- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Fluids

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Integral quantification and phase space analysis of heat transfer in a particle-laden shearless turbulent flow

Hamid Reza Zandi Pour1,2,*, Perry L. Johnson3,†, and Michele Iovieno2,‡

  • *Contact author: hamid.zandipour@polito.it, hamidreza.zandipour@unito.it
  • †Contact author: perry.johnson@uci.edu
  • ‡Contact author: michele.iovieno@polito.it
PDF

Phys. Rev. Fluids 11, 024308 – Published 23 February, 2026

DOI: https://doi.org/10.1103/l7cm-vszk

Abstract

We present a discussion of the enthalpy transport at the interface between two homothermal regions in a particle-laden turbulent flow, in order to quantify the role of inertial particles and of fluid-particle thermal interaction. We use a phase-space analysis of particles in a reduced phase space, and a formulation of a moment of total enthalpy integral (MTEI) applied to data from direct numerical simulations (DNS) at a Taylor microscale Reynolds number equal to 56 in a thermally coupled two-way regime. This allows us to identify the main features of particle statistics and to measure the effects of particle inertia and turbulent convection of the heat transfer, providing a quantitative and interpretable evaluation of the process which does not require any hypothesis of self-similarity. We show how particles dominate the transport mechanisms, bridging enthalpy across eddy structures, in particular when their Stokes number approaches unity, making them accumulate across temperature fronts.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (50)

