Numerical study of the behaviour of a system of parallel line vortices

1970 ◽  
Vol 40 (3) ◽  
pp. 595-602 ◽  
Author(s):  
G. S. Murty ◽  
K. Sankara Rao
Keyword(s):  
Regular Polygon ◽  
Numerical Study ◽  
Parallel Line ◽  
Dynamical Behaviour ◽  
Macroscopic Model ◽  
Inviscid Fluid ◽  
Vortex System ◽  
Plane Normal ◽  
Vortex Lines ◽  
Linear Interactions

The dynamical behaviour of a system of parallel line vortices in an inviscid fluid is studied numerically. The initial configuration of the system is assumed to be such that the points of intersection of the line vortices with a plane normal to the vorticity form a regular polygon. The numerical experiments show that the vortex polygon is rearranged due to non-linear interactions among the line vortices in such a way as to produce a more or less uniform distribution of vortices inside the fluid with an approximately constant mean separation. The average angular velocity of the rotation of the vortex lines about the instantaneous centroid of the vortex system remains approximately constant. These results agree with the conjecture of Raja Gopal (1964). The results may prove to be of some value in a macroscopic model of liquid helium based on hydrodynamical principles.

An Investigation Into the Dynamics of a Pipe Aspirating Fluid

2018 ◽  
Author(s):  
Muhammad Faisal Javed Butt ◽  
Michael P. Paidoussis ◽  
Meyer Nahon
Keyword(s):  
Numerical Study ◽  
Fluid Velocity ◽  
Dominant Frequency ◽  
Dynamical Behaviour ◽  
Working Fluid ◽  
Flexible Pipe ◽  
Recovery Processes ◽  
Underground Caverns ◽  
Comparison Functions ◽  
Cantilevered Beam

Pipes aspirating fluid have applications in the filling and recovery processes for underground caverns — large subterranean cavities used to store hydrocarbons, such as natural gas and oil. This paper deals with the dynamics of a vertical cantilevered flexible pipe, immersed in fluid. Fluid is aspirated from its bottom free end up to the fixed upper end. In this study, the working fluid is assumed to be water. An existing analytical model is used to predict the dynamical behaviour of the aspirating pipe. This model is then discretized with Galerkin’s method, using Euler-Bernoulli eigen-functions for cantilevered beam as comparison functions. Once solved, the model results show a unique kind of flutter comprising three regions, denoted regions 01–03. These regions are delineated by two critical flow velocities, Ucf1 and Ucf2. In addition, two frequencies of oscillation, f1 and f2, are found to characterize the aforementioned flutter. The dominant frequency of oscillation changes from f1 to f2 as the flow velocity is increased from approximately 3 to 6 m/s — a frequency exchange phenomenon observed and reported here for the first time for this system. The analytical/numerical study was followed by a corresponding experimental study. Experiments were performed on a flexible (Silastic) pipe that was completely submerged in water. The behaviour observed experimentally was similar to the numerical study, as the aspirating fluid velocity was increased from zero to 7 m/s.

scholarly journals Dust Evolution in Protoplanetary Disks

1996 ◽  
Vol 150 ◽  
pp. 513-516
Author(s):  
Thomas Henning ◽  
Wolfgang Schmitt ◽  
Hubert Klahr ◽  
Rastislav Mucha
Keyword(s):  
Numerical Study ◽  
Dynamical Evolution ◽  
Dynamical Behaviour ◽  
Young Stellar Objects ◽  
Dust Particles ◽  
Circumstellar Disk ◽  
Stellar Objects ◽  
One Dimensional ◽  
First Results ◽  
Dust Evolution

AbstractThe evolution of dust particles in circumstellar disk-like structures around protostars and young stellar objects is discussed. We especially consider the coagulation of grains due to collisional aggregation and the influence of this process on the optical properties of the particles. These dust opacities are important for both the derivation of the circumstellar dust mass from submillimetre continuum observations and the dynamical behaviour of the disks.We present first results of a numerical study of the coagulation of dust grains in a turbulent protoplanetary accretion disk described by a time-dependent one-dimensional (radial) “alpha” model. The influence of grain opacity changes due to dust coagulation on the dynamical evolution of a protostellar disk is investigated. In addition, we consider the grain motion in two-dimensional disks.

