Transition to turbulence

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. 

Laminar and Turbulent Flow Below a critical Reynolds number of about 2,100, the flow is laminar over the range 2,100 < Re < 5,000 there is a transition to turbulent flow. For laminar flow, the Hagen-Poiseuille equation... 

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. 

Continuous Flat Surface Boundaiy layers on continuous surfaces drawn through a stagnant fluid are shown in Fig. 6-48. Figure 6-48 7 shows the continuous flat surface (Saldadis, AIChE J., 7, 26—28, 221-225, 467-472 [1961]). The critical Reynolds number for transition to turbulent flow may be greater than the 500,000 value for the finite flat-plate case discussed previously (Tsou, Sparrow, and Kurtz, J. FluidMech., 26,145—161 [1966]). For a laminar boundary layer, the thickness is given by... 

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) ... 

For the inlet length of a pipe in which the boundary layers are forming, the equations in the previous section will give an approximate value for the heat transfer coefficient. It should be remembered, however, that the flow in the boundary layer at the entrance to the pipe may be streamline and the point of transition to turbulent flow is not easily defined. The results therefore are, at best, approximate. 

The transition to turbulent flow occurred at Re of about 1,500. The authors noted that for smaller micro-channels, the flow transition would occur at lower Re. The early transition phenomenon might be affected by surface roughness and other factors. 

The transition from laminar to turbulent flow in micro-channels with diameters ranging from 50 to 247 pm was studied by Sharp and Adrian (2004). The transition to turbulent flow was studied for liquids of different polarities in glass micro-tubes having diameters between 50 and 247 pm. The onset of transition occurred at the Reynolds number of about 1,800-2,000, as indicated by greater-than-laminar pressure drop and micro-PIV measurements of mean velocity and rms velocity fluctuations at the centerline. 

Because most applications for micro-channel heat sinks deal with liquids, most of the former studies were focused on micro-channel laminar flows. Several investigators obtained friction factors that were greater than those predicted by the standard theory for conventional size channels, and, as the diameter of the channels decreased, the deviation of the friction factor measurements from theory increased. The early transition to turbulence was also reported. These observations may have been due to the fact that the entrance effects were not appropriately accounted for. Losses from change in tube diameter, bends and tees must be determined and must be considered for any piping between the channel plenums and the pressure transducers. It is necessary to account for the loss coefficients associated with singlephase flow in micro-channels, which are comparable to those for large channels with the same area ratio. 

Darbyshire AG, Mullin T (1995) Transition to turbulence in constant-mass-flux pipe flow. J Fluid Mech 289 83-114... 

Rands C, Webb BW, Maynes D (2006) Characterization of transition to turbulence in microchannels. Int J Heat Mass Transfer 49 2924-2930 Ren L, Qu W, Li D (2001) Interfacial electrokinetic effects on liquid flow in micro-channels. Int J Heat Mass Transfer 44 3125-3134... 

Schutz s correlation for free convection at a sphere, Eq. (25) in Table VII, takes pure diffusion into account by means of the constant term Sh = 2. According to his measurements using local spot electrodes, the flow here is not laminar but already in transition to turbulence. 

It is interesting to note that free convection on a rough surface [see Eq. (35) in Table VII] follows a higher GrSc dependence than that on a smooth plate for the same Ra range. This suggests that surface roughness eases the transition to turbulence. 

Early studies of the transition to turbulence relied on flow visualization techniques for liquid flow through arrays of spheres. Jolls and Hanratty (1966) found a transition from steady to unsteady flow in the range 110<7 e< 150 for flow in a dumped bed of spheres at N — 12, and they observed a vigorous eddying motion that they took to indicate turbulence at Re — 300. In regular beds of spheres, Wegner et al. (1971) found completely steady flow with nine regions of reverse flow on the surface of the sphere for Re — 82, and similar flow elements but with different sizes in an unsteady flow at Re — 200. Dybbs and Edwards (1984) used laser anemometry and flow visualization to study flow... 

Patterson, R.W. and Abernathy, F.H., Transition to turbulence in pipe flow for water and dilute solutions of polyethylene oxide, Journal of Fluid Mechanics, 51, pp. 177-85(1972). 

The transition to turbulent flow is gradual. Turbulence commences initially in the largest channels and eventually extends to the smaller channels. 

The time-dependent simulations of free jets discussed here focus on the vortex dynamics and transition to turbulence downstream of the jet exit. For the sake of computational efficiency, the author concentrates on the study of jet flow initialized with laminar conditions with a thin rectangular vortex sheet having slightly rounded-off corner regions and uniform initial momentum thickness [9]. Initial conditions for the simulated jets involve top>-hat initial velocity profiles... 

Grinstein, F.F., and C. R. DeVore. 1996. Dynamics of coherent structures and transition to turbulence in free square jets. J. Physics Fluids 8 1237-51. 

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