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Effect of density ratio on velocity fluctuations in dispersed multiphase flow from simulations of finite-size particles

  • Vahid Tavanashad
  • Alberto Passalacqua
  • Rodney O. Fox
  • Shankar SubramaniamEmail author
Original Paper
  • 24 Downloads

Abstract

Velocity fluctuations in the carrier phase and dispersed phase of a dispersed multiphase flow are studied using particle-resolved direct numerical simulation. The simulations correspond to a statistically homogeneous problem with an imposed mean pressure gradient and are presented for \({Re}_{m}=20\) and a wide range of dispersed phase volume fractions \(\left( 0.1 \le \phi \le 0.4 \right) \) and density ratios of the dispersed phase to the carrier phase \(\left( 0.001 \le \rho _\mathrm{p}/\rho _\mathrm{f} \le 1000 \right) \). The velocity fluctuations in the fluid and dispersed phase at the statistically stationary state are quantified by the turbulent kinetic energy (TKE) and granular temperature, respectively. It is found that the granular temperature increases with a decrease in the density ratio and then reaches an asymptotic value. The qualitative trend of the behavior is explained by the added mass effect, but the value of the coefficient that yields quantitative agreement is non-physical. It is also shown that the TKE has a similar dependence on the density ratio for all volume fractions studied here other than \(\phi =0.1\). The anomalous behavior for \(\phi =0.1\) is hypothesized to arise from the interaction of particle wakes at higher volume fractions. The study of mixture kinetic energy for different cases indicates that low-density ratio cases are less efficient in extracting energy from mean flow to fluctuations.

