On the hydrodynamic and acoustic wall pressure fluctuations in turbulent pipe flow due to a 90° mitred bend

When the fully-developed turbulent flow in a pipe of circular cross-section is forced to negotiate a 90° mitred bend, flow separation occurs at the inner and outer corners of the bend, with random switching of the separation regions from one side of the plane of symmetry of the bend to the other (as was previously observed by Tunstall and Harvey). The resulting disturbance to the fluctuating pressure field consists of intense non-propagating fluctuations over the region of the inner-wall separation, which near re-attachment have a maximum rms value of about 33% of the undisturbed centre-line dynamic pressure, but are rapidly attenuated with downstream distance from the bend. Beyond about 12 diameters downstream the only remaining disturbance is an acoustic field comprising propagating higher order modes and plane waves, the latter making the larger contribution to the overall mean square pressure. Extensive spectral measurements of the wall pressure field for flow Mach numbers in the range 0·2-0·5 are presented, and regions where higher order modes are detectable are identified. Downstream of the bend, wall pressure spectra generally have two local maxima at frequencies below those at which higher order acoustic modes can propagate. They occur at Strouhal numbers of about 0·4 and 1·6, and turbulent fluctuations at these frequencies in the vicinity of the bend appear to be mainly responsible for the generation of plane acoustic waves. The former Strouhal number does not vary significantly with streamwise position but decreases slightly with increasing flow speed; the latter is somewhat more sensitive to both flow speed and streamwise position. Upstream of the bend wall pressure spectra exhibit only the maximum at a Strouhal number of about 0·4.