Isocorrelation Contours Research Articles

STATISTICAL CHARACTERISTICS OF PRESSURE FLUCTUATION IN SHOCK WAVE AND TURBULENT BOUNDARY LAYER INTERACTION

Shock wave and turbulent boundary layer interaction widely exists in the internal and external flow of high-speed aircraft. The aerodynamic performance and flight safety of aircraft are seriously affected by the strong pressure fluctuation in the interaction region. To investigate statistical characteristics of fluctuating pressure, the interaction between an incident shock of 33.2° and a spatially developed Mach 2.25 turbulent boundary layer is analyzed by means of direct numerical simulation (DNS). The numerical results have been carefully validated against with previous experiment and DNS at similar flow conditions in terms of mean velocity profile, turbulence intensity and wall pressure distribution. Statistics at the wall and in the outer layer, including fluctuation intensity, power spectral density, two-point correlation and space-time correlation, are quantitatively compared. The differences between them are analyzed in detail. It is found that the effect of the shock interaction on the wall-pressure fluctuation and the fluctuating pressure in the outer layer are utterly different. Based on the analysis of the power spectra density, the fluctuations in the separated region are both characterized by the low-frequency content, but in the reattachment region, the peak frequency of outer pressure fluctuations quickly shifts to higher frequency, with the low-frequency energy of wall-pressure fluctuation still being predominant. It is identified that the two-point correlations of pressure fluctuation at the wall and in the outer layer are both more elongated in the spanwise direction than that in the streamwise direction. The integral scale at the wall is generally increased, while the one in the outer layer increases sharply after passing the shock and then gradually decreases. The analysis of space-time correlation indicates that the iso-correlation contours are similar to the elliptical distribution and the convection velocity deduced by the correlation is dramatically decreased. Downstream of the interaction, the convection velocity in the outer layer is higher than that of wall-pressure fluctuation.

Space-time correlations of velocity in a Mach 0.9 turbulent round jet

In a turbulent jet, the numerical investigation of space-time correlations C(r, τ) at two-point and two-time of streamwise fluctuating velocities is presented along the nozzle lipline. Large-eddy simulation (LES) is performed for a Mach 0.9 turbulent jet issuing from a round nozzle. The turbulent boundary layer is well developed at the nozzle outlet, upon the inner wall, by adopting synthetic turbulent inlet boundary conditions. We study the cross correlations of streamwise fluctuating velocities at three particular streamwise positions, i.e., x = 0.71, 7.03, and 34.47r0, corresponding to different stages of jet development, where r0 is the radius of the nozzle. Present results show that the classical Taylor’s frozen-flow model is unable to predict C(r, τ) accurately in this strongly spatially developing shear flow since the distortion of the flow pattern is missing. The isocorrelation contours of C(r, τ) show a clearly elliptical feature, which is found to be well predicted by the elliptic approximation (EA) model [G.-W. He and J.-B. Zhang, “Elliptic model for space-time correlations in turbulent shear flows,” Phys. Rev. E 73, 055303 (2006)]. According to the EA model, C(r, τ) has a scaling form of C(rE, 0) with two characteristic velocities U and V, i.e., rE = (r − Uτ)2 + V2τ2. By examining LES data, it is found that the characteristic velocity U determined in LES is in general consistent with the theoretical Ut in the EA model, while the trend of V in LES also matches with that of the theoretical Vt. Additionally, it is interesting that the ratio of V to Vt is approximately a constant V/Vt ≃ 1.3 in the turbulent jet.

Experimental investigation of longitudinal space–time correlations of the velocity field in turbulent Rayleigh–Bénard convection

