Reynolds number composite

Qt = stoichiometric composition of combustible vapor in air expressed as a volume percent Co = sonic flow discharge orifice constant, varying VvTth Reynolds number... 

Chemical engineers have traditionally approached kinetics studies with the goal of describing the behavior of reacting systems in terms of macroscopically observable quantities such as temperature, pressure, composition, and Reynolds number. This empirical approach has been very fruitful in that it has permitted chemical reactor technology to develop to a point that far surpasses the development of theoretical work in chemical kinetics. 

Comparing (5.377) with (3.105) on p. 85 in the high-Reynolds-number limit (and with e = 0), it can be seen that (5.378) is a spurious dissipation term.149 This model artifact results from the presumed form of the joint composition PDF. Indeed, in a transported PDF description of inhomogeneous scalar mixing, the scalar PDF relaxes to a continuous (Gaussian) form. Although this relaxation process cannot be represented exactly by a finite number of delta functions, Gs and M1 1 can be chosen to eliminate the spurious dissipation term in the mixture-fraction-variance transport equation.150... 

The direct quadrature method of moments (DQMOM) begins with a closed1 joint composition PDF transport equation (see Section 6.3). For simplicity, we will consider the high-Reynolds-number form of (6.30) on p. 251 with the IEM mixing model ... 

Results of experiments in annular flow showed that the over-all mass-transfer coefficient, Kq, based on the tube surface area and the liquid-film compositions, was a function of both gas and liquid superficial Reynolds number, but depended much more strongly on that of the liquid. When plotted as jo factors, that is. 

For top spin at higher rotation rates, Sh first decreases and then increases with increasing rotational Reynolds number, Qc/ /v, at constant translational Reynolds number, Re. The overall change in Sh is generally relatively small except for very rapid rotation. Analyses have been carried out (F4, PI 3) for spheres and cylinders with Re 1 and Pe = ReQ Sc 1 in simple shear. At low Re there are closed streamlines around the body at high Pe these streamlines are also lines of constant composition so that Sh (or Nu) becomes independent of Pe. For a sphere, Sh = 8.9 for Pec oo (PI 3). More complex velocity fields have also been considered at low Re. ... 

Fig. 6.17 Correlation of the Nusselt number with a composite Reynolds number in a finite gap L with a specified inlet velocity U, and a surface rotation rate f2. The Prandtl number is 0.7. The composite Reynolds number has contributions from the inlet Reynolds number Rej/ = UL/v and the rotation Reynolds number Rejj = Q.L /v. The composite Reynolds number is Rec = -/(Ref/)2 + (Re /4.186)2. The square markers represent simulations using many combinations of Rej/ and Ren...

The flow considered is in a 12-inch steel line at a Reynolds number of 6000. With e = 0.00015, Round s equation gives / = 0.0353. The line composition and values of fittings resistances are ... 

Meanwhile, if we take some mixture at atmospheric pressure in a tube of average diameter (15-25 mm) and decrease the pressure without changing the diameter or composition, it is apparently possible to achieve the limit in a number of cases without observing spin 11 the decrease in pressure means an increase in the criterion Dr /d and a decrease in the Reynolds number. In contrast, in the case of a mixture in which spin is observed under ordinary conditions, increasing the diameter does not lead to disappearance of the spin in spite of the decrease in Dr /d instead of disappearance of the spin in wide tubes we observe the appearance of several spirals located like... 

The reactor is modeled by three partial differential equations component balances on A and B [Eqs. (6.1) and (6.2)] and an energy balance [Eq. (6.3) for an adiabatic reactor or Eq. (6.4) for a cooled reactor]. The overall heat transfer coefficient U in the cooled reactor in Eq. (6.4) is calculated by Eq. (6.5) and is a function of Reynolds number Re, Eq. (6.6). Equation (6.7) is used for pressure drop in the reactor using the friction factor /given in Eq. (6.8). The dynamics of the momentum balance in the reactor are neglected because they are much faster than the composition and temperature dynamics. A constant... 

Figure 11.3 Partial fluxes of isoamyl alcohol, ethyl acetate, isoamyl acetate and ethyl hexanoate as a function of their feed crossflow velocity (bottom axis) and Reynolds number (top axis) in a singlechannel module, using a POMS-PEI composite membrane. Notice that external mass-transfer limitations are not fully overcome when soluteswith a high affinity towardsthe membrane are processed (Adapted from Ref. 32.)...

EOF has been applied as a pumping or mixing mechanism in microreactors (Fletcher et al., 2002). Mixing concepts include the introduction of two (or more, see Kohlheyer et al., 2005) parallel streams from a T- of Y-junction, where mixing at the low Reynolds numbers achieved occurs principally by interdiffusion of the two streams. This is a relatively slow process which may take tens of seconds to complete. Faster mixing can be achieved by injection of a sample of a specific composition via, for example, a double T-injector into a stream of liquid with a different composition. 

A turbulent jet diffusion flame was investigated. The apparatus and experimental procedure are described in detail in the article by Rambach et al. (11). The fuel jet had the following properties diameter of 1.6 mm, Reynolds number of 4400, and a fuel composition of 37% methane and 63% hydrogen. 

Satisfactory agreement with experimental data was obtained for Cu-SiC composite deposition in a channel flow. Because of the limited range of experimental data it is not clear if the model is also able to describe important features, like the peak in the particle composite content versus current density curve. In comparison to Valdes model, the particle mass transfer is poorly taken into account by using the Reynolds number. The particle-electrode interaction on the other hand is treated much more adequately by the balance between particle adsorption (Co, Sx and Dm) and particle ejection due to hydrodynamics (Gq). For example, a small value for d is obtained, indicating that, in accordance with experimental data (Section III), electro-osmotic interactions between particles and the cathode (Dm) are negligible. 

In using this friction factor for a tubular reactor, the Reynolds number is evaluated at Borne estimated average condition, and then the corresponding friction factor is used for the whole bed. In calculating the axial pressure profile, the average composition and temperature in a cross section are used to estimate the density of the fluid, and this density is used with the average superficial mass velocity to estimate the axial derivative of pressure. 

The simulation program AIOLOS is developed for the numerical calculation of three-dimensional, stationary, turbulent and reacting flows in pulverised coal-fired utility boilers. AIOLOS contains submodels treating fluid flow, turbulence, combustion and heat transfer. In these submodels equations for calculating the conservation of mass, momentum and energy are solved, presupposing high Reynolds-numbers and steady-state flow conditions. It is assumed that the flow field is weakly compressible which means that the density depends only on temperature and fluid composition but not on pressure. 

The gas flow through tubular reactors is of particular importance because the composition at any point is influenced by the linear velocity of the gas, the size of the reactor and the size of the catalyst particles. When gas flows through a pipe at low linear velocity (low Reynolds number), the radial velocity is not uniform. As the linear velocity increases, turbulence increases and the velocity profile approaches what is called plug flow. However, in a packed bed, plug flow can never be completely attained because of the high voidage near the reactor wall. 

Several factors can affect this enhanced mass transfer. First, as Debenedetti and Reid ( pointed out, the very low kinematic viscosities in conjunction with very high buoyant forces serve to enhance natural convection at the same Reynolds number. This is accentuated by large density differences that can occur as naphthalene dissolves in the C02 It is possible to have very large, negative partial molar volumes (i.e., -2000 cc/mole) for a solute at conditions near the critical point (Eckert et al., (23)) which causes the fluid density to depend strongly on composition. At 35 0 and 100 atm, naphthalene s partial molar volume at infinite dilution is approximately -300 cc/mol. This can cause a significantly higher fluid... 

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