Combined use of dimensional analysis and modern experimental design methodologies in hydrodynamics experiments

In this paper, a combined use of dimensional analysis (DA) and modern statistical design of experiment (DOE) methodologies is proposed for a hydrodynamics experiment where there are a large number of variables. While DA is well-known, DOE is still unfamiliar to most ocean engineers although it has been shown to be useful in many engineering and non-engineering applications. To introduce and illustrate the method, a study concerning the thrust of a propeller is considered. Fourteen variables are involved in the problem and after dimensional analysis this reduces to 11 dimensionless parameters. Then, a two-level fractional factorial design was used to screen out parameters that do not significantly contribute to explaining the dependent dimensionless parameter. With the remaining five statistically significant dimensionless parameters, various response surface methodologies (RSM) were used to obtain a functional relationship between the dependent dimensionless thrust coefficient, and the five dimensionless parameters. The final model was found to be of reasonable accuracy when tested against results not used to develop the model. The methodologies presented in the paper can be similarly applied to systems with a large number of control variables to systematically derive approximate mathematical models to predict the responses of the system economically and accurately.