The Dynamical Behaviour of a Flexible Cable in a Uniform Flow Field

1971 ◽  
Vol 22 (2) ◽  
pp. 183-195 ◽  
Author(s):  
R. R. Huffman ◽  
Joseph Genin
Keyword(s):  
Mathematical Model ◽  
Shock Waves ◽  
Flow Field ◽  
Flow Speed ◽  
Dynamical Behaviour ◽  
Uniform Flow ◽  
Aerodynamic Forces ◽  
Cable Length ◽  
Flow Speeds ◽  
The Stability

SummaryA non-linear mathematical model for the study of the dynamics of an extensible cable subjected to aerodynamic forces generated by a uniform flow field is formulated. Solutions are found considering large displacement caused by suddenly applied loads (i.e., gusts, shock waves, turbulence) for a range of flow speeds and cable lengths. Transition from overdamped to oscillatory motion is observed when flow speed and cable length are increased and decreased respectively. The stability of the system is discussed.

Stability of slender inverted flags and rods in uniform steady flow

2016 ◽  
Vol 809 ◽  
pp. 873-894 ◽  
Author(s):  
John E. Sader ◽  
Cecilia Huertas-Cerdeira ◽  
Morteza Gharib
Keyword(s):  
Multiple Equilibria ◽  
Complex Dynamics ◽  
Flow Direction ◽  
Flow Speed ◽  
Uniform Flow ◽  
Biological Phenomena ◽  
Cantilever Length ◽  
The Stability ◽  
Elastic Sheets ◽  
Clamped Edge

Cantilevered elastic sheets and rods immersed in a steady uniform flow are known to undergo instabilities that give rise to complex dynamics, including limit cycle behaviour and chaotic motion. Recent work has examined their stability in an inverted configuration where the flow impinges on the free end of the cantilever with its clamped edge downstream: this is commonly referred to as an ‘inverted flag’. Theory has thus far accurately captured the stability of wide inverted flags only, i.e. where the dimension of the clamped edge exceeds the cantilever length; the latter is aligned in the flow direction. Here, we theoretically examine the stability of slender inverted flags and rods under steady uniform flow. In contrast to wide inverted flags, we show that slender inverted flags are never globally unstable. Instead, they exhibit bifurcation from a state that is globally stable to multiple equilibria of varying stability, as flow speed increases. This theory is compared with new and existing measurements on slender inverted flags and rods, where excellent agreement is observed. The findings of this study have significant implications to investigations of biological phenomena such as the motion of leaves and hairs, which can naturally exhibit a slender geometry with an inverted configuration.

scholarly journals Aerodynamic Detuning Analysis of an Unstalled Supersonic Turbofan Cascade

1986 ◽  
Vol 108 (1) ◽  
pp. 60-67 ◽  
Author(s):  
D. Hoyniak ◽  
S. Fleeter
Keyword(s):  
Flow Field ◽  
Leading Edge ◽  
Rotor Blades ◽  
Driving Mechanism ◽  
Aeroelastic Stability ◽  
Aerodynamic Forces ◽  
Unsteady Aerodynamic ◽  
Influence Coefficients ◽  
Blade Row ◽  
The Stability

A new, and as yet unexplored, approach to passive flutter control is aerodynamic detuning, defined as designed passage-to-passage differences in the unsteady aerodynamic flow field of a rotor blade row. Thus, aerodynamic detuning directly affects the fundamental driving mechanism for flutter, i.e., the unsteady aerodynamic forces and moments acting on individual rotor blades. In this paper, a model to demonstrate the enhanced supersonic unstalled aeroelastic stability associated with aerodynamic detuning is developed. The stability of an aerodynamically detuned cascade operating in a supersonic inlet flow field with a subsonic leading edge locus is analyzed, with the aerodynamic detuning accomplished by means of nonuniform circumferential spacing of adjacent rotor blades. The unsteady aerodynamic forces and moments on the blading are defined in terms of influence coefficients in a manner that permits the stability of both a conventional uniformly spaced rotor configuration as well as the detuned nonuniform circumferentially spaced rotor to be determined. With Verdon’s uniformly spaced Cascade B as a baseline, this analysis is then utilized to demonstrate the potential enhanced aeroelastic stability associated with this particular type of aerodynamic detuning.

scholarly journals Effect of morphology on the large-amplitude flapping dynamics of an inverted flag in a uniform flow

