an lI/Ecl Unit Operations Review
Flow of Fluids by Murray Weintraub, U . S. Bureau of Mines, Pittsburgh, Pa.
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N e w fields of chemical processing are benefiting from flow analysis
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Empirical knowledge of solid-fluid transport continues to increase
Influence of roughness on laminar-turbulent transition is being studied
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HISTORY
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FLUID
MECHANICS,
as one of the oldest engineering sciences, causes its present growth pattern to be one of diversification and infiltration into many fields of activity rather than one of spectacular development in new directions. As a result, the bibliography which this report summarizes, covering principally the period between May 1959 and October 1960, is divided into its major subdivisions of subject matter in almost exactly the same proportions as in the previous year. Efforts to assist the design engineer in the problems associated with the singlephase steady flow of fluids through different types of equipment continue along various paths. Mathematical and empirical expressions have been derived which permit the application of a single equation to a diversity of channel geometries. Other investigators have concentrated on the simplest geometrythe circular pipe-and have evolved refinements of accepted correlations to include the effects of nonisothermal and non-Newtonian flow. Reports on flow through specific equipment designs include studies of heat exchangers, glass melting tanks, climbing film evaporators, and swirl chambers. Several valuable contributions have been made toward the understanding of flow through open channels, hydroturbines, dams, and other hydraulic works. The utility of fluid mechanics was amply demonstrated in improving the operation of heat exchangers, chemical reactors, furnaces, and mixers. Many of these applications were aided by the intelligent use of aerodynamic models. A qualitative discovery of great potential is that a fluid-filled elastic skin can reduce drag by damping turbulence. A considerable amount of both mathematical and experimental work was published on the boundary layer, with several reports on the influence of surface roughness on boundary-layer transition. Several aspects of the gross transition from laminar to turbulent flow were also subjects of investigations. Knowledge of the distribution of local velocities within a fluid system is important in many types of industrial equipment, as well as constituting a source of basic understanding of the process
of fluid flow. Studies have been made of velocity profiles in thermal entrance regions, in vortex chambers, in boundary layers, and in impinging jets, as well as in liquid drops, stratified flow, and curved channels. Unsteady flow has its most serious effects in the phenomenon of water hammer, and it is in the control of this problem in large water supply systems that much research is undertaken. Other studies have included the effect of flow and pressure transients on gas inhomogeneity, on mine ventilation, and on the pumping of viscous liquids. I n the field of measurement and control, developers of such novel methods as those using ultrasonic beams, phase contrast, nuclear resonance, and similar exotic phenomena may take a good deal of encouragement from the growing commercialization of electromagnetic flowmeters and mass flowmeters which were in the same novelty group only a few years ago. The chemical engineer still finds the orifice plate the instrument of choice where applicable. The current literature contains articles on improving and extending this device by modification of its contours, by utilization of plates with multiple orifices, and by calibration with boiling liquids and with orifices of reduced diameters. Other common primary elements, including the Pitot tube, propeller, weir, and hot-wire anemometer, were also subjects of investigation. Research into multiphase flow has continued in many directions. Reports have been published describing the be-
havior of jets, falling liquid sheets, bubbles, sprays, and solid particles. The interaction of two liquid phases has been studied for flow in simple conduits, through porous media such as geological strata, and through unconsolidated media such as packed columns. Single fluid flow through solid media has also been studied. The two-phase process which has come to be known as fluidization was an especially fertile source of publications, although a large fraction of these described new process applications rather than the discovery of new basic principles. A few research reports discuss particle and fluid relative motion, elutriation of particles from the bed, and mixing within the system. The many possible combinations of multiphase flow, such as gas-liquid, solid-gas, and solid-liquid, have not yet been brought together in any common theoretical area. This is not surprising, however, as their fields of application are generally remote from each other. A number of interesting publications elucidate the flow patterns of single component mixtures that occur in the steam-generating tubes of boilers and in the two-component systems such as air-water or oil-water. Transport of solids by liquids has been of particular interest to the coal industry, although the movement of sewage and of river sediments has also been investigated. Despite the increasing interest in this field, however, many of the basic factors are completely unresolved. The flow of solids-gas mixtures
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has been studied, both from the viewpoint of pneumatic transport and from the viewpoint of the solid as a modifier of the normal gas flow. Separation of solids in both gas and liquid cyclones has also been analyzed. Pipeline engineers have taken advantage of both the newest techniques and the oldest materials. Recent news items include descriptions of the first computerized gas dispatching system and the use of wooden staves in the construction of a 10-foot-diameter pipeline GO50 feet long. roteworthy is the major expansion in trans-European pipeline networks which is currently taking place to accommodate the expanding oil and petrochemical industries. Scientific developments in pipeline design include advances in corrosion protection, in piping stress analysis, and in the calculation of water hammer phenomena. Current reports discuss the application and efficiencies of the familiar centrifugal pumps and turbines but also analyze less familiar devices, such as gear pumps, jet pumps, and screw pumps. Several articles also discuss the basic criteria for pump selection in the process industries.
