Space-time Correlation Research Articles

A 3-D Nonstationary Wideband V2V GBSM With UPAs for Massive MIMO Wireless Communication Systems

This article proposes a novel 3-D nonstationary wideband vehicle-to-vehicle (V2V) geometry-based stochastic model (GBSM) with uniform planar antenna arrays (UPAs) for massive multiple-input–multiple-output (MIMO) wireless communication systems. In the proposed GBSM, a novel method, so-called birth–death (BD) process and seed algorithm-based selective cluster evolution, is developed to capture the space nonstationarity of V2V massive MIMO with UPA channels. The time nonstationarity is further mimicked by employing this novel method over the entire timeline. In addition, the proposed GBSM not only models the reflection of the ground, but also divides clusters into static clusters and dynamic clusters to sufficiently investigate the impact of vehicular traffic density (VTD) on channel statics. The channel parameters are properly calculated by 3-D vectors, resulting in the proposed GBSM with high accuracy and low complexity. Important statistical properties, such as the space-time correlation function (S-T CF), spatial cross-correlation function (CCF), temporal auto-correlation function (ACF), and Doppler power spectrum density (PSD) are derived and thoroughly investigated. Simulation results show that the space-time nonstationarity is successfully mimicked and the VTD has a significant impact on channel statistics. Finally, an excellent agreement is achieved between simulation results and measurements, validating the accuracy of the proposed GBSM.

Aerodynamic noise characteristics of airfoils with morphed trailing edges

Numerical investigation of the aerodynamic and aeroacoustic characteristics of a symmetrical NACA 0012 airfoil developed by National Advisory Committee for Aeronautics (NACA) with a conventional hinged flap and a morphed flap has been carried out. The unsteady flow characteristics over the airfoil surface and at the airfoil wake are captured using high-fidelity Large Eddy Simulations. The tests were carried out for a freestream velocity of U∞=20 m/s, corresponding to a chord-based Reynolds number of Rc=2×105, at angles of attack α=0° and 4°. The results of the airfoil static pressure distribution show that the airfoil with morphed trailing edge produces higher values of lift coefficient than the airfoil with hinged trailing edge due to its higher suction peak resulting in larger pressure difference between the suction and pressure sides. Furthermore, from the wake-flow measurements, boundary-layer analysis, wall-pressure spectra, space–time correlation, it is concluded that the Morphed airfoil produces higher values of surface pressure fluctuations near the trailing edge which extend farther into the wake of the trailing edge compared to the Hinged airfoil. Consequently, the increased pressure fluctuations at the vicinity of the trailing edge results in a higher values of radiated far-field noise for the airfoil with morphed trailing edge flap.

Flow around a Rectangular Cylinder Placed in a Channel with a High Blockage Ratio under a Subcritical Reynolds Number

With the depletion of fossil energy sources, clean energy has become a growing concern for scholars. Vortex-Induced Vibration Aquatic Clean Energy (VIVACE), a device that uses water flow energy to generate electricity, has attracted much attention for its broad applicability and other advantages. Particle Image Velocimetry (PIV) experiments were conducted to improve the efficiency of the VIVACE device in low-velocity areas. The present study investigated the effects of the Blockage ratio (Br), Reynolds number (Re = ρU0D/μ), and Aspect ratio (Ar = B/D, width-to-height) of rectangular cylinders on flow characteristics. The influence of the Ar, Br, and Re on the flow field structure was systematically analyzed in terms of the time-averaged flow field, Reynolds shear stress, space–time correlation, vorticity field, and water pressure characteristics. The vorticity field was deconstructed by Proper Orthogonal Decomposition (POD). The results show that the first two orders of POD modal energy accounted for 75% of the total energy, indicating that the first two modes can be used to identify the large-scale vortex structure. The main water pressure frequency and vortex shedding frequency (f) had a high degree of consistency. Thus, vortex shedding was the main cause of wall water pressure fluctuations. Given the blockage effect, the shear layer’s development spanwise was restricted. Moreover, the blockage effect increased the local flow velocity and accelerated the vortex shedding. The dimensionless time-averaged flow velocity U/U0 increased to 1.5, and the frequency of vortex shedding increased by approximately 25% when the Br increased from 0.067 to 0.25. The frequency increased by 25% when the Ar decreased from 0.5 to 0.2. The experimental results also provide a new idea for optimizing the VIVACE device.

