scholarly journals Conformal Mapping-Based Discrete Vortex Method for Simulating 2-D Flows around Arbitrary Cylinders

2021 ◽  
Vol 9 (12) ◽  
pp. 1409
Author(s):  
Guoqing Jin ◽  
Zhe Sun ◽  
Zhi Zong ◽  
Li Zou ◽  
Yingjie Hu
Keyword(s):  
Conformal Mapping ◽  
Vortex Method ◽  
Reynolds Numbers ◽  
Mapping Method ◽  
Mirror Image ◽  
The Body ◽  
Time Step ◽  
Discrete Vortex ◽  
Fluid Field ◽  
Pressure Distributions

A novel technique based on conformal mapping and the circle theorem has been developed to tackle the boundary penetration issue, in which vortex blobs leak into structures in two-dimensional discrete vortex simulations, as an alternative to the traditional method in which the blobs crossing the boundary are simply removed from the fluid field or reflected back to their mirror-image positions outside the structure. The present algorithm introduces an identical vortex blob outside the body using the mapping method to avoid circulation loss caused by the vortex blob penetrating the body. This can keep the body surface streamlined and guarantees that the total circulation will be constant at any time step. The model was validated using cases of viscous incompressible flow passing elliptic cylinders with various thickness-to-chord ratios at Reynolds numbers greater than Re = 1 × 105. The force and velocity fields revealed that this boundary scheme converged, and the resultant time-averaged surface pressure distributions were all in excellent agreement with wind tunnel tests. Furthermore, a flow around a symmetrical Joukowski foil at Reynolds number Re = 4.62 × 104, without considering the trailing cusp, was investigated, and a close agreement with the experimental data was obtained.

The Importance of Secondary Shedding in Two-Dimensional Wake Formation at Very High Reynolds Numbers

1982 ◽  
Vol 33 (2) ◽  
pp. 105-123 ◽  
Author(s):  
P.K. Stansby ◽  
A.G. Dixon
Keyword(s):  
Vortex Method ◽  
Reynolds Numbers ◽  
Discrete Vortex ◽  
Pressure Distributions ◽  
Pressure Fields ◽  
High Reynolds Numbers ◽  
First Approximation ◽  
High Reynolds ◽  
Very High ◽  
Good Agreement

SummaryUncertainties in the use of the discrete-vortex method in modelling the time development of the wake of a circular cylinder at very high Reynolds numbers are investigated. It is shown that simply introducing vorticity at generally accepted separation positions at a rate of ½Us2, Us being the velocity at separation, gives wholly unrealistic wake predictions. In the base region pressure fields occur which would promote separation in steady flow and so a first approximation for ‘secondary’ separation is incorporated into the model. This brings pressure distributions and vorticity structures at subcritical and supercritical Reynolds numbers into good agreement with experiment. The convection of the vortices is calculated using the cloud-in-cell technique and comparisons are made with direct summation methods.

Numerical Simulation of Rivulet Dynamics Associated With Rain-Wind Induced Vibration

2010 ◽  
Author(s):  
Ian J. Taylor ◽  
Andrew C. Robertson
Keyword(s):  
Flow Field ◽  
Thin Liquid Film ◽  
Vortex Method ◽  
The Body ◽  
Wind Loading ◽  
External Loading ◽  
Discrete Vortex ◽  
Unsteady Aerodynamic ◽  
Karman Vortex ◽  
Wind Induced Vibration

On wet and windy days, the inclined cables of cable-stayed bridges can experience large amplitude, potentially damaging oscillations known as Rain-Wind Induced Vibration (RWIV). The phenomenon is believed to be the result of a complicated nonlinear interaction between rivulets of rain water that run down the cables and the wind loading on the cables due to the unsteady aerodynamic flow field. A numerical method has been developed at the University of Strathclyde, to simulate aspects of RWIV, the results of which can be used to assess the importance of the water rivulets on the instability. This combines a Discrete Vortex Method solver to determine the external flow field and unsteady aerodynamic loading and a pseudo-spectral solver based on lubrication theory to model the water on the surface of the body and which is used to determine the evolution and growth of the water rivulets under external loading. These two models are coupled to simulate the interaction between the aerodynamic field and the thin liquid film on a horizontal circular cylinder. The results illustrate the effects of various loading combinations, and importantly demonstrate rivulet formation in the range of angles previous research has indicated that these may suppress the Karman vortex and lead to a galloping instability. These rivulets are found to be of self limiting thickness in all cases.

