Experimental study of a supersonic turbulent boundary layer using PIV

Particle image velocimetry was applied to the study of the statistical properties and the coherent structures of a flat plate turbulent boundary layer at Mach 3. The nanoparticles with a good flow-following capability in supersonic flows were adopted as the tracer particles in the present experiments. The results show that the Van Driest transformed mean velocity profile satisfies the incompressible scalings and reveals a log-law region that extends to y/ =0.4, which is further away from the wall than that ...     

Analytical investigation velocity fields on mean and turbulent of a plane jet

This paper analyses the downstream developments of the mean and the turbulent velocity fields of a plane jet. Based on the conservation of mass and the conservation of momentum, the mean-velocity half width （reflecting the jet spread rate） and the relative mass flow rate （jet entrainment） are related to the decay rate of the centreline mean velocity. These relations are not subject to self-preservation. Both analytical and experimental results suggest that the jet spread rate （K1） and the entrainment rate （K3） （and thus the decay rate K2） can be well estimated from the centreline velocity, i.e., K1 ≈ 0.6K2 and K3 ∝K2. The effect of initial mean velocity and RMS velocity profiles on the downstream mean velocity field appears to be embodied in the constants K1 K2 and K3. The analytical relationship for the self-preserving Reynolds shear stress, obtained for the first time, works well.     

Analytical investigation on mean and turbulent velocity fields of a plane jet

This paper analyses the downstream developments of the mean and the turbulent velocity fields of a plane jet. Based on the conservation of mass and the conservation of momentum, the mean-velocity half width (reflecting the jet spread rate) and the relative mass flow rate (jet entrainment) are related to the decay rate of the centreline mean velocity. These relations are not subject to self-preservation. Both analytical and experimental results suggest that the jet spread rate (K₁) and the entrainment rate (K₃) (and thus the decay rate K₂) can be well estimated from the centreline velocity, i.e., K₁ ≈ 0.6K₂ and K₃ ∝ K_2. The effect of initial mean velocity and RMS velocity profiles on the downstream mean velocity field appears to be embodied in the constants K₁ K₂ and K₃. The analytical relationship for the self-preserving Reynolds shear stress, obtained for the first time, works well.     

Constrained large-eddy simulation of supersonic turbulent boundary layer over a compression ramp

A supersonic turbulent boundary layer over a compression ramp is numerically investigated using the constrained large-eddy simulation (CLES) method. The compression corner is characterised by a deflection angle of 24°. The free-stream Mach number is Ma_∞ = 2.9, and the Reynolds number based on the momentum thickness of inlet boundary layer is Re_θ = 2300. The mean and statistical quantities, such as mean velocity, wall pressure and Reynolds stresses, are thoroughly analysed and compared with those from traditional large-eddy simulation (LES), experimental measurement and direct numerical simulation (DNS). It turns out that CLES can predict the friction coefficient, wall-pressure distribution, size of separation bubble, Reynolds stresses, etc. more accurately than traditional LES, and the results are in reasonable agreement with the experimental and/or DNS data. Also discussed are the effects of specific parameterisations of the Reynolds constraint and interfacial positions separating the constrained and unconstrained regions on the performance of the CLES method.     

Temporal evolution of optical path difference of a supersonic turbulent boundary layer

The density distribution of a supersonic turbulent boundary layer is measured with the nanoparticle-based planar laser scattering technique, and the temporal evolution of its optical path difference (OPD) in a short time interval is characterized by proper orthogonal decomposition (POD). Based on the advantage of POD in capturing the energy of a signal, a temporal evolution model is suggested for the POD coefficients of OPD. In this model, the first few coefficients vary linearly with time, and the others are modeled by Gaussian statistics. As an application, this method is used to compute the short-exposure optical transfer function.     

Temporal evolution of the optical path difference of a supersonic turbulent boundary layer

The density distribution of a supersonic turbulent boundary layer is measured with the nanoparticle-based planar laser scattering technique, and the temporal evolution of its optical path difference (OPD) in a short time interval is characterized by proper orthogonal decomposition (POD). Based on the advantage of POD in capturing the energy of a signal, a temporal evolution model is suggested for the POD coefficients of the OPD. In this model, the first few coefficients vary linearly with time, and the others are modeled by Gaussian statistics. As an application, this method is used to compute the shortexposure optical transfer function.     