Identification of the cosmogenic ^{11}C background in large volumes of liquid scintillators with Borexino

Cosmogenic radio-nuclei are an important source of background for low-energy neutrino experiments. In Borexino, cosmogenic ^{11}C decays outnumber solar pep and CNO neutrino events by about ten to one. In order to extract the flux of these two neutrino species, a highly efficient identification of this background is mandatory. We present here the details of the most consolidated strategy, used throughout Borexino solar neutrino measurements. It hinges upon finding the space-time correlations between ^{11}C decays, the preceding parent muons and the accompanying neutrons. This article describes the working principles and evaluates the performance of this Three-Fold Coincidence (TFC) technique in its two current implementations: a hard-cut and a likelihood-based approach. Both show stable performances throughout Borexino Phases II (2012–2016) and III (2016–2020) data sets, with a ^{11}C tagging efficiency of sim 90 % and sim 63–66 % of the exposure surviving the tagging. We present also a novel technique that targets specifically ^{11}C produced in high-multiplicity during major spallation events. Such ^{11}C appear as a burst of events, whose space-time correlation can be exploited. Burst identification can be combined with the TFC to obtain about the same tagging efficiency of sim 90% but with a higher fraction of the exposure surviving, in the range of sim 66–68 %.

Formation of a quasi-equilibrium domain structure of crystals of the TGS group near TC

In the temperature range ΔT ≈ 321 K ÷ 322 K, the kinetics of the nonequilibrium domain structure of triglycine sulphate crystals, both pure and with specially introduced defects, has been studied by means of piezoresponse force microscopy technique. The temporal change in the domain structure as a set of regions with a scalar order parameter of P (r, t) = +1 and −1 for oppositely polarized domains was analysed by the behaviour of the space-time correlation function C(r,t) = ·Р(r,t)Р(0,t)Ò. At different distances from the Curie point Tc, the characteristic length Lc, as a scale measure of the average domain size, increases with time according to the power law Lc(t)~(t−t0)a. A decrease of the exponent a with distance from Tc can be a consequence of the transition of the domain structure of TGS crystals from a non-conservative state to aconservative one.

Multi-scale nature of non-blade-order propagating flow disturbances in axial compressors

Non-blade-order flow disturbances, also referred to as pre-stall disturbances or tip flow unsteadiness, are closely related with compressor instabilities. The present work provides a comprehensive investigation on multi-scale nature of non-blade-order disturbances and the underlying flow physics in axial compressors. By applying full-annulus Unsteady Reynolds-Averaged Navier-Stokes (URANS) simulations, along with space–time correlation and spatial Fourier decomposition, to the disturbed pressure, the propagating feature of the non-blade-order disturbances is obtained. Further, a bridge between non-blade-order disturbances and the evolution of unsteady vortex has been set up. The results show that non-blade-order disturbances, featured as short-length-scale (35 modes across annulus), first appear as the occurrence of tip leakage vortex fluctuation, while the compressor still operates far from stall. Leading-edge radial vortex appears at near stall condition, and its movement induces a circumferential propagating disturbance overlaying on the one induced by oscillating tip leakage vortex. The interaction of the short-scale disturbances with a low-amplitude long-scale (of circumference) disturbance is observed, which results in disturbances with multiple scales of consecutive spatial modes, along with multiple frequency peaks in spectra. The compressor falls into stall as the circumferential nonuniform scattering of the leading-edge vortexes occurs. The densely- and sparsely-scattered leading-edge radial vortexes induce a high-amplitude long-scale (of circumference) disturbance, i.e. stall disturbance.

