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 Simulation of Vortex Shedding in Tube Arrays

2002 ◽  
Author(s):  
C. Sweeney ◽  
C. Meskell
Keyword(s):  
Numerical Simulation ◽  
Vortex Shedding ◽  
Complex Geometry ◽  
Vortex Method ◽  
Standard Case ◽  
Discrete Vortex ◽  
Element Discretization ◽  
Fluid Forces ◽  
Tube Arrays ◽  
Flow Through

Vortex shedding may occur in tube arrays, resulting in strong excitation forces at discrete frequencies. In the past the Strouhal numbers governing vortex shedding in these systems were determined experimentally. This paper presents a method of numerical simulation for the unsteady flow through a rigid normal triangular tube array and hence provides a method of determining both the frequency of vortex shedding and the magnitude of the fluid forces acting on the tubes. The technique used is based on a discrete vortex method similar to the cloud-in-cell approach which has been applied to flow problems for small numbers of cylinders. However, in the current implementation the flow velocity calculation is carried out on an unstructured grid using a finite element discretization. Thus, the complex geometry associated with a tube array can be easily accomodated. The method, referred to as the “Cloud-in-element” method, is validated for the standard case of flow over a single cylinder and then applied to flow through a normal triangular array with a pitch diameter of 1.6. The Reynolds number is 2200. The Stouhal number obtained from the numerical simulation is 1.27, which is within 6% of the value available in the literature. Qualitatively, the vortex shedding pattern obtained is in agreement with published flow visualization.

scholarly journals Vortex shedding from an impulsively started rotating and translating circular cylinder

1991 ◽  
Vol 233 ◽  
pp. 265-298 ◽  
Author(s):  
Chien-Cheng Chang ◽  
Ruey-Ling Chern
Keyword(s):  
Circular Cylinder ◽  
Vortex Shedding ◽  
Numerical Study ◽  
Vortex Method ◽  
Reynolds Numbers ◽  
Speed Ratio ◽  
Stagnation Points ◽  
Time Variations ◽  
Strong Competition ◽  
High Reynolds

A numerical study is made of the flow past an impulsively started rotating and translating circular cylinder using a hybrid vortex method. The Reynolds number (Re) ranges from 103 to 106 while the (counter-rotating) rotating-to-translating speed ratio (α) is increased from 0 to 2. It is found that three basic patterns of vortex shedding can be identified according to the behaviour of the stagnation points associated with the first upper and the first lower vortices. Depending on the parameters Re and α, the rotation may favour the shedding of the first upper vortex, or the first lower vortex (typically at high Reynolds numbers). In a transition region, strong competition for shedding exists between the first two vortices in the form of double transposition of stagnation (closure) points associated with the two vortices. Time variations of lift coefficients characterize different shedding patterns; the cylinder may first experience a substantial maximal downward lift when the first shedding vortex is from the upper wake, or a maximal upward lift otherwise.

Vortex shedding from a cylinder vibrating in line with an incident uniform flow

1976 ◽  
Vol 75 (2) ◽  
pp. 257-271 ◽  
Author(s):  
Owen M. Griffin ◽  
Steven E. Ramberg
Keyword(s):  
Vortex Shedding ◽  
Vibration Amplitude ◽  
Cross Flow ◽  
Reynolds Numbers ◽  
Vortex Wake ◽  
Single Vortex ◽  
Vortex Pairs ◽  
Wake Patterns ◽  
Shedding Frequency ◽  
Basic Characteristics

A study has been made of the wake of a cylinder vibrating in line with an incident steady flow. The Reynolds number for the experiments was 190, and the vortex shedding was at all times synchronized with the vibrations of the cylinder, which were in a range of frequencies near twice the Strouhal shedding frequency for the stationary cylinder. Two distinct vortex wake patterns were encountered. The first is a complex regime in which two vortices are shed during each cycle of the vibration and form an alternating pattern of vortex pairs downstream. The second pattern is an alternating street which results from the shedding of a single vortex during each cycle of the cylinder's motion. The street geometry in the latter case shares many basic characteristics with the wake of a cylinder vibrating in cross-flow. These include the effects of vibration amplitude and frequency on the longitudinal and transverse spacing of the vortices. The results obtained from these experiments in air are in agreement with previous findings from free- and forced-vibration experiments in water at both higher and lower Reynolds numbers.

