Spectrum Of Wall Pressure Fluctuations Research Articles

On wall pressure fluctuations in conical shock wave/turbulent boundary layer interaction

The structure and the frequency spectra of wall pressure fluctuations beneath a planar turbulent boundary layer interacting with a conical shock wave at Mach number $M_\infty =2.05$ and Reynolds number $\textit {Re}_\theta \approx 630$ (based on the upstream boundary layer momentum thickness) are examined to elucidate the effects of pressure gradient and flow separation on the characteristics of the wall pressure fluctuations, by exploiting a direct numerical simulation database. Upstream of the interaction, in the zero pressure gradient region, wall pressure statistics compare well with canonical compressible boundary layers in terms of fluctuation intensities and frequency spectra. Across the main interaction zone (APG1), the root-mean-square of wall pressure fluctuations becomes very large (corresponding to approximately 173.3 dB), with maximum increase approximately 12.7 dB from the incoming level. In the second adverse pressure gradient zone (APG2), the root-mean-square of wall pressure fluctuations attains a second peak (corresponding to $164.7$ dB), with an increase of 8.4 dB from the upstream level. Both the APG1 and APG2 regions feature a substantial fraction of flow reversal events, which are, however, scattered and interspersed with regions of attached flow. The wall pressure power spectral density exhibits a broadband and energetic low-frequency component associated with the global unsteadiness of the separation bubble/conical shock system. Analysis of the two-point correlations and wavenumber/frequency spectra of wall pressure fluctuations further suggests that the typical eddies become more elongated along the spanwise direction, as the flow in the separated region tends to escape the centreline, and the convection velocity is significantly reduced.

Numerical study of the natural transition of water boundary layers over heated/cooled flat plates

The natural transition of water boundary layers on heated/cooled flat plates is investigated using numerical methods. The influences of wall temperature, oncoming flow velocity, and onco ming flow temperature on the transition are studied. Laminar basic flows are obtained by solving the Blasius equations, while water temperature is taken into consideration. Linear stability analyses of the basic flows are performed, and the transition positions are predicted using the eN method. The spectra of wall pressure fluctuations in the laminar region are also predicted. The results show that the heated wall produces a fuller velocity profile and a thinner boundary layer for the laminar flow and that a cooled wall causes the opposite effects. Consequently, the heated wall delays transition, while the cooled wall advances transition. As wall temperature increases, the effect of transition delay becomes stronger until the maximal delay effect occurs at an optimal wall temperature. Wall temperatures higher than the optimal value weaken the transition delay effect. This phenomenon of the heated wall is called transition reversal. A heated wall suppresses the wall pressure fluctuation, and a cooled wall has the opposite effect. The oncoming flow velocity has little influence on the non-dimensional transition position, while the oncoming flow temperature has a strong influence on it. At the same wall temperature, a higher oncoming flow temperature leads to a thicker boundary layer, stronger instability, and an earlier transition. A lower oncoming flow temperature leads to stronger sensitivity of the transition to the wall temperature.

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.

On the wavenumber–frequency spectrum of the wall pressure fluctuations in turbulent channel flow

Direct numerical simulations (DNS) of turbulent channel flows up to${Re}_{\tau} \approx 1000$are conducted to investigate the three-dimensional (consisting of streamwise wavenumber, spanwise wavenumber and frequency) spectrum of wall pressure fluctuations. To develop a predictive model of the wavenumber–frequency spectrum from the wavenumber spectrum, the time decorrelation mechanisms of wall pressure fluctuations are investigated. It is discovered that the energy-containing part of the wavenumber–frequency spectrum of wall pressure fluctuations can be well predicted using a similar random sweeping model for streamwise velocity fluctuations. To refine the investigation, we further decompose the spectrum of the total wall pressure fluctuations into the autospectra of rapid and slow pressure fluctuations, and the cross-spectrum between them. We focus on evaluating the assumption applied in many predictive models, that is, the magnitude of the cross-spectrum is negligibly small. The present DNS shows that neglecting the cross-spectrum causes a maximum error up to 4.7 dB in the subconvective region for all Reynolds numbers under test. Our analyses indicate that the approximation of neglecting the cross-spectrum needs to be applied carefully in the investigations of acoustics at low Mach numbers, in which the subconvective components of wall pressure fluctuations make important contributions to the radiated acoustic power.

