Abstract
The characteristics of unsteady surface pressure (USP) created by turbulent flow over a family of asymmetrically beveled trailing edges were studied experimentally. The geometries had a trailing edge angle \(\theta =25^\circ\) with a flat lower surface and a rounded upper surface with radii of curvature between zero and ten times the airfoil thickness. The Reynolds number was \(Re=2.1\times 10^6\) based on chord. A detailed description of the USP and flow field around the trailing edge was obtained using remote microphone probes (RMP) and particle image velocimetry (PIV), respectively. The lower surface exhibited USP auto-spectral density magnitudes that were similar to those of a zero-pressure-gradient turbulent boundary layer at higher frequency. The low-frequency pressure fluctuations were influenced by the turbulent wake, leading to large increases in magnitude closer to the trailing edge. An empirical model of these results is proposed. The beveled upper surface was characterized by a region of favorable pressure gradient, followed by a strong adverse pressure gradient. The cases with smaller radius of curvature were found to exhibit separated flow over the trailing edge. The spectral magnitudes were largest in these regions, and significant attention is given to the proper scaling of these results. The PIV measurements provided the length and velocity scales for this purpose.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Amiet RK (1976) Noise due to turbulent flow past a trailing edge. J Sound Vib 47(3):387–393
Bearman PW (1965) Investigation of the flow behind a two-dimensional model with a blunt trailing edge and fitted with splitter plates. J Fluid Mech 21(2):241–255
Bilka MJ, Paluta MR, Silver JC, Morris SC (2015) Spatial correlation of measured unsteady surface pressure behaind a backward-facing step. Exp Fluids 56:37
Blake WK (1975) A statistical description of pressure and velocity fields at the trailing edges of a flat strut. Technical report TR-4241. David W. Taylor Naval Ship Research and Development Center, Bethesda
Blake WK (1984) Trailing edge flow and aerodynamic sound, part 1. tonal pressure and velocity fluctuations, part 2. random pressure and velocity fluctuations. Technical report DTNSRDC-83/113. David W. Taylor Naval Ship Research and Development Center, Bethesda
Blake WK (ed) (1986) Mechanics of flow induced sound and vibration. Academic Press, Cambridge
Catlett MR, Anderson JM, Forest JB, Stewart DO (2016) Empirical modeling of pressure spectra in adverse pressure gradient turbulent boundary layers. AIAA J 54(2):569–587
Chase DM (1980) Modeling the wavevector-frequency spectrum of turbulent boundary layer wall pressure. J Sound Vib 70(1):29–67
Corcos GM (1963) Resolution of pressure in turbulence. J Acoust Soc Am 35(2):192–199
Corcos GM (1964) Structure of turbulent pressure field in boundary-layer flows. J Fluid Mech 18(3):358–378
Curle N (1955) The influence of solid boundaries upon aerodynamic sound. Proc R Soc Lond A 231(1187):505–514
Dyer I (1959) Response of plates to a decaying and convecting random pressure field. J Acoust Soc Am 31(7):922–928
Gershfeld J, Blake WK, Knisely CW (1988) Trailing edge flows and aerodynamic sound. In: Proceedings of the 1st national fluid dynamics conference, AIAA, Cincinnati, pp 2133–2140
Goody M (2004) Empirical spectral model of surface pressure fluctuations. AIAA J 42(9):1788–1794
Guan Y, Berntsen CR, Bilka MJ, Morris SC (2016a) The measurement of unsteady surface pressure using a remote microphone probe. J Vis Exp. https://doi.org/10.3791/53627
Guan Y, Pröbsting S, Stephens D, Gupta A, Morris SC (2016b) On the wake flow of asymmetrically beveled trailing edges. Exp Fluids 57:78
