Skip to main content
SpringerLink
Log in

Geometric Evaluation of Bluff Bodies Arrangement under Turbulent Flows with Mixed Convection Heat Transfer

  • Published:
Journal of Engineering Thermophysics Aims and scope

Abstract

This work consists of a numerical evaluation of the geometry of an arrangement of square heated obstacles under mixed convective turbulent flows. The geometry is evaluated using the Constructal Design method. The geometry has two degrees of freedom: the longitudinal distance ratio between the frontal bluff body and the posterior ones and the ratio of the transversal distance between the posterior bluff bodies. The flow is also evaluated for three Richardson number values. In all simulations, Reynolds and Prandtl numbers are considered equal to \(Re_{D}= 22,000\) and \(Pr= 0.71\), respectively. The problem is modeled through the classical turbulence modeling with the SST—\(\kappa\)-\(\omega\) closure model. The main objective of the study is to evaluate how the variation in geometry of the arrangement of bluff bodies and different conditions of mixed convection influences the mean drag coefficient and Nusselt number on the arrangement. The variation of mixed convection conditions led to different effects of longitudinal and transversal pitches over the performance indicators, demonstrating that the mechanism of mixed convection strongly influences the arrangement design. For Ri = 1.0, the solutions for the drag coefficient and Nusselt number curves are smoothed due to the natural convection being in the auxiliary flow direction, which thins the boundary layers. The opposite is noticed for \(Ri= -1.0\), where the opposing forces between natural and forced convection intensified the free shear flow, increasing the thickness of turbulent boundary layers.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

REFERENCES

  1. Ikegaya, N., Morishige, S., Matsukura, Y., Onishi, N., and Hagishima, A., Experimental Study on the Interaction between Turbulent Boundary Layer and Wake behind Various Types of Two-Dimensional Cylinders, J. Wind Engin. Ind. Aerodyn., 2020, vol. 204, p. 104250; DOI:10.1016/j.jweia.2020.104250

    Article  Google Scholar 

  2. Lam, K. and Zou, L., Experimental Study and Large Eddy Simulation for the Turbulent Flow around Four Cylinders in an In-Line Square Configuration, Int. J. Heat Fluid Flow, 2009, vol. 30, pp. 276–285; DOI:10.1016/j.ijheatfluidflow.2009.01.005

    Article  Google Scholar 

  3. González-Neria, I., Yáñez-Varela, J.A., Martı́nez-Delgadillo, S.A., Rivadeneyra-Romero, G., and Alonzo-Garcia, A., Analysis of the Turbulent Flow Patterns Generated in Isotropic Porous Media Composed of Aligned or Centered Cylinders, Int. J. Mech. Sci., 2021, vol. 199, p. 106396; DOI:10.1016/ j.ijmecsci.2021.106396

    Article  Google Scholar 

  4. Lam, K., Gong, W.Q., and So, R.M.C., Numerical Simulation of Cross-Flow around Four Cylinders in an In-Line Square Configuration, J. Fluids Struct., 2008, vol. 24, pp. 34–57; DOI:10.1016/ j.jfluidstructs.2007.06.003

    Article  ADS  Google Scholar 

  5. Sumner, D., Two Circular Cylinders in Cross-Flow: A Review, J. Fluids Struct., 2010, vol. 26, pp. 849–899; DOI:10.1016/j.jfluidstructs.2010.07.001

    Article  ADS  Google Scholar 

  6. Page, L.G., Bello-Ochende, T., and Meyer, J.P., Constructal Multi Scale Cylinders with Rotation Cooled by Natural Convection, Int. J. Heat Mass Transfer, 2013, vol. 57, pp. 345–355; DOI:10.1016/ j.ijheatmasstransfer.2012.10.048

    Article  Google Scholar 

  7. Murmu, S.C., Bhattacharyyab, S., Chattopadhyaya, H., and Biswasc, R., Analysis of Heat Transfer around Bluff Bodies with Variable Inlet Turbulent Intensity: A Numerical Simulation, Int. Comm. Heat Mass Transfer, 2020, vol. 117, p. 104779; DOI:10.1016/j.icheatmasstransfer.2020.104779