Vortex Simulation of Propagating Stall in a Linear Cascade of Airfoils

1986 ◽  
Vol 108 (3) ◽  
pp. 304-312 ◽  
Author(s):  
C. G. Speziale ◽  
F. Sisto ◽  
S. Jonnavithula
Keyword(s):  
Experimental Studies ◽  
Vortex Method ◽  
Reynolds Numbers ◽  
Vortex Sheets ◽  
Discrete Vortex ◽  
Linear Cascade ◽  
Attached Flow ◽  
Tracing Algorithm ◽  
High Reynolds ◽  
Stagger Angle

A numerical simulation of propagating stall in a linear cascade of airfoils at high Reynolds numbers is conducted using a vortex method which was first developed by Spalart [7] for this problem. In this approach, the vorticity is discretized into a large collection of vortex blobs whose motion is tracked in time by the use of a well-known vortex tracing algorithm based on the Euler equation. The near-wall effects of viscosity are accounted for by the creation of discrete vortex sheets at the boundaries of the airfoils consistent with the no-slip condition. These boundary vortices are then released into the flow field downstream of the separation points which are obtained from a boundary-layer routine. Calculations are presented for a variety of flow geometries. It is demonstrated that (for a given cascade of airfoils, disturbance wavelength, and stagger angle) several different flow regimes are obtained: Attached flow at lower angles of attack and a chaotic deep stall configuration at larger angles of attack with a narrow intermediate range of such angles where propagating stall occurs. The physical characteristics of this propagating stall are parameterized and a quantitative study of the effects of camber and imposed wavelength is conducted. Comparisons are made with previous theoretical and experimental studies.

Effect of vortex shedding on the coupled roll response of bodies in waves

1988 ◽  
Vol 189 ◽  
pp. 243-261 ◽  
Author(s):  
M. J. Downie ◽  
P. W. Bearman ◽  
J. M. R. Graham
Keyword(s):  
Vortex Shedding ◽  
Degrees Of Freedom ◽  
Rectangular Cross Section ◽  
Vortex Method ◽  
The Body ◽  
Wave Radiation ◽  
Viscous Damping ◽  
Discrete Vortex ◽  
Hydrodynamic Damping ◽  
Main Component

Hydrodynamic damping of floating bodies is due mainly to wave radiation and viscous damping. The latter is particularly important in controlling those responses of the body for which the wave damping is small. The roll response of ship hulls near resonance in beam seas is an example of this. The present paper applies a discrete vortex method as a local solution to model vortex shedding from the bilges of a barge hull of rectangular cross-section and hence provides an analytic method for predicting its coupled motions in three degrees of freedom, including the effects of the main component of viscous damping. The method provides a frequency-domain solution satisfying the full linearized boundary conditions on the free surface.

Numerical Simulation of Vortex Shedding in Normal Triangular Tube Arrays

2006 ◽  
Author(s):  
Bjo¨rn Selent ◽  
Craig Meskell
Keyword(s):  
Vortex Shedding ◽  
Vortex Method ◽  
Reynolds Numbers ◽  
Normal Velocity ◽  
Time Step ◽  
Single Vortex ◽  
Time Stepping ◽  
Tube Arrays ◽  
Flow Through ◽  
Particle Velocities

The unsteady flow through normal triangular tube arrays is simulated applying the Cloud-in-Element method. The scheme realizes time-stepping via a Langrangian vortex method using random-walk to model diffusion in the flow. The vortex particle velocities are computed on a fixed unstructured grid at each time step. Zero normal velocity on solid boundaries is enforced by a source panel method and zero slip is achieved by introducing vorticity into the flow at each time step. Simulations have been carried out for normal triangular tube arryas with pitch ratios of 1.32, 1.61, 2.08, 2.63 at Reynolds numbers of 1000, 3000, 5000 and 10000. Single vortex shedding frequencies have been observed for the smaller pitch ratios while two Strouhal numbers are obtained for the sparse arrays. This is consistent with experimental data in the literature. Also the overall flow structures were captured successfully.

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.

Numerical Analysis of Unsteady Flow in the Weis-Fogh Mechanism by the 3D Discrete Vortex Method With GRAPE3A

1997 ◽  
Vol 119 (1) ◽  
pp. 96-102 ◽  
Author(s):  
Kideok Ro ◽  
Michihisa Tsutahara
Keyword(s):  
High Speed ◽  
Three Dimensional ◽  
Leading Edge ◽  
Vortex Method ◽  
Reynolds Numbers ◽  
Discrete Vortex ◽  
Discrete Vortex Method ◽  
Trailing Edges ◽  
Induced Velocity ◽  
Vortex Systems