Wake-aerofoil interaction noise control with trailing-edge serrations

The present study experimentally investigates the effective reduction of wake-aerofoil interaction noise in a tandem aerofoil configuration using trailing-edge sawtooth serrations. The far-field noise results clearly show that at the ‘head-on’ wake impingement, the use of sawtooth serrations on the trailing-edge of the front aerofoil can lead to substantial reduction of the wake-aerofoil interaction noise of approximately 10 dB without any noticeable increase at other frequencies and changes to directivity pattern. Subsequently, detailed near-field measurements were carried out to investigate further the flow dynamics associated with the reduction of the interaction noise. The flow field and unsteady loading results suggest that the wake-aerofoil interaction primarily takes place within the first 30% of the chord close to the leading-edge area, while towards the trailing-edge, the flow is influenced more heavily by the boundary layer development. The velocity and wall pressure fluctuation spectra show significant decrease of the energy frequency content of the flow structures over the wake-aerofoil interaction frequency range after the wake impingement, due to the modification of the wake turbulence by trailing-edge serrations. This leads to notable reduction in the unsteady aerodynamic loading, particularly in the lift direction. Further coupled pressure–velocity analyses reveal that the sawtooth serrations modify the energy frequency content associated with the dominant turbulence eddies by spreading it over a wider frequency range. Near-field to far-field pressure coherence also reveals the loss of coherence, and thus abatement of the radiated far-field noise. The experimental results are relevant to practical applications in rotor–stator and outlet guide vanes.

Simulation of turbulence induced sound generation inside stenosed femoral artery models with different severities and eccentricities

Background and objectivesRecent developments of low-cost, compact acoustic sensors, advanced signal processing tools and powerful computational resources allow researchers design new scoring systems for acoustic detection of arterial stenoses. In this study, numerical simulations of blood flow inside stenosed arteries are performed to understand the effect of stenosis severity and eccentricity on the turbulence induced wall pressure fluctuations and the generated sound. MethodsAxisymmetric and eccentric elliptic stenoses of five different severities are generated inside a 6.4 mm diameter femoral artery model. Large eddy simulations of pulsatile, non-Newtonian blood flow are performed using the open source software OpenFOAM. ResultsPost-stenotic turbulence activity is found to be almost zero for 50 and 60% severities. For severities of 75% and more, turbulent kinetic energy rises significantly with increasing severity. The location of the highest turbulence activity on the vessel wall from the stenosis exit decreases with increasing severity. The maximum level of turbulent kinetic energy seen in 95% severity models is about 9 and 31 times higher than that of 87% and 75% models, respectively. Spectrum of wall pressure fluctuations show that 50 and 60% axisymmetric models are almost silent. The spectrum starts to get richer with 75% severity, and the fluctuation intensity increases with severity. Compared to the axisymmetric models, more activity is observed in the 0–150 Hz band for the 50 and 60% eccentric models. Axial extent of the acoustically active region is also longer in them. Converting wall pressure data into sound revealed that murmurs that can be considered as signs of vascular stenosis are obtained for models with 75% and higher severity. ConclusionsSound patterns generated from simulation results are similar to the typical sounds obtained by Doppler ultrasonography, and present distinct characters. Together with a sensor technology that can measure these sounds from within the stenosed artery, they can be processed and used for the purpose of non-invasive diagnosis. Computational fluid dynamics studies that simulate large number of cases with different stenosis severities and morphologies will play a critical role in developing the necessary sound databases, which can be used to train new diagnostic devices.

