Computational Methods With Vortices—The 1988 Freeman Scholar Lecture

1989 ◽  
Vol 111 (1) ◽  
pp. 5-52 ◽  
Author(s):  
Turgut Sarpkaya
Keyword(s):  
Computational Methods ◽  
Evolution Equations ◽  
Operator Splitting ◽  
Three Dimensional ◽  
Separated Flow ◽  
Body Representation ◽  
Vortex Sheet ◽  
Personal View ◽  
Discrete Vortex ◽  
Practical Applications

A comprehensive review is presented of the computational methods based upon Helmholtz’s powerful concepts of vortex dynamics, making use of Lagrangian or mixed Lagrangian-Eulerian schemes, the Biot-Savart law or the Vortex-in-Cell methods. The ingenious approximations and smoothing schemes developed in search of predictive models, qualitative solutions, new insights, or just some inspiration in the simulation of often two-dimensional, occasionally three-dimensional, and almost always incompressible fluids are described in detail. One is forewarned at the onset that chaos awaits at the end of the road. The challenge is to produce results in the face of ever accumulating errors within a time scale appropriate for the investigation. The review is organized around two major sections: Theoretical foundations and practical applications of vortex methods. The first covers topics such as vorticity and laws of transportation, evolution equations for a vortex sheet, real vortices and instabilities, Biot-Savart law, smoothing techniques (cutoff schemes, amalgamation of vortices, subvortex methods), cloud-in-cell or vortex-in-cell methods, body representation (Routh’s rule, surface singularity distributions), operator splitting and the random walk method (description and convergence), and asymmetry introduction. The next section covers contra flowing streams, vortical flows in aerodynamics (vortex sheet roll-up; slender-body, two-vortex, multi-discrete vortex, and segment or panel methods; three-dimensional flow models, and vortex-lattice methods), separated flow about cylindrical bodies (circular cylinder, sharp-edged bodies, arbitrarily-shaped bodies), general three-dimensional flows (vortex rings, turbulent spots, temporally and spatially-growing shear layers, and other applications (vortex-blade interactions, combustion phenomena, acoustics, contour dynamics, interaction of line vortices, chaos, and turbulence). The review is concluded with a brief comparison of these methods with others used in computational fluid dynamics and a personal view of their future prospects.

Three-dimensional surfactant-covered flows of thin liquid films on rotating cylinders

2018 ◽  
Vol 844 ◽  
pp. 61-91 ◽  
Author(s):  
Weihua Li ◽  
Satish Kumar
Keyword(s):  
Free Surface ◽  
Flow Visualization ◽  
Evolution Equations ◽  
Thin Liquid Film ◽  
Three Dimensional ◽  
Axial Direction ◽  
Liquid Films ◽  
Practical Applications ◽  
Rotation Rates ◽  
Visualization Experiments

The coating of discrete objects is an important but poorly understood step in the manufacturing of a broad variety of products. An important model problem is the flow of a thin liquid film on a rotating cylinder, where instabilities can arise and compromise coating uniformity. In this work, we use lubrication theory and flow visualization experiments to study the influence of surfactant on these flows. Two coupled evolution equations describing the variation of film thickness and concentration of insoluble surfactant as a function of time, the angular coordinate and the axial coordinate are solved numerically. The results show that surface-tension forces arising from both axial and angular variations in the angular curvature drive flows in the axial direction that tend to smooth out free-surface perturbations and lead to a stable speed window in which axial perturbations do not grow. The presence of surfactant leads to Marangoni stresses that can cause the stable speed window to disappear by driving flow that opposes the stabilizing flow. In addition, Marangoni stresses tend to reduce the spacing between droplets that form at low rotation rates, and reduce the growth rate of rings that form at high rotation rates. Flow visualization experiments yield observations that are qualitatively consistent with predictions from linear stability analysis and the simulation results. The visualizations also indicate that surfactants tend to suppress dripping, slow the development of free-surface perturbations, and reduce the shifting and merging of rings and droplets, allowing more time for solidifying coatings in practical applications.

Singularity formation in three-dimensional motion of a vortex sheet

1995 ◽  
Vol 300 ◽  
pp. 339-366 ◽  
Author(s):  
Takashi Ishihara ◽  
Yukio Kaneda
Keyword(s):  
Asymptotic Analysis ◽  
Numerical Integration ◽  
Finite Time ◽  
Fourier Coefficients ◽  
Evolution Equations ◽  
Three Dimensional ◽  
Vortex Sheet ◽  
Three Dimensions ◽  
Leading Order ◽  
Singularity Formation

The evolution of a small but finite three-dimensional disturbance on a flat uniform vortex sheet is analysed on the basis of a Lagrangian representation of the motion. The sheet at time t is expanded in a double periodic Fourier series: R(λ1, λ2, t) = (λ1, λ2, 0) + Σn,mAn,m exp[i(nλ1 + δmλ2)], where λ1 and λ2 are Lagrangian parameters in the streamwise and spanwise directions, respectively, and δ is the aspect ratio of the periodic domain of the disturbance. By generalizing Moore's analysis for two-dimensional motion to three dimensions, we derive evolution equations for the Fourier coefficients An,m. The behaviour of An,m is investigated by both numerical integration of a set of truncated equations and a leading-order asymptotic analysis valid at large t. Both the numerical integration and the asymptotic analysis show that a singularity appears at a finite time tc = O(lnε−1) where ε is the amplitude of the initial disturbance. The singularity is such that An,0 = O(tc−1) behaves like n−5/2, while An,±1 = O(εtc) behaves like n−3/2 for large n. The evolution of A0,m(spanwise mode) is also studied by an asymptotic analysis valid at large t. The analysis shows that a singularity appears at a finite time t = O(ε−1) and the singularity is characterized by A0,2k ∝ k−5/2 for large k.

