Measurements Of Wall Pressure Fluctuations Research Articles

Transducer Resolution Effect on Pressure Fluctuations Beneath Hypersonic Turbulent Boundary Layers

The size of a pressure transducer is known to affect the accuracy of measurements of wall-pressure fluctuations beneath a turbulent boundary layer because of spatial averaging over the sensing area of the transducer. In this paper, the effect of finite transducer size is investigated by applying spatial averaging or wavenumber filters to a database of hypersonic wall pressure generated from a direct numerical simulation (DNS) that simulates the turbulent portion of the boundary layer over a sharp 7° half-angle cone at nominally Mach 8. A good comparison between the DNS and the experiment in the Sandia Hypersonic Wind Tunnel at Mach 8 is achieved after spatial averaging is applied to the DNS data over an area similar to the sensing area of the transducer. The study shows that a finite sensor size similar to that of the PCB132 transducer can cause significant attenuation in the root-mean-square and power spectral density (PSD) of wall-pressure fluctuations, and the attenuation effect is identical between cone and flat plate configurations at the same friction Reynolds number. The Corcos theory is found to successfully compensate for the attenuated high-frequency components of the wall-pressure PSD.

Wall-pressure spectra, spanwise correlation, and far-field noise measurements of a NACA 0008 airfoil under uniform and turbulent inflows

This paper discusses unique measurements of wall-pressure fluctuations (WPFs), spanwise correlation length, and far-field noise of a NACA 0008 airfoil subjected to uniform, non-turbulent and turbulent inflows. From these measurements, the near-field characteristics of trailing-edge (TE) and leading-edge (LE) noise of a thin airfoil are analyzed. The competing nature of the LE and TE noise mechanisms of an airfoil subjected to a turbulent inflow is also investigated. Experiments were performed in the Aeroacoustic Wind Tunnel of the University of Twente for a chord-based Reynolds number ranging from 3.2×105 to 9×105 for a uniform inflow and a rod-generated turbulent inflow with a turbulence intensity of approximately 18%. The effective angles of attack ranged from -5∘ to 5∘. Measurements of the boundary layer at the TE, the WPFs along the chord and span, and the far-field radiated noise were performed. For the uniform inflow case, laminar-boundary-layer noise, turbulent-boundary-layer (TBL) noise, and blunt TE noise sources are identified. The far-field noise spectrum presents similar components in the frequency domain as the WPF spectrum and the spanwise correlation length at the TE. The angle of attack mainly affects the WPF spectrum and spanwise correlation length for chord-based Strouhal numbers St<10. The angle of attack slightly affects the TE noise with a maximum variation of 3 dB for 10<St<60. For the turbulent inflow case, it is observed that the turbulence significantly affects the WPFs and spanwise correlation length along the chord, increasing considerably compared to the case of uniform inflow. The highest WPF spectral level and the larger spanwise correlation length occur at positions close to the LE. The results show that the turbulent inflow yields a higher WPF spectral level and larger spanwise correlation length at the TE, resulting in higher levels of TE noise. However, LE noise is still the dominant noise source for St<25.2. For higher frequencies, the TE noise level is expected to become higher than the LE noise level.

Effect of the conical diffuser angle on the confined swirling flow induced Precessing Vortex Core

