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CHEMICAL ENGINEERING REVIEWS
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FUNDAMENTALS REVIEW
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I Fluid Dynamics
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I T SEEMS appropriate to strike a celebrating note) while starting this review, as it marks the quintennial of this publication. Because of the vast extent of the field of fluid dynamics, these revicrvs have been continually offered as highlighted summaries striving to rcflect progress, rather than as an attempt to achieve completeness. One of the salient features of this year's review is the increased emphasis given to the section on the dynamics of reactive fluids-aerothcrmochemistryrvhich. in some aspects, attained a Icading role in the progress of fluid dynamics. .Another is the addition of a ne\? section on dynamics of ionized fluidsa reflection of the rapidly qro\ving interest in the study of the motion of the fluids under the influence of electromagnetic forces. .Also notable is the necessity of treating the nurnrrous publications on drops and bubbles under a separate headin?. The most significant charactcristic of last )-ear's publications in fluid dynamics is the large number of reviews and survey, lvhich overshadou. original contributions. In this respect one should perhaps refer to this year as one of "stocktaking." .Among several \vorth-\vhile theoretical discussions of laminar florv is a n interesting comparison betrveeri a n exact solution of the Navier-Stokes equations and corresponding solutions of asyinptotic expansions of these equationsi.e.: the equations of Stokes. Oseen. Prandtl, and Euler. ;\nother contribution shoxvs: surprisingly enough, that the effect of the earth's rotation on flow in pipes can be significant. The nature of turbulence and turbulent diffusion continues to be the subject of intensive research. Significant theoretical contributions concern both the statistical and phenomenological
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treatment of turbiilencr. rvliile expc%rimental studies have added to its quantitative description. .l'hr size and coinplesit?. of this field makes the recciit appearance of a number of excellent surveys especially Lvrlcome; notable is the new book of To\vnsend. As appropriate for the !.ear of stocktaking, the most notable contribution in the stud!. of flor\. stability is the publication of a comprehensive text on the fundamental theories by C:. C. Lin rvho is eminently qualified to he its author. .4 classical example of the expansion of hydrodynamic theories is provided by the fundamental contributions offered recently to f l o ~ v of rotating fluids. hlost of them are concerned rvitli the
motion of a fluid ivhich has a unifuriii angular vclocit> at infinity. instead 01' being there at rest as conventionally assumed in classical li>drod>-nainics. Pul>lication of boundary la).er research receiwd an impetus froin thv observancr of' t h e .iOth anniversary 0 1 Prandtl's original hypothrsis. culrninating in a memorial volume edited by Gortler and Tollrnien. Studies prrsented cover the efT bility and temperature nonuniforinit!.. the onset of turbulence in a boundary layer, transient boundary layers, shockwavt: interactions. and suction and injection tlirouqh the surface. Recent studies of simple subsonic jets are concerned rvith the statistical properties of turbulence in t h e mising
A. K. OPPENHEIM studied aeronautical engineering at the Warsaw Institute of Technology and received the Dipl. Ing. in 1943. He obtained his Ph.D. at the University of London and the D.I.C. (Imperial College) in 1945. Oppenheim served on the faculties of the City and Guilds College (London), 1945-1 948, and of Stanford University, 1948-50. He is now teaching mechanical engineering at Berkeley and serving Shell os a consultant.
INDUSTRIAL AND ENGINEERING CHEMISTRY
R. R. HUGHES attended Massachusetts Institute of Technology, receiving his B.S. in 1942, M.S. in 1947, and Sc.D. in 1949. During the war years, in addition to overseas service, he was an instructor at the U. S. Military Academy. Since 1949 he has been with the Shell Development Co., Emeryville, Calif., where he has specialized in the application of fundamental fluid mechanics and mass and heat transfer to chemical engineering problems.
