Fluidmechanical vortex coils arise as spirally arranged coherent vortex filaments. One can assign physical properties to fluid-mechanical vortex coils, but formally there is no generally valid theory about spiral vortex formations in fluid mechanics. Theoretical key statements about vortex filaments have been known for a long time; the most important are from Helmholtz. A common feature of some modern theoretical approaches to ordered vortex configurations is that they designate coherent vortex formations as connected domains of dominant vortex strength.
For the phenomenology of "multiple fluid-mechanical vortex coils" (global mode n vortex coil) presented here, Helmholtz's vortex filament theory, which is considered to be reliable, is first applied to Lagrangian Coherent Structures and expanded by an approach to the inner milieu of the vortex filaments.
Structures of this kind form systems that are capable of momentum induction, which in turn organizes the field at rest. For the presence of well-grouped vortex filaments, there is a conjecture about the self-organization (autopoiesis) of vortex filaments in a flow field.
From the content
Spiral shape
Gliding bird
Corridor model
Interacting vortex filaments
Conclusion
Bibliography
Fluid flow in spirally vortex structures Notes on bird flight
Michael Dienst, Berlin Germany 2024
Fluidmechanical vortex coils arise as spirally arranged coherent vortex filaments. One can assign physical properties to fluid-mechanical vortex coils, but formally there is no generally valid theory about spiral vortex formations in fluid mechanics. Theoretical key statements about vortex filaments have been known for a long time; the most important are from Helmholtz. A common feature of some modern theoretical approaches to ordered vortex configurations is that they designate coherent vortex formations as connected domains of dominant vortex strength.
For the phenomenology of "multiple fluid-mechanical vortex coils" (global mode n vortex coil) presented here, Helmholtz's vortex filament theory, which is considered to be reliable, is first applied to Lagrangian coherent structures and expanded by an approach to the inner milieu of the vortex filaments.
Structures of this kind form systems that are capable of momentum induction, which in turn organizes the field at rest. For the presence of well-grouped vortex filaments, there is a conjecture about the self-organization (autopoiesis) of vortex filaments in a flow field.
Keywords: field, fluid mechanical vortex coils, vortex filament theory, Lagrangian coherent structures, vortex filaments, autopoiesis
The Spiral shape
The multiple, fluid-mechanical vortex coil remains a synthetic construct. Vortex coils are fluidic compositions of coherent vortex filaments with ascribed properties. The physical properties of the vortex filaments derive from their well- defined internal milieu. Spiral vortex formations occur in nature, but they are "made"! They are synthetic in the sense that systems exist that generate fluid-mechanical vortex coils.
So far, Lagrangian coherent vortex systems have not had a universal definition in fluid mechanics. This also applies to spiral systems. The first formulations of spiral rotationally coherent vortex systems came from observations of particular fingering of the wing tips of land-soaring birds. The descriptions of multiple vortex coil systems had no relation to the natural habitats of the birds, but were only arranged laboratory experiments in the wind tunnel; it was as if the decoding of bird flight had begun in a hall in the mid-1980s. At least that's how it was seen at the Department of Bionics and Evolutionary Technology at the Technical University of Berlin. Later, technical airfoil models were examined in the wind tunnel and their suitability for generating spiral vortex systems.
At the beginning of the investigations by Nachtigall (Saarbrücken) and Rechenberg (Berlin), little was known about the very special fluid mechanics of the vortex coil structures and the theory required for this. In Berlin, the first technical laboratory model of the fingered bird's wing was a splitted edge curve contour of a formerly compact model wing that was now slotted at the end of the wing. At that time, all experimenters in Berlin worked primarily with sheet metal, because lead surfaces offered certain creative freedom when constructing fingered model wings. With an optimization strategy tailored to wind tunnel tests, the glide ratio1 (cL/cW) of a slotted and fingered lead wing was improved by about 10% at the TU Berlin in the 1990s compared to its compact initial geometry. Only the preparation of the stork's wing behaved cheaper in the wind tunnel; with its exorbitantly low drag coefficient.
In the case of the lead wing model, the partial wings or wing tips of the feather fingers form a curved chain of source points. For a long time, this arc-shaped arrangement of the source points was considered less productive for wake flow and momentum exchange there. In fact, the geometry of the vortex-generating system (ellipse or arc) has a great impact on the quality of the vortex-spiral system.
In the 1980s, winglets2 entered the stage of research institutes and a short time later of the development departments of the aviation industry. Winglets are fixed partial wings on aircraft wings.
