Characteristics of wall pressure fluctuations in separated flows over a backward-facing step: Part II. Unsteady wavelet analysis

 Time-dependent characteristics of wall pressure fluctuations in separated and reattaching flows over a backward-facing step were investigated by means of the continuous wavelet transform. Emphasis was placed on the combination of time-localized analyses of the wavelet transform and multi-point measurements of pressure fluctuations. Synchronized wavelet maps revealed the evolutionary behavior of pressure fluctuations and gave further insight into the modulated nature of large-scale vortical structures. It was found that there exist two modes of shed vortices: one is the global oscillation and the other is the vortex convection. The two alternating modes are synchronized with the flapping frequency component of pressure fluctuations. The flapping motion gives rise to the difference in pressure spectra, indicating more intensive pressure activity during the shrinking period of the recirculation region.     

Unsteady separated and reattaching turbulent flow over a two-dimensional square rib

The spatio-temporal characteristics of the separated and reattaching turbulent flow over a two-dimensional square rib were studied experimentally. Synchronized measurements of wall-pressure fluctuations and velocity fluctuations were made using a microphone array and a split-fiber film, respectively. Profiles of time-averaged streamwise velocity and wall-pressure fluctuations showed that the shear layer separated from the leading edge of the rib sweeps past the rib and directly reattaches on the bottom wall (x/H=9.75) downstream of the rib. A thin region of reverse flow was formed above the rib. The shedding large-scale vortical structures (fH/U₀=0.03) and the flapping separation bubble (fH/U₀=0.0075) could be discerned in the wall-pressure spectra. A multi-resolution analysis based on the maximum overlap discrete wavelet transform (MODWT) was performed to extract the intermittent events associated with the shedding large-scale vortical structures and the flapping separation bubble. The convective dynamics of the large-scale vortical structures were analyzed in terms of the autocorrelation of the continuous wavelet-transformed wall pressure, cross-correlation of the wall-pressure fluctuations, and the cross-correlation between the wall pressure at the time-averaged reattachment point and the streamwise velocity field. The convection speeds of the large-scale vortical structures before and after the reattachment point were U_c=0.35U₀ and 0.45U₀, respectively. The flapping motion of the separation bubble was analyzed in terms of the conditionally averaged reverse-flow intermittency near the wall region. The instantaneous reattachment point in response to the flapping motion was obtained; these findings established that the reattachment zone was a 1.2H-long region centered at x/H=9.75. The reverse-flow intermittency in one period of the flapping motion demonstrated that the thin reverse flow above the rib is influenced by the flapping motion of the separation bubble behind the rib.     

Characteristics of wall pressure fluctuations in separated and reattaching flows over a backward-facing step: Part I. Time-mean statistics and cross-spectral analyses

 Laboratory measurements were made of wall pressure fluctuations in separated and reattaching flows over a backward-facing step. An array of 32 microphones in the streamwise as well as the spanwise directions was utilized. The statistical properties of pressure fluctations were scrutinized. Emphasis was placed on the flow inhomogeneity in the streamwise direction. One-point statistics such as the streamwise distribution of rms pressure and autospectra were shown to be generally consistent with the prior results. The peak frequency and the fall-off rate of autospectra demonstrated the shear layer-originated nature of pressure fluctuations. The coherences and wavenumber spectra in the streamwise and spanwise directions were indicative of the presence of dual modes in pressure; one is associated with the large-scale vortical structure in the low-frequency region and the other is the boundary-layer-like decaying mode in the high-frequency region. Received: 18 August 1999/Accepted: 17 May 2000     

Experimental study of wall pressure fluctuations in rigid and elastic pipes behind an axisymmetric narrowing