CFD-based prediction of wall-pressure spectra under a turbulent boundary layer with adverse pressure gradient

A model of the spectrum of wall-pressure fluctuations under a turbulent boundary layer based on an analytical solution of the Poisson equation is presented. This model is suited for aeroacoustic prediction based on CFD-extracted flow information but requires statistical properties of the boundary-layer turbulence that are not resolved in steady-state simulations and need to be modelled. For this reason, this paper uses Lattice-Boltzmann (DNS-LBM) and Navier-Stokes Direct Numerical Simulations (DNS-NS) of an airfoil in a wind-tunnel jet to investigate the link between turbulence and wall-pressure statistics and validate the assumptions made in the application of the analytical model. The use of input from two numerical simulation methods allows generalizing the results of the analytical model.

Updating of wavenumber-frequency spectrum models by a phased array measurement

This study mainly presents the updating of wavenumber-frequency spectrum models (W-F models) based on spatial correlation measurement by a phased array technique, which is critical for the evaluation of the structural vibration caused by a turbulent boundary layer. Measurements are carried out in a wind tunnel, and the effect of background noise on identifying the spatial correlations of pressure fluctuations is discussed. To improve the resolution of the beam map used to estimate the spatial correlation by the beamforming algorithm, focusing functions are introduced to accelerate beam focusing. Then, broadband fluctuations and flow-speed effects on spatial correlation identification are discussed to estimate the adaption scope of the phased array technique. To update W-F models of wall pressure fluctuations, the subsection approaching method (SAM) is employed to extract the power spectrum of wall pressure fluctuations based on the identified spatial correlation. The investigated results reveal that the spatial correlation of wall pressure fluctuations caused by the turbulent boundary layer obeys a statistical law but does not constitute an exact math expression, which further validates the necessity of the phased array technique in spatial correlation identification.

Effect of wall cooling on boundary-layer-induced pressure fluctuations at Mach 6

Direct numerical simulations of turbulent boundary layers with a nominal free-stream Mach number of $6$ and a Reynolds number of $Re_{\unicode[STIX]{x1D70F}}\approx 450$ are conducted at a wall-to-recovery temperature ratio of $T_{w}/T_{r}=0.25$ and compared with a previous database for $T_{w}/T_{r}=0.76$ in order to investigate pressure fluctuations and their dependence on wall temperature. The wall-temperature dependence of widely used velocity and temperature scaling laws for high-speed turbulent boundary layers is consistent with previous studies. The near-wall pressure-fluctuation intensities are dramatically modified by wall-temperature conditions. At different wall temperatures, the variation of pressure-fluctuation intensities as a function of wall-normal distance is dramatically modified in the near-wall region but remains almost intact away from the wall. Wall cooling also has a strong effect on the frequency spectrum of wall-pressure fluctuations, resulting in a higher dominant frequency and a sharper spectrum peak with a faster roll-off at both the high- and low-frequency ends. The effect of wall cooling on the free-stream noise spectrum can be largely accounted for by the associated changes in boundary-layer velocity and length scales. The pressure structures within the boundary layer and in the free stream evolve less rapidly as the wall temperature decreases, resulting in an increase in the decorrelation length of coherent pressure structures for the colder-wall case. The pressure structures propagate with similar speeds for both wall temperatures. Due to wall cooling, the generated pressure disturbances undergo less refraction before they are radiated to the free stream, resulting in a slightly steeper radiation wave front in the free stream. Acoustic sources are largely concentrated in the near-wall region; wall cooling most significantly influences the nonlinear (slow) component of the acoustic source term by enhancing dilatational fluctuations in the viscous sublayer while damping vortical fluctuations in the buffer and log layers.

