Wall Pressure Fluctuations Research Articles

Wavelet analysis of supersonic shock-boundary-layer interaction

We present a wavelet analysis of supersonic shock-boundary-layer interaction. We have used direct numerical simulation data for supersonic flow over a compression ramp and performed orthogonal anisotropic wavelets. The wavelet-based method of extracting coherent structures is applied to the flow vorticity field, decomposed into coherent and incoherent contributions using thresholding of the wavelet coefficients. The statistics of the coherent part of vorticity are close to the statistics of the total field. The study aims to improve our understanding of the shock-boundary-layer interaction, the role of vorticity, and the relationship between the flow's coherent and incoherent vorticity components with the near-wall sound. Our analysis shows a substantial correlation between the incoherent part of vorticity components and wall-pressure fluctuations.

Estimation of wavenumber–frequency spectra of wall pressure due to turbulent flow over a flat plate using large-eddy simulation

The wavenumber–frequency spectra (WFS) of turbulent wall pressure fluctuations are used to design underwater acoustic systems, and a method is presented to determine them for flat plate flow using large-eddy simulations (LES). First, the Reynolds averaged Navier–Stokes (RANS) analysis is carried out for flow over the plate using k–ω shear-stress transport model. Flow parameters are extracted from the output of this analysis and used to impose boundary conditions for large-eddy simulations using a smaller domain with finer mesh. Mesh convergence studies are done to establish the adequacy of the proposed meshing scheme for estimating the turbulent boundary layer wall pressures. The stream-wise velocity profiles, turbulence intensities, and power spectra obtained using LES are compared with other computational and experimental results. The time history of fluctuating pressure on the wall at various stream-wise locations is used to estimate the WFS. Estimations are made of the convective ridge as well as sub-convective and low wavenumber portions of the spectrum. The computations are performed at momentum thickness-based Reynolds numbers (Rθ) of 5761, 7988, and 7709. The effect of downstream distance on the WFS is studied by computing it at three downstream locations and shown that the downstream distance has little effect on the WFS once the flow has become fully turbulent. The use of a desktop workstation for the estimation of WFS has not been reported earlier. The results show that the WFS of turbulent pressure due to flow over more complex geometries can be estimated using a similar method.

Analysis of the remote microphone probe technique for the determination of turbulence quantities

Measuring the statistics of the wall-pressure fluctuations (WPFs) is essential for understanding and evaluating laminar/turbulent boundary layers and flow-induced noise. The remote microphone probe (RMP) technique is one of the most successful experimental approaches to measuring WPFs. Despite its extensive use in academic and industrial research, the scientific literature currently lacks an evaluation of the RMP influence on the determination of turbulence quantities, such as the WPF spectrum, the convection velocity, and the turbulence coherence length. To fulfill this necessity, this paper analyses the effects of the RMP on the determination of turbulence quantities, including comparisons between the results obtained using RMPs and flush-mounted microphones (FMMs). The RMPs and the FMMs measure the WPFs under a turbulent boundary layer developed on a zero-pressure-gradient flat wall. This study shows that the turbulence quantities determined from RMP measurements are influenced by the RMP setup, i.e., tube length and inner diameter. The tube length affects the phase between RMPs, which impacts the turbulent structure convection velocity estimation, which can be determined correctly by considering the calibrated phase. Furthermore, the tube inner diameter influences the coherence between a pair of RMPs, affecting the calculation of the turbulence correlation length. This research also shows that the turbulence quantities determined from the RMP and the FMM measurements differ, mainly in the coherence between pairs of microphones.

