Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-22T02:12:55.826Z Has data issue: false hasContentIssue false

Two-dimensional simulation of unsteady heat transfer from a circular cylinder in crossflow

Published online by Cambridge University Press:  14 October 2021

SALEM BOUHAIRIE
Affiliation:
Department of Civil Engineering and Applied Mechanics, McGill University, Montreal, Québec, H3A 2K6, Canada
VINCENT H. CHU
Affiliation:
Department of Civil Engineering and Applied Mechanics, McGill University, Montreal, Québec, H3A 2K6, Canada

Abstract

The heat transfer from the surface of a circular cylinder into a crossflow has been computed using a two-dimensional model, for a range of Reynolds numbers from Re=200 to 15550. The boundary-layer separation, the local and overall heat-transfer rates, the eddy- and flare-detachment frequencies and the width of the flares were determined from the numerical simulations. In this range of Reynolds numbers, the heat-transfer process is unsteady and is characterized by a viscous length scale that is inversely proportional to the square root of the Reynolds number. To ensure uniform numerical accuracy for all Reynolds numbers, the dimensions of the computational mesh were selected in proportion to this viscous length scale. The small scales were resolved by at least three nodes within the boundary layers. The frequency of the heat flares increases, and the width of each flare decreases, with the Reynolds number, in proportion to the viscous time and length scales. Despite the presence of three-dimensional structures for the range of Reynolds numbers considered, the two-dimensional model captures the unsteady processes and produced results that were consistent with the available experimental data. It correctly simulated the overall, the front-stagnation and the back-to-total heat-transfer rates.

Type
Research Article
Copyright
Copyright © Cambridge University Press 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Adachi, T., Okamoto, S. & Adachi, M. 1979 The effect of sound on the rate of heat transfer from a cylinder placed normal to an air stream. Bulletin JSME 22, 14071415.CrossRefGoogle Scholar
Al-Jamal, H. & Dalton, C. 2004 Vortex induced vibrations using large eddy simulation at moderate reynolds number. J. Fluids Struct. 19, 7392.CrossRefGoogle Scholar
Behr, M. 1992 Stabilized finite element methods for incompressible flows with emphasis on moving boundaries and interfaces. PhD thesis, University of Minnesota, Minnesota.Google Scholar
Behr, M., Hastreiter, D., Mittal, S. & Tezduyar, T. E. 1995 Incompressible flow past a circular cylinder: Dependence of the computed flow field on the location of the lateral boundaries. Comput. Meth. Appl. Mech. Engng 123, 309316.CrossRefGoogle Scholar
Behr, M., Johnson, A., Kennedy, J., Mittal, S. & Tezduyar, T. E. 1993 Computation of incompressible flows with implicit finite element implementations on the connection machine. Comput. Meth. Appl. Mech. Engng 108, 99118.CrossRefGoogle Scholar
Behr, M., Liou, J., Shih, R. & Tezduyar, T. E. 1991 Vorticity-streamfunction formulation of unsteady incompressible flow past a cylinder: sensitivity of the computed flow field to the location of the outflow boundary. Intl J. Num. Meth. Fluids 12, 323342.CrossRefGoogle Scholar
Bouhairie, S. 2005 Computational methods for calculating heat transfer from a circular cylinder in a cross flow. PhD thesis, McGill University, Montreal, Quebec, Canada.Google Scholar
Braza, M., Chassaing, P. & Minh, H. H. 1986 Numerical study and physical analysis of the pressure and velocity fields in the near wake of a circular cylinder. J. Fluid Mech. 165, 79130.CrossRefGoogle Scholar
Chou, M. H. & Huang, W. 1996 Numerical study of high-reynolds-number flow past a bluff object. Intl J. Num. Meth. Fluids 23, 711723.3.0.CO;2-P>CrossRefGoogle Scholar
Collins, W. M. & Dennis, S. C. R. 1973a The initial flow past an impulsively started circular cylinder. Q. J. Mech. Appl. Maths 26 (1), 5375.CrossRefGoogle Scholar