Modelling wall pressure fluctuations under a turbulent boundary layer

The derivation of the wave vector-frequency (w-f) spectrum of wall pressure fluctuations below a turbulent boundary layer developed over a rigid flat plate is re-considered. The Lighthill's equation for pressure fluctuations is derived in a frame of reference fix with respect to the plate, at low Mach numbers, and transformed into the convected frame moving with the flow. To model the source terms of the Lighthill equation, it is assumed that in the inertial range, the turbulence is locally isotropic in the convected frame. The w-f spectrum of isotropic turbulence is obtained from symmetry considerations by extending the isotropy to space time, based on the concept of sweeping velocity. The resulting solution for the pressure w-f spectrum contains a term (the mean shear-turbulence term) which does not fulfill the Kraichnan Philipps theorem, due to the form of the selected turbulent velocity spectrum. The viscous effects are accounted for by a cut-off depending on wall distance; this procedure allows extending the model beyond the inertial range contribution. The w-f pressure spectrum is derived and compared to the experimental low wavenumber data of Farabee and Geib (1991) [8] and Bonness et al. (2010) [5], for which a good agreement is obtained. The derived expression is also compared to Chase theoretical model Chase (1987) [6] and found to agree well in the vicinity of the convective ridge of the subsonic domain and to differ significantly both in supersonic and subsonic low wavenumber limits. The pressure spectrum derived from the model and its scaling are discussed and compared to experimental data and to the empirical model of Goody (2002) [23], which results from the compilation of a large set of experimental data. Very good agreement is obtained, except at vanishing frequencies where it is claimed that the experimental results lack of significance due to the limited size of the experimental facilities. This hypothesis supported by the results obtained from numerical simulations.

Shock wave–boundary layer interaction in supersonic flow over a forward-facing step

We study in the present work a Mach 2.5 flow over a forward-facing step. The focus of the work is the flow ahead of the step, in particular, the unsteady interactions between the shock, the boundary layer and the separation bubble. The primary geometrical parameter in the problem is the ratio of the step height to the incoming boundary layer thickness,$h/\unicode[STIX]{x1D6FF}$, which is kept fixed at 2. Results are presented from detailed particle image velocimetry (PIV) measurements in two orthogonal planes to obtain a reasonable picture of the whole flow field. The mean velocity field in the central cross-stream or wall-normal ($x$–$y$) plane shows that the incoming boundary layer separates upstream of the step forming a large separation bubble ahead of the step, which can be relatively well resolved in PIV measurements compared to the compression ramp cases. Wall pressure fluctuation spectra close to the separation location show a dominant frequency ($f$) that is two orders of magnitude smaller than the characteristic frequency of the incoming boundary layer ($U_{\infty }/\unicode[STIX]{x1D6FF}$), consistent with low-frequency motions of the shock that have received a lot of recent attention ($U_{\infty }$ $=$ free-stream velocity,$\unicode[STIX]{x1D6FF}$ $=$ boundary layer thickness). PIV measurements in the wall-normal plane show large variations in shock position with time. The shock position measured from velocity data outside the boundary layer is found to be well correlated with the reverse flow area ahead of the step, and weakly correlated to structures in the incoming boundary layer. In contrast, the shock foot, determined from velocity data within the boundary layer, is found to be well correlated to the low- and high-speed streaks in the incoming boundary layer, in addition to the reverse flow area ahead of the step. Instantaneous velocity fields in the spanwise ($x$–$z$) plane parallel to the lower wall show that the shock is broadly two-dimensional with small spanwise ripples, while the recirculation region has very large spanwise variations. The spanwise-averaged shock location is found to be well correlated to the most upstream location of the recirculation region over a spanwise length ($x_{r,min}^{sp}$). Instantaneous velocity fields show that when some part of the recirculation region is far upstream, the corresponding nearly two-dimensional shock is also far upstream. On the other hand, when$x_{r,min}^{sp}$is relatively downstream, the resulting shock is also found to be downstream. Hence, the present results suggest that for the forward-facing step configuration, the large-scale streamwise motions of the shock are mainly correlated to the most upstream point of the recirculation region, which has large spanwise variations.