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.

Vortex Shedding Frequencies of the Flow through Two-Row Banks of Tubes

1969 ◽  
Vol 11 (5) ◽  
pp. 498-502 ◽  
Author(s):  
A. R. J. Borges
Keyword(s):  
Vortex Shedding ◽  
Reynolds Numbers ◽  
Dominant Frequency ◽  
Experimental Results ◽  
Circular Cylinders ◽  
Single Row ◽  
Flow Through ◽  
Set Up

This paper deals with the problem of vortex shedding from parallel rows of circular cylinders of equal diameter set normal to an airstream. A single row of cylinders is first discussed. The experimental results show that when the lateral spacing between the axes of two adjacent cylinders is less than two diameters the flow downstream of the row does not exhibit any obvious single dominant frequency of vortex shedding. The flow set up by two rows of cylinders is next considered for both tandem and staggered arrangements of the cylinders. The sets of measured values reported are complete in the sense that they cover the whole range of spacings for which a dominant frequency of vortex shedding could be measured. The Reynolds numbers of these tests correspond to the high subscritical range for a cylinder in isolation.

On Direct and Semi-Direct Inverse of Stokes, Helmholtz and Laplacian Operators in View of Time-Stepper-Based Newton and Arnoldi Solvers in Incompressible CFD

2013 ◽  
Vol 14 (4) ◽  
pp. 1103-1119 ◽  
Author(s):  
H. Vitoshkin ◽  
A. Yu. Gelfgat
Keyword(s):  
Three Dimensional ◽  
Reynolds Numbers ◽  
Computational Effort ◽  
Stokes Operator ◽  
Time Step ◽  
Time Stepping ◽  
Fast Direct Solvers ◽  
Large Time Step ◽  
Helmholtz Operators ◽  
Laplacian Operators

AbstractFactorization of the incompressible Stokes operator linking pressure and velocity is revisited. The main purpose is to use the inverse of the Stokes operator with a large time step as a preconditioner for Newton and Arnoldi iterations applied to computation of steady three-dimensional flows and study of their stability. It is shown that the Stokes operator can be inversed within an acceptable computational effort. This inverse includes fast direct inverses of several Helmholtz operators and iterative inverse of the pressure matrix. It is shown, additionally, that fast direct solvers can be attractive for the inverse of the Helmholtz and Laplace operators on fine grids and at large Reynolds numbers, as well as for other problems where convergence of iterative methods slows down. Implementation of the Stokes operator inverse to time-stepping-based formulation of the Newton and Arnoldi iterations is discussed.

scholarly journals An Advance-Tracing Boundary Element Method in the Time Domain for Solving the Radiating Problem of an Arbitrary Obstacle Accelerating Randomly

2017 ◽  
Vol 2017 ◽  
pp. 1-12
Author(s):  
Jui-Hsiang Kao
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Time Domain ◽  
Boundary Integral ◽  
Normal Velocity ◽  
Time Step ◽  
Random Acceleration ◽  
The Time Domain ◽  
First Time ◽  
Element Method

This research develops an Advance-Tracing Boundary Element Method in the time domain to calculate the waves that radiate from an immersed obstacle moving with random acceleration. The moving velocity of the immersed obstacle is multifrequency and is projected along the normal direction of every element on the obstacle. The projected normal velocity of every element is presented by the Fourier series and includes the advance-tracing time, which is equal to a quarter period of the moving velocity. The moving velocity is treated as a known boundary condition. The computing scheme is based on the boundary integral equation in the time domain, and the approach process is carried forward in a loop from the first time step to the last. At each time step, the radiated pressure on each element is updated until obtaining a convergent result. The Advance-Tracing Boundary Element Method is suitable for calculating the radiating problem from an arbitrary obstacle moving with random acceleration in the time domain and can be widely applied to the shape design of an immersed obstacle in order to attain security and confidentiality.

