Hostname: page-component-5cf477f64f-tx7qf Total loading time: 0 Render date: 2025-04-06T11:27:55.514Z Has data issue: false hasContentIssue false
  • English
  • Français

Acceleration statistics of tracer and light particles in compressible homogeneous isotropic turbulence

Published online by Cambridge University Press:  03 February 2022

Xiangjun Wang ,
Minping Wan Open the ORCID record for Minping Wan [Opens in a new window]  and
Luca Biferale Open the ORCID record for Luca Biferale [Opens in a new window]
Xiangjun Wang
Affiliation:
Guangdong Provincial Key Laboratory of Turbulence Research and Applications, Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Nanshan District, Shenzhen, Guangdong 518055, PR China Harbin Institute of Technology, Nangang District, Harbin, Heilongjiang 150090, PR China
Minping Wan*
Affiliation:
Guangdong Provincial Key Laboratory of Turbulence Research and Applications, Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Nanshan District, Shenzhen, Guangdong 518055, PR China Southern Marine Science and Engineering Guangdong Laboratory (Guangzhou), 1119 Haibin Road, Nansha District, Guangzhou, Guangdong 511458, PR China
Luca Biferale
Affiliation:
Department of Physics and INFN University of Rome ‘Tor Vergata’, Via della Ricerca Scientifica 1, 00133 Rome, Italy
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The accelerations of tracer and light particles (bubbles) in compressible homogeneous isotropic turbulence are investigated by using data from direct numerical simulations up to turbulent Mach number $M_t =1$. For tracer particles, the flatness factor of acceleration components, $F_a$, increases gradually for $M_t \in [0.3, 1]$. On the contrary, $F_a$ for bubbles develops a maximum around $M_t \sim 0.6$. The probability density function of longitudinal acceleration of tracers is increasingly skewed towards the negative value as $M_t$ increases. By contrast, for light particles, the skewness factor of longitudinal acceleration, $S_a$, first becomes more negative with the increase of $M_t$, and then goes back to $0$ when $M_t$ is larger than $0.6$. Similarly, differences among tracers and bubbles appear also in the zero-crossing time of acceleration correlation. It is argued that all these phenomena are intimately linked to the flow structures in the compression regions close to shocklets.

JFM classification

Multiphase and Particle-laden Flows: Particle/fluid flow Turbulent Flows: Compressible turbulence Turbulent Flows: Turbulence theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 935 , 25 March 2022 , A36
Check for updates
Copyright
© The Author(s), 2022. Published by Cambridge University Press

