Reynolds number chemical

Shekunov, B. Yu., Baldyga, J. and York, P., 2001. Particle formation by mixing with supercritical antisolvent at high Reynolds numbers. Chemical Engineering Science, 56(7), 2421-2433. 

Nienow, A.W., Kendall, A., Moore, LPT., Ozcan-Taskin, GJ4., andBadham, R.S. (1995), The characteristics of aerated 12- and 18-blade Rushton turbines at transitional Reynolds numbers, Chemical Engineering Science, 50(4) 593-599. 

Cross, M.M. (1965). Rheology of non-Newtonian flow equation for pseudoplastic systems. Journal of Colloid Science, Vol.20, pp. 417-437 de Waele, A. (1923). Oil Color, Chemical Association Journal, Vol.6, pp. 23-88 Edwards, M.F., Jadallah, M.S.M. and Smith, R. (1985). Head losses in pipe fittings at low Reynolds numbers. Chemical Engineering Research and Design, Vol.63, (January 1985) pp. 43-50... 

FIG. 20-38 Newton number as a Function of Reynolds number for a horizontal stirred bead mill, with fluid alone and with various filling fractious of 1-mm glass beads [Weit and Schwedes, Chemical Engineering and Technology, 10(6), 398 04 (1987)]. (N = power input, W d = stirrer disk diameter, m n = stirring speed, 1/s i = liquid viscosity, Pa-s Qj = feed rate, mVs.)... 

The value of tire heat transfer coefficient of die gas is dependent on die rate of flow of the gas, and on whether the gas is in streamline or turbulent flow. This factor depends on the flow rate of tire gas and on physical properties of the gas, namely the density and viscosity. In the application of models of chemical reactors in which gas-solid reactions are caiTied out, it is useful to define a dimensionless number criterion which can be used to determine the state of flow of the gas no matter what the physical dimensions of the reactor and its solid content. Such a criterion which is used is the Reynolds number of the gas. For example, the characteristic length in tire definition of this number when a gas is flowing along a mbe is the diameter of the tube. The value of the Reynolds number when the gas is in streamline, or linear flow, is less than about 2000, and above this number the gas is in mrbulent flow. For the flow... 

Damkdhler (1936) studied the above subjects with the help of dimensional analysis. He concluded from the differential equations, describing chemical reactions in a flow system, that four dimensionless numbers can be derived as criteria for similarity. These four and the Reynolds number are needed to characterize reacting flow systems. He realized that scale-up on this basis can only be achieved by giving up complete similarity. The recognition that these basic dimensionless numbers have general and wider applicability came only in the 1960s. The Damkdhler numbers will be used for the basis of discussion of the subject presented here as follows ... 

This section examines and reviews some of the basic principles diat engineers and sciendsts employ in performing design calculations mid predicting die performance of plant equipment. Topics include die tlicrmochemistry, chemical reacdon equilibrimii, chemical kinedcs, die ideal gas law, pardal pressure, pliase equilibrimii, and die Reynolds Number. These basic principles will assist die reader in acquiring a better miderslmidiiig of some of the material diat appears later in die book. 

Several basic principles that engineers and scientists employ in performing design calculations and predicting Uie performance of plant equipment includes Uieniiochemistiy, chemical reaction equilibrimii, chemical kinetics, Uie ideal gas law, partial pressure, pliase equilibrium, and Uie Reynolds Number. 

Owing to the exponential increase in the computational power, today s DNS reaches fully turbulent Reynolds numbers and can use detailed chemical schemes, once affordable only for one-dimensional laminar flames computations. 

Fluid flow and reaction engineering problems represent a rich spectrum of examples of multiple and disparate scales. In chemical kinetics such problems involve high values of Thiele modulus (diffusion-reaction problems), Damkohler and Peclet numbers (diffusion-convection-reaction problems). For fluid flow problems a large value of the Mach number, which represents the ratio of flow velocity to the speed of sound, indicates the possibility of shock waves a large value of the Reynolds number causes boundary layers to be formed near solid walls and a large value of the Prandtl number gives rise to thermal boundary layers. Evidently, the inherently disparate scales for fluid flow, heat transfer and chemical reaction are responsible for the presence of thin regions or "fronts in the solution. 

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. 

Several correlating equations for the friction factor have been proposed for both the laminar and turbulent flow regimes, and plots of fM (or functions thereof) versus Reynolds number are frequently presented in standard fluid flow or chemical engineering handbooks (e.g., 96, 97). Perhaps the most useful of the correlations is that represented by the Ergun equation (98)... 

Correlation of average Peclet number with Reynolds number and the ratio of particle to tube diameter (DP/Dr). ([From Chemical Engineering Kinetics by J. M. Smith. Copyright 1970. Used with permission of McGraw-Hill Book Company.]... 

Heat transfer in packed beds. Effective thermal conductivity as a function of Reynolds number. Curve 1 Coberly and Marshall. Curve 2 Campbell and Huntington. Curve 3 Calderbank and Pogorski. Curve 4 Kwong and Smith. Curve 5 Kunii and Smith. (From G. F. Froment, Chemical Reaction Engineering, Adv. Chem. Ser., 109, 1970.)... 

In chemical reacting systems, the Reynolds number of the flow is not the only source of computational challenges. Indeed, even for laminar reacting flows the chemical source term can be extremely stiff and tightly coupled to the diffusive transport terms. Averaging, as done above to treat turbulent flows, does not... 

The first term on the right-hand side of this expression is the molecular transport term that scales as Sc Re 1. Thus, at high Reynolds numbers,26 it can be neglected. The two new unclosed terms in (3.88) are the scalar flux (u.ja), and the mean chemical source term (Sa(chemical reacting flows, the modeling of (Sa(0)) is of greatest concern, and we discuss this aspect in detail in Chapter 5. 

Based on these data, particle-liquid Reynolds numbers were calculated to range from Re = 25 (50 rpm) to Re = 90 (150 rpm) for coarse grade particles with a median diameter of 236 pm. In contrast, Reynolds numbers for a batch of micronized powder of the same chemical entity with a median diameter of 3 pm were calculated to be significantly lower (Re < 1), indicating less sensitivity towards convective hydrodynamics [(10), Chapter 12.3.8]. Based on the aforementioned considerations for spheres, bulk Reynolds numbers of about Re > 50 appear to be sufficient to produce the laminar-turbulent transition around a rough drug particle of coarse grade dimensions. 

For a better understanding of this type of flame occurrence and for more explicit conditions that define each of these turbulent flame types, it is necessary to introduce the flame stretch concept. This will be done shortly, at which time the regions will be more clearly defined with respect to chemical and flow rates with a graph that relates the nondimensional turbulent intensity, Reynolds numbers, Damkohler number, and characteristic lengths /. 

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