This paper presents the effect of the conical diffuser angle (θ=0°,2°,4°) on the Precessing Vortex Core (PVC) induced in confined swirling airflows generated by axial swirlers with two swirl number (Sw=1.1,0.7). Planar Particle Image Velocimetry (2D-PIV) synchronized with unsteady wall pressure fluctuation measurements are performed to identify the Strouhal number of the precession frequency and pressure fluctuations amplitude induced by the PVC, as well as the PVC parameters related to its phase-averaged vortex structure. Furthermore, the distribution of pressure recovery rate based on the mass flow averaged pressure, and the relationship between the local axial pressure gradient and the local PVC structure is also investigated to understand the relationship between the PVC parameters and pipe geometries. These relationships are derived from transient simulations with the Shear Stress Transport Curvature Correction model, since the pressure field data cannot be obtained from the experiments conducted in this paper. Experimental and numerical results in pipe configurations 1 (diffuser followed by a straight pipe) and 2 (diffuser followed by an open exit) clarify the diffuser angle effect. As the diffuser angle increases, the Strouhal number decreases, whereas the pressure fluctuations amplitude increases. Moreover, the PVC parameters are also affected by increased diffuser angle: the vortex trajectory radius is enlarged, and the helical vortex pitch is shortened. In addition, the geometry change (from diffuser to straight pipe) leads to a sudden change in the vortex pitch and a modification of the pressure recovery rate evolution. The vortex structure in the conical diffuser is affected by a difference in the diffuser angle, but the latter does not affect the vortex structure in the downstream straight pipe. This highlights that the local vortex pitch depends only on the local pipe geometry. Finally, a theoretical model of the relationship between the pressure fluctuation amplitude and PVC parameters is proposed, and the relationship between the local pressure gradient and the local vortex trajectory radius gradient is clarified. The amplitude factor Cp∗ is a function of the dimensionless vortex trajectory radius r∗. Positive or negative local pressure gradient leads to the mitigation or promotion of the PVC development.

Spatial structure and wavenumber filtering of wall pressure fluctuations on a full-scale cockpit model

Measurements of wall pressure fluctuations have been performed with arrays of MEMS microphones on a full-scale model of a business jet fore part. The boundary layers are characterised in terms of mean and root-mean-square velocity profiles and key parameters are computed to serve for the normalisation of pressure-related quantities. Frequency spectra are compared with classical models and strong discrepancies are highlighted, which are attributed to the non-canonical state of the boundary layers. The spatial structure of the pressure field is first characterised by the study of coherence and associated length scales. The hypothesis of auto-similarity on only one parameter, that is the frequency normalised by the separation to convective velocity ratio, is proven to reach its limits in the present case. In turn, the coherence length scales do not exhibit the classical $$-1$$ power law decay with frequency. The wavenumber–frequency formalism is used to differentiate the acoustic and hydrodynamic components of the pressure fluctuations in the spectral space. In the presence of an external acoustic source, the acoustic components are correctly extracted from the total field by spectral filtering, and the resulting frequency spectra are satisfactorily checked against the purely acoustic reference spectrum.

Single and Multivariate Statistics of Jet-Induced Pressure Fluctuations over an Infinite Plate

Motivated by the problem of the installation effects of modern turbofan engines, we experimentally investigated the interaction between a compressible subsonic jet and a tangential flat plate. Measurements of wall pressure fluctuations were performed in a semi-anechoic environment addressing the effect of several governing parameters, such as the stream-wise and span-wise location, the jet Mach number and the radial distance of the plate surface from the jet axis. The statistical properties of the wall pressure signals were analyzed in terms of both power spectra and cross-correlations, with the latter providing the estimation of the phase speed. The analysis is also carried out in the time-frequency domain through the application of the wavelet transform to further characterize the dynamics of the wall pressure signatures.

Aeroacoustics of Rounded Forward-Facing Steps: Near-Field Behavior

Measurements of wall pressure fluctuations induced by forward-facing steps with rounded corners immersed in a turbulent boundary layer were performed. Four different roundings of the step corner () equal to 0, 6.25, 12.5, and 25% of the step height () were considered. The step height was 26.2% of the undisturbed boundary-layer thickness, and the Reynolds number based on step height ranged between 35,000 and 104,000. The results show that both mean and fluctuating pressure upstream of the step remain independent of the corner rounding, whereas they are a strong function of rounding on the downstream surface. The latter was found to be due to a reduction in the spatial extent of the separation bubble with increasing rounding. The fluctuating pressure on the vertical face of the steps was found to increase with increasing corner rounding. For , the pressure spectra within the downstream separation bubble, and sufficiently away from the salient corner, were found to scale on the reattachment length and free-stream velocity. Downstream of the separation bubble, the spectra evolve differently and a separate scaling, one which suggests that the pressure fluctuations evolve independently of the incoming boundary layer, is shown to collapse the spectra.

