The motion generated by a slowly rising disk in an unbounded rotating fluid for arbitrary Taylor number

1994 ◽  
Vol 262 ◽  
pp. 1-26 ◽  
Author(s):  
D. Vedensky ◽  
M. Ungarish
Keyword(s):  
Equations Of Motion ◽  
Ekman Layer ◽  
The Body ◽  
Taylor Number ◽  
Present Formulation ◽  
Rotating Fluid ◽  
Asymptotic Results ◽  
Dual Integral Equations ◽  
Axis Of Rotation ◽  
Insight Into

The motion of a disk rising steadily parallel to the axis of rotation in a uniformly rotating unbounded liquid is considered. In the limit of zero Rossby number the linear viscous equations of motion are reduced to a system of dual integral equations which renders an ‘exact’ solution for arbitrary values of the Taylor number, Ta. The investigation is focused on the drag and the flow field. In the limits of small and large Ta the asymptotic results of the present formulation agree with – and extend – previous investigations by different approaches.A particular novel feature, for large Ta, is the contribution of the Ekman-layer flux to the outer motion. New insight into the structure of the Taylor column is gained; in particular, it is shown that the main part of the column is a ‘bubble’ of recirculating fluid, detached from the body and not communicating with the Ekman layer. However, it turns out that the essential discrepancy in drag between experiments (Maxworthy 1970) and previous theories cannot be attributed to the Ekman-layer suction effect.

The motion of a rising disk in a rotating axially bounded fluid for large Taylor number

1995 ◽  
Vol 291 ◽  
pp. 1-32 ◽  
Author(s):  
Marius Ungarish ◽  
Dmitry Vedensky
Keyword(s):  
Exact Solution ◽  
Boundary Value Problem ◽  
Equations Of Motion ◽  
Taylor Number ◽  
Rossby Number ◽  
Rotating Fluid ◽  
Asymptotic Results ◽  
Dual Integral Equations ◽  
Wall Distance ◽  
Taylor Column

The motion of a disk rising steadily along the axis in a rotating fluid between two infinite plates is considered. In the limit of zero Rossby number and with the disk in the middle position, the boundary value problem based on the linear, viscous equations of motion is reduced to a system of dual-integral equations which renders ‘exact’ solutions for arbitrary values of the Taylor number, Ta, and disk-to-wall distance, H (scaled by the radius of the disk). The investigation is focused on the drag and on the flow field when Ta is large (but finite) for various H. Comparisons with previous asymptotic results for ‘short’ and ‘long’ containers, and with the preceding unbounded-configuration ‘exact’ solution, provide both confirmation and novel insights.In particular, it is shown that the ‘free’ Taylor column on the particle appears for H > 0.08 Ta and attains its fully developed features when H > 0.25 Ta (approximately). The present drag calculations improve the compatibility of the linear theory with Maxworthy's (1968) experiments in short containers, but for the long container the claimed discrepancy with experiments remains unexplained.

Forces on bodies moving transversely through a rotating fluid

1975 ◽  
Vol 71 (3) ◽  
pp. 577-599 ◽  
Author(s):  
P. J. Mason
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
Vertical Axis ◽  
The Body ◽  
Rotating Fluid ◽  
Size And Shape ◽  
Relative Direction ◽  
Axis Of Rotation

Measurements have been made of the net force F acting on a bluff rigid body moving with velocity U (relative to a fluid rotating about a vertical axis with uniform angular velocity Ω) in a plane perpendicular to the axis of rotation. The force F is of magnitude 2ΩρVU, where ρ is the density of the fluid and V is a volume which depends on the size and shape of the body. The relative direction of F and U is found to depend on the quantity \[ {\cal S}\equiv \frac{2\Omega L}{U}\bigg(\frac{h}{D}\bigg), \] where L and h are horizontal and vertical lengths characterizing the object and D is the depth of the fluid in which the object is placed.

scholarly journals Experiments on the motion of solid bodies in rotating fluids

1923 ◽  
Vol 104 (725) ◽  
pp. 213-218 ◽  
Keyword(s):  
Equations Of Motion ◽  
Three Dimensional ◽  
Steady Motion ◽  
The Body ◽  
Two Dimensional ◽  
Experimental Conditions ◽  
Axis Of Rotation ◽  
Rotating Liquid ◽  
Steady Motions ◽  
Solid Bodies