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References

  1. 1.
    Akiki, G., Moore, W., Balachandar, S.: Pairwise-interaction extended point-particle model for particle-laden flows. J. Comput. Phys. 351, 329–357 (2017)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Balachandar, S.: A scaling analysis for point-particle approaches to turbulent multiphase flows. Int. J. Multiphase Flow 35(9), 801–810 (2009)CrossRefGoogle Scholar
  3. 3.
    Balachandar, S., Eaton, J.K.: Turbulent dispersed multiphase flow. Annu. Rev. Fluid Mech. 42(1), 111–133 (2010)CrossRefGoogle Scholar
  4. 4.
    Biesheuvel, A., Spoelstra, S.: The added mass coefficient of a dispersion of spherical gas bubbles in liquid. Int. J. Multiph. Flow 15(6), 911–924 (1989)CrossRefGoogle Scholar
  5. 5.
    Brenner, H.: Dispersion resulting from flow through spatially periodic porous media. Phil. Trans. R. Soc. Lond. A 297(1430), 81–133 (1980)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Brenner, H., Gaydos, L.J.: The constrained Brownian movement of spherical particles in cylindrical pores of comparable radius: models of the diffusive and convective transport of solute molecules in membranes and porous media. J. Colloid Interface Sci. 58(2), 312–356 (1977)CrossRefGoogle Scholar
  7. 7.
    Bunner, B., Tryggvason, G.: Dynamics of homogeneous bubbly flows part 2. Velocity fluctuations. J. Fluid Mech. 466, 53–84 (2002)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Capecelatro, J., Desjardins, O.: An Euler–Lagrange strategy for simulating particle-laden flows. J. Comput. Phys. 238, 1–31 (2013)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Colombet, D., Legendre, D., Risso, F., Cockx, A., Guiraud, P.: Dynamics and mass transfer of rising bubbles in a homogenous swarm at large gas volume fraction. J. Fluid Mech. 763, 254–285 (2015)CrossRefGoogle Scholar
  10. 10.
    Cundall, P.A., Strack, O.D.L.: A discrete numerical model for granular assemblies. Géotechnique 29(1), 47–65 (1979)CrossRefGoogle Scholar
  11. 11.
    Derksen, J.J.: Simulations of scalar dispersion in fluidized solid-liquid suspensions. AIChE J. 60(5), 1880–1890 (2014)CrossRefGoogle Scholar
  12. 12.
    Dijkhuizen, W., Roghair, I., Annaland, M.V.S., Kuipers, J.: DNS of gas bubbles behaviour using an improved 3D front tracking model-Drag force on isolated bubbles and comparison with experiments. Chem. Eng. Sci. 65(4), 1415–1426 (2010)CrossRefGoogle Scholar
  13. 13.
    Edwards, D.A., Shapiro, M., Brenner, H., Shapira, M.: Dispersion of inert solutes in spatially periodic, two-dimensional model porous media. Trans. Porous Med. 6(4), 337–358 (1991)CrossRefGoogle Scholar
  14. 14.
    Elghobashi, S., Truesdell, G.C.: Direct simulation of particle dispersion in a decaying isotropic turbulence. J. Fluid Mech. 242, 655–700 (1992)CrossRefGoogle Scholar
  15. 15.
    Esmaeeli, A., Tryggvason, G.: A direct numerical simulation study of the buoyant rise of bubbles at \({O(100)}\) Reynolds number. Phys. Fluids 17(9), 093303 (2005)CrossRefGoogle Scholar
  16. 16.
    Fox, R.O.: On multiphase turbulence models for collisional fluid-particle flows. J. Fluid Mech. 742, 368–424 (2014)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Garg, R., Tenneti, S., Mohd-Yusof, J., Subramaniam, S.: Direct numerical simulation of gas-solids flow based on the immersed boundary method. In: Pannala, S., Syamlal, M., O’Brien, T.J. (eds.) Computational Gas-Solids Flows and Reacting Systems: Theory, Methods and Practice, pp. 245–276. IGI Global, Hershey (2010)Google Scholar
  18. 18.
    Gillissen, J.J.J., Sundaresan, S., Van Den Akker, H.E.A.: A lattice Boltzmann study on the drag force in bubble swarms. J. Fluid Mech. 679, 101–121 (2011)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Gore, R., Crowe, C.: Effect of particle size on modulating turbulent intensity. Int. J. Multiph. Flow 15(2), 279–285 (1989)CrossRefGoogle Scholar
  20. 20.
    Koch, D.L., Brady, J.F.: Dispersion in fixed beds. J. Fluid Mech. 154, 399–427 (1985)CrossRefGoogle Scholar
  21. 21.
    Koch, D.L., Brady, J.F.: A non-local description of advection-diffusion with application to dispersion in porous media. J. Fluid Mech. 180, 387–403 (1987)CrossRefGoogle Scholar
  22. 22.
    Koch, D.L., Brady, J.F.: Nonlocal dispersion in porous media: nonmechanical effects. Chem. Eng. Sci. 42(6), 1377–1392 (1987)CrossRefGoogle Scholar
  23. 23.
    Martìnez-Mercado, J., Palacios-Morales, C.A., Zenit, R.: Measurement of pseudoturbulence intensity in monodispersed bubbly liquids for \(10<\text{ Re }<500\). Phys. Fluids 19(10), 103302 (2007)CrossRefGoogle Scholar
  24. 24.
    Mehrabadi, M., Tenneti, S., Garg, R., Subramaniam, S.: Pseudo-turbulent gas-phase velocity fluctuations in homogeneous gas-solid flow: fixed particle assemblies and freely evolving suspensions. J. Fluid Mech. 770, 210–246 (2015)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Mohd-Yusof, J.: Interaction of massive particles with turbulence. Ph.D. thesis, Cornell University (1996)Google Scholar
