ESDU Engineer

Aerodynamics and aero-acoustics of rectangular planform cavities:
Part II: Unsteady flow and aero-acoustics

The effects of flow instabilities on the liquid or gas within an enclosed volume withan aperture open to a static or moving external flow, or related matters, have been studied for at least the last 150 years. For example, in 1854 Sondhaus studied the effects of a jet impinging upon an edge, producing an acoustic effect known as an edge tone, associated with the production of sound in organ pipes and other musical instruments. Tyndall, in 1867, studied the effect that sound had on the stability of jets, while in 1868 Helmholtz published the results of, among other things, his analysis of the natural frequency of an enclosed volume with a small aperture,subsequently called a Helmholtz resonator. Later, in 1877, Lord Rayleigh (John William Strutt) published a widely used book on the theory of sound, including the effects of sound on the stability of vortex sheets and the development of a theory for the resonant conditions of an open-ended pipe. Much of this work has provided a foundation for the subsequent development of the various theories associated with cavity aerodynamics and aero-acoustics.

The study of cavity acoustics in general, and jet impingement in relation to edge tones in particular, continued at a steady pace for the next 70 years, with various applications. However, in the late 1940s and early 1950s activity in the aircraft industry spurred the accelerating growth of research into cavity aerodynamics, and especially acoustics, that has occurred over the last 50 years. At that time there was an increasing awareness of the effects that the oscillation of the airflow in and around open cavities such as wheel wells and bomb bays were having on the aerodynamics, and even the structural integrity of such cavities and their contents. At the same time as work on specific aircraft was being carried out in the 1950s and 1960s, a number of investigations, mainly wind tunnel and flight tests, involving general research into the unsteady aerodynamics and noise due to cavities were also under way. All these areas of research provided a firm basis for the rapidly expanding work, both experimental and theoretical, including computational fluid dynamics (CFD), from the 1970s onwards.

The information given in Item No. 04023 concerns unsteady flow and the associated aero-acoustics of rectangular planform cavities. Following a general introduction concerning the ranges of cavity geometry over which sustained oscillations can be expected, the three oscillationtypes, i.e. fluid-dynamic, fluid-resonant – including the special case of normal mode resonance, and fluid-elastic, as suggested by Rockwell and Naudascher, are discussed together with the various mechanisms involved. The parameters that can affect the frequency and amplitude ofcavity oscillations for the important fluid-dynamic and fluid-resonant types involved in aircraft applications are detailed.

The physical processes involved in a length mode fluid-resonant oscillation cycle are discussed. The historical view of the oscillation process as suggested by the classical work of Rossiter, Bilanin and Covert, Heller and Bliss, Rockwell and Naudascher, with later work by Heller and Delfs, precedes the more detailed analyses made possible by the CFD simulations of Zhang et al., Tam et al. and Henderson.

The various "engineering" methods for the prediction of cavity oscillations are outlined and examined. The range of empirical and analytical methods for predicting tonal frequencies in length mode, including the widely used modified form of Rossiter’s method, are presented. So is a development of East’s semi-empirical method for predicting the fundamental depth mode frequency at low speeds, based on the theoretical pressure amplification equation established by the work of Plumblee et al. The new development uses East’s simple equation as a basis for the provision of a more general equation providing a fairing between the low width/length ratios covered by Plumbleeet al. and the high, quasi-two-dimensional, values for which East’s original method was derived. The scope of the available engineering methods for tonal amplitude prediction is limited to that of the Cavity Acoustics rediction (CAP) Code for length modes and the Plumblee et al. method for depth modes.

Concluding remarks include a list of those areas requiring further information to provide a firmer basis for some of the discussion in the Data Item.

Appendix A contains basic information on the various measures of fluctuating pressure and their analysis.

Item No. 04023 is one of a group of Data Items intended to act as an introduction to the aerodynamics and aero-acoustics of rectangular planform cavities. The group will consist of five parts:
Part I: Time-averaged Flow – Item No. 02008,
Part II Unsteady Flow and Aero-acoustics –Item No. 04023,
Part III: Drag and Alleviation of Unsteady Flow Effects,
Part IV: Overview of CFD methods,
Part V: Bibliography and Tabular Survey.

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