Two-step hybrid calibration of remote microphones.

A two-step, hybrid procedure to calibrate the remote microphones is presented. The calibration obtained in this manner can be directly applied to the measured pressure spectrum without resorting to any modeling or assumptions about the shape of the calibration curve. To demonstrate an application of the methodology, measurements of wall pressure fluctuations underneath a zero pressure gradient turbulent boundary layer were made. The calibrated pressure spectrum is shown to be qualitatively and quantitatively consistent with previous experimental studies and an empirical model, indicating the accuracy of the hybrid calibration technique.

Flow regimes in a trapped vortex cell

This paper presents results of an experimental investigation on the flow in a trapped vortex cell, embedded into a flat plate, and interacting with a zero-pressure-gradient boundary layer. The objective of the work is to describe the flow features and elucidate some of the governing physical mechanisms, in the light of recent investigations on flow separation control using vortex cells. Hot-wire velocity measurements of the shear layer bounding the cell and of the boundary layers upstream and downstream are reported, together with spectral and correlation analyses of wall-pressure fluctuation measurements. Smoke flow visualisations provide qualitative insight into some relevant features of the internal flow, namely a large-scale flow unsteadiness and possible mechanisms driving the rotation of the vortex core. Results are presented for two very different regimes: a low-Reynolds-number case where the incoming boundary layer is laminar and its momentum thickness is small compared to the cell opening, and a moderately high-Reynolds-number case, where the incoming boundary layer is turbulent and the ratio between the momentum thickness and the opening length is significantly larger than in the first case. Implications of the present findings to flow control applications of trapped vortex cells are also discussed.

Coherent flow noise beneath a flat plate in a water tunnel experiment

Results from a combined experimental and numerical study on the properties of flow noise on the reverse side of a flat plate excited by a turbulent boundary layer flow are reported. Particular focus is given to the coherence between wall pressure fluctuations, plate vibrations, and interior flow noise. The plate was immersed in water and laterally attached to a streamlined model inside the HYKAT cavitation tunnel at HSVA Hamburg (Germany). The flow velocity in the tunnel was U=7m/s. Simultaneous measurements of wall pressure fluctuations, structural vibrations, and interior flow noise as well as a numerical response and eigenvalue analysis provide evidence that evanescent plate modes excited by wall pressure fluctuations play a crucial role in flow noise generation. Flow noise in the (quiescent) water inside of the model is found to have large coherence lengths and pronounced amplitudes for distinct frequencies below f≈300Hz.

Wall-pressure fluctuations of separated and reattaching flow over blunt plate with chord-to-thickness ratio c/d = 9.0

The separated and reattaching turbulent flow over a finite blunt plate with the chord-to-thickness ratio c/d=9.0 was experimentally studied; the Reynolds number based on the plate’s thickness (d) was Red=1.58×104. Wall-pressure fluctuations on the plate surface were taken into extensive consideration, which are closely related to unsteady flow behaviors buried in the separated and reattaching flow and the unsteady wake. Toward this end, synchronized measurements of wall-pressure fluctuations and velocity fluctuations were performed by using a microphone array and a split-fiber film probe, respectively. Characteristics of the separated and reattaching flow were discussed in terms of time-averaged streamwise velocity and its fluctuation intensity, reverse-flow intermittency, wall-pressure fluctuation coefficient, cross-correlation and coherence of wall pressure and velocity. The results showed that the peaked wall-pressure fluctuation coefficient (x/d=4.25) appears 1d behind the time-mean reattachment point (x/d=3.25), which is due to the intensified impingement fluid induced by the growing large-scale vortical structures in the reattachment zone. Two characteristic frequencies fd/U0=0.118 and 0.162 were determined, which correspond to the shedding large-scale vortical structures and the unsteady wake, respectively. Cross-correlation of the wall-pressure field demonstrated rapid decay of the large-scale vortical structures beyond the reattachment zone (x/d>4.75), which might be due to strong interference with the unsteady wake at higher frequency fd/U0=0.162. The wall-pressure auto-spectra showed that wall-pressure fluctuations near the trailing edge are overwhelmingly dominated by the unsteady wake at fd/U0=0.162. Coherence of the wall-pressure field and the streamwise velocity at x/d⩾7.75 elucidated that unsteady behaviors of the redeveloping boundary layer at both frequencies fd/U0=0.118 and 0.162 play important role in wall-pressure fluctuations in large upstream area of the surface.

