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Correlations for inclined prolates based on highly resolved simulations

Published online by Cambridge University Press:  19 August 2020

Konstantin Fröhlich Open the ORCID record for Konstantin Fröhlich [Opens in a new window] ,
Matthias Meinke  and
Wolfgang Schröder
Konstantin Fröhlich*
Affiliation:
Institute of Aerodynamics, RWTH Aachen University, Wüllnerstr. 5a, 52062Aachen, Germany
Matthias Meinke
Affiliation:
Institute of Aerodynamics, RWTH Aachen University, Wüllnerstr. 5a, 52062Aachen, Germany JARA–CSD, RWTH Aachen University, 52074Aachen, Germany
Wolfgang Schröder
Affiliation:
Institute of Aerodynamics, RWTH Aachen University, Wüllnerstr. 5a, 52062Aachen, Germany JARA–CSD, RWTH Aachen University, 52074Aachen, Germany
*
†Email address for correspondence: [email protected]
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Abstract

Efficient solution-adaptive simulations are conducted by a Cartesian cut-cell method to analyse the flow field of prolate ellipsoids in uniform flow. The parameter space defined by Reynolds numbers $1 \leq Re \leq 100$, aspect ratios $1 \leq \beta \leq 8$ and inclination angles $0^\circ \leq \phi \leq 90^\circ$ is covered by approximately 4400 simulations. Flow visualizations and skin friction distributions are presented for selected configurations. Aspect ratios $1\leq \beta \lesssim 3$ are identified as transitional geometries to fibres. For $\beta \gtrsim 3$, the flow topology is qualitatively unaffected by higher aspect ratios. If the major axis is aligned with the free stream, i.e. $\phi = 0^\circ$, the ellipsoids are slender bodies, whereas for $\phi = 90^\circ$ a bluff body flow is observed. Conditions for the onset of flow separation are reported. The data base is used to determine correlations for drag, lift and torque. The correlations are incorporated into dynamic equations for ellipsoidal Lagrangian models and limitations are discussed.

JFM classification

Multiphase and Particle-laden Flows: Multiphase flow Multiphase and Particle-laden Flows: Particle/fluid flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 901 , 25 October 2020 , A5
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