Characteristics of reattached boundary layer in shock wave and turbulent boundary layer interaction

The reattached boundary layer in the interaction of an oblique shock wave with a flat-plate turbulent boundary layer at Mach number 2.25 is studied by means of Direct Numerical Simulation (DNS). The numerical results are carefully compared with available experimental and DNS data in terms of turbulence statistics, wall pressure and skin friction. The coherent vortex structures are significantly enhanced due to the shock interaction, and the reattached boundary layer is characterized by large-scale structures in the outer region. The space-time correlation of fluctuating wall shear stress and streamwise velocity fluctuation reveals that the structural inclination angle exhibits a gradual decrease during the recovery process. The scale interactions are analyzed by using a two-point amplitude modulation correlation. A possible mechanism is proposed to account for the strong amplitude modulation in the downstream region. Moreover, the mean skin-friction is decomposed to understand the physically informed contributions. Unlike the upstream Turbulent Boundary Layer (TBL), the contribution associated with the Turbulence Kinetic Energy (TKE) production is greatly amplified, while the spatial growth contribution induced by the pressure gradient largely inhibits skin-friction generation. Based on bidimensional empirical mode decomposition, the turbulence kinetic energy production contribution is further split into different terms with specific spanwise length scales.

Investigation of vortical and near-acoustic fields in three-stream jets.

The connections between the vortical and near-acoustic fields of three-stream, high-speed jets are investigated for the ultimate purpose of developing linear surface-based models for the noise source. Those models would be informed by low-cost, Reynolds-averaged Navier-Stokes (RANS) computations of the flow field. The study uses two triple-stream jets, one is coaxial and the other has eccentric tertiary flow that yields noise suppression in preferred directions. Large eddy simulations (LES) validate the RANS-based models for the convective velocity Uc of the noise-generating turbulent eddies. In addition, the LES results help define a "radiator surface" on which the jet noise source model would be prescribed. The radiator surface is located near the boundary between the rotational and irrotational fields and defined as the surface on which the Uc distribution, obtained from the space-time correlations of the pressure, matches that inferred from the RANS model. The edge of the mean vorticity field is nearly coincident with the radiator surface, which suggests a RANS-based criterion for locating this surface. The two-dimensional space-time correlations show how the asymmetry of the tertiary stream and the resulting thicker low-speed flow weakens the generation of acoustic disturbances from the vortical field.

Imprint of Vortical Structures on the Near-Field Pressure of a Turbulent Jet

The distributions of turbulent scales in a Mach 0.9 isothermal round jet are investigated for the purpose of developing linear surface-based models for the noise source that can be informed by a Reynolds-averaged Navier–Stokes (RANS) solution of the flowfield. The jet is calculated by large-eddy simulation (LES), which enables the computation of two-point space–time correlations throughout the jet and its near-acoustic field. Time, length, and convective-velocity scales are examined on the surface of peak Reynolds stress (SPS), representing the location of the most energetic eddies, and on a “radiator surface” at the boundary between the rotational and irrotational fields. The nature of the space–time correlations is different for axial velocity fluctuations and pressure fluctuations. Velocity-based correlations appear to capture localized turbulent events, whereas pressure-based correlations appear dominated by the interaction of large eddies with the surrounding potential flow. The correlation length scales are larger on the radiator surface than on the SPS, thus indicating that small-scale eddies do not make a significant imprint on the radiator surface. The scales associated with an emulated RANS solution of the flow are compared to the LES-based scales. Simple relationships are inferred that may aid the development of rapid predictive models.

