Annulus Reynolds number

Annular orifices can also be used to advantage for gas metering when there is a possibility of entrained liquids or solids and for liquid metering with entrained gas present in small concentrations. Coefficient K was found by Bell and Bergelin [Trans. Am. Soc. Mech. Eng., 79, 593-601 (1957)] to range from about 0.63 to 0.67 for annulus Reynolds numbers in the range of 100 to 20,000 respectively for values of 2L/(D — d) less than 1 where L = thickness of orifice at outer edge, D = inside pipe diameter, and d = diameter of orifice disk. The annulus Reynolds number is defined as... 

Equation (11) is expected to apply even for H < (Grbravcic et al., 1976) and for annulus Reynolds number one or two orders of magnitude larger than the upper limit of Darcy s law (Epstein et al., 1978). 

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. 

Calculate Reynolds number for the fluid (1) inside drill pipe, (2) inside drill collars, (3) in drill collar annulus, and (4) in drill pipe annulus. 

Optimal hydraulics is the proper balance of hydraulic parameters (flowrate and equivalent nozzle size) that satisfy chosen criteria of optimization. Hydraulic quantities used to characterize jet bit performance include hydraulic horsepower, jet impact force, jet velocity, Reynolds number at the nozzle, generalized drilling rate or cost per foot drilled. While designing the hydraulic program the limitations due to cuttings transport in the annulus and pump performance characteristics must be included. 

In order to predict Lhe transition point from stable streamline to stable turbulent flow, it is necessary to define a modified Reynolds number, though it is not clear that the same sharp transition in flow regime always occurs. Particular attention will be paid to flow in pipes of circular cross-section, but the methods are applicable to other geometries (annuli, between flat plates, and so on) as in the case of Newtonian fluids, and the methods described earlier for flow between plates, through an annulus or down a surface can be adapted to take account of non-Newtonian characteristics of the fluid. 

The coefficient CD depends on the shape of the float and the Reynolds number (based on the velocity in the annulus and the mean hydraulic diameter of the annulus) for the... 

The film coefficients for the water jacket were in the range 635-1170 W/nr K for water rates of l. 44—9.23 1/s, respectively. It may be noted that 7.58 1/s corresponds to a vertical velocity of only 0.061 m/s and to a Reynolds number in the annulus of 5350. The thermal resistance of the wall of the pan was important, since with the sulphonator it accounted for 13 per cent of the total resistance at 32.3 K and 31 per cent at 403 K. The change in viscosity with temperature is important when considering these processes, since, for example, the viscosity of the sulphonation liquors ranged from 340 mN s/rn2 al 323 K to 22 mN s/m2 at 40.3 K. 

Based on a plot of Re/(C), showing the universal relationship between the annulus geometry and the Reynolds-number-friction-factor product, explain the results in physical terms. 

In Fig. 15.2 the average relative flame position in the TC apparatus, measured from the top of the TC annulus, is plotted vs. time (measured from the time of ignition) for the equivalence ratio

average Reynolds number Reat e = 7500. The square (diamond) symbols represent the location of the left (right) side of the annular flame, relative to the fixed location of the observer,... 

Rothfus, Monrad, Sikchi, and Heideger [Ind. Eng. Chem., 47, 913 (1955)] report that the friction factor for the outer wall bears the same relation to the Refolds number for the outer portion of the annular stream 2(ri - A )Vp/ra 4 as the friction factor for circular tubes does to the Reynolds number for circular tubes, where ra is the radius of the outer tube and is the position of maximum velocity in the annulus, estimated from... 

The change in static pressure of the gas passing through the annulus at low particle Reynolds number should be in accordance with Darcy s law since the annular solids are essentially in the packed-bed condition. Therefore... 

The mixing characteristics of the fluid in a spouted bed of solids have not been studied. Since the particle Reynolds numbers involved in both the annulus and the spout are relatively high, the extent of any axial mixing experienced by the fluid in either channel is likely to be small, especially for the more common case of gas spouting. For the bed as a whole, however, it could be significant due to the very uneven velocity distribution as between spout and annulus, which would cause an effect akin to Taylor diffusion. 

Modeling Concepts We shall model the axial flow in the annular region as being laminar. This assumption is reasonable because a typical Reynolds number for flow in a LPCVD reactor is less than 1. As the reactant gases flow through the annulus, the reactants diffuse from the annulus radially inward between the wafers to eoat them. 

Using the geometric parameter method, estimate the pressure gradient required to sustain the flow in each of these conduits, all of which have the same hydraulic radius as the concentric annulus referred to in (iii). Also, calculate the Reynolds number for each case to test whether the flow is streamline. 

Flow through resistive porous elements has been studied by many in the particle filtration community to determine basic relations and empirical correlations (Ergun, 1952 Jones and Krier, 1982 Laws and Livesey, 1978 Munson, 1988 Brundrett, 1993 Olbricht, 1996 Sodre and Parise, 1997 Wakeland and Keolian, 2003 Wu et al 2005 Valli et al 2009). A detailed and rigorous review of previous analytical and numerical solutions in porous pipe, annulus, and channel flow is reserved in Appendix F only highlights are presented here. Porous channel flow is classified by the size of flow within the channel (laminar or turbulent), the number of porous walls (one or two), the size (small, large, arbitrary), and nature (uniform or variable) of injection into the porous element, the type of transverse and axial boundary conditions at the porous surface (suction or injection), and whether or not there is heat transfer and/or electrical or magnetic component, where the injection Reynolds number is defined as ... 

Moussy, Y., Snider, A.D., 2011. Flow within a pipe annulus with injection and suction through a porous waR with high wall Reynolds numbers. ASME J. Fluids Eng. 133, 014501. 

ReA and Res- Reynold s Number - criteria for annulus and fountain, and H/D-height simplex of the added active coal bed versus column diameter. 

Use the Reynolds analogy to derive an expression for the Nusselt number for fully developed turbulent flow in an annulus in which the inner wall is heated to a uniform temperature and the outer wall is adiabatic. Assume that the friction factor can be derived by introducing the hydraulic diameter concept. 

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