Collins, W. M. & Dennis, S. C. R. 1973b Flow past an impulsively started circular cylinder. J. Fluid Mech. 60, 105127.CrossRefGoogle Scholar
Coutanceau, M. & Bouard, R. 1979 Mécanique des fluides – sur la formation de tourbillons ≪secondaires≫ dans le sillage d'un cylindre soumis à un départ impulsif. C. R. Acad. Sci. Paris 288 B, 4560.Google Scholar
Coutanceau, M. & Defaye, J. 1991 Circular cylinder wake configurations: a flow visualisation survey. Appl. Mech. Rev. 44, 255305.CrossRefGoogle Scholar
Daube, O. & Ta Phouc Loc, 1978 Étude numérique d'écoulements instationnaires de fluide visqueux incompressible autour de corps profiles par une méthode combinée d'ordre 0(h 2) et 0(h 4). J. Méc. 17, 651678.Google Scholar
Dennis, S. C. R. & Chang, G.-Z. 1969 Numerical integration of the navier-stokes equations for steady two-dimensional flow. Phys. Fluids Suppl. II 12, 8893.Google Scholar
Dennis, S. C. R. & Chang, G.-Z. 1970 Numerical solutions for steady flow past a circular cylinder at reynolds numbers up to 100. J. Fluid Mech. 42, 471489.CrossRefGoogle Scholar
Dennis, S. C. R., Hudson, J. D. & Smith, N. 1968 Steady laminar forced convection from a circular cylinder at low reynolds numbers. Phys. Fluids 11, 933940.CrossRefGoogle Scholar
Dennis, S. C. R. & Staniforth, A. N. 1971 A numerical method for calculating the initial flow past a cylinder in a viscous fluid. In Proc. 2nd Intl Conf. Num. Meth. Fluid Dyn., Lect. Notes Phys., vol. 8, pp. 343349. Springer.Google Scholar
Dimopoulos, H. G. & Hanratty, T. J. 1968 Velocity gradients at the wall for flow around a cylinder for reynolds numbers between 60 and 360. J. Fluid Mech. 33, 303319.CrossRefGoogle Scholar
Dong, S. & Karniadakis, G. E. 2005 Dns of flow past a stationary and oscillating cylinder at Re = 10000. J. Fluids Struct. 20, 519531.CrossRefGoogle Scholar
Eckert, E. R. G. & Drake, R. M. 1972 Analysis of Heat and Mass Transfer. McGraw-Hill.Google Scholar
Eckert, E. R. G. & Soehngen, E. 1952 Distributions of heat transfer coefficients around circular cylinders in crossflow at reynolds numbers from 20 to 500. Trans. ASME 75, 343347.Google Scholar
Engelman, M. S. & Jamnia, M. A. 1990 Transient flow past a circular cylinder: a benchmark solution. Intl J. Num. Meth. Fluids 11, 9851000.CrossRefGoogle Scholar
Evangelinos, C. & Karniadakis, G. E. 1999 Dynamics and flow structures in the turbulent wake of rigid and flexible cylinders subject to vortex-induced vibrations. J. Fluid Mech. 400, 91124.CrossRefGoogle Scholar
Fage, A. & Falkner, V. M. 1931 Further experiments on the flow around a circular cylinder. Tech. Rep. 1369. Aero. Res. Ctee.Google Scholar
Frossling, N. 1958 Evaporation, heat transfer and velocity distribution in two-dimensional and rotationally symmetrical laminar boundary-layer flow. Tech. Rep. 1432. Nat. Advisory Ctee Aero.Google Scholar
Grove, A. S., Shair, F. H., Peterson, E. E. & Acrivos, A. 1964 An experimental investigation of the steady separated flow past a circular cylinder. J. Fluid Mech. 19, 6085.CrossRefGoogle Scholar
Hatanaka, K. & Kawahara, M. 1995 A numerical study of vortex shedding around a heated/cooled circular cylinder by the three-step taylor-galerkin method. Intl J. Num. Meth. Fluids 21, 857867.CrossRefGoogle Scholar
Hayase, T., Humphrey, J. A. C. & Greif, R. 1992 A consistently formulated quick scheme for fast and stable convergence using finite-volume iterative calculation procedures. J. Comp. Phys. 98, 108118.CrossRefGoogle Scholar
Henderson, R. D. 1997 Nonlinear dynamics and pattern formation in turbulent wake transition. J. Fluid Mech. 352, 65112.CrossRefGoogle Scholar
Henderson, R. D. 1998 Turbulent wake transition. In Advances in the Understanding of Bluff Body Wakes and Vortex-Induced Vibrations (ed. Bearman, P. W. & Williamson, C. H. K.). ASME.Google Scholar
