(Fernandez-Feria,Phys. Rev. Fluids, vol. 1, 2016, 084502), the formulation is corrected here at low frequencies by adding a constant representing the viscous drag. It is shown first that the thrust coefficient and propulsive efficiency thus computed agree quite well with several sets of available experimental data, even for not so small flapping amplitudes. For a pure pitching motion, it is found that the maximum propulsion efficiency is reached for the airfoil pitching close to the three-quarter chord point from the leading edge with a relatively large reduced frequency, corresponding to a relatively low thrust coefficient. According to the theory, this efficiency peak may approach unity. For smaller$k$, other less pronounced local maxima of the propulsive efficiency are attained for pitching points ahead of the leading edge, with larger thrust coefficients. The linear theory also predicts that no thrust is generated at all for a pitching axis located between the three-quarter chord point and the trailing edge. These findings contrast with the results obtained from the classical linear thrust by Garrick, with the addition of the same quasi-static thrust, which are also computed in the paper. For a combined heaving and pitching motion, the behaviour of the propulsive efficiency in relation to the pitching axis is qualitatively similar to that found for a pure pitching motion, for given fixed values of the feathering parameter (ratio between pitching and heaving amplitudes) and of the phase shift between the pitching and heaving motions. The peak propulsive efficiency predicted by the linear theory is for an airfoil with a pitching axis close to, but ahead of, the three-quarter chord point, with a relatively large reduced frequency, a feathering parameter of approximately$0.9$and a phase shift slightly smaller than $90^{\circ }$.

Hydromechanics of lunate-tail swimming propulsion

1974 ◽  
Vol 64 (2) ◽  
pp. 375-392 ◽  
Author(s):  
M. G. Chopra
Keyword(s):  
Aspect Ratio ◽  
Leading Edge ◽  
Vortex Sheet ◽  
The Body ◽  
Uniform Motion ◽  
Physical Parameters ◽  
Thrust Coefficient ◽  
Propulsive Efficiency ◽  
Reduced Frequency ◽  
General Motion

This paper investigates the non-uniform motion of a thin plate of finite aspect ratio, with a rounded leading edge and sharp trailing edge, executing heaving and pitching oscillations at zero mean lift. Such vertical motions characterize the horizontal lunate tails with which cetacean mammals propel themselves, and the same motions, turned through 90° to become horizontal motions of sideslip and yaw, characterize the vertical lunate tails of certain fast-swimming fishes. An oscillating vortex sheet consisting of streamwise and spanwise components is shed to trail behind the body and it is this additional feature of the streamwise component resulting from the finiteness of the plate that makes this study a generalization of the two-dimensional treatment of lunate-tail propulsion by Lighthill (1970). The forward thrust, the power required, the energy imparted to the wake and the hydromechanical propulsive efficiency are determined for this general motion as functions of the physical parameters defining the problem: namely the aspect ratio, the reduced frequency, the feathering parameter and the position of the pitching axis. The dependence of the thrust coefficient and propulsive efficiency on these physical parameters, for the complete range of variation consistent with the assumptions of the problem, has been depicted graphically.

On the propulsion efficiency of swimming flexible hydrofoils of finite thickness

1968 ◽  
Vol 32 (1) ◽  
pp. 29-53 ◽  
Author(s):  
J. P. Uldrick
Keyword(s):  
Kinetic Energy ◽  
Flat Plate ◽  
Finite Thickness ◽  
Leading Edge ◽  
The Body ◽  
Suction Force ◽  
Inviscid Incompressible Fluid ◽  
Reduced Frequency ◽  
Non Linear ◽  
Order Of Magnitude

