Session: 08-01 Education Issues I

Paper Number: 81558

81558 - An Alternate Means to Form Non-Dimensional Products in Dimensional Analysis 

Dimensional analysis is taught early in an undergraduate curriculum, usually during the very first course in fluid mechanics.  Such analysis has its root in the work of Lord Rayleigh, and the mechanics of the process as typically taught to undergraduates follows directly from the classic paper due to Buckingham on what has become known as the Π Theorem.   Students are meant to learn that dimensional analysis is a powerful tool for: developing insight with respect to flow physics, creating new models of physical processes, guiding the performance of experiments and flowfield simulations, aiding the sensible presentation of technical results, and fostering the replication of experiments and simulations.  A critical step in process involves the selection of scaling parameters that are used in the formation of each non-dimensional product.  Unfortunately, this selection can seem mysterious and arbitrary to the student encountering dimensional analysis for the first time.  This can leave the student thinking that dimensional analysis is all well and good so long as one already knows the answer to a problem (e.g. that the drag on a cylinder in crossflow depends on the Reynolds number).  However, an alternate technique for forming Π products called the “step-by-step” method exists, and that is due to the late Prof. B. S. Massey of University College London.  Discussion of the technique is largely absent from standard undergraduate textbooks on fluid mechanics.  So, this paper is intended to present his method to a wider audience and thus to encourage the adoption of the technique for use in undergraduate curricula.  It requires no prior selection of scaling parameters, and it is amenable to easy implementation in a computer scripting language.  It is also far less tedious and less prone to simple errors than the usual method.  Accordingly, it encourages the student to explore the formation of various non-dimensional formulations and thereby fosters learning.  The method is briefly described, and examples of its application are presented for: the processes of vortex shedding from a circular cylinder, the variation of the heat-transfer distribution along a flat plate, and the development of a model for the onset of transition to turbulence in turbine flows.  Needless to say, the form of the latter was not known at the outset, and dimensional analysis was essential to the formulation of the model and its successful application.  An implementation of the technique in Matlab is available for distribution to interested parties.

Presenting Author: John Clark AFRL

Presenting Author Biography: John Clark is Principal Engineer and Lead for in-house research in turbines at the Air Force Research Laboratory. He earned his doctorate in Engineering Science from the University of Oxford. He has industrial experience from the Turbine Aerodynamics group at Pratt & Whitney.

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