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

Anderson, J.D. Jr 2010 Fundamentals of Aerodynamics. Tata McGraw-Hill Education.Google Scholar
Ayyalasomayajula, S., Gylfason, A., Collins, L.R., Bodenschatz, E. & Warhaft, Z. 2006 Lagrangian measurements of inertial particle accelerations in grid generated wind tunnel turbulence. Phys. Rev. Lett. 97 (14), 144507.CrossRefGoogle ScholarPubMed
Ayyalasomayajula, S., Warhaft, Z. & Collins, L.R. 2008 Modeling inertial particle acceleration statistics in isotropic turbulence. Phys. Fluids 20 (9), 095104.CrossRefGoogle Scholar
Barth, E.L. & Rafkin, S.C.R. 2007 TRAMS: a new dynamic cloud model for Titan's methane clouds. Geophys. Res. Lett. 34 (3), L03203.CrossRefGoogle Scholar
Bec, J., Biferale, L., Boffetta, G., Celani, A., Cencini, M., Lanotte, A., Musacchio, S. & Toschi, F. 2006 Acceleration statistics of heavy particles in turbulence. J. Fluid Mech. 550, 349–358.CrossRefGoogle Scholar
Biferale, L., Boffetta, G., Celani, A., Devenish, B.J., Lanotte, A. & Toschi, F. 2004 Multifractal statistics of Lagrangian velocity and acceleration in turbulence. Phys. Rev. Lett. 93 (6), 064502.CrossRefGoogle ScholarPubMed
Biferale, L. & Toschi, F. 2005 Joint statistics of acceleration and vorticity in fully developed turbulence. J. Turbul. 6, N40.CrossRefGoogle Scholar
Bourgoin, M. & Xu, H. 2014 Focus on dynamics of particles in turbulence. New J. Phys. 16 (8), 085010.CrossRefGoogle Scholar
Bragg, A.D., Ireland, P.J. & Collins, L.R. 2015 Mechanisms for the clustering of inertial particles in the inertial range of isotropic turbulence. Phys. Rev. E 92 (2), 023029.CrossRefGoogle ScholarPubMed
Coleman, S.W. & Vassilicos, J.C. 2009 A unified sweep-stick mechanism to explain particle clustering in two-and three-dimensional homogeneous, isotropic turbulence. Phys. Fluids 21 (11), 113301.CrossRefGoogle Scholar
Curran, E.T., Heiser, W.H. & Pratt, D.T. 1996 Fluid phenomena in scramjet combustion systems. Annu. Rev. Fluid Mech. 28 (1), 323–360.CrossRefGoogle Scholar
Dai, Q., Jin, T., Luo, K. & Fan, J. 2018 Direct numerical simulation of particle dispersion in a three-dimensional spatially developing compressible mixing layer. Phys. Fluids 30 (11), 113301.Google Scholar
Dai, Q., Luo, K., Jin, T. & Fan, J. 2017 Direct numerical simulation of turbulence modulation by particles in compressible isotropic turbulence. J. Fluid Mech. 832, 438–482.CrossRefGoogle Scholar
Federrath, C., Roman-Duval, J., Klessen, R.S., Schmidt, W. & Mac Low, M.-M. 2010 Comparing the statistics of interstellar turbulence in simulations and observations – solenoidal versus compressive turbulence forcing. Astron. Astrophys. 512, A81.CrossRefGoogle Scholar
Ferri, A. 1973 Mixing-controlled supersonic combustion. Annu. Rev. Fluid Mech. 5 (1), 301–338.CrossRefGoogle Scholar
Fuster, D. & Colonius, T. 2011 Modelling bubble clusters in compressible liquids. J. Fluid Mech. 688, 352–389.CrossRefGoogle Scholar
Gatignol, R. 1983 The Faxén formulae for a rigid particle in an unsteady non-uniform Stokes flow. J. Méc. Théor. Appl. 1 (2), 143–160.Google Scholar
Goto, S. & Vassilicos, J.C. 2008 Sweep-stick mechanism of heavy particle clustering in fluid turbulence. Phys. Rev. Lett. 100 (5), 054503.CrossRefGoogle ScholarPubMed
Gotoh, T. & Rogallo, R.S. 1999 Intermittency and scaling of pressure at small scales in forced isotropic turbulence. J. Fluid Mech. 396, 257–285.CrossRefGoogle Scholar
Gustavsson, K. & Mehlig, B. 2016 Statistical models for spatial patterns of heavy particles in turbulence. Adv. Phys. 65 (1), 1–57.CrossRefGoogle Scholar
Haugen, N.E.L., Brandenburg, A., Sandin, C. & Mattsson, L. 2022 Spectral characterisation of inertial particle clustering in turbulence. J. Fluid Mech. 934, A37.CrossRefGoogle Scholar
Heisenberg, W. 1985 Zur statistischen theorie der turbulenz. In Original Scientific Papers Wissenschaftliche Originalarbeiten, pp. 82–111. Springer.CrossRefGoogle Scholar
