Early Development of an "Acoustic Analogy" Approach to Aeroacoustic Theory

Abstract

I is a special pleasure to contribute with this brief historical paper to AIAA's celebrations of its 50th anniversary. I am, also, particularly glad that the paper gives me an opportunity to commemorate the energy and vision shown in 1949 by the late H. B. Irving, in his then position as Assistant Director of Scientific Research (Air) within Britain's government machine. Part of his job was to think about the future of aeronautics, with the object of identifying serious problems likely to arise as part of that future; and to draw attention to new research fields that needed to be opened up without delay if timely solutions to those problems were to be found. Remarkable vision was shown by Irving in recognizing so clearly, as early as 1949, that jet engines were bound to cause severe noise problems when (as must ultimately happen) they penetrated the civil transport market. This may have made him the first person in the world to identify research on jet noise and means for its reduction as a major new field of research to which effort urgently needed to be devoted. Great energy, too, was shown by Irving when he followed up that insight by a vigorous campaign waged with the object of setting up substantial research groups in this field within British university institutions. These groups (supported, where necessary, by contributions from the modest funds at Irving's disposal) were invited to pursue basic experimental and theoretical studies of the noise of jets; studies that might be usefully complementary to a large-scale program of empirical studies of jet-engine noise and schemes for its reduction initiated at Rolls Royce Ltd. Irving ensured, too, that the university groups created in this way (especially, the group including G. M. Lilley at the College of Aeronautics in Cranfield, the University of Southampton group that included E. J. Richards and A. Powell, and the University of Manchester group including myself on the theoretical side and J. H. Gerrard on the experimental side) would all take part together in frequent meetings with the outstanding Rolls Royce team under the leadership of F. B. Greatrex. These regular meetings very powerfully influenced the progress of the research work. I remember this in my own case: as the participant mainly concerned with developing theoretical approaches, I was helped by constant contact with several growing bodies of experimental data to adopt the necessary critical and selective approach to my own growing collection of theoretical ideas. The only Satisfactory theories are those that simultaneously accord with empirical data and with scientific logic!—a formidable pair of requirements. I recall Irving coming up to my attic room in the deeply blackened old Owens College building (since revealed by modern stone-cleaning technology as a charming blend of light brown and blue shades!) at Manchester University. In 1949, I was a 25-year-old Senior Lecturer in Applied Mathematics, already copiously involved in compressibleflow theory (especially, high-speed aerodynamics and shockwave dynamics). Somehow, Irving convinced me that jet noise was an exceptionally exciting theoretical challenge. I recognized that a jet was one of the classical turbulent flows, characterized to be sure by a complex pattern of vorticity; but not (according to views then current) by any dilatation. Compressibility had not been regarded hitherto as a significant factor in vortex motions or turbulence; yet it must be playing a part if any radiated sound were to result. Next morning I had to go to London, which in 1949 necessitated a four-hour train journey. Once in the train J could not stop thinking about the j£t-noise conundrum. It is, furthermore, the literal truth that the only piece of paper I had on me was the proverbial back of an envelope'M How fortunate that was. Sitting in the impersonal confines of the railway compartment, after having awakened that morning still more clearly conscious of what an exceptionally exciting theoretical problem in mechanics of fluids had been put to me, I had four hours to think about it while prevented from succumbing to the theoretician's besetting weakness; namely, rushing into filling sheets of paper with endless equations.... The essential idea of the acoustic analogy approach came before my journey's end. Iremember that the first part of the journey was entirely devoted to considering what would be the appropriate dependent variable in a system of equations to describe jet noise. I had found in many problems of compressible flow that the key to producing tractable equations was the correct choice of dependent variable. Often the pressure was an optimum choice (for example, in the aerodynamics of disturbances to a nonuniform oncoming stream). However, I soon decided against use of the pressure,