Reynolds studies

REYNOLDS NUMBER AND TRANSITION FROM LAMINAR TO TURBULENT PLOW. Reynolds studied the conditions under which one type of flow changes into the other and found that the critical velocity, at which laminar flow changes into turbulent flow, depends on four quantities the diameter of the tube and the viscosity, density, and average linear velocity the liquid. Furthermore, he found that these four factors can be combined into one group and that the change in kind of flow occurs at a definite value of the group. The grouping of variables so found was... 

H. Y. Choi and J. M. Reynolds, Study of Electrostatic Effects on Condensing Heat Transfer, Air Force Flight Dynamics Laboratory TR-65-51, 1966. 

Reynolds studied the conditions at which the flow pattern transitioned from laminar to turbulent and derived the following relationship that is now known as the Reynolds number, ArcI... 

The first use of an internal standard technique was reported in 1936 by Clark and Reynolds. Studies in the 1930s and the 1940s by Brentano, Shaffer, Taylor, and Brindley provided the basis for the appropriate corrections in the experimental intensities, particularly for absorption, and the microabsorption phenomena. (Grain-related effect occurs in polyphase samples. It occurs when large crystals preferentially interact with the beam, causing an appreciable reduction in the ratio of the diffracted intensities.)... 

J. Ashmore, A. B. Hastings, F.B.Nesbett and A. E. Reynold, Studies on Carbohydrate Metabolism in Rat Liver Slices. VI. Hormonal Factors Influencing Glucose-6-Phosphatase, J. biol. Chem. 218, 77-88 (1956). 

In 1883, Reynolds study on fluid flow was published in the Philosophical Transactions of the Royal Society [7]. Reynolds used streams of colored water in glass piping to visually observe fluid flow over a range of parameters. The apparatus used is depicted in a drawing by Reynolds himself (Figure 1.3), which shows flared glass... 

Reynolds Number. The Reynolds number, Ke, is named after Osborne Reynolds, who studied the flow of fluids, and in particular the transition from laminar to turbulent flow conditions. This transition was found to depend on flow velocity, viscosity, density, tube diameter, and tube length. Using a nondimensional group, defined as p NDJp, the transition from laminar to turbulent flow for any internal flow takes place at a value of approximately 2100. Hence, the dimensionless Reynolds number is commonly used to describe whether a flow is laminar or turbulent. Thus... 

A numerical study of the effect of area ratio on the flow distribution in parallel flow manifolds used in a Hquid cooling module for electronic packaging demonstrate the useflilness of such a computational fluid dynamic code. The manifolds have rectangular headers and channels divided with thin baffles, as shown in Figure 12. Because the flow is laminar in small heat exchangers designed for electronic packaging or biochemical process, the inlet Reynolds numbers of 5, 50, and 250 were used for three different area ratio cases, ie, AR = 4, 8, and 16. 

Figure 2.2.4 (Berty 1983) shows a tubular reactor that has a thermosiphon temperature control system. The reaction is conducted in the vertical stainless steel tube that can have various diameters, 1/2 in. being the preferred size. If used for fixed bed catalytic studies, it can be charged with a single string of catalytic particles just a bit smaller than the tube, e.g., 5/16 particles in a l/2 O.D. tube. With a smaller catalyst, a tube with an inside diameter of up to three to four particle diameters can be used. With such catalyst charges and a reasonably high Reynolds number— above 500, based on particle diameter—this reactor...

Damkdhler (1936) studied the above subjects with the help of dimensional analysis. He concluded from the differential equations, describing chemical reactions in a flow system, that four dimensionless numbers can be derived as criteria for similarity. These four and the Reynolds number are needed to characterize reacting flow systems. He realized that scale-up on this basis can only be achieved by giving up complete similarity. The recognition that these basic dimensionless numbers have general and wider applicability came only in the 1960s. The Damkdhler numbers will be used for the basis of discussion of the subject presented here as follows ... 

Figure 3-8b. Turbine map. (Balje, O.E., A Study of Reynolds Number Effects in Turbomachinery, Journal of Engineering for Power, ASME Trans., Vol. 86, Series A, p. 227.)...

The same water tunnel was used for tests to study the effect of casing treatment in axial-flow compressors. In this study, the same Reynolds number and specific speeds were maintained as those experienced in an actual axial-flow compressor. 

Li et al. [36] performed an extensive study on AP in a Sulzer SMX statie mixer with both Newtonian and non-Newtonian fluids. They showed that AP inereased by a faetor of 23 in a SMX statie mixer in the laminar flow regime. Figure 7-24 shows their eorrelation between the Fanning frietion faetor and the Reynolds number for experimental points under various operating eonditions. 

