Experimental Investigation of the Natural Frequencies of Liquids in Toroidal Tanks

Several toroidal configurations applicable to missile and space-vehicle liquid storage systems were oscillated to study the natural frequencies of the antisymmetric modes of contained liquids over a range of liquid depths and tank sizes. Natural frequencies for tank oscillations parallel to the free surface of both vertical and horizontal tank orientations. Natural frequencies were obtained. The data are presented in terms of dimensionless parameters which are obtained by relating experimentally determined natural liquid frequencies to analytical expressions developed through consideration of the physics of the problem and from existing solutions for liquids in tanks having similar boundaries at the liquid surface. The experimental results obtained for the toroids indicate that these parameters are applicable to the prediction of the natural frequencies of fluids in toroids of general geometry and size.