Coherent Structures and Pressure Fluctuations over an Airfoil Using Time-Resolved Measurements

This study focused on the unsteady behaviors of large-scale vortical structures and wall pressure fluctuations and their coupling mechanism on a low-Reynolds-number airfoil. Three incidence angles were chosen for comparison: , and (representing two flow regimes, namely, the separation bubble formation and separation without subsequent reattachment). Simultaneous measurements of velocity fields and wall-pressure fluctuations were performed using a high-resolution time-resolved particle image velocimetry operating at 2 kHz and an array of flush-mounted microphones sampled at 10 kHz. The results provided a detailed description of the shear layer transition and the coherent structures development on the airfoil. The roll-up process, pairing process, spatial-temporal growth of the vortical structure, and vortex break-up were clarified through a long-period analysis. Spectral analysis demonstrated that vortical structures at the fundamental frequency were spatially and temporally localized and that their subharmonics were significantly enhanced. Frequency–wavenumber spectra revealed that the energy was dominantly concentrated along the convective ridge. With increasing incidence angle, the energy level of the inclined ridge increased, with a lower extension in the frequency domain and a higher dispersion in the wavenumber domain. The conditional averaging and quadrant analysis results demonstrated that strong events in the near-wall region were dominated by the sweep motion and ejection motion, which enhanced the interaction between the inner and outer layers. This also indicated the existence of a strong relationship between the wall-pressure peaks and turbulence production mechanisms.

Wall-pressure fluctuations in an axisymmetric boundary layer under strong adverse pressure gradient

Measurements of fluctuating wall pressure in a high-Reynolds-number flow over a body of revolution are described. With a strong axial pressure gradient and moderate lateral curvature, this non-equilibrium flow is relevant to marine applications as well as short-haul urban transportation. The wall-pressure spectrum and its scaling are discussed, along with its relation to the space–time structure. As the flow decelerates downstream, the root-mean-square level of the pressure drops together with the wall shear stress ( $\tau _w$ ) and is consistently approximately 7 $\tau _w$ . While the associated dimensional spectra see a broadband reduction of over 15 dB per Hz, they appear to attain a single functional form, collapsing to within 2 dB when normalized with the wall-wake scaling where $\tau _w$ is the pressure scale and $U_e/\delta$ is the frequency scale. Here, $\delta$ is the boundary layer thickness and $U_e$ is the local free-stream velocity. The general success of the wall-wake scaling, including in the viscous $f^{-5}$ region, suggests that the large-scale motions in the outer layer play a predominant role in the near-wall turbulence and wall pressure. On investigating further, we find that the instantaneous wall-pressure fluctuations are characterized by a quasi-periodic feature that appears to convect downstream at speeds consistent with the outer peak in the turbulence stresses. The conditional structure of this feature, estimated through peak detection in the time series, resembles that of a roller, supporting the embedded shear layer hypothesis (Schatzman & Thomas, J. Fluid Mech., vol. 815, 2017, pp. 592–642; Balantrapu et al., J. Fluid Mech., vol. 929, 2021, A9). Therefore, the outer-region shear-layer-type motions may be important when devising strategies for flow control, drag and noise reduction for decelerating boundary layers.

The Effect of the Step Height on the Wall Pressure Fluctuations near Its Side Edge in the Turbulent Boundary Layer

The Effect of the Step Height on the Wall Pressure Fluctuations near Its Side Edge in the Turbulent Boundary Layer

Influence of Reynolds number on the natural transition of boundary layers over underwater axisymmetric bodies

The influence of the Reynolds number on the natural transition of boundary layers over underwater axisymmetric bodies is studied using numerical approaches. This is a fundamental problem in fluid mechanics and is of great significance in practical engineering problems. The transition locations are predicted over diameter Reynolds numbers ranging from 1.79 × 105 to 2.32 × 108 for eight different forebody shapes. The transition onsets are predicted using the semi-empirical eN method based on the linear stability theory (LST), and the wall pressure fluctuation spectra are estimated. The effects of the forebody shapes and the Reynolds numbers on the transition location are studied. At the same Reynolds number, the forebody shape has a great influence on transition. As the Reynolds number increases, the changes in the dimensionless transition location are qualitatively similar for different forebody shapes. The dimensionless transition location shifts closer to the leading edge as the Reynolds number increases and is more sensitive at lower Reynolds numbers. However, the quantitative changes in transition location for different forebody shapes are distinctly different. Consequently, the sequential order of the transition locations for the eight forebody shapes is not fixed but changes dramatically with increasing Reynolds number. This irregularity in the sequential order of the transition locations is called the “Reynolds number effect.” Finally, the fundamental causes of this effect are analyzed.