Huete, C., Urzay, J., Sánchez, A.L. & Williams, F.A. 2016 Weak-shock interactions with transonic laminar mixing layers of fuels for high-speed propulsion. AIAA J. 54 (3), 966–979.CrossRefGoogle Scholar
Johansen, A., Oishi, J.S., Mac Low, M.-M., Klahr, H., Henning, T. & Youdin, A. 2007 Rapid planetesimal formation in turbulent circumstellar disks. Nature 448 (7157), 1022–1025.CrossRefGoogle ScholarPubMed
Kida, S. & Orszag, S.A. 1990 Energy and spectral dynamics in forced compressible turbulence. J. Sci. Comput. 5 (2), 85–125.CrossRefGoogle Scholar
Kolmogorov, A.N. 1941 a Dissipation of energy in the locally isotropic turbulence. Dokl. Akad. Nauk SSSR 31, 538–540.Google Scholar
Kolmogorov, A.N. 1941 b The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk SSSR 30, 301–305.Google Scholar
La Porta, A., Voth, G.A., Crawford, A.M., Alexander, J. & Bodenschatz, E. 2001 Fluid particle accelerations in fully developed turbulence. Nature 409 (6823), 1017–1019.CrossRefGoogle ScholarPubMed
Lavezzo, V., Soldati, A., Gerashchenko, S., Warhaft, Z. & Collins, L.R. 2010 On the role of gravity and shear on inertial particle accelerations in near-wall turbulence. J. Fluid Mech. 658, 229–246.CrossRefGoogle Scholar
Maxey, M.R. 1987 The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields. J. Fluid Mech. 174, 441–465.CrossRefGoogle Scholar
Maxey, M.R. & Riley, J.J. 1983 Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids 26 (4), 883–889.CrossRefGoogle Scholar
Monchaux, R., Bourgoin, M. & Cartellier, A. 2012 Analyzing preferential concentration and clustering of inertial particles in turbulence. Intl J. Multiphase Flow 40, 1–18.CrossRefGoogle Scholar
Mordant, N., Crawford, A.M. & Bodenschatz, E. 2004 Three-dimensional structure of the Lagrangian acceleration in turbulent flows. Phys. Rev. Lett. 93 (21), 214501.CrossRefGoogle ScholarPubMed
Ni, R., Huang, S.-D. & Xia, K.-Q. 2012 Lagrangian acceleration measurements in convective thermal turbulence. J. Fluid Mech. 692, 395–419.CrossRefGoogle Scholar
Ott, S. & Mann, J. 2000 An experimental investigation of the relative diffusion of particle pairs in three-dimensional turbulent flow. J. Fluid Mech. 422, 207–223.CrossRefGoogle Scholar
Pan, L., Padoan, P., Scalo, J., Kritsuk, A.G. & Norman, M.L. 2011 Turbulent clustering of protoplanetary dust and planetesimal formation. Astrophys. J. 740 (1), 6.CrossRefGoogle Scholar
Parmar, M., Haselbacher, A. & Balachandar, S. 2011 Generalized Basset-Boussinesq-Oseen equation for unsteady forces on a sphere in a compressible flow. Phys. Rev. Lett. 106 (8), 084501.CrossRefGoogle Scholar
Parmar, M., Haselbacher, A. & Balachandar, S. 2012 Equation of motion for a sphere in non-uniform compressible flows. J. Fluid Mech. 699, 352–375.CrossRefGoogle Scholar
Reisman, G.E., Wang, Y.-C. & Brennen, C.E. 1998 Observations of shock waves in cloud cavitation. J. Fluid Mech. 355, 255–283.CrossRefGoogle Scholar
Stelzenmuller, N., Polanco, J.I., Vignal, L., Vinkovic, I. & Mordant, N. 2017 Lagrangian acceleration statistics in a turbulent channel flow. Phys. Rev. Fluids 2 (5), 054602.CrossRefGoogle Scholar
Toschi, F. & Bodenschatz, E. 2009 Lagrangian properties of particles in turbulence. Annu. Rev. Fluid Mech. 41, 375–404.CrossRefGoogle Scholar
Urzay, J. 2018 Supersonic combustion in air-breathing propulsion systems for hypersonic flight. Annu. Rev. Fluid Mech. 50, 593–627.CrossRefGoogle Scholar
Vedula, P. & Yeung, P.-K. 1999 Similarity scaling of acceleration and pressure statistics in numerical simulations of isotropic turbulence. Phys. Fluids 11 (5), 1208–1220.CrossRefGoogle Scholar
Volk, R., Calzavarini, E., Verhille, G., Lohse, D., Mordant, N., Pinton, J.-F. & Toschi, F. 2008 a Acceleration of heavy and light particles in turbulence: comparison between experiments and direct numerical simulations. Physica D 237 (14–17), 2084–2089.CrossRefGoogle Scholar