To date, we only know the impulse effectiveness of spiral arrangements from the few vortex structures that have been experimentally investigated and measured in wind tunnels with precisely this question in mind. Also, we do not know whether the fluid mechanical effects are scalable or not. It can be observed that the impulse induction of Lagrangian coherent vortices in the flow field is cumulative and thus appears to be a conservative phenomenon. Compensations often occur in cumulative processes: physical effects cancel each other out. In this way, an inducing system can couple momentum into the field at the body-fixed, Lagrangen level without this production becoming visible at the Euler level.
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Fig.1: Specimen of the stork wing in the wind tunnel under flow load. The seven source points at the feather finger tips are marked in yellow. Photo: Fachgebiet Bionik und Evolutionstechnik, Technische Universität Berlin (1995).
Vortex generators were able to continuously synthesize more or less compact, but in any case coherent vortex filaments and release them into the flow. Passive ordering processes were involved in what happened. It was observed that neighboring vortex threads influence each other and, immediately after their formation, begin to rotate around a common center, even to literally “dance with each other”. This dance is optimal for an elliptical configuration of vortex filament sources and forms a compact, shell-shaped vortex filament coil downstream.
Downstream from the wind tunnel and in the wake of the perturbation contour, the spiral vortex structure remains stable. In the interior and along this helically wound vortex tube, the flow actually remains just as "rotor-free" as predicted by the widely unpopular potential theory. v^ is the fluid velocity at the mouth of the open wind tunnel and thus the so-called "apparent fluid velocity" at the specimen to be examined. Inside the vortex coil, the flow velocities take on a multiple of the amplifying flow v^.
At that time efforts were being made to find a theoretical model. In his dissertation, Peintinger (1988) proposed a method for calculating fluid-mechanical vortex coils according to Biot and Savart's law3, a formula derived from general field theory. Unfortunately, the method does not go beyond the doctrine of that time and the one hundred and seventy years that followed, which originated from the axis-conform calculation, and was only mentioned once as a theoretical model of fluid-mechanical vortex structures (Kaschub 1988).
The biological wing is a complex structure and bearer of different physical effects. So what is the typical thing about a bird's wing? Every flying system has a set of basic design ideas: high performance, low weight and the aerodynamic shape. For a safe flight, the senses, especially vision, must be sharp. Birds possess excellent eyesight, perhaps the most powerful of any vertebrate. The entire physique of a bird is adapted to the flying way of life. His bone system is a lesson in lightweight construction. Another weight loss adjustment is the absence of some organs. In the course of evolutionary optimization, today's modern birds are toothless and have no muscular jaws. The bird's beak is an adjustment that reduces the weight significantly.
Gliding bird
The first investigations into fluid-mechanical vortex coils took place in the laboratory. The wind tunnels and measuring devices of the TU Berlin were suitable for carrying out quantitative investigations into the air resistance and the dynamic lift of exhibits of different bird wings. The traditional tasks and methods in the wind tunnel included determining the vorticity of the flow being examined. In the 1980s, this was only possible qualitatively at the measuring facilities of the TU Berlin. However, spatial maps of the emergence of gradual vorticity in the field have been made. This work result from vortex probe analyses crystallizes for the first time the spatial form of spiral systems in the wake of a bird's wing flow: The observed vortex areas form (i) stationary structures; they are (ii) discrete, distinct from the surrounding flow, and the domains appear (iii) as threads to be connected (coherence). The vortex filaments are (iv) ordered into a radially symmetrical spiral, which apparently happens by itself. Later it was found that these vortex threads (v) have an astonishing stability, and even more: bundles of these vortex threads are stable against external disturbances. However, what is phenomenal about these vortex coils is (vi) that the vortex body flowing off behind the interfering contour rotates! In the center of the vortex spiral, (vii) a higher fluid velocity is registered than in the inflow boundary condition (vcoil/v^)>1 of the wing.
Wind tunnels have long been established and widespread as a simulation method and laboratory instrument. A wind tunnel is more of a building than an apparatus. Here the medium, in our case the air, moves towards the measurement object, flows around it and flows off. We measure selected physical variables on a stationary measurement object. If we examine the flight of birds, we cannot avoid recognizing that with a wind tunnel the principle of measurement and effect subject, i.e. the cause of a physical event and its effect on a biological flight system, is exactly reversed! The wind tunnel reverses the flow events to be described.