Wall pressure fluctuations, p_t, in rigid and elastic pipes behind a local axisymmetric narrowing are studied. A sharp increase in their rms level in a finite region immediately downstream of the narrowing, leading up to a pronounced maximum upstream of the point of jet reattachment, is found. Approximate estimates both for the distance from the narrowing to the point of maximum rms pressure and for the rms magnitude at this point are obtained. Inspection of the wall pressure power spectrum, P, reveals the presence of low-frequency maxima. The maxima are found to be associated with the large-scale eddies in the regions of separated and reattached flow, and their frequencies are close to the characteristic frequencies of the eddies’ formation. These maxima are the main distinguishing features of the spectrum under investigation compared to the power spectrum of the wall pressure fluctuations in a fully-developed turbulent flow in a pipe without narrowing. A comparative analysis of the data for rigid and elastic pipes shows that changes in the pipe wall bending stiffness cause alterations in the flow structure near the wall and the corresponding redistribution of flow energy among the vortices. This results in an increase in the wall pressure amplitude and the low-frequency level of the wall pressure power spectrum, as well as the appearance of new frequency components in this domain.     

Numerical Investigation of the Robustness of an Axisymmetric Separating/Reattaching Flow to an External Perturbation Using ZDES

The present article focuses on the influence of an external perturbation on the dynamics and the topology of an axisymmetric separating/reattaching flow for a Mach number equal to 0.7. Zonal Detached Eddy Simulation (ZDES) is used to reproduce the flow dynamics downstream an axisymmetric backward facing step with and without a surrounding mixing layer. The instantaneous flowfield shows the influence of the outer shear layer whose structures interact with the separated flow of interest. The instantaneous flowfield depicts the scales of the two axisymmetric mixing layers. Then, the statistical properties of the flow illustrate an excellent agreement between the experiments (PIV and LDV) and the numerical simulation (ZDES). The second-order moment of the pressure coefficient unveils the very high fluctuation levels of the perturbed case compared to the unperturbed one. The analysis of the spectral content reveals a remarkable alteration of the spatial organization for the fluctuating pressure field at the wall and the normal velocity component fluctuations in the afterbody shear layer. Finally, the impact of the perturbation on the energy distribution of the afterbody unsteady side-loads is evidenced by single-point power spectral densities.     

Effects of flow width in nominally two-dimensional turbulent separated flows

Pulsed-wire measurements of mean and fluctuating wall shear stress have been measured beneath a nominally two-dimensional separated and reattaching flow, where the flow width has been varied by means of end plates. End effects are much larger near the surface than they are in the outer flow. Residual effects of the presence of the end walls on the mean wall shear stress are seen for a flow width as large as seven bubble lengths. It is inferred that the effects of the end-wall boundary layers extend to a substantially smaller distance. The influence of the end plates on the rms of the fluctuations is markedly less than that on the mean stress.     

Acceleration and wall pressure fluctuations generated by an incompressible jet in installed configuration

In this work, the cross-statistics of acceleration and wall pressure fluctuations generated by an incompressible jet interacting with a tangential flat-plate are presented. The results are derived from an experimental test campaign on a laboratory-scale model involving simultaneous velocity and wall pressure measurements. The pressure footprint of the jet on the surface was measured through a cavity-mounted microphone array, whereas pointwise velocity measurements were carried out by a hot wire anemometer. The time derivative of the velocity signal has been taken as an estimation of the local acceleration of the jet. The multivariate statistics between acceleration and wall pressure are achieved through cross-correlations and cross-spectra, highlighting that the causality relation is more significant in the potential core where the Kelvin–Helmholtz instability is dominant. The application of a conditional sampling procedure based on wavelet transform allowed us to educe the acceleration flow structures related to the energetic wall-pressure events. The analysis revealed that, unlike the velocity, the acceleration signatures were detected only for positions where the jet had not yet impinged on the plate, their shape being related to a convected wavepacket structure.     

Numerical prediction of locally forced turbulent separated and reattaching flow

An unsteady numerical simulation was performed for locally forced separated and reattaching flow over a backward-facing step. The local forcing was given to the separated and reattaching flow by means of a sinusoidally oscillating jet from a separation line. A version of the k––f_μ model was employed, in which the near-wall behavior without reference to distance and the nonequilibrium effect in the recirculation region were incorporated. The Reynolds number based on the step height (H) was fixed at Re_H=33 000, and the forcing frequency was varied in the range 0St_H2. The predicted results were compared and validated with the experimental data of Chun and Chun. It was shown that the unsteady locally forced separated and reattaching flows are predicted reasonably well with the k––f_μ model. To characterize the large-scale vortex evolution due to the local forcing, numerical flow visualizations were carried out.     