zone. For supersonic jets, emphasis is naturally on the nature of the wave pattern produced. Studies of more complex geometries, such as confined and transverse jets, include cases with both subsonic and supersonic flow. With reference to ducted flow, most notable is the attention given to the study of diffusion and dispersion in pipe flow, which received particular impetus because of the contributions of Taylor, Batchelor, and coworkers at Cambridge University. Studies of flow around simple solids a t low speeds are primarily concerned with refinements of theory for low Reynolds numbers and with experimental investigation of the effect of acceleration on drag; similar contributions concerning high speed flow are plentiful, but are usually of intereit only to the aerodynamicist. Several experimental studies of packed beds and porous media have increased our empirical knowledge of flow in such systems. The fascination-of research on drops and bubbles is again shown by the appearance of many significant papers. Those on atomization are mostly concerned with transient jets, swirl nozzles, and spinning disk atomizers. The corresponding problem of bubble formation is still in the experimental stage, undoubtedly because of the many variables that must be studied. The gross and detailed mechanics of moving drops or bubbles interest many investigators; their contributions concern such varied aspects as circulation within drops, drop distortion, bubble pulsation and collapse, and separation of entrained droplets. The more general case of a n over# all dispersion of two or more phases has also been studied. Two different correlations of gas-liquid flow should be of considerable value to engineers. Other studies cover the behavior of froth in a n aerated vessel, turbulence propagation across a liquid-liquid interface, and two-fluid flow in porous media or packed beds. No new work has appeared on gas-solid fluidization, although one interesting paper covers flow of solid powders alone. I n contrast, numerous papers give results o n liquid-solid flow, including hydraulic conveying, sediment transport in rivers, and small-scale studies of suspension behavior. Most important to the subject of transient flow is, of course, the study of shock-tube phenomena, which continue to attract a great deal of attention among the research laboratories. Especially worth noting is the sucessful exploitation of shock tube techniques for physicochemical studies and for the determination of thermodynamic properties at elevated pressures and temperatures. As a result of interest in flow a t low
gas pressures and high shearing stress, the fundamental equations of gas dynamics became a subject of close scrutiny. The most striking outcome of these activities is, perhaps, the realization that the various corrections to the Navier-Stokes equations, proposed by Burnett, Graetz, and others, are so inadequate under these conditions that their consideration makes the approximation worse rather than better. The interest in flow under extremely high temperature conditions has prompted so much work on the motion of ionized fluids and plasmas that it can no longer be omitted from a comprehensive survey of progress in fluid dynamics. The added effect of the electromagnetic forces makes, of course, the analysis of flow in “magneto-hydrodynamics” more complex and intricate than in conventional fluid dynamics.
Books of General interest Of major importance this year is the publication of Townsend’s book, “Structure of Turbulent Shear Flow” ( 7 A ) . Such a survey of the nature of turbulence and its effect on all types of flow has long been needed. The book describes a n attempt to develop a single consistent picture of turbulent flow by considering the observed properties of some very simple forms of turbulent flow and to use it in interpreting observations of the more common types of turbulent shear flow. This attempt is highly successful. Mathematical derivations are complete and well presented. This is a n important landmark in the literature of modern fluid dynamics. The trend towards a n increased number of survey articles has continued this year. With the recent tremendous growth in engineering literature, s;ch survey articles are especidl) valuable. This year, Volume IV of “Advances in Applied Mechanics,” edited by Dryden and von KBrmln ( 4 A ) , is augmented by the first volume of a new series o n “Advances in Chemical Engineering,” edited by Drew and Hoopes ( 3 4 . Several articles in each volume which are of importance in fluid dynamics are discussed below. T h e volume celebrating Taylor’s 70th birthday, which is edited by Batchelor and Davies ( I A ) , includes 10 important survey articles, seven in the general field of fluid dynamics. T h e special issue of the Journal of the Aeronautical Sciences, edited by Dryden and others (54 to commemorate the 75th birthday of Theodore von K l r m l n , contains 12 articles (all written by von Klrmln’s students), which are necessarily more concise than those in the foregoing volume. Nevertheless, each represents a clear contribution in a special field of interest to von Kgrmln.
