Subsonic Turbulent Boundary Layer Research Articles

Optical Diagnostics of Spanwise-Uniform Flows

Aerooptical aberrations along the spanwise direction of a canonical subsonic turbulent boundary layer were measured and studied nonintrusively using a Shack–Hartmann wave front sensor. It was demonstrated that in this case some important fluidic statistics in the wall-normal direction, like the mean velocity profiles, the local skin friction, and the spanwise integral scales, can be directly extracted from aerooptical aberrations. To avoid various spectral contamination in optical data at low frequencies, a model function for the deflection angle autospectral density at low frequencies was proposed. The spectral cross-correlation method and the dispersion method were used to extract the local convective velocities, and the dispersion analysis was demonstrated to be most accurate in computing the velocities. It was shown that it is possible to reconstruct the spectra above the Nyquist frequencies through the newly proposed stacking method. Convective velocities in the log region of the turbulent boundary layer were found to agree well with the direct measurements using a single hot wire. From the convective velocities, the local wall shear stress was nonintrusively extracted, using the Clauser method. Using corrected deflection angle spectra and the convective velocity, the local values of aerooptical aberrations were reconstructed. Finally, using the strong Reynold’s analogy, a wall-normal profile of the spanwise density correlation length was estimated and shown to be in good qualitative agreement with velocity-based spanwise length scales observed in the literature.

Effects of temperature on drag reduction in a subsonic turbulent boundary layer via micro-blowing array

A comparative study of two micro-blowing temperature cases has been performed to investigate the characteristics of drag reduction in a subsonic flat-plate flow (where the freestream Mach number is 0.7) by means of Direct Numerical Simulation (DNS). With minute amount of blowing gas injected from a 32 × 32 array of micro-holes arranged in a staggered pattern, the porosity of micro-holes is 23% and the blowing coefficient is 0.125%. The simulation results show that a drag reduction is achieved by micro-blowing, and a lower wall-friction drag can be obtained at a higher blowing temperature. The role of micro-blowing is to redistribute the total kinetic energy in the boundary layer, and the proportion of stream-wise kinetic energy decreases, resulting in the thickened boundary layer. Increasing micro-blowing temperature can accelerate this process and obtain an enhanced drag reduction. Moreover, an explanation of drag reduction by micro-blowing related to the micro-jet vortex clusters is proposed that these micro-jet vortex clusters firmly attached to the wall constitute a stable barrier, which is to prevent the direct contact between the stream-wise vortex and the wall. By Dynamic Mode Decomposition (DMD) from temporal/spatial aspects, it is revealed that small structures in the near-wall region play vital role in the change of turbulent scales. The high-frequency patterns are clearly strengthened, and the low-frequency patterns just maintain but are lifted up.

Large-scale coherent structures in compressible turbulent boundary layers

Abstract

Turbulence Amplitude Amplification in an Externally Forced, Subsonic Turbulent Boundary Layer

Experimental studies of the changes in turbulence characteristics inside a boundary layer due to external forcing were performed using hot-wire anemometry. The forcing was created by a periodically forced shear layer that was external to a compressible subsonic turbulent boundary layer. The convecting coherent structures in the shear layer create a concomitant unsteady pressure and velocity field and provide an external disturbance for the turbulent boundary layer on the wall of the tunnel close to the forced shear layer. Both the pressure and velocity fluctuations inside the boundary layer were simultaneously measured along with the forcing signal, and a phase-locked analysis was performed. Regions of amplified turbulence inside the boundary layer were observed. Near the wall, the region of amplified turbulence was slightly upstream or lagging of the external forcing and away from the wall it was downstream or leading the forcing signal. Analysis of the convective speeds in the region of amplified turbulence supported the existence of the critical layer inside the wake region of the boundary layer, and the critical layer is believed to be responsible for the amplified levels of the turbulence in the wake region. Various modulation and amplification correlation coefficients were computed and analyzed, and the results also indicated the presence of the critical layer. Examination of the phase-locked turbulence revealed similarities between the turbulence amplitude amplification results due to these externally forced experiments and modulation response of an internally forced, subsonic boundary layer in the literature.

Turbulent/nonturbulent interfaces in high-resolution direct numerical simulation of temporally evolving compressible turbulent boundary layers

Turbulent-nonturbulent interfaces are studied in temporally evolving subsonic and supersonic turbulent boundary layers by comparing the results of direct numerical simulations with the entrainment model based on a single vortex and the theory for spatially evolving boundary layers.