Numerical Study on the Two-Dimensional Vortex System with Random Pinning

1999 ◽  
Vol 16 (9) ◽  
pp. 689-691 ◽  
Author(s):  
Yi-gang Cao ◽  
Ya-bin Yu ◽  
Zheng-kuan Jiao
Keyword(s):  
Numerical Study ◽  
Two Dimensional ◽  
Vortex System

scholarly journals A Numerical Study of the 6 May 2012 Tsukuba City Supercell Tornado. Part I: Vorticity Sources of Low-Level and Midlevel Mesocyclones

2016 ◽  
Vol 144 (3) ◽  
pp. 1069-1092 ◽  
Author(s):  
Wataru Mashiko
Keyword(s):  
Numerical Study ◽  
Streamwise Vorticity ◽  
Retrograde Motion ◽  
Low Level ◽  
Vortex Lines ◽  
Supercell Storm ◽  
Nested Grids ◽  
Generation Mechanisms ◽  
Eastern Japan ◽  
Gust Front

Abstract On 6 May 2012, an F3 supercell tornado, one of the most destructive tornadoes ever recorded in Japan, hit Tsukuba City in eastern Japan and caused severe damage. To clarify the generation mechanisms of the tornadic storm and tornado, high-resolution numerical simulations were conducted under realistic environmental conditions using triply nested grids. The innermost simulation with a 50-m mesh successfully reproduced the Tsukuba City tornadic supercell storm. In this study (the first of a two-part study), the vorticity sources responsible for mesocyclogenesis prior to tornadogenesis were investigated by analyzing vortex lines and the evolution of circulation of the mesocyclones. Vortex lines that passed through the midlevel mesocyclone (4-km height) originated from the environmental streamwise vorticity, whereas the low-level mesocyclone and low-level mesoanticyclone were connected by several arching vortex lines over the rear-flank downdraft associated with the hook-shaped distribution of hydrometeors (hereafter hook echo). Most of the circulation for the circuit surrounding the midlevel mesocyclone was conserved, although the baroclinity associated with positive buoyancy within the storm led to an up-and-down trend. The circulation of the material circuit encircling the low-level mesocyclone showed a gradual increase caused by baroclinity along the forward-flank gust front. Friction also had a positive net effect on the circulation. In contrast, most of the negative circulation of the low-level mesoanticyclone was rapidly acquired owing to baroclinity around the tip of the hook echo. Just after tornadogenesis, the low-level mesocyclone intensified significantly and developed upward, which caused retrograde motion of the midlevel mesocyclone.

Physical and Numerical Study of the Interaction Between a Fluid and an Oscillating Cylinder

2008 ◽  
Author(s):  
Marion Duclercq ◽  
Daniel Broc
Keyword(s):  
Physical System ◽  
Stokes Equations ◽  
Extreme Values ◽  
Numerical Study ◽  
Force Balance ◽  
Power Balance ◽  
Inviscid Fluid ◽  
Fluid Viscosity ◽  
Computational Domain ◽  
Line Force

This paper deals with a vibratory problem of fluid-structure interaction. It considers the two-dimensional case of a rigid, smooth and circular cylinder undergoing transverse sinusoidal oscillations and immersed in a viscous fluid otherwise at rest. Our work is focused on the in-line force acting on the cylinder in unsteady laminar flow. The aim is to understand the variations of the force with time according to the configuration of the physical system. For that the analysis will also use an energetic approach based on the power balance. The physical system can be characterized by two non-dimensional numbers: the Reynolds number (Re) compares the importance of the fluid viscosity to its inertia, and the Keulegan-Carpenter number (Kc) measures the amplitude of the cylinder displacement compared to its diameter. First the incompressible Navier-Stokes equations are solved numerically by means of a finite elements method. The flow structure is analyzed by determining the evolution with time and throughout the computational domain of flow quantities, such as pressure field, vorticity field or stream lines. We also calculate the values versus time of the different terms occurring in the mean force balance and power balance. We compare these results for several pairs (Kc, Re) of “extreme” values. Thus it appears three characteristic configurations: the inertial Euler case (Kc≪1 and inviscid fluid), the Stokes case (Kc≪1 and Re≫1) and the drag case (Kc≫1). For these three reference configurations the physical mechanisms operating in the system are identified. But in intermediate cases, particularly when Kc>1, every mechanisms interact. Consequently the evolution of the force acting on the cylinder versus time is more complex and its interpretation becomes less straightforward. That is why a quantitative energetic analysis is carried out. We define a measure of the dissipative energy present in the flow. Then we compare the values of that coefficient for different cases throughout the map (Kc, Re).