This paper presents some recent theoretical results on the energy exchange between a swimming flexible two-dimensional hydrofoil of finite profile thickness and the inviscid incompressible fluid in which the body swims. The rate at which kinetic energy is transferred to the fluid by the undulating hydrofoil, the power required to maintain the prescribed motion, and the resulting power available for propulsion are calculated in terms of the thickness to chord ratio and the displacement and rate of displacement of the hydrofoil. With a small unsteady perturbation theory, the analysis is decomposed to show separately the effects of the circulatory and non-circulatory flows, both depending on the first-order terms of the unsteady perturbation velocity components. In addition, an analysis is presented showing the effect of the non-linear unsteady pressure distribution on the surface of the hydrofoil. Contrary to what might be expected, this latter effect is of the same order of magnitude for a thick rounded-nose profile as for the flat plate where the effect is concentrated at the sharp leading edge and is related to the so-called suction force. However, except for small values of the reduced frequency, the non-linear contribution is negligible in comparison with the linear contribution.New functions associated with the retarded flow in the wake are introduced and special techniques for their solution are presented, these being related to Theodorsen's function of unsteady airfoil theory for the special case of the undulating flat plate.The numerical results reveal that the kinetic energy imparted to the fluid, the power required to maintain the motion, and the resulting propulsive power, follow closely those of an infinitesimal model for small values of the reduced frequency of oscillation, but diverge somewhat from the classical thin plate analysis for large reduced frequencies. Of particular interest is the fact that a very large percentage of the power required to maintain the motion is used in the generation of the wake, whereas a very small percentage of the power available for propulsion comes from the wake. This indicates that, if some mechanism could be devised to control the wake, very high swimming efficiencies could be attained. Fish, in all probability, have been succeeding in doing this for millions of years.

Unsteady force generation and vortex dynamics of pitching and plunging aerofoils

2012 ◽  
Vol 709 ◽  
pp. 37-68 ◽  
Author(s):  
Yeon Sik Baik ◽  
Luis P. Bernal ◽  
Kenneth Granlund ◽  
Michael V. Ol
Keyword(s):  
Strouhal Number ◽  
Vortex Dynamics ◽  
Angle Of Attack ◽  
Leading Edge ◽  
Leading Edge Vortex ◽  
Reduced Frequency ◽  
Unsteady Force ◽  
Edge Vortex ◽  
Effective Angle ◽  
Flow Evolution

AbstractExperimental studies of the flow topology, leading-edge vortex dynamics and unsteady force produced by pitching and plunging flat-plate aerofoils in forward flight at Reynolds numbers in the range 5000–20 000 are described. We consider the effects of varying frequency and plunge amplitude for the same effective angle-of-attack time history. The effective angle-of-attack history is a sinusoidal oscillation in the range $\ensuremath{-} 6$ to $2{2}^{\ensuremath{\circ} } $ with mean of ${8}^{\ensuremath{\circ} } $ and amplitude of $1{4}^{\ensuremath{\circ} } $. The reduced frequency is varied in the range 0.314–1.0 and the Strouhal number range is 0.10–0.48. Results show that for constant effective angle of attack, the flow evolution is independent of Strouhal number, and as the reduced frequency is increased the leading-edge vortex (LEV) separates later in phase during the downstroke. The LEV trajectory, circulation and area are reported. It is shown that the effective angle of attack and reduced frequency determine the flow evolution, and the Strouhal number is the main parameter determining the aerodynamic force acting on the aerofoil. At low Strouhal numbers, the lift coefficient is proportional to the effective angle of attack, indicating the validity of the quasi-steady approximation. Large values of force coefficients (${\ensuremath{\sim} }6$) are measured at high Strouhal number. The measurement results are compared with linear potential flow theory and found to be in reasonable agreement. During the downstroke, when the LEV is present, better agreement is found when the wake effect is ignored for both the lift and drag coefficients.

scholarly journals Leading Edge Blowing to Mimic and Enhance the Serration Effects for Aerofoil

2021 ◽  
Vol 11 (6) ◽  
pp. 2593
Author(s):  
Yasir Al-Okbi ◽  
Tze Pei Chong ◽  
Oksana Stalnov
Keyword(s):  
Boundary Layer ◽  
Angle Of Attack ◽  
Leading Edge ◽  
Boundary Layer Separation ◽  
Shear Instability ◽  
Vortical Flow ◽  
High Angle ◽  
High Angle Of Attack ◽  
Layer Separation ◽  
Aerodynamic Performances

