Scaling properties of the Ffowcs-Williams and Hawkings equation for complex acoustic source close to a free surface

We perform a scaling analysis of the terms composing the Ffowcs-Williams and Hawkings (FWH) equation, which rules the propagation of noise generated by a rigid body in motion. Our analysis extends the seminal work of Lighthill (Proc. R. Soc. Lond. A, vol. 211, 1952, pp. 564–587) and the dimensional analysis of classical sources (monopole, dipole and quadrupole) considering all the FWH integral terms. Scaling properties are analysed in light of perfect/imperfect similarity when laboratory-scale data are used for full-scale predictions. As a test case we consider a hydrodynamic example, namely a laboratory-scale ship propeller. The data, obtained numerically in a previous study, were post-processed according to the scaling analysis presented herein. We properly scale the speed of sound to obtain perfect similarity and quantify the error with respect to the imperfect scaling. Imperfect similarity introduces errors in the acoustic response related both to the linear terms and to the nonlinear terms, the latter of great importance when the wake is characterized by robust and organized vorticity. Successively, we analyse the effect of a free surface, often present in hydrodynamic applications. We apply the method of images to the FWH equation. The free surface may generate a frequency-dependent constructive/destructive interference. The analysis of an archetypal acoustic field (monopole) provides robust explanation of these interference effects. Finally, we find that imperfect similarity and the absence of a free surface may introduce errors when model-scale data are used to obtain the full-scale acoustic pressure. The error is small for microphones placed in the near field and becomes relevant in the far field because of the nonlinear terms.

Measuring diameter of water jets affecting propeller blade surface under cavitation wear

The article analyses the structure of cavitated areas of the ship propeller blades made from aluminum bronzes with different composition. The most informative zones of cavitation wear are the cold-hardening zone and the peripheral one that help estimate the mechanical parameters causing the cavities to collapse. The dents formed on the metal surface in the process of hydrodynamic cavitation wear have spherical parts on their bottoms, in which it is possible to inscribe a circle of a definite diameter. There were conducted the experiments on forcing the ball indentors into the surface of different metal alloys. The first run of the experiments includes forcing of a steel ball with a diameter of 1.588 mm into the surface of 33 alloys with different hardness under the loads of 1 470, 980 and 588 N. The impression diameters were measured using Brinell magnifying glass. There has been found the power dependence between deformation of dents on the metals tested under hydrodynamic cavitation and hardness of the materials, which is similar to the dependence of deformation after forcing the ball indentors into the alloys of different hardness. The second run of the experiments included modeling the cold-hardening zone of the cavitation wear area by repeated forcing the ball indentors with the diameters of 1.588, 2.5, 3.175 and 5.0 mm into the bronze BrAZhNMts9-4-4-1 plates with area of 100 × 50 × 20 mm. Forcing was made into the side 100 × 50 mm previously ground and polished. The equal strain rate in impressions of different diameters was observed during forcing. A direct proportional relationship was obtained between the arithmetic mean deviation of the surface profile and the indenter diameter. The arithmetical mean deviation of the assessed profile of the side plotted against the ball indentor yields a direct proportional relationship. Using the dependence for the case of cavitation attack on the propeller blades helps to infer that the diameter of water jets striking against the propeller blade surface with diameter of 3 700 mm makes about 10 mm. The obtained value allows to choose reasonably the experimental equipment and the parameters of testing the ship propeller materials for cavitation wear.