Single-phase Flow The primary problems in the design of fluid-handling equipment can usually be associated either with geometry of the equipment or with variations in fluid properties. The hydraulic radius has been used for many years as a means of converting conduits of various cross sections to an equivalent circular section. Lohrenz and Kurata (26) advanced a new formulation for the equivalent diameter of concentric annuli and parallel plates which is well supported by experimental data and is considerably more convenient to use than previous parameters. The swirl of a fluid has important effects on flow phenomena a t pump inlets, in cyclone separating devices, and in heat-transfer and other processing equipment. The experiments of Binnie and Kame1 ( 3 ) provided interesting data
on this fluid motion. These investigators reported that in swirling flow down a long tube two regimes may exist. In one range of swirl, a previously reported flow reversal was observed. At higher swirl rates, five separate streams were generated. Another problem which is difficult to analyze, even for simple geometries, is the effect of radial temperature gradients on fluid flow. When the viscosity of the fluid is particularly sensitive to temperature, the difficulties are multiplied. Petukhov and Krasnoschekov (35) made an experimental study of viscous nonisothermal flow through circular and rectangular tubes and offered a generalized expression for the resistance coefficient when the viscosity varies over the flow cross section. Typical of the commonly used process equipment about which few data on fluid flow have been published is the plate-type heat exchanger. Watson and others (44) reported an unusually comprehensive study of this device with measurement of flow characteristics by means of motion pictures and electrical conductivity, dye patterns, and “cookon” patterns. They showed how velocity patterns, residence times, and pressure drops could be used to aid sound design and effective use. Fluid dynamics was applied, by Hadley and Thomas (75), to facilitate understanding of a more unusual device, the climbing film evaporator, and correlate power requirements, flow rate, and volume hold-up for the equipment. The classical wetted-wall column was used by McCarter and Stutzman (27) to show that film thicknesses calculated from fluid-flow theory gave good agreement with effective film thicknesses measured by mass transfer. Hence, wettedwall column data may prove a valuable source of molecular difhivity constants. The transverse stresses induced by Bernoulli forces when fluids flow at high velocities between parallel plates were analyzed by Miller (32),who calculated the critical velocities above which collapse of the structure occurs. Miller
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then discussed the applicability of his formulas to design of atomic reactors. Several authors have discussed mixing of fluids by forces of longitudinal diffusivity of flowing streams. Mixing by shear and recirculation mechanically induced by agitators were correlated with the flow patterns that produced them, by Norwood and Metzner (33). Many analyses o f chemical processes and equipment must be made on the basis of similarity with models. A particularly complex situation exists where flow patterns in a cold model must be related to the patterns that would exist in a hot unit within which a chemical reaction is taking place. Such a correlation was performed by Thurlow (42),who developed a theory generally applicable to furnaces and obtained confirming experimental data. Two important fields of current research are jet flow and the transition from the laminar flow regime to the turbulent regime. Sato (38) provided some interesting information in both these fields by his research on the instability of a two-dimensional jet. H e measured the velocity fluctuations whose growth or damping determine the gross behavior of the fluid stream, investigated the influence of external excitation on these fluctuations, and determined theoretical equations which were in good agreement with his experimental results. Other work on the transition process which is worthy of special note included that of Lindgren (241,who suggested a new parameter, the maximum relative spot velocity, as a criterion of transition, and that of Smith and Clutter ( 3 9 ) ,who are typical of a number of investigators