Turbulent Internal Flow

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... 

There are two main reasons why a pump should not operate below its MCSF (/) the radial force (radial thmst) is increased as a pump operates at reduced flow (44,45). Depending on the specific speed of a pump, this radial force can be as much as 10 times greater near the shut off, as compared to that near the BEP and (2) the low flow operation results in increased turbulence and internal flow separation from impeller blades. As a result, highly unstable axial and radical fluctuating forces take place. 

Internal Flow. Depending on the atomizer type and operating conditions, the internal fluid flow can involve compHcated phenomena such as flow separation, boundary layer growth, cavitation, turbulence, vortex formation, and two-phase flow. The internal flow regime is often considered one of the most important stages of Hquid a tomiza tion because it determines the initial Hquid disturbances and conditions that affect the subsequent Hquid breakup and droplet dispersion. 

Miller Internal Flow Systems, 2d ed.. Chap. 13, BHRA, Cranfield, 1990) gives the most complete information on losses in bends and curved pipes. For turbulent flow in circular cross-seclion bends of constant area, as shown in Fig. 6-14 7, a more accurate estimate of the loss coefficient K than that given in Table 6-4 is... 

In this diagram the key features are A - Diffusion baffle this serves four roles. First to dissipate the velocity head, thereby improving the overall hydraulic characteristics of the separator. Next, to direct incoming flow downward and outward maximizing the use of the separator volume. Third, to reduce flow turbulence and to distribute the flow evenly over the separator s cross-sectional area. Finally, to isolate inlet turbulence from the rest of the separator. B- Internal chambers In the sediment chamber, heavy solids settle out, and concentrated slugs of oil rise to the surface. As the oily water passes through the parallel corrugated... 

Nullaswamy, M., Turbulence models and their applications to the predictions of internal flows, Computers and Eluids, 15, 151, 1987. 

Cate etal. (2001) propose a method for the calculation of crystal-crystal collisions in the turbulent flow field of an industrial crystallizer. It consists of simulating the internal flow of the crystallizer as a whole and of simulating the motion of individual particles suspended in the turbulent flow in a small subdomain (box) of the crystallizer. 

Its unique compact and efficient design is made possible by the use of the principle of zero velocity eliminating internal water turbulence (see below). The flocculated water thus stands still in the flotation tank for optimum clarification. The unit is complete with automatic backwash filter in which dirty backwash water is recycled back to the unit inlet for reprocessing. The average waste flow from the process is less than 1.0% of the incoming raw water. 

Branley, N., and W. P. Jones. 1997. Large-eddy simulation of a turbulent non-premixed flame. 11th Symposium (International) on Turbulent Shear Flow Proceedings. Grenoble, Prance. 21.1-21.6. 

In the case of internal flows extensive experimental data are available for turbulent pipe flow. The study of turbulent-friction coefficients in pipe flow has brought forth a number of effects displayed by flowing polymer solutions. Furthermore, many hydro-dynamic investigations in pipe flow have been made to elucidate the flow behavior (laminar and turbulent) of Newtonian fluids. Thus, the pipe is one of the most investigated and traditional pieces of test apparatus and one can easily compare the flow behavior of Newtonian fluids and polymer solutions under constant boundary conditions. 

While flowing through the internal, bubbles rise along the undersurface of the baffles and collide with the tongue-like bars, and are broken up into smaller bubbles as shown in Fig. 10. The difference in the direction of adjacent baffles increases the liquid turbulent intensity, which is beneficial to the breakup of large bubbles. With increasing distance from the internal, the turbulent intensity decreases and coalescence becomes dominant until a new equilibrium between the breakup and coalescence of bubbles is reached. 

Consider a fluid that is contained between parallel plates as shown in Figure 6.2. The fluid can be made to flow as follows. If the upper plate is moved, it exerts a force across the nearest plane layer of fluid. Depending on the force per unit area (F/A) some deformation is produced (parallel to the plane). If the fluid is visualized as a set of thin plane layers, the uppermost layer will move with the plate while the lowermost layer remains motionless (no-slip condition). Intermediate layers will have intermediate velocities. The flow situation just described is termed laminar flow (turbulent flow is discussed in Section 10.3.1). The distance between adjacent layers is dy and between adjacent layers, there exists a velocity difference, dV, thus a velocity gradient dV/dy. This velocity gradient arises out of a competition between the applied force per unit area (F/A) and an internal resistance provided by the fluid,... 

