The wall pressure signature of transonic shock/boundary layer interaction

2011 ◽  
Vol 671 ◽  
pp. 288-312 ◽  
Author(s):  
MATTEO BERNARDINI ◽  
SERGIO PIROZZOLI ◽  
FRANCESCO GRASSO
Keyword(s):  
Boundary Layer ◽  
Dynamic Pressure ◽  
Pressure Fluctuations ◽  
Low Frequency ◽  
Space Time ◽  
Wall Pressure ◽  
Spanwise Direction ◽  
Frequency Spectra ◽  
Wall Pressure Fluctuations ◽  
Time Correlations

The structure of wall pressure fluctuations beneath a turbulent boundary layer interacting with a normal shock wave at Mach number M∞ = 1.3 is studied exploiting a direct numerical simulation database. Upstream of the interaction, in the zero-pressure-gradient region, pressure statistics compare well with canonical low-speed boundary layers in terms of fluctuation intensities, space–time correlations, convection velocities and frequency spectra. Across the interaction zone, the root-mean-square wall pressure fluctuations attain very large values (in excess of 162 dB), with a maximum increase of about 7 dB from the upstream level. The two-point wall pressure correlations become more elongated in the spanwise direction, indicating an increase of the pressure-integral length scales, and the convection velocities (determined from space–time correlations) are reduced. The interaction qualitatively modifies the shape of the frequency spectra, causing enhancement of the low-frequency Fourier modes and inhibition of the higher ones. In the recovery region past the interaction, the pressure spectra collapse very accurately when scaled with either the free-stream dynamic pressure or the maximum Reynolds shear stress, and exhibit distinct power-law regions with exponent −7/3 at intermediate frequencies and −5 at high frequencies. An analysis of the pressure sources in the Lighthill's equation for the instantaneous pressure has been performed to understand their contributions to the wall pressure signature. Upstream of the interaction the sources are mainly located in the proximity of the wall, whereas past the shock, important contributions to low-frequency pressure fluctuations are associated with long-lived eddies developing far from the wall.

The structure of wall-pressure fluctuations in turbulent boundary layers with adverse pressure gradient and separation

1998 ◽  
Vol 377 ◽  
pp. 347-373 ◽  
Author(s):  
Y. NA ◽  
P. MOIN
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Separation Bubble ◽  
Reynolds Shear Stress ◽  
Pressure Fluctuations ◽  
Adverse Pressure Gradient ◽  
Wall Pressure ◽  
Spanwise Direction ◽  
Frequency Spectra ◽  
Wall Pressure Fluctuations

Space–time correlations and frequency spectra of wall-pressure fluctuations, obtained from direct numerical simulation, are examined to reveal the effects of pressure gradient and separation on the characteristics of wall-pressure fluctuations. In the attached boundary layer subjected to adverse pressure gradient, contours of constant two-point spatial correlation of wall-pressure fluctuations are more elongated in the spanwise direction. Convection velocities of wall-pressure fluctuations as a function of spatial and temporal separations are reduced by the adverse pressure gradient. In the separated turbulent boundary layer, wall-pressure fluctuations are reduced inside the separation bubble, and enhanced downstream of the reattachment region where maximum Reynolds stresses occur. Inside the separation bubble, the frequency spectra of wall-pressure fluctuations normalized by the local maximum Reynolds shear stress correlate well compared to those normalized by free-stream dynamic pressure, indicating that local Reynolds shear stress has more direct influence on the wall-pressure spectra. Contour plots of two-point correlation of wall-pressure fluctuations are highly elongated in the spanwise direction inside the separation bubble, implying the presence of large two-dimensional roller-type structures. The convection velocity determined from the space–time correlation of wall-pressure fluctuations is as low as 0.33U0 (U0 is the maximum inlet velocity) in the separated zone, and increases downstream of reattachment.

LES Prediction of Wall-Pressure Fluctuations and Noise of a Low-Speed Airfoil

2009 ◽  
Vol 8 (3) ◽  
pp. 177-197 ◽  
Author(s):  
Meng Wang ◽  
Stephane Moreau ◽  
Gianluca Iaccarino ◽  
Michel Roger
Keyword(s):  
Boundary Layer ◽  
Wind Tunnel ◽  
Pressure Fluctuations ◽  
Wall Pressure ◽  
Transition To Turbulence ◽  
Trailing Edge ◽  
Frequency Spectra ◽  
Potential Core ◽  
Low Speed ◽  
Wall Pressure Fluctuations

This paper discusses the prediction of wall-pressure fluctuations and noise of a low-speed flow past a thin cambered airfoil using large-eddy simulation (LES). The results are compared with experimental measurements made in an open-jet anechoic wind-tunnel at Ecole Centrale de Lyon. To account for the effect of the jet on airfoil loading, a Reynolds-averaged Navier-Stokes calculation is first conducted in the full wind-tunnel configuration, and the mean velocities from this calculation are used to define the boundary conditions for the LES in a smaller domain within the potential core of the jet. The LES flow field is characterized by an attached laminar boundary layer on the pressure side of the airfoil and a transitional and turbulent boundary layer on the suction side, in agreement with experimental observations. An analysis of the unsteady surface pressure field shows reasonable agreement with the experiment in terms of frequency spectra and spanwise coherence in the trailing-edge region. In the nose region, characterized by unsteady separation and transition to turbulence, the wall-pressure fluctuations are highly sensitive to small perturbations and thus diffcult to predict or measure with certainty. The LES, in combination with the Ffowcs Williams and Hall solution to the Lighthill equation, also predicts well the radiated trailing-edge noise. A finite-chord correction is derived and applied to the noise prediction, which is shown to improve the overall agreement with the experimental sound spectrum.

