Noise generation by a supersonic leading edge. Part 2: examples of two-dimensional sound fields

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

“…The pressure field may be called the three-dimensional supersonic edgelet, since it is the sound produced by an individual point on the leading edge. This field is much simpler than the subsonic three-dimensional edgelet, given as a contour integral in [8], where it is referred to as the edgelet function E 1 ; and it is slightly simpler than the two-dimensional supersonic edgelet given in [10]. Expression (7) applies in the Mach cone |ȳ 2 +z 2 | 1/2 <x emanating downstream from the origin; elsewhere the field is zero.…”

“…Inside the Mach coneR h = 0, the acoustic field produced by (17) is three-dimensional; elsewhere the field is two-dimensional. It follows from a basic two-dimensional result in [10] that outside the Mach cone, but inside the Mach wedger h = 0, the field is p(x, y, t) = −ρ 0 Mc 0v0 sgn(y) sgn(z)e −iω 0 (t−Mx/c 0 ) J 0 (kr h ).…”

“…Substantial progress has been made over many years in related subsonic problems, of which representative work in two dimensions is [1][2] and in three dimensions is [3][4][5][6][7][8]. For the supersonic problem, the amount of published work is smaller, but important two-dimensional fields have been determined in [9][10][11], and three-dimensional fields in [12][13][14][15][16][17]. 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.…”

“…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 Most of the three-dimensional sound fields calculated in the thesis remain unpublished.…”

Basic singular fields in the theory of impulsive supersonic leading-edge noise

“…For a supersonic edge, some three-dimensional impulsive fields have been calculated in [10][11][12][13], and a general theory of the generation of such fields is given in [14]. This theory is applied in the special case of two dimensions in [15], and in three dimensions in the PhD thesis [16], but most of the three-dimensional impulsive fields calculated in the thesis are unpublished. The aim of this paper is to present these fields, together with their derivations; a companion paper [17] gives a large number of corresponding non-impulsive fields, produced by single-frequency gusts.…”