NASA NTRS2017
A number of valuable conclusions can be drawn from this study. First, knockdown factors for a specific fluid are not constant but instead are dependent on the mode shape, although the largest this variability gets is about 10% for LOX, the densest fluid. The factors decrease the most for lower frequency shapes and less for higher ones. It follows, therefore, that mode number mismatch between air and fluid operation becomes not only possible, but common, as a knockdown factor for a particular mode shape may be higher than for another mode shape. Since this is a function of added mass, the mismatch is more prevalent for higher density fluids, but it initiates even for very low density ones. Another important conclusion reached is that it appears that the basic mode shapes of a structure do not change if it is fully symmetric, which includes its geometry and boundary conditions. There is some indication of small changes in the relative magnitudes within the mode shape. This conclusion is evident in the results from the cantilever rectangular plate and the inducer, which are not symmetric, and the fixed-fixed plate and the annular disk, which are. For non-symmetric structures, though, the mode shapes almost universally change for dense fluids, as shown by the very low MAC calculations. For the inducer in particular, the changes follow a trend of reduced parabolic and sine wavelengths with increasing density. It is critical to recognize the change in mode shape for several reasons. First, model updating with modal test becomes problematic if the shapes change. Second, design to avoid resonance is highly critical on the mode shape for modes other than the primary ones, as resonance is only a factor when the excitation shape matches the mode shape. Finally, application of the modal superposition method of forced response analysis is dependent on the use of accurate mode shapes. A more-refined assessment of the "knockdown" factor values and ranges than any previously reported in the literature for a realistic engineering structure is also presented in this paper. This data is of tremendous benefit for preliminary analysis and design, where a quick estimate is necessary. These results are important not just for rocket engine turbomachinery, but for water pumps and turbines, propellers, and any other structure operating in a heavy fluid with dynamic excitation. The clear avenue for future work for this endeavor is to expand the analytical techniques discussed in the literature to develop analytical expressions and justification for the mode shape changes and associated frequency knockdowns. These expressions must be able to accurately predict the functional relationship to the shapes, which will enable accurate tracing of the mode number from vacuum analysis (or testing in air) to analysis and operation in the intended fluid environment.