Fluid Dynamics PDF
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METHODS OF EXPERIMENTAL PHYSICS: L. Marton and C. Marton, Editors-in-Chief Volume 18 Fluid Dynamics PART B Edited by R. J. EMRICH Department of Physics Lehigh University Bethlehem, Pennsylvania @ 1981 ACADEMIC PRESS A Subsidlory of Horcourt Broce jovonovrch. Publishers New York London Toronto Sydney San Francisco C<)PYKI<JIII @ 198 1, I4Y ACADMI IC PRI S,I NC ALL RIGHTS RFSI RVLD NO PART Or THIS PUI3I ICATION MAY BE REPRODUCED OR TRANSMITTED IN ANY FORM OR BY ANY MEANS, ELECTRONIC OR MI C HANIC Al , INCl UDINC PliOTOCOPY, RI CORDING. OR ANY IN1 ORMATION SlORAG1 AND KI IRIf VAI SYSTI M, WITIIOUT PFRMISSION IN WRITING FROM THF PIJRI ISHTR. ACADEMlC PRESS, INC. 1 I1 Fifth Avenrie. New York, New York IO(103 C/iri/ctl Kiir,grloni Edilion pirhlislied by ACADEMIC PRESS, INC. (LONDON) LTD. 24/78 OV;II Ko;ld. I.ondon NWI 7DX Library of Conpress Cataloging in Publication Data Main entry under title: Fluid dynamics. (Methods of experimental physics; v. 18) 1. Fluid dynamic measurements. 2. Fluid dynamics. I. Emrich, Raymond Jay, Date 11. Series. TA357.FL83 620.1 'U64 80-27897 1SBP.l 0-12-475956-4 (V. 188) PRINT1 D IN 1HT UNITID STATFS OF AMtRICA XI828184 9 8 7 6 5 4 . 1 2 1 CONTRIBUTORS Numbers in parentheses indicate the pages on which the authors' contributions begin. DANIELB ERSHADEDRe,p artment of Aeronautics and Astronautics, Stan- ford University, Stanford, California 94305 (756) C. W.C URTIS,D" epartment of Physics, Lehigh University, Bethlehem, Pennsylvania 18015 (499) JOHN E. DOVED, epartment of Chemistry, University of Toronto, Toronto, Canada M5S 1Al (611) R. J. EMR ICH, Department of Physics, Lehigh University, Bethlehem, Pennsylvania 18015 (405, 499, 755) ALANJ . FALLERIn, stitute for Physical Science and Technology, Uni- versity of Maryland, College Park, Maryland 20742 (801) N. A. GENERALOIVns,t itute of Problems of Mechanics, USSRA cademy of Sciences, Moscow A-40, USSR (463) MAURICEH OLT,D epartment of Mechanical Engineering, University of California, Berkeley, California 94720 (821) M. HUGENSCHMIDDTeu, tsch-Franzosisches Forschungsinstitut, Saint- Louis, 7858 Weil am Rhein, Federal Republic of Germany (687) MARSHALLL APP,G eneral Electric Research and Development Center, Schenectady, New York 12301 (408, 487) E. P. MUNTZ,D epartment of Aerospace Engineering, University of Southern California, Los Angeles, California 90007 (434, 489) C. MURRAYPE NNEYG, eneral Electric Research and Development Cen- ter, Schenectady, New York 12301 (408, 487) R. I. SOLOUKHIINns, titute of Heat and Mass Transfer, Byelorussian Academy of Sciences, Minsk 220728, USSR (499) W.P AULT HOMPSOANd,v anced Systems Technology Division, The Aero- space Corporation, Los Angeles, California 90009 (457, 663) K. VOLLRATHD, eutsch-Franzosisches Forschungsinstitut, Saint- Louis, 7858 Weil am Rhein, Federal Republic of Germany (687) * Professor Emeritus. ix CONTRIBUTORS TO VOLUME 18, PART A RON F. BLACKWELDEDRep, artment of Aerospace Engineering, Uni- versity of Southern California, Los Angeles, California 90007 R. J. EMRICHD,e partment of Physics, Lehigh University, Bethlehem, Pennsylvania 18015 W. MERZKIRCIHns,t itut fiir Thermo- und Fluiddynnmik, Ruhr-Univer- sitat Bochum, 4630 Bochum, Federal Republic of Germany A. N. PAPYRINIn,s titute of Theoretical and Applied Mechanics, USSR Academy of Sciences, Siberian Division, Novosibirsk 630090, USSR R. I. SOLOUKHIINns,t itute of Heat and Mass Transfer, Byelorussian Academy of Sciences, Min.\X 220728, USSR E. F. C. SOMERSCALDEeSp,a rtment of Mechanical Engineering, Rens- Jelaer Polytechnic Institute, Troy, New York 12181 ... XI11 3. MEASUREMENT OF DENSITY BY BEAM ABSORPTION AND SCATTERING 3.0. Introduction * The fields of plasma physics, astrophysics, and all of chemistry use ab- sorption and scattering of optical radiation as primary diagnostic methods. Volumes 9 and 12 of this series present a great deal of material relevant to the measurement of the existence of matter by beam absorp- tion and scattering, and Part 6 of this volume furnishes guidance to the experimentalist seeking to learn of methods for measurement of the com- position of a fluid in motion. Usually consideration of the interaction of the different species making up the fluid with the beam of radiation is nec- essary in order to interpret measurements to yield the total density. This becomes less true as the radiation considered becomes “harder,” i.e., for x rays, gamma rays, mesons, and neutrinos. For measurements of density of fluids in motion, the chief character- istic of interest is short-time response. The achievement of microsecond, nanosecond, and even picosecond responses usually involve intense sources emitting for short periods of time or short-time recording periods. These methods are described in Part 8 of this volume. In this part, the qualitative aspects of the density sensitivity of matter to beams of radia- tion are outlined, and some of the nomenclature is introduced. The anal- ysis of electron beam excited radiation has resulted in a method used suc- cessfully for steady rarefied gas flows, which is unique to the subject of this volume. 