AbstractWe report an experimental investigation of the longitudinal space–time cross-correlation function of the velocity field, $C(r, \tau )$, in a cylindrical turbulent Rayleigh–Bénard convection cell using the particle image velocimetry (PIV) technique. We show that while Taylor’s frozen-flow hypothesis does not hold in turbulent thermal convection, the recent elliptic model advanced for turbulent shear flows (He & Zhang, Phys. Rev. E, vol. 73, 055303) is valid for the present velocity field for all over the cell, i.e. the isocorrelation contours of the measured $C(r, \tau )$ have an elliptical curve shape and hence $C(r, \tau )$ can be related to $C({r}_{E} , 0)$ via ${ r}_{E}^{2} = (r\ensuremath{-} U\tau )^{2} + {V}^{2} {\tau }^{2} $ with $U$ and $V$ being two characteristic velocities. We further show that the fitted $U$ is proportional to the mean velocity of the flow, but the values of $V$ are larger than the theoretical predictions. Specifically, we focus on two representative regions in the cell: the region near the cell sidewall and the cell’s central region. It is found that $U$ and $V$ are approximately the same near the sidewall, while $U\simeq 0$ at the cell centre.

Elliptic model for space-time correlations in turbulent shear flows

An elliptic model for space-time correlations in turbulent shear flows is proposed based on a second order approximation to the iso-correlation contours, while Taylor's hypothesis implies a first-order approximation. It is shown that the space-time correlations are mainly determined by their space correlations and the convection and sweeping velocities. This model accommodates two extreme cases: Taylor's hypothesis at vanishing sweeping velocity and the sweeping hypothesis at vanishing convection velocity. The result is supported by the data from the direct numerical simulation of turbulent channel flows.

Spatial Correlation Analysis of Atrial Activation Patterns during Sustained Atrial Fibrillation in Conscious Goats

In this study we applied both linear and nonlinear spatial correlation measures to characterize epicardial activation patterns of sustained atrial fibrillation in instrumented conscious goats. It was investigated if nonlinearity was involved in the spatial coupling of atrial regions and to what extent fibrillation was organized in the experimental model of sustained atrial fibrillation (AF) in instrumented goats. Data were collected in five goats during experiments to convert AF by continuous infusion of cibenzoline. Spatial organization during AF was quantified with the linear spatial cross correlation function and the nonlinear spatial cross redundancy which was calculated using the Grassberger-Procaccia correlation integral. Two different types of correlation were evaluated to distinguish simultaneous interaction from non-simultaneous interaction, for instance resulting from propagation of fibrillation waves. The nonlinear association length and the linear correlation length were estimated along the principal axes of iso-correlation contours in two-dimensional correlation maps of the nonlinear spatial redundancy and the linear spatial correlation function, respectively. To quantitatively assess the degree of nonlinearity, the association length was also estimated from the linearized spatial redundancy using multivariate surrogate data. The differences between the nonlinear and linearized association lengths indicated that a nonlinear component in the spatial organization of AF predominantly existed in the right atrium. The degree of organization characterized by association length along the short principal axis was higher in the right atrium (15 ± 7 mm) than in the left atrium (8 ± 4 mm). The spatial extension of coherent atrial patches was estimated from a surface of association equal to the area spanned by the principal axes of iso-correlation contours from the redundancy, including the effects from non-simultaneous interaction. Interpreting this area as the spatial domain of a fibrillation wavelet, the results suggest that the mapped region was activated on average by two wavelets in the left atrium and by one wavelet in the right atrium. Therefore, the activation pattern of sustained AF in goats was relatively organized, consistent with type II of AF. It is suggested that the surface of association is a measure of the number of independent wavelets present in the atria during sustained AF, and that larger association lengths result from fewer and larger reentrant circuits.

The turbulent shear flow around a rotating cylinder in a quiescent fluid. (2nd report. Structure of large eddy).

Measurements have been made for space-time correlations of velocity fluctuations in the turbulent shear flow around a circular cylinder spinning in a quiescent fluid. Optimum delay time and the associated motion of lumps of eddies are considered. In order to examine the spatial structure of the turbulent field, Taylor's hypothesis is used to transform the time coordinate to the peripheral one, and various contour maps of spatial iso-correlations are obtained in plane perpendicular to the cylinder axis. The change in the iso-correlation contours for Q2, 2 in the plane of ys = 0 with the cut-off frequency of a high-pass filter suggests that the mean shear has only a little effect on large eddies with low frequency. The contours for Q2, 3 show that the range over which the correlation holds the finite value extends in the axial direction over nearly twice the radius of the cylinder, and that there exists a comlex large-eddy structure.