Numerical Investigation of the Three-Dimensional Flow Structure About a Revolving Wing

2012 ◽  
Author(s):  
Daniel J. Garmann ◽  
Miguel R. Visbal ◽  
Paul D. Orkwis
Keyword(s):  
Turbulent Flows ◽  
Numerical Study ◽  
Three Dimensional ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Vortex System ◽  
Aerodynamic Loads ◽  
Eddy Simulation ◽  
Data Reduction Technique ◽  
The Stability

A numerical study is conducted to examine the vortex structure about a revolving wing in quiescent flow employing a high-fidelity, implicit large eddy simulation (ILES) technique found to be effective in simulating flows that exhibit interspersed regions of laminar, transitional, and turbulent flows. The revolving wing configuration consists of a single, aspect ratio one rectangular plate extended out a distance of 0.5 chords from the origin. Shortly after the onset of the motion, the rotating wing generates a stable and coherent vortex system across the leading edge and wing root that remains throughout the motion. The aerodynamic loads are also analyzed and found to remain mostly constant during the maneuver. Transitional effects on the vortex system are investigated over a range of Reynolds numbers (3,000 < Re < 15,000). It is found that higher Reynolds numbers promote more breakdown of the leading edge and root vortices, but do not alter the stability of the vortex system. The aerodynamic loads also show little sensitivity to Reynolds number with the higher Reynolds numbers producing only moderately higher forces. Comparisons with recent experimental PIV measurements using a PIV-like data reduction technique applied to the computational solution show very favorable agreement with the mid-span velocity and vorticity contours.

An Experimental and Numerical Investigation of the Effect of Combustor-Nozzle Platform Misalignment on Endwall Heat Transfer at Transonic High Turbulence Conditions

2016 ◽  
Author(s):  
A. Arisi ◽  
D. Mayo ◽  
Z. Li ◽  
W. F. Ng ◽  
H. K. Moon ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Numerical Study ◽  
Horseshoe Vortex ◽  
Aerodynamic Characteristics ◽  
Secondary Flows ◽  
Navier Stokes ◽  
Vortex System ◽  
Ansys Fluent ◽  
Heat Transfer Augmentation ◽  
Exit Mach Number

A detailed experimental and numerical study has been conducted to investigate the endwall heat transfer characteristics on a nozzle platform that has been misaligned with the combustor exit, resulting in a backward facing step at the nozzle inlet. The study was carried out under transonic engine representative conditions with an exit Mach number of 0.85 (Reexit = 1.5 × 106), and an inlet turbulence intensity of 16%. A transient infrared thermography technique coupled with endwall static pressure ports, were used to map the endwall surface heat transfer and aerodynamic characteristics respectively. A numerical study was also conducted by solving the steady state Reynolds Averaged Navier Stokes (RANS) equations using the commercial CFD solver ANSYS Fluent v.15. The numerical results were then validated by comparing to experiment data and good agreement was observed. The results reveal that the classical endwall secondary flows (endwall crossflows, horseshoe and passage vortices) are weakened and a unique auxiliary vortex system develops within the passage and interacts with the weakened horseshoe vortex. It is observed that heat transfer in the first half of the passage endwall is heavily influenced by this auxiliary vortex system. Heat transfer augmentation of between 15% and 40% was also observed throughout the NGV endwall. Furthermore, the auxiliary vortex system results in a delayed cross-passage migration of the horseshoe vortex which consequently results in large lateral gradient in heat transfer downstream of the throat.

scholarly journals On the vortex theory of screw propellers

1929 ◽  
Vol 123 (792) ◽  
pp. 440-465 ◽  
Keyword(s):  
Exact Solution ◽  
Unit Length ◽  
Inviscid Fluid ◽  
Vortex System ◽  
Vortex Theory ◽  
Trailing Vortices ◽  
Screw Surface ◽  
Blade Section ◽  
Flow Round ◽  
Irrotational Motion

The vortex-theory of screw propellers develops along similar lines to aerofoil theory. There is circulation of flow round each blade; this circulation vanishes at the tip and the root. The blade may be replaced by a bound vortex system, which, for the sake of simplicity, may be taken, as a first approximation, to be a bound vortex line. The strength of the vortex at any point is equal to Γ, the circulation round the corresponding blade section. From every point of this bound vortex spring free, trailing vortices, whose strength per unit length is —∂Γ/∂ r , where r is distance from the axis of the screw. When the interference flow of this vortex system is small compared with the velocity of the blades, the trailing vortices are approximately helices, and together build a helical or screw surface. Part of the work supplied by the motor is lost in producing the trailing vortex system. When the distribution of Γ along the blade is such that, for a given thrust, the energy so lost per unit time is a minimum, then the flow far behind the screw is the same as if the screw surface formed by the trailing vortices was rigid, and moved backwards in the direction of its axis with a constant velocity, the flow being that of classical hydro dynamics in an inviscid fluid, continuous, irrotational, and without circulation. The circulation round any blade section is then equal to the discontinuity in the velocity potential at the corresponding point of the screw surface. Further, for symmetrical screws, the interference flow at the blade is half that at the corresponding point of the screw surface far behind the propeller. An approximate solution for the irrotational motion of a screw surface in an inviscid fluid was given by Prandtl. The accuracy of the approximation increases with the number of blades and with the ratio of the tip speed to the velocity of advance, but for given values of these numbers we have no means of estimating the error, since the exact solution of the problem has not yet been found. It is the main object of this work to find the exact solution.

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