    Article  Google Scholar 

  8. Igarashi, T., Heat Transfer from a Square Prism to an Air Stream, Int. J. Heat Mass Transfer, 1985, vol. 28, pp. 175–181; DOI:10.1016/0017-9310(85)90019-5

    Article  Google Scholar 

  9. Lyn, D.A., Einav, S., Rodi, W., and Park, J.H., A Laser-Doppler Velocimetry Study of Ensemble-Averaged Characteristics of the Turbulent near Wake of a Square Cylinder, J. Fluid Mech., 1995, vol. 304, pp. 285–319; DOI:10.1017/S0022112095004435

    Article  ADS  Google Scholar 

  10. Perng, S.W. and Wu, H.W., Buoyancy-Aided/Opposed Convection Heat Transfer for Unsteady Turbulent Flow across a Square Cylinder in a Vertical Channel, Int. J. Heat Mass Transfer, 2007, vol. 50, pp. 3701–3717; DOI:10.1016/j.ijheatmasstransfer.2007.02.026

    Article  MATH  Google Scholar 

  11. Ranjan, P. and Dewan, A., Partially Averaged Navier Stokes Simulation of Turbulent Heat Transfer from a Square Cylinder, Int. J. Heat Mass Transfer, 2015, vol. 89, pp. 251–266; DOI:10.1016/ j.ijheatmasstransfer.2015.05.029

    Article  Google Scholar 

  12. Ranjan, P., Dewan and A., Effect of Side Ratio on Fluid Flow and Heat Transfer from Rectangular Cylinders Using the PANS Method, Int. J. Heat Fluid Flow, 2016, vol. 61, pp. 309–322; DOI:10.1016/ j.ijheatfluidflow.2016.05.004

    Article  Google Scholar 

  13. Chen, X. and Xia, H., A Hybrid LES-RANS Study on Square Cylinder Unsteady Heat Transfer, Int. J. Heat Mass Transfer, 2017, vol. 108, pp. 1237–1254; DOI:10.1016/j.ijheatmasstransfer.2016.10.081

    Article  Google Scholar 

  14. Wang, J., Zhuang, Y., and Liu, X., The Flow and Heat Transfer Characteristics in a Rectangular Channel with Miniature Cuboid Dimples, Int. Commun. Heat Mass Transfer, 2021, vol. 126, p. 105474; DOI:10.1016/j.icheatmasstransfer.2021.105474

    Article  Google Scholar 

  15. Wang, J., Ge, J., Fan, Y., Fu, Y., and Liu, X., Flow Behavior and Heat Transfer in a Rectangular Channel with Miniature Riblets, Int. Commun. Heat Mass Transfer, 2022, vol. 135, p. 106049; DOI:10.1016/ j.icheatmasstransfer.2022.106049

    Article  Google Scholar 

  16. Lorenzini, G., Rocha, L.A.O., Biserni, C., dos Santos, E.D., and Isoldi, L.A., Constructal Design of Cavities Inserted into a Cylindrical Solid Body, ASME J. Heat Transfer 2012, vol. 134, no. 7, p. 071301; DOI:10.1115/1.4006103

    Article  Google Scholar 

  17. Razera, A.L., da Fonseca, R.J.C., Isoldi, L.A., dos Santos, E.D., Rocha, L.A.O., and Biserni, C., Constructal Design of a Semi-Elliptical Fin Inserted in a Lid-Driven Square Cavity with Mixed Convection, Int. J. Heat Mass Transfer, 2018, vol. 126, pp. 81–94; DOI:10.1016/j.ijheatmasstransfer.2018.05.157

    Article  Google Scholar 

  18. Page, L.G., Bello-Ochende, T., and Meyer, J.P., Constructal Multi Scale Cylinders with Rotation Cooled by Natural Convection, Int. J. Heat Mass Transfer, 2012, vol. 57, pp. 345–355; DOI:10.1016/ j.ijheatmasstransfer.2012.10.048

  19. Barros, G.M., Lorenzini, G., Isoldi, L.A., Rocha, L.A.O., and dos Santos, E.D., Influence of Mixed Convection Laminar Flows on the Geometrical Evaluation of a Triangular Arrangement of Circular Cylinders, Int. J. Heat Mass Transfer, 2017, vol. 114, pp. 1188–1200.