REFERENCES

Andersson, H. I. & Jiang, F. 2019 Forces and torques on a prolate spheroid: low-Reynolds-number and attack angle effects. Acta Mechanica 230 (2), 431–447.CrossRefGoogle Scholar
Arcen, B., Ouchene, R., Khalij, M. & Tanière, A. 2017 Prolate spheroidal particles behavior in a vertical wall-bounded turbulent flow. Phys. Fluids 29 (9), 093301.CrossRefGoogle Scholar
Ardekani, M. N. & Brandt, L. 2019 Turbulence modulation in channel flow of finite-size spheroidal particles. J. Fluid Mech. 859, 887–901.CrossRefGoogle Scholar
Ardekani, M. N., Costa, P., Breugem, W. P. & Brandt, L. 2016 Numerical study of the sedimentation of spheroidal particles. Intl J. Multiphase Flow 87, 16–34.CrossRefGoogle Scholar
Aris, R. 2012 Vector, Tensors and the Basic Equations of Fluid Mechanics. Dover.Google Scholar
Chesnakas, C. J., Taylor, D. & Simpson, R. L. 1997 Detailed investigation of the three-dimensional separation about a 6 : 1 prolate spheroid. AIAA J. 35 (6), 990–999.CrossRefGoogle Scholar
Clift, R., Grace, J. R. & Weber, M. E. 2005 Bubbles, Drops, and Particles. Courier Corporation.Google Scholar
Dabade, V., Marath, N. K. & Subramanian, G. 2015 Effects of inertia and viscoelasticity on sedimenting anisotropic particles. J. Fluid Mech. 778, 133–188.CrossRefGoogle Scholar
El Khoury, G. K., Andersson, H. I. & Pettersen, B. 2012 Wakes behind a prolate spheroid in crossflow. J. Fluid Mech. 701, 98–136.CrossRefGoogle Scholar
Fröhlich, K., Schneiders, L., Meinke, M. & Schröder, W. 2018 Assessment of non-spherical point-particle models in LES using direct particle-fluid simulations. AIAA Paper 2018-4714.CrossRefGoogle Scholar
Fröhlich, K., Schneiders, L., Meinke, M. & Schröder, W. 2019 Direct particle-fluid simulation of Kolmogorov-length-scale size ellipsoidal particles in isotropic turbulence. In Eleventh Intl Symp. on Turbulence and Shear Flow Phenomena, Southampton, UK.Google Scholar
Fu, T. C., Shekarriz, A., Katz, J. & Huang, T. T. 1994 The flow structure in the lee of an inclined 6 : 1 prolate spheroid. J. Fluid Mech. 269, 79–106.CrossRefGoogle Scholar
Han, T. & Patel, V. C. 1979 Flow separation on a spheroid at incidence. J. Fluid Mech. 92 (4), 643–657.CrossRefGoogle Scholar
Happel, J. & Brenner, H. 2012 Low Reynolds Number Hydrodynamics: with Special Applications to Particulate Media. Springer.Google Scholar
Hartmann, D., Meinke, M. & Schröder, W. 2008 An adaptive multilevel multigrid formulation for Cartesian hierarchical grid methods. Comput. Fluids 37 (9), 1103–1125.CrossRefGoogle Scholar
Hartmann, D., Meinke, M. & Schröder, W. 2011 A strictly conservative Cartesian cut-cell method for compressible viscous flows on adaptive grids. Comput. Meth. Appl. Mech. Engng 200, 1038–1052.CrossRefGoogle Scholar
Hölzer, A. & Sommerfeld, M. 2008 New simple correlation formula for the drag coefficient of non-spherical particles. Powder Technol. 184 (3), 361–365.CrossRefGoogle Scholar
Jeffery, G. B. 1922 The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. A 102 (715), 161–179.Google Scholar
Jiang, F., Andersson, H. I., Gallardo, J. P. & Okulov, V. L. 2016 On the peculiar structure of a helical wake vortex behind an inclined prolate spheroid. J. Fluid Mech. 801, 1–12.CrossRefGoogle Scholar
Jiang, F., Gallardo, J. P. & Andersson, H. I. 2014 The laminar wake behind a 6 : 1 prolate spheroid at 45 incidence angle. Phys. Fluids 26 (11), 113602.CrossRefGoogle Scholar
Johnson, T. A. & Patel, V. C. 1999 Flow past a sphere up to a Reynolds number of 300. J. Fluid Mech. 378, 19–70.CrossRefGoogle Scholar
Kuerten, J. G. M. 2016 Point-particle DNS and LES of particle-laden turbulent flow – a state-of-the-art review. Flow Turbul. Combust. 97 (3), 689–713.CrossRefGoogle Scholar
Loth, E. 2008 Drag of non-sperical solid particles of regular and irregular shape. Powder Technol. 182 (3), 342–353.CrossRefGoogle Scholar
Mao, W. & Alexeev, A. 2014 Motion of spheroid particles in shear flow with inertia. J. Fluid Mech. 749, 145–166.CrossRefGoogle Scholar
Marchioli, C., Fantoni, M. & Soldati, A. 2010 Orientation, distribution, and deposition of elongated, inertial fibers in turbulent channel flow. Phys. Fluids 22 (3), 033301.CrossRefGoogle Scholar
Marchioli, C. & Soldati, A. 2013 Rotation statistics of fibers in wall shear turbulence. Acta Mechanica 224 (10), 2311–2329.CrossRefGoogle Scholar