Volk, R., Mordant, N., Verhille, G. & Pinton, J.-F. 2008 b Laser Doppler measurement of inertial particle and bubble accelerations in turbulence. Europhys. Lett.) 81 (3), 34002.CrossRefGoogle Scholar
Voth, G.A., La Porta, A., Crawford, A.M., Alexander, J. & Bodenschatz, E. 2002 Measurement of particle accelerations in fully developed turbulence. J. Fluid Mech. 469, 121–160.CrossRefGoogle Scholar
Voth, G.A., Satyanarayan, K. & Bodenschatz, E. 1998 Lagrangian acceleration measurements at large Reynolds numbers. Phys. Fluids 10 (9), 2268–2280.CrossRefGoogle Scholar
Wang, J., Wang, L.-P., Xiao, Z., Shi, Y. & Chen, S. 2010 A hybrid numerical simulation of isotropic compressible turbulence. J. Comput. Phys. 229 (13), 5257–5279.CrossRefGoogle Scholar
Wang, L.-P., Wexler, A.S. & Zhou, Y. 1998 On the collision rate of small particles in isotropic turbulence. I. Zero-inertia case. Phys. Fluids 10 (1), 266–276.CrossRefGoogle Scholar
Wang, X., Wan, M., Yang, Y., Wang, L.-P. & Chen, S. 2020 Reynolds number dependence of heavy particles clustering in homogeneous isotropic turbulence. Phys. Rev. Fluids 5, 124603.CrossRefGoogle Scholar
Wang, Y.C. & Brennen, C.E. 1999 Numerical computation of shock waves in a spherical cloud of cavitation bubbles. Trans. ASME J. Fluids Engng 121 (4), 872–880.CrossRefGoogle Scholar
Wilkinson, M., Mehlig, B. & Bezuglyy, V. 2006 Caustic activation of rain showers. Phys. Rev. Lett. 97, 048501.CrossRefGoogle ScholarPubMed
Xiao, W., Jin, T., Luo, K., Dai, Q. & Fan, J. 2020 Eulerian–Lagrangian direct numerical simulation of preferential accumulation of inertial particles in a compressible turbulent boundary layer. J. Fluid Mech. 903, A19.CrossRefGoogle Scholar
Xu, H., Ouellette, N.T. & Bodenschatz, E. 2007 a Curvature of Lagrangian trajectories in turbulence. Phys. Rev. Lett. 98 (5), 050201.CrossRefGoogle ScholarPubMed
Xu, H., Ouellette, N.T., Vincenzi, D. & Bodenschatz, E. 2007 b Acceleration correlations and pressure structure functions in high-Reynolds number turbulence. Phys. Rev. Lett. 99 (20), 204501.CrossRefGoogle ScholarPubMed
Yaglom, A.M. 1949 On the acceleration field in a turbulent flow. C. R. Akad. USSR 67, 795–798.Google Scholar
Yang, Y., Wang, J., Shi, Y., Xiao, Z., He, X.T. & Chen, S. 2013 Acceleration of passive tracers in compressible turbulent flow. Phys. Rev. Lett. 110 (6), 064503.CrossRefGoogle ScholarPubMed
Yang, Y., Wang, J., Shi, Y., Xiao, Z., He, X.T. & Chen, S. 2014 Interactions between inertial particles and shocklets in compressible turbulent flow. Phys. Fluids 26 (9), 091702.CrossRefGoogle Scholar
Yang, Y., Wang, J., Shi, Y., Xiao, Z., He, X.T. & Chen, S. 2016 Intermittency caused by compressibility: a Lagrangian study. J. Fluid Mech. 786, R6.CrossRefGoogle Scholar
Yeung, P.K. 1997 One- and two-particle Lagrangian acceleration correlations in numerically simulated homogeneous turbulence. Phys. Fluids 9 (10), 2981–2990.CrossRefGoogle Scholar
Yeung, P.-K. & Pope, S.B. 1989 Lagrangian statistics from direct numerical simulations of isotropic turbulence. J. Fluid Mech. 207, 531–586.CrossRefGoogle Scholar
Zhang, Q., Liu, H., Ma, Z. & Xiao, Z. 2016 Preferential concentration of heavy particles in compressible isotropic turbulence. Phys. Fluids 28 (5), 055104.CrossRefGoogle Scholar
Zhang, Q. & Xiao, Z. 2018 Single-particle dispersion in compressible turbulence. Phys. Fluids 30 (4), 040904.CrossRefGoogle Scholar
Zhang, Z., Legendre, D. & Zamansky, R. 2019 Model for the dynamics of micro-bubbles in high-Reynolds-number flows. J. Fluid Mech. 879, 554–578.CrossRefGoogle Scholar
Zhou, Y., Wexler, A.S. & Wang, L.-P. 1998 On the collision rate of small particles in isotropic turbulence. II. Finite inertia case. Phys. Fluids 10 (5), 1206–1216.CrossRefGoogle Scholar