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Eulerian–Lagrangian direct numerical simulation of preferential accumulation of inertial particles in a compressible turbulent boundary layer

Published online by Cambridge University Press:  22 September 2020

Wei Xiao ,
Tai Jin ,
Kun Luo Open the ORCID record for Kun Luo [Opens in a new window] ,
Qi Dai  and
Jianren Fan Open the ORCID record for Jianren Fan [Opens in a new window]
Wei Xiao
Affiliation:
State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou310027, PR China
Tai Jin
Affiliation:
State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou310027, PR China School of Aeronautics and Astronautics, Zhejiang University, Hangzhou310027, PR China
Kun Luo
Affiliation:
State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou310027, PR China
Qi Dai
Affiliation:
State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou310027, PR China
Jianren Fan*
Affiliation:
State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou310027, PR China
*
†Email address for correspondence: [email protected]
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Abstract

In this study, direct numerical simulation of the dispersion and motion of inertial particles in a spatially developing compressible turbulent boundary layer at a Mach number of 2 is performed with the Eulerian–Lagrangian point particle method. Two cases are simulated with different particle diameters (Stokes number) but identical inflow particle numbers. Statistical characteristics and preferential accumulation of particles in the very-near-wall and wake regions are systematically investigated through conditional sampling and mechanism analysis. The results reveal that particle streaks are formed in low-speed regions near the wall because of the influence of dominating ejection events. After normalization with the local minimum particle number density, the particle number density profile reveals a self-similar feature at different streamwise positions. Compared with small particles, large particles are more significantly influenced by turbophoresis and demonstrate stronger preferential accumulation; thus, more large particles are clustered in the near-wall regions and the deviation between the mean velocities of the particle and the fluid increases. With the wall effect, both large and small particles are selectively accumulated in high-vorticity regions in the buffer layer in contrast to turbulence without walls. In comparison with incompressible wall-bounded turbulence, a new mechanism for particle preferential accumulation based on local fluid density is discovered. Large particles are located in low-density regions in the inner zones and high-density regions in the outer zones. Nevertheless, small particles remain located in regions with low fluid density, as illustrated by the mechanism analysis of particle dilatation.

JFM classification

Turbulent Flows: Turbulent boundary layers Turbulent Flows: Compressible turbulence Multiphase and Particle-laden Flows: Multiphase flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 903 , 25 November 2020 , A19
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© The Author(s), 2020. Published by Cambridge University Press

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References

Adrian, R. J., Meinhart, C. D. & Tomkins, C. D. 2000 Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech. 422, 1–54.CrossRefGoogle Scholar