3.1. Beam Attenuation Densitometry Radiation may be directed at a sample of matter from a source of such small extent that it may be considered a point source; it may radiate in all directions into a solid angle of 47r, or have a quite directional radiation pattern. Or a source may be a broad source, each little area of which is * Chapters 3.0 and 3.1 are by R. J. Emrich. 405 Copyright @ 1981 by Academic Press, Inc. METHODS OF EXPERIMENTAL PHYSICS, VOL. 18B All rights of reproduction in any form reserved. ISBN 0-12-475956-4 3. MEASUREMENT OF DENSITY BY BEAM ABSORPTION AND SCATTERING 3.0. Introduction * The fields of plasma physics, astrophysics, and all of chemistry use ab- sorption and scattering of optical radiation as primary diagnostic methods. Volumes 9 and 12 of this series present a great deal of material relevant to the measurement of the existence of matter by beam absorp- tion and scattering, and Part 6 of this volume furnishes guidance to the experimentalist seeking to learn of methods for measurement of the com- position of a fluid in motion. Usually consideration of the interaction of the different species making up the fluid with the beam of radiation is nec- essary in order to interpret measurements to yield the total density. This becomes less true as the radiation considered becomes “harder,” i.e., for x rays, gamma rays, mesons, and neutrinos. For measurements of density of fluids in motion, the chief character- istic of interest is short-time response. The achievement of microsecond, nanosecond, and even picosecond responses usually involve intense sources emitting for short periods of time or short-time recording periods. These methods are described in Part 8 of this volume. In this part, the qualitative aspects of the density sensitivity of matter to beams of radia- tion are outlined, and some of the nomenclature is introduced. The anal- ysis of electron beam excited radiation has resulted in a method used suc- cessfully for steady rarefied gas flows, which is unique to the subject of this volume. 3.1. Beam Attenuation Densitometry Radiation may be directed at a sample of matter from a source of such small extent that it may be considered a point source; it may radiate in all directions into a solid angle of 47r, or have a quite directional radiation pattern. Or a source may be a broad source, each little area of which is * Chapters 3.0 and 3.1 are by R. J. Emrich. 405 Copyright @ 1981 by Academic Press, Inc. METHODS OF EXPERIMENTAL PHYSICS, VOL. 18B All rights of reproduction in any form reserved. ISBN 0-12-475956-4 406 3. MEASUREMENT OF DENSITY radiating in all directions (more usually thought of as being into solid angles of 27r because other parts of the source get in the way of backward radiation), or each part may have its own directional radiation pattern. In some cases, the broad source may be thought of as many sources all ra- diating only in a single common direction, in which cases one speaks of a beam ofradiation. Since there can be no radiation into zero solid angle absolutely all in a single direction, a beam always involves a range of directions, and different parts of the source may or may not be emitting equally intensely in a given direction; the degree to which they do is mea- sured by the spatiaf coherence of the beam. In addition to the intensity and direction of the components of radiation making up the beam, there are various frequencies in any one direction, and for each of them there can be various phases. The specification of the content of any beam is therefore rather complex. When a beam is passing through a sample of matter, its interaction with the matter depends on the density and the constitution of the matter, and somewhat on the temperature, as well as on the content of the beam. The types of interaction are roughly classified as absorption, scattering and reradiation. Negative absorption, or amplification, is an important type of interaction which leads to laser sources. Assuming that there is no am- plification, the most gross method of employing radiation for the measure- ment of the density of matter deals with the removal of radiation from a beam by absorption and scattering. The measurement of simply “what is left” after a beam has traversed a given thickness of matter is called beam attenuation densitometry . Under the overwhelmingly large set of circumstances, the intensity 1 left in the beam after traversing a thickness dx of material, where loi s the incident intensity, can be described as’ p is called the linear attenuation coefficient, pm the mass attenuation co- efficient, and p, the atomic attenuation coefficient; p is the mass density of the material, N is the Avogadro number (= 6.02 X lV3 mol-l), and A is the atomic or molecular weight of the material. The radiation leaving the beam is either absorbed or scattered. If the beam is monochromatic and narrow (so that scattered radiation does not reenter the beam), Eq. (3.1.1) can be integrated for homogeneous material to yield (3.1.2) ’ R. D. Evans, Gamma rays. In “American Institute of Physics Handbook” (D. E. Gray, ed.), 3rd ed., pp. 8-190 to 8-218. McGraw-Hill, New York, 1957. 