Eccentric annular flow

This section is concluded by noting that analogous treatments for the concentric and eccentric annular flow of Herschel-Bulkley and other viscosity... 

Bryden, M.D. and Brenner, H.A. (1996) Effect of laminar chaos on reaction and dispersion in eccentric annular flow. J. Fluid Meek, 325, 219-237. 

Eccentric Annular Flow Modeling for Highly Deviated Boreholes, Offshore, Aug. 1993... 

Levy et al. (L5) have studied the effect of eccentricity on the bum-out flux in upward vertical annular flow. Eccentricity does not affect the burn-out flux until the annular separation is about 20% or less of its concentric value. Bum-out fluxes for great eccentricities are increased about 30%, which is ascribed to poor fluid mixing pressure-drop at the same conditions is reduced. The small effect of moderate eccentricity in downward annular flow of steam-water mixtures was also reported earlier by Stein et al. (Sll) in their study of pressure-drop and critical flow. 

Before closing this chapter, we feel that it is useful to list in tabular form some isothermal pressure-flow relationships commonly used in die flow simulations. Tables 12.1 and 12.2 deal with flow relationships for the parallel-plate and circular tube channels using Newtonian (N), Power Law (P), and Ellis (E) model fluids. Table 12.3 covers concentric annular channels using Newtonian and Power Law model fluids. Table 12.4 contains volumetric flow rate-pressure drop (die characteristic) relationships only, which are arrived at by numerical solutions, for Newtonian fluid flow in eccentric annular, elliptical, equilateral, isosceles triangular, semicircular, and circular sector and conical channels. In addition, Q versus AP relationships for rectangular and square channels for Newtonian model fluids are given. Finally, Fig. 12.51 presents shape factors for Newtonian fluids flowing in various common shape channels. The shape factor Mq is based on parallel-plate pressure flow, namely,... 

Effects of Eccentricity. In practice, a perfect concentric annular duct cannot be achieved because of manufacturer tolerances, installation, and so forth. Therefore, eccentric annular ducts are frequently encountered. The velocity profile for fully developed flow in an eccentric annulus has been analyzed by Piercy et al. [105]. Based on Piercy s solution, Shah and London [1] have derived the friction factor formula, as follows ... 

Cheng and Hwang [108] analyzed the heat transfer problem in eccentric annular ducts. The Nusselt numbers for fully developed flow in eccentric annular ducts with the and thermal boundary conditions are given in Table 5.26. For eccentric annular ducts with boundary conditions different from the four described in the section entitled Four Fundamental... 

TABLE 5.26 Nusselt Number NuHi and NuH2 for Fully Developed Laminar Flow in Eccentric Annular Ducts [1,108]... 

Effects of Eccentricity. Jonsson and Sparrow [119] have conducted a careful experimental investigation of fully developed turbulent flow in smooth, eccentric annular ducts. The researchers have provided the velocity measurements graphically in terms of the wall coordinate h+ as well as the velocity-defect representation. From their results, the circumferentially averaged fully developed friction factor is correlated by a power-law relationship of the following type ... 

Few investigations have been conducted on hydrodynamically developing flow in eccentric annular ducts. Jonsson [120] has obtained experimental information on the pressure gradient in hydrodynamically developing flow and provided the hydrodynamic lengths LhyIDh for 1.8 x 104 < Re < 1.8 x 105. These are presented in Table 5.29. 

TABLE 5.29 Turbulent Flow Hydrodynamic Entrance Lengths for Smooth, Eccentric Annular Ducts [120]... 

V. K. Jonsson, and E. M. Sparrow, Experiments on Turbulent Flow Phenomena in Eccentric Annular Ducts, J. Fluid Mech., (25) 65-68,1966. 

Fang, R, R.M. Manglik, and M.A. Jog, Characteristics of laminar viscous shear-thinning fluid flows in eccentric annular channels. Journal of Non-Newtonian Fluid Mechanics, 1999. 84(1) 1—17. 

Dynamic filtration in Newtonian fluids. While borehole annular flows are rarely Newtonian (e.g., fluids such as water or air, where viscous stress is linearly proportional to the rate of strain), many drilling fluids are thin and briny, and at times, simply water. Thus, for analysis purposes, the study of Newtonian flows is more than academic. Furthermore, the mathematical simplicity that it offers sheds some insight into the parameters that influence the value of equilibrium cake thickness in the presence of erosive annular flow. Whether our annular flow is Newtonian or power law, concentric or eccentric, it is important to consider two underlying asymptotic fluid-dynamical models. The first applies during small times when borehole fluid enters the formation radially as filtrate, decelerating with time, while the second deals with large times, when invasion rates are so slow that we essentially have classical no-slip velocity boundary conditions. We will first eonsider the small time limit, assuming that the drill pipe does not rotate. 

In this section, the characteristics of laminar flow and heat transfer in concentric annular ducts are presented, and the effect of eccentricity is discussed. 

Rovinsky, J., Brauner, N. Moalem Maron, D. (1997). Analytical solution for laminar two-phase flow in a fully eccentric core-annular configuration. International journal of multiphase flow, 23, 523-543. 

More recently, HNP Mikrosysteme GmbH [14] has commercialized a type of rotary pump called micro annular gear pump. This t3q>e of pump is a positive displacement pump with an externally toothed rotor and internally toothed ring, which are assembled with a small eccentricity of their rotation axes with respect to each other. The rotation of the internal rotor forces the fluid pockets which are interlocked between two gears to flow. The pump flow rates vary from product to product, but are in a range of 1 pL/h to 1.2 1/min. Advantages of this product include accurate control of flow rate and minimum pulsation in delivery. 

This liquid flow trapping affects the quality of distribution. Hoftyzer (196 ) analyzed the dispersion from a variety of distributors e.g., a central stream, disc, ring, annular disc and an eccentric stream. This study showed that the characteristic dimensionless group for all geometries is given by... 

The measurements are done with an external mix twin-fluid nozzle in which inner diameter for the liquid is 0.7 mm and the annular outer diameter for the gas is 1.5 mm. The aspect ratio of the length and diameter of the inner liquid pipe is 4.5. This nozzle is made by Biichi GmbH and is an equipment of the laboratory spray dryer B191, which is also used for spray drying the polymer solutions. To avoid pulsation of the spray, the nozzle is fed with an eccentric screw pump. The gas flow is controlled with a mass flow controller by Bronkhorst B.V. 

The simplest flow that can exhibit chaos is two-dimensional flow. Ottino and co-workers (Chien et al., 1986 Khakhar et al., 1986 Leong and Ottino, 1989) produced chaotic mixing in simple prototypical devices, such as cavity flow, partitioned-pipe mixer (e.g., a Kenics static mixer as discussed in Section 8.5), and eccentric helical annular mixer with Newtonian fluids. Of prime interest in the area of polymer processing, of course, is the work in cavity flows. A typical cavity was constructed with the ability of movement of both top and bottom plates. Typical cavity flow, which is described in Chapter 8, corresponds to the steady movement of the top plate only. However, corotational (in the opposite direction) movement of both plates in a periodic fashion induces chaos in the cavity. Leong and Ottino (1989) used two types of movement discontinuous and continuous in a sinusoidal manner (Fig. 6.28). In the discontinuous corotational flow, the top plate first moves for a half period, then it stops for 5 s, and the cycle ends with the bottom plate moving for a half period in the opposite direction. In the continuous type of movement, both plates move sinusoidally at the same time, but with a phase difference of %/2. 

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