A two-experiment finite similitude approach to experimental fluid mechanics

Abstract

Fluid dynamics experimentation at scale provides an important means of investigation that is presently underpinned by dimensional analysis and computational fluid dynamics (CFD). Unfortunately, despite the obvious success of this twin approach, dimensional analysis provides no solution if scale effects are prevalent and CFD offers reduced practical advantage in the absence of a theory that links information across scaled experiments. This issue is addressed in this paper with the introduction of a new approach to scaled experimentation founded on the theory of finite similitude. Finite similitude is founded on the metaphysical concept of space scaling, where experimental apparatuses, facilities, prototypes, systems, wind tunnels etc., are scaled by the means of space contraction or expansion. There exists no practical means to contract or expand space but what is possible is a mathematical description of space scaling and its impact on governing physics, so providing a means for comparison with scaled systems and real-world experimental behaviours. This paper examines an adaptation of the finite-similitude theory, where two scaled experiments are involved but a second-order version of the theory is applied. All previous work has been limited to zeroth and first-order applications, but in the case of fluid dynamics, second order is shown necessary to capture more accurately convective terms. It is demonstrated in the paper by means of two scaled experiments (designed using second-order theory) that the approach is able to represent behaviours at the full scale that hitherto would have been deemed impossible with traditional dimensional analysis. Numerical and analytical case studies on gravity impacted flows are trialled to illustrate the benefits of the approach with percentage errors reduced from double to single digits.