An experimental study of two flows through an axisymmetric sudden expansion

Two turbulent separated and reattaching flows produced by a sudden expansion in a pipe have been studied. The first was produced by a simple axisymmetric sudden enlargement from a nozzle of diameter 80 mm to a pipe of diameter 150 mm. The second was the flow at the same enlargement with the addition of a centerbody 90 mm downstream of the nozzle exit. Detailed measurements of velocity and skin friction (made primarily using pulsed wires) and of wall static pressure are presented. Without the centerbody the flow structure is similar to that observed in other sudden pipe expansions and over backward-facing steps. A turbulent free shear layer, bearing some similarity to that of a round jet, grows from separation and then reattaches to the pipe wall downstream. Reattachment is a comparatively gradual process, the shear layer approaching the wall at a glancing angle. The introduction of the centerbody causes the shear layer to curve towards the wall and reattach at a much steeper angle. Reattachment is much more rapid; gradients of skin friction and pressure along the wall are many times those without the centerbody. The high curvature of the shear layer strongly influences its turbulent structure, locally suppressing turbulence levels and reducing its growth rate.     

Wall pressure fluctuations and topology in separated flows over a forward-facing step

Laboratory measurements of wall pressure fluctuations and aerodynamic fields were made in separated flows over a forward facing step (h = 30, 40 and 50 mm with U _e = 15–40 m/s). An array of 16 off-set pressure probes extending in the streamwise and the spanwise directions was especially developed for sensing the wall pressure fluctuations. The flow field was also investigated by wall flow visualizations and PIV to analyze the flow topology in an open section wind tunnel. The results show a different behavior of the flow depending on the aspect ratio l/h and δ/h for high Reynolds numbers. The space time correlations between the wall pressure and the velocity fields were highlighted. The results show that high levels of these correlations are located at the top of the recirculation bubble, mainly in the shear layer and are extended downstream of the re-attachment point. Indeed, the results indicate that the flapping motion at the separation is important in the flow organization at the re-attachment point.     

Wavelet spectrum analysis on energy transfer of multi-scale structures in wall turbulence

The streamwise velocity components at different vertical heights in wall turbulence were measured. Wavelet transform was used to study the turbulent energy spectra, indicating that the global spectrum results from the weighted average of Fourier spectrum based on wavelet scales. W＇avelet transform with more vanishing moments can express the declining of turbulent spectrum. The local wavelet spectrum shows that the physical phenomena such as deformation position in the boundary layer, and the or breakup of eddies are related to the vertical energy-containing eddies exist in a multi-scale form. Moreover, the size of these eddies increases with the measured points moving out of the wall. In the buffer region, the small scale energy-containing eddies with higher frequency are excited. In the outer region, the maximal energy is concentrated in the low-frequency large-scale eddies, and the frequency domain of energy-containing eddies becomes narrower.     

Wall temperature effects on shock unsteadiness in a reattaching compressible turbulent shear layer

In this study, the effect of heat transfer on the compressible turbulent shear layer and shockwave interaction in a scramjet has been investigated. To this end, highly resolved Large Eddy Simulations (LES) are performed to explore the effect of wall thermal conditions on the behavior of a reattaching free shear layer interacting with an oblique shock in compressible turbulent flows. Various wall-to-recovery temperature ratios are considered, and results are compared to the adiabatic wall. It is found that the wall temperature affects the reattachment location and the shock behavior in the interaction region. Furthermore, fluctuating heat flux exhibits a strong intermittent behavior with severe heat transfer compared to the mean, characterized by scattered spots. The distribution of the Stanton number shows a strong heat transfer and complex pattern within the interaction, with the maximum thermal (heat transfer rates) and dynamic loads (root-mean-square wall pressure) found for the case of the cold wall. The analysis of LES data reveals that the thermal boundary condition can significantly impact the wall pressure fluctuations level. The primary mechanism for changes in the flow unsteadiness due to the wall thermal condition is linked to the reattaching shear layer, which agrees with the compressible turbulent boundary layer theory.     

