New simple correlation formula for the drag coefficient of non-spherical particles

A simple correlation formula for the standard drag coefficient (i.e. a single stationary particle in a uniform flow) of arbitrary shaped particles is established using a large number of experimental data from the literature and a comprehensive numerical study [A. Holzer, M. Sommerfeld, IUTAM Symposium on Computational Approaches to Multiphase Flow, Springer, 2006]. This new correlation formula accounts for the particle orientation over the entire range of Reynolds numbers up to the critical Reynolds number. Such a correlation may be easily used in the frame of Lagrangian computations where also the particle orientation along the trajectory is computed.

[1]  G. Batchelor,et al.  Slender-body theory for particles of arbitrary cross-section in Stokes flow , 1970, Journal of Fluid Mechanics.

[2]  C. Wieselsberger,et al.  Ergebnisse der aerodynamischen Versuchsanstalt zu Göttingen , 1921 .

[3]  J. Masliyah,et al.  Numerical study of steady flow past spheroids , 1970, Journal of Fluid Mechanics.

[4]  S. G. Ward,et al.  Studies of the viscosity and sedimentation of suspensions: Part 3. - The sedimentation of isometric and compact particles , 1955 .

[5]  Paul S. Lee,et al.  The Dynamics of Particles with Translation–Rotational Coupling in the Stokes Flow Regime , 1982 .

[6]  H. Heywood.  Measurement of the Fineness of Powdered Materials , 1938 .

[7]  H. S. A. M. B.Sc..  XXXI. The motion of a sphere in a viscous fluid , 1900 .

[8]  David Leith,et al.  Drag on Nonspherical Objects , 1987 .

[9]  R. G. Lunnon.  Fluid Resistance to Moving Spheres , 1926 .

[10]  J. S. Mcnown,et al.  Effects of particle shape on settling velocity at low Reynolds numbers , 1950 .

[11]  H. A. Becker.  The effects of shape and reynolds number on drag in the motion of a freely oriented body in an infinite fluid , 1959 .

[12]  Efstathios E. Michaelides,et al.  Drag coefficients of irregularly shaped particles , 2004 .

[13]  C. W. Oseen,et al.  Neuere Methoden und Ergebnisse in der Hydrodynamik , 1927 .

[14]  Drag on modified rectangular prisms , 1987 .

[15]  G. Williams.  Particle roundness and surface texture effects on fall velocity , 1966 .

[16]  O. Levenspiel,et al.  Drag coefficient and terminal velocity of spherical and nonspherical particles , 1989 .

[17]  A. Oberbeck,et al.  Ueber stationäre Flüssigkeitsbewegungen mit Berücksichtigung der inneren Reibung. , 1876 .

[18]  John D. Hottovy,et al.  Drag Coefficients for Irregularly Shaped Particles , 1979 .

[19]  G. Kasper,et al.  Measurements of viscous drag on cylinders and chains of spheres with aspect ratios between 2 and 50 , 1985 .

[20]  W. Gauvin,et al.  Effects of acceleration, deceleration and particle shape on single‐particle drag coefficients in still air , 1979 .

[21]  Patrick D. Weidman,et al.  Stokes drag on hollow cylinders and conglomerates , 1986 .

[22]  E. B. Christiansen,et al.  The effect of shape and density on the free settling of particles at high Reynolds numbers , 1965 .

[23]  E. Achenbach,et al.  Experiments on the flow past spheres at very high Reynolds numbers , 1972, Journal of Fluid Mechanics.

[24]  O. Levenspiel,et al.  A short note on the drag correlation for spheres , 1986 .

[25]  M. D. Matthews,et al.  Reply to a discussion of "Use and presentation of Janke's empirical formula for the settling velocity of spheres" , 1971 .

[26]  Some influences of particle shape on drag and heat transfer , 1990 .

[27]  Gary H. Ganser,et al.  A rational approach to drag prediction of spherical and nonspherical particles , 1993 .

[28]  Norman E. Hawk,et al.  Steady and Unsteady Motions and Wakes of Freely Falling Disks , 1964 .

[29]  William W. Willmarth,et al.  Some experimental results on sphere and disk drag , 1971 .

[30]  P. Komar.  Settling Velocities of Circular Cylinders at Low Reynolds Numbers , 1980, The Journal of Geology.

[31]  H. Liebster.  Über den Widerstand von Kugeln , 1927 .

[32]  H. D. Arnold.  LXXIV. Limitations imposed by slip and inertia terms upon Stoke's law for the motion of spheres through liquids , 1911 .

[33]  G. Mckay,et al.  Settling Characteristics of Discs and Cylinders , 1988 .