Proper orthogonal decomposition of wall-pressure fluctuations under the constrained wake of a square cylinder

The proper orthogonal decomposition (POD) analysis of the wall-pressure fluctuations below the constrained wake of a two-dimensional square cylinder in proximity to a plane wall was made on two systems, i.e., G/ D = 0.25 and 0.5, which corresponds to the wakes with and without suppression of the vortex shedding, respectively. Here, G is the gap distance and D is the width of the square cylinder. Synchronized measurements of wall-pressure fluctuations were made using a microphone array. For the system G/ D = 0.5, the first two energetic modes contribute 34.7% and 23.4% to the total fluctuation energy, respectively; however, the fluctuation energy corresponding to the third mode are relatively small and less than 10%. This sharp variation in eigenvalue is due to the presence and dominance of the Karman-like vortex shedding. However, for the system G/ D = 0.25, the considerable reduction in the eigenvalues of the first several modes is due to the suppression of the Karman-like vortex shedding. The spatial wavy pattern of the first several energetic eigenmodes was shown to be a good reflection of convective vortices superimposed in the wakes. The spectra of the POD coefficients determined the frequency of the dominant structures. Based on the coherence of the POD coefficients, an effective method of determining the number of POD modes for reconstruction of the low-order wall-pressure field was proposed. Accordingly, the low-order wall-pressure fluctuations in the systems G/ D = 0.5 and 0.25 were reconstructed by using the first four and five POD modes, respectively. The coherence and cross-correlation analysis of the reconstructed wall-pressure fluctuations, which excluded the influence of the small-scale structures and background ‘noise’, gave an insight view of the footprints of the dominant flow structures, which otherwise could not be effectively captured by using the original wall-pressure fluctuations.

Measurements of roughness noise

Experiments have been performed on the roughness noise produced by a two-dimensional turbulent wall jet boundary layer flowing over short fetches of sandpaper roughness. A range of rough surface sizes were studied from hydrodynamically smooth through fully rough. Velocity measurements were made to document the form of the wall jet boundary layer and the influence of the roughness upon it. Acoustic measurements showed background noise levels to be very low so that the sound produced by the rough surfaces could be clearly detected with signal to noise ratios as large as 20 dB. Even hydrodynamically smooth roughness was found to produce noise, conclusively indicating the presence of scattering as a source mechanism. Variations of the roughness noise spectra with flow speed and roughness size are found to be inconsistent with any simple parameter scaling. Boundary layer wall pressure fluctuation measurements made within the roughness fetches reveal a spectral form quite different than the roughness noise, and fluctuation levels some 50–70 dB higher. Despite these differences the wall pressure and roughness noise are found to be very simply related, at least at lower frequencies (<6 kHz). The roughness noise spectrum varies closely as the product of the wall pressure spectrum, the frequency squared, and the mean-square roughness height. This is the scaling predicted by scattering theory and implies a major simplification to the problem of roughness noise prediction for stochastic surfaces.

Experimental Flow Measurements of a Spouted Bed Using Pressure Transducer and X-Ray CT Scanner

Flow behaviour of an air-glass bead spouted bed (20 cm diameter, 1.31 m high) was investigated using wall pressure fluctuation measurements and X-ray Computed Tomography (CT) scanning. Spout shape, spout dimension, fountain shape and fountain height were visualized from CT images. Statistical and spectral analyses were applied to pressure fluctuation series measured along the column wall. Local and global gas-solids flow dynamics were compared. Gas velocity greatly affects hydrodynamics of the spout bed. A stable spouting regime was identified. This study enhances the understanding of gas-solid flow patterns and provides detail hydrodynamics for further modelling work.