Direct Measurements of Turbulent Boundary Layer Wall Pressure Wavenumber-Frequency Spectra

1998 ◽  
Vol 120 (1) ◽  
pp. 29-39 ◽  
Author(s):  
B. M. Abraham ◽  
W. L. Keith
Keyword(s):  
Boundary Layer ◽  
Pressure Fluctuations ◽  
Pressure Sensors ◽  
Streamwise Velocity ◽  
Accurate Estimate ◽  
Wall Pressure ◽  
Frequency Spectra ◽  
Wall Pressure Fluctuations ◽  
Direct Measurements ◽  
Displacement Thickness

Direct measurements of streamwise wavenumber-frequency spectra of turbulent wall pressure fluctuations were made in an acoustically quiet water tunnel. A linear array of evenly spaced flush mounted pressure sensors was used to measure the wall pressure field at 48 streamwise locations. This array provided over 24 dB of resolution (sidelobe rejection) in the wavenumber domain, leading to an accurate estimate of the “convective ridge” and part of the subconvective and low wavenumber portions of the spectrum at discrete frequencies. Boundary layer parameters, including the mean wall shear stress, boundary layer thickness, displacement thickness, and momentum thickness, were derived from mean streamwise velocity measurements for 8100 < Rθ < 16,700. Time and length scales derived from these parameters were used to nondimensionalize the measured spectra. The effectiveness of different scalings for nondimensionalizing the low and convective wavenumber regions at discrete frequencies was evaluated.

Modeling the Wavevector-Frequency Spectrum of Boundary-Layer Wall Pressure During Transition on a Flat Plate

1990 ◽  
Vol 112 (4) ◽  
pp. 523-534 ◽  
Author(s):  
M. A. Josserand ◽  
G. C. Lauchle
Keyword(s):  
Boundary Layer ◽  
Frequency Spectrum ◽  
Pressure Fluctuations ◽  
Basic Result ◽  
Space Time ◽  
Wall Pressure ◽  
Boundary Layer Transition ◽  
Layer Transition ◽  
Turbulent Layer ◽  
Wall Pressure Fluctuations

A spectral model for the wall-pressure fluctuations induced on a zero pressure gradient, flat, rigid surface by a transitioning boundary layer at low Mach number is developed in this paper. The central assumption used in this modeling is that the space-time statistics associated with the formation, convection, and interaction of turbulent spots in a naturally occurring boundary-layer transition are independent of the space-time statistics of the wall-pressure fluctuations that are induced by the turbulence in the individual spots. Space-time correlations for the spots were determined experimentally and semi-empirical formulae are developed to predict these correlations. Previously published statistical descriptions of turbulence-induced wall-pressure fluctuations are coupled with the spot statistics to arrive at the model for the wavevector-frequency spectrum of the transition region. The basic result suggests that the wall-pressure wavevector-frequency spectrum of a transitioning boundary layer is approximately that produced by a fully-turbulent layer weighted by the intermittency factor.

Measurements of Fluctuating Wall Pressure for Separated/Reattached Boundary Layer Flows

1986 ◽  
Vol 108 (3) ◽  
pp. 301-307 ◽  
Author(s):  
T. M. Farabee ◽  
M. J. Casarella
Keyword(s):  
Boundary Layer ◽  
Pressure Field ◽  
Pressure Fluctuations ◽  
Plate Boundary ◽  
Low Frequency ◽  
Wall Pressure ◽  
Boundary Layer Flows ◽  
Backward Facing Step ◽  
Wall Pressure Fluctuations ◽  
Layer Flow

Measurements were made of the wall pressure field beneath separated/reattached boundary layer flows. These flows consisted of two types; flow over a forward-facing step and flow over a backward-facing step. Wall pressure fluctuations from an equilibrium flat plate boundary layer flow were also measured and used as a baseline for comparative purposes. Values of the RMS fluctuating pressure as well as the frequency spectral density, phase velocity, and coherence of the surface pressure field were measured at various locations upstream and downstream of the steps. The experimental results show that the separation-reattachment process produces large-amplitude, low-frequency pressure fluctuations. The measured spectral statistics of the wall pressure fluctuations are consistent with the view that at reattachment there exists a region of coherent highly energized velocity fluctuations located near the wall which, as it convects downstream, decays and diffuses away from the wall. This energized region remains identifiable in the wall pressure statistics as far as 72 step heights downstream of the backward-facing step.

Predicting Turbulent Boundary Layer Wall Pressure Fluctuations in Adverse Pressure Gradients

2005 ◽  
Author(s):  
Frank J. Aldrich
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Pressure Fluctuations ◽  
Adverse Pressure Gradient ◽  
Wall Pressure ◽  
Prediction Tool ◽  
Pressure Gradients ◽  
Wall Pressure Fluctuations ◽  
The Difference

A physics-based approach is employed and a new prediction tool is developed to predict the wavevector-frequency spectrum of the turbulent boundary layer wall pressure fluctuations for subsonic airfoils under the influence of adverse pressure gradients. The prediction tool uses an explicit relationship developed by D. M. Chase, which is based on a fit to zero pressure gradient data. The tool takes into account the boundary layer edge velocity distribution and geometry of the airfoil, including the blade chord and thickness. Comparison to experimental adverse pressure gradient data shows a need for an update to the modeling constants of the Chase model. To optimize the correlation between the predicted turbulent boundary layer wall pressure spectrum and the experimental data, an optimization code (iSIGHT) is employed. This optimization module is used to minimize the absolute value of the difference (in dB) between the predicted values and those measured across the analysis frequency range. An optimized set of modeling constants is derived that provides reasonable agreement with the measurements.

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