Noise generation by a supersonic leading edge. Part 1: general theory

Powles, Christopher

doi:10.1016/j.jsv.2003.11.014

Cited by 4 publications

(11 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This field on the two lines does not attenuate with distance from the source, as noted in general after (12). Our formulae (15) and (16) differ slightly from those in [19] because of a different multiplicative factor in the definition of the upwash. Figure 3 gives contour plots of the pressure field on vertical transverse sectionsx = kā 2 /2 andx = 2kā 2 for Mach number M = kā 2 , because (provided kā > 1) this is the distance at which far-field approximations start to apply.…”

Section: The Gaussian Gustmentioning

confidence: 55%

“…a remarkable exact result for a fully three-dimensional problem. The first result of this type was obtained in [12], for a time-domain field, and its single-frequency form is derived in [19]. On the Mach wedge at a given value of z, the acoustic field is influenced only by the leading edge upwash at the same value of z; this explains the proportionality of p(x, y, z, t) to g(z) in (12).…”

Section: Green's Functionmentioning

confidence: 92%

“…(3) applies in the Mach wedge |ȳ| ≤x emanating downstream from the leading edge of the aerofoil; outside of this wedge there is no sound. Reference [19] provides a full derivation of (3) from the convected wave equation and boundary conditions of the problem, and also derives a far-field approximation in the form p p + + p − where…”

Section: General Theorymentioning

confidence: 99%

“…An account of the Gaussian gust is given in [19], as an illustration of the general theory there developed. Here we extend this account to include plots and further discussion of the structure of the acoustic field.…”

Section: The Gaussian Gustmentioning

confidence: 99%

“…In the PhD thesis [18], a general analytical formula was derived for the sound field produced by a gust of arbitrary shape striking the supersonic leading edge of a flat-plate aerofoil at zero angle of attack, and it was used to calculate many two-and three-dimensional sound fields. The general formula and its derivation are in [19], and the calculated two-dimensional sound fields are in [10]. Most of the three-dimensional sound fields calculated in the thesis remain unpublished.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Canonical sound fields in the frequency-domain theory of supersonic leading-edge noise

Powles

Chapman

2019

Wave Motion

View full text Add to dashboard Cite

This paper determines the three-dimensional structure of certain single-frequency canonical sound fields occurring in the theory of blade-vortex interaction when the flow velocity relative to the blade is supersonic. A relative velocity of this magnitude occurs at the outer part of the fan blades in an aeroengine, at which the incoming vorticity has either been ingested from the atmosphere or created in the aeroengine itself. The sound fields analysed are those produced by the leading edge of a flat-plate blade at zero angle of attack on being struck by a gust which is either (i) localised along the span, or (ii) non-localised but discontinuous. The canonical gusts of type (i) have either a deltafunction or Gaussian shape, and those of type (ii) are either anti-symmetric or described by a Heaviside function; these gusts give rise to the four basic canonical sound fields. The paper also analyses a fifth sound field, produced by a single-frequency top-hat gust. This sound field has a complex structure involving aspects of both (i) and (ii), but can nevertheless be analysed in terms of the canonical sound fields. The main results of the paper are exact and approximate analytical formulae giving the dependence of the acoustic field on gust-shape and flow parameters, and also a simple formula which is ideal for numerical work. The last of these is used to assess in detail the numerical accuracy of all the approximate formulae, which are of either Fresnel or Keller type. A key result is that Keller-type formulae, representing sound rays produced in accord with the geometrical theory of diffraction, have a very wide range of validity. A companion paper (Chapman & Powles 2019) in this special issue of Wave Motion determines the canonical sound fields in the corresponding time-domain theory.

show abstract

Section: The Gaussian Gustmentioning

confidence: 55%