Bai, B. & Li, X. 2016 Deposition of particles in the supersonic flow past a wedge. Powder Technol. 304, 268–273.CrossRefGoogle Scholar
Balachandar, S. & Eaton, J. K. 2010 Turbulent dispersed multiphase flow. Annu. Rev. Fluid Mech. 42, 111–133.CrossRefGoogle Scholar
Bec, J., Biferale, L., Cencini, M., Lanotte, A., Musacchio, S. & Toschi, F. 2007 Heavy particle concentration in turbulence at dissipative and inertial scales. Phys. Rev. Lett. 98, 084502.CrossRefGoogle ScholarPubMed
Bechlars, P. & Sandberg, R. D. 2017 Variation of enstrophy production and strain rotation relation in a turbulent boundary layer. J. Fluid Mech. 812, 321–348.CrossRefGoogle Scholar
Bradshaw, P. 1977 Compressible turbulent shear layers. Annu. Rev. Fluid Mech. 9, 33–52.CrossRefGoogle Scholar
Brooks, J. M., Gupta, A. K., Smith, M. S. & Marineau, E. C. 2018 Particle image velocimetry measurements of Mach 3 turbulent boundary layers at low Reynolds numbers. Exp. Fluids 59, 83.CrossRefGoogle Scholar
Caporaloni, M., Tampieri, F., Trombetti, F. & Vittori, O. 1975 Transfer of particles in nonisotropic air turbulence. J. Atmos. Sci. 32, 565–568.2.0.CO;2>CrossRefGoogle Scholar
Chuvakhov, P. V., Fedorov, A. V. & Obraz, A. O. 2019 Numerical modelling of supersonic boundary-layer receptivity to solid particulates. J. Fluid Mech. 859, 949–971.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, 113301.Google Scholar
Dai, Q., Jin, T., Luo, K. & Fan, J. 2019 a Direct numerical simulation of a three-dimensional spatially evolving compressible mixing layer laden with particles. I. Turbulent structures and asymmetric properties. Phys. Fluids 31, 083302.CrossRefGoogle Scholar
Dai, Q., Jin, T., Luo, K., Xiao, W. & Fan, J. 2019 b Direct numerical simulation of a three-dimensional spatially evolving compressible mixing layer laden with particles. II. Turbulence anisotropy and growth rate. Phys. Fluids 31, 083303.CrossRefGoogle 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
Di Marco, A., Camussi, R., Bernardini, M. & Pirozzoli, S. 2013 Wall pressure coherence in supersonic turbulent boundary layers. J. Fluid Mech. 732, 445–456.CrossRefGoogle Scholar
van Driest, E. 1951 Turbulent boundary layer in compressible fluids. J. Aeronaut. Sci. 18, 145–160.CrossRefGoogle Scholar
van Driest, E. R. 1956 The problem of aerodynamic heating. Aeronaut. Engng Rev. 15, 26–41.Google Scholar
Duan, L., Beekman, I. & Martín, M. P. 2010 Direct numerical simulation of hypersonic turbulent boundary layers. Part 2. Effect of wall temperature. J. Fluid Mech. 655, 419–445.CrossRefGoogle Scholar
Duan, L., Beekman, I. & Martín, M. P. 2011 Direct numerical simulation of hypersonic turbulent boundary layers. Part 3. Effect of Mach number. J. Fluid Mech. 672, 245–267.CrossRefGoogle Scholar
Duan, L., Choudhari, M. M. & Wu, M. 2014 Numerical study of acoustic radiation due to a supersonic turbulent boundary layer. J. Fluid Mech. 746, 165–192.CrossRefGoogle Scholar
Duan, L., Choudhari, M. M. & Zhang, C. 2016 Pressure fluctuations induced by a hypersonic turbulent boundary layer. J. Fluid Mech. 804, 578–607.CrossRefGoogle Scholar
Erdem, E., Kontis, K., Johnstone, E., Murray, N. P. & Steelant, J. 2013 Experiments on transitional shock wave–boundary layer interactions at Mach 5. Exp. Fluids 54, 1598.CrossRefGoogle Scholar
Fedorov, A. V. 2013 Receptivity of a supersonic boundary layer to solid particulates. J. Fluid Mech. 737, 105–131.CrossRefGoogle Scholar
