Sphere Drag in Flows of Almost‐Free Molecules
dc.contributor.author | Liu, Vi‐Cheng | en_US |
dc.contributor.author | Pang, Sing‐Chin | en_US |
dc.contributor.author | Jew, Howard | en_US |
dc.date.accessioned | 2010-05-06T22:22:31Z | |
dc.date.available | 2010-05-06T22:22:31Z | |
dc.date.issued | 1965-05 | en_US |
dc.identifier.citation | Liu, Vi‐Cheng; Pang, Sing‐Chin; Jew, Howard (1965). "Sphere Drag in Flows of Almost‐Free Molecules." Physics of Fluids 8(5): 788-796. <http://hdl.handle.net/2027.42/70574> | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/70574 | |
dc.description.abstract | A kinetic theory of sphere drag in the transition flows, based on the Boltzmann equation for the Maxwellian molecules, is presented. The exact binary collision integral, in the first order Knudsen iteration, is expanded as a function of Hermite polynomials in molecular velocity. The drag of a sphere at free stream temperature with molecular diffuse reflection is calculated. The results agree well with Millikan's measured values over a wide range of Knudsen number (0.5 < λ∕d < 10). It is found that the sphere drag of the almost‐free molecular flows normalized by the corresponding collisionless drag is essentially independent of the speed ratio for the present range of calculations. | en_US |
dc.format.extent | 3102 bytes | |
dc.format.extent | 676660 bytes | |
dc.format.mimetype | text/plain | |
dc.format.mimetype | application/pdf | |
dc.publisher | The American Institute of Physics | en_US |
dc.rights | © The American Institute of Physics | en_US |
dc.title | Sphere Drag in Flows of Almost‐Free Molecules | en_US |
dc.type | Article | en_US |
dc.subject.hlbsecondlevel | Physics | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Department of Aeronautical and Astronautical Engineering, The University of Michigan, Ann Arbor, Michigan | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/70574/2/PFLDAS-8-5-788-1.pdf | |
dc.identifier.doi | 10.1063/1.1761321 | en_US |
dc.identifier.source | Physics of Fluids | en_US |
dc.identifier.citedreference | G. N. Patterson, Molecular Flow of Gases (John Wiley & Sons, Inc., New York, 1956). | en_US |
dc.identifier.citedreference | D. R. Willis, Rand Report R‐339 (1959). | en_US |
dc.identifier.citedreference | R. M. L. Baker and A. F. Charwat, Phys. Fluids 1, 73 (1958). | en_US |
dc.identifier.citedreference | Z. Szymanski, Arch. Mech. Stos (Warsaw) 8, 449 (1956); 9, 35 (1957). | en_US |
dc.identifier.citedreference | R. A. Millikan, Phys. Rev. 22, 1 (1923). | en_US |
dc.identifier.citedreference | V. C. Liu, J. Aeron. Sci. 25, 779 (1958); also J. Fluid Mech. 5, 481 (1959). | en_US |
dc.identifier.citedreference | S. Chapman and T. G. Cowling, Mathematical Theory of Non‐Uniform Gases (Cambridge University Press, New York, 1951). | en_US |
dc.identifier.citedreference | H. Grad, Commun. Pure Appl. Math. 2, 325 (1949). [Note: the definition of B(θ)B(θ) is different from Grad’s by a factor of B1B1]. | en_US |
dc.identifier.citedreference | For the Maxwellian molecules, B1 = B1(n)B1=B1(n) following the notations used in Ref. 8. | en_US |
dc.identifier.citedreference | C. S. Wang Chang and G. E. Uhlenbeck, University of Michigan ERI Report M999 (1953); D. R. Willis, thesis, Princeton University (1959). | en_US |
dc.identifier.citedreference | V. C. Liu, University of Michigan ORA Report 02885‐11‐F (1962). | en_US |
dc.identifier.citedreference | R. Goldberg, thesis, New York University (1954). | en_US |
dc.identifier.citedreference | J. C. Maxwell, Collected Works (Dover Publications, Inc., New York). | en_US |
dc.identifier.citedreference | The suggestion of the reviewer is appreciated. | en_US |
dc.identifier.citedreference | In this comparison the same expression for the mean free path is used in calculating Knudsen numbers. | en_US |
dc.identifier.citedreference | H. Grad, in Handbuch der Physik, edited by S. Flügge (Springer‐Verlag, Berlin, 1958), Vol. 12, p. 292. | en_US |
dc.identifier.citedreference | The only approximation introduced is at representation of the molecular flux of the reflected molecules other than the truncation of the Hermite expansion. | en_US |
dc.owningcollname | Physics, Department of |
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