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Abstract:
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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 . |