Numerical Study of Unsteady Flow Around Airfoil With Spoiler

1998 ◽  
Vol 65 (1) ◽  
pp. 164-170 ◽  
Author(s):  
Cheng Xu ◽  
W. W. H. Yeung
Keyword(s):  
Numerical Study ◽  
Piecewise Linear ◽  
Separated Flow ◽  
Vortex Sheet ◽  
Time Step ◽  
Discrete Vortex ◽  
Vortex Model ◽  
Bernoulli’S Equation ◽  
Pressure Distributions ◽  
Rapid Deployment

A discrete vortex model based on the panel method has been developed to simulate the two-dimensional unsteady separated flow generated by the rapid deployment of a spoiler on the upper surface of an airfoil. This method represents the boundary surfaces by distributing piecewise linear-vortex and constant source singularities on discrete panels. The wake of the spoiler and airfoil is represented by discrete vortices. At each sharp edge, a vortex sheet is used to feed discrete vortices at every time-step to form the downstream wake. The length and strength of each shed vortex sheet are determined by the continuity equation and a condition such that the flow, the net force, and the pressure difference across the vortex sheet are zero. The flow patterns behind the spoiler at different time-steps are presented. The pressure distributions on the airfoil based on the unsteady Bernoulli’s equation are compared, where possible, with the experimental results and other computational results. The adverse lift effects have been obtained, and similar effects have been measured in experiments.

Prediction of Roll Damping in the Frequency Domain Using the Discrete Vortex Method

2010 ◽  
Author(s):  
Mohammad Hajiarab ◽  
J. Michael R. Graham ◽  
Martin Downie
Keyword(s):  
Frequency Domain ◽  
Model Test ◽  
Theoretical Approach ◽  
Three Dimensional ◽  
Separated Flow ◽  
Vortex Method ◽  
Roll Damping ◽  
Discrete Vortex ◽  
Discrete Vortex Method ◽  
Good Agreement

This paper describes a theoretical approach to predict roll damping for a three-dimensional barge shaped vessel in the frequency domain by matching a simple discrete vortex method (DVM), describing local separated flow, to an inviscid 3-D seakeeping code. The results are compared with model test experiments to demonstrate validity of the method. A good agreement between the model test RAO and the damped RAO is achieved.

Three-dimensional Graphene Coated Shape Memory Polyurethane Foam with Fast Responsive Performance

2021 ◽  
Author(s):  
Tianjiao Wang ◽  
Jun Zhao ◽  
Chuanxin Weng ◽  
Tong Wang ◽  
Yayun Liu ◽  
...  
Keyword(s):  
Shape Memory ◽  
Polyurethane Foam ◽  
Three Dimensional ◽  
Shape Memory Polymers ◽  
Practical Applications ◽  
External Stimuli ◽  
Shape Memory Polyurethane

Shape memory polymers (SMPs) that change shapes as designed by external stimuli have become one of the most promising materials as actuators, sensors, and deployable devices. However, their practical applications...

scholarly journals Three-Dimensional Structures of Carbohydrates and Where to Find Them

2020 ◽  
Vol 21 (20) ◽  
pp. 7702 ◽  
Author(s):  
Sofya I. Scherbinina ◽  
Philip V. Toukach
Keyword(s):  
Experimental Data ◽  
Molecular Modeling ◽  
Computational Methods ◽  
Three Dimensional ◽  
Structural Diversity ◽  
Structural Data ◽  
Structural Features ◽  
Data Validation ◽  
Data Generation ◽  
Efficient Treatment

Analysis and systematization of accumulated data on carbohydrate structural diversity is a subject of great interest for structural glycobiology. Despite being a challenging task, development of computational methods for efficient treatment and management of spatial (3D) structural features of carbohydrates breaks new ground in modern glycoscience. This review is dedicated to approaches of chemo- and glyco-informatics towards 3D structural data generation, deposition and processing in regard to carbohydrates and their derivatives. Databases, molecular modeling and experimental data validation services, and structure visualization facilities developed for last five years are reviewed.

Separated Flow Past a Slender Delta Wing at Incidence

1973 ◽  
Vol 24 (2) ◽  
pp. 120-128 ◽  
Author(s):  
J E Barsby
Keyword(s):  
Delta Wing ◽  
Separated Flow ◽  
Leading Edge ◽  
Vortex Sheet ◽  
Simultaneous Equations ◽  
Delta Wings ◽  
Nested Iteration ◽  
Finite Difference Technique ◽  
Flow Past ◽  
Vortex Systems

SummarySolutions to the problem of separated flow past slender delta wings for moderate values of a suitably defined incidence parameter have been calculated by Smith, using a vortex sheet model. By increasing the accuracy of the finite-difference technique, and by replacing Smith’s original nested iteration procedure, to solve the non-linear simultaneous equations that arise, by a Newton’s method, it is possible to extend the range of the incidence parameter over which solutions can be obtained. Furthermore for sufficiently small values of the incidence parameter, new and unexpected results in the form of vortex systems that originate inboard from the leading edge have been discovered. These new solutions are the only solutions, to the author’s knowledge, of a vortex sheet leaving a smooth surface.Interest has centred upon the shape of the finite vortex sheet, the position of the isolated vortex, and the lift, and variations of these quantities are shown as functions of the incidence parameter. Although no experimental evidence is available, comparisons are made with the simpler Brown and Michael model in which all the vorticity is assumed to be concentrated onto an isolated line vortex. Agreement between these two models becomes very close as the value of the incidence parameter is reduced.

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