Transitional flow Reynolds number

Transitional Flow. Reynolds numbers and friction factors at which the flow changes from laminar to turbulent are indicated by the breaks in the plots of Figures 6.4(a) and (b). For Bingham models, data are shown directly on Figure 6.6. For power-law liquids an equation for the critical Reynolds number is due to Mishra and Triparthi [Trans. IChE 51, T141 (1973)],... 

Laminar Flow Reynolds numbers less than 2,100 Transition Flow Reynolds numbers between 2,100 and 10,000 Turbulent Flow Reynolds numbers greater than 10,000... 

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. 

Deposition of wax following crystallisation depends on the temperature differential between the bulk crude stream and the pipewall, and the Reynolds number. The larger the temperature differential, the greater the chance of wax deposition since molecular diffusion of dissolved wax to the pipewall intensifies as a result of the increase in wax concentration near the pipewall brought about by the temperature differential. With respect to Reynolds number, maximum wax accumulation is expected in the transition range (Reynolds number between 2000 and 4000). At low (laminar) flew, the net transport of wax to the wall 1s reduced by a relatively thick laminar layer adjacent to the pipewall and during turbulent flow, wax build-up 1s limited by erosion. 

Transition from laminar to turbulent flow Reynolds number. The factors that determine the point at which turbulence appears in a laminar boundary layer are coordinated by the dimensionless Reynolds number defined by the equation... 

To determine the proper flow for each mold, the Reynolds number should be determined. The Reynolds nnmber (N = DVP/M, where D is pipe diameter, V is fluid velocity, P is fluid density, and M is fluid viscosity) is a nondimensional parameter used to determine the nature of the flow along surfaces. Numbers between 2100 represent laminar flow, numbers from 2100 to 3000 represent transitional flow, and numbers above 5000 represent turbulent flow. 

Laminar to turbulent flow transition Critical Reynolds number... 

While Figure 6-14 provides the power number data in a wide range of Re, the information should not be used below an impeller Reynolds number of 1000. The flow regimes are (1) laminar flow below a Reynolds number of 10, (2) transition between Reynolds numbers of 10 and 10", and (3) turbulent above a Reynolds number of 10". The functionality between Np and Re can be described as follows ... 

In general, it is normal for the flow to start to change from laminar to transitional at Reynolds numbers of about 2000, and for flow to be turbulent at Reynolds numbers of above 3000. However, the precise point at which the transition will take place depends also on the roughness with respect to diameter (and geometry) of the pipe. There is no such thing as stable transitional flow. 

A low Reynolds number indicates laminar flow and a paraboHc velocity profile of the type shown in Figure la. In this case, the velocity of flow in the center of the conduit is much greater than that near the wall. If the operating Reynolds number is increased, a transition point is reached (somewhere over Re = 2000) where the flow becomes turbulent and the velocity profile more evenly distributed over the interior of the conduit as shown in Figure lb. This tendency to a uniform fluid velocity profile continues as the pipe Reynolds number is increased further into the turbulent region. 

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. 

The phenomena are quite complex even for pipe flow. Efforts to predict the onset of instabiHty have been made using linear stabiHty theory. The analysis predicts that laminar flow in pipes is stable at all values of the Reynolds number. In practice, the laminar—turbulent transition is found to occur at a Reynolds number of about 2000, although by careful design of the pipe inlet it can be postponed to as high as 40,000. It appears that linear stabiHty analysis is not appHcable in this situation. 

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... 

For Reynolds numbers > 1000, the flow is fully turbulent. Inertial forces prevail and becomes constant and equal to 0.44, the Newton region. The region in between Re = 0.2 and 1000 is known as the transition region andC is either described in a graph or by one or more empirical equations. 

Transition Region Turbulent-flow equations for predicting heat transfer coefficients are usually vahd only at Reynolds numbers greater than 10,000. The transition region lies in the range 2000 < < 10,000. 

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 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]). 

Curved Pipes and Coils For flow through curved pipe or coil, a secondary circiilation perpendicular to the main flow called the Dean effect occurs. This circulation increases the friction relative to straight pipe flow and stabilizes laminar flow, delaying the transition Reynolds number to about... 

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... 

Continuous Cylindrical Surface The continuous surface shown in Fig. 6-48b is apphcable, for example, for a wire drawn through a stagnant fluid (Sakiadis, AIChE ]., 7, 26-28, 221-225, 467-472 [1961]). The critical-length Reynolds number for transition is Re = 200,000. The laminar boundary laver thickness, total drag, and entrainment flow rate may be obtained from Fig. 6-49 the drag and entrainment rate are obtained from the momentum area 0 and displacement area A evaluated at x = L. 

Turbulent flow occurs when the Reynolds number exceeds a critical value above which laminar flow is unstable the critical Reynolds number depends on the flow geometry. There is generally a transition regime between the critical Reynolds number and the Reynolds number at which the flow may be considered fully turbulent. The transition regime is very wide for some geometries. In turbulent flow, variables such as velocity and pressure fluctuate chaotically statistical methods are used to quantify turbulence. 

Those particles with sizes d > d" at a given set of conditions (v, p, Pp, and a ) will settle only in the turbulent flow regime. For particles with sizes d < d, d" will settle only when the flow around the object is in the transitional regime. Recall that the transitional zone occurs in the Reynolds number range of 0.2 to 500. The sedimentation numbers corresponding to this zone are 3.6 < S, < 82,500 and 0.0022 < S2 < 1,515. 

Reynolds number A dimensionless parameter that represents the ratio of the inertia forces to the viscous forces in a flow. Its magnitude denotes the actual flow regime, such as streamline (laminar), transitional, or turbulent. 

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