3.1. BEAM ATTENUATION DENSITOMETRY 407 x is the distance traversed from the place where the intensity was Zo. Chemists call this exponential relation Eq. (3.1.2) the Lambert-Beer rela- tion. It is valid for a monochromatic beam of spatially coherent radiation of very small cross section. p is strongly dependent on the frequency of the radiation and on the density and molecular weight of the absorbing material. The study of processes that lead to attenuation shows that there are several competing processes, called photoelectric effect, Ray- leigh scattering, Compton effect, pair production, photodisintegration of the nucleus and meson production, for example. The probabilities of the many competing processes occurring are expressed in terms of cross sec- tions for the processes, and extensive tables are available to predict the total attenuation. When the radiation is not monochromatic, but contains many fre- quencies, the character of the radiation changes with depth of penetra- tion. For example, radiation produced by bremsstrahlung from electrons of 0.1 MeV or less (x rays) typically has the lower frequencies removed and consists of the “harder” high frequency components after traversing a few centimeters of water or aluminum. All frequency components are attenuated, of course, but the total intensity does not follow the simple exponential relation Eq. (3.1.2). A variety of radiation detectors is used, ranging from photographic film, ionization chambers, and photomultipliers to scintillating crystals in combination with photomultipliers. The efficiency of the detector varies with the radiation frequency, and the overall combination of the radiation source, the attenuation, and the detector finally determines the accuracy with which a density value is measured. Imaging is often desirable, so that inhomogeneities in a material are de- tected. This procedure is highly developed in medical radiography and in metallurgical flaw detection. The radiation, typically x rays, is emitted from a small area by concentrating a fine electron beam on a copper or tungsten target. The radiation is emitted with about equal intensity in dif- ferent directions over a large solid angle, showers the specimen to be studied, and falls on photographic film, whose sensitivity is increased by being in contact with an intensifying screen-a luminescent material effectively converting x rays to visible radiation to which the film is more sensitive. If the specimen is fairly thick, radiation scattered out of one line may reach the detector at a different place; this may seriously affect the quality of the image produced. Since sources of penetrating radiation are seldom monochromatic, and since the exponentiallike attenuation of the radiation puts great stress on detectors in their need to serve over many orders of magnitude, the method of attenuation densitometry turns out to be used only under spe- 408 3. MEASUREMENT OF DENSITY cia1 conditions where other methods fail. Achievement of reliability and high accuracy requires careful attention to the problem of scattered radia- tion reentering the beam. Interaction of x rays and gamma rays with the matter being studied can change the state of the matter, as is illustrated by radiation damage to living tissue. Nevertheless flash radiography has played an important role in diagnosing explosive events, and measure- ments in shocked solids have given information on high pressure proper- ties up to 20-30 GPa.2 Information on the techniques employed is given in book^^,^ and conference proceeding^.^ An x-ray source consisting of a linear accelerator for electrons impacting a tungsten target with energies as high as 30 MeV and emitting with a duration of the order of 100 ns is employed for measuring shock angles, arrival times of detonation waves loading solids, and densities in both solids and high-explosive gas products .6 Shadowgraphs of laser-imploded microballoons have been made’ with x rays from a separate laser-produced plasma of duration 100 ps. 3.2. Analysis of Raman and Rayleigh Scattered Radiation”? 3.2.1. Introduction During the past decade, light scattering has developed into a powerful approach for measurements in fluid This scattering arises when a beam of light, passing through a medium, interacts with it and con- sequently part of the beam is diverted or “scattered.” A fraction of this diverted light can be collected and analyzed to determine thermodynamic * T. Neal, J. Appl. Phys. 46,2521-2527 (1975). K. Vollrath and G. Thomer, “Kurzzeitphysik.” Springer-Verlag, Berlin and New York, 1967. ‘ F. Jamet and G. Thomer, “Flash Radiography.” Elsevier, Amsterdam, 1976. “Proceedings of the 4th Symposium (International) on Detonation.” US Govt. Printing Office, Washington, D.C., 1965; 5th, 1970; 6th, 1976. Available from Clearinghouse for Sci- entific and Technical Information, Springfield, Virginia. D. Venable, ed., “PHERMEX: A Pulsed High-energy Radiographic Machine Emitting X-rays,” Rep. LA-3241 Los Alamos Sci. Lab., Los Alamos, New Mexico, 1967. Available from Clearinghouse for Scientific and Technical Information, Springfield, Virginia. ’ M. H. Key, C. L. S. Lewis, J. G. Lunney, A. Moore, T. A. Hall, and R. G. Evans, Phys. Rev. Lett. 41, 1467 (1978). * Chapter 3.2 is by Marshall Lapp and C. Murray Penney. t The work described in this chapter is treated in greater detail in a forthcoming book ten- tatively titled “Light Scattering for Fluid Dynamics,” to be published by Academic Press.
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