Stochastic geometry and dynamics of infinitely many particle systems—random matrices and interacting Brownian motions in infinite dimensions

We explain the general theories involved in solving an infinite-dimensional stochastic differential equation (ISDE) for interacting Brownian motions in infinite dimensions related to random matrices. Typical examples are the stochastic dynamics of infinite particle systems with logarithmic interaction potentials such as the sine, Airy, Bessel, and also for the Ginibre interacting Brownian motions. The first three are infinite-dimensional stochastic dynamics in one-dimensional space related to random matrices called Gaussian ensembles. They are the stationary distributions of interacting Brownian motions and given by the limit point processes of the distributions of eigenvalues of these random matrices. The sine, Airy, and Bessel point processes and interacting Brownian motions are thought to be geometrically and dynamically universal as the limits of bulk, soft edge, and hard edge scaling. The Ginibre point process is a rotation- and translation-invariant point process on R 2 \mathbb {R}^2 , and an equilibrium state of the Ginibre interacting Brownian motions. It is the bulk limit of the distributions of eigenvalues of non-Hermitian Gaussian random matrices. When the interacting Brownian motions constitute a one-dimensional system interacting with each other through the logarithmic potential with inverse temperature β = 2 \beta = 2 , an algebraic construction is known in which the stochastic dynamics are defined by the space-time correlation function. The approach based on the stochastic analysis (called the analytic approach) can be applied to an extremely wide class. If we apply the analytic approach to this system, we see that these two constructions give the same stochastic dynamics. From the algebraic construction, despite being an infinite interacting particle system, it is possible to represent and calculate various quantities such as moments by the correlation functions. We can thus obtain quantitative information. From the analytic construction, it is possible to represent the dynamics as a solution of an ISDE. We can obtain qualitative information such as semi-martingale properties, continuity, and non-collision properties of each particle, and the strong Markov property of the infinite particle system as a whole. Ginibre interacting Brownian motions constitute a two-dimensional infinite particle system related to non-Hermitian Gaussian random matrices. It has a logarithmic interaction potential with β = 2 \beta = 2 , but no algebraic configurations are known.The present result is the only construction.

Discrimination information for intensity distributions of a collimated wave beam

The results of a nonlinear thermodynamic analysis of the process of refractive distortions of a collimated wave beam profile at the optical path output are presented. The formalism of q-deformed entropy functionals is used, which makes it possible to describe both extensive additive systems and nonextensive systems for which the entropy superposition principle or internal energy is not implemented. Non-extensive thermodynamic systems should be considered as a class of nonlinear systems for which deviation from the Boltzmann–Shannon–Gibbs axiomatics is associated with the structure of the phase space, the presence of predetermined space-time correlations that determine the nonlocality of interactions admissible in the system. A method of discrimination information maps for various types of q-deformed entropies, a method of marginal projections of the first and second spatial moments for the video sequences series of the wave beam intensity profile are proposed. The values of the spatio-temporal correlations of the process, the stationarity time of the dispersion properties of the mappings are obtained. Similar properties are inherent in complex nonextensive systems and lead to nonlinear responses when creating multicomponent systems.

In-situ visualisation of the micro-structure of a Carbopol gel during a confined microscopic flow

An in-situ visualisation of the microstructure of a Carbopol gel flowing in a micro-channel is presented. By means of a novel chemical protocol able to stain the solid material units of the gel with a fluorescent molecule we are able to accurately identify the solid/fluid material units advected by the confined microscopic flow. Based on this novel visualisation technique a full statistical description of the distributions of solid–fluid material units in the flow in terms of space and time averages, probability density functions and space–time correlations is reported for the first time. • A novel fluorescent labeling protocol of the Carbopol microstructure is developed. • A full description of the statistics of solid/fluid material elements is provided. • The size distribution of solid material elements follows the Weibull distribution. • The confinement leads to the emergence of secondary flows and time dependent flow fields.

Sound and vibration measurements for pipe wall condition assessment of concrete pressure pipes

The condition of buried watermains and similar pipelines can be assessed by non-intrusive means. To this end certain features of sound propagation in the water column within the main are measured. Most applications use the Korteweg-Lamb correction to estimate the average wall thickness for homogeneous pipes. For complex composite structures such as concrete pressure pipes, condition assessment is presently based on a great deal of empiricism. This can now be replaced with proper physical models based on measurements conducted on a 25 m long test pipe. Using controlled sound sources, hydrophones and surface mounted accelerometers, features of the acoustic waves inside the water column and the associated wall vibrations were deduced from two-point space-time correlations. The data permits the determination of the complex-valued wavenumbers as well as the dynamic coupling of the liquid column and the pipe wall from which certain properties of the pipe wall can be characterized to ascertain if the pipe is fit for purpose.