Some years ago it was pointed out by Prof. Proudman that all slow steady motions of a rotating liquid must be two-dimensional. If the motion is produced by moving a cylindrical object slowly through the liquid in such a way that its axis remains parallel to the axis of rotation, or if a two-dimensional motion is conceived as already existing, it seems clear that it will remain two-dimensional. If a slow three-dimensional motion is produced, then it cannot be a steady one. On the other hand, if an attempt is made to produce a slow steady motion by moving a three-dimensional body with a small uniform velocity (relative to axes which rotate with the fluid) three possibilities present themselves:— ( a ) The motion in the liquid may never become steady, however long the body goes on moving. ( b ) The motion may be steady but it may not be small in the neighbourhood of the body. ( c ) The motion may be steady and two-dimensional. In considering these three possibilities it seems very unlikely that ( a ) will be the true one. In an infinite rotating fluid the disturbance produced by starting the motion of the body might go on spreading out for ever and steady motion might never be attained, but if the body were moved steadily in a direction at right angles to the axis of rotation, and if the fluid were contained between parallel planes also perpendicular to the axis of rotation, it seems very improbable that no steady motion satisfying the equations of motion could be attained. There is more chance that ( b ) may be true. A class of mathematical expressions representing the steady motion of a sphere along the axis of a rotating liquid has been obtained. This solution of the problem breaks down when the velocity of the sphere becomes indefinitely small, in the sense that it represents a motion which does not decrease as the velocity of the sphere decreases. It seems unlikely that such a motion would be produced under experimental conditions.

A study of motions in a rotating liquid

1951 ◽  
Vol 206 (1084) ◽  
pp. 108-130 ◽  
Keyword(s):  
Angular Velocity ◽  
Equations Of Motion ◽  
Vertical Axis ◽  
The Body ◽  
Forced Oscillations ◽  
Infinite Cylinder ◽  
Two Dimensional ◽  
Small Motion ◽  
Axis Of Rotation ◽  
Rotating Liquid

Starting with the equations of motion for a perfect, incompressible fluid referred to a coordinate system which rotates about a vertical axis with uniform angular velocity R , the physical condition of ‘small motion’ is determined which permits the equations to be linearized. The small motions resulting from forced oscillations of a rotating liquid are investigated. It is shown that there are three types of flow depending on the relative magnitudes of the impressed frequency β and the angular velocity R of the fluid. Two of the regimes are studied in detail. A similarity law is developed which gives the solution of a class of problems of oscillations for β > 2 R in terms of the solutions to similar irrotational problems. An attempt is made to explain how slow, two-dimensional motion can be produced by introducing a boundary condition which is three-dimensional (as observed in experiments performed by G. I. Taylor), by considering problems from the moment at which the disturbance is created from rest relative to the rotating system, with the only initial assumption that the fluid is rotating uniformly like a solid body. For the particular cases studied the results are in agreement with Taylor’s experiments, in that the flow is found to become steady and two-dimensional if the disturbance which causes it approaches a steady state. If the disturbance is due to a body which moves along the axis of rotation of the fluid, the steady two-dimensional behaviour may be expected everywhere except in the neighbourhood of the surface of an infinite cylinder which encloses the body and whose generators are parallel to the axis of rotation. To resolve an apparent disagreement between certain theoretical results by Grace on the one hand, and experimental evidence by Taylor and the author’s conclusions, on the other, arguments are advanced that the various results may be in agreement, provided Grace’s are given a new interpretation.