Organized structures in a turbulent plane jet: topology and contribution to momentum and heat transport

In the self-preserving region of a slightly heated turbulent plane jet, conventional isocorrelation contours of velocity and temperature fluctuations support the existence of organized large-scale structures. Temperature fronts associated with these structures were visually detected using a spanwise rake of cold wires. This method of detection was then used to condition velocity and temperature fluctuations and products of these fluctuations. Ensemble-averaged velocity vectors, constructed in the plane of main shear, suggest a topology for the organized motion in which the temperature front is identified with the diverging separatrix connecting adjacent structures on the same side of the centreline. Coherent stresses and heat fluxes are particularly significant near the diverging separatrix. Contributions by the coherent and random motions to the averaged momentum and heat transports are generally of the same order of magnitude.

Some two-point statistical properties of a three-dimensional wall jet

The effects of both a straight and a curved wall on the two-point space-time velocity correlations of a turbulent jet are documented. From the correlations, isocorrelation contours are constructed which allow a picture of the various flow patterns to be determined. Autoand cross-correlations of the fluctuating concentration field are also obtained for the different flow configurations. The confining surfaces served to radically change the flow pattern for the freely expanding turbulent jet. The velocity measurements are made with a laser Doppler velocimeter in conjunction with a phase locked-loop processor, while the concentration field is monitored with a laser light-scattering technique.

Rainfall Fields in Israel and Jordan and the Effect of Cloud Seeding on Them

Spatial correlation functions of daily rainfall were derived separately for various parts of the study area and for unseeded and seeded days. The structure of respective rainfall fields was studied by means of the relationship between the geometry of iso-correlation contours of daily rainfall and the average geometry and/or kinematics of cloud systems that produce the rainfall. Results were obtained on 1) the prevalent direction of storm movement over the study area and 2) the change in size of rainfall areas under varying conditions. Evidence is presented of an average increase of about 10 km in the dimensions of rainfall areas on seeded days. It is suggested that expanded rainfall areas have a twofold effect on the augmentation of the total yield of individual storms: 1) an increase of point rainfall resulting from prolonged exposure to moving cloud systems, and 2) an increase in the area thus affected. Consequently, the increase in water yield of a storm over the entire area covered by it, may not be fully represented by point measurements. In the regional context, a contraction of storm areas was found in the transition to the arid zone. It is suggested that the size of rainfall areas is one of the fundamental factors controlling regional variations of rainfall as well as variations resulting from cloud seeding.

An experimental investigation of a three-dimensional wall jet

One and two point statistical properties are measured in the flow fields of a coflowing turbulent jet. Two different confining surfaces (one flat, one with large curvature) are placed adjacent to the lip of the circular nozzle; and the resultant effects on the flow field are determined. The one point quantities measured include mean velocities, turbulent intensities, velocity and concentration autocorrelations and power spectral densities, and intermittencies. From the autocorrelation curves, the Taylor microscale and the integral length scale are calculated. Two point quantities measured include velocity and concentration space-time correlations and pressure velocity correlations. From the velocity space-time correlations, iso-correlation contours are constructed along with the lines of maximum maximorum. These lines allow a picture of the flow pattern to be determined. The pressures monitored in the pressure velocity correlations are measured both in the flow field and at the surface of the confining wall(s).

Space-time correlations of the transverse velocity fluctuation in pipe flow

Memory times are smaller for transverse velocity components than for longitudinal components. For the former less downstream-upstream asymmetries are apparent in the optimal space-time isocorrelation contours.

Correlation characteristics and dimensionality of speech spetra.

Statistical properties of spectral samples derived from the continuous speech of six talkers and summarized by means of covariance-matrix eigenvectors are used to study the dimensionality of the data space. The importance of eliminating low-level samples by means of a fixed threshold is emphasized, and criteria for selecting such a threshold are presented. Measurements of spectral correlations stabilize after about 30 sec of speech, suggesting that short-term examination of a talker's output may prove sufficient to calculate parameters useful in recognition schemes. Some features of the correlation matrix, which are readily displayed via isocorrelation contours, appear to be related to talker characteristics, while others are talker independent. The results suggest that the separation of speech data into gross classes prior to the application of statistical procedures will enhance the performance of processing schemes.