Simulation of near-diffraction- and near-dispersion-free OAM pulses with controllable group velocity by combining multiple frequencies, each carrying a Bessel mode

Optical pulses carrying orbital angular momentum (OAM) have recently gained interest. In general, it might be beneficial to simultaneously achieve: (i) minimum diffraction, (ii) minimum dispersion, and (iii) controllable group velocity. Here, we explore via simulation the generation of near-diffraction-free and near-dispersion-free OAM pulses with arbitrary group velocities by coherently combining multiple frequencies. Each frequency carries a specific Bessel mode with the same topological charge (ℓ) but different kr (spatial frequency) values based on space-time correlations. Moreover, we also find that (i) both positive and negative group velocities could be achieved and continuously controlled from the subluminal to superluminal values and (ii) when the ℓ is varied from 0 to 10, the simulated value of the group velocity remains the same. However, as the ℓ value increases, the pulse duration becomes longer for a given number of frequency lines.

Two-point polarization correlations of random paraxial and nonparaxial electromagnetic fields

We investigate the two-point polarization correlation properties of random, statistically stationary, two-dimensional (2D) and three-dimensional (3D) electromagnetic fields. To this end two specific mutual polarization correlation functions are introduced, one based on a geometric approach using the Poincar\'e vectors and the other on the energy distribution employing the Jones vectors. Both approaches provide equivalent information about the space-time polarization correlations and enable one to associate with the field a polarization length over which the equal-time polarization states remain essentially unchanged. For fields obeying Gaussian statistics, the polarization correlation functions take on simple forms in terms of measurable quantities representing electromagnetic coherence. The formalism is demonstrated with two examples: blackbody radiation inside a cavity and in the far zone of a cavity wall aperture.

Characteristics of wall-shear stress fluctuations in shock wave and turbulent boundary layer interaction

The wall-shear stress (WSS) fluctuations in the interaction of an oblique shock wave with a flat-plate turbulent boundary layer are investigated by means of direct numerical simulation (DNS) at Mach 2.25. The numerical results agree very well with previous experiments and DNS data in terms of turbulence statistics, wall pressure, and skin friction. The fluctuating WSS characteristics, including probability density function (PDF), frequency spectrum, space–time correlation, and convection velocity, are analysed systematically. It is found that the positively skewed PDF shape of the streamwise WSS fluctuations is significantly changed due to the presence of a separation bubble, while the PDF shape of the spanwise component is slightly affected, exhibiting a symmetric behaviour across the interaction. The weighted power-spectrum density map indicates that the low-frequency unsteadiness associated with the separated shock - exhibits little influence on the spectrum for either component, and no enhancement of the low-frequency energy is observed. A significant reduction in the spatial extent of the two-point correlation is observed, causing spanwise elongated coherence for the streamwise WSS fluctuations in the separation region. Moreover, the elliptic behaviour of the space–time correlations is essentially preserved throughout the interaction, and this is accompanied by a sudden reduction of the convection velocity in the separation bubble.

Numerical study on wetted and cavitating tip-vortical flows around an elliptical hydrofoil: Interplay of cavitation, vortices, and turbulence