Interaction between plasma synthetic jet and subsonic turbulent boundary layer

This paper experimentally investigates the interaction between a plasma synthetic jet (PSJ) and a subsonic turbulent boundary layer (TBL) using a hotwire anemometer and phase-locked particle imaging velocimetry. The PSJ is interacting with a fully developed turbulent boundary layer developing on the flat wall of a square wind tunnel section of 1.7 m length. The Reynolds number based on the freestream velocity (U∞ = 20 m/s) and the boundary layer thickness (δ99 = 34.5 mm) at the location of interaction is 44 400. A large-volume (1696 mm3) three-electrode plasma synthetic jet actuator (PSJA) with a round exit orifice (D = 2 mm) is adopted to produce high-speed (92 m/s) and short-duration (Tjet = 1 ms) pulsed jets. The exit velocity variation of the adopted PSJA in a crossflow is shown to remain almost identical to that in quiescent conditions. However, the flow structures emanating from the interaction between the PSJ and the TBL are significantly different from what were observed in quiescent conditions. In the midspan xy plane (z = 0 mm), the erupted jet body initially follows a wall-normal trajectory accompanied by the formation of a distinctive front vortex ring. After three convective time scales the jet bends to the crossflow, thus limiting the peak penetration depth to approximately 0.58δ99. Comparison of the normalized jet trajectories indicates that the penetration ability of the PSJ is less than steady jets with the same momentum flow velocity. Prior to the jet diminishing, a recirculation region is observed in the leeward side of the jet body, experiencing first an expansion and then a contraction in the area. In the cross-stream yz plane, the signature structure of jets in a crossflow, the counter-rotating vortex pair (CVP), transports high-momentum flow from the outer layer to the near-wall region, leading to a fuller velocity profile and a drop in the boundary layer shape factor (1.3 to 1.2). In contrast to steady jets, the CVP produced by the PSJ exhibits a prominent spatiotemporal behaviour. The residence time of the CVP is estimated as the jet duration time, while the maximum extent of the affected flow in the three coordinate directions (x, y, and z) is approximately 32D, 8.5D, and 10D, respectively. An extremely high level of turbulent kinetic energy production is shown in the jet shear-layer, front vortex ring, and CVP, of which the contribution of the streamwise Reynolds normal stress is dominant. Finally, a conceptual model of the interaction between the PSJ and the TBL is proposed.

Acoustic responses of the composite sandwich plates with lattice truss core to the subsonic turbulent boundary layer

Acoustic responses of composite sandwich plates with lattice truss core to the subsonic turbulent boundary layer are investigated. The lattice truss core is composed of four sets of orthogonal stiffeners, two sets of oblique rods and one set of vertical columns, which establishes a significant transfer path of the reactive loadings. Bending and axial motion of the vertical columns makes a great impact on the power spectral density (PSD) of the transverse displacements for the sandwich plates with lattice truss core. The convective region of the high subsonic turbulent boundary layer pressure fluctuation spectra is the predominant vibrational source in the wide frequency bands, which makes the skin plate effectively radiate sound power into the mean air flow and the trim plate transmit sound waves into the static air by wavenumber conversion. Radiated acoustic power of skin plate is much larger than transmitted sound power of the trim plate and the sandwich plates can attenuate wave propagation of the airflow turbulent wall-pressure. The principal energy of the turbulent boundary layer wall-pressure for the water flow with a low speed can be transformed into the vibrational and acoustic energy of the sandwich plates in the low frequency band, to great extent.

Experimental vibroacoustic testing of plane panels using synthesized random pressure fields.

The experimental reproduction of random pressure fields on a plane panel and corresponding induced vibrations is studied. An open-loop reproduction strategy is proposed that uses the synthetic array concept, for which a small array element is moved to create a large array by post-processing. Three possible approaches are suggested to define the complex amplitudes to be imposed to the reproduction sources distributed on a virtual plane facing the panel to be tested. Using a single acoustic monopole, a scanning laser vibrometer and a baffled simply supported aluminum panel, experimental vibroacoustic indicators such as the Transmission Loss for Diffuse Acoustic Field, high-speed subsonic and supersonic Turbulent Boundary Layer excitations are obtained. Comparisons with simulation results obtained using a commercial software show that the Transmission Loss estimation is possible under both excitations. Moreover and as a complement to frequency domain indicators, the vibroacoustic behavior of the panel can be studied in the wave number domain.

