Practical aspects of designing background-oriented schlieren (BOS) experiments for vortex measurements

Setup-related aspects of background-oriented schlieren (BOS) experiments are discussed focusing on a sensitivity parameter S, which represents the relation between light deflection and resulting BOS signal, and the geometric blur. An analytic expression for the geometric blur by means of the circle of confusion (CoC) was derived which shows a proportional relation to the sensitivity factor S. The theoretical findings were validated in a reference experiment using generic distortions in glass plates. It was found that the filtering effect of the blur decreases the maximum background shift and its influence can be expressed with a blur loss factor B, which depends on the size of the CoC in relation to the investigated object. Multiplying the setup sensitivity S with the blur loss B results in the effective sensitivity \(S _{{\rm eff}}\) that determines the maximum achievable BOS signal of a schlieren object. For the investigated reference objects, the maximum effective sensitivity \(S _{{\rm eff}}\) was found to occur at CoC sizes in the object domain from 2.5 to 3.8 times the extent of the investigated objects. A step-by-step method is proposed for designing BOS experiments to obtain a maximum signal strength. The design parameters are further discussed specifically in regard to rotor tip vortex visualization, for which a variety of previously reported experiments are compared. A simple prediction method for the BOS signal of blade tip vortices is proposed and validated with experimental data from a rotor test stand. The application of the method to rotor systems of different size shows the requirement for increasingly higher sensitivity values for visualizing vortices of small-scale rotors.

Graphical abstract