The final volume, prepared by Gortler and Tollmien ( I I F ) , in honor of the 50th anniversary of Prandtl’s original presentation of his boundary layer theory, is more specialized in nature and is organized in a different manner. The 44 articles included are not really survey articles but more in the nature of new contributions to the many fields related to boundary layer theory. Because of the specialized nature of this book, it is discussed in the boundary layer section, although a few special articles have been reviewed in appropriate sections. A recent book by Slezkin (FA, 8 A ) on the dynamics of viscous incompressible fluids is indicative of Russian activity in this field. The review by Vodicka shows that this is a thorough coverage of viscous incompressible flow. Finally, a small volume deserves a brief mention. J. R. Caddell has edited a series of contributions under the title, “Fluid Flow in Practice” (ZA). Most of the articles are of a practical nature and are directed to practicing engineers.
laminar Flow
Theory of Viscous Flow. I n a wellwritten paper, Synge (6B, 78) discusses the equations of motion of a heatconducting viscous fluid. Although these equations are already available in a somewhat different form, he feels that they need emphatic reiteration. Laggerstrom and Cole (4B) present a thorough comparative analysis of the nature of various asymptotic expansions to the Navier-Stokes equations. They point out that Stokes’ and Oseen’s methods for small Reynolds numbers, Prandtl’s boundary layer theory, and Euler’s equations for inviscid fluids can all be considered as approximation methods for the Navier-Stokes equations. T o provide a comparison, they discuss a basic flow problem in detail and draw some general conclusions concerning the various approximation methods. Another approximation method especially valuable for unsteady flows is discussed by Chow (2%) using generalized vector coordinates. H e transforms the Navier-Stokes equations into a relatively simple differential equation for the Fourier coefficients. Chow applies this equation to prove the existence of the solution of the equations of motion for wave interaction with given initial conditions in a n unbounded flow. Non-Newtonian Flow. Rivlin (5B) presents a fundamental analysis of the exact theory of viscoelasticity. For a generafized fluid in which the stress components are expressible as polynomials in the gradients of velocity, acceleration, second acceleration, and so forth, he discusses specific examples, chiefly to provide a demon-
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The dynamics of reactive fluids-aerothermochemistry-in leading role in the progress of fluid dynamics.
stration of the use of the equations. A more specific treatment of this type of problem is that of Gutkin (3B), who treats the motion of a viscoplastic medium in the gap between t\vo rotating cones. Experimental Aspects. LIany attempts have been made to study hydrodynamic phenomena by the use of streaming birefringence. LVayland ( S B ) now presents an experimental analysis of this method. He manages to obtain a number of interesting results for the flow patterns in the annular space between a rotating and a fixed cylinder. However, in most cases the results of the birefringence measurements can be considered only as a qualitative picture. Although we are today firmly convinced that the earth rotates, we are accustomed to ignore this rotation except for such large scale problems as those of meteorology. A very interesting study of Benton (7B) shows that this may be incorrect even for laboratory studies of laminar floiv in pipes. His analysis sholvs that the earth's rotation can have a significant effect on the velocity profile in laminar flow. Turbulence
As a part of the commemoration of von Kirmin's 75th birthday, Lin (74C) contributes a survey of the problem of turbulent motion. As he states, the selection of material is paid>-determined by his personal interest and competence; however, the revieiv actually covers the theoretical side of turbulence studies thoroughly. .A qood qualitative discussion of the problem is included. One of rhe most interesting contributions revie\\.ed last year !vas the theoretical treatment of turbulence by Chandrasekhar (1 956 Fluid Dynamics Revieivj. This !-ear there have been tu-o extensions to this theoretical lvork. Chamberlain and Roberts ( 3 C ) show that Chandrasekhar's fundamental differential equation is greatly simplified when transformed into wave number space. For the simplified case corresponding to small separation in space and time betlveen the two correlation points, a direct solution is possible even for a finite Reynolds number. Of
