Two-point Space Correlations Research Articles

Comparison between velocity- and vorticity-based POD methods in a turbulent wake

In this paper, the velocity-based POD and the vorticity-based POD have been systematically compared in three characteristic regions of the flow downstream of a two-dimensional circular cylinder, namely the near, intermediate and far wakes. The two-point space correlation function is used to determine which of the two methods is better suited for extracting the large-scale flow structures based on the repartition of energy among the different POD modes. It is found that the POD, based on the lateral velocity fluctuation v, leads to the most optimum extraction in all three flow regions, while the vorticity-based POD is only effective in the near and intermediate wakes. Based on two-point space correlation functions, a scenario is proposed for the application of POD to the present two-dimensional wake .

2D PIV measurements in the near field of grid turbulence using stitched fields from multiple cameras

We present measurements of grid turbulence using 2D particle image velocimetry taken immediately downstream from the grid at a Reynolds number of ReM = 16500 where M is the rod spacing. A long field of view of 14M × 4M in the down- and cross-stream directions was achieved by stitching multiple cameras together. Two uniform biplanar grids were selected to have the same M and pressure drop but different rod diameter D and cross-section. A large data set (104 vector fields) was obtained to ensure good convergence of second-order statistics. Estimations of the dissipation rate \(\varepsilon\) of turbulent kinetic energy (TKE) were found to be sensitive to the number of mean-squared velocity gradient terms included and not whether the turbulence was assumed to adhere to isotropy or axisymmetry. The resolution dependency of different turbulence statistics was assessed with a procedure that does not rely on the dissipation scale η. The streamwise evolution of the TKE components and \(\varepsilon\) was found to collapse across grids when the rod diameter was included in the normalisation. We argue that this should be the case between all regular grids when the other relevant dimensionless quantities are matched and the flow has become homogeneous across the stream. Two-point space correlation functions at x/M = 1 show evidence of complex wake interactions which exhibit a strong Reynolds number dependence. However, these changes in initial conditions disappear indicating rapid cross-stream homogenisation. On the other hand, isotropy was, as expected, not found to be established by x/M = 12 for any case studied.

Batchelor’s fourth order velocity correlation.

The Lighthill theory for aerodynamic noise relates far field sound pressure to complex fourth order two point two-time space-time velocity correlations. The Mani–Gliebe–Balsa (MGB) jet noise prediction code follows Lighthill’s theory in the development of its algorithm. Since fourth order turbulence correlations are not modeled in the MGBs flow solver, it is necessary to resort to some form of approximation. The MGB invokes Batchelor’s fourth order decomposition, which is exact for homogeneous and isotropic turbulence. For anistropic flow, like that of a jet, it is not known what the error is in adopting Batchelor’s isotropic decomposition. The question here is can stereo particle image velocimetry (SPIV) provide a means to establish the error incurred with adoption of this decomposition. In an attempt to define the penalty for adopting the Batchelor’s decomposition, a simple 2×94; diameter laboratory jet was operated at ambient temperatures at Mach 0.85. SPIV measurements were acquired of the fourth order two-point space correlation and all of the other second order correlations. A comparison was made to numerical plume simulations with an advanced numerical flow solver running in the RANS mode. This paper provides an explanation for observed variations between measured and predicted jet noise.

Large-Eddy Simulation of a Turbulent Compressible Round Jet

A large-eddy simulation (LES) of a high-Reynolds-number jet was performed. A numerical scheme that is uniformly fourth-order accurate in time and space was used to solve the Favre-e ltered Navier ‐Stokes equations. The subgrid-scale stresses were computed using a compressible form of Smagorinsky’ s model. A cold Mach 1.4 nozzlewithaReynoldsnumberof1 :2 ££ 106 wassimulated.Incontrasttosimilarstudies,theentirenozzlegeometry including the nozzle lip was modeled. The LES simulation accurately captures the physics of the turbulent e ow. The agreement with experimental data is relatively good and improves on results in the current literature. This improvement can be attributed to the numerical scheme and the modeling of the nozzle. In addition, a twopoint correlation technique was used to quantify the turbulent structures in the jet mixing layer and showed that computational techniques can be used to characterize such structures for application to Lighthill’ s acoustic analogy. Two-point space correlations were used to obtain a measure of the integral length scale, which proved to be approximately 1 Dj. Two-point space-time correlations were used to estimate the convection velocity for the turbulent structures. This velocity estimates ranged from 0.57 to 0.71 Uj and is in agreement with theory.

Large-scale turbulence phenomena in compound rectangular channels

In this article we investigate turbulent flow of air through compound rectangular channels to experimentally investigate the turbulence phenomena in compound channels. Detailed experimental data of axial mean velocity, wall shear stresses, five of six Reynolds stresses, auto- and cross-spectral densities, and two-point space correlations were measured by hot-wire anemometry in 18 geometrical configurations. The symmetry of the present flow appears to be better than that of previous measurements and the range of measurments is more extensive. The most interesting result is the existence of a quasi-periodic large-scale turbulence structure in most of the geometries investigated. This structure is stationary and independent of the axial position in the channel. It exists in any longitudinal slot or groove in a wall or a connecting gap between two flow channels, provided its depth is more than approximately twice its width. The frequency of this flow oscillation is determined by the geometry of the slot and is linearly dependent on the bulk velocity.