Experimental studies of aero-optical properties of subsonic turbulent boundary layers

AbstractThis paper gives the most-complete characterization to date of the optical aberrations imposed on a laser beam propagated through a subsonic, compressible, turbulent boundary layer in a zero-pressure gradient environment, over a range of boundary-layer thicknesses, oblique propagation angles and Mach numbers. This characterization is based on optical measurements using optical-wavefront-sensing instruments that have only become available in the last decade. The optical characterization includes and discusses in detail: optical-wavefront spectra, convective velocities of optically active large-scale structures and correlation functions in both streamwise and cross-stream directions, as well as root-mean-square optical path difference levels for different apertures. The scaling law based on the extended strong Reynolds analogy is derived and is shown to successfully collapse optical data collected in a number of facilities. Anisotropy of aero-optical distortions for different oblique viewing angles was experimentally quantified and is discussed.

Reproduction of random pressure fields based on planar nearfield acoustic holography

This article discusses an open-loop approach based on planar nearfield acoustic holography (P-NAH) for the reproduction of random pressure fields, mainly intended for the measurement of vibroacoustic properties of plane panels. The main application is the simulation of turbulent boundary layer excitation in a laboratory environment, as an alternative to in-flight or wind tunnel experiments. The problem under study is the synthesis of random pressure distributions on a plane reproduction surface using acoustic monopoles distributed on a plane source surface facing the reproduction surface. The problem of reproducing a pressure distribution on a plane surface is addressed using the theoretical framework of P-NAH, which is extended to random pressure fields with corresponding imposed cross-spectral density functions. Results of numerical simulations are presented for the reproduction of a diffuse acoustic field, and a subsonic and supersonic turbulent boundary layer. The influence on the reproduction accuracy of the respective sizes of the two planes, their separation and the reproduction source separation are studied. The reproduction approach shows to be effective for the reproduction of diffuse acoustic field and turbulent boundary layer, but with different requirements in terms of plane separation and reproduction sources separation. In the specific case of subsonic turbulent boundary layer and associated sub-wavelength correlation scales reproduction, possible improvements of the method are suggested.

Generalized characteristic relaxation boundary conditions for unsteady compressible flow simulations

We develop numerical boundary conditions for the compressible Navier–Stokes equations based on a generalized relaxation approach (GRCBC), which hinges on locally one-dimensional characteristic projection at the computational boundaries, supplemented with available information from the flow exterior. The basic idea is to estimate the amplitude of incoming characteristic waves through first-order one-sided finite-difference approximations which involve the value of the reference flow state at the first exterior (ghost) point. Unlike other characteristic-based relaxation methods, the present one requires minimal user-supplied input, including the reference flow state, which may be totally or partially known, and in general may vary both in space and time. Furthermore, it can be applied to any type of computational boundary, either inflow or outflow, either subsonic or supersonic. The method is theoretically predicted to convey reduced reflection of waves at computational boundaries compared to other ones, and to have better properties of frequency response to injected disturbances. Numerical tests confirm the improvement of the nonreflecting performance, and demonstrate high degree of flexibility, also for problems with non-trivial far-field boundary conditions (e.g. flows in rotating reference frames) and for the artificial stimulation of subsonic turbulent boundary layers.

Conformal phased array aero-optical modeling and compensation

The effect of subsonic turbulent boundary layer aero-optical disturbances on a conformal phased array for laser beam projection operating on a high-speed aircraft is considered. We employ a basic model for subsonic boundary layer disturbances developed by Cress et al. which is governed by the displacement thickness δ ∗ to bound the magnitude of the problem, to determine the basic phenomenology affecting phased array performance, and to quantify requirements for compensation of these disturbances in the array subapertures. We used δ ∗ =15 mm as a baseline value in quantifying phased array effects on a 7-aperture hexagonal array with 10 cm subapertures. Boundary layer piston and tilt disturbances dominate array effects, but higher-order disturbances are similar in magnitude to the differential piston over the array and 2× greater in magnitude than an upper bound on free-stream turbulence. Adaptive optics compensation of turbulent boundary layer disturbances in such a phased array requires error rejection bandwidths >1 kHz for high-fidelity array performance.

On the accuracy of Malley probe measurements of aero-optical effects: a numerical investigation

Numerical databases established by large-eddy simulations of subsonic turbulent boundary layers and separated shear layers are utilized to simulate Malley probe measurements and investigate their accuracy and consistency with the data obtained from two-dimensional (2-D) wavefront sensors. It is found that the Malley probe data give a good approximation for the boundary layer and a reasonable approximation for the separated shear layer in terms of the root mean square of optical path difference (OPD rms ) and the streamwise correlations of OPD. The OPD rms from the Malley probe is slightly smaller than that from the 2-D wavefront sensor with the same streamwise aperture size for both flows. It is shown that the use of multiple Malley probes in the transverse direction of the flow can enhance the accuracy of measurements. The spatial correlations of OPD obtained from simulated multi-Malley-probe data are also examined and compared to those from 2-D wavefront sensors.

