scholarly journals A first simulation of a model aquatic canopy at high Cauchy number

2020 ◽  
pp. 152-158
Author(s):  
B. Löhrer ◽  
D. Doppler ◽  
S. Puijalon ◽  
N. Rivière ◽  
J.J.S. Jerome ◽  
...  
Keyword(s):  
Cauchy Number

scholarly journals Scaling of the performance of insect-inspired passive-pitching flapping wings

2019 ◽  
Vol 16 (161) ◽  
pp. 20190609 ◽  
Author(s):  
Kit Sum Wu ◽  
Jerome Nowak ◽  
Kenneth S. Breuer
Keyword(s):  
Scaling Laws ◽  
Aerodynamic Force ◽  
Lift Coefficient ◽  
Angle Of Attack ◽  
Flapping Wing ◽  
Dimensionless Parameters ◽  
Linear Elastic ◽  
Simple Implementation ◽  
Pitch Regulation ◽  
Cauchy Number

Flapping flight using passive pitch regulation is a commonly used mode of thrust and lift generation in insects and has been widely emulated in flying vehicles because it allows for simple implementation of the complex kinematics associated with flapping wing systems. Although robotic flight employing passive pitching to regulate angle of attack has been previously demonstrated, there does not exist a comprehensive understanding of the effectiveness of this mode of aerodynamic force generation, nor a method to accurately predict its performance over a range of relevant scales. Here, we present such scaling laws, incorporating aerodynamic, inertial and structural elements of the flapping-wing system, validating the theoretical considerations using a mechanical model which is tested for a linear elastic hinge and near-sinusoidal stroke kinematics over a range of scales, hinge stiffnesses and flapping frequencies. We find that suitably defined dimensionless parameters, including the Reynolds number, Re , the Cauchy number, Ch , and a newly defined ‘inertial-elastic’ number, IE, can reliably predict the kinematic and aerodynamic performance of the system. Our results also reveal a consistent dependency of pitching kinematics on these dimensionless parameters, providing a connection between lift coefficient and kinematic features such as angle of attack and wing rotation.

scholarly journals On the Dynamics of Flexible Plates under Rotational Motions

Energies ◽  
2018 ◽  
Vol 11 (12) ◽  
pp. 3384 ◽  
Author(s):  
Shifeng Fu ◽  
Yaqing Jin ◽  
Jin-Tae Kim ◽  
Zhongyu Mao ◽  
Yuan Zheng ◽  
...  
Keyword(s):  
Local Maximum ◽  
Constant Factor ◽  
Small Scale ◽  
Simple Formulation ◽  
Maximum Deformation ◽  
Pure Rotation ◽  
Flexible Plates ◽  
Angular Velocities ◽  
Induced Flow ◽  
Cauchy Number

The reconfiguration of low-aspect-ratio flexible plates, required power and induced flow under pure rotation were experimentally inspected for various plate stiffness and angular velocities ω. Particle tracking velocimetry (PTV) and particle image velocimetry (PIV) were used to characterize the plate deformation along their span as well as the flow and turbulence statistics in the vicinity of the structures. Results show the characteristic role of stiffness and ω in modulating the structure reconfiguration, power required and induced flow. The inspected configurations allowed inspecting various plate deformations ranging from minor to extreme bending over 90∘ between the tangents of the two tips. Regardless of the case, the plates did not undergo noticeable deformation in the last ∼30% of the span. Location of the maximum deformation along the plate followed a trend s m ∝ l o g ( C a ) , where C a is the Cauchy number, which indicated that s m is roughly fixed at sufficiently large C a. The angle (α) between the plate in the vicinity of the tip and the tangential vector of the motions exhibited two distinctive, nearly-linear trends as a function of C a , within C a ∈ ( 0 , 15 ) and C a ∈ ( 20 , 70 ), with a matching within these C a at C a > 70, α ≈ 45 ∘. Induced flow revealed a local maximum of the turbulence levels at around 60% of the span of the plate; however, the largest turbulence enhancement occurred near the tip. Flexibility of the plate strongly modulated the spatial distribution of small-scale vortical structures; they were located along the plate wake in the stiffer plate and relatively concentrated near the tip in the low-stiffness plate. Due to relatively large deformation, rotational and wake effects, a simple formulation for predicting the mean reconfiguration showed offset; however, a bulk, constant factor on ω accounted for the offset between predictions and measurements at deformation reaching ∼ 60 ∘ between the tips.

