Flow models study

Cold flow studies have several advantages. Operation at ambient temperature allows construction of the experimental units with transparent plastic material that provides full visibility of the unit during operation. In addition, the experimental unit is much easier to instrument because of operating conditions less severe than those of a hot model. The cold model can also be constructed at a lower cost in a shorter time and requires less manpower to operate. Larger experimental units, closer to commercial size, can thus be constructed at a reasonable cost and within an affordable time frame. If the simulation criteria are known, the results of cold flow model studies can then be combined with the kinetic models and the intrinsic rate equations generated from the bench-scale hot models to construct a realistic mathematical model for scale-up. 

Fig. 17. Flow model study for a three-stage fluidized leacher—comparison of computed particle size (solid lines) with experimental results (open circles). [After Kwauk and Wang, 1981.]...

ICAC Publication No. EP 7. Gas Flow Model Studies Institute of Clean Air Companies, 1993. Schwab, M.J. Johnson, R.W. Numerical design method for improving gas distribution within electrostatic precipitators. Proceedings of the American Power Conference 56th Annual Meeting, Chicago, U.S.A., April 25-27, 1994. 

A study of the influence of two-dimensional nonuniformities in inlet fluid temperatures [138] indicates that there is a smaller reduction in the exchanger effectiveness for the nonuniform inlet temperature than that for the nonuniform inlet flow. For various nonuniform flow models studied, the inlet nonuniform flow case showed a decrease in the effectiveness of up to 20 percent whereas, for the nonuniform inlet temperature case, a decrease in the effectiveness of up to 12 percent occurred with even an increase in the effectiveness for some cases of the nonuniform inlet temperature. 

Rhizosphere modeling remains difficult and complex, as it combines technical know-how from several fields such as plant physiology, soil physics, soil chemistry and mathematics. Mechanistic rhizosphere models do not always operate with adequate precision (Rengel, 1993 Darrah and Roose, 2001). Two main fields of application of mechanistic rhizosphere models are carbon flow in the rhizosphere and nutrient uptake by plants. While carbon flow models study the exudation of carbon compounds into the soil and its consequences on the microbial population, uptake models focus on the transport and uptake of ions by roots. In the following sections, we will concentrate on uptake models on the single root scale. 

Consider coupling with fluid flow modelling studies to optimize electrolyte flow patterns... 

A well-designed wet stack system has minimum droplet carry-over from the mist eliminators, uses sloped duct floors, has properly located and amply sized liquid collectors and drains in the outlet ductwork and stack, limits the gas velocity particularly in the stack, and has smooth outlet ductwork and stack walls to allow entrained liquid collected on the walls to flow to the drains. Most of the entrained liquid is removed in the outlet ductwork. Usually, reduced-scale flow model studies are performed to evaluate the best locations and sizes for liquid collectors and drains. EPRI s Entrainment in Wet Stacks (Maioti and Doie, 1982) provide some guidelines which aid in evaluating and solving wet stack entraimnent problems. 

Mueller M A, Yetter R A and Dryer F L 1999 Flow reactor studies and kinetic modelling of the... 

The engineer is offered a large variety of flow-modeling methods, whose complexity ranges from simple order-of-magnitude analysis to direct numerical simulation. Up to now, the methods of choice have ordinarily been experimental and semi-theoretical, such as cold flow simulations and tracer studies. 

This involves knowledge of chemistry, by the factors distinguishing the micro-kinetics of chemical reactions and macro-kinetics used to describe the physical transport phenomena. The complexity of the chemical system and insufficient knowledge of the details requires that reactions are lumped, and kinetics expressed with the aid of empirical rate constants. Physical effects in chemical reactors are difficult to eliminate from the chemical rate processes. Non-uniformities in the velocity, and temperature profiles, with interphase, intraparticle heat, and mass transfer tend to distort the kinetic data. These make the analyses and scale-up of a reactor more difficult. Reaction rate data obtained from laboratory studies without a proper account of the physical effects can produce erroneous rate expressions. Here, chemical reactor flow models using matliematical expressions show how physical... 