Aero-optics of subsonic turbulent boundary layers

AbstractCompressible large-eddy simulations are carried out to study the aero-optical distortions caused by Mach 0.5 flat-plate turbulent boundary layers at Reynolds numbers of ${\mathit{Re}}_{\theta } = 875$, 1770 and 3550, based on momentum thickness. The fluctuations of refractive index are calculated from the density field, and wavefront distortions of an optical beam traversing the boundary layer are computed based on geometric optics. The effects of aperture size, small-scale turbulence, different flow regions and beam elevation angle are examined and the underlying flow physics is analysed. It is found that the level of optical distortion decreases with increasing Reynolds number within the Reynolds-number range considered. The contributions from the viscous sublayer and buffer layer are small, while the wake region plays a dominant role, followed by the logarithmic layer. By low-pass filtering the fluctuating density field, it is shown that small-scale turbulence is optically inactive. Consistent with previous experimental findings, the distortion magnitude is dependent on the propagation direction due to anisotropy of the boundary-layer vortical structures. Density correlations and length scales are analysed to understand the elevation-angle dependence and its relation to turbulence structures. The applicability of Sutton’s linking equation to boundary-layer flows is examined, and excellent agreement between linking equation predictions and directly integrated distortions is obtained when the density length scale is appropriately defined.

A wave field synthesis approach to reproduction of spatially correlated sound fields

This article discusses an open-loop wave field synthesis (WFS) approach for the reproduction of spatially correlated sound fields. The main application concerns laboratory reproduction of turbulent boundary layer wall pressure on aircraft fuselages and measurement of their sound transmission loss. The problem configuration involves reconstruction of random sound pressure distributions on a planar reproduction surface using a planar array of reproduction monopoles parallel to the reproduction plane. In this paper, the WFS formulation is extended to sound fields with imposed time and spatial correlation properties (or equivalently imposed cross-spectral density in the frequency and wave number domains). Numerical examples are presented for the reproduction of a propagating plane wave, diffuse acoustic field and wall pressure in subsonic or supersonic turbulent boundary layers. The reproduction accuracy is examined in terms of the size of the source plane and reproduction plane, their separation, and the number of reproduction sources required per acoustic wavelength. While the reproduction approach cannot reconstruct sub-wavelength correlation scales of subsonic turbulent boundary layers, it effectively reconstructs correlation scales larger than the acoustic wavelength, making it appropriate for diffuse acoustic field and supersonic turbulent layers.

Seedless Velocimetry Measurements by Schlieren Image Velocimetry

Schlieren optical systems have been used to perform velocity measurements in refractive turbulent flows using image velocimetry algorithms. This schlieren image velocimetry (schlieren particle image velocimetry) technique makes use of naturally occurring refractive turbulent eddies in a flow as virtual seed particles upon which velocimetry is performed. Current experiments are performed in a supersonic wind tunnel to measure the Mach 3 turbulent boundary-layer mean velocity profile. Results from schlieren, shadowgraph, and focusing schlieren image velocimetry are compared with the boundary-layer velocity profile derived from a pitot-pressure survey. Focusing schlieren optics allow the visualization of refractive disturbances within a limited depth of focus, resulting in seedless velocimetry within a narrower depth of field. The natural intermittency of the turbulent boundary layer complicates schlieren image velocimetry, but useful measurements are still possible. The velocity profile in a subsonic turbulent boundary layer is also measured using this technique through thermal seeding of the boundary layer to provide refractive turbulent structures for velocimetry. An important improvement in schlieren image velocimetry, the use of a pulsed light-emitting-diode light source in place of the twin pulsed lasers required for traditional image velocimetry measurements, is introduced. This comparatively inexpensive white-light source eliminates traditional problems of coherent laser illumination in schlieren imaging and improves the overall results.