Henderson, R. D. & Karniadakis, G. E. 1995 Unstructured spectral element methods for simulation of turbulent flows. J. Comp. Phys. 122, 191217.CrossRefGoogle Scholar
Hiemenz, K. 1911 Die grenzschicht an einem in den gleichformigen flussigkeitsstrom eingetauchten geraden kreiszylinder. thesis, gottingen. Dingl. Polytechn. J. 326, 321.Google Scholar
Hilpert, R. 1933 Wärmeabgabe von geheizten drähten und rohren im luftstrom. Forschung Auf Dem Gebiete Des Ingenieurwesens 4, 215224.Google Scholar
Holman, J. P. 1990 Heat Transfer, 7th edn. McGraw-Hill.Google Scholar
Jain, P. C. & Rao, K. S. 1969 Numerical solution of unsteady viscous incompressible fluid flow past a circular cylinder. Phys. Fluids Supp. II 12, 5764.Google Scholar
Jordan, S. A. & Ragab, S. A. 1998 A large-eddy simulation of the near wake of a circular cylinder. Trans. ASME: J. Fluids Engng 120, 243252.Google Scholar
Jordan, S. K. & Fromm, J. E. 1972 Oscillatory drag, lift, and torque on a circular cylinder in a uniform flow. Phys. Fluids 15, 371376.CrossRefGoogle Scholar
Karniadakis, G. E. 1988 Numerical simulation of forced convection heat transfer from a cylinder in crossflow. Intl J. Heat Mass Transfer 31, 107118.CrossRefGoogle Scholar
Karniadakis, G. E. & Triantafyllou, G. S. 1992 Three-dimensional dynamics and transition to turbulence in the wake of bluff objects. J. Fluid Mech. 238, 130.CrossRefGoogle Scholar
Kawaguti, M. & Jain, P. 1966 Numerical study of a viscous fluid flow past a circular cylinder. J. Phys. Soc. Japan 21, 20552062.CrossRefGoogle Scholar
Krall, K. M. & Eckert, E. R. G. 1973 Local heat transfer around a cylinder at low reynolds number. J. Heat Transfer 95, 273275.CrossRefGoogle Scholar
Lange, C. F., Durst, F. & Breuer, M. 1998 Momentum and heat transfer from cylinders in laminar crossflow at 10−4 < re <200. Intl J. Heat Mass Transfer 41 (22), 34093430.CrossRefGoogle Scholar
Leonard, B. P. 1979 A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Comp. Meth. Appl. Mech. Engng 19, 5998.CrossRefGoogle Scholar
Mittal, R. 1996 Progress on les of flow past a circular cylinders. In Annual Research Briefs. Stanford, California: Center for Turbulence Research.Google Scholar
Mittal, R. & Balachandar, S. 1995 Effect of three-dimensionality on the lift and drag of nominally two-dimensional cylinders. Phys. Fluids 7, 18411865.Google Scholar
Mittal, S. 2001 Computation of three-dimensional flows past circular cylinder of low aspect ratio. Phys. Fluids 13, 177191.CrossRefGoogle Scholar
Nair, M. T. & Sengupta, T. K. 1996 Onset of asymmetry: flow past circular and elliptic cylinders. Intl J. Num. Meth. Fluids 23, 13271345.3.0.CO;2-Q>CrossRefGoogle Scholar
Nakamura, H. & Kamemoto, K. 2001 Numerical simulation of unsteady heat transfer around a circular cylinder to a uniform flow by a vortex and heat element method. Trans. Japan Soc. Mech. Engng B 67 (662), 137144.Google Scholar
Norberg, C. 2003 Fluctuating lift on a circular cylinder: review and new measurements. J. Fluids Struct. 17, 5796.CrossRefGoogle Scholar
Patel, V. A. 1976 Time-dependent solutions of the viscous incompressible flow past a circular cylinder by the method of series truncation. Computers Fluids 4, 1327.CrossRefGoogle Scholar
Patnaik, B. S. V., Narayana, P. A. A. & Seetharamu, K. N. 1999 Numerical simulation of vortex shedding past a circular cylinder under the influence of buoyancy. Intl J. Heat Mass Transfer 42, 34953507.CrossRefGoogle Scholar
Patnaik, B. S. V. P., Seetharamu, K. N. & Narayana, P. A. A. 1996 Simulation of laminar confined flow past a circular cylinder with integral wake splitter involving heat transfer. Intl J. Num. Meth. Heat Fluid Flow 6 (4), 6581.Google Scholar
Payne, R. B. 1958 Calculations of unsteady viscous flow past a circular cylinder. J. Fluid Mech. 4, 8186.Google Scholar
Persillon, H. & Braza, M. 1998 Physical analysis of the transition to turbulence in the wake of a circular cylinder by three-dimensional Navier-Stokes simulation. J. Fluid Mech. 365, 2388.CrossRefGoogle Scholar