Fessler, J. R., Kulick, J. D. & Eaton, J. K. 1994 Preferential concentration of heavy particles in a turbulent channel flow. Phys. Fluids 6, 3742–3749.CrossRefGoogle Scholar
Ganapathisubramani, B., Clemens, N. T. & Dolling, D. S. 2006 Large-scale motions in a supersonic turbulent boundary layer. J. Fluid Mech. 556, 271.CrossRefGoogle Scholar
Guarini, S. E., Moser, R. D., Shariff, K. & Wray, A. 2000 Direct numerical simulation of a supersonic turbulent boundary layer at Mach 2.5. J. Fluid Mech. 414, 1–33.CrossRefGoogle Scholar
Hadinoto, K., Jones, E. N., Yurteri, C. & Curtis, J. S. 2005 Reynolds number dependence of gas-phase turbulence in gas–particle flows. Intl. J. Multiphase Flow 31, 416–434.CrossRefGoogle Scholar
Hunt, J. C. R., Wray, A. A., Moin, P. 1988 Eddies, streams, and convergence zones in turbulent flows. In Proceedings of Summer Program 1988. Centre for Turbulence Research, Stanford University.Google Scholar
Ignatius, J. K., Sathiyavageeswaran, S. & Chakravarthy, S. R. 2014 Hot-flow simulation of aeroacoustics and suppression by water injection during rocket liftoff. AIAA J. 53, 235–245.CrossRefGoogle Scholar
Jiménez, J. 2018 Coherent structures in wall-bounded turbulence. J. Fluid Mech. 842, P1.CrossRefGoogle Scholar
Jin, T., Luo, K., Dai, Q. & Fan, J. 2015 Simulations of cellular detonation interaction with turbulent flows. AIAA J. 54, 419–433.CrossRefGoogle Scholar
Jin, T., Luo, K., Dai, Q. & Fan, J. 2016 Direct numerical simulation on supersonic turbulent reacting and non-reacting spray jet in heated coflow. Fuel 164, 267–276.CrossRefGoogle Scholar
Kaftori, D., Hetsroni, G. & Banerjee, S. 1995 a Particle behavior in the turbulent boundary layer. I. Motion, deposition, and entrainment. Phys. Fluids 7, 1095–1096.CrossRefGoogle Scholar
Kaftori, D., Hetsroni, G. & Banerjee, S. 1995 b Particle behavior in the turbulent boundary layer. II. Velocity and distribution profiles. Phys. Fluids 7, 1107–1121.CrossRefGoogle Scholar
Lagha, M., Kim, J., Eldredge, J. D. & Zhong, X. 2011 Near-wall dynamics of compressible boundary layers. Phys. Fluids 23, 065109.CrossRefGoogle Scholar
Lapsa, A. P. & Dahm, W. J. A. 2011 Stereo particle image velocimetry of nonequilibrium turbulence relaxation in a supersonic boundary layer. Exp. Fluids 50, 89–108.CrossRefGoogle Scholar
Lele, S. K. 1994 Compressibility effects on turbulence. Annu. Rev. Fluid Mech. 26, 211–254.CrossRefGoogle Scholar
Li, D., Fan, J., Luo, K. & Cen, K. 2011 Direct numerical simulation of a particle-laden low Reynolds number turbulent round jet. Intl J. Multiphase Flow 37, 539–554.CrossRefGoogle Scholar
Li, D., Luo, K. & Fan, J. 2016 a Modulation of turbulence by dispersed solid particles in a spatially developing flat-plate boundary layer. J. Fluid Mech. 802, 359–394.CrossRefGoogle Scholar
Li, D., Wei, A., Luo, K. & Fan, J. 2016 b Direct numerical simulation of a particle-laden flow in a flat plate boundary layer. Intl J. Multiphase Flow 79, 124–143.CrossRefGoogle Scholar
Li, X. & Bai, B. 2014 Motion of submicron particles in supersonic laminar boundary layers. AIAA J. 53, 1037–1047.CrossRefGoogle Scholar
Li, X. & Bai, B. 2015 Motion of submicron particles in a supersonic laminar boundary layer under hypergravity. Procedia Engng 102, 1193–1203.CrossRefGoogle Scholar