Icebreaking Modeling

1975 ◽  
Vol 19 (01) ◽  
pp. 40-43 ◽  
Author(s):  
A. G. Atkins
Keyword(s):  
Large Scale ◽  
Laboratory Data ◽  
Model Data ◽  
Tank Model ◽  
Geometric Similarity ◽  
Cauchy Number ◽  
Strength And Toughness

It is shown that the mechanics of cracking do not follow geometric similarity in the normal meaning of that term. Thus, translation of laboratory data concerning strength and toughness of ice to large-scale applications should be done with care. Regarding ice tank model data, it is demonstrated that a new nondimensional group should be satisfied if ice fracture effects are to be scaled properly. The Cauchy number is not appropriate.

Flow-induced motions of flexible plates: fluttering, twisting and orbital modes

2019 ◽  
Vol 864 ◽  
pp. 273-285 ◽  
Author(s):  
Yaqing Jin ◽  
Jin-Tae Kim ◽  
Shifeng Fu ◽  
Leonardo P. Chamorro
Keyword(s):  
Large Scale ◽  
Flow Instability ◽  
Aerodynamic Force ◽  
Three Dimensional ◽  
Force Sensor ◽  
Flexible Plates ◽  
Second Mode ◽  
Cauchy Numbers ◽  
Inclination Angles ◽  
Cauchy Number

The unsteady dynamics of wall-mounted flexible plates under inclined flows was fundamentally described using theoretical arguments and experiments under various Cauchy numbers $Ca=\unicode[STIX]{x1D70C}_{f}bL^{3}U_{0}^{2}/(EI)\in [7,81]$ (where $\unicode[STIX]{x1D70C}_{f}$ is the fluid density, $b$ and $L$ are the plate width and length, $U_{0}$ is the incoming velocity, $E$ is Young’s modulus and $I$ is the second moment of the area) and inclination angles $\unicode[STIX]{x1D6FC}$. Three-dimensional particle tracking velocimetry and a high-resolution force sensor were used to characterize the evolution of the plate dynamics and aerodynamic force. We show the existence of three distinctive, dominant modes of tip oscillations, which are modulated by the structure dynamic and flow instability. The first mode is characterized by small-amplitude, planar fluttering-like motions occurring under a critical Cauchy number, $Ca=Ca_{c}$. Past this condition, the motions are dominated by the second mode consisting of unsteady twisting superimposed onto the fluttering patterns. The onset of this mode is characterized by a sharp increase of the force fluctuation intensity. At sufficiently high $Ca$ and $\unicode[STIX]{x1D6FC}$, the plate may undergo a third mode given by large-scale tip orbits about the mean bending. Using the equation of motion and first-order approximations, we propose a formulation to estimate $Ca_{c}$ as a function of $\unicode[STIX]{x1D6FC}$; it exhibits solid agreement with experiments.

scholarly journals Physical principles of optimization of the static regime of a cantilever type power-effect sensor with a constant rectangular cross-section

2018 ◽  
Vol 2 (5) ◽  
Author(s):  
Petro Kosobutskyy ◽  
Mariia Kuzmynykh ◽  
Yaroslav  Matviychuk
Keyword(s):  
Cross Section ◽  
Rectangular Cross Section ◽  
Static Mode ◽  
Characteristic Numbers ◽  
Mode Of Operation ◽  
Power Effect ◽  
Static Regime ◽  
Cauchy Number ◽  
Type Power ◽  
Physical Principles

Abstract - In this paper an analysis of the physical principles of two-criterion optimization Pareto static mode of operation of power sensors cantilever type of rectangular type with a stable cross-section. The proposed criterion based on the Cauchy number is one of the characteristic numbers of the proportional miniaturization of microsystem technology. It is established that for a rectangular cantilever with a stable cross-section, the value of the Cauchy does not depend on the width of the micro-console and the material from which it is made.

scholarly journals Drag reduction of flexible plates by reconfiguration

2010 ◽  
Vol 650 ◽  
pp. 319-341 ◽  
Author(s):  
FRÉDÉRICK GOSSELIN ◽  
EMMANUEL de LANGRE ◽  
BRUNO A. MACHADO-ALMEIDA
Keyword(s):  
Experimental Investigation ◽  
Simple Model ◽  
Drag Reduction ◽  
Large Deformation ◽  
Large Range ◽  
Asymptotic Regime ◽  
Area Reduction ◽  
Flexible Plates ◽  
Cauchy Numbers ◽  
Cauchy Number