Analytic-Holistic Two-Segment Model of Quadruped Back-Bending in the Sagittal Plane

2011 ◽  
Author(s):  
Justin E. Seipel
Keyword(s):  
Sagittal Plane ◽  
Mechanistic Model ◽  
Equations Of Motion ◽  
Mathematical Structure ◽  
Legged Locomotion ◽  
The Body ◽  
Whole Body ◽  
Body Segments ◽  
Segment Model ◽  
Insight Into

Back-bending in the sagittal plane is common in many animals during legged locomotion and could be useful for robots. However, to our knowledge, there exists no analytical mechanistic model of sagittal-plane back bending legged locomotion of quadrupeds. Such a mechanistic model and knowledge derived from it is expected to enable direct analysis and insight into back bending locomotion and can be applied to the study of biomechanics or the design of robots. Here a whole-body mechanistic model is developed and governing equations of motion are derived to provide insight into the mathematical structure of the system dynamics. The model is energy conserving, consisting of massless elastic legs pinned to two body segments. The two body segments are pin-joined together with a rotational spring. The massless legs are returned to a resting angle relative to the body during swing phase. We discover: 1) Whole-body configuration variables simplify the resulting equations of motion. 2) The sagittal-plane back-bending two-segment model of legged locomotion yields stable periodic gaits.

Basic Concepts and Definitions of Allergology

2019 ◽  
Author(s):  
Zoran Vrucinic
Keyword(s):  
Immune Reaction ◽  
The Body ◽  
The Other ◽  
Specific Response ◽  
Other Hand ◽  
Medical Vocabulary ◽  
The Future ◽  
Basic Concepts ◽  
Basic Insight ◽  
Insight Into

The future of medicine belongs to immunology and alergology. I tried to not be too wide in description, but on the other hand to mention the most important concepts of alergology to make access to these diseases more understandable, logical and more useful for our patients, that without complex pathophysiology and mechanism of immune reaction,we gain some basic insight into immunological principles. The name allergy to medicine was introduced by Pirquet in 1906, and is of Greek origin (allos-other + ergon-act; different reaction), essentially representing the reaction of an organism to a substance that has already been in contact with it, and manifested as a specific response thatmanifests as either a heightened reaction, a hypersensitivity, or as a reduced reaction immunity. Synonyms for hypersensitivity are: altered reactivity, reaction, hypersensitivity. The word sensitization comes from the Latin (sensibilitas, atis, f.), which means sensibility,sensitivity, and has retained that meaning in medical vocabulary, while in immunology and allergology this term implies the creation of hypersensitivity to an antigen. Antigen comes from the Greek words, anti-anti + genos-genus, the opposite, anti-substance substance that causes the body to produce antibodies.

Force in Nature

2020 ◽  
pp. 146-160
Author(s):  
David Carus
Keyword(s):  
Natural Science ◽  
The Body ◽  
The Core ◽  
Thing In Itself ◽  
The Will ◽  
Insight Into

This chapter explores Schopenhauer’s concept of force, which lies at the root of his philosophy. It is force in nature and thus in natural science that is inexplicable and grabs Schopenhauer’s attention. To answer the question of what this inexplicable term is at the root of all causation, Schopenhauer looks to the will within us. Through will, he maintains that we gain immediate insight into forces in nature and hence into the thing in itself at the core of everything and all things. Will is thus Schopenhauer’s attempt to answer the question of the essence of appearance. Yet will, as it turns out, cannot be known immediately as it is subject to time, and the acts of will, which we experience within us, do not correlate immediately with the actions of the body (as Schopenhauer had originally postulated). Hence, the acts of will do not lead to an explanation of force, which is at the root of causation in nature. Schopenhauer sets out to explain what is at the root of all appearances, derived from the question of an original cause, or as Schopenhauer states “the cause of causation,” but cannot determine this essence other than by stating that it is will; a will, however, that cannot be immediately known.

scholarly journals Minimally Invasive Autopsy Practice in COVID-19 Cases: Biosafety and Findings

Pathogens ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 412
Author(s):  
Natalia Rakislova ◽  
Lorena Marimon ◽  
Mamudo R. Ismail ◽  
Carla Carrilho ◽  
Fabiola Fernandes ◽  
...  
Keyword(s):  
Minimally Invasive ◽  
Cause Of Death ◽  
Diffuse Alveolar Damage ◽  
The Body ◽  
Protective Equipment ◽  
Safe Alternative ◽  
Minimally Invasive Autopsy ◽  
Postmortem Studies ◽  
Death Investigation ◽  
Insight Into

