Kinetics Reynolds number

Contributing to f are losses for the entrance to the pipe, the three sections of straight pipe, the butterfly valve, and the 90 bend. Note that no exit loss is used because the discharged jet is outside the control volume. Instead, the V v2 term accounts for the kinetic energy of the discharging stream. The Reynolds number in the pipe is... 

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. 

This chapter is organized into two main parts. To give the reader an appreciation of real fluids, and the kinds of behaviors that it is hoped can be captured by CA models, the first part provides a mostly physical discussion of continuum fluid dynamics. The basic equations of fluid dynamics, the so-called Navier-Stokes equations, are derived, the Reynolds Number is defined and the different routes to turbulence are described. Part I also includes an important discussion of the role that conservation laws play in the kinetic theory approach to fluid dynamics, a role that will be exploited by the CA models introduced in Part II. 

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. 

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.]... 

As mentioned before in Eq. (3), the most common source of SGS phenomena is turbulence due to the Reynolds number of the flow. It is thus important to understand what the principal length and time scales in turbulent flow are, and how they depend on Reynolds number. In a CFD code, a turbulence model will provide the local values of the turbulent kinetic energy k and the turbulent dissipation rate s. These quantities, combined with the kinematic viscosity of the fluid v, define the length and time scales given in Table I. Moreover, they define the local turbulent Reynolds number ReL also given in the table. 

The relationship between the various length scales can be best understood by looking at their dependence on the turbulence Reynolds number defined in terms of the turbulent kinetic energy k, the turbulent dissipation rate e, and the kinematic viscosity v by... 

The scalar-dissipation wavenumber /cd is defined in terms of /cdi by /cd = Sc1/2kdi-Like the fraction of the turbulent kinetic energy in the dissipation range kn ((2.139), p. 54), for a fully developed scalar spectrum the fraction of scalar variance in the scalar dissipation range scales with Reynolds number as... 

Even though the Reynolds number gives some measure of turbulent phenomena, flow quantities characteristic of turbulence itself are of more direct relevance to modeling turbulent reacting systems. The turbulent kinetic energy q may be assigned a representative value <7o at a suitable reference point. The relative intensity of the turbulence is then characterized by either q()KH2 U2) or (77(7, where (/ = (2q0)m is a representative root-mean-square velocity fluctuation. Weak turbulence corresponds to U /U < 1 and intense turbulence has (77(7 of the order unity. 

The first term represents the pressure loss due to viscous drag (this is essentially the Carman-Kozeny equation) whilst the second term represents kinetic energy losses, which are significant at higher velocities (kinetic energy being proportional to velocity squared). Equation 1.43 is valid in the range 1 < Re < 2000 where the Reynolds number is defined by... 

Co304 pellets used in practice are of 4-5 mm in size. Thus, they are much larger than the diameter of wires in platinum gauzes. For this reason, in contrast to the reaction on gauzes, the reaction on Co304 pellets under atmospheric pressure is characterized by the Reynolds number much larger than 1, the Reynolds number being defined by Re = ul/v where u is the linear velocity of the stream, / is the characteristic dimension, v is the kinetic viscosity coefficient. The thickness of the diffusion layer for such pellets is... 

Note that both a small disc in the large volume of a liquid and a large disc in the small volume of a liquid will hardly produce reliable data on the dissolution kinetics of the solid in the liquid. In the former case, the small disc will not ensure suffucient convective agitation of the liquid phase. In the latter, the treshould of turbulency may happen to be exceeded. Turbulence is known to occur at Reynolds numbers in excess of 105. The Reynolds number, Re = wr2/v, r being the disc radius, is a dimensionless parameter characterising the hydrodynamic regime of flow of liquids.299 300 Reproducible results are readily obtained if the flow is laminar. 

Fluid dynamics, 31 Fluid mechanics, 45 Fluid properties, 31 drag, 49-56 gas behavior, 33-40 kinetic theory for, 32-33 macroscopic, 45-56 Reynolds number for, 45-49 viscosity, conductivity, and diffusion, 40-42... 

Both in hydrodynamics and in chemical kinetics, instability may occur due to nonlinear conditions far from equilibrium. In hydrodynamic systems, nonlinear conditions are produced by the inertia terms, such as the critical Reynolds number or Rayleigh number. However, nonequilibrium kinetic conditions may lead to a variety of structures. In chemical systems, some autocatalytic effect is required for instability. 

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