Influence of unsteady wake on a turbulent separation bubble

 An experimental study was made of turbulent separated and reattaching flow over a blunt body, where unsteady wake was generated by a spoked-wheel type of wake generator with cylindrical rods. The influence of unsteady wake was scrutinized by altering the rotation direction (clockwise and counter-clockwise) and the normalized passing frequency (0 ≤ St _H  ≤ 0.20). The Reynolds number based on the cylindrical rod was Re _d =375. A phase-averaging technique was employed to characterize the unsteady wake. The effect of different rotation directions, which gave a significant reduction of x _R , was examined in detail. The wall pressure fluctuations on the blunt body were analyzed in terms of the spectrum and the coherence. Received: 15 January 2001 / Accepted: 17 July 2001     

Visualization of a locally-forced separated flow over a backward-facing step

A laboratory water channel experiment was made of the separated flow over a backward-facing step. The flow was excited by a sinusoidally oscillating jet issuing from a separation line. The slit was connected to a cavity in which water was forced through a rigid pipe by a scotch-yoke system. The Reynolds number based on the step height (H) was fixed at Re _H =1200. The forcing frequency was varied in the range 0.305?St _H ?0.955 at the forcing amplitude A ₀=0.3. Time-averaged flow measurements were made by a LDV system, especially in the recirculating region behind the backward-facing step. To characterize the large-scale vortex evolution due to the local forcing, flow visualizations were performed by a dye tracer method with fluorescent ink. The vortex amalgamation process was captured at the effective forcing frequency (St _H =0.477) for laminar separation. This vortex merging process enhances flow mixing, which leads to the shortening of the reattachment length.     

Flow regime identification in a two-phase flow using wavelet transform

This study addresses the problem of the automatic flow regime identification in two-phase flows in pipes. A novel wavelet transform-based approach is proposed and validated using time series of differential pressure fluctuations. The experimental data on the differential pressure measured in a vertically installed Venturi meter for air-water flow were analyzed and found to be appropriate for flow regime identification. The wavelet spectrum of the measured signal is shown to characterize the flow patterns completely, and the vector of the wavelet variances is proposed as the characteristic vector for use in an on-line flow regime identification system.     

Unsteadiness of Flow Separation and End-Effects Regime in a Thrust-Optimized Contour Rocket Nozzle

Turbulent flow separation in over-expanded rocket nozzles is investigated experimentally in a sub-scale model nozzle fed with cold air and having a thrust-optimized contour. Depending upon the pressure ratio either a free shock separation (FSS) or a restricted shock separation (RSS) is observed with a significant hysteresis between these two flow regimes. It is shown that the RSS configuration may involve several separated regions. Analysis of wall pressure fluctuations give quantitative information on the fluctuating pressure field directly connected with the occurrence of significant side loads. Direct measurements of the evolution of the side loads with respect to the pressure ratio show the occurrence of three distinct peaks which are explained by the wall pressure fluctuations measurements.     

Experimental investigation of micro-scale temperature transients in sub-cooled flow boiling on a horizontal heater