studying the effect of roughness on the boundary-layer transition. The magnitude of the forces involved in unsteady flow of the tremendous quantities of water inherent in municipal water systems makes control of transients imperative. Combes ( 8 ) presented a graphical method which overcomes many of the difficulties found in standard analytical techniques when these are applied to complex installations. A mathematical solution of a simpler problem, but one which should be noted because of its vital importance, was performed by Maczynski (29), who developed equations describing the transient response of mine ventilation networks during fan reversal. Although lubrication and bearings are generally outside the scope of this review, the chemical engineer should be cognizant of the operating problems of the gas lubricated bearing, an interesting fluid-dynamic device which may see service in many chemical areas where liquid lubricants have serious handicaps. Constantinescu ( 9 ) outlined some of the
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operating conditions which influence the stability of such bearings. Although the computation of flow of a homogeneous fluid through a length of pipe is generally considered to be a simple process based on the measured properties of the fluid, large deviations from the theoretical are often found in commonplace situations such as the pumping of fuel oil. Davenport and Russell (70) investigated the causes of several such discrepancies and determined that they were due to changes in the gel structure of the oil during long storage and that these changes were not reflected in the standard methods of viscosity measurement. A coaxial viscometer, operated at approximately the same rate of shear as existed in the pumped oil and upon samples that had been mechanically worked, was necessary to obtain meaningful viscosities.
Metering and Controls
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Although the control of fluid flow rates in relatively simple systems is generally a matter of choice of hardware, the design of a stable control often requires the solution of a formidable array of differential equations when the system becomes complicated by long signal-transmission distances, signal lags, nonlinear transmitter responses, and similar phenomena. Ceaglske (6) presented a systematic approach to a relatively complete analysis which gives the engineer a good picture of the effect of each parameter upon the final response. An exciting possibility of advancement in the use of the orifice plate is a method of calibration developed by Martin and Passi (30)) in which a pressure measurement on the face of the orifice plate can be used to replace the frequently awkward measurement of large fluid volumes. Another recent development is the extension of the range in which orifices can conveniently be used, that is the range of constant flow coefficient, by using profiles other than the knife edge. Bogema and Monkmeyer (4) discussed the advantages of the quadrant edge orifice for metering low flow rates and considered the errors introduced by machining difficulties. The venturi tube also has been subjected to modification in efforts to decrease its length and retain or improve its low permanent head loss characteristic. An analysis by Kalinske (27) of the twin throat venturi, which is a device similar to the recently publicized Dall tube, shows that these apparently simple modifications are, in principle, quite different from the classic venturi, for they utilize boundary layer effects in addition to gross kinetic energy changes to produce the pressure changes which are a measure of flow rate.
The range of application of the broadcrested weir has been appreciably extended by Smith (40). H e analyzed the use of this instrument in the fully submerged condition and showed the difference in controlling parameters between this type of operation and operation with free fall discharge. The hot wire anemometer is probably second only to the positive displacement and head-type meters in fluid flow research. Therefore, a new correlation of heat transfer from hot wire sensing elements constitutes a valuable contribution to the accurate use of this instrument. Such a correlation was given by Collis and Williams (7))who also delineated the range in which free convection, and hence wire orientation, becomes insignificant.