Let us now look at power- and work processes in a fluid at rest! A bird or a model airplane soaring through a fluid at rest works off a height potential in a very elegant way. In the still fluid (and also in the moving fluid) this process is a "work process" and means: The flight system couples energy into the field.
A wind turbine is completely different. The flow energy that a moving fluid transports depends on the density of the medium; in the case of air, the energy density is rather low. That is why windmills are usually large. The energy conversion is a “power process” here. The wind turbine's repeller decouples energy from the field. Windmills are power machines.
Completely different, the propeller. As a power machine, a propeller couples energy into the field with the aim of generating reaction forces. The reactive forces become measurable as "thrust". From this perspective, the difference between a wind turbine and a hair dryer, is easy to understand. In fact, measurements in the plane of a wind turbine repeller show that the flow is decelerated here and flow impulse is transmitted: out of the field and into the machine!
Traditional theoretical investigation methods and modern numerical models of fluid mechanics (Computational Fluid Dynamics, CFD) examine exactly this. Immediately and effortlessly we find ourselves in the classic situation of a wind tunnel setup, in which a fluid flows around a body at rest. As a rule, control volumes are declared there, in which the "internal components" to be examined are located. A parameter of the initial boundary conditions is usually the velocity vector for v^ at the edges of the flow space; the pressure condition or a defined volume flow then prevails at the other system boundaries.
So let's follow the process of flying in the three-dimensional field. When driving a wing through a standing fluid, this fluid continuum experiences complicated deformations. The deformations come from the interaction of the fluidic space with the driving wing. Driving means: clamped down on one side and finite; we imagine a wing profile, an upper and lower side and a tip area at the wing tip. From the perspective of the fluid and the initial boundary condition of a pristine field, the wing is an interference contour! Below this interfering contour, the fluid responds to the impulse input required for the deformation of the continuum with a downward movement. This downward movement of the fluid is local. It takes place in the immediate vicinity of the interference contour. The moving wing carries this environment with it: it practically plows through the continuum! The term "downwash" has become established on the wing and for the observation of the phenomenon "downward movement of the fluid after impulse input". The term downwash4 comes from the time when people began to study the flow field around helicopter propellers.
If we follow the argument about a moving interfering contour in a stagnant fluid, then kinetic energy is coupled into the field during the downwash as well as with the edge vortices from the flow around the finite contour. The kinetic energy comes from a movement cause and is lost for the driving system. The term “induced drag” has been established around the energy loss from the tip vortices, in semantic differentiation from frictional and form drag forces of an interference contour moving in the fluid. The edge vortex and the fluid mass accelerated downwards from the wing consumes energy. The "induced drag of a tip vortex" is very probably an unfortunate term in the argumentation about tip vortices at a disruptive contour. In fact, "induction processes in a field" are always discussed when there is talk of the impulse effectiveness of a vortex structure. Unfortunately, however, there is no force induced in the field by a boundary vortex, as we know it along a line of force, for example. Nevertheless, Prandtl's calculation approach for the "induced drag" delivers such accurate results that even after a hundred years it is part of the repertoire of flow simulation.
In addition to the downwash, the "sidewash" is now known, a narrative that actually comes closer to the physical processes on the wing!
The Corridor model
Compared to the wind tunnel setup, corridors have the major disadvantage that to date there are definitely no measurement data whatsoever. Unfortunately, worldwide. And this applies to biological bird flight. This, in turn, is not to be lamented, simply because the biological flight system (bird) does not want to fly anywhere through a predefined corridor (Euler). Experiments are known, but I do not want to discuss them in this context.
Perhaps it is necessary and advantageous at this point to emphasize that all (emphasize: all) simulation models of biological bird flight prefer the "wind tunnel setup". Simply and only because experimental equivalents from the 1980s exist for this model (the numerical model). From wind tunnel experiments. At Bionik und Evolutionstechnik Department of the Technical University of Berlin.
Without a perturbation, no flow will flow out of a control volume in a fluid at rest. In a mind game, we stake out a three-dimensional control area in a fluidic space, the field, so that a kind of "canal with standing fluid" is created: the corridor! This is where the following experiments will take place. As the first interfering contour, a wing of a model aircraft sails through the field in such a way that its wing tip glides through the control corridor. In this scenario, the flight system should not suffer any altitude loss. In flight: a continuous vortex track is now forming along the central axis of the corridor. The thread-like vortex track originates from the flow around the edge of the moving wing in the stationary fluid.
