46 Test-Analysis Modal Correlation of Rocket Engine Structures in Liquid Hydrogen – Phase II 415 Fig. 46.1 J2-X LOX turbopump inducer (not to scale) water flow test, hydroelastic analysis and testing, acoustic modeling, and unique natural frequency testing of the sub-scale stainless-steel inducer in LH2 that was used in the water-flow test. The first phase of this integrated program was completed in 2017 and reported by the authors [1]. That paper detailed the testing of a titanium cantilever beam in water and LH2 and presented the detailed correlation of the numerical model with analytical techniques and the new experimental data. The data proved invaluable to the program in reducing the uncertainties associated with representing the fluid-added mass and the modulus at cryogenic temperatures. This paper discusses the results and on-going work from the second phase of the integrated test/analysis program. In this phase, first the titanium cantilever plate was re-tested in water and LH2 but this time with plates along its edges to exercise the tip clearance effect. Next, the sub-scale stainless steel inducer was extensively tested with the following series of tests: modal testing in air and water, modal testing in water with a tight clearance, frequency testing in LH2, and testing in a water flow facility which can replicate cavitation and hydroelastic effects (this test will not be discussed in this paper). In concert with the testing, an extensive correlation effort incorporating all the effects from the parameters discussed above was performed for finite/acoustic models of the beam and sub-scale inducer. 46.2 Literature Survey Harrison, et al. [2] performed extensive tight-tip clearance testing on a micro-cantilever beam, 1.45 mm×1.8mm×20μm, to examine the effects for sensors. Although much smaller in scale, the effects on natural frequency are the same as for the case discussed in this paper, and two of configurations tested, called “sweep” and “wipe”, match the configurations matched in this paper, which will be discussed in the next section. Key findings from this work are that the fluid-added mass multiplier is approximately proportional to the inverse of the root of the tip-clearance, but that the value plateaus at close clearances. Green and Sader [3] developed an analytical technique using boundary integrals to calculate the forces on an object when immersed in a fluid with a close rigid boundary vibrating normal to the wall, including the dissipative forces. This technique is then applied by Xiu and Davis [4] to the case of the object vibrating in a direction parallel to the wall, which is the case of the turbopump inducer blades. The paper presents both the adapted theory and experimental validation for cantilever beams in both the “sweep” and “wiping” configurations previously described by Harrison. Results include detailed curves for both the fluid-added mass (relative to the value without a close boundary) as a function of a non-dimensionalized boundary distance and the fluid-added damping relative to the same parameter. These relationships are extremely valuable and were chosen to serve as a basis for similar testing at MSFC, with the idea of developing numerical modeling techniques using the analytical expressions, and validating these techniques with the experimental results presented by Harrison, Xiu, and at MSFC. With respect to the effect of compressibility, Davis, Virgin, and Brown [5] examined structural/acoustic interaction extensively; acoustic modes can only exist if compressibility is included in the structural acoustic modal formulations,
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