Through an extensive and systematic experimental investigation of two geometries of flexible plates in air, it is shown that a properly defined scaled Cauchy number allows collapsing all drag measurements of the reconfiguration number. In the asymptotic regime of large deformation, it is shown that the Vogel exponents that scale the drag with the flow velocity for different geometries of plates can be predicted with a simple dimensional analysis reasoning. These predicted Vogel exponents are in agreement with previously published models of reconfiguration. The mechanisms responsible for reconfiguration, namely area reduction and streamlining, are studied with the help of a simple model for flexible plates based on an empirical drag formulation. The model predicts well the reconfiguration observed in the experiments and shows that for a rectangular plate, the effect of streamlining is prominent at the onset of reconfiguration, but area reduction dominates in the regime of large deformation. Additionally, the model demonstrates for both geometries of plates that the reconfiguration cannot be described by a single value of the Vogel exponent. The Vogel exponent asymptotically approaches constant values for small and for very large scaled Cauchy numbers, but in between both extremes it varies significantly over a large range of scaled Cauchy number.

Passive Pitching Mechanism of Three-Dimensional Flapping Wings in Hovering Flight

2019 ◽  
Author(s):  
Chengyu Li ◽  
Junshi Wang ◽  
Geng Liu ◽  
Xiaolong Deng ◽  
Haibo Dong
Keyword(s):  
Computational Study ◽  
Fluid Dynamic ◽  
Flapping Wings ◽  
Clear Understanding ◽  
Basal Region ◽  
Mass Ratio ◽  
Hovering Flight ◽  
Pitching Motion ◽  
Wide Range ◽  
Cauchy Number

Abstract Flapping wings of insects can passively maintain a high angle of attack due to the torsional flexibility of wing basal region without the aid of the active pitching motion. However, the lift force generated by such passive pitching motion has not been well explored in the literature. Consequently, there is no clear understanding of how torsional wing flexibility should be designed for optimal performance. In this work, a computational study was conducted to investigate the passive pitching mechanism of flapping wings in hovering flight using a torsional spring model. The torsional wing flexibility was characterized by Cauchy number. The impacts of the inertial effect of wings were evaluated using the mass ratio. The aerodynamic forces and associated unsteady flow structures were simulated by an in-house immersed-boundary-method based computational fluid dynamic solver. A parametric study on the Cauchy number was performed with a Reynolds number of 300 at a mass ratio of 1.0, which covers a wide range of species of insect wings. According to the analysis of the aerodynamic performance, we found that the optimal lift can be achieved at a Cauchy number around 0.16, while the optimal efficiency in terms of lift-to-power ratio was reached at a Cauchy number around 0.3. All the corresponding wing pitching kinematics had a pitching magnitude around 60 degrees with slightly advanced rotation. In addition, 3D wake structures generated by the passive flapping wings were analyzed in detail. The findings of this work could provide important implications for designing more efficient flapping-wing micro air vehicles.

Wind Tunnel Test on Cable Dome of Geiger Type

2007 ◽  
Vol 2 (3) ◽  
pp. 218-224 ◽  
Author(s):  
Zhi-hong Zhang ◽  
Yukio Tamura
Keyword(s):  
Wind Tunnel ◽  
Dynamic Instability ◽  
Wind Tunnel Test ◽  
Harmonic Excitation ◽  
Degree Of Freedom ◽  
Shaking Table ◽  
Frequency Components ◽  
The One ◽  
Cable Dome ◽  
Cauchy Number

This paper presents preliminary results of an aeroelastic wind tunnel test on a cable dome. The structural design of the model is given in detail. Similarity requirements based on dimensional analysis are discussed, including Froude number, Cauchy number, and Scruton number. Structural tests are conducted on the aeroelastic model. Dynamic instability subject to harmonic excitation like a single-degree-of-freedom hardening system is verified. Both odd and even frequency components are excited when the shaking table shakes at 29Hz. For the one-degree-of-freedom Duffing model, even frequency components will be impossible due to the symmetry of the motion equation if symmetry-breaking bifurcation behaviors do not occur. Phase plane is checked and discussed when the shaking table shakes at 7Hz. A strange attractor appears to exist on the basis of the Poincare map. Some statistical results of wind tunnel tests are presented. The possibility of aeroelastic instability of the cable dome is discussed.

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