Turbulent flow, transition from

Hwang and Kim (2006) investigated the pressure drop in circular stainless steel smooth micro-tubes ks/d <0.1%) with inner diameters of 244 pm, 430 pm and 792 pm. The measurements showed that the onset of flow transition from laminar to turbulent motion occurs at the Reynolds number of slightly less than 2,000. It... 

Convection in Melt Growth. Convection in the melt is pervasive in all terrestrial melt growth systems. Sources for flows include buoyancy-driven convection caused by the solute and temperature dependence of the density surface tension gradients along melt-fluid menisci forced convection introduced by the motion of solid surfaces, such as crucible and crystal rotation in the CZ and FZ systems and the motion of the melt induced by the solidification of material. These flows are important causes of the convection of heat and species and can have a dominant influence on the temperature field in the system and on solute incorporation into the crystal. Moreover, flow transitions from steady laminar, to time-periodic, chaotic, and turbulent motions cause temporal nonuniformities at the growth interface. These fluctuations in temperature and concentration can cause the melt-crystal interface to melt and resolidify and can lead to solute striations (25) and to the formation of microdefects, which will be described later. 

Laminar flow to turbulent flow transition — When increasing the velocity of the flow, a transition from -> laminar flow to rippling and finally to turbulent flow will occur [i]. The transition from laminar to turbulent flow is governed by the dimensionless -> Reynolds number. Ref [i] Levich VG (1962) Physicochemical hydrodynamics. Prentice-Hall, Englewood Cliffs... 

Experiments were conducted to measure flow and heat transfer characteristics of gaseous flows in microchannels in [12]. Their experimental result of the Poiseuille number is 118 for laminar flow, which is higher than the expected value. They also reported that the flow transition from laminar to turbulent occurs at Reynolds numbers around 400 to 900, which is lower than the conventional value of... 

To keep the particles in suspension, the flow should be at least 0.15m/sec faster than either 1) the critical deposition velocity of the coarsest particles, or 2) the laminar/turbulent flow transition velocity. The flow rate should also be kept below approximately 3 m/sec to minimize pipe wear. The critical deposition velocity is the fluid flow rate that will just keep the coarsest particles suspended, and is dependent on the particle diameter, the effective slurry density, and the slurry viscosity. It is best determined experimentally by slurry loop testing, and for typical slurries it will lie in the range from 1 m/s to 4.5 m/sec. Many empirical models exist for estimating the value of the deposition velocity, such as the following relations, which are valid over the ranges of slurry characteristics typical for coal slurries ... 

Fig. 5.6 The suspension characteristic for the 1-s criterion for a double turbine (partly covered on both sides), Type EKATO (for geometry see the original publication) in the transition and turbulent flow range from [284]... 

Since the speed near the surface in a laminar boundary layer has a lower velocity than its turbulent counterpart, the laminar boundary layer is more likely to separate. When this occurs, the laminar boundary layer leaves the surface and usually undergoes a transition to a turbulent flow away from the surface. This process takes place over a certain distance that is inversely related to Re, but if it happens quickly enough, the flow may reattach as a turbulent boundary layer and continue along the surface. To compute when the separation will occur, we can solve the Navier-Stokes equations or apply one of the several separation criteria to the solutions of the boundary layer equations. 

He became in 1946 chief, the Aerodynamics Section of the National Bureau of Standards NBS, having previously been in its Electrical Division from 1929 to 1930. He and Harold K. Skramstad (1908-2000) were the winners of the 1948 S.A. Reed Award for contributions to the imderstanding of the mechanism of laminar to turbulent flow transition . Schubauer became Fellow of the Aeronautical Society in 1949, and recipient of the Gold Medal for aerodynamic research in 1956, as the chief of the NBS Fluid Mechanics Section, in recognition of outstanding contributions to basic aerodynamics over the past 20 years . 

Re <2.1 X 10 is laminar Re >4 x 10 is turbulent. The transition from laminar to turbulent flow in porous channels and tubes, e.g. tubular membranes, Re<2 x 10. Flow is considered turbulent because of mesh spacers. 

In turbulent flows. Re is important because it can be used to determine when the flow transitions from laminar to turbulent flow and also when the flow achieves a fully turbulent state. For macroscale pipe and channel flows, transition to turbulence can occur in the range 1,800 < Re < 2,300, depending of flow conditions, and the flow becomes fully turbulent at a Reynolds number of approximately 4,000. As will be shown later in this chapter, whether flows in microchannels agree with this macroscale behavior has long been a topic of debate, as some researchers have reported transitional Reynolds numbers in microchannel flows far lower than the 1,800-2,300 reported for macroscale flows. However, recent studies using newly developed experimental techniques and also careful reexamination of the results of some of the earlier studies strongly suggest that microchannel flows... 

At low Reynolds numbers, inertial forces are small compared to viscous forces and the flow remains laminar. At high Reynolds numbers, viscous forces become dominant and disturb the flow, which thus becomes turbulent The transition from a laminar flow regime to a turbulent flow regime never occurs suddenly there is always a transition flow regime. For example, the laminar flow inside tubular pipes occurs at the Reynolds number around 2300. The turbulent flow in the same pipe occurs at the Reynolds number higher than around 3000. The flow between the Reynolds numbers 2300 and 3000 is thus considered the transition flow. 

