Combined Use of Dimensional Analysis and Statistical Design of Experiment Methodologies in Hydrodynamics Experiments

Abstract: In this paper, a combined use of dimensional analysis (DA) and statistical design of experiments (DOE) 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 extremely useful in many engineering applications. To illustrate the method, a study concerning the thrust of a podded propeller is considered. Fifteen variables are involved in the problem and after dimensional analysis this reduces to 12 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 dimensional parameters, response surface methodology (RSM) was used to obtain a functional relationship between the dependent dimensionless thrust coefficient, and the five dimensionless parameters. The model was found to be of reasonable accuracy. The methodology presented in the paper can be applied to any system with a large number of control variables to derive an approximate mathematical model to predict the response of the system economically and accurately.