Prediction of the broadband noise of a low-speed axial fan by CFD similations

An extensive research program has been conducted for several years by CETIAT with scientific and industrial partners to predict one of the major broadband noise sources of low-speed axial fans, namely the blade trailing-edge noise. In the first part of the paper, comparisons of measured and predicted fan sound power spectra due to this mechanism are presented and discussed. The second part of the paper is devoted to the prediction of the wall-pressure fluctuation spectra on the blades of the test fan, which are the main input data of the trailing-edge noise model used. The prediction is made with an empirical model using results of RANS simulations of the flow in the blade boundary layer.

Spectral Characteristics of Separation Shock Unsteadiness

Spectra of wall-pressure fluctuations caused by separation shock unsteadiness were compared for data obtained from wind-tunnel experiments, the Hypersonic International Flight Research Experimentation flight test 1, and large-eddy simulations. The results were found to be in generally good agreement, despite differences in Mach number and two orders of magnitude difference in Reynolds number. Relatively good agreement was obtained between these spectra and the predictions of a theory developed by Plotkin. The predictions of this theory are also qualitatively consistent with the results of experiments in which the shock motion was synchronized to controlled perturbations. The results presented here support the idea that separation unsteadiness has common features across a broad range of compressible flows and that it behaves as a selective amplifier of large-scale disturbances in the incoming flow.

Experimental estimate of wave spectra of wall pressure fluctuations of the turbulent boundary layer in the subconvective region

A technique is developed for measuring the intensity of the frequency-wave spectrum components of wall pressure fluctuations of the turbulent boundary layer in a quiet aeroacoustic installation with the use of wave filters in the form of rectangular plates. Aluminium-alloy and organic-glass plates of various thickness under a fine-meshed screen are used, set up rigidly flush with the polished wall of the working part of the installation. The experimental data testify to the fundamental possibility of determining the field components of wall pressure fluctuations of the turbulent boundary layer using similar wave filters in the subconvective region, where a substantially lower pressure fluctuation intensity is observed in comparison to the intensity in the region of the convective maximum of the frequency-wave spectrum at a small flow velocity.

Modelling and computation of boundary layer flow around body of revolution

The characteristic parameters of boundary layer are inputs for the flow noise calculation, their change influence the power spectra of wall pressure fluctuations, so as to affect the analysis of the flow radiation noise. In this paper Hess-Smith boundary element method was adopted to model thick boundary layer for body of revolution. The corresponding code is developed. The computation of characteristic parameters of boundary layer for a body of revolution is carried out. The computed results including boundary layer thickness, shape factor, momentum thickness and friction coefficient are analyzed. The variation of characteristic parameter is obtained. The result showed that the code developed in this paper can be applied to the analysis of the body of revolution's 3D boundary layer calculation, which can offer input parameter for flow noise calculation. Key words: flow noise, characteristic parameter, boundary layer, body of revolution, Hess-Smith boundary element

Computation of wall pressure fluctuations and flow induced noise by large eddy simulation

In industrial practice, the cavity-type oscillation is undesirable from the perspective of inducement of structure vibration and fatigue, generation of noise and drastic increase in drag on the body. A numerical work for the prediction of wall pressure fluctuations and flow-induced noise of cavity is performed in the paper. Firstly, the wall pressure fluctuations of a plate are computed and compared with experimental results of Small Anechoic Flow Facility in CSSRC. The robustness of large eddy simulation (LES) in unsteady flow calculation is analyzed. Secondly, the calculations of wall pressure fluctuations of shuttle holes are accomplished. The power spectra of wall pressure fluctuations are analyzed. The numerical predictions are compared with measured data. Finally, the flow induced noises of three cavities are predicted through LES and FW-H acoustic analogy. The computed results including flow pattern in cavity, vorticity distribution and radiated sound spectrum are analyzed. The computed results are compared with experimental data of Large Circulation Channel in CSSRC, and the numerical prediction method is validated. It shows that the numerical prediction method in the paper is credible. Key words: wall pressure fluctuations; flow induced noise; Large eddy simulation; FW-H acoustic analogy; cavity

