Numerical Study of Oscillatory Flow Past a Pair of Cylinders in a Side-by-Side Arrangement

2005 ◽  
Author(s):  
P. Anagnostopoulos ◽  
A. Koutras ◽  
S. A. Seitanis
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Hydrodynamic Forces ◽  
Circular Cylinders ◽  
Navier Stokes ◽  
Constant Frequency ◽  
Navier Stokes Equations ◽  
Symmetry Of The Solution ◽  
Time Histories ◽  
Line Force

The results of a numerical study of the viscous oscillating flow around a pair of circular cylinders are presented herein, for a constant frequency parameter, β, equal to 50, and Keulegan-Carpenter numbers, KC, ranging between 0.2 and 10. The cylinders were placed side-by-side to the oncoming flow, for a pitch to diameter ratio, P/D, equal to 2. The finite-element method was employed for the solution of the Navier-Stokes equations, in the formulation where the stream function and the vorticity are the field variables. The vorticity contours generated from the solution were used mainly for the flow visualization, whereas the stream-lines and isobars are shown in some cases. At low values of the Keulegan-Carpenter number the flow remains symmetrical with respect to the horizontal axis of symmetry of the solution domain. As the Keulegan-Carpenter number is increased asymmetries appear in the flow, which are eventually amplified and lead finally to more complicated vortex-shedding patterns. These asymmetries generate an aperiodic flow configuration at consecutive cycles, which becomes almost chaotic as KC grows larger. For the various Keulegan-Carpenter numbers examined the time-histories of the hydrodynamic forces are presented, and the r.m.s. values of the hydrodynamic forces and the coefficients of the in-line force were evaluated.

Numerical Study of Oscillatory Flow Past a Pair of Cylinders at Low Reynolds and Keulegan-Carpenter Numbers

2002 ◽  
Author(s):  
P. Anagnostopoulos ◽  
A. Koutras ◽  
S. A. Seitanis
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Hydrodynamic Forces ◽  
Circular Cylinders ◽  
Navier Stokes ◽  
The Finite Element Method ◽  
Constant Frequency ◽  
Navier Stokes Equations ◽  
Line Force ◽  
Axis Of Symmetry

The results of a numerical study of the viscous oscillating flow around a pair of circular cylinders are presented herein, for a constant frequency parameter, β, equal to 50, and Keulegan-Carpenter numbers, KC, ranging between 0.2 and 10. The cylinders were placed side-by-side to the oncoming flow, for a pitch to diameter ratio, P/D, equal to 1.2. The finite-element method was employed for the solution of the Navier-Stokes equations, in the formulation where the stream function and the vorticity are the field variables. The streamlines and vorticity contours generated from the solution were used for the flow visualization. At low values of the Keulegan-Carpenter number the flow remains symmetrical with respect to the horizontal axis of symmetry of the domain. As the Keulegan-Carpenter number is increased asymmetries appear in the flow, which are eventually amplified and lead finally to more complicated vortex-shedding patterns. These asymmetries generate an aperiodic flow configuration at consecutive cycles, which becomes almost chaotic as KC grows larger. For the various Keulegan-Carpenter numbers examined the traces of the hydrodynamic forces are presented, and the r.m.s. values of the hydrodynamic forces and the coefficients of the in-line force were evaluated.

Numerical Study of Oscillatory Flow Past Four Cylinders in Square Arrangement for Pitch Ratio Equal to 4

2011 ◽  
Author(s):  
P. Anagnostopoulos ◽  
Ch. Dikarou ◽  
S. A. Seitanis
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Central Line ◽  
Circular Cylinders ◽  
Navier Stokes ◽  
Constant Frequency ◽  
Navier Stokes Equations ◽  
Symmetry Of The Solution ◽  
Pitch Ratio ◽  
Two Sides

The results of a numerical study of the viscous oscillating flow around four circular cylinders are presented herein, for a constant frequency parameter, β, equal to 50, and Keulegan-Carpenter numbers, KC, ranging between 0.2 and 10. The cylinders were placed on the vertices of a square, whose two sides were perpendicular and two parallel to the oncoming flow, for a pitch ratio, P/D, equal to 4. The finite-element method was employed for the solution of the Navier-Stokes equations, in the formulation where the stream function and the vorticity are the field variables. The streamlines and the vorticity contours generated from the solution were used for the flow visualization. When the Keulegan-Carpenter number is lower than 4, the flow remains symmetrical with respect to the horizontal axis of symmetry of the solution domain and periodic at consecutive cycles. As KC increases to 4 the flow becomes aperiodic in different cycles, although symmetry with respect to the horizontal central line of the domain is preserved. For KC equal to 5 asymmetries appear intermittently in the flow, which are eventually amplified as KC increases still further. These asymmetries, in association with the aperiodicity at different cycles, lead to an almost chaotic configuration, as KC grows larger. For characteristic cases the flow pattern and the traces of the hydrodynamic forces are presented. In addition, the mean and r.m.s. values of the in-line and transverse forces and the hydrodynamic coefficients of the inline force were evaluated for the entire range of Keulegan-Carpenter numbers examined.