  1. I. Saito, T. Watanabe, and T. Gotoh, Modulation of fluid temperature fluctuations by particles in turbulence, J. Fluid Mech. 931, A6 (2022).
  2. M. Carbone, A. D. Bragg, and M. Iovieno, Multiscale fluid-particle thermal interaction in isotropic turbulence, J. Fluid Mech. 881, 679 (2019).
  3. M. Carbone and M. Iovieno, Accurate direct numerical simulation of two-way coupled particle-laden flows through the nonuniform Fast Fourier Transform, IJSSE 10, 191 (2020).
  4. L. I. Zaichik and V. M. Alipchenkov, Pair dispersion and preferential concentration of particles in isotropic turbulence, Phys. Fluids 15, 1776 (2003).
  5. L. I. Zaichik and V. M. Alipchenkov, Statistical models for predicting pair dispersion and particle clustering in isotropic turbulence and their applications, New J. Phys. 11, 103018 (2009).
  6. J. Chun, D. L. Koch, S. L. Rani, A. Ahluwalia, and L. R. Collins, Clustering of aerosol particles in isotropic turbulence, J. Fluid Mech. 536, 219 (2005).
  7. J. Bec, H. Homann, and G. Krstulovic, Clustering, fronts, and heat transfer in turbulent suspensions of heavy particles, Phys. Rev. Lett. 112, 234503 (2014).
  8. J. Bec and R. Vallée, Homogeneous turbophoresis of heavy inertial particles in turbulent flow, J. Fluid Mech. 999, A83 (2024).
  9. L. Chen, S. Goto, and J. C. Vassilicos, Turbulent clustering of stagnation points and inertial particles, J. Fluid Mech. 553, 143 (2006).
  10. S. W. Coleman and J. C. Vassilicos, A unified sweep-stick mechanism to explain particle clustering in two- and three-dimensional homogeneous, isotropic turbulence, Phys. Fluids 21, 113301 (2009).
  11. E. Meneguz and M. W. Reeks, Statistical properties of particle segregation in homogeneous isotropic turbulence, J. Fluid Mech. 686, 338 (2011).
  12. S. Lee and C. Lee, Identification of a particle collision as a finite-time blowup in turbulence, Sci. Rep. 13181 (2023).
  13. H. R. Zandi Pour and M. Iovieno, On the formation of thermal caustics in turbulent particle-laden flows, Phys. Fluids 36, 121711 (2024).
  14. Z. Warhaft, Passive scalars in turbulent flows, Annu. Rev. Fluid Mech. 32, 203 (2000).
  15. L. Mydlarski and Z. Warhaft, Passive scalar statistics in high Péclet number grid turbulence, J. Fluid Mech. 358, 135 (1998).
  16. M. Iovieno, S. Di Savino, L. Gallana, and D. Tordella, Mixing of a passive scalar across a thin shearless layer: Concentration of intermittency on the sides of the turbulent interface, J. Turbul. 15, 311 (2014).
  17. H. R. Zandi Pour and M. Iovieno, Heat transfer in a non-isothermal collisionless turbulent particle-laden flow, Fluids 7, 345 (2022).
  18. H. R. Zandi Pour and M. Iovieno, Heat transfer enhancement by suspended particles in a turbulent shearless flow, in 33rd Congress of the International Council of the Aeronautical Sciences (ICAS 2022), Stockholm, Sweden (ICAS, 2022), Vol. 4, pp. 2452–2463.
  19. H. R. Zandi Pour and M. Iovieno, The role of particle inertia and thermal inertia in heat transfer in a non-isothermal particle-laden turbulent flow, Fluids 9, 29 (2024).
  20. A. Halle, S. Colombi, and S. Peirani, Phase-space structure analysis of self-gravitating collisionless spherical systems, Astronomy & Astrophysics 621, A8 (2019).
  21. A. Elnahhas and P. L. Johnson, On the enhancement of boundary layer skin friction by turbulence: An angular momentum approach, J. Fluid Mech. 940, A36 (2022).
  22. A. Kianfar, A. Elnahhas, and P. L. Johnson, Quantifying how turbulence enhances boundary layer skin friction and surface heat transfer, AIAA J. 61, 3900 (2023).
  23. A. Kianfar and P. L. Johnson, Moment of momentum integral analysis of turbulent boundary layers with pressure gradient, J. Fluid Mech. 1002, A29 (2025).
  24. A. Kianfar, M. Di Renzo, C. Williams, A. Elnahhas, and P. L. Johnson, Angular momentum and moment of total enthalpy integral equations for high-speed boundary layers, Phys. Rev. Fluids 8, 054603 (2023).
  25. A. A. Townsend, The Structure of Turbulent Shear Flow (Cambridge University Press, Cambridge, UK, 1980).
  26. T. Wei, Self-similarity analysis of turbulent wake flows, J. Fluids Eng. 139, 051203 (2017).
  27. X.-L. Xiong, S. Laima, H. Li, and Y. Zhou, Self-similarity in single-point turbulent statistics across different quadrants in turbulent rotor wakes, Phys. Rev. Fluids 9, 054608 (2024).
  28. M. R. Maxey and J. J. Riley, Equation of motion for a small rigid sphere in a nonuniform flow, Phys. Fluids 26, 883 (1983).
  29. R. Gatignol, Faxen formulae for a rigid particle in an unsteady non-uniform Stokes flow, J. Mec. Theor. Appl. 2, 143 (1983).
  30. H. Homann and J. Béc, Finite-size effects in the dynamics of neutrally buoyant particles in turbulent flow, J. Fluid Mech. 651, 81 (2010).
  31. V. Armenio and V. Fiorotto, The importance of the forces acting on particles in turbulent flows, Phys. Fluids 13, 2437 (2001).
  32. J.-P. Minier and C. Henry, The dynamics of discrete particles in turbulent flows: Open issues and current challenges in statistical modeling, arXiv:2311.01921 [physics.flu-dyn].
  33. J. A. K. Horwitz, S. Ganguli, and S. K. Lele, Settling of two-way momentum and energy coupled particles subject to Boussinesq and non-Boussinesq heating, Theor. Comput. Fluid Dyn. 35, 539 (2021).
  34. S. Sundaram and L. R. Collins, Numerical considerations in simulating a turbulent suspension of finite-volume particles, J. Comput. Phys. 124, 337 (1996).
  35. H. R. Zandi Pour and M. Iovieno, The impact of collisions on heat transfer in a particle-laden shearless turbulent flow, Journal of Fluid Flow, Heat and Mass Transfer 10, 140 (2023).
  36. H. R. Zandi Pour and M. Iovieno, On the heat transfer in particle-laden turbulent flows: The effect of collision in an anisothermal regime, in Proceedings of the 9th World Congress on Mechanical, Chemical, and Material Engineering, MCM 2023 (Brunel University, London, UK, 2023), p. HTFF 126-1.
  37. C. S. Ng, V. Spandan, R. Verzicco, and D. Lohse, Non-monotonic transport mechanisms in vertical natural convection with dispersed light droplets, J. Fluid Mech. 900, A34 (2020).
  38. H. Pouransari and A. Mani, Particle-to-fluid heat transfer in particle-laden turbulence, Phys. Rev. Fluids 3, 074304 (2018).
  39. I. Saito, T. Watanabe, and T. Gotoh, A new time scale for turbulence modulation by particles, J. Fluid Mech. 880, R6 (2019).
  40. M. Carbone and M. Iovieno, Application of the non-uniform Fast Fourier Transform to the Direct Numerical Simulation of two-way coupled turbulent flows, WIT Trans. Eng. Sci. 120, 237 (2018).
  41. J.-P. Minier, M. Ferrand, and C. Henry, Statistical modeling of particle transport in turbulent flows, in Understanding Turbulent Systems: Progress in Particle Dynamics Modeling (Springer Nature Switzerland, Cham, 2025) pp. 75–95.
  42. C. Liu, S. Tang, and Y. Dong, Effect of inertial particles with different specific heat capacities on heat transfer in particle-laden turbulent flow, Appl. Math. Mech. 38, 1149 (2017).
  43. M. Pan, L. Shen, Q. Zhou, and Y. Dong, Particle transport and turbulence modification in unstably stratified mixed convection within a horizontal channel, Int. J. Heat Mass Transf. 236, 126377 (2025).
  44. Y. Pei, W. Chen, X.-L. Xiong, X. Xu, and Y. Zhou, Direct numerical simulation of turbulent flow and heat transfer in a particle-laden turbulent channel flow, Int. J. Heat Fluid Flow 110, 109617 (2024).
  45. T. Zhou, L. Zhao, W. Huang, and C. Xu, Non-monotonic effect of mass loading on turbulence modulations in particle-laden channel flow, Phys. Fluids 32, 043304 (2020).
  46. M. Nakhaei and B. Lessani, Effects of solid inertial particles on the velocity and temperature statistics of wall bounded turbulent flow, Int. J. Heat Mass Transf. 106, 1014 (2017).
  47. www.hpc-rivr.si
  48. eurohpc-ju.europa.eu
  49. www.izum.si
  50. www.hpc.polito.it

Outline

Information

Phys. Rev. Fluids 11, 024308– Published 23 February, 2026
  • Received 25 July 2025
  • Accepted 12 January 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation