Open Access Open Access  Restricted Access Subscription or Fee Access

Formation and Dissipation of Karman Vortex Street in an Accelerating Flow Past a Circular Cylinder


(*) Corresponding author


Authors' affiliations


DOI: https://doi.org/10.15866/irease.v8i2.5846

Abstract


Prediction of Karman vortex street in a flow past circular cylinder has become a benchmark problem and many new numerical methods are validated by reproducing the phenomena. The formation and dissipation of Karman vortex street occurs in a range of Reynolds number. But, the conventional Navier-Stokes equations derived in inertial frame of reference based on constant relative velocity are limited to fluid flow problem at a given freestream velocity or Reynolds number. Therefore, in order to capture the formation and dissipation of karman vortex street, several simulations are to be carried out at different freestream velocites. Even then, such simulations will not reveal the continous phenomena of formation and dissipation of vortices. In this work, Navier-Stokes equations are obtained from first principles for fluid flow problems with linear external acceleration in relative acceleration frame of reference, in a form most suited for numerical study. Using these equations, numerical simulation of accelerating flow over circular cylinder is carried out for Reynolds number range, 68 to 1360. The formation and dissipation of Karman vortex street is captured in a single simulation and the results are compared with conventional simulations at various Reynolds numbers. The issues in physical modeling and numerics of using constant freestream acceleration are also discussed in brief. From these simulations, it is demonstrated that the physical phenomena obtained by solving conventional Navier-Stokes equations at various freestream velocities can obtained in a single simulation by using the Navier-Stokes equations written in relative acceleration frame of reference. These equation can be used to explore the physics of accelerating flows in a continuous scenario, without undertaking numerous conventional simulations at various constant freestream velocities.
Copyright © 2015 Praise Worthy Prize - All rights reserved.

Keywords


Karman Vortex Street; Freestream Acceleration; Circular Cylinder

Full Text:

PDF


References


von Karman, T., Aerodynamics, McGrraw-Hill, New York, 1963.

Ahamad, R. A., A steady state numerical solution of the Navier-Stokes and Energy equation around a horizontal cylinder at Reynolds numbers from 100 to 500," in AIAA 28th Thermophysics conference," Orlando, FL, Paper No: AIAA 93{2748, 1993.
http://dx.doi.org/10.2514/6.1993-2748

Marris, A. W., A review on vortex streets, periodic wakes, and induced vibration phenomena," Journal of Basic Engineering, pp. 185{193.
http://dx.doi.org/10.1115/1.3653027

Taslin, M. E. and Kinney, R. B., Analysis of two-dimensional viscous ow over cylinder in unsteady motion," AIAA Journal, 1984, Vol. 22, No. 5.
http://dx.doi.org/10.2514/3.8642

K. Izumi, K. K., Unsteady ow _eld, lift and drag measurements of impulsively started elliptic cylinder and circular-arc airfoil," in AIAA 16th Fluid and Plasma dynamics conference," Danvers, Massachusets, Paper No: AIAA 83{1711, 1983.
http://dx.doi.org/10.2514/6.1983-1711

Ericsson, L. E., Moving wall e_ects in unsteady ow," Journal of Aircraft, 1988, Vol. 25, No. 11.
http://dx.doi.org/10.2514/3.45691

Ericsson, L. E., Flat spin of circular cylinder," Journal of Aircraft, 1996,, Vol. 33, No. 4.
http://dx.doi.org/10.2514/3.47007

Marzouk, O. A. and Nayfeh, A. H., Hydrodynamic forces on a moving cylinder with time-dependent frequency variation," AIAA Paper No: 2008{680.
http://dx.doi.org/10.2514/6.2008-680

Lecointe, Y. and Piquet, J., Unsteady viscous ow round moving circular cylinders and airfoils," AIAA Journal, , No. Paper No: 85-1490, 1985, pp. 38{49.
http://dx.doi.org/10.2514/6.1985-1490

Jones, G. S. and Horvath, T. J., Literature review and experimental results for a cylinder with perforations and protusions," in AIAA 19th Fluid dynamics, Plasma dynamics and Lasers Conference," Honolulu, Hawaii, 1987.
http://dx.doi.org/10.2514/6.1987-1388

Sarpkaya, T., Nonimpulsively started steady ow about a circular cylinder," AIAA Journal, , No. 29, 1991, pp. 1283{1289. 23
http://dx.doi.org/10.2514/3.10733

Ericsson, L. E., Fluid dynamics of cylinder response to Karman vortex shedding," in AIAA 24th Aerospace Sciences Meeting, January 6-9, Reno, Nevada," AIAA-86-0119, 1986.
http://dx.doi.org/10.2514/6.1986-119

Ericsson, L. E., Karman vortex shedding: Friend or Foe of the structural dynamicist," Journal of Aircraft, 1986, Vol. 23, No. 8.
http://dx.doi.org/10.2514/3.45353

Ericsson, L. E., Circular cylinder response to Karman vortex shedding," J. Aircraft, 1988,, Vol. 25, No. 9.
http://dx.doi.org/10.2514/3.45658

Vatsa, V. N. and Singer, B. A., Evaluation of a second-order detached eddy simulation past a circular cylinder," in 21st Applied Aerodynamics conference," Oriando, Florida, Paper No: AIAA 2003{4085, 2003.
http://dx.doi.org/10.2514/6.2003-4085

M. Sato, T. K., A fundamental study of the ow past a circular cylinder using Abaqus/CFD," in SIMULIA Community conference," , 2012.

A. Feymark, R. E. B., N. Alin and Fureby, C., Large-eddy simulationn of an oscillating cylinder in a steady ow," AIAA Journal, Vol. 51, No. 4, 2013, pp. 773{783.
http://dx.doi.org/10.2514/1.j050653

Kim, S. E., Large-eddy simulation of turbulent ow past a circular cylinder in subcrtical regime," in 44th AIAA Aerospce Sciences Meeting and Exhibit," Reno, Nevada, Paper No: AIAA 2006{1418, 2006.
http://dx.doi.org/10.2514/6.2006-1418

Lakshmipathy, S. and Girimaji, S. S., Partially averaged Navier-Stokes (PANS) method for Turbulence simulations: ow past a circular cylinder," Journal of Fluids Engineering, 2010,, Vol. 132.
http://dx.doi.org/10.1115/1.4003154

Zdravkovich, M. M., Flow around circular cylinders - Volume 1: Fundamentals, Oxford University Press, New york, 1997.
http://dx.doi.org/10.1017/s0022112097227291

Zdravkovich, M. M., Flow around circular cylinders - Volume 2: Applications, Oxford University Press, New york, 2003.

Deslandes, R., A grid overlapping technique with smart monoblocks for unsteady, time accurate Euler solutions applied to store separation problems," AIAA 32nd Aerospace Sciences Meeting and Exhibit, Paper no: AIAA 94-0055. 24
http://dx.doi.org/10.2514/6.1994-55

C W Hirt, A. A. A. and Cook, J. K., An Arbitrary Lagrangian-Eulerian Computing methods for all ow speeds," J. Computational Physics, Vol. 14, No. 3, 1974, pp. 227{234.
http://dx.doi.org/10.1016/0021-9991(74)90051-5

Donea, J. and et. al, Arbitrary Lagrangian-Eulerian Methods, Encylopedia of Computational Mechanics, Volume I: Fundamentals, John Wiley & Sons, 2004.

Gledhill, I. M. A. and et. al, Investigation of acceleration e_ects on missile aerodynamics using computational uid dynamics," Aerospace Science and Technology, Vol. 13, No. 4 - 5, 2009, pp. 197{203.
http://dx.doi.org/10.1016/j.ast.2009.04.008

Roohani, H. and Skews, B. W., Unsteady aerodynamics e_ects experienced by airfoil during acceleration and retardation," Proceedings of IMechE, Part G, Journal of Aerospace Engineering, Vol. 222, 2008, pp. 631{636.
http://dx.doi.org/10.1243/09544100jaero280

Kumaravel, G., Investigation of acceleration e_ects on rocket aerodynamics, Ph.D. thesis, Department of Aerospace Engineering, IIT Kanpur, India, 2012.

Anderson, J. D., Computational Fluid Dynamics, the basics with applications, McGraw-Hill International Editions, Singapore, 1995.

White, F. M., Fluid Mechanics, WCB McGraw-Hill, seventh edition ed., 2011.

Jones, G. M. . P., The equivalence principle, uniformly accelerated reference frames, and the uniform gravitational _eld," American Journal of Physics, Vol. 78, No. 4, 2010, pp. 377{383.
http://dx.doi.org/10.1119/1.3272719

METACOMP, CFD++ Users Manual, Version 8.0," M/s Metacomp Technologies, USA, 2009.

Uranga, A., Assessment of turbulence modeling for compressible ow around stationary and oscillating cylinder, Master's thesis, Univesity of Victoria, 2006.

Verstappan, R. W. C. P. and Veldman, A. E. P., Numerical computation of a viscous ow around a circular cylinder on a Cartesian grid," in European Congress on Computational methods in Applied Sciences and Engineering, ECCOMAS 2000," Barcelona, 2000.

A L F Lima. E. Silva, A. S.-N. and Damasceno, J. J. R., Numerical simulation of two-dimensional ows over a circular cylinder using the immersed boundary method," Journal of Computational Physics, Vol. 189, 2003, pp. 351{270.
http://dx.doi.org/10.1016/s0021-9991(03)00214-6

Patel, Y., Numerical investigation of ow past a circular cylinder and in a staggered tube bundle using various turbulence models, Master's thesis, Department of Mathematics and Physics, Lappeenranta University of Technology, Finland, 2010.

Schlichting, H. and Gersten, K., Boundary layer theory, Springer, Germany, eighth edition ed., 2003. 26


Refbacks

  • There are currently no refbacks.



Please send any question about this web site to info@praiseworthyprize.com
Copyright © 2005-2024 Praise Worthy Prize