Laminar-to-turbulent transition

Diffusion Flames in the Transition Region. As the velocity of the fuel jet increases in the laminar to turbulent transition region, an instabihty develops at the top of the flame and spreads down to its base. This is caused by the shear forces at the boundaries of the fuel jet. The flame length in the transition region is usually calculated by means of empirical formulas of the form (eq. 13) where I = length of the flame, m r = radius of the fuel jet, m v = fuel flow velocity, m/s and and are empirical constants. 

If flow becomes turbulent, the corrosion rate increases even more rapidly. In practice, most engineering materials have a critical velocity above which the corrosion rate is unacceptably high. This does not correspond with the laminar-to-turbulence transition. Surface roughness is an important consideration. 

The results related to the laminar-to-turbulent transition can be generalized by using the Obot-Jones model (Jones 1976 Obot 1988). A detailed discussion of this model is found in the paper by Morini (2004). 

Moiini GL (2004) Laminar-to-turbulent transition in microchannels. Microscale Thermophys Eng... 

When running a CFD simulation, a decision must be made as to whether to use a laminar-flow or a turbulent-flow model. For many flow situations, the transition from laminar to turbulent flow with increasing flow rate is quite sharp, for example, at Re — 2100 for flow in an empty tube. For flow in a fixed bed, the situation is more complicated, with the laminar to turbulent transition taking place over a range of Re, which is dependent on the type of packing and on the position within the bed. 

In Eq. 14.31, the quantity (1 - pglpe) may be safely taken as unity since pglp( is very small, except at pressures approaching the critical pressure of the fluid. For xf> 11, Rohsenow et al. [21] reasoned that a limiting Reynolds number exists, and Butterworth [28] recommends it to be 50. In reality, as shown by the data of Blangetti and Schliinder [29], a distinct laminar to turbulent transition does not exist. 

The laminar regime in a channel holds until the Reynolds number reaches a critical value above which the laminar motion becomes unstable and a transition to a turbulent flow will generally occur. It has been demonstrated experimentally that for a microchannel the critical value of the Reynolds number depends on the entrance conditions, on the cross-sectional geometry, and on the wall roughness. The effect of the roughness on the laminar-to-turbulent transition is very important, and it can be evidenced by observing Fig. 8 in which the experimental values of the Poiseuille number (f Re) are shown as a function of the Reynolds number for two microtubes made in stainless steel and in fused silica. The stainless steel microtube has an internal... 

The friction factor can thus be determined without measuring the pressure drop along the microchannel but by means of temperature and flow rate measurements. This kind of measurement is unsuitable when macrochannels are tested. For this reason Eq. 25 can be considered as an example of the role of scaling effects and to suggest new measurement procedures at the microscale. This relation has been used by Celata et al. [4] in order to determine the friction factor in microchannels. In addition, since Eq. 25 is valid only in the laminar regime, one can use it to individuate the laminar-to-turbulent transition in tnicrochannels. This has been experimentally demonstrated by Celata et al. [4] and Rands et al. [5]. 

In Fig. 6 the experimental results obtained by Rands et al. [5] are compared with Eq. 27 it is evident that the comparison between Eq. 27 and the experimental results allows one to individuate the laminar-to-turbulent transition in microchannels without the need to use pressure gauges. 

At 29.5°C, which is very close to the measured cloud point of 29.7°C the surfactant solution has very high relative viscosity ( S,7) and exhibits "concentrated" drag reducing behavior (16). That is, the data show a gradual departure from a slope parallel to the laminar line. If measurements could be made at higher solvent Reynolds numbers, they would show no laminar to turbulent transition but would gradually decrease in slope. 

G.L. Morini, M. Lorenzini, S. Colin, A. Geoffroy, Experimental analysis of pressure drop and laminar to turbulent transition for gas flows in smooth... 

Pressure-Driven Single Phase Liquid Flows, Figure 8 Effect of the relative roughness on the laminar-to-turbulent transition in a microtube... 

Where H is the charmel height (the smaller dimension in a rectangular channel), tw,av the average wall shear stress, V the kinematic viscosity, and p the density of the fluid. In internal flows, the laminar to turbulent transition in abrupt entrance rectangular ducts was found to occur at a transition Reynolds number Ret = 2200 for an aspect ratio ac = I (square ducts), to Ret = 2500 for flow between parallel planes with = 0 [4]. For intermediate channel aspect ratios, a linear interpolation is recommended. For circular tubes. Ret = 2300 is suggested. These transition Reynolds number values are obtained from experimental observations in smooth channels in macroscale applications of 3 mm or larger hydraulic diameters. Their applicability to microchannel flows is still an open question. 

The laminar to turbulent transition in pipe fittings are also discussed. The experimental work done to date on contractions, expansions, valves and orifices is reviewed in addition to similar work published in literature. 

Fig. 13. Trends in loss coefficients in the laminar to turbulent transition region (Miller, 1978)...

The Brinkman number is a nondimensional number, which influences the convective heat transfer coefficient, the thermal development length, and laminar to turbulent transition phenomena. It is defined as... 

Pohar, A., Plazl, I. (2008) Laminar to turbulent transition and heat transfer in a microreactor mathematical modeling and experiments. Ind. Eng. Chem. Res, 47,19, (August 2008) 7447-7455, ISSN 0888-5885. 

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