Ling, Y., Parmar, M. & Balachandar, S. 2013 A scaling analysis of added-mass and history forces and their coupling in dispersed multiphase flows. Intl J. Multiphase Flow 57, 102–114.CrossRefGoogle Scholar
Loth, E. 2008 Compressibility and rarefaction effects on drag of a spherical particle. AIAA J. 46, 2219–2228.CrossRefGoogle Scholar
Lowe, K. T., Byun, G. & Simpson, R. L. 2014 The effect of particle lag on supersonic turbulent boundary layer statistics. AIAA Paper 2014-0233.CrossRefGoogle Scholar
Luo, K., Jin, T., Lu, S. & Fan, J. 2013 DNS analysis of a three-dimensional supersonic turbulent lifted jet flame. Fuel 108, 691–698.CrossRefGoogle Scholar
Marchioli, C. & Soldati, A. 2002 Mechanisms for particle transfer and segregation in a turbulent boundary layer. J. Fluid Mech. 468, 283–315.CrossRefGoogle Scholar
Martín, M. P., Taylor, E. M., Wu, M. & Weirs, V. G. 2006 A bandwidth-optimized WENO scheme for the effective direct numerical simulation of compressible turbulence. J. Comput. Phys. 220, 270–289.CrossRefGoogle Scholar
McLaughlin, J. B. 1989 Aerosol particle deposition in numerically simulated channel flow. Phys. Fluids A 1, 1211–1224.CrossRefGoogle Scholar
Morkovin, M. V. 1962 Effects of compressibility on turbulent flows. Méc. Turbul. 367, 380.Google Scholar
Mortimer, L. F., Njobuenwu, D. O. & Fairweather, M. 2019 Near-wall dynamics of inertial particles in dilute turbulent channel flows. Phys. Fluids 31, 063302.CrossRefGoogle Scholar
Nagata, T., Nonomura, T., Takahashi, S., Mizuno, Y. & Fukuda, K. 2018 Direct numerical simulation of flow around a heated/cooled isolated sphere up to a Reynolds number of 300 under subsonic to supersonic conditions. Intl J. Heat Mass Transfer 120, 284–299.CrossRefGoogle Scholar
Nasr, H., Ahmadi, G. & McLaughlin, J. B. 2009 A DNS study of effects of particle–particle collisions and two-way coupling on particle deposition and phasic fluctuations. J. Fluid Mech. 640, 507–536.CrossRefGoogle Scholar
Neeb, D., Saile, D. & Gülhan, A. 2018 Experiments on a smooth wall hypersonic boundary layer at Mach 6. Exp. Fluids 59, 68.CrossRefGoogle Scholar
Ninto, Y. & Garcia, M. H. 1996 Experiments on particle–turbulence interactions in the near-wall region of an open channel flow: implications for sediment transport. J. Fluid Mech. 326, 285–319.CrossRefGoogle Scholar
Pan, Y. & Banerjee, S. 1996 Numerical simulation of particle interactions with wall turbulence. Phys. Fluids 8, 2733–2755.CrossRefGoogle Scholar
Patel, A., Boersma, B. J. & Pecnik, R. 2016 The influence of near-wall density and viscosity gradients on turbulence in channel flows. J. Fluid Mech. 809, 793–820.CrossRefGoogle Scholar
Pedinotti, S., Mariotti, G. & Banerjee, S. 1992 Direct numerical simulation of particle behaviour in the wall region of turbulent flows in horizontal channels. Intl J. Multiphase Flow 18, 927–941.CrossRefGoogle Scholar
Peltier, S. J., Rice, B. E., Bisek, N. J., McKenna, C. K., Hofferth, J. W. 2018 Structure of secondary motion in a Mach 2 boundary layer. AIAA Paper 2018-0583.CrossRefGoogle Scholar
Picano, F., Battista, F., Troiani, G. & Casciola, C. M. 2011 Dynamics of PIV seeding particles in turbulent premixed flames. Exp. Fluids 50, 75–88.CrossRefGoogle Scholar
Picciotto, M., Marchioli, C., Reeks, M. W. & Soldati, A. 2005 a Statistics of velocity and preferential accumulation of micro-particles in boundary layer turbulence. Nucl. Eng. Technol. 235, 1239–1249.CrossRefGoogle Scholar