Multiphase Flow Fundamentals. The relative importance of fundamental studies can be rated in terms of three questions: Do they present new concepts, do they challenge old ones, or do they apply to important practical problems? Two novel methods of interphase contacting which depend primarily on fluid-dynamic mechanisms are the use of falling liquid sheets, described by Bromley and others (5)) and the semifluidized bed studied by Fan and others (77). The semifluidized bed is the system of a packed bed, above a fluidized bed, formed when a fluidized bed is constrained by an upper sieve plate and operated near carry-over velocity. Many investigators of flow through porous solids have used the concept of a bundle of capillaries as a model for analysis. As part of an extensive symposium on the physicochemical influences on the conduction of water through geological strata, Philip (36) showed how and when this model fails and how classical hydrodyamics can still be used on the problems of porous media. Of great practical importance in the design of Raschig ring-filled masstransfer columns is a knowledge of the gas-liquid interfacial area. An investigation by Whitt (46) established that the surface wetted by the liquid is not the same as that effective for contact with flowing gas and that an optimum ring diameter exists. Also noteworthy, for its combination of theoretical importance and possible application to many fluid-solid systems, is the investigation by So0 and others (47) of the difference in turbulence characteristics of solid and gas phases. Fluidization. The present activity in fluidization seems to be primarily one of consolidation of ideas rather than major advances against the formidable problems which still exist. In such a situation, the almost simultaneous ap-
v d Unit Operations Review
pearance of two comprehensive texts by Leva (22) and by Zenz and Othmer (47) is not to be construed as a duplication but as a useful summing-up of the present state of the art from somewhat different viewpoints. One topic which is still deficient in usable design information is that of reactor computation, a situation which arises from the complex and variable nature of the fluid-solid contact in the fluidized bed. Several tracer and kinetics studies have been reported in the literature, but one by May (37) is noteworthy for its interrelation of pilot plant and fullscale measurements. Removal of particles from a fluidized bed by entrainment in the gas stream is an important consideration in design of the solids recovery system, in the conduct of entrained phase reactions, and in the use of the process as a means of particle classification. A comprehensive study of the effects of 10 parameters was reported by Wen and Hashinger (45),who proposed a correlation that satisfactorily described their measurements, as well as the somewhat fragmentary data of other investigators. A generalized correlation between bed expansion and fluid velocity has been established for ideal particulate fluidization. A recent publication by Hoffman and others (77) demonstrated that the correlation also holds for some deviation from the ideal conditions. Transport a n d Separation Processes. While some attempts have been made to develop a basic theory for solids transport by fluids, it remains unfortunately true that the equipment engineer must resort to empirical formulations in the specific range of parameters within which he is designing. The work of Gopichand and others (74) demonstrated the failure of the pneumatic transport correlations of Vogt and White outside the range of pressure drop and loading ratios for which the correlations were developed and presented new data covering ranges common to circulation lines in fluidization processes. One of the reasons for the unsatisfactory state of understanding of particle transport processes was shown by Torobin and Gauvin (43),who demonstrated the wide deviations of nonsteady motion, which is the major characteristic of particle transport, from steady-state drag-the reference condition for many transport correlations. The importance of acceleration forces has also been noted in the field of sediment transport in open channels such as river beds, by Irmay (70). In this case, the radial accelerations affect the motion of the particles into the fluid layers near the wall that have substantially different flow patterns than the bulk of the fluid. In hydraulic transport, also, the construction enVOL 53, NO. 5
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gineer must therefore resort to empirical studies. Fraser (72) described the elaborate test work which preceded the design of a system for pumping 1800 tons per day of ore concentrate a distance of 7.5 miles. One of the most difficult problems associated with solids transport is the introduction of the solids into a pressurized system. Aref ( 7 ) reported the results of his study of various methods of pressuring powdered fuels and concluded that, with the present state of the art, the simple lock hopper is the most economical device currently available, despite power loss from venting. Another aspect of solids-fluid flow is the interaction of the particle-laden stream on pipe walls or other objects upon which the stream impinges. Gillespie and Gunter (73) found that the drag coefficient for small spheres and cylinders in air suspensions containing particles with diameters from 50 to 400 microns is the same as that of the accepted curve for clean air, provided that suspension density is used in the drag coefficient and clean air density is used in the Reynolds number. The large number of configurations possible in gas-liquid flow, such as slug floiv, annular flow, and bubble flow, make it appear unlikel) that a single correlation \vi11 be found to describe all regimes completely. Correlation of the pressure drop with void fraction was suggested by Isbin and others ( Z O ) , who provided data on the adiabatic flow of steam-water at several high pressures. The annular pattern, Tvhere liquid flows along the tube wall and gas occupies the central core, has been measured by McManus (28), who found that an appreciable eccentricity of the liquid film occurs. He believes that this may be responsible for the difficulties of previous analytical approaches.