The length of the circulation zone (bubble), L, created when the linear jet is supplied at an angle a to the surface was studied experimentally by Bourque and Newman and theoretically by Sawyer.The effect of the angle between the jet axis at the outlet and the surface on the length of the circulation bubble is shown in Fig. 7.32, reproduced from Awbi. The data presented in Fig. 7.32 show that at sufficiently high Reynolds number the length of the circulation zone is independent of the Reynolds number. 

Linear jet attachment to a plane not parallel to the supply direction was studied by Katz. The critical angle, 9, of the plane to the jet supply direction, as indicated in Fig. 7.33, was found to be dependent on the supply velocity (Reynolds number). It also depends on the distance of the plane edge from the supply outlet (see Fig. 7.34). 

Oosthuizen, P. H. 1983. An Experimental Study of Low Reynolds Number Circular jet Flott. ASME Preprint 83-FE-36. 

It is necessary to study the Reynolds number independence in the hill scale and in the model as part of a complete model experiment. The threshold or the critical Reynolds number, Re, for the problem considered should be found by the experiments, and measurements should be made at either the same Reynolds number as in the full scale or at a Reynolds number equal to or larger than Re if the Reynolds number in the full scale is larger than Re. for the problem considered. 

Since the process is more complex, the proposed method may not be valid for scale-up calculation. The combination of power and Reynolds number was the next step for correlating power and fluid-flow dimensionless number, which was to define power number as a function of the Reynolds number. In fact, the study by Rushton summarised various geometries of impellers, as his findings were plotted as dimensionless power input versus impeller... 

The correlation studies of heat and mass transfer in pellet beds have been investigated by many, usually in terms of the. /-factors (113-115). According to Chilton and Colburn the two. /-factors are equal in value to one half of the Fannings friction factor / used in the calculation of pressure drop. The. /-factors depend on the Reynolds number raised to a factor varying from —0.36 to —0.68, so that the Nusselt number depends on the Reynolds number raised to a factor varying from 0.64 to 0.32. In the range of the Reynolds number from 10 to 170 in the pellet bed, jd should vary from 0.5 to 0.1, which yields a Nusselt number from 4.4 to 16.1. The heat and mass transfer to wire meshes has received much less attention (110,116). The correlation available shows that the /-factor varies as (Re)-0-41, so that the Nusselt number varies as (Re)0-69. In the range of the Reynolds number from 20 to 420, the j-factor varies from 0.2 to 0.05, so that the Nusselt number varies from 3.6 to 18.6. The Sherwood number for CO is equal to 1.05 Nu, but the Sherwood number for benzene is 1.31 Nu. 

While dimensional analysis is often a useful tool for dealing with a problem, it has not yet been successful for studying this phenomenon, mainly because the fluid properties of importance in forced-convection boiling have not been identified. Burn-out correlations based on dimensional analysis have appeared, e.g., Griffith (G5), Reynolds (R2), Zenkevitch (Zl), Ivashkevich (12), Tong et al. (T6), but the fluid properties used in these cases have been chosen on the basis of various assumptions without any demonstration that the properties used were the correct ones. They have, in fact, been shown in recent work by Barnett (B5), (to be considered later) to be either incorrect or incomplete. 

The group udp/p, known as the Reynolds number, is one which frequently arises in the study of fluid flow and affords a criterion by which the type of flow in a given geometry may be characterised. Equation 1.8 involves the reciprocal of the Reynolds number, although this may be rewritten as ... 

Many materials of practical interest (such as polymer solutions and melts, foodstuffs, and biological fluids) exhibit viscoelastic characteristics they have some ability to store and recover shear energy and therefore show some of the properties of both a solid and a liquid. Thus a solid may be subject to creep and a fluid may exhibit elastic properties. Several phenomena ascribed to fluid elasticity including die swell, rod climbing (Weissenberg effect), the tubeless siphon, bouncing of a sphere, and the development of secondary flow patterns at low Reynolds numbers, have recently been illustrated in an excellent photographic study(18). Two common and easily observable examples of viscoelastic behaviour in a liquid are ... 

The relation between c and / and X (defined by equation 5.1) is shown in Figure 5.4, where it is seen that separate curves are given according to the nature of the flow of the two phases. This relation was developed from studies on the flow in small tubes of up to 25 mm diameter with water, oils, and hydrocarbons using air at a pressure of up to 400 kN/m . For mass flowrates per unit area of U and G for the liquid and gas, respectively, Reynolds numbers Rei L d/fii ) and Rec(G d/fia) may be used as criteria for defining the flow regime values less than 1000 to 2000, however, do not necessarily imply that the fluid is in truly laminar flow. Later experimental work showed that the total pressure has an influence and data presented by Gr1H ITH(i9) may be consulted where... 

ROWE et al.(36 having analysed a large number of previous studies in this area and provided further experimental data, have concluded that for particle Reynolds numbers in the range 20-2000, equation 9.99 may be written as ... 

---