Postmortem studies are crucial for providing insight into emergent diseases. However, a complete autopsy is frequently not feasible in highly transmissible diseases due to biohazard challenges. Minimally invasive autopsy (MIA) is a needle-based approach aimed at collecting samples of key organs without opening the body, which may be a valid alternative in these cases. We aimed to: a) provide biosafety guidelines for conducting MIAs in COVID-19 cases, b) compare the performance of MIA versus complete autopsy, and c) evaluate the safety of the procedure. Between October and December 2020, MIAs were conducted in six deceased patients with PCR-confirmed COVID-19, in a basic autopsy room, with reinforced personal protective equipment. Samples from the lungs and key organs were successfully obtained in all cases. A complete autopsy was performed on the same body immediately after the MIA. The diagnoses of the MIA matched those of the complete autopsy. In four patients, COVID-19 was the main cause of death, being responsible for the different stages of diffuse alveolar damage. No COVID-19 infection was detected in the personnel performing the MIAs or complete autopsies. In conclusion, MIA might be a feasible, adequate and safe alternative for cause of death investigation in COVID-19 cases.

scholarly journals Closed-form time derivatives of the equations of motion of rigid body systems

2021 ◽  
Author(s):  
Andreas Müller ◽  
Shivesh Kumar
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Alternative Formulation ◽  
Dynamics Of Rigid Body ◽  
Control Forces ◽  
And Control ◽  
Derivatives Of ◽  
Insight Into

AbstractDerivatives of equations of motion (EOM) describing the dynamics of rigid body systems are becoming increasingly relevant for the robotics community and find many applications in design and control of robotic systems. Controlling robots, and multibody systems comprising elastic components in particular, not only requires smooth trajectories but also the time derivatives of the control forces/torques, hence of the EOM. This paper presents the time derivatives of the EOM in closed form up to second-order as an alternative formulation to the existing recursive algorithms for this purpose, which provides a direct insight into the structure of the derivatives. The Lie group formulation for rigid body systems is used giving rise to very compact and easily parameterized equations.

Numerical modelling of swirling momentumless turbulent wake dynamics

2018 ◽  
pp. 37-48
Author(s):  
Андрей Геннадьевич Деменков ◽  
Геннадий Георгиевич Черных
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Mathematical Models ◽  
Equations Of Motion ◽  
Turbulent Wake ◽  
The Body ◽  
Jet Flows ◽  
Reynolds Stresses ◽  
Bodies Of Revolution ◽  
Averaged Equations

С применением математической модели, включающей осредненные уравнения движения и дифференциальные уравнения переноса нормальных рейнольдсовых напряжений и скорости диссипации, выполнено численное моделирование эволюции безымпульсного закрученного турбулентного следа с ненулевым моментом количества движения за телом вращения. Получено, что начиная с расстояний порядка 1000 диаметров от тела течение становится автомодельным. На основе анализа результатов численных экспериментов построены упрощенные математические модели дальнего следа. Swirling turbulent jet flows are of interest in connection with the design and development of various energy and chemical-technological devices as well as both study of flow around bodies and solving problems of environmental hydrodynamics, etc. An interesting example of such a flow is a swirling turbulent wake behind bodies of revolution. Analysis of the known works on the numerical simulation of swirling turbulent wakes behind bodies of revolution indicates lack of knowledge on the dynamics of the momentumless swirling turbulent wake. A special case of the motion of a body with a propulsor whose thrust compensates the swirl is studied, but there is a nonzero integral swirl in the flow. In previous works with the participation of the authors, a numerical simulation of the initial stage of the evolution of a swirling momentumless turbulent wake based on a hierarchy of second-order mathematical models was performed. It is shown that a satisfactory agreement of the results of calculations with the available experimental data is possible only with the use of a mathematical model that includes the averaged equations of motion and differential equations for the transfer of normal Reynolds stresses along the rate of dissipation. In the present work, based on the above mentioned mathematical model, a numerical simulation of the evolution of a far momentumless swirling turbulent wake with a nonzero angular momentum behind the body of revolution is performed. It is shown that starting from distances of the order of 1000 diameters from the body the flow becomes self-similar. Based on the analysis of the results of numerical experiments, simplified mathematical models of the far wake are constructed. The authors dedicate this work to the blessed memory of Vladimir Alekseevich Kostomakha.

Sign in / Sign up

Export Citation Format

Share Document