Numerical Study on the Effect of Tandem Spacing on Flow Induced Motions of Two Cylinders With Passive Turbulence Control

2015 ◽  
Author(s):  
Lin Ding ◽  
Li Zhang ◽  
Chunmei Wu ◽  
EunSoo Kim ◽  
Michael M. Bernitsas
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Circular Cylinders ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Turbulence Control ◽  
Frequency Responses ◽  
Simulation Results ◽  
Passive Turbulence Control ◽  
Reynolds Average

The effect of tandem spacing on the flow induced motions (FIM) of two circular cylinders with passive turbulence control is investigated using two-dimensional Unsteady Reynolds-Average Navier-Stokes equations with the Spalart-Allmaras turbulence model. Results are compared to experiments in the range of Reynolds number of 30,000<Re<100,000. The center-to-center spacing between the two cylinders is varied from 2 to 6 diameters. Simulation results predict well all ranges of FIM including VIV and galloping and match well with experimental measurements. For the upstream cylinder, the amplitude and frequency responses are not considerably influenced by the downstream cylinder when the spacing is greater than 2D. For the downstream cylinder, a rising amplitude trend in the VIV upper branch can be observed in all cases as is typical of flows in the TrSL3 regime. The galloping branch merges with the VIV upper branch for spacing greater than 3D. Vortex structures show significant variation in different flow regimes in accordance with experimental observations. High-resolution post-processing shows that the interaction between the wakes of cylinders result in various types of FIM.

Numerical Study on the Effect of Tandem Spacing on Flow-Induced Motions of Two Cylinders With Passive Turbulence Control

2016 ◽  
Vol 139 (2) ◽  
Author(s):  
Lin Ding ◽  
Li Zhang ◽  
Chunmei Wu ◽  
Eun Soo Kim ◽  
Michael M. Bernitsas
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Circular Cylinders ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Turbulence Control ◽  
Flow Regime Transition ◽  
Vortex Induced Vibrations ◽  
Passive Turbulence Control

The effect of tandem spacing on the flow-induced motions (FIM) of two circular cylinders with passive turbulence control is investigated using two-dimensional (2D) unsteady Reynolds-averaged Navier–Stokes equations with the Spalart–Allmaras turbulence model. Results are compared to experiments in the range of Reynolds number of 30,000 < Re < 100,000. The center-to-center spacing between the two cylinders is varied from 2 to 6 diameters. Simulation results predict well all the ranges of FIM including vortex-induced vibrations (VIV) and galloping and match well with experimental measurements. For the upstream cylinder, the amplitude and frequency responses are not considerably influenced by the downstream cylinder when the spacing is greater than 2D. For the downstream cylinder, a rising amplitude trend in the VIV upper-branch can be observed in all the cases as is typical of flows in the TrSL3 flow regime (transition in shear layer 3; 2 × 104 < Re < 3 × 105). The galloping branch merges with the VIV upper-branch for spacing greater than three-dimensional (3D). Vortex structures show significant variation in different flow regimes in accordance with experimental observations. High-resolution postprocessing shows that the interaction between the wakes of cylinders results in various types of FIM.

scholarly journals Dynamics of Single Droplet Splashing on Liquid Film by Coupling FVM with VOF

Processes ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 841
Author(s):  
Yuzhen Jin ◽  
Huang Zhou ◽  
Linhang Zhu ◽  
Zeqing Li
Keyword(s):  
Liquid Film ◽  
Weber Number ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Single Droplet ◽  
Navier Stokes Equations ◽  
Volume Method ◽  
The Relationship

A three-dimensional numerical study of a single droplet splashing vertically on a liquid film is presented. The numerical method is based on the finite volume method (FVM) of Navier–Stokes equations coupled with the volume of fluid (VOF) method, and the adaptive local mesh refinement technology is adopted. It enables the liquid–gas interface to be tracked more accurately, and to be less computationally expensive. The relationship between the diameter of the free rim, the height of the crown with different numbers of collision Weber, and the thickness of the liquid film is explored. The results indicate that the crown height increases as the Weber number increases, and the diameter of the crown rim is inversely proportional to the collision Weber number. It can also be concluded that the dimensionless height of the crown decreases with the increase in the thickness of the dimensionless liquid film, which has little effect on the diameter of the crown rim during its growth.

A numerical study of the interaction between unsteay free-stream disturbances and localized variations in surface geometry

1989 ◽  
Vol 209 ◽  
pp. 285-308 ◽  
Author(s):  
R. J. Bodonyi ◽  
W. J. C. Welch ◽  
P. W. Duck ◽  
M. Tadjfar
Keyword(s):  
Numerical Solutions ◽  
Free Stream ◽  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Surface Geometry ◽  
Navier Stokes Equations ◽  
S Waves ◽  
Tollmien Schlichting

A numerical study of the generation of Tollmien-Schlichting (T–S) waves due to the interaction between a small free-stream disturbance and a small localized variation of the surface geometry has been carried out using both finite–difference and spectral methods. The nonlinear steady flow is of the viscous–inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier–Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of the T–S waves generated by the interaction between the free-stream disturbance and the surface distortion, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T–S waves.