2019 ◽  
Vol 874 ◽  
pp. 526-547 ◽  
Author(s):  
Boyu Fan ◽  
Cecilia Huertas-Cerdeira ◽  
Julia Cossé ◽  
John E. Sader ◽  
Morteza Gharib
Keyword(s):  
Large Amplitude ◽  
Free Edge ◽  
Flow Speed ◽  
Uniform Flow ◽  
Analytical Theory ◽  
Natural Occurrence ◽  
Fluid Forces ◽  
Elastic Sheet ◽  
Divergence Instability ◽  
Flow Speeds

The stability of a cantilevered elastic sheet in a uniform flow has been studied extensively due to its importance in engineering and its prevalence in natural structures. Varying the flow speed can give rise to a range of dynamics including limit cycle behaviour and chaotic motion of the cantilevered sheet. Recently, the ‘inverted flag’ configuration – a cantilevered elastic sheet aligned with the flow impinging on its free edge – has been observed to produce large-amplitude flapping over a finite band of flow speeds. This flapping phenomenon has been found to be a vortex-induced vibration, and only occurs at sufficiently large Reynolds numbers. In all cases studied, the inverted flag has been formed from a cantilevered sheet of rectangular morphology, i.e. the planform of its elastic sheet is a rectangle. Here, we investigate the effect of the inverted flag’s morphology on its resulting stability and dynamics. We choose a trapezoidal planform which is explored using experiment and an analytical theory for the divergence instability of an inverted flag of arbitrary morphology. Strikingly, for this planform we observe that the flow speed range over which flapping occurs scales approximately with the flow speed at which the divergence instability occurs. This provides a means by which to predict and control flapping. In a biological setting, leaves in a wind can also align themselves in an inverted flag configuration. Motivated by this natural occurrence we also study the effect of adding an artificial ‘petiole’ (a thin elastic stalk that connects the sheet to the clamp) on the inverted flag’s dynamics. We find that the petiole serves to partially decouple fluid forces from elastic forces, for which an analytical theory is also derived, in addition to increasing the freedom by which the flapping dynamics can be tuned. These results highlight the intricacies of the flapping instability and account for some of the varied dynamics of leaves in nature.

Supersonic and hypersonic flow with attached shock waves over delta wings

1971 ◽  
Vol 325 (1561) ◽  
pp. 251-268 ◽  
Keyword(s):  
Shock Waves ◽  
Flow Field ◽  
Hypersonic Flow ◽  
Delta Wing ◽  
Cross Flow ◽  
Flow Region ◽  
Lower Surface ◽  
Uniform Flow ◽  
Nonuniform Flow ◽  
Sonic Line

A unified theory is developed for supersonic and hypersonic flow with attached shock waves over the lower surface of a delta wing at an angle of attack. The flow field on the lower surface of a delta wing consists of uniform flow regions near the leading edges, where the cross flow is supersonic and a nonuniform flow region near the central part, where the cross flow is subsonic. In the nonuniform flow region, the theory is based on the assumption that the flow differs slightly from the corresponding two-dimensional flow over a flat plate. Thus a linearized perturbation on a nonlinear flow field is first calculated and then strained and corrected so that the flow is matched continuously to the uniform flow which is obtained exactly. When compared with available exact numerical solutions the theory gives, in all cases, almost identical results, except near the crossflow sonic line where existing numerical methods fail to produce a discontinuous slope in the pressure curve, whereas the present theory predicts such a discontinuity and shows that the slope has a square root singularity at the crossflow sonic line similar to that in the supersonic linear theory.

Aerodynamic-Rotordynamic Interaction in Axial Compression Systems: Part II — Impact of Interaction on Overall System Stability

2002 ◽  
Author(s):  
Ammar A. Al-Nahwi ◽  
James D. Paduano ◽  
Samir A. Nayfeh
Keyword(s):  
Flow Field ◽  
Axial Compression ◽  
Coupling Parameter ◽  
Stability Margin ◽  
Integrated Treatment ◽  
Tip Clearance ◽  
System Stability ◽  
Aerodynamic Forces ◽  
Design Point ◽  
The Stability