Pinol, S. & Grau, F. X. 1998 Influence of the no-slip boundary condition on the prediction of drag, lift, and heat transfer coefficients in the flow past a 2-d cylinder. Num. Heat Transfer, A: Applics. 34, 313330.Google Scholar
Sa, J. Y. & Chang, K. S. 1990 On the far-field stream function condition for two-dimensional incompressible flows. J. Comp. Phys. 91, 398412.CrossRefGoogle Scholar
Schlichting, H. 1979 Boundary-Layer Theory, 7th edn. McGraw-Hill.Google Scholar
Schmidt, E. & Wenner, K. 1943 Heat transfer over the circumference of a heated cylinder in transverse flow. Tech. Rep. 1050. Nat. Advisory Cttee Aero.Google Scholar
Singh, S. P. & Mittal, S. 2003 Simulation of drag crisis in flow past a circular cylinder using 2D computations. J. Aero. Sci. Tech. 55, 5662.Google Scholar
Singh, S. P. & Mittal, S. 2004 Energy spectra of flow past a circular cylinder. Intl J. Comput. Fluid Dyn. 18, 671679.CrossRefGoogle Scholar
Smith, P. A. & Stansby, P. K. 1988 Impulsively started flow around a circular cylinder by the vortex method. J. Fluid Mech. 194, 4577.CrossRefGoogle Scholar
Son, J. S. & Hanratty, T. J. 1969 Numerical solution for the flow around a cylinder at reynolds numbers of 40, 200 and 500. J. Fluid Mech. 35, 369386.CrossRefGoogle Scholar
Song, C. C. S. & Yuan, M. 1990 Simulation of vortex-shedding flow about a circular cylinder at high reynolds numbers. Trans. ASME: J. Fluids Engng 112, 155163.Google Scholar
Squire, H. B. 1938 Forced convection from a cylinder near the forward stagnation point. In Modern Developments in Fluid Dynamics (ed. Goldstein, S.), pp. 631632. Oxford University Press.Google Scholar
Sunden, B. 1983 Influence of buoyancy forces and thermal conductivity on flow field and heat transfer of circular cylinders at small reynolds number. Intl J. Heat Mass Trans. 26, 13291338.CrossRefGoogle Scholar
Ta Phouc Loc, 1980 Numerical analysis of unsteady secondary vortices generated by an impulsively started circular cylinder. J. Fluid Mech. 100, 111128.Google Scholar
Ta Phouc Loc, & Bouard, R. 1985 Numerical solution of the early stage of the unsteady viscous flow around a circular cylinder: a comparison with experimental visualization and measurements. J. Fluid Mech. 160, 93117.Google Scholar
Tezduyar, T. E. & Liou, J. 1991 On the downstream boundary conditions for the vorticity-stream function formulation of two-dimensional incompressible flows. Comp. Meth. App. Mech. Engng. 85, 207217.CrossRefGoogle Scholar
Thom, A. 1933 The flow past circular cylinders at low speeds. Proc. R. Soc. Lond. A 141, 651669.Google Scholar
Thoman, D. C. & Szewczyk, A. A. 1969 Time-dependent viscous flow over a circular cylinder. Phys. Fluids Supp. II 12, 7686.Google Scholar
White, F. M. 1991 Viscous Fluid Flow, 2nd edn. McGraw-Hill.Google Scholar
Willden, R. J. & Graham, J. M. R. 2004 Multi-modal vortex-induced vibrations of a vertical riser pipe subject to a uniform current profile. Eur. J. Mech. B 23, 209218.Google Scholar
Williamson, C. H. K. 1996 Vortex dynamics in the cylinder wake. Annu. Rev. Fluid Mech. 28, 477539.CrossRefGoogle Scholar
Wood, W. W. 1968 Calculations for anemometry with fine hot wires. J. Fluid Mech. 32, 919.CrossRefGoogle Scholar
Xia, M. & Karniadakis, G. E. 1997 Three-dimensional modeling of unsteady heat transfer. In Proc. 1997 ASME Fluids Engineering Division Summer Meeting, Paper No. FEDSM97-3658, Part 7 of (of 24), pp. 16. ASME.Google Scholar
Zdravkovich, M. M. 1997 Flow Around Circular Cylinders. Vol. 1: Fundamentals. Oxford University Press.Google Scholar
Zdravkovich, M. M. 2003 Flow Around Circular Cylinders. Vol. 2: Applications. Oxford University Press.Google Scholar
Zhang, J. & Dalton, C. 1998 A three-dimensional simulation of a steady approach flow past a circular cylinder at low reynolds number. Intl J. Num. Meth. Fluids 26, 10031022.3.0.CO;2-W>CrossRefGoogle Scholar
Zukauskas, A. & Ziugzda, J. 1986 Heat Transfer of a Cylinder in Crossflow. Hemisphere.Google Scholar