The three-dimensional flows in the Weis-Fogh mechanism are studied by flow visualization and numerical simulation by a discrete vortex method. In this mechanism, two wings open, touching their trailing edges (fling), and rotate in opposite directions in the horizontal plane. At the “fling” stage, the flow separates at the leading edge and the tip of each wing. Then they rotate, and the flow separates also at the trailing edges. The structure of the vortex systems shed from the wings is very complicated and their effect on the forces on the wings have not yet been clarified. Discrete vortex method, especially the vortex stick method, is employed to investigate the vortex structure in the wake of the two wings. The wings are represented by lattice vortices, and the shed vortices are expressed by discrete three-dimensional vortex sticks. In this calculation, the GRAPE3A hardware is used to calculate at high speed the induced velocity of the vortex sticks and the viscous diffusion of fluid is represented by the random walk method. The vortex distributions and the velocity field are calculated. The pressure is estimated by the Bernoulli equation, and the lift and moment on the wing are also obtained. However, the simulations, especially those for various Reynolds numbers, should be treated with caution, because there is no measurement to compare them with and the discrete vortex method is approximate due to rudimentary modeling of viscosity.

The Influence of Viscous Effects on the Motion of a Body Floating in Waves

1993 ◽  
Vol 115 (1) ◽  
pp. 40-45 ◽  
Author(s):  
M. J. Downie ◽  
J. M. R. Graham ◽  
X. Zheng
Keyword(s):  
Three Dimensional ◽  
Vortex Method ◽  
Inviscid Flow ◽  
The Body ◽  
Viscous Effects ◽  
Local Flow ◽  
Discrete Vortex ◽  
Outer Flow ◽  
Viscous Forces ◽  
Singularity Distribution

This paper describes a method for calculating the forces experienced by a body floating in waves, including those due to vortex shedding from its surface. The method uses a purely theoretical approach, incorporating viscous forces, for calculating the motions of the body in the frequency domain. It involves the matching of an outer inviscid flow with the local flow in the regions of flow separation on the body, which must be well defined. The outer flow is computed by a three-dimensional singularity distribution technique and the inner flow by the discrete vortex method. The technique has been applied to the prediction of the motion response of barges floating in waves. The results compare favorably with experimental data.

Numerical Simulation of the Hole-Tone Feedback Cycle Based on the Discrete Vortex Method and the Acoustic Analogy

2003 ◽  
Author(s):  
Mikael A. Langthjem ◽  
Masami Nakano
Keyword(s):  
Numerical Simulation ◽  
Shear Layer ◽  
Vortex Method ◽  
Vortex Rings ◽  
Acoustic Analogy ◽  
Noise Sources ◽  
Time Step ◽  
Discrete Vortex ◽  
Discrete Vortex Method ◽  
Flow Noise

An axisymmetric numerical simulation approach to the holetone feedback problem is developed. It is based on the discrete vortex method and an ‘acoustic analogy’ representation of flow noise sources. The shear layer of the jet is represented by ‘free’ discrete vortex rings, and the jet nozzle and the end plate by bound vortex rings. A vortex ring is released from the nozzle at each time step in the simulation. The newly released vortex rings are disturbed by acoustic feedback. The simulated frequencies f follow the criterion L/uc + L/c0 = n/f where L is the gap length, uc is the shear layer convection velocity, c0 is the speed of sound, and n is a mode number (n = 1/2, 1, 3/2, ...). This is in agreement with experimental observations. The numerical model also display mode shifts (jumps in the chosen value of n), as seen in experiments.

A Turbine Airfoil Aerodynamic Design Process

2001 ◽  
Author(s):  
C. Xu ◽  
R. S. Amano
Keyword(s):  
Design Process ◽  
Splitting Method ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Vortex Method ◽  
Aerodynamic Design ◽  
Discrete Vortex ◽  
Pressure Distributions ◽  
Industry Practice ◽  
Flux Difference

A turbine airfoil aerodynamic design process, similar to the current industry practice, is used to design turbine airfoil sections. The airfoil generator code employs Bezier polynomial curves to produce smooth airfoil shapes. For the calculations of the airfoil pressure distributions a discrete vortex method is used after the airfoil is designed and the novel Navier-Stokes (N-S) solver is developed for further examination of the airfoil performance. The vortex method can provide a fast way to calculate the airfoil pressure distributions. The N-S code is used to obtain the blade-to-blade quasi-three-dimensional, turbulent, and viscous flow characteristics. The time-dependent N-S equations are discretized and integrated in a coupled manner based on a finite-volume formulation as well as a flux-difference splitting. The flux-difference splitting method enables us to compute with a rapid convergence. After the flow solver is validated with experimental data, this new code is further used to obtain an optimal airfoil design by analyzing the cascade flows. The present N-S code can handle computations of both subsonic and supersonic flows and can be connected to an external optimizer code with the airfoil generator.

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