Density and velocity statistics in variable density turbulent mixing

We experimentally study variable–density mixing of miscible gases in an open-circuit wind tunnel using simultaneous particle image velocimetry and planar laser-induced fluorescence. Experiments of a high Atwood number (0.6) and low Atwood number (0.1) are performed to compare non-Boussinesq cases with the Boussinesq limit. The higher density gas is injected into the wind tunnel co-flow using a round jet configuration, and near-field and far-field measurements are performed to examine mixing in both momentum and buoyancy-dominated regimes. The effects of buoyancy are measurable and important in both large-scale mixing features and in turbulence quantities. The low Atwood number PDFs (probability density functions) show fast and uniform mixing. The high Atwood number PDFs of density have skewness towards the larger densities, indicating less mixing of the heavy fluid due to its inertia. The skewness in the density gradient PDFs at high Atwood number displays strong density local variations that can enhance mixing at molecular scales. Turbulent kinetic energy decreases with streamwise distance from the jet for low Atwood number but increases for high Atwood number due to larger buoyancy and density-driven shear. Over 3000 experimental realisations are used to calculate statistical characteristics of the mixing, including valuable and rarely given data such as Favre-averaged turbulent quantities: mass flux velocity, Reynolds stress, turbulent kinetic energy, and density-specific volume correlation. Buoyancy effects are observed in these quantities and the trends are compared qualitatively with direct numerical simulations.     

Assessment of acoustic pressure holograms from membrane velocity measurements

The aim of this paper is to demonstrate experimentally the possibility of acquiring acoustic pressure holograms using a light membrane and a scanning laser vibrometer. The velocity of a light membrane placed in an acoustic field can be measured without contact by means of a laser vibrometer. The ideal membrane must be optically reflective, acoustically transparent (having as little mass as possible), impermeable, and mounted without tension. The measured velocity is equal for continuity reasons to the normal acoustic velocity, but differs from the acoustic velocity without the membrane because the membrane is never completely transparent to acoustic waves. The effect of the mass of the membrane can be taken into account to correct this difference. Then, acoustic pressure holograms can be deduced from velocity holograms using the 2D Discrete Fourier Transform. An experimental validation is carried out; acoustic pressures derived from laser measurements are compared with microphone measurements, with a very satisfying match over a wide frequency range.     

Direct numerical simulation of a supersonic turbulent boundary layer on a flat plate and its analysis

In the past three decades, considerable progress has been made in the investigation of incompressible turbulent boundary layer through experiments, DNS and theoretical works, including: (1) the statistics characteristic and structure of turbulence; (2) the co-herent structures in turbulent flows; (3) turbulence modeling and the large eddy simula-tion (LES). In contrast, the progress was very slow for the compressible, in particular, the super-sonic turbulent boundary layer. Recent works on d…     

Direct numerical simulation of shock/turbulent boundary layer interaction in a supersonic compression ramp

A direct numerical simulation of the shock/turbulent boundary layer interaction flow in a supersonic 24-degree compression ramp is conducted with the free stream Mach number 2.9.The blow-and-suction disturbance in the upstream wall boundary is used to trigger the transition.Both the mean wall pressure and the velocity profiles agree with those of the experimental data,which validates the simulation.The turbulent kinetic energy budget in the separation region is analyzed.Results show that the turbulent production term increases fast in the separation region,while the turbulent dissipation term reaches its peak in the near-wall region.The turbulent transport term contributes to the balance of the turbulent conduction and turbulent dissipation.Based on the analysis of instantaneous pressure in the downstream region of the mean shock and that in the separation bubble,the authors suggest that the low frequency oscillation of the shock is not caused by the upstream turbulent disturbance,but rather the instability of separation bubble.     

Map for Simultaneous Measurements for a Quantum Logic

In this paper we will study a function of simultaneous measurements for quantum events (s-map) which will be compared with the conditional states on an orthomodular lattice as a basic structure for quantum logic. We will show the connection between s-map and a conditional state. On the basis of the Rényi approach to the conditioning, conditional states, and the independence of events with respect to a state are discussed. Observe that their relation of independence of events is not more symmetric contrary to the standard probabilistic case. Some illustrative examples are included.     

Response of a panel to a supersonic turbulent boundary layer: studies on a theoretical model

The response of a clamped panel to a supersonic turbulent boundary layer is studied on the basis of a recently developed theoretical model. This model, in the form of an integro-differential equation, incorporates the effect of coupling between the panel motion and the flow of the surrounding fluid. A Ritz-Galerkin method is used to obtain approximate solutions for the statistics of the panel response to the turbulence. Comparisons of the numerical results with previous experimental data are presented and assessments of the theoretical model in the light of such comparisons are made.     

Fluctuation measurements in a supersonic boundary layer implying in-situ calibration of the hot-wire anemometer

A calibration technique for the constant-temperature hot-wire anemometer is presented, which is based on traversing the probe through the boundary layer of a flat plate while simultaneously performing fluctuation measurements. The free stream Mach number was M = 2.54, and the Reynolds number Re_d, based on wire diameter, ranged from 9 to 23. A comparison of the sensitivity values obtained with the aid of such a calibration procedure — under the condition of neglecting low temperature loadings (t<0.6) — agrees well with sensitivities determined with free-stream data-The use of a modified transfer function for correcting the power spectra of flow perturbations revealed a conformity of wide parts of the corrected spectra with the Kolmogorov decay. The fluctuation levels of total temperature and mass flux were computed for the boundary layer of a flat plate. This work was presented at the International Conference on the Methods of Aerophysical Research ICMAR 2007, which was held in Novosibirsk on 5–10 February 2007.     