Piping and Pumps The major problems in the design of piping that is to feed a pump properly are greatly magnified when the pump is reciprocating and the fluid is dense, viscous, and non-Newtonian, as in the oil field “mud pump.” A substantial step toward solving these problems was made by Liljestrand (23) when he described a simplified approach, utilizing available knowledge, and outlined analytical and experimental work which must precede further progress. Frequently neglected aspects of proper pump and compressor operation may be seriously affected by minor changes in the associated piping. Harnish (76) demonstrated how improper suction pipc layout can result in failure to supply compressors with adequate lubrication.
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A number of operating difficulties, such as loss of efficiency, cavitation damage, and corrosion may arise from poor design or failure to maintain some of the design dimensions. Excessive clearance loss in centrifugal pumps and compressors was shown by Petermann (34) to affect primarily the pump delivery; it also causes a reduction in head by creating secondary fluid circulation patterns. Cavitation damage is generally ascribed to the formation and sudden collapse of vapor bubbles of the liquid being pumped. Holl (18) showed that although the formation of bubbles from extraneous gases such as air is much sloiver than the vapor phenomena, it occurs at much higher ambient pressures and can make a significant contribution to the total cavitation. Corrosion is a difficulty that must be fought by proper mechanical design, as well as by proper choice of materials of construction. Piccardo (37) discussed both the new materials and the new forms of pumps for corrosive situations and described advances in design of pump elements which permit longer pump life. Satisfactory and economic operation of pumping equipment starts kvith proper selection of the pump. A number of articles explaining the principles of selecting pumps for chemical plant use are in the current literature. A somewhat different point of vieiv is involved in the study by Beres and Potts (2) of the optimum combinaton of feed pump and drive for the boiler of a 265-mw. power plant. Besides operating costs and capital cost, the analysis included consideration of the effect of the chosen design on primary equipment size, load variation, and forced outage. The one type of pump whose design and construction may fall within the province of the chemical engineer is the jet pump. Reference may be made to a publication by van der Lingen (25) for a generalized theory leading to a correlation of results and design.
Literature Cited (1) Aref, M. N., Trans. Am. So(;. Mech. Engrs., Ser. A 82, 156 (1960). (2) Beres, J. C., Potts, R. W.,Heating, Pzping, Air Conditioning 32, No. 6, 148 (1960). (3) Binnie, A. M., Kamel, M. Y. M., Houille blanche 14, 348 (1959). (4) Bogema, M., Monkmeyer, P. L., Trans. Am. Soc. rtlech. Eners., Ser. D 82, 729 (1960). (5) Bromley, L. A., Read, S.M., Bupara, S.S.,IND.ENG.CHEM.52, 311 (1960). (6) Ceaglske, N. H., A.Z.Ch.E. Journal 5, 524 (1959). (7) Collis, D. C Williams, M. J., J . Fluid iMech. 6, 357 (1959). (8) Combes, G., Houille blanche 14, 366 (1959). (9)’ Cohantinescu, V. N., Rev. me‘can. apjl. Acad. rip,. populaire Roumaine 4, 627 (1959).