M. Kroger, R. Makhloufi. Wormlike micelles under shear flow A microscopic model studied by nonequihbrium molecular dynamics computer simulations. Phys Rev E 55 2531-2536, 1996. 

We shall start out with elementary general topological considerations of flow by studying network flow. We shall follow this by a variety of models from operations research that illustrate analytical methods and problems. No illustrations of statistical methods will be given here because statistics, a fundamental tool of science, is abundantly discussed in the literature of science. 

The quasi-one-dimensional model of laminar flow in a heated capillary is presented. In the frame of this model the effect of channel size, initial temperature of the working fluid, wall heat flux and gravity on two-phase capillary flow is studied. It is shown that hydrodynamical and thermal characteristics of laminar flow in a heated capillary are determined by the physical properties of the liquid and its vapor, as well as the heat flux on the wall. 

Consider the scaleup of a small, tubular reactor in which diffusion of both mass and heat is important. As a practical matter, the same fluid, the same inlet temperature, and the same mean residence time will be used in the small and large reactors. Substitute fluids and cold-flow models are sometimes used to study the fluid mechanics of a reactor, but not the kinetics of the reaction. 

Many results with model systems and also biological particle systems indicate that the stress in technical bioreactors, in which turbulent flow conditions exist, could not be simulated by model studies in small bioreactors, where no fully turbulent flow exists, and especially with laminar flow devices such as viscosimeters, tubes or channels. 

Airlift loop reactor (ALR), basically a specially structured bubble column, has been widely used in chemical industry, biotechnology and environmental protection, due to its high efficiency in mixing, mass transfer, heat transfer etc [1]. In these processes, multiple reactions are commonly involved, in addition to their complicated aspects of mixing, mass transfer, and heat transfer. The interaction of all these obviously affects selectivity of the desired products [2]. It is, therefore, essential to develop efficient computational flow models to reveal more about such a complicated process and to facilitate design and scale up tasks of the reactor. However, in the past decades, most involved studies were usually carried out in air-water system and the assumed reactor constructions were oversimplified which kept itself far away from the real industrial conditions [3] [4]. 

Compared with the use of arbitrary grid interfaces in combination with reduced-order flow models, the porous medium approach allows one to deal with an even larger multitude of micro channels. Furthermore, for comparatively simple geometries with only a limited number of channels, it represents a simple way to provide qualitative estimates of the flow distribution. However, as a coarse-grained description it does not reach the level of accuracy as reduced-order models. Compared with the macromodel approach as propagated by Commenge et al, the porous medium approach has a broader scope of applicability and can also be applied when recirculation zones appear in the flow distribution chamber. However, the macromodel approach is computationally less expensive and can ideally be used for optimization studies. 

Fixed-bed reactors are used for testing commercial catalysts of larger particle sizes and to collect data for scale-up (validation of mathematical models, studying the influence of transport processes on overall reactor performance, etc.). Catalyst particles with a size ranging from 1 to 10 mm are tested using reactors of 20 to 100 mm ID. The reactor diameter can be decreased if the catalyst is diluted by fine inert particles the ratio of the reactor diameter to the size of catalyst particles then can be decreased to 3 1 (instead of the 10 to 20 recommended for fixed-bed catalytic reactors). This leads to a lower consumption of reactants. Very important for proper operation of fixed-bed reactors, both in cocurrent and countercurrent mode, is a uniform distribution of both phases over the entire cross-section of the reactor. If this is not the case, reactor performance will be significantly falsified by flow maldistribution. 

Finally, for relevant fuel cell modeling, the kinetic model studies should be performed under similar temperature and pressure conditions, i.e., at temperatures in the range of 80-120 °C and pressures up to 3 bar, and at comparable space velocities. The first flow-cell and DBMS measurements under such temperature and pressure conditions are currently underway in our laboratory. 

---