This paper presents an integrated treatment of the dynamic coupling between the flow field (aerodynamics) and rotor structural vibration (rotordynamics) in axial compression systems. This work is motivated by documented observations of tip clearance effects on axial compressor flow field stability, the destabilizing effect of fluid-induced aerodynamic forces on rotordynamics, and their potential interaction. This investigation is aimed at identifying the main nondimensional design parameters governing this interaction, and assessing its impact on overall stability of the coupled system. The model developed in this work employs a reduced-order Moore-Greitzer model for the flow field, and a Jeffcott-type model for the rotordynamics. The coupling between the fluid and structural dynamics is captured by incorporating a compressor pressure rise sensitivity to tip clearance, together with a momentum based model for the aerodynamic forces on the rotor (presented in Part I of this paper). The resulting dynamic model suggests that the interaction is largely governed by two nondimensional parameters: the sensitivity of the compressor to tip clearance and the ratio of fluid mass to rotor mass. The aerodynamic-rotordynamic coupling is shown to generally have an adverse effect on system stability. For a supercritical rotor and a typical value of the coupling parameter, the stability margin to the left of the design point is shown to decrease by about 5% in flow coefficient (from 20% for the uncoupled case). Doubling the value of the coupling parameter not only produces a reduction of about 8% in the stability margin at low flow coefficients, but also gives rise to a rotordynamic instability at flow coefficients 7% higher than the design point.

Forces on Nets With Bending Stiffness: An Experimental Study on the Effects of Flow Speed and Angle of Attack

2012 ◽  
Author(s):  
L. C. Gansel ◽  
Ø. Jensen ◽  
E. Lien ◽  
P. C. Endresen
Keyword(s):  
Flow Direction ◽  
Angle Of Attack ◽  
Flow Speed ◽  
Bending Stiffness ◽  
Torque Sensor ◽  
Drag And Lift Coefficients ◽  
Flow Speeds ◽  
Drag And Lift ◽  
The Stability ◽  
Good Agreement

This study investigates the effects of changes in flow speed and angle of attack on drag and lift forces on nets with bending stiffness. Today most fish cage nets are made from nylon, but new cage materials are proposed in order to improve the stability of cages in currents and waves, to reduce biofouling, prevent escapes, and to secure fish from predator attacks. The use of some of these materials leads to nets with bending stiffness in at least one direction. However, not much is known about the performance of such nets in currents and waves. In this study three different nets with bending stiffness were tested together with nylon nets. Net panels were subjected to different flow speeds at different angles between flow direction and net plane, and the forces on the nets were measured with a multi-axis force/torque sensor system. Based on the experiments, drag and lift coefficients were determined for the different net materials and compared to existing theory [1,2]. The results are in reasonably good agreement with the existing theory for the nets with low solidity, however, for nets with higher solidity the results are significantly lower than the drag and lift coefficients provided by Aarsnes [1] and Løland [2].

Effect of three non-axisymmetric stator schemes on compressor performance with distorted inlet

2021 ◽  
pp. 095441002110498
Author(s):  
Wenguang Fu ◽  
Peng Sun
Keyword(s):  
Flow Field ◽  
Stability Margin ◽  
Aerodynamic Performance ◽  
Uniform Flow ◽  
Transonic Compressor ◽  
Maximum Stability ◽  
Compressor Performance ◽  
Twisted Blade ◽  
The Stability ◽  
Stator Design

In the boundary layer ingesting propulsion system, the compressor suffers from a non-uniform flow field. The compressor operating with distorted inflow continuously results in the loss of aerodynamic performance and stability margin. In this paper, three non-axisymmetric configurations are described for the stator of a transonic compressor to match the non-uniform flow field. The flow fields with distorted inflow at near stall condition are obtained and analyzed, the effects of the prototype stator and the three non-axisymmetric stators on aerodynamic performance are compared in detail. Results show that the non-axisymmetric stator schemes can effectively improve the stability margin of the transonic compressor and the maximum stability margin is relatively increased by 22.3% in all the three non-axisymmetric stators. The non-axisymmetric stator design is effective on decreasing the aerodynamic losses and improving the performance of the compressor operating with distorted inflow. Overall, the results show that in the design of the non-axisymmetric stator, the adoption of a curved-twisted blade and the increase of cascade solidity have the potential to reduce loss sources caused by distorted inflow.