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special interest is the fact that the solution shows that the spectrum must degenerate for eddies smaller than a certain critical size. These authors suggest that these small eddies may be the ones that are completely overcome by viscosity. The second extension to this work is a correction and amplification of the theory by Chandrasekhar (C) himself. The author originally had difficulty showing the relationship of his equations to Kolmogoroff's similarity principles. This came from the impossibility of keeping the correlations finite as separation distance and time tended to infinity. I n his new paper Chandrasekhar shoivs rhat these difficulties are overcome if the equations are transformed into relationships involving vorticity rather than velocity correlations. I n addition, a slight modification of Kolmogoroff's principles must be made. As his contribution to the 50th anniversary volume on boundary layer theory, Theodorsen (7SC) presents a further discussion of his theory of rurbulrnce generation. From the equations of motion, he sholvs that the turbulence srructure must contain elements of shrinking vortex tubes. Since this radial shrinking requires a force exerted along the length of the tube, it must have the horseshoe shape he proposed earlier. If this horseshoe is large enough, it exerts a shear on the surrounding fluid and, accordingly, can generate secondary horseshoes a t its surface. The figure shoivs his schematic picture of this mechanism. Experimental Studies. .\ review of turbulrnce cxperimenrs and their significance is presented by Cooper and Tulin (5C). The review includes a comprehensive bibliography and a convcnicnt table of the most importanr experimental hot \vire investigations. A more specific summary of a particular development project is that of Kovasznay ( 7 2 C ) , Mhich describes in detail the development of a hot \\,ire anemometer. The thorough study by Sandborn and Laurence (77C) of the heat loss from yalved hot wires at subsonic Mach numbers should also be of considerable value in the development of hot wire techniques. Craya and Milliat (6C) report
INDUSTRIAL AND ENGINEERING CHEMISTRY
some aspects has attained a
measurements of the spectrum of turbtilence in a divergent channel with a 2' total angle. The spectra can all be brought into a single curve by plotting in dimensionless coordinates obtained by using the micro scale of the turbulence. Tlvo papers describe experiments concerning turbulence produced in ii ivind tunnel by the use of grids. Tsuji (/E) studies the effects resulting from the use of tivo grids placed a t various distancrs apart. His work is particularl!. concerned with the decay r a t a of the turbulence. A second study, b y Favre and cotcorkers (SC),is devoted to the comparison of correlations betwren measurements at two points and (hat for measurements a t the same point at differrnt times. They find that G. I. Taylor's hypothesis is essentially correct. A valuable and rather unique contribution is that of Mickelseri (75C). ivho has measured both Laqangian and Eulerian correlation coefficients in the homogeneous isotropic. central C O K of a turbulent pipe flow. The Eulerian values \Yere determined in the usual manner by hot wire anemometry. M u c h more difficult \vas the measurrment of the Lagrangian coefficient. As this pertains to the corrrlation betJvecn successive velocities of the same particle, it can tie measured only by some internal method : this experiment used the lateral spread of' helium injected a t the axis. Spreadinq coefficients obtained from the data