Large eddy simulation of shock wave/turbulent boundary layer interaction under incipient and fully separated conditions

Large eddy simulations of shock wave/turbulent boundary layer interaction on a compression ramp at the Mach number M a ∞ = 5 and Reynolds number R e ∞ = 14 000 are performed to investigate the impact of the incipient and fully separated conditions on the development of the flow field. The quasi-dynamic subgrid-scale kinetic energy equation model, which combines the benefits of the gradient model with the eddy-viscosity model, has been applied. Compared with the previous experimental and numerical results, the simulation was validated. The flow structures, turbulence properties, vortex structures, and low-frequency unsteadiness are all investigated. The flow field of the incipient separation is attached and rarely impacted by shock. An evident separation bubble and localized high wall temperatures in fully separated flow are caused by the separation shock's significant reverse pressure gradient. The Reynolds stress components exhibit significant amplification in both cases, and the peak outward shifts from the near-wall region to the center of the free shear layer. Turbulent kinetic energy terms were analyzed, and the two scenarios show a significant difference. The power spectral density of the wall pressure fluctuations shows that the low-frequency motion of the incipient separation is not apparent relative to the fully separated flow.

On the effect of adverse pressure gradients on wall-pressure statistics in a controlled-diffusion aerofoil turbulent boundary layer

Wall-pressure and velocity statistics in the turbulent boundary layer (TBL) on a cambered controlled-diffusion aerofoil at $8^{\circ }$ incidence, a Mach number of 0.25 and a chord-based Reynolds number ${Re}_c=1.5\times 10^{5}$ are analysed at four locations on the suction side with zero and adverse pressure gradients (ZPG and APG), characterised by increasing Reynolds numbers based on momentum thickness, ${Re}_{\theta }=319$ , 390, 877 and $1036$ . The strong APG yields a highly non-equilibrium TBL at the trailing edge that significantly affects the turbulent flow statistics. Different normalisations of the full wall-pressure statistics involved in trailing-edge noise are analysed for the first time in such strong APG with convex curvature, and compared with available experimental and numerical data. Good overall agreement is found in the ZPG region, and most results obtained in previous APG TBL can be extended to the present highly non-equilibrium case. The presence of strong APG augments the intensity of wall-pressure fluctuations noticeably at low frequencies, shortens the streamwise and broadens the spanwise coherence of wall-pressure fluctuations in both time and space, and significantly reduces the convection velocity. The wall-pressure power spectral density are found to scale with the displacement thickness, the Zaragola–Smits velocity and the root-mean-squared pressure, the latter possibly being replaced by the local maximum Reynolds shear stress. The other two key parameters to trailing-edge noise modelling, the spanwise coherence length and the convection velocity, rather scale with displacement thickness and friction velocity, respectively.

Trailing-edge noise reduction through finlet-induced turbulence

Biologically inspired finlet treatments have been shown to effectively reduce the trailing-edge noise of a flat plate and hence are a viable noise-suppression technology for engineering applications. The present work performs a thorough experimental investigation on the near-field dynamics of finlet surface treatments applied to a flat plate. To examine the underlying noise-reduction mechanism, the manipulated flow field is analysed using data from detailed static, unsteady wall-pressure as well as velocity measurements and their correlations. Specifically, the densely populated dynamic transducers allow for the tracking of the turbulent boundary-layer development from upstream to the wake of the finlet-treated area (see supplementary movies), which elucidates the formation of ‘finlet-induced turbulence’ through flow–finlet interaction. Associated turbulence structures are found to further develop within the treated area and structures shed from the top of the finlets are observed to mix and merge with the turbulence being channelled through the space between the finlets in the finlet wake. While the mixing process increases the spanwise turbulence length scale, it significantly attenuates the unsteady wall-pressure fluctuation at the trailing edge and thus leads to broadband reduction of the trailing-edge noise. Moreover, it corroborates the findings of earlier studies suggesting that there exists an optimal distance between finlets and trailing-edge where the mixing effects are most beneficial.

