Reynolds Number and Flow Regimes

In fluid mechanics, the physical implication of a Reynolds number is the ratio of inertial forces (up) to viscous forces (ju/L). It is, therefore, used to illustrate the relative importance and dominance of these two types of forces for a given flow. Depending on the magnitude of the Reynolds number, the flow regimes can be classified as either laminar or turbulent flow. If a flow has a low Reynolds number, a laminar flow occurs, where viscous forces are dominant. The flow is therefore smooth. When the Reynolds number for a flow is greater than a critical value, the flow becomes turbulent flow and is dominated by inertial forces, resulting in random eddies, vortices and other flow fluctuations. Some of the examples are illustrated in Table 2.7. 

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. 

The evaluation of the parameters for this flow regime requires the calculation of the Reynolds number and hydraulic diameter for each continuous phase. The hydraulic diameter can be determined only if the holdup of each phase is known. This again illustrates the importance of understanding the fluid mechanics of two phase systems. Once the hydraulic diameter is known, the Reynolds number can be evaluated with the knowledge of the in situ phase velocity, and the parameters of the model equations can be evaluated. 

For gas-liquid flows in Regime I, the Lockhart and Martinelli analysis described in Section I,B can be used to calculate the pressure drop, phase holdups, hydraulic diameters, and phase Reynolds numbers. Once these quantities are known, the liquid phase may be treated as a single-phase fluid flowing in an open channel, and the liquid-phase wall heat-transfer coefficient and Peclet number may be calculated in the same manner as in Section lI,B,l,a. The gas-phase Reynolds number is always larger than the liquid-phase Reynolds number, and it is probable that the gas phase is well mixed at any axial position therefore, Pei is assumed to be infinite. The dimensionless group M is easily evaluated from the operating conditions and physical properties. 

It is well known in fluid flow studies that below a certain critical value of the Reynolds number the flow will be mainly laminar in nature, while above this value, turbulence plays an increasingly important part. The same is true of film flow, though it must be remembered that in thin films a large part of the total film thickness continues to be occupied by the relatively nonturbulent laminar sublayer, even at large flow rates (N e ARecr J- Hence, the transition from laminar to turbulent flow cannot be expected to be so sharply marked as in the case of pipe flow (D12). Nevertheless, it is of value to subdivide film flow into laminar and turbulent regimes depending on whether (Ar6 5 Ar u). 

The constants in this relation will be different for different critical Reynolds numbers. Also, the surfaces are assumed to be smooth, and the free stream to be turbulent free. For laminar flow, the friction coefficient depends on only the Reynolds number, and the surface roughness has no effect. For turbulent flow, however, surface roughness causes the friction coefficient to increase sevcralfold, to the point that in fully turbulent regime the friction coefficient is a function of surface roughness alone, and independent of the Reynolds number (Fig. 7-8). Tliis is also the case in pipe flow. 

An additional complication that occurs with oscillating flow is the existence of several regimes of laminar and turbulent flow that are functions of frequency as well as Reynolds number, as shown in Figure 3 for the case of smooth circular tubes [2]. These flow regimes are the subject of much research [3]. They are shown as a function of the peak Reynolds number Nr,peak and the ratio of channel radius R to the viscous penetration depth Sv This ratio is sometimes referred to as the dynamic Reynolds number and is similar to the Womersley number Wo = D 28y). In the weakly turbulent regime... 

When the flow is in the self-similar regime, the Euler number becomes more or less a constant independent of the Reynolds. Figure 10.2 shows the relationship between the Reynolds number and Euler number for a particular flow category. 

Based on the dimensionless equation of continuity [i.e., eq. (12-18dimensionless equation of motion [i.e., eq. (12-18e)] in the laminar flow regime, one concludes that both v and v are functions of dimensionless spatial coordinates x and y, as well as the Reynolds number and the geometiy of the flow configuration. Unfortunately, the previous set of equations does not reveal the specific dependence of v and v on Re. 

Reynolds number for flow is a dimensionless number characterizing the turbulence in the reactor. When the Reynolds number is below 2500, the flow regime is described as laminar, and suitable scale-up approaches are used. The Reynolds nuiriber range, 2500 to 10,000, is considered by many as transitional, and engineers are very careful not to operate in that regime because of its imique characteristics. Reynolds numbers above 10,000 describe fully developed turbulence. 

An unknown hydrocarbon flows through a 10 cm diameter pipe at a volumetric flow rate of 0.09 m s The flow regime is barely turbulent. Based on the equation for the Reynolds number and the data in Table Q6.8, determine the most likely hydrocarbon. 

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