Numerical Study of Viscous Flows Inside Partially Filled Spinning and Coning Cylinders

1996 ◽  
Vol 118 (2) ◽  
pp. 335-340 ◽  
Author(s):  
Mohamed Selmi
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Center Of Mass ◽  
Steady Motion ◽  
Practical Interest ◽  
Nonlinear Effects ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Practical Applications ◽  
Analysis And Design

This paper is concerned with the solution of the 3-D-Navier-Stokes equations describing the steady motion of a viscous fluid inside a partially filled spinning and coning cylinder. The cylinder contains either a single fluid of volume less than that of the cylinder or a central rod and a single fluid of combined volume (volume of the rod plus volume of the fluid) equal to that of the cylinder. The cylinder rotates about its axis at the spin rate ω and rotates about an axis that passes through its center of mass at the coning rate Ω. In practical applications, as in the analysis and design of liquid-filled projectiles, the parameter ε = τ sin θ, where τ = Ω/ω and θ is the angle between spin axis and coning axis, is small. As a result, linearization of the Navier-Stokes equations with this parameter is possible. Here, the full and linearized Navier-Stokes equations are solved by a spectral collocation method to investigate the nonlinear effects on the moments caused by the motion of the fluid inside the cylinder. In this regard, it has been found that nonlinear effects are negligible for τ ≈ 0.1, which is of practical interest to the design of liquid-filled projectiles, and the solution of the linearized Navier-Stokes equations is adequate for such a case. However, as τ increases, nonlinear effects increase, and become significant as ε surpasses about 0.1. In such a case, the nonlinear problem must be solved. Complete details on how to solve such a problem is presented.

Experimental and Numerical Study of Vortex Induced Vibrations on a Spool Model

2018 ◽  
Author(s):  
David Gross ◽  
Yann Roux ◽  
Benjamin Rousse ◽  
François Pétrié ◽  
Ludovic Assier ◽  
...  
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Fluid Dynamic ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow Perturbation ◽  
Industry Standards ◽  
Vortex Induced Vibrations ◽  
Recommended Practices ◽  
Decay Tests

The problem of Vortex-Induced Vibrations (VIV) on spool and jumper geometries is known to present several drawbacks when approached with conventional engineering tools used in the study of VIV on risers. Current recommended practices can lead to over-conservatism that the industry needs to quantify and minimize within notably cost reduction objectives. Within this purpose, the paper will present a brief critical review of the Industry standards and more particularly focus on both experimental and Computational Fluid Dynamic (CFD) approaches. Both qualitative and quantitative comparisons between basin tests and CFD results for a 2D ‘M-shape’ spool model will be detailed. The results presented here are part of a larger experimental and numerical campaign which considered a number of current velocities, heading and geometry configurations. The vibratory response of the model will be investigated for one of the current velocities and compared with the results obtained through recommended practices (e.g. Shear7 and DNV guidelines). The strategy used by the software K-FSI to solve the fluid-structure interaction (FSI) problem is a partitioned coupling solver between fluid solver (FINE™/Marine) and structural solvers (ARA). FINE™/Marine solves the Reynolds-Averaged Navier-Stokes Equations in a conservative way via the finite volume method and can work on structured or unstructured meshes with arbitrary polyhedrons, while ARA is a nonlinear finite element solver with a large displacement formulation. The experiments were conducted in the BGO FIRST facility located in La Seyne sur Mer, France. Particular attention was paid towards the model design, fabrication, instrumentation and characterization, to ensure an excellent agreement between the structural numerical model and the actual physical model. This included the use of a material with low structural damping, the performance of stiffness and decay tests in air and in still water, plus the rationalization of the instrumentation to be able to capture the response with the minimum flow perturbation or interaction due to instrumentation.

Numerical Prediction of Turbulent Wakes Behind a Square Cylinder

1998 ◽  
Vol 14 (1) ◽  
pp. 23-29
Author(s):  
Robert R. Hwang ◽  
Sheng-Yuh Jaw
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Wall Region ◽  
Square Cylinder ◽  
Mean Velocity ◽  
Navier Stokes Equations ◽  
Turbulent Vortex Shedding ◽  
Model Equations ◽  
Good Agreement

ABSTRACTThis paper presents a numerical study on turbulent vortex shedding flows past a square cylinder. The 2D unsteady periodic shedding motion was resolved in the calculation and the superimposed turbulent fluctuations were simulated with a second-order Reynolds-stress closure model. The calculations were carried out by solving numerically the fully elliptic ensemble-averaged Navier-Stokes equations coupled with the turbulence model equations together with the two-layer approach in the treatment of the near-wall region. The performance of the computations was evaluated by comparing the numerical results with data from available experiments. Results indicate that the present study gives good agreement in the shedding frequency and mean drag as well as in some phase profiles of the mean velocity.

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