Let's underlay the mind game with the calculation results of a computer simulation based on field theory. In the numerical corridor model, a wing sails through a stationary field just such that its wing tip glides through the control room from end to end. A vortex track becomes visible (Fig.2. left in the picture). This one-dimensional vortex thread is coherent, energetic and stable!
We know from vortices that their inner milieu is characterized by the vector vorticity ro [s-[1]]5. In the model presentation, the vortex thread is a one-dimensional (vortex-) filament in the sense of Helmholtz's vorticity laws and a Lagrange Coherent System (LCS) as described by Haller (Haller2000). In a graphic for the numerical simulation of the corridor model and for the movement of an interference contour in a fluid at rest, vectorial flow quantities are perpendicular to the direction of movement (YZ plane, Fig. 2., middle) and along the vortex track (XY plane, Fig. 2., on the right in the picture). The specific induced impulse corresponds to the velocity induced in the field6.
The vortex thread "organizes the flow field!" The diagrams in Fig.4 show a Y-Z section and the components of the Lagrangian velocity gradient in the axial direction of the vortex filament: u; radial components, perpendicular to the main direction of movement: v, w; and the resulting velocity r in the field.
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Fig.2: Numerical simulation of a vortex track in a fluid at rest. Schematic: wing and corridor model (left); Distribution of the velocity vectors in the YZ plane (middle) and in the XY plane, on the right in the picture. (Felgenhauer (2023)).
One result of the simulation is the visualization of the vectorial induced velocity vi in a sectional plane of the flow field. We see that the stretched vortex filament applies little velocity in the axial direction u and the radial component w of the velocity dominates what happens along the core of the vortex filament in the UVW-field: the resultant R is fed almost entirely from the radial component. This means that the drag, which comes from the flow around the edges of the lift-generating wing, is primarily due to the radial flow, which is fanned by the driving system. This is exactly what the "SideWash" mentioned above as a metaphor is.
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Fig.3: Y-Z section (X=15LE) and the components of the velocity gradients in the direction of the axis of the vortex thread: U; radial components, V, W; Resulting local velocity in the field: R. (Felgenhauer 2023).
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Fig.4: Section through the calculated field in the X-Y plane (Z=15LE). Impulse effect of an “elongated” vortex filament in a fluid at rest (Fig. 3); the components of the velocity gradient u, v, w; and the resultant r. (left to right; Felgenhauer (2023)).
Interacting vortex filaments
For a long time we did not have a working model of a fluid-structure interaction for a group of spatially distributed vortices. The complicated combinatorial fluid-filament interaction of the simulation model leads to a vortex coil system that organizes the field so that flows start to follow a physically based fluctuation. This appears unreal to the observer at first! How can it be, that flow lines form “by themselves” in a field?
The numerical model assumes that a wing tip, splitted into five feather fingers - also encloses five identical circulations. Elsewhere it will be shown what non- homogeneous circulation distributions at a feathered marginal arc, cause spiral formations. The oddness of the fanning plays no significant role in the simulation. The five-fold interaction scenario is discretized 5 times p-dimensional on the part of the vortex filament: Each finite section on the vortex filament contributes to the induction of a velocity and a specific impulse at each location in the field. The vortex sources are now finite small but localizable sections on each vortex filament. The very small sector of an inductively active vortex filament in Lagrange coordinates affects all locations in the field in Euler coordinates. The entire scenario of vortex threads has an inductive effect on every point in the field. This combinatorial balance is complex in the numerical simulation. The effects in the points of the field are cumulative.
The fluidic vortex coil (WSP) now considered is a spiral structure made up of five interaction partners: global-Mode5-WSP! The following applies to a 5-way interaction: If a moving or stationary fluid encounters flexible forms of moving interfering contours, these systems influence each other. In addition, they always shape the fluid surrounding them when the interfering contours are flow- inductively vital. If filaments manipulate other filaments inductively, one can speak of a fluid-filament interaction.
The autopoietic7, self-referential interaction of five eddy threads in a fluidic field means an a priori simultaneity of all fluidic partners that are impulse-effective in the field8. This includes interactions with neighbour structures that are able to shape each other. Each location on each vortex filament is a source point; every location on each vortex filament is a reference point. Near, but also far from any place on the vortex filament, each vortex source has an induction-effective influence "on itself". The physics of the mutual filament-filament interaction is simulated using a recursive numerical method, which we call the “Ramsey permutation method”. Each vortex filament successively influences every other vortex filament. The induced momentum leads to a collective transport process.