Cavitation in a tip vortex remains a challenging issue in a variety of engineering problems. In this study, we perform large eddy simulation of wetted and cavitating flows around a stationary elliptical hydrofoil with the cross section of NACA (National Advisory Committee for Aeronautics) 16–020. The Schnerr–Sauer cavitation model is adopted for phase transport. The numerical results are verified by comparing with the experimental measurements. Instantaneous vorticity and pressure in both wetted and cavitating flows are studied. It is found that the cavitation promotes the production of vorticity and increases the boundary layer thickness. To further analyze the influence of cavitation on the tip vortices, each term in the transport equation of enstrophy is examined. In the cavitating flow, the dilatation and baroclinic torque terms are promoted to be equally dominant as the vortex stretching term, while in the wetted flow the stretching term is the only dominant one. The axial and azimuthal velocities in the cavity are smaller than those in wetted tip-vortical flow, while the pressure inside is nearly equal to the constant saturation pressure. A tip vortex model with four regions in cavitating flow is built and compared to the wetted flow model. A weakly meandering motion of the tip vortex is observed in the near field. To study the surface wave behaviors of the tip vortex, the space-time velocity correlation analysis is carried out. The surface wave moves at a speed smaller than the incoming flow. A dominating helical mode is found and is consistent with the analytical and experimental results.

The driven cavity turbulent flow with porous walls: Energy transfer, dissipation, and time-space correlations

The driven cavity turbulent flow with porous walls: Energy transfer, dissipation, and time-space correlations

Distinctions between single and twin impinging jet dynamics.

Impinging jets are characterized by an acoustic feedback resonance capable of generating intense tones. This investigation examines changes in single impinging jet (SIJ) dynamics when another jet is added alongside to form a dual impinging jet (DIJ) arrangement of interest in vertical takeoff and landing applications. The emphasis is on the hydrodynamic and acoustic coupling in the region between the jets, which affects aircraft surface loading. Well-resolved large eddy simulations of SIJ and DIJ are employed with under-expanded Mach 1.27 jets; the nozzle exits are placed 4 diameters from the ground plane and, for the DIJ, separated 4.3 diameters from each other to mimic ongoing experiments. Three different SIJ feedback harmonics of the fundamental frequency are identified using two-point space-time correlations. Using spectral proper orthogonal decomposition, these tones are classified as either asymmetric or axisymmetric modes in the SIJ. Each individual jet in the DIJ configuration also exhibits these nominal tones. However, differences are observed on the inboard sides between the jets, where coupling effects engender an azimuthally localized Kelvin-Helmholtz instability and impingement mechanism. The global coupling between the two jets manifests as counter-rotating helical modes, which reinforce the lowest of the three identified SIJ impinging tones.

Correlations of power output fluctuations in an offshore wind farm using high-resolution SCADA data

Abstract. Space–time correlations of power output fluctuations of wind turbine pairs provide information on the flow conditions within a wind farm and the interactions of wind turbines. Such information can play an essential role in controlling wind turbines and short-term load or power forecasting. However, the challenges of analysing correlations of power output fluctuations in a wind farm are the highly varying flow conditions. Here, we present an approach to investigate space–time correlations of power output fluctuations of streamwise-aligned wind turbine pairs based on high-resolution supervisory control and data acquisition (SCADA) data. The proposed approach overcomes the challenge of spatially variable and temporally variable flow conditions within the wind farm. We analyse the influences of the different statistics of the power output of wind turbines on the correlations of power output fluctuations based on 8 months of measurements from an offshore wind farm with 80 wind turbines. First, we assess the effect of the wind direction on the correlations of power output fluctuations of wind turbine pairs. We show that the correlations are highest for the streamwise-aligned wind turbine pairs and decrease when the mean wind direction changes its angle to be more perpendicular to the pair. Further, we show that the correlations for streamwise-aligned wind turbine pairs depend on the location of the wind turbines within the wind farm and on their inflow conditions (free stream or wake). Our primary result is that the standard deviations of the power output fluctuations and the normalised power difference of the wind turbines in a pair can characterise the correlations of power output fluctuations of streamwise-aligned wind turbine pairs. Further, we show that clustering can be used to identify different correlation curves. For this, we employ the data-driven k-means clustering algorithm to cluster the standard deviations of the power output fluctuations of the wind turbines and the normalised power difference of the wind turbines in a pair. Thereby, wind turbine pairs with similar power output fluctuation correlations are clustered independently from their location. With this, we account for the highly variable flow conditions inside a wind farm, which unpredictably influence the correlations.