Large-scale fluid flow

In most cases one is interested in fluid flows at scales that are much larger than the distance between the molecules. The value of the molecular mean free path in air at room temperature and 1 atm of pressure is A = 6.7 x 10-8 m and in water A = 2.5 x 10-10 m. When the Knudsen number - defined as the ratio of the molecular mean-free-path to a characteristic length scale of the flow (e.g. the size of the smallest eddies) - is small, the fluid can be described as a continuous medium in motion. In this continuum approximation the flow can be characterized by the velocity field v(x, t) representing the instantaneous velocity of infinitesimal fluid elements at time t and at position x. Fluid elements represent small volumes of fluid that are much smaller than the smallest characteristic scale of the flow, but sufficiently large to contain a large number of molecules so that a well defined local velocity exists and molecular fluctuations can be neglected. 

Scale-Up Principles. Key factors affecting scale-up of reactor performance are nature of reaction zones, specific reaction rates, and mass- and heat-transport rates to and from reaction sites. Where considerable uncertainties exist or large quantities of products are needed for market evaluations, intermediate-sized demonstration units between pilot and industrial plants are usehil. Matching overall fluid flow characteristics within the reactor might determine the operative criteria. Ideally, the smaller reactor acts as a volume segment of the larger one. Elow distributions are not markedly influenced by... 

Traditionally, this process has been utilized primarily for simple soap bars because it tends to be time-consuming and thus somewhat limited for large-scale bar production. However, advances have been reported in automating this approach (14). Furthermore, the process requires fluid cmtcher compositions for flow into the molds. This typically requires the formulation to contain either a high level of solvents, including water, glycerol, and alcohol, and be at elevated temperatures (>80° C) when poured into the frames. Despite these limitations, it has proven to be the preferred route to producing certain specialty products, for example, transparent bars. 

The ROTOBERTY internal recycle laboratory reactor was designed to produce experimental results that can be used for developing reaction kinetics and to test catalysts. These results are valid at the conditions of large-scale plant operations. Since internal flow rates contacting the catalyst are known, heat and mass transfer rates can be calculated between the catalyst and the recycling fluid. With these known, their influence on catalyst performance can be evaluated in the experiments as well as in production units. Operating conditions, some construction features, and performance characteristics are given next. 

Even if satisfactory equations of state and constitutive equations can be developed for complex fluids, large-scale computation will still be required to predict flow fields and stress distributions in complex fluids in vessels with complicated geometries. A major obstacle is that even simple equations of state that have been proposed for fluids do not always converge to a solution. It is not known whether this difficulty stems from the oversimplified nature of the equatiorrs, from problems with ntrmerical mathematics, or from the absence of a lamirrar steady-state solution to the eqrratiorrs. 

P. Clavin and F.A. Williams. Effects of molecular diffusion and of thermal expansion on the structure and dynamics of premixed flames in turbulent flows of large scale and low intensity. Journal of Fluid Mechanics, 116 251-282,1982. 

For most medium- and large-scale micromanifold structures, where one passage feeds multiple parallel channels, flow traverses through turbulent and transition flows in the micromanifold region. This fluid in turbulent to transition flow also turns in the micromanifold region as it drops flow into parallel microchannels, which are primarily in the laminar flow regime. 

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. 

A gas condenses to a liquid if it is cooled sufficiently. Condensation occurs when the average kinetic energy of motion of molecules falls below the value needed for the molecules to move about independently. Thus, the molecules in a liquid are confined to a specific volume by intermolecular forces of attraction. Although they cannot readily escape, liquid molecules remain free to move about within the liquid phase, hi this behavior, liquid molecules behave like the molecules of a gas. The large-scale consequences of the molecular-level properties are apparent. Like gases, liquids are fluid, so they flow easily from place to place. Unlike gases, however, liquids are compact, so they cannot expand or contract significantly. 

A physical model to predict the large-scale application for MEOR has been developed. This model simulates both the radial flow of fluids toward the wellbore and bacteria transport through porous media [1235]. 

Kaper, T. J., and Wiggins, S., An analytical study of transport in Stokes flows exhibiting large scale chaos in the eccentric journal bearing. J. Fluid Mech. 253, 211-243 (1993). 

Injections and infusion fluids must be manufactured in a manner that will minimize or eliminate extraneous particulate matter. Parenteral solutions are generally filtered through 0.22 pm membrane filters to achieve sterility and remove particulate matter. Prefiltration through a coarser filter is often necessary to maintain adequate flow rates, or to prevent clogging of the filters during large-scale manufacturing. A talc or carbon filtration aid (or other filter aids) may also be necessary. If talc is used, it should be pretreated with a dilute acid solution to remove surface alkali and metals. 

Zhang K., W.Y.S., et al. Parallel computing techniques for large-scale reservoir simulation of multi-component and multi-phase fluid flow. In Proceeding of the 2001 SPE reservoir simulation synposium, Texas.2001 SPE. 

On the basis of different assumptions about the nature of the fluid and solid flow within each phase and between phases as well as about the extent of mixing within each phase, it is possible to develop many different mathematical models of the two phase type. Pyle (119), Rowe (120), and Grace (121) have critically reviewed models of these types. Treatment of these models is clearly beyond the scope of this text. In many cases insufficient data exist to provide critical tests of model validity. This situation is especially true of large scale reactors that are the systems of greatest interest from industry s point of view. The student should understand, however, that there is an ongoing effort to develop mathematical models of fluidized bed reactors that will be useful for design purposes. Our current... 

CFD models for turbulent multiphase reacting flows do not solve the laminar two-fluid balances (Eqs. 164 and 165) directly. First, Reynolds averaging is applied to eliminate the large-scale turbulent fluctuations. Using Eq. (164) as an example, we can apply Reynolds averaging to find (with pg constant)... 

A laminar-flow reactor (LFR) is rarely used for kinetic studies, since it involves a flow pattern that is relatively difficult to attain experimentally. However, the model based on laminar flow, a type of tubular flow, may be useful in certain situations, both in the laboratory and on a large scale, in which flow approaches this extreme (at low Re). Such a situation would involve low fluid flow rate, small tube size, and high fluid viscosity, either separately or in combination, as, for example, in the extrusion of high-molecular-weight polymers. Nevertheless, we consider the general features of an LFR at this stage for comparison with features of the other models introduced above. We defer more detailed discussion, including applications of the material balance, to Chapter 16. 

---