The evolution of synthesised vortices in turbulent boundary layer

Particle image velocimetry technique has been used to investigate the evolution of synthesised vortical structures in the turbulent boundary layer. Synthetic jet actuator is implemented on the flat plate surface to synthesise various vortical structures by operating the actuator at varying operating parameters. The vortices are issued into the boundary layer and their evolution and subsequent interaction with the relatively less energetic near wall fluid is studied. The investigation is based on the quantitative measurements that are made both on the central and parallel lateral planes. Finally, the enhancement of the wall shear stress resulted in by the passing vortices is measured to evaluate the effectiveness of the actuator towards flow separation control.     

Evolution of turbulent kinetic energy in a perturbed turbulent boundary layer

The paper considers the evolution of turbulent kinetic energy in a turbulent boundary layer perturbed by suction. The results show that the boundary layer equilibrium is altered in a non-linear manner due to suppression of the structures near the wall. The behavior, however, suggests that the wavelength of alteration of the equilibrium of the layer is unaffected by a change in Reynolds number and suction rate.     

Low-wavenumber turbulent boundary layer wall-pressure measurements from vibration data on a cylinder in pipe flow

The response of a structure to turbulent boundary layer (TBL) excitation has been an area of research for roughly 50 years, although uncertainties persist surrounding the low-wavenumber levels of the TBL surface pressure spectrum. In this experimental investigation, a cylindrical shell with a smooth internal surface is subjected to TBL excitation from water in fully developed pipe flow. The cylinder's vibration response to this excitation is used to determine low-wavenumber TBL surface pressure levels at lower streamwise wavenumbers than previously reported (k₁/k_c<0.01). An experimental modal analysis is also conducted on the water-filled cylindrical shell to determine structural parameters which are used to extract TBL pressures. The measured low-wavenumber pressure data falls midway between TBL models by Smol’yakov [Acoustical Physics 52(3) (2006) 331-337] and Chase [Journal of Sound and Vibration 112(1) (1987) 125-147] and is roughly 23 dB lower than an early TBL model by Corcos [Journal of the Acoustical Society of America 35(2) (1963) 192-198]. The current data is a few decibels below the lower bound of related measurements in air by Farabee and Geib [ICIASF ‘75 Record, 1975, pp. 311-319] and Martin and Leehey [Journal of Sound and Vibration 52(1) (1977) 95-120]. A simple wavenumber white form for the TBL surface pressure spectrum at low-wavenumber is suggested.     

Probability density function of velocity fluctuations in a rectangular T-junction duct

The streamwise and the spanwise velocity time series are measured from the wall to the centre of the cross duct for the flow in a rectangular T-junction duct, which is similar to airflow conditions of high-speed train ventilation system. The turbulent statistical properties are reported at three streamwise locations which correspond to the upstream/downstream and the centreline of the T-junction (x/D?=?±1 and 0, respectively). Turbulence intensities, skewness and flatness factor, as well as probability density functions, have been investigated at the range of Re_τ?=?5400–8700. Furthermore, the multiscale properties of the flatness factor are analysed by using orthogonal wavelet transform. It is found that the turbulent intensities remain a constant in the centre region for three streamwise locations while they are weakened in the turbulent boundary layer at x/D?=?1 by effect of suction. The location of the strongest intermittency is located at y/h?=?0.56 for x/D?=??1 and 0. While at downstream of T-junction (x/D?=?1), the location of the strongest intermittency shifts down to y/h?=?0.28. Also, the wavelet flatness factor is more clearly distinguished the intermittency of the small-scale turbulent structure compared with the conventional flatness factor and, the obtained experimental data are fitted and used to predict the mean streamwise velocity profiles.     

Distribution of mean velocity in turbulent boundary layer over permeable surface with air blowing

In the present article, we investigate the possibility of using simple physical models for predicting properties of incompressible turbulent boundary layer on permeable wall at various values of air-microblowing mass flow rate. It is shown that the velocity scaling U _??*/?? ₉₉ can be successfully used to approximate the distribution of mean velocity in the outer region of the boundary layer. The use of this scaling makes the velocity profiles invariant with respect to Reynolds-number variation; this circumstance largely facilitates the analysis of experimental data, making it independent of upstream flow conditions. The distribution of mean velocity in the logarithmic flow region of the boundary layer over permeable surface can be described with a modified law of the wall involving a constant C ₀ equal to the same constant for canonical boundary layer, and a quantity K being a weak function of blowing ratio.