Experimental Flow Measurements of a Spouted Bed Using Pressure Transducer and X-Ray CT Scanner

Flow behaviour of an air-glass bead spouted bed (20 cm diameter, 1.31 m high) was investigated using wall pressure fluctuation measurements and X-ray Computed Tomography (CT) scanning. Spout shape, spout dimension, fountain shape and fountain height were visualized from CT images. Statistical and spectral analyses were applied to pressure fluctuation series measured along the column wall. Local and global gas-solids flow dynamics were compared. Gas velocity greatly affects hydrodynamics of the spout bed. A stable spouting regime was identified. This study enhances the understanding of gas-solid flow patterns and provides detail hydrodynamics for further modelling work.

Initial noise predictions for rudimentary landing gear

A four-wheel “rudimentary” landing gear (RLG) truck was designed for public-domain research, with a level of complexity which is manageable in current numerical simulations, and a weak Reynolds-number sensitivity. Experimental measurements of wall-pressure fluctuations are allowing a meaningful test of unsteady simulations with emphasis on noise generation. We present three Detached-Eddy Simulations (DES) using up to 18 million points in the high-order NTS code. The first is incompressible with the model placed in the wind tunnel, as requested for the 2010 workshop on Benchmark problems for Airframe Noise Computations (BANC-I), intended for force and surface-pressure studies. The second and third are at Mach 0.115 and Mach 0.23, with only one wall, a “ceiling” analogous to a wing (but infinite and inviscid), and are used to exercise far-field noise prediction by coupling the Detached-Eddy Simulations and a Ffowcs-Williams/Hawkings calculation. The results include wall-pressure, and far-field-noise intensities and spectra. The wall pressure signals in the three simulations are very similar and, in a comparison published separately, agree well with experiment and other simulations. In the absence of experimental noise data, the attention is focused on internal quality checks, by varying the permeable Ffowcs-Williams/Hawkings calculation surface and then by using only the solid surface. An unexpected finding at these Mach numbers is an apparent strong role for quadrupoles, revealed by a typical deficit of 3 dB in the solid-surface results, relative to the permeable-surface results. The solid-surface approach has variants, related to the presence of the ceiling (a plane of symmetry), which can increase this error further; there is little consensus on the exact configuration of the solid surfaces in the Ffowcs-Williams/Hawkings calculation procedure. Tentative theoretical arguments suggest that a balance somewhat in favor of quadrupoles over dipoles is plausible at Mach 0.115. However, the scaling of sound with Mach number does not follow the eighth power, as quadrupoles do in theory: it is closer to the sixth power. This trend gives a muddled theoretical picture, but agrees with the scaling observed in experiments. If it is confirmed, this finding will complicate airframe-noise calculations, and prevent the attribution of noise to a given component of the aircraft. Progress in airframe-noise simulations appears real, but systematic grid-refinement studies and noise comparisons with experiment or other simulations have yet to occur, and the theoretical uncertainty is high.

On the wake with and without vortex shedding suppression behind a two-dimensional square cylinder in proximity to a plane wall

A comparative study of the wake characteristics behind a two-dimensional square cylinder in proximity to a plane wall was made on two systems, i.e. G/ D=0.25 and 0.5, which corresponds to the wakes with and without suppression of the vortex shedding, respectively. Here, G is the gap distance and D is the width of the square cylinder. Synchronized measurements of wall-pressure fluctuations and velocity fluctuations were made using a microphone array and a split-fiber film, respectively. For the system G/ D=0.5, a regular Karman-like vortex shedding at fD/ U 0=0.13 was found by inspection of the streamwise velocity spectra. When the gap width is reduced to G/ D=0.25, a low-speed separation bubble was formed in the region 4.25< x/ D<9.25, while the intermittent existence of large-scale vortices at the reduced frequency fD/ U 0=0.116 was identified in the upper shear layer. The convective vortex dynamics were analyzed in terms of the cross-correlation of the wall-pressure fluctuation, coherence and cross-correlation of wall-pressure fluctuations with velocity fluctuations at various positions located at the lower edge of the cylinder ( y/ D= G/ D) and the outer edge of the upper shear layer. The convection velocities of the Karman-like vortices in the system G/ D=0.5 was determined to be U c / U 0=0.64. However, in the system G/ D=0.25 the convection velocities before and behind x/ D=3.25 were determined to be U c / U 0=0.32 and 0.64, respectively.

