Noncircular Channels

Noncircular Channels Calciilation of fric tional pressure drop in noncircular channels depends on whether the flow is laminar or tumu-lent, and on whether the channel is full or open. For turbulent flow in ducts running full, the hydraulic diameter shoiild be substituted for D in the friction factor and Reynolds number definitions, Eqs. (6-32) and (6-33). The hydraiilic diameter is defined as four times the channel cross-sectional area divided by the wetted perimeter. For example, the hydraiilic diameter for a circiilar pipe is = D, for an annulus of inner diameter d and outer diameter D, = D — d, for a rectangiilar duct of sides 7, h, Dij = ah/[2(a + h)].T ie hydraulic radius Rii is defined as one-fourth of the hydraiilic diameter. 

Sadatomi Y, Sato Y, Saruwatari S (1982) Two-phase flow in vertical noncircular channels. Int J Multiphase Flow 8 641-655... 

Perhaps the simplest classification of flow regimes is on the basis of the superficial Reynolds number of each phase. Such a Reynolds number is expressed on the basis of the tube diameter (or an apparent hydraulic radius for noncircular channels), the gas or liquid superficial mass-velocity, and the gas or liquid viscosity. At least four types of flow are then possible, namely liquid in apparent viscous or turbulent flow combined with gas in apparent viscous or turbulent flow. The critical Reynolds number would seem to be a rather uncertain quantity with this definition. In usage, a value of 2000 has been suggested (L6) and widely adopted for this purpose. Other workers (N4, S5) have found that superficial liquid Reynolds numbers of 8000 are required to give turbulent behavior in horizontal or vertical bubble, plug, slug or froth flow. Therefore, although this classification based on superficial Reynolds number is widely used... 

The critical Reynolds number for transition from laminar to turbulent flow in noncircular channels varies with channel shape. In rectangular ducts, 1,900 < Rec < 2,800 (Hanks and Ruo, Ind. Eng. Chem. Fundam., 5, 558-561 [1966]). In triangular ducts, 1,600 < Rec < 1,800 (Cope and Hanks, Ind. Eng. Chem. Fundam., 11, 106-117 [1972] Bandopadhayay and Hinwood, J. Fluid Mech., 59, 775-783 [1973]). 

The same statement can be made about inelastic non-Newtonian fluids, such as the Power Law fluid, from a mathematical solution point of view. In reality, most non-Newtonian fluids are viscoelastic and exhibit normal stresses. For fluids such as those (i.e., fluids described by constitutive equations that predict normal stresses for viscometric flows), theoretical analyses have shown that secondary flows are created inside channels of nonuniform cross section (78,79). Specifically it can be shown that a zero second normal stress difference is a necessary (but not sufficient) condition to ensure the absence of secondary flow (79). Of course, the analyses of flows in noncircular channels in terms of constitutive equations—which, strictly speaking, hold only for viscometric flows—are expected to yield qualitative results only. Experimentally low Reynolds number flows in noncircular channels have not been investigated extensively. In particular, only a few studies have been conducted with fluids exhibiting normal stresses (80,81). Secondary flows, such as vortices in rectangular channels, have been observed using dyes in dilute aqueous solutions of polyacrylamide. Interestingly, these secondary flow vortices (if they exist) seem to have very little effect on the flow rate. 

Rehme, K., A Simple Method of Predicting Friction Factors of Turbulent Row in Noncircular Channels , Int, J. Heat Mass Transfer, Vol. 16, pp. 933-950, 1973. 

Although the hydraulic-diameter concept frequently yields satisfactory relations for fluid friction and heat transfer in many practical problems, there are some notable exceptions where the method does not work. Some of the problems involved in heat transfer in noncircular channels have been summarized by Irvine [20] and Knudsen and Katz [9]. The interested reader should consult these discussions for additional information. 

Low pressure drop. Because of the shape of the void space through which the fluid flows, i.e., noncircular channels that are straight in the direction of the flow, the pressure drop across a BSR is comparable to that of a monolithic reactor. This feature is most profitable in processes operating at low pressure and high space velocities, such as catalytic removal of NO, SO, or volatile organic compounds (VOCs) from flue gases. The pressure drop can be manipulated by means of the voidage (see next item). 

Equation (7) is based on the universal flow profile for turbulent flow. Values of A and G were obtained from the theoretical analysis of the laminar and turbulent pressure drop characteristics of assemblies of circular channels with different diameters. These values also proved to give accurate friction factor predictions for noncircular channels, such as symmetric and asymmetric annuli and rod bundles. 

Kuznetsov, V.V., Shamirzaev, A.S., (1999), Two-phase flow pattern and boiling heat transfer in noncircular channel with a small gap, Proc. of Two-Phase Flow Modeling and Experimentation, Pisa, V.l, pp. 249-253. 

Development of additional models for pressure drop in noncircular channels, and for heat transfer coefficients and transition criteria based on nondimensional parameters is underway. This integrated approach using flow visualization, pressure drop and heat transfer measurements, and analytical modeling, is yielding a comprehensive understanding of condensation in microchannels. 

Diameter, m or ft D, of impeller or scraper D, outside diameter of coil tubing equivalent diameter of noncircular channel D,-, inside diameter of tube of outside of tube Dp, of particle D, inside diameter of exchanger shell D of agitated vessel logarithmic mean of inside and outside diameters of tube Tube arrangement factor for crossflow [Eq. (15.6)]... 

In contrast to circular channels, there is less information available on Taylor flow in noncircular channels and most of the information that is available refers to square channels. In square channels at Ca < 0.1, the bubble is not axisym-metric and flattens out against the tube walls leaving liquid regions in the comers which are joined by thin flat films at the sides of the channels. As Ca increases, the bubble becomes axi-symmetric, and for high values of Ca, the bubble radius reaches an asymptotic minimum value, approximately equal to 0.68 times the square channel half-width [15]. A stagnation ring forms... 

Investigations on Taylor flow in noncircular channels originated from flows in porous materials, for instance, in enhanced oil recovery. They are also relevant to microstructured reactors and to the many monolithic systems which in many cases have noncircular reaction channels. 

It is possible to demonstrate analytically [7] that the link between the average Nusselt and Brinkman numbers can be expressed by means of a general relationship for circular and noncircular channels ... 

It is considered that for pipe flows, the deposit velocity is a function of the pipe diameter raised to the power of 0.4 for noncircular channels and the friction loss gradient is a function of the ratio V lDu. 

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