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A body in nonlinear near-wall shear flow: impacts, analysis and comparisons

Published online by Cambridge University Press:  13 October 2020

Ryan A. Palmer Open the ORCID record for Ryan A. Palmer [Opens in a new window]  and
Frank T. Smith
Ryan A. Palmer*
Affiliation:
Department of Mathematics, University College London, LondonWC1H 0AY, UK 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]
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Abstract

Interaction between body motion and fluid motion is considered inside a nonlinear viscous wall layer, with this unsteady two-way coupling leading to impact of the body on the wall. The present paper involves a reduced system analysis which is shown to be consistent with computational solutions from direct numerical simulations for a basic flat-plate shape presented in an allied paper (Palmer & Smith, J. Fluid Mech., 2020). The occurrence of impact depends mainly on fluid parameters and initial conditions. The body considered is translating upstream or downstream relative to the wall. Subsequent analysis focusses on the unusual nature of the impact at the leading edge. The impacting flow structure is found to have two nonlinear viscous–inviscid regions lying on either side of a small viscous region. The flow properties in the regions dictate the lift and torque which drive the body towards the wall. Pronounced flow separations are common as the impact then cuts off the mass flux in the gap between the body and the wall; here, a nonlinear similarity solution sheds extra light on the separations. Comparisons are made between results from direct simulations and asymptotics at increased flow rate.

JFM classification

Multiphase and Particle-laden Flows: Particle/fluid flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 904 , 10 December 2020 , A32
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

REFERENCES

Anderson, D., Tannehill, J. C. & Pletcher, R. H. 2016 Computational Fluid Mechanics and Heat Transfer. CRC Press.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
Einav, S. & Lee, S. L. 1973 Particles migration in laminar boundary layer flow. Intl J. Multiphase Flow 1 (1), 73–88.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. 19790071148, National Aeronautics and Space Administration.Google 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
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
Norde, E. 2017 Eulerian Method for Ice Crystal Icing in Turbofan Engines. University of Twente.CrossRefGoogle Scholar
Palmer, R. A. & Smith, F. T. 2019 When a small thin two-dimensional body enters a viscous wall layer. Eur. J. Appl. Maths, in press.CrossRefGoogle Scholar
Palmer, R. A. & Smith, F. T. 2020 A body in nonlinear near-wall shear flow: numerical results for a flat plate (under review). J. Fluid Mech.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. No. TR-93-07, 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, 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, paper 1621. AIAA.CrossRefGoogle Scholar
Smith, F. T. 1976 Flow through constricted or dilated pipes and channels: part 2. Q. J. Mech. Appl. Maths 29 (3), 365–376.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. & Daniels, P. G. 1981 Removal of Goldstein's singularity at separation, in flow past obstacles in wall layers. J. Fluid Mech. 110, 1–37.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), 0164.CrossRefGoogle ScholarPubMed
Smith, F. T., Ovenden, N. C., Franke, P. T. & Doorly, D. J. 2003 What happens to pressure when a flow enters a side branch? J. Fluid Mech. 479, 231–258.CrossRefGoogle Scholar
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. & Timoshin, S. N. 1996 Blade-wake interactions and rotary boundary layers. Proc. R. Soc. Lond. A 452 (1949), 1301–1329.Google 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
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