Experimental characterisation and data-driven modelling of unsteady wall pressure fields induced by a supersonic jet over a tangential flat plate

This work deals with the investigation and modelling of wall pressure fluctuations induced by a supersonic jet over a tangential flat plate. The analysis is performed at several nozzle pressure ratios around the nozzle design Mach number, including slightly over-expanded and under-expanded conditions, and for different radial positions of the rigid plate. Pitot measurements and flow visualizations through the background oriented schlieren technique provided a general overview of the aerodynamic interactions between the jet flow and the plate at the different regimes and configurations. Wall pressure fluctuations were measured using a couple of piezoelectric pressure transducers flush mounted over the plate surface. The spectral analysis has been carried out to clarify the effect of the plate position on the single and multivariate wall pressure statistics, including the screech tone amplitude. The experimental dataset is used to assess and validate a surrogate model based on artificial neural networks. Sound pressure levels and coherence functions are modelled by means of a single fully connected network, built on the basis of a recently implemented fully deterministic topology optimization algorithm. The metamodel uncertainty is also quantified using the spatial correlation function. It is shown that the flow behaviour as well as the screech and broadband noise signatures are significantly influenced by the presence of the plate, and the effects on spectral quantities are correctly reproduced by the proposed data-driven model that provides predictions in agreement with the available data.

The Effect of the Step Height on the Wall Pressure Fluctuations near Its Side Edge in the Turbulent Boundary Layer

Wall pressure fluctuations in a turbulent flow are a source of noise and vibrations in elastic structures immersed in a flow. This paper presents the results of an experimental study on the effect produced by the height of a step on the spatiotemporal structure of wall pressure fluctuations in the vicinity of its side edge in the turbulent boundary layer. Measurements were performed in a subsonic low-noise wind tunnel of the Moscow Complex of the Zhukovsky Central Aerohydrodynamic Institute. The height of a step was varied from 3 to 17% of the incident-boundary-layer thickness. It has been shown that the area of the most intensive pressure fluctuations is located near the frontal side corner of the step. The characteristic Strouhal number determining the spectra of pressure fluctuations behind the leading edge of the step was established. An essential effect of the step height on the spatiotemporal structure of the pressure field in the vicinity of the side edge was shown. The obtained results evidence the existence of a strong correlation with the field of pressure fluctuations in the incident turbulent boundary layer in the case of steps with a small height.

Microphones as Airspeed Sensors for Unmanned Aerial Vehicles

This paper puts forward a novel design for an airspeed instrument aimed at small fixed-wing tail-sitter unmanned aerial vehicles. The working principle is to relate the power spectra of the wall-pressure fluctuations beneath the turbulent boundary layer present over the vehicle's body in flight to its airspeed. The instrument consists of two microphones; one flush-mounted on the vehicle's nose cone, which captures the pseudo-sound caused by the turbulent boundary layer, and a micro-controller that processes the signals and computes the airspeed. A feed-forward single-layer neural network is used to predict the airspeed based on the power spectra of the microphones' signals. The neural network is trained using data obtained from wind tunnel and flight experiments. Several neural networks were trained and validated using only flight data, with the best one achieving a mean approximation error of 0.043 m/s and having a standard deviation of 1.039 m/s. The angle of attack has a significant impact on the measurement, but if the angle of attack is known, the airspeed could still be successfully predicted for a wide range of angles of attack.

