Electric Analogy

This analogy is based on the relation between the equation governing the electrical potential in a conductor and the velocity potential of fluid flows. In the absence of interior sources within the conductor, the electric potential ф is governed by

V. (aVф) = 0

where a is the conductivity.

For homogeneous conductors with constant conductivity, the above equation reduces to the Laplacian

V2 ф = 0

which is the same equation for the velocity potential of inviscid, incompressible fluid flow, even for unsteady problems (for example oscillating wing).

For two-dimensional models, it is possible to represent variable conductivity by a model having variable thickness. In this case, the electric potential is governed by

(13.58)

Moreover, one can introduce a stream function ф, such that

The equation for ф is given by

The Dirichlet and Neumann boundary conditions are simple to reproduce in the electrical model. For ф = const., the boundary is covered by an electrode which is raised to the potential level specified. For дф/дп = 0, the boundary is insulated (i. e. no electric current crosses the boundary).

The conducting media can be a weak electrolyte contained in a tank leading to “electrolytic basin” technique metallic plates or special conducting papers are also used.

Notice, for compressible (subsonic) flow studies, the height distribution must be adjusted iteratively to be related to the density distribution Which is unknown a priori).

For details of the apparatus and the experimental techniques, see Malavard [12]. In the following, some applications are discussed.