The simulation tells us how the flow space, which is initially at rest, is set in motion and thus organized by the induction effects of the spiral vortex structure. As expected, the rotating vortex coil system (globaMode5WSP) "pumps" fluid through its interior: from the left to the right (Fig.6); namely “rotor-free”! The corridor contains the fluid at rest. A 5-fold vortex coil is created in this 3D corridor model successively and self referentially (Fig. 5). We see that the vortex coil in the inductive interaction process "degenerates a little" with progressive iterations.
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Abb.5: Corridor model of a 5-fold vortex coil: globaMode5WSP.
Let us consider the fluid mechanical process again. In the setup of the model, the calculated vortex coil structure exists from a height of X=10LE, sucks in fluid from its surroundings, conveys matter along its central axis and out astern. If the vortex filaments are close together, for whatever reason, there is an intensive induction effect in the flow. This is an important finding for future design issues.
To a bird, the fluid mechanics vortex coil is nothing less than a “biological jet propulsion!” To an engineer, it is a very elegant fluidic aggregate that generates reaction forces.
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Fig.6: Flow pattern in the XY section plane (Z=15 LE)
Conclusion
In the classic sense, the flow-mechanical vortex coil does not reduce the so-called induced drag of a lift-generating wing. However, it does add a thrust to the movement system that opposes the resistance. Induced drag is often referred to as the price to pay when ordering lift: no free lunch! In this rhetoric, the impulse-inducing interaction events in and around a fluid-mechanical vortex coil would be the payback points in the balance sheet. You get something back!
Summary. The gliding flight of a lift-generating wing through a fluid at rest leaves a vortex pattern in the fluidic room. Such a flow process, in which several vortex thread systems communicating with each other interact, so that impulse exchange prevails simultaneously at every point in a previously stationary space, has not yet been experimentally investigated for a stationary fluid.
The numerical experiment deliberately reverses the conditions prevailing in a wind tunnel: a moving interfering contour passes through a fluid at rest. Model calculations show that left to themselves vortex filaments in the wake of an interference contour begin to "dance with each other" in order to form a rotating spiral structure: the vortex coil. This theoretical knowledge confirms assumptions from real observations and from measurement results on vortex coils in the wind tunnel.
Well, the functional structure of vortex coils is quite complex. And it's not explored in any way. With the theoretical models discussed here, it can be shown that in simulations of vortex coils, the current threads are compressed, analogous to a compression of magnetic field lines in an electric field. This was the prediction of the transfer of a general field theory to the fluid-mechanical concerns of a three-dimensional fluidic field.
The formation of a structure of fluidic vortex filaments left to its own devices is “self-referential, autopoietic and interactive”. A model of interacting vortices is motivated by observations, fluidmechanical investigations and measurements in wind tunnels (resting interfering contour, moving medium) and was successfully applied in this study to a stationary fluid with a moving interfering contour (corridor model).
The essay develops the principle and the formal requirements of modelling and numerical simulation of five-thread fluid-mechanically effective vortex coil systems made of filaments against the background of self-referential fluid-filament interactions. The Ramsey permutation method is integrated into the numerical model as the algorithmic core of the calculation method for a flow field containing vortex coil systems. The result of the work is the simulation and calculation of the impulse induction through an interference contour in a fluidic space at rest. The numerical model is to be further developed.
Michael Dienst, Summer 2024
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[6]The components (u,v,w) of the velocity vi induced in the field, which is equal to the vector specific induced impulse ji[ms-[1]].
[...]
1 Glide ratio of an airfoil, characteristic value from aeromechanics (Lilienthal coefficient) and calculated from the measured or calculated drag coefficient cw and the coefficient of fluid dynamic lift Cl (lift). In the case of the unpowered gliding flight of a bird or a (flight) model, the glide ratio also corresponds to the ratio of the distance covered and the loss of altitude. Gleitzahl eines Tragflügels, Kennwert aus der Aeromechanik (Lilienthal-Beiwert) und berechnet aus gemessenem oder berechneten Widerstandskoeffizienten cw und dem Koeffizienten des fluiddynamischen Auftriebs Cl (Lift). Im Falle des antriebslosen Gleitflugs eines Vogels oder eines (Flug-) Modells entspricht die Gleitzahl zugleich dem Verhältnis aus zurückgelegter Wegstrecke und Höhenverlust.