    Article  Google Scholar 

  20. Salcedo, E., Treviño, C., Palacios-Morales, C., Zenite, R., and Martı́nez-Suástegui, L., Experimental Study on Laminar Flow over Two Confined Isothermal Cylinders in Tandem during Mixed Convection, Int. J. Thermal Sci., 2017, vol. 115, pp. 176–196; DOI:10.1016/j.ijthermalsci.2017.01.015

    Article  Google Scholar 

  21. Pedrotti, V., de Escobar, C.C., dos Santos, E.D., and Souza, J.A., Thermal Analysis of Tubular Arrangements Submitted to External Flow Using Constructal Theory, Int. Comm. Heat Mass Transfer, 2020, vol. 111, p. 104458; DOI:10.1016/j.icheatmasstransfer.2019.104458

    Article  Google Scholar 

  22. Teixeira, F.B., Biserni, C., Conde, P.V., Rocha, L.A.O., Isoldi, L.A., and dos Santos, E.D., Geometrical Investigation of Bluff Bodies Array Subjected to Forced Convective Flows for Different Aspect Ratios of Frontal Body, Int. J. Therm. Sci., 2021, vol. 161, p. 106724; DOI:10.1016/j.ijthermalsci.2020.106724

    Article  Google Scholar 

  23. Teixeira, F.B., Lorenzini, G., Errera, M.R., Rocha, L.A.O., Isoldi, L.A., and dos Santos, E.D., Constructal Design of Triangular Arrangements of Square Bluff Bodies under Forced Convective Turbulent Flows, Int. J. Heat Mass Transfer, 2018, vol. 126, pp. 521–535; DOI:10.1016/j.ijheatmasstransfer.2018.04.134

    Article  Google Scholar 

  24. Patankar, S.V., Numerical Heat Transfer and Fluid Flow, New York: McGraw-Hill, 1980.

    MATH  Google Scholar 

  25. Malisca, C.R., Transferência de Calor e Mecânica dos Fluidos Computacional, Rio de Janeiro: LTC–Livros Técnicos e Cientı́ficos Editora S.A., 2nd ed., 2004.

  26. ANSYS. 18.1.—FLUENT User’s Guide, ANSYS. 2017.

  27. Wilcox, D.C., Turbulence Modeling for CFD, 3d ed., DCW Industries, 2006.

  28. Menter, F.R., Zonal Two Equation \(\kappa\)-\(\omega\) Turbulence Models For Aerodynamic Flows, AIAA 24th Fluid Dynamics Conf, 1993, 1993, AIAA 93-2906.

  29. Wilcox, D.C., Reassessment of the Scale-Determining Equation for Advanced Turbulence Models, AIAA J., 1988, vol. 26, pp. 1299–1310; DOI:10.2514/3.10041

    Article  ADS  MathSciNet  MATH  Google Scholar 

  30. Jones, W.P. and Launder, B.E., The Prediction of Laminarization with a Two-Equation Model of Turbulence, Int. J. Heat Mass Transfer, 1972, vol. 15, pp. 301–314.

    Article  Google Scholar 

  31. Menter, F.R., Kuntz, M., and Langtry, R., Ten Years of Industrial Experience with the SST Turbulence Model, Turbul., Heat Mass Transfer, 2003, vol. 4, pp. 625–632.

