An efficient scaling methodology for dynamic models using dimensional and activity analyses

Previous work in the literature developed similitude-based design scaling techniques that make it possible to take a proven system design and scale it to meet new desired dynamic characteristics. However, such similitude-based scaling is often too restrictive because it may not be feasible to satisfy all of the resulting scaling laws exactly. This paper uses a novel combination of activity-based model reduction and dimensional analysis to scale only the important components of a given dynamic system, thereby providing more freedom than pure similitude-based scaling. The viability of this proposed method is highlighted by two examples. The first example demonstrates the proposed efficient scaling methodology on a simple two-degree-of-freedom mass-spring-damper system. The second example uses the developed methodology to scale a fuel cell stack's air supply system design for a new set of fuel cell system power requirements. The examples highlight the flexibility that activity analysis adds to similitude-based scaling methods.