2 Winglets or sharklets (Airbus), are outer wings that are usually extended upwards and less frequently upwards and downwards at the ends of the wings of aircraft. They provide better lateral stability, reduce induced air resistance and thus improve the glide angle and the climb rate at low speeds. Winglets (wörtlich: englisch Flügelchen) bzw. Sharklets (Bezeichnung für Winglets bei Airbus), deutsch Flügelohren, sind meistens nach oben und seltener nach oben und unten verlängerte Außenflügel an den Enden der Tragflächen von Luftfahrzeugen. Sie sorgen für eine bessere Seitenstabilität, verringern den induzierten Luftwiderstand und verbessern so den Gleitwinkel sowie die Steigzahl bei niedriger Geschwindigkeit. https://de.wikipedia.org/wiki/Winglet
3 In physics, specifically electromagnetism, the Biot-Savart law is an equation describing the magnetic field generated by a constant electric current. It relates the magnetic field to the magnitude, direction, length, and proximity of the electric current. The Biot-Savart law is fundamental to magnetostatics. It is valid in the magnetostatic approximation and consistent with both Ampère's circuital law and Gauss's law for magnetism. When magnetostatics does not apply, the Biot-Savart law should be replaced by Jefimenko's equations. The law is named after Jean-Baptiste Biot and Félix Savart, who discovered this relationship in 1820. Benannt wurde dieses Gesetz nach den beiden französischen Mathematikern Jean-Baptiste Biot und Félix Savart, die es 1820 formuliert hatten.Es stellt neben dem ampèreschen Gesetz eines der Grundgesetze der Magnetostatik, eines Teilgebiets der Elektrodynamik, dar. https://de.wikipedia.org/wiki/Biot-Savart-Gesetz
4 In aeronautics, downwash is the change in direction of air deflected by the aerodynamic action of an airfoil, wing, or helicopter rotor blade in motion, as part of the process of producing lift. In helicopter aerodynamics discussions, it may be referred to as induced flow. In der Luftfahrt bezeichnet Abwind (englisch downwash) einen technischen Abwind, wie er von Flugzeugen und Hubschraubern von den Tragflächen bzw. Rotoren bei der Erzeugung von dynamischem Auftrieb entsteht.
5 In der Simulationspraxis wird die statt der Wirbelstärke ro [s-1] häufig die Zirkulation r [m2s-1] verwendet. Also: In continuum mechanics, vorticity is a pseudovector field that describes the local spinning motion of a continuum near some point (the tendency of something to rotate), as would be seen by an observer located at that point and traveling along with the flow. It is an important quantity in the dynamical theory of fluids and provides a convenient framework for understanding a variety of complex flow phenomena, such as the formation and motion of vortex rings. https://en.wikipedia.org/wiki/Vorticity
6 Die Komponenten (u,v,w) der in das Feld induzierten Geschwindigkeit vi, die gleich dem vektoriellen spezifischen induzierten Impuls ji[ms-1] ist.
7 The term autopoiesis (self-creation) is a neologism coined in 1972 by Varela and Maturana, Chilean cellular biologists and systems theorists, to describe the capacity of living cells to reproduce and organise themselves. The term was picked up and deployed by Niklas Luhmann (1927 - 1998), a German sociologist and philosopher,
Häufig gestellte Fragen
Worum geht es in "Fluid flow in spirally vortex structures Notes on bird flight"?
Das Dokument befasst sich mit fluidmechanischen Wirbelspulen, die als spiralförmig angeordnete, kohärente Wirbelfäden entstehen. Es wird untersucht, welche physikalischen Eigenschaften diesen Wirbelspulen zugeordnet werden können und wie die Wirbelfadentheorie von Helmholtz angewendet und erweitert werden kann, um diese Strukturen zu beschreiben. Ein besonderer Fokus liegt auf der Selbstorganisation (Autopoiesis) von Wirbelfäden in einem Strömungsfeld und deren Fähigkeit, Momentum zu induzieren.
Was sind die wichtigsten Schlüsselwörter im Zusammenhang mit fluidmechanischen Wirbelspulen?
Die wichtigsten Schlüsselwörter sind: Feld, fluidmechanische Wirbelspulen, Wirbelfadentheorie, Lagrangesche kohärente Strukturen, Wirbelfäden, Autopoiesis.
Was wird unter der "Spiralform" in diesem Kontext verstanden?