    Article  Google Scholar 

  32. Bejan, A., Convection Heat Transfer, 4th ed., Durham, USA: Wiley, 2013; DOI:10.1002/9781118671627

    Book  MATH  Google Scholar 

  33. Bejan, A., Shape and Structure, from Engineering to Nature, Cambridge, UK: Cambridge Univ. Press, 2000.

    MATH  Google Scholar 

  34. Bejan, A. and Lorente, S., Design with Constructal Theory, Hoboken: Wiley, 2008.

    Book  MATH  Google Scholar 

  35. Teixeira, F.B., Santos, A.L.G., Rocha, L.A.O., Isoldi, L.A., and dos Santos, E.D., Meshing Strategy Evaluation for a Square Shaped Bluff Body under High Reynolds Number Cross Flow, Procs. of the XX ENMC—Encontro Nacional de Modelagem Computacional e VIII ECTM—Encontro de Ciências e Tecnologia de Materiais, Nova Friburgo, RJ, Brazil, 2017.

  36. Roache, P.J., Perspective: A Method for Uniform Reporting of Grid Refinement Studies, J. Fluids Engin., 1994, vol. 116, no. 3, pp. 405–413; DOI:10.1115/1.2910291

    Article  Google Scholar 

  37. Durao, D.F.G., Heitor, M.V., and Pereira, J.C.F., Measurements of Turbulent and Periodic Flows around a Square Cross-Section Cylinder, Exp. Fluids., 1988, vol. 6, pp. 298–304; DOI:10.1007/BF00538820

    Article  ADS  Google Scholar 

  38. Bouris, D. and Bergeles, G., 2D LES of Vortex Shedding from a Square Cylinder, J. Wind Eng. Ind. Aerodyn. 1999, vol. 80, pp. 31–46; DOI:10.1016/S0167-6105(98)00200-1

    Article  Google Scholar 

  39. Hilpert, R., Wärmeabgabe von beheizten Drähten und Rohren im Luftstrom, Forsch. Ingenieurwesen, 1933, vol. 4, pp. 215–224.

  40. Sparrow, E.M., Abraham, J.P., and Tong, J.C.K., Archival Correlations for Average Heat Transfer Coefficients for Non-Circular Cylinders and for Spheres in Cross-Flow, Int. J. Heat Mass Transfer, 2004, vol. 47, pp. 5285–5296; DOI:10.1016/j.ijheatmasstransfer.2004.06.024

    Article  Google Scholar 

  41. Franke, J. and Frank. W., Large Eddy Simulation of the Flow past a Circular Cylinder at Re = 3900, J. Wind Eng. Ind. Aerodyn., 2002, vol. 90, pp. 1191–1206; DOI:10.1016/S0167-6105(02)00232-5

    Article  Google Scholar 

  42. Wiesche, S.a.d., Large-Eddy Simulation Study of an Air Flow past a Heated Square Cylinder, Heat Mass Transfer, 2006, vol. 43, pp. 515-525; DOI:10.1007/s00231-006-0122-x

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Graduate Program of Mechanical Engineering, School of Engineering, Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil

    F. B. Teixeira & L. A. O. Rocha

  2. Università degli Studi di Parma, Dipartimento di Ingegneria e Architettura, Parma, Italy

    G. Lorenzini

  3. Graduate Program of Ocean Engineering, School of Engineering, Universidade Federal do Rio Grande, Rio Grande, Brazil

    L. A. Isoldi, E. D. dos Santos & L. A. O. Rocha

Authors
  1. F. B. Teixeira
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Lorenzini
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. L. A. Isoldi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. E. D. dos Santos
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. L. A. O. Rocha
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. Lorenzini.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Teixeira, F.B., Lorenzini, G., Isoldi, L.A. et al. Geometric Evaluation of Bluff Bodies Arrangement under Turbulent Flows with Mixed Convection Heat Transfer. J. Engin. Thermophys. 32, 279–311 (2023). https://doi.org/10.1134/S1810232823020078

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1810232823020078

Search

Navigation