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r froni t i \ ti-dinieiisional theor!.. hIo(~rc's arriclc i:, ii ( ~ ) t n 1 ) 1 ( ' t ( dis~ cussion of tlic subject. > c t i t is roncisr and \vel1 Ivritten. rTliiis i t coiistituic~.; not only a rwir.\v 1'01. \ \ ( J l ' l \ ? i ' S i n 111t. field but also an for the I'i!man. 'Thr bibliygi .iliIi!. ( ~ f 79 refert=nces includes niosi of' tlic ill:portant tvork in tlir field. .4nothcr siurimary i'rciin '1 sliglitl! diKerent vic\\.point is tliat of (.;cis (O/,'). Lvhich has an introciucLion 1)). Gijrtlcr. This survey is nicit'e tnatiicmaticai iii nature and also c.in])liasi;.cs (kriiiiiti literature. Ho\vever. t h r clositiq st'('tion does give a brief pli! sical dr~sct~iptioii of some prohletns. l f a i i y r(1iiii I i [Jiis i i t.(' included, so rhar i t s l i i ~ i i l d I)nedimensional medium. The ficld is regarded as a succession of small density discontinuities separated by uniforni regions. Previous solutions of this problem involve the notoriously cuinbcrsoiiic numerical or graphical methods 01' characteristics. In Chisnell's solution although disturbances arc still followed along characteristics. the final results emerge in analytic form \\.hich. as the author classically understatrc. "ma\provide a useful alternative.'' The interaction bet\veen traveling shock fronts and stationary discontinuities is treated in the followins publications: Bowinan and Niblett ( / . l f ) drscribe the passage of a shock wave through a wire gauze. Dosanl h's ( /O.lf) experiments demonstrate that ivhen a sufficiently strong shock hits a grid there appears. besides the reflected and transmitted shocks. a n additional shock at rhe grid? and not a vortes as prrviously inferred by Glass and Patterson (1056 Fluid Dynamics Revie\\,). T h e problem of shock wave reflection at the opt:" end of a duct is treated by RudinTer (J7,11: 42.i4). Billington (3.tl) reports on a study of the interaction brt\veen one-dimensional rarefaction wave and a contact discontinuity made up o r the interface between air-argon and airhelium mixtures: Griffith (/ti.tf) t t ' r a t s the problem of the intcractiori o C ;I
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~ivc. \ \ , i t t i ii t h c r i i i a l boitndar! Kiliner's study ol shock-ttii t i i i lent interaction and its cllcct o n ilir generation o f noise (, I O i G Fluid 111.namics Kevic\v) is n m v available as ii s.4c.A r r p o r t (,%.\f), v o r t i ~ c s produccd t i ) . shock-\va\-e diffraction ~ v r r c sttidirtl ti\ \\.nldron i -??.\I) and ti). Ho\\.ard and hIatthe\vs 117.11). both danionsrrarinq yood aqrct%mrnc. esprciall)- for t h e lveaker ivavrs. Lvith Rott'a theor\.. IIan!. drtails of t h e H o ~ v i m t t e r n \vert re\-ralrd by t h e rsccllrnt intcrfrroyrams putilishcd by H(n\nrci and Rlatthe\vs (.2/.tf) as csc~niplificd tiy the abota ~jhotograph. I\'ortti notinq is the suhstantial rxploiiation of thy shock-tube technique< for ~~li~.sicocIir~inical studies. .\pplications i i f ihrsr techniques in dynamics o f rcactivr fluids and ionized inrdia arc described later. Hrrc mention is onl!made of investigations rising shock propaqation rnrasuremcnts for sccurinq equation ol state data. \\'alsli and (:hristian [ i$.\I) s h m v ho\v to detrrniirir in t h i s m a n n e t ' the equation of state of metals. \\.hilt IIuvalI and Z\volinski ( 71.11) provide a simple hydrodynaniic theor). of t h r propagation of shock \vatt>s t h r o u g h Inelals. For ttie dcteiminatioti ol qas properties. Christian and co\\orlitrs use an interestinq csperimcnLa1 procedure \vhich consists of drivinq a metal platr a t constant velocity by means of high esiilosive into a chamber of the gas undcr invcstigation. The results are obtained from thc iiieasurenient o f shock vrlocit!. b!. recording transit lime of the front ovcr many icno\\.n space intervals and material velocity by observing the motion or thr driver plate. I n this manner tlie Rankine-Huqoniot C U T V C is determined for arson (0.tf) and the dissociation enerq\of niuqt*ri is nicasiircd f,Y.\f). .I siinilar method of qencratinq plane ~vavc's
slioc,k la!.cr.
INDUSTRIAL AND ENGINEERING CHEMISTRY
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is described b y .\llr.n and otliers (1.11). hIeasurrinrnis oi' shock ftxint- I hickncsh and b u l k viscosit!, of carbon diosidr and nitroqen rnonusidr are rt,portrrt t)\ hndrrscn and Fforriing (2.11). '['tic\ find very stnall real Iilllk \ C:onct,rned rvit h instriiirit,ntatioii i \ Krsler and Schribc's [,.17.11) tlcscril)tioti ii il(JVd r ~ s l ~ t ~ r i m r l i t ~ i ir c ~ c ~ l r i i c l \ l c ~ \\,liich c(init)iiit:s the schlit~rc*noli~i(~:iI systc~rll: a ~ i l l l i t ~ l l r l l l l t i ~ ~l l~i lctrl t ~and , ill1 oscilloscope i n it inanncr t1i;it Ix'rtiiils the nirasur(~iiii~nt o l driisity c1istrit)uLiciii i n shock \\a\-c:s, ~ ~ i w l u c rin d a shii[.k tube. 'l'hc rt~sults a1r ll.;Vtl I'cir. l t l f , Stlid). o f rela\;atio11 p l l c n o l ~ l l ~ n
