Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-25T22:40:35.474Z Has data issue: false hasContentIssue false
  • English
  • Français

A body in nonlinear near-wall shear flow: numerical results for a flat plate

Published online by Cambridge University Press:  11 March 2021

Ryan A. Palmer Open the ORCID record for Ryan A. Palmer [Opens in a new window]  and
Frank T. Smith Open the ORCID record for Frank T. Smith [Opens in a new window]
Ryan A. Palmer*
Affiliation:
Department of Mathematics, University College London, LondonWC1H 0AY, UK Recently changed institution: School of Mathematics, Fry Building, Woodland Road, BristolBS8 1UG, UK
Frank T. Smith
Affiliation:
Department of Mathematics, University College London, LondonWC1H 0AY, UK
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Direct numerical solutions are described for flow past a body placed in an otherwise uniform shear layer adjoining a wall. The study is associated with potential impact of the body onto the wall. Steady two-dimensional flow solutions are calculated for an inclined flat plate in particular, covering cases of zero wall velocity, positive wall velocity and negative wall velocity, with the plate being at varying orientations and distances from the wall. Substantial flow separation is found with reduced proximity to the wall or increased plate incidence, caused partly by the cutting off of the mass flux in the gap between the body and the wall as impact is neared. Other distinct flow characteristics that emerge with increased local Reynolds number are the extent of the enhanced wake responses, greatly condensed upstream influence near the leading edge, increased sensitivity to body orientation, the pressure dominance in the total lift and moment on the body, new insight into the complex flow structure and quantitative agreement with a recent viscous–inviscid interaction analysis on scales.

JFM classification

Multiphase and Particle-laden Flows: Particle/fluid flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 915 , 25 May 2021 , A35
Check for updates
Copyright
© The Author(s), 2021. 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