Laminar flow to turbulent flow transition — When increasing the velocity of the flow, a transition from lam-... 

In physical as well as mathematical modeling of transport phenomena, it is important to consider the existence or otherwise in the real process, any possible flow transition from laminar to turbulent flow, natural convection to forced convection, or subsonic to supersonic flow. This is because of the significant impact that such transitions may have on the process. 

From Eq. (34) a plot of ln[(l - / q)// q] versus (using a as a fitting parameter) would give a straight-line plot with slope of 1/<1> and an ordinate intercept from which / max be determined. Since d) can be seen to be constant by Eq. (33) for any solute—membrane combination of constant cross-sectional area, plots of Eq. (34) should provide better linearity than plots of Eq. (31). Once d) is determined, values ofR can be calculated. A plot for lipase cross-flow filtered at a constant applied pressure through an A002 membrane is shown in Fig. 18. Note that the linearity is almost perfect until the laminar-to-turbulent flow transition occurs in the film. 

The transition from laminar to turbulent flow occurs at Reynolds numbers varying from ca 2000 for n > 1 to ca 5000 for n = 0.2. In the laminar region the Fanning friction factor (Fig. 2) is identical to that for Newtonian fluids. In the turbulent region the friction factor drops significantly with decreasing values of producing a family of curves. 

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... 

No simple equation exists for accomplishing a smooth mathematical transition from laminar flow to turbulent flow. Of the relationships proposed, Hausen s equation [Z. Ver Dtsch. Ing. Beih. Veifahrenstech., No. 

Laminar and Turbulent Flow, Reynolds Number These terms refer to two distinct types of flow. In laminar flow, there are smooth streamlines and the fuiid velocity components vary smoothly with position, and with time if the flow is unsteady. The flow described in reference to Fig. 6-1 is laminar. In turbulent flow, there are no smooth streamlines, and the velocity shows chaotic fluctuations in time and space. Velocities in turbulent flow may be reported as the sum of a time-averaged velocity and a velocity fluctuation from the average. For any given flow geometry, a dimensionless Reynolds number may be defined for a Newtonian fluid as Re = LU p/ I where L is a characteristic length. Below a critical value of Re the flow is laminar, while above the critical value a transition to turbulent flow occurs. The geometry-dependent critical Reynolds number is determined experimentally. 

Roughness may also affect the transition from laminar to turbulent flow (Schhchting). 

The critical Reynolds number for transition from laminar to turbulent flow in noncirciilar channels varies with channel shape. In rectangular ducts, 1,900 < Re < 2,800 (Hanks and Ruo, Ind. Eng. Chem. Fundam., 5, 558-561 [1966]). In triangular ducts, 1,600 < Re < 1,800 (Cope and Hanks, Ind. Eng. Chem. Fundam., II, 106-117 [1972] Bandopadhayay and Hinwood, j. Fluid Mech., 59, 775-783 [1973]). 

The transition to turbulent flow begins at Re R in the range of 2,000 to 2,500 (Metzuer and Reed, AIChE J., 1, 434 [1955]). For Bingham plastic materials, K and n must be evaluated for the condition in question in order to determine Re R and establish whether the flow is laminar. An alternative method for Bingham plastics is by Hanks (Hanks, AIChE J., 9, 306 [1963] 14, 691 [1968] Hanks and Pratt, Soc. Petrol. Engrs. J., 7, 342 [1967] and Govier and Aziz, pp. 213-215). The transition from laminar to turbulent flow is influenced by viscoelastic properties (Metzuer and Park, J. Fluid Mech., 20, 291 [1964]) with the critical value of Re R increased to beyond 10,000 for some materials. 

Between about Rop = 350,000 and 1 X 10 , the drag coefficient drops dramatically in a drag crisis owing to the transition to turbulent flow in the boundary layer around the particle, which delays aft separation, resulting in a smaller wake and less drag. Beyond Re = 1 X 10 , the drag coefficient may be estimated from (Clift, Grace, and Weber) ... 

In laminar flow there are no disturbances, and therefore all flow particles move in the same direction. Transitional flow is the flow regime that takes place during the change from streamline to turbulent flow. In the case of turbulent flow the particles move in a given flow direction, but the flow is erratic and random. 

Deflagration-to-Detonation Transition (DDT) The transition phenomenon resulting from the acceleration of a deflagration flame to detonation via flame-generated turbulent flow and compressive heating... 

The basis for single-phase and some two-phase friction loss (pressure drop) for fluid flow follows the Darcy and Fanning concepts. The exact transition from laminar or dscous flow to the turbulent condition is variously identified as between a Reynolds number of 2000 and 4000. 

This is the basis for establishing the condition or type of fluid flow in a pipe. Reynolds numbers below 2000 to 2100 are usually considered to define laminar or thscous flow numbers from 2000 to 3000-4000 to define a transition region of peculiar flow, and numbers above 4000 to define a state of turbulent flow. Reference to Figure 2-3 and Figure 2-11 will identify these regions, and the friction factors associated with them [2]. 

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