  26. 26.
    Peters, F., Els, C.: An experimental study on slow and fast bubbles in tap water. Chem. Eng. Sci. 82, 194–199 (2012)CrossRefGoogle Scholar
  27. 27.
    Pope, S.B.: Turbulent Flows. Cambridge University Press, Port Chester, NY (2000)CrossRefGoogle Scholar
  28. 28.
    Prakash, V.N., Martìnez Mercado, J., van Wijngaarden, L., Mancilla, E., Tagawa, Y., Lohse, D., Sun, C.: Energy spectra in turbulent bubbly flows. J. Fluid Mech. 791, 174–190 (2016)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Riboux, G., Risso, F., Legendre, D.: Experimental characterization of the agitation generated by bubbles rising at high Reynolds number. J. Fluid Mech. 643, 509–539 (2010)CrossRefGoogle Scholar
  30. 30.
    Risso, F.: Agitation, mixing, and transfers induced by bubbles. Annu. Rev. Fluid Mech. 50(1), 25–48 (2018)MathSciNetCrossRefGoogle Scholar
  31. 31.
    Risso, F., Ellingsen, K.: Velocity fluctuations in a homogeneous dilute dispersion of high-Reynolds-number rising bubbles. J. Fluid Mech. 453, 395–410 (2002)CrossRefGoogle Scholar
  32. 32.
    Schwarz, S., Kempe, T., Fröhlich, J.: A temporal discretization scheme to compute the motion of light particles in viscous flows by an immersed boundary method. J. Comput. Phys. 281, 591–613 (2015)MathSciNetCrossRefGoogle Scholar
  33. 33.
    Sierakowski, A.J., Prosperetti, A.: Resolved-particle simulation by the Physalis method: enhancements and new capabilities. J. Comput. Phys. 309, 164–184 (2016)MathSciNetCrossRefGoogle Scholar
  34. 34.
    Simeonov, J.A., Calantoni, J.: Modeling mechanical contact and lubrication in direct numerical simulations of colliding particles. Int. J. Multiph. Flow 46, 38–53 (2012)CrossRefGoogle Scholar
  35. 35.
    Spelt, P.D., Sangani, A.S.: Properties and averaged equations for flows of bubbly liquids. Appl. Sci. Res. 58(1), 337–386 (1997)CrossRefGoogle Scholar
  36. 36.
    Sun, B., Tenneti, S., Subramaniam, S., Koch, D.L.: Pseudo-turbulent heat flux and average gas-phase conduction during gas-solid heat transfer: flow past random fixed particle assemblies. J. Fluid Mech. 798, 299–349 (2016)MathSciNetCrossRefGoogle Scholar
  37. 37.
    Takagi, S., Matsumoto, Y.: Surfactant effects on bubble motion and bubbly flows. Annu. Rev. Fluid Mech. 43(1), 615–636 (2011)CrossRefGoogle Scholar
  38. 38.
    Tang, Y., Peters, E.A.J.F., Kuipers, J.A.M.: Direct numerical simulations of dynamic gas-solid suspensions. AIChE J. 62(6), 1958–1969 (2016)CrossRefGoogle Scholar
  39. 39.
    Tenneti, S., Garg, R., Hrenya, C., Fox, R., Subramaniam, S.: Direct numerical simulation of gas–solid suspensions at moderate Reynolds number: quantifying the coupling between hydrodynamic forces and particle velocity fluctuations. Powder Technol. 203(1), 57–69 (2010)CrossRefGoogle Scholar
  40. 40.
    Tenneti, S., Garg, R., Subramaniam, S.: Drag law for monodisperse gas-solid systems using particle-resolved direct numerical simulation of flow past fixed assemblies of spheres. Int. J. Multiph. Flow 37(9), 1072–1092 (2011)CrossRefGoogle Scholar
  41. 41.
    Tenneti, S., Mehrabadi, M., Subramaniam, S.: Stochastic Lagrangian model for hydrodynamic acceleration of inertial particles in gas-solid suspensions. J. Fluid Mech. 788, 695–729 (2016)MathSciNetCrossRefGoogle Scholar
  42. 42.
    Uhlmann, M.: Interface-resolved direct numerical simulation of vertical particulate channel flow in the turbulent regime. Phys. Fluids 20(5), 053305 (2008)CrossRefGoogle Scholar
  43. 43.
    Wijngaarden, L.V., Jeffrey, D.J.: Hydrodynamic interaction between gas bubbles in liquid. J. Fluid Mech. 77(1), 27–44 (1976)CrossRefGoogle Scholar
  44. 44.
    Wylie, J.J., Koch, D.L., Ladd, A.J.C.: Rheology of suspensions with high particle inertia and moderate fluid inertia. J. Fluid Mech. 480, 95–118 (2003)MathSciNetCrossRefGoogle Scholar
  45. 45.
    Xu, Y., Subramaniam, S.: Consistent modeling of interphase turbulent kinetic energy transfer in particle-laden turbulent flows. Phys. Fluids 19(8), 085101 (2007)CrossRefGoogle Scholar
  46. 46.
    Xu, Y., Subramaniam, S.: Effect of particle clusters on carrier flow turbulence: a direct numerical simulation study. Flow Turbul. Combust. 85(3), 735–761 (2010)CrossRefGoogle Scholar
  47. 47.
    Zuber, N.: On the dispersed two-phase flow in the laminar flow regime. Chem. Eng. Sci. 19(11), 897–917 (1964)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  • Vahid Tavanashad
    • 1
    • 3
  • Alberto Passalacqua
    • 1
    • 3
  • Rodney O. Fox
    • 2
    • 3
  • Shankar Subramaniam
    • 1
    • 3
  1. 1.Department of Mechanical EngineeringIowa State UniversityAmesUSA
  2. 2.Department of Chemical and Biological EngineeringIowa State UniversityAmesUSA
  3. 3.Center for Multiphase Flow Research and Education (CoMFRE)Iowa State UniversityAmesUSA

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