Picciotto, M., Marchioli, C. & Soldati, A. 2005 b Characterization of near-wall accumulation regions for inertial particles in turbulent boundary layers. Phys. Fluids 17, 098101.CrossRefGoogle Scholar
Pirozzoli, S. & Bernardini, M. 2011 Turbulence in supersonic boundary layers at moderate Reynolds number. J. Fluid Mech. 688, 120–168.CrossRefGoogle Scholar
Pirozzoli, S. & Bernardini, M. 2013 Probing high-Reynolds-number effects in numerical boundary layers. Phys. Fluids 25, 021704.CrossRefGoogle Scholar
Pirozzoli, S., Bernardini, M. & Grasso, F. 2008 Characterization of coherent vortical structures in a supersonic turbulent boundary layer. J. Fluid Mech. 613, 205–231.CrossRefGoogle Scholar
Pirozzoli, S., Grasso, F. & Gatski, T. B. 2004 Direct numerical simulation and analysis of a spatially evolving supersonic turbulent boundary layer at M = 2.25. Phys. Fluids 16, 530–545.CrossRefGoogle Scholar
Poggie, J., Bisek, N. J. & Gosse, R. 2015 Resolution effects in compressible, turbulent boundary layer simulations. Comput. Fluids 120, 57–69.CrossRefGoogle Scholar
Poinsot, T. J. & Lelef, S. K. 1992 Boundary conditions for direct simulations of compressible viscous flows. J. Comput. Phys. 101, 104–129.CrossRefGoogle Scholar
Reeks, M. W. 1983 The transport of discrete particles in inhomogeneous turbulence. J. Aerosol Sci. 14, 729–739.CrossRefGoogle Scholar
Ringuette, M. J., Wu, M. & Martín, M. P. 2008 Coherent structures in direct numerical simulation of turbulent boundary layers at Mach 3. J. Fluid Mech. 594, 59–69.CrossRefGoogle Scholar
Robinson, S. K., Kline, S. J. & Spalart, P.R. 1989 A review of quasi-coherent structures in a numerically simulated turbulent boundary layer. NASA Tech. Memo. 102191.Google Scholar
Rouson, D. W. I. & Eaton, J. K. 2001 On the preferential concentration of solid particles in turbulent channel flow. J. Fluid Mech. 428, 149–169.CrossRefGoogle Scholar
Samimy, M. & Lele, S. K. 1991 Motion of particles with inertia in a compressible free shear layer. Phys. Fluids A 3, 1915–1923.CrossRefGoogle Scholar
Sardina, G., Schlatter, P., Brandt, L., Picano, F. & Casciola, C. M. 2012 a Wall accumulation and spatial localization in particle-laden wall flows. J. Fluid Mech. 699, 50–78.CrossRefGoogle Scholar
Sardina, G., Schlatter, P., Picano, F., Casciola, C. M., Brandt, L. & Henningson, D. S. 2012 b Self-similar transport of inertial particles in a turbulent boundary layer. J. Fluid Mech. 706, 584–596.CrossRefGoogle Scholar
Schiller, L. & Naumann, A. 1933 Fundamental calculations in gravitational processing. Z. Ver. Dtsch. Ing. 77, 318–320.Google Scholar
Schlatter, P. & Örlü, R. 2010 Assessment of direct numerical simulation data of turbulent boundary layers. J. Fluid Mech. 659, 116–26.CrossRefGoogle Scholar
Shadloo, M. S., Hadjadj, A. & Hussain, F. 2015 Statistical behavior of supersonic turbulent boundary layers with heat transfer at Ma=2. Intl J. Heat Fluid Flow 53, 113–34.CrossRefGoogle Scholar
Shu, C.-W. & Osher, S. 1988 Efficient implementation of essentially non-oscillatory shock-capturing schemes. J. Comput. Phys. 77, 439–471.CrossRefGoogle Scholar
Smits, A. J., Matheson, N. & Joubert, P. N. 1983 Low-Reynolds-number turbulent boundary layers in zero and favorable pressure gradients. J. Ship Res. 27, 147–157.Google Scholar
Smits, A. J., Spina, E. F., Alving, A. E., Smith, R. W., Fernando, E. M. & Donovan, J. F. 1989 A comparison of the turbulence structure of subsonic and supersonic boundary layers. Phys. Fluids A 1, 1865–1875.CrossRefGoogle Scholar
