Analog Representation of Circulation Around Lifting Airfoils
In this case, the velocity potential is not single-valued function. The analogy in which it is identified with an electric potential is not simple since cuts must be provided in the conductor in order to make the electric potential single-valued.
Instead, the stream function of the fluid flow, which is continuous, will be identified with an electric potential. However, to give the circulation around the body a prescribed value, the model must function as an extra electrode. it must be connected through an adjustable resistance, R, to one of the poles (chosen to give the correct sign of Г). It is possible, however, to establish a “cut” in the electric field, which can be chosen along an equipotential line, extending outward from the surface of the body. This cut is realized in the electric tank by two auxiliary electrodes separated by a thin insulating strip. The potential difference between theses two electrodes corresponds to the value of the circulation (the flux crossing the cut must be conservative).
Studies of interaction problems using combination of airfoil sections are possible. Also, airfoils with flaps and hinged leading edges as well as slots have been considered. Since conformal mappings satisfy the Cauchy-Riemann equations, it is feasible to construct electric analog of conformal transformation of an airfoil (or any closed region) onto a circle.
Analog study of airfoil cascades is based on representing the periodicity of the field.