Maskell, E. C. 1955 Flow separation in three dimensions. RAE Aero. Report 2565.Google 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
Mortensen, P. H., Andersson, H. I., Gillissen, J. J. J. & Boersma, B. J. 2008 On the orientation of ellipsoidal particles in a turbulent shear flow. Intl J Multiphase Flow 34 (7), 678–683.CrossRefGoogle Scholar
Oberbeck, A. 1876 Ueber stationäre Flüssigkeitsbewegungen mit Berücksichtigung der inneren Reibung. J. Reine Angew. Math. 81, 62–90.Google Scholar
Ouchene, R., Khalij, M., Arcen, B. & Tanière, A. 2016 A new set of correlations of drag, lift and torque coefficients for non-spherical particles and large Reynolds numbers. Powder Technol. 303, 33–43.CrossRefGoogle Scholar
Panahi, A., Levendis, Y. A., Vorobiev, N. & Schiemann, M. 2017 Direct observations on the combustion characteristics of miscanthus and beechwood biomass including fusion and spherodization. Fuel Process. Technol. 166, 41–49.CrossRefGoogle Scholar
Press, W. H., Flannery, B. P., Teukolsky, S. A. & Vetterling, W. T. 1988 Numerical Recipes in C: The Art of Scientific Computing. Cambridge University Press.Google Scholar
Ravnik, J., Marchioli, C. & Soldati, A. 2018 Application limits of Jeffery's theory for elongated particle torques in turbulence: a DNS assessment. Acta Mechanica 229 (2), 827–839.CrossRefGoogle Scholar
Sanjeevi, S. K. P., Kuipers, J. A. M. & Padding, J. T. 2018 Drag, lift and torque correlations for non-spherical particles from Stokes limit to high Reynolds numbers. Intl J Multiphase Flow 106, 325–337.CrossRefGoogle Scholar
Sanjeevi, S. K. P. & Padding, J. T. 2017 On the orientational dependence of drag experienced by spheroids. J. Fluid Mech. 820, R1.CrossRefGoogle Scholar
Schiller, L. & Naumann, Z. 1933 Über die grundlegenden Berechnungen bei der Schwerkraftaufbereit ung. Ver. Deut. Ing. 77, 318–320.Google Scholar
Schneiders, L., Fröhlich, K., Meinke, M. & Schröder, W. 2019 The decay of isotropic turbulence carrying non-spherical finite-size particles. J. Fluid Mech. 875, 520–542.CrossRefGoogle Scholar
Schneiders, L., Günther, C., Meinke, M. & Schröder, W. 2016 An efficient conservative cut-cell method for rigid bodies interacting with viscous compressible flows. J. Comput. Phys. 311, 62–86.CrossRefGoogle Scholar
Schneiders, L., Hartmann, D., Meinke, M. & Schröder, W. 2013 An accurate moving boundary formulation in cut-cell methods. J. Comput. Phys. 235, 786–809.CrossRefGoogle Scholar
Sheikh, M. Z., Gustavsson, K., Lopez, D., Mehlig, B., Pumir, A. & Naso, A. 2020 Importance of fluid inertia for the orientation of spheroids settling in turbulent flow. J. Fluid Mech. 886, A9.CrossRefGoogle Scholar
Siewert, C., Kunnen, R. P. J., Meinke, M. & Schröder, W. 2014 a Orientation statistics and settling velocity of ellipsoids in decaying turbulence. Atmos. Res. 142, 45–56.CrossRefGoogle Scholar
Siewert, C., Kunnen, R. P. J. & Schröder, W. 2014 b Collision rates of small ellipsoids settling in turbulence. J. Fluid Mech. 758, 686–701.CrossRefGoogle Scholar
Thornber, B., Mosedale, A., Dikakis, D., Youngs, D. & Williams, R. 2008 An improved reconstruction method for compressible flows with low Mach number features. J. Comput. Phys. 227 (10), 4873–4894.CrossRefGoogle Scholar
Voth, G. A. & Soldati, A. 2017 Anisotropic particles in turbulence. Annu. Rev. Fluid Mech. 49, 249–276.CrossRefGoogle Scholar
Wang, K. C. 1972 Separation patterns of boundary layer over an inclined body of revolution. AIAA J. 10 (8), 1044–1050.CrossRefGoogle Scholar
Wang, K. C. 1974 Boundary layer over a blunt body at high incidence with an open-type of separation. Proc. R. Soc. Lond. A 340 (1620), 33–55.Google Scholar
Wang, K. C., Zhou, H. C., Hu, C. H. & Harrington, S. 1990 Three-dimensional separated flow structure over prolate spheroids. Proc. R. Soc. Lond. A 429 (1876), 73–90.Google Scholar
White, F. M. 1991 Viscous Fluid Flow. McGraw-Hill.Google Scholar
Zastawny, M., Mallouppas, G., Zhao, F. & van Wachem, B. 2012 Derivation of drag and lift force and torque coefficients for non-spherical particles in flows. Intl J. Multiphase Flow 39, 227–239.CrossRefGoogle Scholar
Zdravkovich, M. M. 1997 Flow Around Circular Cylinders. Oxford University Press.Google Scholar
Zhao, L., Challabotla, N. R., Andersson, H. I. & Variano, E. A. 2015 Rotation of nonspherical particles in turbulent channel flow. Phys. Rev. Lett. 115 (24), 244501.CrossRefGoogle ScholarPubMed