Bhattacharyya, S., Mahapatra, S. & Smith, F.T. 2004 Influence of surface roughness on shear flow. J. Appl. Mech. 71 (4), 459–464.CrossRefGoogle Scholar
Bureau d'Enquêtes et d'Analyses 2012 Final report on the accident on 1st June 2009 to the Airbus A330-203 registered F-GZCP operated by Air France flight AF 447 Rio de Janeiro–Paris. Tech. Rep. BEA f-cp090601.Google Scholar
Degani, A.T., Walker, J.D.A. & Smith, F.T. 1998 Unsteady separation past moving surfaces. J. Fluid Mech. 375, 1–38.CrossRefGoogle Scholar
Dehghan, M. & Basirat Tabrizi, H. 2014 Effects of coupling on turbulent gas-particle boundary layer flows at borderline volume fractions using kinetic theory. J. Heat Mass Transfer Res. 1 (1), 1–8.Google Scholar
Diplas, P., Dancey, C.L., Celik, A.O., Valyrakis, M., Greer, K. & Akar, T. 2008 The role of impulse on the initiation of particle movement under turbulent flow conditions. Science 322 (5902), 717–720.CrossRefGoogle ScholarPubMed
Einav, S. & Lee, S.L. 1973 Particles migration in laminar boundary layer flow. Intl J. Multiphase Flow 1 (1), 73–88.CrossRefGoogle Scholar
Eldredge, J.D. 2008 Dynamically coupled fluid–body interactions in vorticity-based numerical simulations. J. Comput. Phys. 227 (21), 9170–9194.CrossRefGoogle Scholar
Foucaut, J-M. & Stanislas, M. 1997 Experimental study of saltating particle trajectories. Exp. Fluids 22 (4), 321–326.CrossRefGoogle Scholar
Frank, M., Anderson, D., Weeks, E.R. & Morris, J.F. 2003 Particle migration in pressure-driven flow of a Brownian suspension. J. Fluid Mech. 493, 363–378.CrossRefGoogle Scholar
Gavze, E. & Shapiro, M. 1997 Particles in a shear flow near a solid wall: effect of nonsphericity on forces and velocities. Intl J. Multiphase Flow 23 (1), 155–182.CrossRefGoogle Scholar
Gent, R.W., Dart, N.P. & Cansdale, J.T. 2000 Aircraft icing. Phil. Trans. R. Soc. Lond. A 358 (1776), 2873–2911.CrossRefGoogle Scholar
Hall, G.R. 1964 On the mechanics of transition produced by particles passing through an initially laminar boundary layer and the estimated effect on the LFC performance of the X-21 aircraft. NASA Tech. Rep. HQ-E-DAA-TN42874.Google Scholar
Inoue, O. 1981 A numerical investigation of flow separation over moving walls. J. Phys. Soc. Japan 50 (3), 1002–1008.CrossRefGoogle Scholar
Jones, M.A. & Smith, F.T. 2003 Fluid motion for car undertrays in ground effect. J. Engng Maths 45 (3–4), 309–334.CrossRefGoogle Scholar
Kishore, N. & Gu, S. 2010 Wall effects on flow and drag phenomena of spheroid particles at moderate Reynolds numbers. Ind. Engng Chem. Res. 49 (19), 9486–9495.CrossRefGoogle Scholar
Labraga, L., Kahissim, G., Keirsbulck, L. & Beaubert, F. 2007 An experimental investigation of the separation points on a circular rotating cylinder in cross flow. Trans. ASME: J. Fluids Engng 129 (9), 1203–1211.Google Scholar
Ladd, A.J.C. 1994 Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 2. Numerical results. J. Fluid Mech. 271, 311–339.CrossRefGoogle Scholar
Loisel, V., Abbas, M., Masbernat, O. & Climent, E. 2013 The effect of neutrally buoyant finite-size particles on channel flows in the laminar-turbulent transition regime. Phys. Fluids 25 (12), 123304.CrossRefGoogle Scholar
Loth, E. & Dorgan, A.J. 2009 An equation of motion for particles of finite Reynolds number and size. Environ. Fluid Mech. 9 (2), 187–206.CrossRefGoogle Scholar
Mason, J., Strapp, W. & Chow, P. 2006 The ice particle threat to engines in flight. In 44th AIAA Aerospace Sciences Meeting and Exhibit, p. 206.Google Scholar
Muller, K., Fedosov, D.A. & Gompper, G. 2014 Margination of micro- and nano-particles in blood flow and its effects on drug delivery. Sci. Rep. 4, 4871.CrossRefGoogle Scholar
Palmer, R.A. & Smith, F.T. 2019 When a small body enters a viscous wall layer. Eur. J. Appl. Maths. 31 (6), 1002–1028.CrossRefGoogle Scholar
Palmer, R.A. & Smith, F.T. 2020 A body in nonlinear near-wall shear flow: impacts, analysis and comparisons. J. Fluid Mech. 904, A32.CrossRefGoogle Scholar
Patankar, S.V. & Spalding, D.B. 1972 A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows. Intl J. Heat Mass Transfer 15 (10), 1787–1806.CrossRefGoogle Scholar
Patankashar, S. 1980 Numerical Heat Transfer and Fluid Flow. CRC Press.Google Scholar
Petrie, H.L., Morris, P.J., Bajwa, A.R. & Vincent, D.C. 1993 Transition induced by fixed and freely convecting spherical particles in laminar boundary layers. Tech. Rep. Pennsylvania State University, University Park Applied Research Lab.Google Scholar
Poesio, P., Ooms, G., Ten Cate, A. & Hunt, J.C.R. 2006 Interaction and collisions between particles in a linear shear flow near a wall at low Reynolds number. J. Fluid Mech. 555, 113–130.CrossRefGoogle Scholar
Portela, L.M., Cota, P. & Oliemans, R.V.A. 2002 Numerical study of the near-wall behaviour of particles in turbulent pipe flows. Powder Technol. 125 (2–3), 149–157.CrossRefGoogle Scholar
Purvis, R. & Smith, F.T. 2016 Improving aircraft safety in icing conditions. In UK Success Stories in Industrial Mathematics (ed. P.J. Aston, A.J. Mulholland & K.M.M. Tant), pp. 145–151. Springer.CrossRefGoogle Scholar
Schmidt, C. & Young, T. 2009 Impact of freely suspended particles on laminar boundary layers. In 47th AIAA Aerospace Sciences Meeting including The New Horizons Forum and Aerospace Exposition, p. 1621.Google Scholar
Shao, Y., Raupach, M.R. & Findlater, P.A. 1993 Effect of saltation bombardment on the entrainment of dust by wind. J. Geophys. Res. 98 (D7), 12719–12726.CrossRefGoogle Scholar
Smith, F.T. 1984 Concerning upstream influence in separating boundary layers and downstream influence in channel flow. Q. J. Mech. Appl. Maths 37 (3), 389–399.CrossRefGoogle Scholar
Smith, F.T. 2017 Free motion of a body in a boundary layer or channel flow. J. Fluid Mech. 813, 279–300.CrossRefGoogle Scholar
Smith, F.T., Balta, S., Liu, K. & Johnson, E.R. 2019 On dynamic interactions between body motion and fluid motion. In Mathematics Applied to Engineering, Modelling, and Social Issues (ed. F.T. Smith, H. Dutta & J.N. Mordeson), pp. 45–89. Springer.CrossRefGoogle Scholar
Smith, F.T. & Ellis, A.S. 2010 On interaction between falling bodies and the surrounding fluid. Mathematika 56 (1), 140–168.CrossRefGoogle Scholar
Smith, F.T. & Johnson, E.R. 2016 Movement of a finite body in channel flow. Proc. R. Soc. A 472 (2191), 20160164.CrossRefGoogle ScholarPubMed
Smith, F.T. & Palmer, R. 2019 A freely moving body in a boundary layer: nonlinear separated-flow effects. Appl. Ocean Res. 85, 107–118.CrossRefGoogle Scholar
Smith, F.T. & Servini, P. 2019 Channel flow past a near-wall body. Q. J. Mech. Appl. Maths 72, 359–385.CrossRefGoogle Scholar
Smith, F.T. & Wilson, P.L. 2013 Body-rock or lift-off in flow. J. Fluid Mech. 735, 91–119.CrossRefGoogle Scholar
Van Dommelen, L.L. & Shen, S.F. 1983 Boundary layer separation singularities for an upstream moving wall. Acta Mech. 49 (3–4), 241–254.CrossRefGoogle Scholar
Wang, C. & Eldredge, J.D. 2015 Strongly coupled dynamics of fluids and rigid-body systems with the immersed boundary projection method. J. Comput. Phys. 295, 87–113.CrossRefGoogle Scholar
Wang, J. & Levy, E.K. 2006 Particle behavior in the turbulent boundary layer of a dilute gas-particle flow past a flat plate. Exp. Therm. Fluid Sci. 30 (5), 473–483.CrossRefGoogle Scholar
Willetts, B. 1998 Aeolian and fluvial grain transport. Phil. Trans. R. Soc. Lond. A 356 (1747), 2497–2513.CrossRefGoogle Scholar
Yu, Z., Phan-Thien, N. & Tanner, R.I. 2007 Rotation of a spheroid in a Couette flow at moderate Reynolds numbers. Phys. Rev. E 76 (2), 026310.CrossRefGoogle Scholar