Aerodynamic-Rotordynamic Interaction in Axial Compression Systems—Part II: Impact of Interaction on Overall System Stability

2003 ◽  
Vol 125 (3) ◽  
pp. 416-424 ◽  
Author(s):  
Ammar A. Al-Nahwi ◽  
James D. Paduano ◽  
Samir A. Nayfeh
Keyword(s):  
Flow Field ◽  
Axial Compression ◽  
Coupling Parameter ◽  
Stability Margin ◽  
Integrated Treatment ◽  
Tip Clearance ◽  
System Stability ◽  
Aerodynamic Forces ◽  
Design Point ◽  
The Stability

This paper presents an integrated treatment of the dynamic coupling between the flow field (aerodynamics) and rotor structural vibration (rotordynamics) in axial compression systems. This work is motivated by documented observations of tip clearance effects on axial compressor flow field stability, the destabilizing effect of fluid-induced aerodynamic forces on rotordynamics, and their potential interaction. This investigation is aimed at identifying the main nondimensional design parameters governing this interaction, and assessing its impact on overall stability of the coupled system. The model developed in this work employs a reduced-order Moore-Greitzer model for the flow field, and a Jeffcott-type model for the rotordynamics. The coupling between the fluid and structural dynamics is captured by incorporating a compressor pressure rise sensitivity to tip clearance, together with a momentum based model for the aerodynamic forces on the rotor (presented in Part I of this paper). The resulting dynamic model suggests that the interaction is largely governed by two nondimensional parameters: the sensitivity of the compressor to tip clearance and the ratio of fluid mass to rotor mass. The aerodynamic-rotordynamic coupling is shown to generally have an adverse effect on system stability. For a supercritical rotor and a typical value of the coupling parameter, the stability margin to the left of the design point is shown to decrease by about 5% in flow coefficient (from 20% for the uncoupled case). Doubling the value of the coupling parameter not only produces a reduction of about 8% in the stability margin at low flow coefficients, but also gives rise to a rotordynamic instability at flow coefficients 7% higher than the design point.

Kinematic Variation and Modeling for Design in Ornithoptic Flight

Materials ◽  
2005 ◽  
Author(s):  
John M. Dietl ◽  
Ephrahim Garcia
Keyword(s):  
Genetic Algorithm ◽  
Mathematical Model ◽  
Flow Field ◽  
Power Consumption ◽  
Degrees Of Freedom ◽  
Flapping Flight ◽  
Kinematic Parameters ◽  
Aerodynamic Forces ◽  
Forward Flight ◽  
Strip Theory

During soaring forward flight, larger birds such as raptors generate most of their lift in a manner consistent with the lift generated by fixed-wing aircraft. However, in flapping flight there is an additional flow field that must be superimposed to account for thrust generated. The aerodynamic forces can be analyzed using conventional strip theory techniques and integrated across the wingspan and over the entire flapping cycle. Oscillating wing pitch causes the lift vector to contribute to forward thrust and effects useful angles of attack. This paper seeks to predict which kinematic parameters of flapping flight will allow for sustained forward flight. Using a mathematical model for flapping flight and a genetic algorithm, kinematic parameters are selected that provide sufficient lift and thrust while attenuating aerodynamic power consumption. The results show that separate degrees of freedom are necessary for twisting and heaving motions to yield acceptable flight conditions.

scholarly journals Enhanced Optic Flow Speed Discrimination While Walking: Contextual Tuning of Visual Coding

Perception ◽  
10.1068/p5845 ◽  
2007 ◽  
Vol 36 (10) ◽  
pp. 1465-1475 ◽  
Author(s):  
Frank H Durgin ◽  
Krista Gigone
Keyword(s):  
Flow Field ◽  
Optic Flow ◽  
Flow Speed ◽  
Visual Coding ◽  
Choice Procedure ◽  
Flow Speeds ◽  
Forced Choice Procedure ◽  
Speed Discrimination ◽  
Self Motion ◽  
Perceived Speed

We tested the hypothesis that long-term adaptation to the normal contingencies between walking and its multisensory consequences (including optic flow) leads to enhanced discrimination of appropriate visual speeds during self-motion. In experiments 1 (task 1) and 2 a two-interval forced-choice procedure was used to compare the perceived speed of a simulated visual flow field viewed while walking with the perceived speed of a flow field viewed while standing. Both experiments demonstrated subtractive reductions in apparent speed. In experiments 1 and 3 discrimination thresholds were measured for optic flow speed while walking and while standing. Consistent with the optimal-coding hypothesis, speed discrimination for visual speeds near walking speed was enhanced during walking. Reduced sensitivity was found for slower visual speeds. The multisensory context of walking alters the coding of optic flow in a way that enhances speed discrimination in the expected range of flow speeds.

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