Die mehrfache, fluidmechanische Wirbelspule ist ein Konstrukt aus kohärenten Wirbelfäden mit zugeschriebenen Eigenschaften. Sie sind synthetisch, da es Systeme gibt, die solche Spulen erzeugen. Die ersten Formulierungen kamen aus Beobachtungen an den Flügelspitzen von Landsegelfliegern. Die Geometrie des Systems (Ellipse oder Bogen) hat großen Einfluss auf die Qualität des resultierenden Wirbelsystems.
Was wurde bei den ersten Untersuchungen zum Thema "gleitende Vögel" im Labor festgestellt?
Die ersten Untersuchungen fanden in Windkanälen der TU Berlin statt. Man konnte die räumliche Form von spiralförmigen Systemen im Nachlauf der Flügelströmung erkennen. Die beobachteten Wirbelbereiche bilden stationäre, diskrete Strukturen, die als zusammenhängende Fäden angeordnet sind und eine radialsymmetrische Spirale bilden. Diese Fäden sind stabil und rotieren um das Zentrum der Wirbelspirale, wobei höhere Fluidgeschwindigkeiten als im Zuflussbereich festgestellt wurden.
Was ist das "Korridormodell" und wie unterscheidet es sich vom Windkanalaufbau?
Das Korridormodell ist ein Gedankenexperiment, bei dem ein Flügel durch einen stehenden Fluidkanal segelt. Im Gegensatz zum Windkanal, bei dem ein Fluid um einen ruhenden Körper strömt, bewegt sich hier der Körper durch das Fluid. Das Modell zeigt, dass ein Wirbelfaden entlang der zentralen Achse des Korridors entsteht, der das Strömungsfeld organisiert. Die induzierte Geschwindigkeit ist senkrecht zur Bewegungsrichtung.
Wie interagieren Wirbelfäden miteinander?
Die Wechselwirkung mehrerer räumlich verteilter Wirbel führt zu einem Wirbelspulensystem, das das Feld so organisiert, dass Fluktuationen entstehen. Das Modell nimmt an, dass ein in Federfinger aufgeteilter Flügel identische Zirkulationen einschließt. Jeder Abschnitt des Wirbelfadens trägt zur Induktion einer Geschwindigkeit und eines Impulses an jedem Ort im Feld bei. Die simultane Interaktion aller impuls-wirksamen Partner führt zu einer kollektiven Transportbewegung.
Was ist die Schlussfolgerung der Analyse der fluidmechanischen Wirbelspulen?
Die fluidmechanische Wirbelspule reduziert nicht den induzierten Widerstand einer tragenden Fläche, sondern fügt dem System einen Schub hinzu, der dem Widerstand entgegenwirkt. Die im Feld stattfindenden Wechselwirkungen gleichen den induzierten Widerstand aus. Die Simulationen zeigen, dass Wirbelfäden im Nachlauf einer Störkontur beginnen, miteinander zu tanzen, um eine rotierende Spiralstruktur zu bilden. Die Bildung dieser Strukturen ist selbstbezüglich, autopoietisch und interaktiv.
Was ist die Ramsey-Permutationsmethode?
Die Ramsey-Permutationsmethode ist ein rekursives numerisches Verfahren, das zur Simulation der Physik der gegenseitigen Filament-Filament-Interaktion verwendet wird. Jeder Wirbelfaden beeinflusst sukzessive jeden anderen Wirbelfaden. Der induzierte Impuls führt zu einem kollektiven Transportprozess. Es ist der algorithmische Kern der Berechnungsmethode für ein Strömungsfeld, das Wirbelspulensysteme enthält.
Was ist die Bedeutung von "Autopoiesis" in diesem Zusammenhang?
Autopoiesis (Selbstherstellung) bezieht sich auf die Fähigkeit von Wirbelfäden, sich selbst zu organisieren und zu erhalten, indem sie durch ihre Interaktionen mit anderen Wirbelfäden und dem umgebenden Fluid ein kohärentes System bilden. Diese selbstbezügliche Interaktion ermöglicht es dem Wirbelspulensystem, sich an Veränderungen in der Umgebung anzupassen und seine Struktur aufrechtzuerhalten.
- Citar trabajo
- Michael Dienst (Autor), 2024, Fluid Flow in Spirally Vortex Structures. Notes on Bird Flight, Múnich, GRIN Verlag, https://www.grin.com/document/1487367
