On Virtual Mass of a Cascade of Flat Plates which vibrates in Water

Abstract

In connection with the torsional vibration (in water) of marine propeller, it is required to find the effect of surrounding water upon a cascade of flat plates, which vibrates in water.In this paper the author has estimated the amount of virtual mass for the vibration of a series of flat plates arranged in cascades, assuming the potential flow.The result of calculation is shown as a chart for coefficient K. Virtual (or added) mass per each blade per unit lehgth is given by the formulaM=ρl2π/4Kwhere ρ is the density of water, l is the chord length of each blade. In case t/l→∞, that is, for a single blade, we have K=1.The above value was obtained on the assumption that there is no stream-flow around blades. But, when a marine propeller is working, there are set up a relative stream around each blade. We assume a stream attacking the blades with incidence angle α, and circulating flows around each blades. The amount of circulation is determined in usual manner by condition at trailing edge of blades. Calculating the amount of virtual mass of a cascade of blades which vibrate in the abovementioned stream, we find it to be the same when they vibrate in still water. Thus we see that, at least for a potential flow of ideal fluids, the relative flow does not affect the value of virtual mass which is mentioned above.