DESIGN OF SCALE MODELS

Design of Scale Models Using the Simplified Set of Scaling... 

In addition, dimensional analysis can be used in the design of scale experiments. For example, if a spherical storage tank of diameter dis to be constmcted, the problem is to determine windload at a velocity p. Equations 34 and 36 indicate that, once the drag coefficient Cg is known, the drag can be calculated from Cg immediately. But Cg is uniquely determined by the value of the Reynolds number Ke. Thus, a scale model can be set up to simulate the Reynolds number of the spherical tank. To this end, let a sphere of diameter tC be immersed in a fluid of density p and viscosity ]1 and towed at the speed of p o. Requiting that this model experiment have the same Reynolds number as the spherical storage tank gives... 

A technique which can assist in the scale-up of commercial plants designs is the use of scale models. A scale model is an experimental model which is smaller than the hot commercial bed but which has identical hydrodynamic behavior. Usually the scale model is fluidized with air at ambient conditions and requires particles of a different size and density than those used in the commercial bed. The scale model relies on the theory of similitude, sometimes through use of Buckingham s pi theorem, to design a model which gives identical hydrodynamic behavior to the commercial bed. Such a method is used in the wind tunnel testing of small model aircraft or in the towing tank studies of naval vessels. 

In later sections, the use of the scaling relationships to design small scale models will be illustrated. For scaling to hold, all of the dimensionless parameters given in Eqs. (36), (37) or (39) must be identical in the scale model and the commercial bed under study. If the small scale model is fluidized with air at ambient conditions, then the fluid density and viscosity are fixed and it will be shown there is only one unique modeling condition which will allow complete similarity. In some cases this requires a model which is too large and unwieldy to simulate a large commercial bed. 

The second contribution spans an even larger range of length and times scales. Two benchmark examples illustrate the design approach polymer electrolyte fuel cells and hard disk drive (HDD) systems. In the current HDDs, the read/write head flies about 6.5 nm above the surface via the air bearing design. Multi-scale modeling tools include quantum mechanical (i.e., density functional theory (DFT)), atomistic (i.e., Monte Carlo (MC) and molecular dynamics (MD)), mesoscopic (i.e., dissipative particle dynamics (DPD) and lattice Boltzmann method (LBM)), and macroscopic (i.e., LBM, computational fluid mechanics, and system optimization) levels. 

The table below lists the atomic radii (plural of radius) for the main-group elements. Design different scale models that could help you visualize and compare the sizes of the atoms. Your models can be two-dimensional or three-dimensional, large or small. 

Fig. 5-6. Commercial chemical plant designed with aid of scale model in Fig. 5-5. (Courtesy of Btaw-Knox Co., Pittsburgh, Pa.)...

In order to create a durable, flexible, and autonomous microrotorcraft that can be used in a variety of applications, more work is needed on a number of fronts. Additional experimental data should be gathered on the effects of blade design, and these data should be used to both improve existing 2-D microrotorcraft representations and to generate more detailed 3-D Navier-Stokes computational models. These data could be created using actual small rotor systems or through the use of scale models. 

English engineer William Froude was the first to prove the validity of scale-model tests in the design of full-size vessels. He did this in the 1870 s, building and operating a model basin for this purpose. 

An alternate approach is to design a scale model so that the ratio of all of the important forces is the same in the model as it is in the full-scale bed, and a the scale model uses geometry similar to that of the larger fluidized bed. If the ratio of forces acting on a particle in the scale model bed have the same ratio as they do for a particle in the full bed, then the trajectory of the particle motion should be the same for both beds. The same follows for the motion of the gas and the motion of clusters of particles or particles in a dense phase. From this point of view, we must identify all the important forces in the system. Table 1 lists these forces. 

Major reactor system components, including the reactor internals and hot duct, fuel handling equipment and reactor service equipment require detailed design and validation through testing of scale models and assemblies, and in some cases demonstration testing of prototypical components... 

In the next two sections of this chapter we describe by way of examples, detailed practical designs of scale-down bioreactors for investigating the effects of dissolved oxygen and pH gradients and the results obtained. B. subtilis is employed as the model culture given its sensitivity to dissolved oxygen and pH. 

Many engineering problems are so complex that a complete analytical solution is impractical, either due to lack of time or because the general problem cannot be resolved into components for which known solutions exist. Even if a problem can be divided into subproblems that can be solved, the composite solution will sometimes be inadequate due to important interactions among the subproblems. In such cases, it often proves expedient to study the performance of a physical model of the full-scale prototype. One of the most important uses of dimensional analysis lies in the design of engineering models and the interpretation of their performance. 

Industrial scale polymer forming operations are usually based on the combination of various types of individual processes. Therefore in the computer-aided design of these operations a section-by-section approach can be adopted, in which each section of a larger process is modelled separately. An important requirement in this approach is the imposition of realistic boundary conditions at the limits of the sub-sections of a complicated process. The division of a complex operation into simpler sections should therefore be based on a systematic procedure that can provide the necessary boundary conditions at the limits of its sub-processes. A rational method for the identification of the subprocesses of common types of polymer forming operations is described by Tadmor and Gogos (1979). 

The scale-up of filtration centrifuges is usually done on an area basis, based on small-scale tests. Buchner funnel-type tests are not of much value here because the driving force for filtration is not only due to the static head but also due to the centrifugal forces on the Hquid in the cake. A test procedure has been described with a specially designed filter beaker to measure the intrinsic permeabiHty of the cake (7). The best test is, of course, with a small-scale model, using the actual suspension. Many manufacturers offer small laboratory models for such tests. The scale-up is most reHable if the basket diameter does not increase by a factor of more than 2.5 from the small scale. 

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