Surface temperature fluctuations that occur locally underneath departing bubbles in pool boiling are shown to result in local heat transfer coefficients ranging from 1 to 10 kW/cm². These estimates were reported in the literature involved both numerical and experimental approaches. Significantly higher heat fluxes are associated with flow boiling than pool boiling under similar conditions of wall superheat and liquid subcooling (e.g. at boiling inception and at critical heat flux). These enhancements are primarily caused by the convective transport, acceleration/distortion of the bubble departure process as well as the resultant potential enhancement of the local surface temperature fluctuations.In this study we measure the surface temperature fluctuations using temperature micro/nano-sensors fabricated on a silicon wafer during flow boiling on the silicon wafer which is heated from below. The silicon wafer is clamped on a constant heat flux type calorimeter consisting of a vertical copper cylinder with embedded cartridge heaters and K-type thermocouples. Micro/nano-thermocouples (thin film thermocouples or “TFT”) are fabricated on the surface of the silicon wafer. High speed data acquisition apparatus is used to record temperature data from the TFT at 1 kHz. A fluorinert was used as the test fluid (PF-5060, manufacturer: 3M Co.). The calorimeter and surface temperature measurement apparatus is housed in a test section with glass walls for visual observation. The liquid is pumped from a constant temperature bath to maintain a fixed subcooling during the experiments under steady state conditions. The transient temperature data from the FFT array during flow boiling on the silicon wafer is analyzed using fast Fourier transform (FFT). The FFT data is analyzed as a function of the wall heat flux and wall superheat. The number of temperature peaks in the FFT data is observed to increase with increase in wall heat flux and the peaks are found to cover a wider spectrum with peaks at higher frequencies with enhancement of heat flux. The surface temperature fluctuations, especially at small length and time scales, are perturbed potentially by the coupled hydrodynamic and thermal transport processes, resulting in enhanced local and global heat flux values. Boiling incipience condition and the flow boiling data are compared with correlations reported in the literature.     

吹吸扰动对壁湍流相干结构的影响

采用热线风速仪测量受吹吸扰动的壁湍流边界层的流向速度,用傅里叶变换和子波变换研究 吹吸扰动对壁湍流能谱的影响,结果显示施加的低频扰动使边界层内层大尺度结构的能量减 少,小尺度结构的能量有所增强,远离壁面时扰动强度逐步衰减直到在外层中消失;通过VITA 法和子波变换法检测猝发事件,表明该扰动降低了猝发强度,使猝发周期延长,条件平均速 度波形的幅值降低、持续时间变短,说明扰动明显抑制了相干结构的猝发过程. 利用子波变 换可以实现湍谱分析,能有效检测猝发中的湍流结构,是一种客观的分析工具.     

Enhancement of channel wall vibration due to acoustic excitation of an internal bubbly flow

The effect of an internal turbulent bubbly flow on vibrations of a channel wall is investigated experimentally and theoretically. Our objective is to determine the spectrum and attenuation rate of sound propagating through a bubbly liquid flow in a channel, and connect these features with the vibrations of the channel wall and associated pressure fluctuations. Vibrations of an isolated channel wall and associated wall pressure fluctuations are measured using several accelerometers and pressure transducers at various gas void fractions and characteristic bubble diameters. A waveguide-theory-based model, consisting of a solution to the three-dimensional Helmholtz equation in an infinitely long channel with the effective physical properties of a bubbly liquid is developed to predict the spectral frequencies of the wall vibrations and pressure fluctuations, the corresponding attenuation coefficients and propagation phase speeds. Results show that the presence of bubbles substantially enhances the power spectral density of the channel wall vibrations and wall pressure fluctuations in the 250–1200 Hz range by up to 27 and 26 dB, respectively, and increases their overall rms values by up to 14.1 and 12.7 times, respectively. In the same frequency range, both vibrations and spectral frequencies increase substantially with increasing void fraction and slightly with increasing bubble diameter. Several weaker spectral peaks above that range are also observed. Trends of the frequency and attenuation coefficients of spectral peaks, as well as the phase velocities are well predicted by the model. This agreement confirms that the origin of enhanced vibrations and pressure fluctuations is the excitation of streamwise propagating pressure waves, which are created by the initial acoustic energy generated during bubble formation.     

Near-wall investigation of backward-facing step flows

The electrodiffusion technique has been used to investigate reattaching and recirculating flows behind a backward-facing step. The instantaneous wall shear rate vectors were determined using the current signals provided by a three-segment electrodiffusion probe. The near-wall extents of two counter-rotating recirculation zones located behind the step were determined under turbulent flow conditions in a water channel. The near-wall flow inside these recirculation zones was found to be very unsteady, with strong low-frequency fluctuations. The streamwise profiles of the wall shear stress were measured at several values of the Reynolds number and a high level of skin friction was obtained in the reverse-flow region. The strong dependence of the peak value of skin friction on the Reynolds number confirms the viscous-dominated character of the reverse flow appearing inside the recirculation zone. Received: 22 May 2000/Accepted: 28 March 2001