Spina, E. F., Smits, A. J. & Robinson, S. K. 1994 The physics of supersonic turbulent boundary layers. Annu. Rev. Fluid Mech. 26, 287–319.CrossRefGoogle Scholar
Squires, K. D. & Eaton, J. K. 1991 Measurements of particle dispersion obtained from direct numerical simulations of isotropic turbulence. J. Fluid Mech. 226, 1–35.CrossRefGoogle Scholar
Sutherland, W. 1893 LII. The viscosity of gases and molecular force. Lond. Edinb. Dubl. Phil. Mag. J. Sci. 36, 507–531.CrossRefGoogle Scholar
Teh, E. J. & Johansen, C. T. 2016 Effect of particle momentum transfer on an oblique-shock-wave/laminar-boundary-layer interaction. Acta Astron. 128, 431–439.CrossRefGoogle Scholar
Toschi, F. & Bodenschatz, E. 2009 Lagrangian properties of particles in turbulence. Annu. Rev. Fluid Mech. 41, 375–404.CrossRefGoogle Scholar
Trettel, A. & Larsson, J. 2016 Mean velocity scaling for compressible wall turbulence with heat transfer. Phys. Fluids 28, 026102.CrossRefGoogle Scholar
Urzay, J. 2018 Supersonic combustion in air-breathing propulsion systems for hypersonic flight. Annu. Rev. Fluid Mech. 50, 593–627.CrossRefGoogle Scholar
Wang, L.-P. & Maxey, M. R. 1993 Settling velocity and concentration distribution of heavy particles in homogeneous isotropic turbulence. J. Fluid Mech. 256, 27–68.CrossRefGoogle Scholar
Wenzel, C., Selent, B., Kloker, M. & Rist, U. 2018 DNS of compressible turbulent boundary layers and assessment of data/scaling-law quality. J. Fluid Mech. 842, 428–468.CrossRefGoogle Scholar
Williams, O. J. H., Sahoo, D., Baumgartner, M. L. & Smits, A. J. 2018 Experiments on the structure and scaling of hypersonic turbulent boundary layers. J. Fluid Mech. 834, 237–270.CrossRefGoogle Scholar
Wu, B., Bi, W., Hussain, F. & She, Z.-S. 2017 On the invariant mean velocity profile for compressible turbulent boundary layers. J. Turbul. 18, 186–202.CrossRefGoogle Scholar
Wu, X. & Moin, P. 2009 Direct numerical simulation of turbulence in a nominally zero-pressure-gradient flat-plate boundary layer. J. Fluid Mech. 630, 5–41.CrossRefGoogle Scholar
Xia, Z., Shi, Y., Zhang, Q. & Chen, S. 2016 Modulation to compressible homogenous turbulence by heavy point particles. I. Effect of particles’ density. Phys. Fluids 28, 016103.CrossRefGoogle Scholar
Young, J. & Leeming, A. 1997 A theory of particle deposition in turbulent pipe flow. J. Fluid Mech. 340, 129–159.CrossRefGoogle Scholar
Zhang, H. & Ahmadi, G. 2000 Aerosol particle transport and deposition in vertical and horizontal turbulent duct flows. J. Fluid Mech. 406, 55–80.CrossRefGoogle Scholar
Zhang, Q., Liu, H., Ma, Z. & Xiao, Z. 2016 Preferential concentration of heavy particles in compressible isotropic turbulence. Phys. Fluids 28, 055104.CrossRefGoogle Scholar
Zhang, Y. S., Bi, W. T., Hussain, F., Li, X. L. & She, Z. S. 2012 Mach-number-invariant mean-velocity profile of compressible turbulent boundary layers. Phys. Rev. Lett. 109, 054502.CrossRefGoogle ScholarPubMed
Zhang, Y.-S., Bi, W.-T., Hussain, F. & She, Z.-S. 2014 A generalized Reynolds analogy for compressible wall-bounded turbulent flows. J. Fluid Mech. 739, 392–420.CrossRefGoogle Scholar
Zhao, L. H., Marchioli, C. & Andersson, H. I. 2012 Stokes number effects on particle slip velocity in wall-bounded turbulence and implications for dispersion models. Phys. Fluids 24, 021705.CrossRefGoogle Scholar