Solid Suspension and Liquid Phase Mixing in Solid−Liquid Stirred Tanks

Stirred tanks are widely used in chemical process industries for catalytic reactions, dissolution of solids, crystallization, and so on. In designing and optimizing such processes, suspension quality of slurry is an important parameter. Suspension quality depends upon complex interactions of impeller generated flow, turbulence, and solid loading. Most of the earlier work on solid suspension focuses on identifying critical impeller speed for just suspension of solids (Njs). In this study, apart from Njs, aspects like cloud height and liquid phase mixing in solid−liquid suspensions were also studied. A new way of characterizing solid−liquid suspensions and liquid phase mixing using nonintrusive wall pressure fluctuation measurements has been developed. Systematic experimental data on Njs, cloud height, power consumption, mixing time, and circulation time over a range of solid volume fraction and impeller speeds have been presented here. The results and discussion presented here will have useful implications for designing solid−liquid stirred tanks.

G0501-6-2 衝撃波管を用いた軸流圧縮機の失速過渡特性に関する研究(回転機械)

Unsteady flow structure between rotor blade-to-blade passages in a three-stage axial flow compressor is experimentally investigated by detailed measurements of wall pressure fluctuations, unsteady velocities and their wavelet analyses. The feature of the present tested compressor is a shock tube facility connected in series to the compressor outlet in order to apply a compression wave from the compressor downstream. Research attention is focused on the inception and post-stall transient characteristics of surge and rotating stall which occurs simultaneously. The unsteady behavior of the compressor operating point on the performance curve under surging may largely depends on the stall configuration of the compressor blade rows. The unsteady flow filed under coexistence system of surge and rotating stall are also discussed.

0601 矩形ダクト内のコーナはく離を伴う超音速流動現象に関する研究(OS6-1 超音速流と衝撃波,オーガナイズドセッション)

This report describes experimental results on the supersonic flow phenomena in rectangular ducts which are the models of isolators of cramjet engine, using the pressure-vacuum type Mach 4 supersonic wind tunnel. This investigation shows the effects of duct cross-section aspect ratio and length on the supersonic flow structure in the rectangular ducts by schlieren photographs, duct wall pressure fluctuation measurements and detailed total pressure distribution measurements.

Turbulent wall pressure fluctuation measurements on a towed model at high Reynolds numbers

Turbulent wall pressure fluctuation measurements were made in water on a towed model of length 129.8 (m) and diameter 3.8 (cm) for steady speeds from 6.2 (m/s) to 15.5 (m/s). The drag on the model was measured with a strut mounted load cell which provided estimates of the momentum thickness and friction velocity. Momentum thickness Reynolds numbers Reθ varied from 4.8 × 105 to 1.1 × 106. The ratio of momentum thickness to viscous length scale is significantly greater than for flat plate cases at comparable Reθ. The effectiveness of inner and outer velocity and length scales for collapsing the pressure spectra are discussed. The wavenumber–frequency spectra show a convective ridge at higher frequencies similar to flat plate boundary layers. At low frequencies, energy broad in wavenumber extends outside the convective ridge and acoustic cone, with no characteristic wave speed. Wall pressure cross-spectral levels scaled with similarity variables are shown to increase with increasing tow speed, and to follow decay constants consistent with flat plate cases. The convection velocities also display features similar to flat plate cases.