Internal flows of the type here being considered occur in heat exchangers, for example, where the fluid may flow through pipes or between closely spaced plates that effectively form a duct Although laminar duct flows do not occur as extensively as turbulent duct flows, they do occur in a number of important situations in which the size of the duct involved is small or in which the fluid involved has a relatively high viscosity. For example, in an oil cooler the flow is usually laminar. Conventionally, it is usual to assume that a higher heat transfer rate is achieved with turbulent flow than with laminar flow. However, when the restraints on possible solutions to a particular problem are carefully considered, it often turns out that a design that involves laminar flow is the most efficient from a heat transfer viewpoint. 

This chapter has been concerned with flows in wb ch the buoyancy forces that arise due to the temperature difference have an influence on the flow and heat transfer values despite the presence of a forced velocity. In extemai flows it was shown that the deviation of the heat transfer rate from that which would exist in purely forced convection was dependent on the ratio of the Grashof number to the square of the Reynolds number. It was also shown that in such flows the Nusselt number can often be expressed in terms of the Nusselt numbers that would exist under the same conditions in purely forced and purely free convective flows. It was also shown that in turbulent flows, the buoyancy forces can affect the turbulence structure as well as the momentum balance and that in turbulent flows the heat transfer rate can be decreased by the buoyancy forces in assisting flows whereas in laminar flows the buoyancy forces essentially always increase the heat transfer rate in assisting flow. Some consideration was also given to the effect of buoyancy forces on internal flows. 

The Chilton-Colburn analogy has been obserx ed to hold quite well in laminar or turbulent flow over plane surfaces. But this is not always the case for internal flow and flow over irregular geometries, and in such cases specific relations developed should be used. When dealing with flow over blunt bodies, it is important to note that/in these relations is the skin friction coefficient, not the total drag coefficient, which also includes tlie pressure drag. 

The modeled transport equations for z differ mainly in the diffusion and secondary source term. Launder and Spalding (1972) and Chambers and Wilcox (1977) discuss the differences and similarities in more detail. The variable, z = e is generally preferred since it does not require a secondary source, and a simple gradient diffusion hypothesis is fairly good for the diffusion (Launder and Spalding, 1974 Rodi, 1984). The turbulent Prandtl number for s has a reasonable value of 1.3, which fits the experimental data for the spread of various quantities at locations far from the walls, without modification of any constants. Because of these factors, the k-s model of turbulence has been the most extensively studied and used and is recommended as a baseline model for typical internal flows encountered by reactor engineers. 

Saffman, P.G. (1977), Results of a two-equation model for turbulent flows and development of relaxation stress model for application to staining and rotating flows. Proceedings of Project SQUID Workshop on Turbulence in Internal Flows, Hemisphere, New York, p. 191. 

Drag reduction (DR), which was discovered more than 50 yr ago, is a turbulent flow phenomenon in which frictional energy losses can be significantly reduced by the addition of a small amount of a DR additive (DRA) to a turbulent flow system) Drag reduction in internal flows is calculated using the following equation ... 

To enable simulations of two-phase bubbly flows [67] [65] the single phase k — e model has been extended by including a semi-empirical production term to take into account the additional turbulence production induced by the bubbles motion relative to the liquid (i.e., based on the idea of [128] [129]). In this approach it was assumed that the internal flow inside the dispersed phase (gas bubbles) does not affect the liquid phase turbulence. The shear work performed on the liquid by a single bubble, representing the additional turbulence production due to the bubble, was thus assumed to be equal to the product of the drag force and the relative velocity. 

If the velocity in the tubes was high enough to ensure turbulent flow, the difference in film coefficients would be reduced, but not by enough to favor internal flow. 

In a turbulent flow, turbulent pulsations with different amplitudes are superimposed on the averaged motion. These pulsations are characterized by both the velocity un and the distance (known as the scale of pulsations), at which the velocity of pulsations undergoes an appreciable change. Each of them can be associated with Reynolds number Re i = UxX/vi. For large pulsations, 2 L, where L is the characteristic linear scale of the region where viscous forces do not have a noticeable influence, while for small pulsations, they can dominate. The scale 2o for which Re o = 1, is called the internal scale of turbulence. Viscous forces are important for pulsations with X < Xq. Under the action of pulsations, bubbles can move chaotically. In [10], it is shown that the form of Do depends on the type of pulsations that cause bubbles to perform random motion ... 

In turbulent internal flows, drag reduction, often expressed as a percentage, is calculated as follows ... 

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