Possible Inhomogeneities in the Universe on Scales of 100–300 MPC from Observations with the 6-Meter Telescope

In 1986 the programme “The Northern Cone of Metagalaxy” has been finished with the 6-meter Telescope. In the course of the programme redshifts of all very rich compact clusters of galaxies inside the cone with galactic latitude and indirect estimates of redshifts ZLB < 0.28 have been measured. The total volume of the investigated region is V ≈ 500·106 Mpc3 (we accept Hubble constant H=50 km/s Mpc−1). A number of possible indications of existence of inhomogeneities in the Universe on scales greater than 100 Mpc are obtained: 1) the void of 400 Mpc in size; 2) the flat stratum of 150 Mpc thickness and 1000 Mpc diameter; 3) two-point space correlation function ξ (R = 200–300 Mpc) = 0.5±0.2. We found no indications that topology of the Universe is non-Euclidean on scales of 20–200 Mpc.

Large-scale coherent structures in the wake of axisymmetric bodies

The unsteady flow past a circular disk is studied with hot-wire and microphone probes positioned in planes normal to the axis of symmetry at 3 and 9 disk diameters down-stream. Both the fluctuating velocity and pressure signals are shown to be continuously dominated by large-scale coherent motions enveloping the wake flow as a whole. This suggests narrowband two-point space correlations as an experimental tool for describing spatial coherence and phase characteristics of the basically random signals. The specific symmetry imposed by the axisymmetric boundary conditions of the disk enables a decomposition of the large-scale flow phenomena into relatively simple elementary structures or modes. The resulting azimuthal constituents are quantified in terms of their respective magnitudes and individual power spectra.The capability of the approach to uncover characteristic features of turbulence as far as its large-scale domain is concerned is demonstrated by a comparison of the present results with certain remarkably different features found in earlier jet flow investigations: the m = 1 and m = 2 modes are found to clearly dominate in wakes whereas the m = 0 and m = 1 modes were dominant in jets in a relevant range of Strouhal numbers. These large-scale coherent structures are more than just an interesting flow phenomenon; they must have a tremendou back-reaction on rigid flow boundaries (particularly if these allow a vibrational response) and may give rise to specific feedback mechanisms.The analysing technique proposed for studying large-scale flow phenomena injets and wakes removes part of the randomness in the turbulent signals without artificially exciting or forcing them in one way or another. No conditional sampling of the naturally occurring fluctuations is required, either. The method may be applicable to other than strictly axisymmetric flow configurations, too.

Velocity correlation structure in the turbulent near wakes of bluff bodies

Two-point space correlations of streamwise fluctuations have been measured in the turbulent near wakes of two-dimensional bluff body models like 90-deg wedges, circular and rectangular cylinders in the Reynolds number range of 2x 104 to 10 5. Two single hot-wire probes operated by constant temperature anemometers were used for this purpose. The data show that the streamwise, lateral, and spanwise extents of eddies, in general, are larger in the free shear layer region compared to the centerline region of the turbulent near wakes. Integral scales increase with distance downstream. In particular, the streamwise and lateral integral scales increase linearly with distance after about 1.5 times the diameter or base height of the model. For 90-deg wedge models of different BR up to 25%, the correlation curves show similarity when length scale is nondimensionalized with the base height. The correlation curves for one BR models of different bluffness also indicate approximately similar trends. Hot-wire traces show intermittency between laminar and turbulent states in the region of free reattachment point for all two-dimensional models.

Fully developed asymmetric flow in a plane channel

The paper presents the results of a detailed experimental examination of fully developed asymmetric flow between parallel planes. The asymmetry was introduced by roughening one of the planes while the other was left smooth; the ratio of the shear stresses at the two surfaces was typically about 4:1.The main emphasis of the research has been on establishing the turbulence structure, particularly in the central region of the channel where the two dissimilar wall flows (generated by the smooth and rough surfaces) interact. Measurements have included profiles of all non-zero double and triple velocity correlations; spectra of the same correlations at several positions in the channel; skewness and flatness factors; and lateral two-point space correlations of the streamwise velocity fluctuation.The region of greatest interaction is characterized by strong diffusional transport of turbulent shear stress and kinetic energy from the rough towards the smooth wall region, giving rise,inter alia, to an appreciable separation between the planes of zero shear stress and maximum mean velocity. The profiles of length scales of the larger-scale motion are, in contrast to the turbulent velocity field, nearly symmetric. Moreover, it appears that at high Reynolds numbers the small-scale motion may in many respects be treated as isotropic.

Results of an attempt to generate a homogeneous turbulent shear flow

An approximately homogeneous turbulent shear flow is generated in an open-return wind tunnel test-section by a plane parallel-rod grid of uniform rod diameter and non-uniform rod spacing. The grid design is based upon an analysis by Owen & Zienkiewicz (1957). Hot-wire measurements taken in this flow include mean velocities, component turbulence intensities, shear and two-point space correlations, and energy spectra. In addition, microscales, obtained both from instantaneous time derivatives of the hot-wire signal and from two-point space correlations, and integral scales, calculated both from correlations and energy spectra, are reported.Based upon these results, it is concluded that, far enough away from the grid and the test-section wall boundary layers:The turbulence intensities are maintained at uniform values by the nearly constant mean shear.The turbulent shear stress approaches an asymptotic value.Measured two-point space correlation coefficients and one-dimensional energy spectra attain self-preserving forms.When distance downstream of the grid is measured in terms of the number of ‘local’ grid rod spacings, (see discussion of microscales obtained from time derivatives), the Taylor microscale defined by the correlation coefficientRuu(rX, 0, 0) grows linearly with this ‘effective’ distance over most of the region measured.The limited number of integral scale determinations and experimental uncertainty allow only the statements that the magnitude of the longitudinal scale is roughly one-eighth the lateral dimension of the square test-section and tends to increase slightly with ‘effective’ distance from the grid.The lateral integral scales are approximately one-half the longitudinal scales and also increases with distance from the grid.The integral scale which characterizes the size of the eddy primarily responsible for momentum transfer is roughly one-tenth the test-section lateral dimension (measured at one point only).