Leading edge serration is now a well-established and effective passive control device for the reduction of turbulence–leading edge interaction noise, and for the suppression of boundary layer separation at high angle of attack. It is envisaged that leading edge blowing could produce the same mechanisms as those produced by a serrated leading edge to enhance the aeroacoustics and aerodynamic performances of aerofoil. Aeroacoustically, injection of mass airflow from the leading edge (against the incoming turbulent flow) can be an effective mechanism to decrease the turbulence intensity, and/or alter the stagnation point. According to classical theory on the aerofoil leading edge noise, there is a potential for the leading edge blowing to reduce the level of turbulence–leading edge interaction noise radiation. Aerodynamically, after the mixing between the injected air and the incoming flow, a shear instability is likely to be triggered owing to the different flow directions. The resulting vortical flow will then propagate along the main flow direction across the aerofoil surface. These vortical flows generated indirectly owing to the leading edge blowing could also be effective to mitigate boundary layer separation at high angle of attack. The objectives of this paper are to validate these hypotheses, and combine the serration and blowing together on the leading edge to harvest further improvement on the aeroacoustics and aerodynamic performances. Results presented in this paper strongly indicate that leading edge blowing, which is an active flow control method, can indeed mimic and even enhance the bio-inspired leading edge serration effectively.

scholarly journals Towards higher aerodynamic efficiency of propeller-driven aircraft with distributed propulsion

2021 ◽  
Author(s):  
Dennis Keller
Keyword(s):  
Performance Indicator ◽  
Leading Edge ◽  
Substantial Improvement ◽  
Initial Assessment ◽  
Local Flow ◽  
Propulsive Efficiency ◽  
Thrust Distribution ◽  
Distributed Propulsion ◽  
Wing Tip ◽  
Cruise Flight

AbstractThe scope of the present paper is to assess the potential of distributed propulsion for a regional aircraft regarding aero-propulsive efficiency. Several sensitivities such as the effect of wingtip propellers, thrust distribution, and shape modifications are investigated based on a configuration with 12 propulsors. Furthermore, an initial assessment of the high-lift performance is undertaken in order to estimate potential wing sizing effects. The performance of the main wing and the propellers are thereby equally considered with the required power being the overall performance indicator. The results indicate that distributed propulsion is not necessarily beneficial regarding the aero-propulsive efficiency in cruise flight. However, the use of wing tip propellers, optimization of the thrust distribution, and wing resizing effects lead to a reduction in required propulsive power by $$-2.9$$ - 2.9 to $$-3.3\,\%$$ - 3.3 % compared to a configuration with two propulsors. Adapting the leading edge to the local flow conditions did not show any substantial improvement in cruise configuration to date.

scholarly journals Effects of flexibility on the aerodynamic performance of flapping wings

2011 ◽  
Vol 689 ◽  
pp. 32-74 ◽  
Author(s):  
C.-K. Kang ◽  
H. Aono ◽  
C. E. S. Cesnik ◽  
W. Shyy
Keyword(s):  
Reynolds Number ◽  
Density Ratio ◽  
Flapping Wings ◽  
Mass Force ◽  
Propulsive Force ◽  
Propulsive Efficiency ◽  
Reduced Frequency ◽  
Moving Body ◽  
Order Of Magnitude ◽  
Direct Guidance

AbstractEffects of chordwise, spanwise, and isotropic flexibility on the force generation and propulsive efficiency of flapping wings are elucidated. For a moving body immersed in viscous fluid, different types of forces, as a function of the Reynolds number, reduced frequency (k), and Strouhal number (St), acting on the moving body are identified based on a scaling argument. In particular, at the Reynolds number regime of $O(1{0}^{3} \ensuremath{-} 1{0}^{4} )$ and the reduced frequency of $O(1)$, the added mass force, related to the acceleration of the wing, is important. Based on the order of magnitude and energy balance arguments, a relationship between the propulsive force and the maximum relative wing-tip deformation parameter ($\gamma $) is established. The parameter depends on the density ratio, St, k, natural and flapping frequency ratio, and flapping amplitude. The lift generation, and the propulsive efficiency can be deduced by the same scaling procedures. It seems that the maximum propulsive force is obtained when flapping near the resonance, whereas the optimal propulsive efficiency is reached when flapping at about half of the natural frequency; both are supported by the reported studies. The established scaling relationships can offer direct guidance for micro air vehicle design and performance analysis.

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