Measured wavenumber: Frequency spectrum associated with acoustic and aerodynamic wall pressure fluctuations

Direct measurements of the wavenumber-frequency spectrum of wall pressure fluctuations beneath a turbulent plane channel flow have been performed in an anechoic wind tunnel. A rotative array has been designed that allows the measurement of a complete map, 63×63 measuring points, of cross-power spectral densities over a large area. An original post-processing has been developed to separate the acoustic and the aerodynamic exciting loadings by transforming space-frequency data into wavenumber-frequency spectra. The acoustic part has also been estimated from a simple Corcos-like model including the contribution of a diffuse sound field. The measured acoustic contribution to the surface pressure fluctuations is 5% of the measured aerodynamic surface pressure fluctuations for a velocity and boundary layer thickness relevant for automotive interior noise applications. This shows that for aerodynamically induced car interior noise, both contributions to the surface pressure fluctuations on car windows have to be taken into account.

Measuring surface pressure with far field acoustics

This paper presents measurements of the wavenumber frequency spectrum of wall pressure fluctuations under a turbulent boundary layer made using sound radiated from hydrodynamically smooth ridges in the surface. The measurements also serve as a test of the scattering theory of roughness noise. The radiated sound reveals a cut through the full three-dimensional wavenumber frequency spectrum of the wall pressure at the wavenumber of the surface. Since ridges can be made with very small wavelengths, this technique can be used to probe the structure of the wall pressure spectrum on scales far smaller than those that can be reached using conventional wall-mounted transducers. Furthermore, the method reveals the wavenumber frequency spectrum directly, without the need for multi-point measurements or the spatial Fourier transforming of data. Measured spectra bear a close similarity to Corcos’ and Chase's model forms, and confirm the applicability of the theory of roughness noise and its prediction of roughness noise directivity.

Wall pressure fluctuation spectra due to boundary-layer transition

Boundary-layer transition has been expected to be an important contributor to sensor flow-induced self-noise. The pressure fluctuations caused by this spatially bounded, and intermittent, phenomenon encompass a very wide range of wavenumbers and temporal frequencies. Here, we analyze the wavevector–frequency spectrum of the wall pressure fluctuations due to subsonic boundary-layer transition as it occurs on a flat plate under zero-pressure gradient conditions. Based on previous measurements of the statistics of the boundary-layer intermittency, it is found that transition induces higher low-streamwise wavenumber wall pressure levels than does a fully developed turbulent boundary layer that might superficially exist at the same location and at the same Reynolds number. The transition zone spanwise wavenumber pressure components are virtually unchanged from the fully developed turbulent boundary-layer case. The results suggest that transition may be more effective than the fully developed turbulent boundary layer in forcing structural excitation at low Mach numbers, and it may have a more intense radiated noise contribution. This may help explain increases in measured sensor self-noise when the sensors are placed near the transition zone. We believe, based on the presented analytical calculation and numerical simulation, that the rapid growth and subsequent decay of turbulent spots in the intermittent transition zone causes the higher low-(streamwise) wavenumber spectra.

Wave number-frequency spectrum of turbulent pressure fluctuations: Methods of measurement and results

The methods proposed earlier for measuring the wave number-frequency spectrum of wall pressure fluctuations beneath a turbulent boundary layer are considered: the spatial filtering of the pressure field components by special-purpose transducers (wave filters) and the digital processing of signals obtained from an array of transducers. It is shown that, for the wave filters, transducers with a rectangular shape of sensitive surface rather than those with a circular one are necessary. Results of measuring the wave number-frequency spectrum of turbulent pressure fluctuations in a low-noise wind tunnel are presented. The measurements are performed with the use of four wave filters consisting of rectangular transducers with a constant sensitivity distribution over their surfaces. The mathematical model of the wave number-frequency spectrum proposed earlier by the authors is compared with the measurement data reported by Abraham and Keith. The model is used for processing the results of measurements in the wind tunnel. The measured spectra are compared with the data obtained by Martin and Leehey.