Physical Models and Similitude

To validate models based on transfer equations or stochastic models and, especially, to develop a coherent and planned experimental investigation of the studied process, the researcher has to imagine and build up a reduced scale experimental installation (laboratory device or model, LM). The goal using this reduced scale pilot plant is to obtain the experimental data necessary to validate the models. 

Major chemical engineering projects involving structures, tray or packed columns, reactors, separators, heat exchangers and heaters, reservoirs and special deposits, fluid pumping as well as compressing devices, frequently involve the use of small scale studies using laboratory scale devices. According to the context. 

The pilot laboratory units, which are generally a different size, may involve different fluids, and often operate under different conditions (temperature, pressure, velocity, etc.). These units are frequently designed so that the parameters can be varied independently. The idea is not only to facilitate the study of the influence of the different process parameters but also to include the complexity of industrial scale units in the study. 

This is the basic question of the similitude theory To what extent can experimental data be relied upon when the dimensions of the experimental devices increase or decrease  

In the following sections we will present some procedures and examples which show how LM can be designed in order to have a similar behaviour evolution for different device scales such as laboratory device (small scale) and prototype units (medium scale). 

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One of the limitations of dimensional similitude is that it shows no direct quantitative information on the detailed mechanisms of the various rate processes. Employing the basic laws of physical and chemical rate processes to mathematically describe the operation of the system can avert this shortcoming. The resulting mathematical model consists of a set of differential equations that are too complex to solve by analytical methods. Instead, numerical methods using a computerized simulation model can readily be used to obtain a solution of the mathematical model. 

Dimensional similitude is based on principles of similarity and uses dimensionless ratios of the physical and chemical parameters that govern the working model to design the scaled-up prototype. This method is followed when the prototypical unit is expected to be dimensionally similar to the small-scale unit. The degree of success in using dimensional similitude as an approach to scaleup depends mainly on the extent to which the physical parameters necessary to achieve a desired result influence the process. 

Physical properties for all flows are inputted. The user must specify certain parameters such as mixing models, kinetic rates, turbulence, and others as required. The CFD model is generally full-scale with complete similitude. The governing differential equations that solve all aspects of mixing, heat transfer, chemistry, turbulence, fluid mechanics, species, and continuity are iterated across the entire model until a converged solution is obtained for all cells and boundary conditions. 

Concepts are now drawn from the subject of Similitude and Theory of Models. For comparisons between prototype (p) and model (m) to be valid, conditions associated with each must be physically similar. Physical similarity may take different forms ... 

Derivation of the correct scaling laws constitutes a necessary first step in an experimental study. The similitude relationships are essential for interpreting the experimental data and also for scaling up the results to real prototypes. There are two ways to scale up the model test results as shown in Fig. 26.2. The first is to use standard tables (look-up approach) for scaling the model observations by pertinent factors to predict the prototype response. The alternative is to study the underlying mechanics/physics of the problem based on the model tests recognizing that not aU the interaction mechanisms can be scaled accurately in a particular test. Once the mechanics/physics of the problem are identified in terms of pertinent dimensionless... 

The seismic input used to quaUfy the candidate item should envelop the design spectra for that item and the seismic input used for the reference item it should also equal or exceed those required for the candidate item. Proper similitude relationships should be considered in input to scale models. The physical and support conditions, the functional characteristics for active items and the requirements for the candidate item should closely resemble those for the reference item. 

The experimental apparatus is schematically shown in Fig. 8.18. The vessel made of transparent acrylic resin had an inner length of 1,000 mm, an inner width of 100 mm, and an inner height of 70 mm. These dimensions were decided with reference to the current continuous slab casting molds of steel in practice. Specifically, the model was approximately half the size of real slab casting molds. Only the geometrical similitude for the inner length and the inner width were taken into consideration in the model because the effects of the physical properties of upper and lower liquids and the depths of the two layers on the onset of the KHI could be evaluated from existing correlations. Salt water and silicone oils with different physical properties... 

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