Experimental Study on a Generic Side-View Mirror with Slotted Cylindrical Foot

A simple model consisting of a mirror-housing and its cylindrical foot is applied to represent the automobile side-view mirror that causes unwanted aerodynamic noise and wind drag during high-speed driving. An additional slot is made on the solid foot to modify the flow around the mirror and thus reduce the side wall pressure fluctuation and aerodynamic drag. Flow fields and wall pressure fluctuations of these side-view mirror models have been investigated experimentally in a wind tunnel. The airflow rate through the slot varies with the changing of the slot area. Wall surface pressure sensors, particle image velocimetry (PIV), and six-component balance were applied to measure the acoustic and flow characteristics. The results demonstrated that, with the increase of slot airflow rate to 30%, the side wall pressure fluctuations were reduced by 5.1 dB and the drag coefficient decreased by 10.2%. The PIV measurements showed that the vortex cluster center behind the mirror was moved upward from the wall surface due to the slot airflow injection into the wake. The turbulent kinetic energy in the side-view mirror wake near the wall decreased with the increment of the airflow rate, reducing the side wall pressure fluctuations and thereby suppressing the noise generation.

An experimental investigation into the influence of installed passively controlled jet flows on wall-pressure fluctuations

Jet-surface interaction(JSI) represents a significant noise problem in the installation of modern ultra-high bypass ratio turbofan engines. The use of chevron nozzles is known to reduce low-frequency jet mixing noise(JM) by increasing the velocity gradient in the jet shear layer. This effect is expected to influence the jet flow in the vicinity of the wing and to modify the jet-surface interaction noise. To clarify the physics of these two(JSI and JM) noise source mechanisms, an extensive experimental investigation has been conducted in the anechoic chamber of the Doak Laboratory at the University of Southampton. Various measurements were carried out on an isolated subsonic jet and an installed beneath a 2D NACA4415 airfoil using different nozzle shapes and passive vortex generator geometries. The wall-pressure field on the airfoil surface was investigated using a set of wall-pressure transducers flush-mounted in the streamwise and spanwise directions on the pressure side of the airfoil. The unsteady wall-pressure data were analysed in both time and frequency domains to assess changes in: 1) surface trailing edge spanwise correlation length, 2) streamwise convection velocity of the hydrodynamic pressure field, and 3) modification of the hydrodynamic pressure field in the vicinity of the surface trailing edge.

Characteristics of self-excited shock wave oscillations in a supersonic isolator with exit duct configurations

The structure and dynamics of multiple shock waves inside a constant area isolator of a model scramjet engine are studied numerically using a finite volume solver. The flow is accelerated through a nozzle with an exit Mach number of 1.75 and continues in the constant area isolator where multiple shock waves are formed. To analyze the effect of duct acoustics on the dynamics of shock train oscillations, three ducts with a duct length of 0D, 50D, and 150D are attached to the exit of the isolator, where D is the isolator exit height. The wall static pressure variation along the bottom wall and four specific locations are monitored. The wall shear stress variation along the wall provides the location of separation and reattachment points in the flow field. The statistical analysis provided more insights into the oscillation mechanisms. The lower frequency components from the duct resonance are enhanced as the duct length is increased and it altered the dominant frequency of shock oscillation. The dependence of shock train length on the exit duct confirmation is analyzed by the pressure ratio method. The different frequency components in the flow field are analyzed using the power spectral density of wall static pressure fluctuations and are distinguished based on the frequency range. The cross-spectral analysis of the wall pressure fluctuations provided the correlation between pressure signals and their narrowband time delay. Thus, the origin and directions of the perturbations are obtained and discussed. The increase in exit duct length decreases the downstream disturbance velocity, indicating the duct resonance effect on shock train oscillations. • Simulation of the supersonic isolator flow field to understand the duct resonance effect on self-excited oscillations of shock train. • The duct resonance is varied by attaching ducts of different lengths to the exit of the isolator. • As the duct length is increased, the amplitude of shock oscillation is increased and the dominant frequency of shock oscillation is decreased. • The length of the shock train is increased with an increase in duct length. • The cross-spectral analysis of the wall pressure fluctuations provided the correlation between pressure signals and their narrowband time delay.

