Skip to main content
SpringerLink
Log in

Direct Numerical Simulation of Flow and Heat Transfer in Complex Ducts

  • Original article
  • Published:
Aerotecnica Missili & Spazio Aims and scope Submit manuscript

Abstract

A series of Direct Numerical Simulations (DNS) at low Reynolds number is performed to investigate the flow and the heat transfer in ducts with complex geometry, which are frequently encountered in many engineering fields, especially in aeronautics. A finite-difference approach and the immersed-boundary method are adopted to solve the governing equations in the computational domain. The flow and heat transfer phenomena in a circular pipe are studied in detail for laminar and turbulent regimes; thus the code is validated through a comparison of present DNS results with those provided by some trusted references. Straight ducts with regular polygonal cross sections represent the first type of ducts with complex geometry analyzed in this paper. The behavior of the pumping power expenditure is studied when the number of polygonal sides changes. The secondary motions are then investigated, and their effects on the mean velocity and temperature contours are studied. The shapes of vortices in secondary motions are compared with those provided by an analytical approach, which is based on the eigenfunctions of the Laplacian operator. Also the geometries pioneeringly studied by Nikuradse in 1930 are taken into account.

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
Fig. 17

Similar content being viewed by others

References

  1. Nasuti, F., Pizzarelli, M,. Onofri, M.: Evolution of cooling-channel properties for varying aspect ratio. In: 5th European Conference for Aeronautics and Space Sciences (EUCASS), 07 (2013)

  2. Shah, R.K.: Laminar flow friction and forced convection in duct of arbitrary geometry. Int. J. Heat Mass Transf. 18, 849–862 (1975)

    Article  MathSciNet  Google Scholar 

  3. Demuren, A.O., Rodi, W.: Calculation of turbulence-driven secondary motion in non-circular ducts. J. Fluid Mech. 140, 189–222 (1984)

    Article  Google Scholar 

  4. Rokni, M., Olsson, C.O., Sundén, B.: Numerical and experimental investigation of turbulent flow in a rectangular duct. Int. J. Numer. Methods Fluids 28, 225–242 (1998)

    Article  Google Scholar 

  5. Stankovic, B., Belosevi, S., Crnomarković, N., Stojanovic, A., Tomanović, I., Milicevic, A.: Specific aspects of turbulent flow in rectangular ducts. Thermal Sci. 20(6), S1–S16 (2016)

    Google Scholar 

  6. Demissie, M., Soong, T.W., Bhowmik, N.G., Fitzpatrick, W.P., Maxwell, W.: Secondary Circulation in Natural Streams. Wrc Research Report No. 200. University of Illinois, Water Resources Center, Urbana, IL (1986)

  7. Prandtl, L.: Über die ausgebildete Turbulenz. Proc. Int. Congr. for Applied Mechanics, Zurich, Vol. 9 (1926)

  8. Nikuradse, J.: Untersuchungen über turbulente Strömungen in nicht kreisförmigen Rohren. Ingenieur Arch. 1, 306–332 (1930)

    Article  Google Scholar 

  9. Deissler, R. G., Taylor, M.: Analysis of turbulent flow and heat transfer in noncircular passages. In: NACA Tech. Rep. (1958)

  10. Hoagland, L.: Fully Developed Turbulent Flow in Straight Rectangular Ducts: Secondary Flow, its Cause and Effect on the Primary Flow. PhD thesis, Massachusetts Institute of Technology (1960)

  11. Launder, B.E., Ying, W.M.: Prediction of flow and heat transfer in ducts of square cross-section. Proc. Inst. Mech. Eng. 187(1), 455–461 (1973)

    Article  Google Scholar 

  12. Modesti, D.: A priori tests of eddy viscosity models in square duct flow. Theor. Comput. Fluid Dyn. 34, 713–734 (2020)

    Article  MathSciNet  Google Scholar 

  13. Nikitin, N., Yakhot, A.: Direct numerical simulation of turbulent flow in elliptical ducts. J. Fluid Mech. 532, 141–164 (2005)

    Article  MathSciNet  Google Scholar 

  14. Orlandi, P., Modesti, D., Pirozzoli, S.: DNS of turbulent flows in ducts with complex shape. Flow Turbul. Combust. 100, 1–17 (2018)

    Article  Google Scholar 

  15. Nikitin, N., Chernyshenko, S., Wang, H.: Turbulent flow and heat transfer in eccentric annulus. J. Fluid Mech. 638, 95–116 (2009)

    Article  Google Scholar 

  16. Gavrilakis, S.: Numerical simulation of low-Reynolds-number turbulent flow through a straight square duct. J. Fluid Mech. 244, 101–129 (1992)

    Article  Google Scholar 

  17. Duan, Z., Yovanovich, M., Muzychka, Y.: Pressure drop for fully developed turbulent flow in circular and noncircular ducts. J. Fluids Eng. 134, 061201 (2012)

    Article  Google Scholar 

  18. Pirozzoli, S., Bernardini, M., Orlandi, P.: Passive scalars in turbulent channel flow at high Reynolds number. J. Fluid Mech. 788, 614–639 (2016)

    Article  MathSciNet  Google Scholar 

  19. Pirozzoli, S., Sengupta, T. K.: High-Performance Computing of Big Data for Turbulence and Combustion. CISM International Centre for Mechanical Sciences 592. Springer International Publishing (2020)

  20. Orlandi, P.: Fluid Flow Phenomena: A Numerical Toolkit. Fluid Mechanics and Its Applications. Springer, Netherlands (2000)

    Book  Google Scholar 

  21. O’Rourke, J.: Computational Geometry in C. Cambridge University Press, Cambridge (1998)

    Book  Google Scholar 

  22. Wu, X., Moin, P.: A direct numerical simulation study on the mean velocity characteristics in turbulent pipe flow. J. Fluid Mech. 608, 81–112 (2008)

    Article  Google Scholar 

  23. Rohsenow, W., Hartnett, J., Cho, Y.: Handbook of Heat Transfer. McGraw-Hill handbooks. McGraw-Hill, New York (1993)

    Google Scholar 

  24. Pirozzoli, S., Modesti, D., Orlandi, P., Grasso, F.: Turbulence and secondary motions in square duct flow. J. Fluid Mech. 840, 631–655 (2018)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

I wish to thank my faculty advisor, prof. Sergio Pirozzoli, for supervising the progress of this work and for his precious and crucial contribution to the implementation and tuning of the CFD code.

Author information

Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, Sapienza University of Rome, Via Eudossiana 18, Rome, 00184, Italy

    Federico Deprati

Authors
  1. Federico Deprati
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Federico Deprati.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Deprati, F. Direct Numerical Simulation of Flow and Heat Transfer in Complex Ducts. Aerotec. Missili Spaz. 100, 263–276 (2021). https://doi.org/10.1007/s42496-021-00093-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s42496-021-00093-3

Keywords

Search

Navigation