ESDU 04023:2009

INTRODUCTION

Background

The effects of flow instabilities on the liquid or gas within an
enclosed volume with an aperture open to a static or moving
external flow, or related matters, have been studied for at least
the last 150 years. For example, Sondhaus in 1854 (Reference 1),
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 (Reference 2), studied the effect that sound had
on the stability of jets, while in 1868 Helmholtz published
(Reference 3) 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 (Reference 4) 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
the work in References 1 to 4 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 a particular problem 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. Early work in this area was carried out in
relation to the bomb bays of the English Electric Canberra
(References 6, 8, 9, 13, 19, 21, 29 and 39) and Boeing B47
(Reference 10). At the same time as this work on specific aircraft
was being carried out in the 1950s and 1960s, a number of
investigations, mainly wind tunnel and flight tests, involving more
general research into the unsteady aerodynamics and noise due to
cavities were also under way (for example, References 7, 11, 14 to
18, 20, 22 to 28 and 30 to 38). 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.

Although nearly all the research on the unsteady aerodynamics
and acoustics of cavities has been in relation to weapons bays,
much of the resulting information could also be applied to
undercarriage bays or wheel wells. However, in that application
there is usually less of a problem due to the unsteadiness and
noise arising from the flow within such cavities (although drag is
obviously a concern), and more of a problem in relation to the
far-field noise generated by the wheel bay and the extended
undercarriage unit (for example, References 44, 48, 49, 51 and 68).
Such considerations are outside the scope of this Data Item and are
more relevant to the work of the ESDU Noise Committee, see ESDU
90023 (Reference 95) for example.

The main problems involving the use of rectangular planform
cavities for weapons carriage are twofold.

(a) Flow unsteadiness and the possibility of self-sustained
oscillations and the likelihood of acoustic phenomena for deep to
moderately deep cavities with open or
transitional flow (see ESDU 00007 – Reference 97).

(b) Weapon release difficulties from shallow cavities with
closed flow (see ESDU 00006 – Reference 96) arising from
the strong upwash at the forward end of the cavity coupled with the
equally strong downwash at the rear. The flow is, however,
comparatively steady compared to that in transitional or open
flow.

Of the two, problem area (a) has attracted by far the most
research effort, not least because it poses the greater challenge
due to the complexity of the unsteady flow involved.

The adverse cavity flow effects affecting weapons carriage and
release can be alleviated by various means, both active and
passive, see Parts IIIA to IIID (References 99 to 102)*. However,
in order for the alleviation mechanism to be effective, a knowledge
of the nature of the unsteady flow is essential, and the primary
purpose of the present Data Item is to provide wide-ranging
information on that aspect.

* Acoustic peaks as high as 180 dB are possible, implying
pressures around 2 × 10⁴ N/m² (418
lbf/ft²); even levels of 160 dB can cause damage
(Reference 71).

* This Data Item forms Part II of a series on cavity flows. All
the Parts are listed in Section 2.2 of Part I (Reference 98)