Fast Conjugate Heat Transfer Simulation of Long Transient Flexible Operations Using Adaptive Time Stepping

2018 ◽  
Vol 140 (9) ◽  
Author(s):  
R. Maffulli ◽  
L. He ◽  
P. Stein ◽  
G. Marinescu
Keyword(s):  
Heat Transfer ◽  
Conjugate Heat Transfer ◽  
Time Derivative ◽  
Computational Cost ◽  
Strong Impact ◽  
Time Step ◽  
Time Stepping ◽  
Adaptive Time ◽  
Fully Coupled ◽  
Adaptive Time Stepping

The emerging renewable energy market calls for more advanced prediction tools for turbine transient operations in fast startup/shutdown cycles. Reliable numerical analysis of such transient cycles is complicated by the disparity in time scales of the thermal responses in fluid and solid domains. Obtaining fully coupled time-accurate unsteady conjugate heat transfer (CHT) results under these conditions would require to march in both domains using the time-step dictated by the fluid domain: typically, several orders of magnitude smaller than the one required by the solid. This requirement has strong impact on the computational cost of the simulation as well as being potentially detrimental to the accuracy of the solution due to accumulation of round-off errors in the solid. A novel loosely coupled CHT methodology has been recently proposed, and successfully applied to both natural and forced convection cases that remove these requirements through a source-term based modeling (STM) approach of the physical time derivative terms in the relevant equations. The method has been shown to be numerically stable for very large time steps with adequate accuracy. The present effort is aimed at further exploiting the potential of the methodology through a new adaptive time stepping approach. The proposed method allows for automatic time-step adjustment based on estimating the magnitude of the truncation error of the time discretization. The developed automatic time stepping strategy is applied to natural convection cases under long (2000 s) transients: relevant to the prediction of turbine thermal loads during fast startups/shutdowns. The results of the method are compared with fully coupled unsteady simulations showing comparable accuracy with a significant reduction of the computational costs.

An Experimental Study on the Vertical Flow Past a Finite-Length Horizontal Cylinder at Low Reynolds Numbers

2014 ◽  
Vol 493 ◽  
pp. 68-73 ◽  
Author(s):  
Willy Stevanus ◽  
Yi Jiun Peter Lin
Keyword(s):  
Finite Length ◽  
Vortex Shedding ◽  
Vortex Formation ◽  
Reynolds Numbers ◽  
Horizontal Cylinder ◽  
Vortex Street ◽  
Vertical Flow ◽  
Low Reynolds Numbers ◽  
Vortex Shedding Frequency ◽  
Shedding Frequency

The research studies the characteristics of the vertical flow past a finite-length horizontal cylinder at low Reynolds numbers (ReD) from 250 to 1080. The experiments were performed in a vertical closed-loop water tunnel. Flow fields were observed by the particle tracer approach for flow visualization and measured by the Particle Image Velocimetry (P.I.V.) approach for velocity fields. The characteristics of vortex formation in the wake of the finite-length cylinder change at different regions from the tip to the base of it. Near the tip, a pair of vortices in the wake was observed and the size of the vortex increased as the observed section was away from the tip. Around a distance of 3 diameters of the cylinder from its tip, the vortex street in the wake was observed. The characteristics of vortex formation also change with increasing Reynolds numbers. At X/D = -3, a pair of vortices was observed in the wake for ReD = 250, but as the ReD increases the vortex street was observed at the same section. The vortex shedding frequency is analyzed by Fast Fourier Transform (FFT). Experimental results show that the downwash flow affects the vortex shedding frequency even to 5 diameters of the cylinder from its tip. The interaction between the downwash flow and the Von Kármán vortex street in the wake of the cylinder is presented in this paper.

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