Hu N, Herr M (2016) Characteristics of wall pressure fluctuations for a flat plate turbulent boundary layer with pressure gradients. In: 22nd AIAA/CEAS aeroacoustics conference, AIAA, Lyon, pp 2016–2749
Ji M, Wang M (2012) Surface pressure fluctuations on steps immersed in turbulent boundary layers. J Fluid Mech 712:471–504
Kraichnan RH (1956) Pressure fluctuations in turbulent flow over a flat plate. J Acoust Soc Am 28:378–390
Landahl MT (1967) A wave-guide model for turbulent shear flow. J Fluid Mech 29(3):441–459
Mueller TJ, Scharpf D, Batill S, Strebinger R, Sullivan C, Subramanian S (1992) The design of a low-noise, low-turbulence wind tunnel for acoustic measurements. In: Proceedings of the 28th joint propulsion conference and exhibit, Nashville, AIAA, pp 1992–3883
Panton RL, Linebarger JH (1974) Wall pressure spectra calculations for equilibrium boundary layers. J Fluid Mech 65(2):261–287
Powell A (1958) On the fatigue failure of structures due to vibrations excited by random pressure fields. J Acoust Soc Am 30(12):1130–1135
Pröbsting S, Gupta A, Scarano F, Guan Y, Morris SC (2014) Tomographic PIV for beveled trailing edge aeroacoustics. In: Proceedings of the 20th AIAA/CEAS aeroacoustics conference, AIAA< Atlanta, pp 2014–3301
Pröbsting S, Zamponi M, Ronconi S, Guan Y, Morris SC, Scarano F (2016) Vortex shedding noise from a beveled trailing edge. Int J Aeroacoust 15(8):712–733
Roger M, Moreau S (2002) Trailing edge noise measurements and prediction for subsonic loaded fan blades. In: Proceedings of the 8th AIAA/CEAS aeroacoustics conference and exhibit, AIAA, Breckenridge, pp 2002–2460
Rozenberg Y, Robert G (2012) Wall-pressure spectral model including the adverse pressure gradient effects. AIAA J 50(12):2168–2179
Scharpf DF (1993) An experimental investigation of propeller noise due to turbulence ingestion. Phd thesis, University of Notre Dame, Notre Dame
Schloemer H (1967) Effects of pressure gradients on turbulent-boundary-layer wall-pressure fluctuations. J Acoust Soc Am 42(1):93–113
Shannon DW, Morris SC (2006) Experimental investigation of a blunt trailing edge flow field with application to sound generation. Exp Fluids 41(5):777–788
Shannon DW, Morris SC (2008) Trailing edge noise measurements using a large aperture phased array. Int J Aeroacoust 7(2):147–176
Simpson RL, Ghodbane M, McGrath BE (1987) Surface pressure fluctuations in a separating turbulent boundary layer. J Fluid Mech 177:167–186
van der Velden WCP, Pröbsting S, van Zuijlen AH, de Jong AT, Guan Y, Morris SC (2016) Numerical and experimental investigation of a beveled trailing-edge flow field and noise emission. J Sound Vib 384:113–129
Wang M (2005) Computation of trailing-edge aeroacoustics with vortex shedding. Center for Turbulence Research Annual research Briefs, Stanford University, Stanford
Wang M, Moin P (2000) Computation of trailing-edge flow and noise using large-eddy simulation. AIAA J 38(12):2201–2209
Welch PD (1967) The use of fast Fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms. IEEE Trans Audio Electroacoust 15:70–73
Willmarth WW, Wooldridge CE (1962) Measurements of fluctuating pressure at wall beneath thick turbulent boundary layer. J Fluid Mech 14(2):187–210
Acknowledgements
This research was supported by the US Office of Naval Research (ONR), under Grant Number N00014-09-1-0050 and by the European Community’s Seventh Framework Programme (FP7/2007-2013) under the AFDAR project (Advanced Flow Diagnostics for Aeronautical Research), Grant Agreement No. 265695.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Guan, Y., Pröbsting, S. & Morris, S.C. Unsteady surface pressure characteristics of asymmetrically beveled trailing edges. Exp Fluids 59, 118 (2018). https://doi.org/10.1007/s00348-018-2572-6
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00348-018-2572-6