Scale physical modeling

Dimensional analysis techniques are especially useful for manufacturers that make families of products that vary in size and performance specifications. Often it is not economic to make full-scale prototypes of a final product (e.g., dams, bridges, communication antennas, etc.). Thus, the solution to many of these design problems is to create small scale physical models that can be tested in similar operational environments. The dimensional analysis terms combined with results of physical modeling form the basis for interpreting data and development of full-scale prototype devices or systems. Use of dimensional analysis in fluid mechanics is given in the following example. 

The laboratory scale physical model of the catalytic sulfur dioxide oxidation is a 0.05 m-diameter reactor containing 3 mm-diameter pellets of catalyst over a height of 0.15 m. The bed is flushed through at 430 °C by a gas flow that contains 0.07 kmol S02/kmol total gas, 0.11 kmol 02/kmol total gas and 0.82 kmol N2/kmol total gas. The gas spatial velocity is 0.01 m/s. 

As the structure, dynamics and properties are determined by phenomena on many length and time scales physical modelling is subdivided into the quantum mechanical, atomistic, mesoscale, microscale and continuum levels, while research into the way in which these levels are linked is known as hierarchical or multiscale modelling. The typical structural levels arising in the polymer field are shown Figure 1. 

Banerjee and Evans [97] constructed a one-twelfth scale physical model to study... 

Construction of a scale model must be accompanied with an analysis to determine test conditions that ensure the test results from the scale model are representative of the processes in the prototype. In combustion applications, although most of the processes are inherently at elevated temperatures, physical modeling is usually carried out under isothermal conditions. Isothermal physical modeling technique is based on the principle of relaxation. Under this principle, the variables that are important for the phenomena under study are stressed. The variables that are stressed are duplicated as necessary to obtain a representative result. No scale physical model can be an exact model of the reality unless an exact full-scale prototype is made. However, by using accurate correlations the modeling work can provide a good qualitative understanding of the fluid dynamics in the prototype. This chapter attempts to answer the question How does one ensure that the scale model test results are representative of the actual processes in the prototype ... 

Geometric similarity requires that the scale physical model is dimensionally similar to the prototype. Such similarity exists between the scale model and the prototype if the raho of all corresponding dimensions and all angles in the model and prototype are equal. Figure 10.1 illustrates the geometric similarity between a prototype and a scale model. 

Alternatives are small-scale reacting tests, scale physical models, and mathematical models ranging from simple one-dimensional (ID) correlations to three-dimensional (3D) computer solutions using computational fluid d5mamics (CFD). The selection of the correct simulation or model is driven by the information needed coupled with the models ability to accurately predict the full-scale resulfs from fhe simulation. 

The FCT built a small-scale physical model of the preheater tower, up to cyclones lA and IB, having the scale of a laboratory model to an actual plant of 1 35.5. The model was made of transparent acrylic for visibility inside to visualize the flow streams and mixing (Figure 31.20). The existing burners were modeled as slots on the acrylic model, and new FCT design auxiliary model burners were tested as a possible solution. A water-bead modeling reveals the aerod5mamics inside of the riser duct the kiln exhaust was represented by water in the model. For the visualization of flow, neutrally buoyant polystyrene beads follow the water flow accurately and beads allow the flow streams to be visualized ... 

Small-scale physical model of the preheater tower. (From FCT-Combustion Pty Ltd. With permission.)... 

In designing full-size equipment from tests on small-scale physical models, it is necessary to scale up, keeping the values of the pertinent dimensionless groups the same for model and full-size equipment. 

Dynamically-Scaled Physical Models of Antennules Reveal When Fluid Flows into Arrays of Aesthetascs... 

Each flick starts with a rapid, outward lateral movement followed by a slower return medial movement (Fig. 11.5a). Experiments studying flow around dynamically scaled physical models suggest that water is pushed into an array of aesthetascs during the rapid outstroke of a flick (Mead et al. 1999 Mead and Koehl... 

D full-scale physical model of patterned IPMCs... 

Measurements from large-scale laboratory tests indicate that formulae for overtopping volumes, based largely upon small-scale physical model studies, scale well (Fig. 16.24). No data from the field is available to support scale-ability from large-scale laboratory scales to protot3rpe conditions. 

Volumetric Sweep Efficiency. As discussed in Chap. 4, reduction of the mobility ratio in a displacement process results in an improvement of volumetric sweep efficiency. However, calculation of sweep from the empirical correlations presented in Chap. 4 is probably not justified in a WAG process because of the complex nature of the flow in the region behind the oil bank. In application, the process usually is modeled with computer-based mathematical models, 165,166 Limited results from properly scaled physical models have also been reported. 

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