On low-frequency unsteadiness in swept shock wave–boundary layer interactions

We derive a scaling law for the characteristic frequencies of wall pressure fluctuations in swept shock wave/turbulent boundary layer interactions in the presence of cylindrical symmetry, based on analysis of a direct numerical simulations database. Direct numerical simulations in large domains show evidence of spanwise rippling of the separation line, with typical wavelength proportional to separation bubble size. Pressure disturbances around the separation line are shown to be convected at a phase speed proportional to the cross-flow velocity. This information is leveraged to derive a simple model for low-frequency unsteadiness, which extends previous two-dimensional models (Piponniau et al., J. Fluid Mech., vol. 629, 2009, pp. 87–108), and which correctly predicts growth of the typical frequency with the sweep angle. Inferences regarding the typical frequencies in more general swept shock wave/turbulent boundary layer interactions are also discussed.

Unsteadiness characterisation of shock wave/turbulent boundary-layer interaction at moderate Reynolds number

A direct numerical simulation of an oblique shock wave impinging on a turbulent boundary layer at Mach number 2.28 is carried out at moderate Reynolds number, simulating flow conditions similar to those of the experiment by Dupont et al. (J. Fluid Mech., vol. 559, 2006, pp. 255–277). The low-frequency shock unsteadiness, whose characteristics have been the focus of considerable research efforts, is here investigated via the Morlet wavelet transform. Owing to its compact support in both physical and Fourier spaces, the wavelet transformation makes it possible to track the time evolution of the various scales of the wall-pressure fluctuations. This property also makes it possible to define a local intermittency measure, representing a frequency-dependent flatness factor, to pinpoint the bursts of energy that characterise the shock intermittency scale by scale. As a major result, wavelet decomposition shows that the broadband shock movement is actually the result of a collection of sparse events in time, each characterised by its own temporal scale. This feature is hidden by the classical Fourier analysis, which can only show the time-averaged behaviour. Then, we propose a procedure to process any relevant time series, such as the time history of the wall pressure or that of the separation bubble extent, in which we use a condition based on the local intermittency measure to filter out the turbulent content in the proximity of the shock foot and to isolate only the intermittent component of the signal. In addition, wavelet analysis reveals the intermittent behaviour also of the breathing motion of the recirculation bubble behind the reflected shock, and allows us to detect a direct, partial correspondence between the most significant intermittent events of the separation region and those of the wall pressure at the foot of the shock.

Influence of orifice thickness and chamfer on broadband noise in a water circuit

An incompressible large-eddy simulation (LES) is used to predict broadband noise generation by an orifice in a water circuit. Flow conditions are chosen in order to avoid cavitation. The model’s results are compared to measured wall pressure fluctuations for three orifices: a thin sharp-square-edge orifice, a thick sharp-square-edge orifice and a thick narrower orifice with an upstream chamfer. Reynolds-averaged Navier–Stokes (RANS) and large-eddy simulations (LES) fail to reproduce the steady-flow drag coefficient of the thick sharp-edge orifice and of the upstream-chamfered orifice. Large differences are found in the steady-flow drag coefficient of different samples of the thick orifice. An edge-tone like instability is observed in the near-field pressure fluctuations of one of the thick sharp-square-edge orifices, which does not appear in the other samples and is suppressed by the upstream chamfer. However, there are only minor differences in far-field radiated sound for these thick sharp-edged orifices. A plane-wave model with acoustic source from the LES predicts the power spectral density (PSD) of the acoustic pressures within a factor 3. At low Strouhal numbers (based on the orifice diameter and the cross-sectional averaged velocity in the orifice) the thin orifice behaves similarly to the thicker strongly chamfered orifices, with thin central cylindrical section. At higher Strouhal numbers the measured and predicted acoustic-pressure fluctuations due to these orifices are two orders of magnitude lower than those of thick orifices with sharp square edges. As orifices are used for the control of the flow distribution through complex water-cooling networks, the good results for thick chamfered narrow orifices call for a further study to find shapes that minimize the sound production at constant static pressure drop.

Measurements of turbulent wall pressure fluctuation field in a turbulent boundary layer and the wing-flat plate juncture flow using the many-channel microphone array

Measurements of turbulent wall pressure fluctuation field in a turbulent boundary layer and the wing-flat plate juncture flow using the many-channel microphone array