Measurement in a Zero-Pressure Gradient Turbulent Boundary Layer with Forced Thermal Convection

A subsonic zero-pressure gradient turbulent boundary layer developing on a uniformly heated surface at a Reynolds number in the range of 3, 560 ≤ Re θ ≤ 5,360 was investigated. Particle-image velocimetry measurements were performed at various positions in the streamwise direction for several wind-tunnel speeds and for different wall excess temperatures to show the thermal convection effects to expand the boundary-layer thickness δ 0.99 and to enlarge the turbulence intensities in the log-law and wake region. The mean velocity profiles are found to be self-preserving. The inclination of large-scale ramp-like vortex packets increases to higher characteristic angles, i.e., the mean angles are enlarged by approximately 5–10°. Hairpin-like vortex structures originating from the near-wall region seem to undergo higher climbing rates in the wall-normal direction causing the above mentioned significant changes in the boundary-layer thickness δ 0.99 and the strongly increased distributions of turbulence intensities in the wake region of the boundary layer. Changes in the distributions of the skewness and flatness of the probability density function (PDF) of the streamwise fluctuations corroborate these findings. The two-point correlation distribution of the streamwise velocity fluctuations R uu is increased for wall distances y/δ 0.99 = 0.1 to y/δ 0.99 = 0.75 indicating the existence of coherent structures in higher regions of the boundary layer.

Compressibility and Variable Density Effects in Turbulent Boundary layers

Two compressible turbulent boundary layers have been calculated by using direct numerical simulation. One case is a subsonic turbulent boundary layer with constant wall temperature for which the wall temperature is 1.58 times the freestream temperature and the other is a supersonic adiabatic turbulent boundary layer subjected to a supersonic freestream with a Mach number 1.8. The purpose of this study is to test the strong Reynolds analogy (SRA), the Van Driest transformation, and the applicability of Morkovin’s hypothesis. For the first case, the influence of the variable density effects will be addressed. For the second case, the role of the density fluctuations, the turbulent Mach number, and dilatation on the compressibility will be investigated. The results show that the Van Driest transformation and the SRA are satisfied for both of the flows. Use of local properties enable the statistical curves to collapse toward the corresponding incompressible curves. These facts reveal that both the compressibility and variable density effects satisfy the similarity laws. A study about the differences between the compressibility effects and the variable density effects associated with heat transfer is performed. In addition, the difference between the Favre average and Reynolds average is measured, and the SGS terms of the Favre-filtered Navier-Stokes equations are calculated and analyzed.

Acoustical properties of a long rectangular cavity of constant cross-section immersed in a thick boundary layer

An experimental investigation was undertaken to examine the effect of cavity length on flow oscillations produced by an open cavity placed within a subsonic turbulent boundary layer. A narrow rectangular cavity with a constant width to depth ratio, W/ D, of 1 was placed within a thick fully developed turbulent boundary layer with a corresponding R e θ = 10.5 × 1 0 3 . Pressure time histories were acquired for six separate cavity lengths (or L/ D values) using microphone type pressure transducers. The spectral character of these signals was analyzed in terms of their magnitude and frequency content. This study indicates that large changes in the fluctuating pressure level can occur as L/ D is varied from 1.47 to 8.73. A state of acoustic resonance was only observed at L / D = 1.47 , while fluid-acoustic resonance occurred at L/ D between 1.47 and 8.73. Relative SPL calculations indicate that energy within the cavity was increased by approximately 60% over this L/ D range. It is also suggested that this increase was a result of vortical structure shedding and growth. In addition, the location of maximum unsteadiness was estimated to coincide with the location of vortical structure saturation.

The Acoustics Associated With A Long Rectangular CavityOf Constant Cross-section Immersed In A Thick Boundary Layer

The flows over cavities are of interest in many different areas of engineering from thermal equipment to engines and machinery and can be found in landinggear wells, surface-mounted instrumentation on aircraft, cut-outs on marine vehicles, printed circuit boards and land vehicles. The very nature of these flows can cause large changes in pressure, velocity, and density fluctuations as well as generate strong propagating acoustic waves. These are typical cavity applications where reductions in pressure fluctuation levels, heat transfer, vibration, noise, and structural fatigue are still of considerable interest. This experimental study was undertaken to examine the effect of cavity length on flow oscillations produced by an open cavity placed within a subsonic turbulent boundary layer. A narrow rectangular cavity with a constant width-to-depth ratio was immersed within such a boundary layer. Microphone-type pressure transducers were used to record the pressure time histories for six separate cavity lengths (or L/D values) and the spectral character of these signals was analyzed in terms of their magnitude and frequency content. A state of acoustic resonance was only observed at L/D = 1.47, while fluid-acoustic resonance occurred at LID between 1.47 and 8.73. Relative sound pressure level (RSPL) calculations indicate that energy within the cavity was increased by approximately 60% over this L/D range. It is also suggested that this increase in the RSPL was a result of vortical structure shedding and growth, with the location of maximum unsteadiness coinciding with the location of vortical structure saturation. Transactions on the Built Environment vol 71, © 2004 WIT Press, www.witpress.com, ISSN 1743-3509