Turbulent flow transition

The maximum rate of polymerization has been confirmed to occur at the laminar-turbulent flow transition. The rate of polymerization was observed to be maximum at the transition for both straight reactors as well as for the helically-coiled reactor for which the transition is at a Reynolds number higher than that of the straight tube. The helically coiled tubular reactor is of industrial interest since it is much more compact and, consequently, the cost and the temperature control problems are more tractable. 

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... 

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 ... 

V. E. Kaupas, P. S. Poskas, and J. V. Vilemas, Heat Transfer to a Transition-Range Gas Flow in a Pipe at High Heat Fluxes (2. Heat Transfer in Laminar to Turbulent Flow Transition), Heat Transfer-Sov. Res, (21/3) 340-351,1989. 

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 . 

In experimental aerodynamics, the surface hot wire probe has proved to be the most successful standard measurement technique to determine the laminar-to-turbulent flow transition, local separation, and shear stress fluctuations. The flush-mounted thermal shear stress sensor is one of the most successful techniques for shear stress measurement and is available in various forms, i.e., sensor skin, etc. [4], due to the rapid development of MEMS manufacturing processes. 

Critical Reynolds number Laminar to turbulent flow transition... 

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

The p-Prv has been used for flow studies in microfluidic devices by many researchers. Meinhart et al. (1999) studied pressure-driven flow in a microchannel. Kim et al. (2001) studied electroosmotically driven flows in various microchannel configurations to examine their feasibility for micropumping and microvalve applications. Shinohara et al. (2004) studied two-phase uansient flow in microfluidic devices by using high-speed p-PIV. The laminar to turbulent flow transition in microtubes was studied by Sharp and Adrian (2004). Nguyen et al. 

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. 

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