Advances in empirical similitude method
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Dimensional Analysis is a technique that has allowed engineering evaluation of complex objects by scaling analysis results of representative simpler models. The original premise of the procedure stems from the idea of developing non-dimensional parameters to relate physical events and underlying analytical basis. Extending the process to incorporate non-linear and time variant behavior has led to development of a novel process of similitude called the Empirical Similitude Method (ESM) where experimental data of test specimen is combined to produce the required prediction values. Using the original motivation and hypothesis of ESM, this research has expanded the experimental similitude process by using adapted matrix representations and continuous functional mapping of test results. This new approach has provided more rigorous mathematical definitions for similarity and prediction estimations based on an innovative error minimization algorithm. Shape factors are also introduced and integrated into ESM to obtain comprehensive evaluation of specimen choices. A detailed overview is provided summarizing methods, principles and laws of traditional similitude (TSM) and systems that satisfy extension into ESM. Applicability of ESM in different systems is described based on the limitations of TSM in the evaluation of complex structures. Several examples and ideas spanning aerodynamic, thermal, mechanical and electro-magnetic domains are illustrated to complement inherent technical analysis. For example, the new ESM procedure is shown to be considerably more accurate than earlier methods in predicting the values of drag coefficient of an airfoil. A final foray into the regime of \design evaluation by similarity" is made to elucidate applicability and efficiency of developed techniques in practical systems and products. A thorough methodology is also presented highlighting pertinent procedures and processes in usage of this method.