INDUSTRIAL A N D ENGINEERING CHEMISTRY
(10) Davenport, T. C., Russell, R. J., J . Znst. Petrol. 46, No. 437, 143 (1960). (11) Fan, L.-T., Yang, Y.-C., Wen, C.-Y., A.I.Ch.E. Journal 6 , 482 (1960). (12) Fraser, D. A., Mining Congr. J . 46, No. 3, 44 (1960). (13) Gillespie, T., Gunter, A. W., Trans. Am. Sac. Mech. Engrs., Ser. E 81, 584 (1959). (14) Gopichand, T., Sarma, K. J. R., Rao, M. N., IXD.ENG.CHEW51, 1449 ley, G. F., Thomas, A. L., Ibid.,
(17) Hoffman, R. F., Lapidus, L., Elgin, J. C., A.I.Ch.E. Journal 6, 321 (1960). (18) Holl, J. W.,Paper 60-Hyd-8, Am. SOC.Mech. Engrs., Gas Turbine Power and Hydraulic Conf., Houston, Tex., March 1960. (19) Irmay, S., Ibid., 60-Hyd-3. (20) Isbin, H. S.,Rodriguez, H. A.: others,
A.Z.Ch.E. Journal 5, 427 (1959). (21) Kalinske, A. X., Trans. A m . Soc. Mech. Engrs., Ser. D 82, 710 (1960). (22) Leva, M., “Fluidization,” McGrawHill, New York, 1959. (23) Liljestrand, W. E.: Trans. Am. Soc. Mech. Engrs., Ser. B 82, 87 (1960). (24) Lindgren, E. R., Arkio. Fysik 16, 101 (1959). (25) Lingen, T. E. van der, Paper 60-Hyd6, Am. Soc. Mech. Engrs. Gas Turbine
Power and Hydraulic Conf., Houston, Tex., March 1960. (26) Lohrenz, J., Kurata, F., IXD. ENG. CHEW 52, 703 (1960). (27) McCarter, R. J., Stutzman, L. F., A.I.Ch.E. Journal 5, 502 (1959). (28) McManus, H. S . , Jr., “Proc. 6th Midwest. Conf. Fluid Mech.,” p. 292, Texas Univ. Press, Austin, Tex., 1959. (29) Ivlaczynski, J., Bull. mad. polon. sei. 7 , 407 (1959). (30) Martin, J. J., Passi, V. R., A.Z.Ch.E. Journal 6, 318 (1960). (31) May, W. G., Chem. Eng. Progr. 55, No. 12, 49 (1959). (32) Miller, D. R., Trans. Am. SUG.Mech. Engrs., Ser. A 82, 8 3 (1960). (33) Norwood, K. W., Metzner, A. B., A.I.Ch.E. Journal 6 , 432 (1960). (34) Petermann, H., V D Z ZeitschriJt 101, 430 (1959). (35) Petukhov, B. S., Krasnoschekov, E. A., Soviet Phys.-Tekh. Phys. 3, 1123 (1959). (36) Philip, J. R., Highway Research Board Spec. Rept. 40, p. 147, Natl. -4cad. Sci. U. S.Publ. 629, 1959. (37) Piccardo, J. E., Corrosion 15, No. 9, 41 (1959). (38) Sato, H., J . Fluid Mech. 7, 53 (1960). (39) Smith, A. M. O., Clutter, D. W., J . AerolSpace Sci. 26, 229 (1959). (40) Smith, R. A , , Proc. A m . Sac. Czv z , Engrs. 85, HY 3 (J. Hydr. Div.), 1 (1959). (41) Soo, S. L., Ihrig, H. K., El Kouh, A. F., Trans. A m . Sac. Mech. Engrs., Ser. D 82, 609 (1960). (42) Thurlow, G. G., Combustion and Flame 3, No. 3, 373 (1959). (43) Torobin, L. B., Gauvin, W. H., Can. J . Chem. Eng. 37, 129, 224 (1959). (44) Watson, E. L., McKillop, A. A., others, IND. ENG.CHEM.52, 733 (1960). (45) \.lien, C.-Y., Hashinger, R. F., A.Z.Ch.E. Journal 6 , 220 (1960). (46) Whitt, F. R., Brit. Chem. Eng. 5, 179 (1960). (47) Zenz, F. A,, Othmer, D. F., “Fluicl;
ization and Fluid-Particle Reinhold, New York, 1960.
Systems,
