Statistics Of Velocity Field Research Articles

Radiated Sound from a Circular Cylinder in a Turbulent Shear Layer

The effect of turbulent approach flow on the radiated sound from a circular cylinder was studied experimentally. The approach flow turbulence was provided by a single stream shear layer produced by an open jet anechoic tunnel facility. An instrumented cylinder was used to measure steady and unsteady surface pressure. The sound radiated from the cylinder placed in both an irrotational approach flow and the highly turbulent approach flow of the shear-layer was measured and compared. The cylinders located within the shear layer produced a less tonal sound with a higher broadband amplitude when compared to that of the free-stream approach flow. Secondly, the radiated sound from cylinders of different diameters was investigated to assess the effect of the ratio of cylinder diameter to approach flow length scale. It was found that as this ratio decreased, the broadband sound levels decreased as well. A simple theoretical model was then used to provide a prediction of the radiated sound for the cylinder within the shear layer. The theoretical model used statistics of the velocity field of the approach shear layer and the radiated sound spectrum the cylinder placed in a free stream. It was found that this method provided a similar spectral shape to the measured radiated sound.

Comparison of thermal scaling properties between turbulent pipe and channel flows via DNS

A systematic comparison of thermal scaling properties of pipe and channel flows is presented. DNS data are used to compute thermal statistics for friction Reynolds numbers of 180 and 395 and Prandtl numbers ranging between 0.025 and 7. A distinct four layer regime for the thermal field is clearly identified in both channel and pipe flows. The analysis reveals that the balance breaking and exchange of leading order terms in the mean energy equation that occurs across an intermediate layer is similar to the exchange of terms in the mean momentum equation. The present analysis suggests that, at high Peclet numbers in the four layer regime, the scaling characteristics of the temperature field become increasingly similar to those of the momentum field at high Reynolds number. The intermediate normalisation found by adopting the theory used for the momentum field provides a convincing scaling for the mean temperature and turbulent heat flux profiles for both pipe and channel flows. In contrast to velocity field statistics, the inner normalized mean temperature and heat flux profiles show significant discrepancies between pipe and channel flows.

Self-Similar Prior and Wavelet Bases for Hidden Incompressible Turbulent Motion

This work is concerned with the ill-posed inverse problem of estimating turbulent flows from the observation of an image sequence. From a Bayesian perspective, a divergence-free isotropic fractional Brownian motion (fBm) is chosen as a prior model for instantaneous turbulent velocity fields. This self-similar prior characterizes accurately second-order statistics of velocity fields in incompressible isotropic turbulence. Nevertheless, the associated maximum a posteriori involves a fractional Laplacian operator which is delicate to implement in practice. To deal with this issue, we propose to decompose the divergence-free fBm on well-chosen wavelet bases. As a first alternative, we propose to design wavelets as whitening filters. We show that these filters are fractional Laplacian wavelets composed with the Leray projector. As a second alternative, we use a divergence-free wavelet basis, which takes implicitly into account the incompressibility constraint arising from physics. Although the latter decomposi...

Laser-Induced Spark Ignition of Premixed Confined Swirled Flames

Optimization of the ignition location is of crucial importance for many combustion systems and requires advanced knowledge of the ignition process for both fundamental and applied configurations. In this article, a premixed swirl burner was designed to experimentally study the impact of the spark location on successful ignition and to detail the scenario from ignition to flame stabilization. Two swirl numbers were investigated to evaluate their impact on the ignition process. Particular attention was paid to providing accurate data on cold flow velocity field statistics (obtained by stereoscopic particle image velocimetry) as well as on ignition conditions. Ignition probability maps were obtained for a constant level of deposited energy. Contrary to previous studies, no correlation between local turbulent kinetic energy and ignition probability was observed, and a deeper analysis of the temporal evolution of the flame kernel within the combustion chamber is required. Coupling fast flame visualization with the corresponding pressure signal demonstrated that the efficiency of the ignition location was not only controlled by the local flow properties, but also by the early flame kernel development, linked by its typical trajectories within the combustion chamber.

Towards Comprehensive Coal Combustion Modelling for LES

Large eddy simulations of pulverised coal combustion (PCC-LES) stabilised on a laboratory-scale piloted jet burner are carried out. The joint simulation effort of three research groups at Freiberg University (FG), Imperial College (IC) and Stuttgart University (ST) is presented, and the details of the comprehensive coal combustion models and their numerical implementation in three different computer programs are discussed. The (standard) coal sub-models and parameters used by the different groups are unified wherever possible. Differences amongst the groups are a different code basis and an Eulerian treatment of the coal particles by IC, while FG and ST use the Lagrangian framework for particle transport. The flow modelling is first validated for the corresponding non-reacting case and all LES calculations accurately capture the experimental trends. Velocity field statistics for the PCC case are in good accordance with the experimental evidence, but scalar statistics illustrate the complexity of coal combustion modelling. The results show notable differences amongst the groups that cannot only be attributed to the different treatment of the particle phase, and they highlight the difficulty to assess and interpret the quality of specific modelling approaches, and a need for further work by the research community. The present study is the first to compare three originally independent transient coal simulations and a step towards comprehensive PCC-LES.

Quantifying effects of hyperviscosity on isotropic turbulence

Isotropic hyperviscous turbulence is modelled with a pseudospectral Navier-Stokes model and comparisons are made with regular-viscosity isotropic turbulence. Two proposed means of measuring the (hyperviscous) turbulent Reynolds number are presented and critiqued, leading to a proposal for a hyperviscous turbulent Reynolds number measured as a linear function of L/λ. An analysis of the statistics of velocity and velocity-derivative fields leads to comments on appropriate uses for hyperviscosity in theoretical and practical turbulence modelling and research.

MHD turbulence in the intracluster medium

AbstractIn this work we discuss the turbulent evolution of structures in the intracluster medium based on the two fluid approximations: MHD and collisionless plasma under Chew Goldberger Low (CGL) closure. Turbulence excited by galactic motions and gas inflow in intracluster medium will develop in very different ways considering the two fluid approaches. Statistics of density distributions, and velocity and magnetic fields are provided. Compared to the standard MHD case, the instabilities that arise from CGL-MHD models strongly modify the probability distribution functions of the plasma velocity and density, basically increasing their dispersion. Moreover, the spectra of both density and velocity show increased power at small scales, due to the instabilities growth rate that are larger as smaller scales. Finally, in high beta plasmas, i.e. B2 << P, a fast increase of the magnetic energy density is observed in the CGL-MHD models, faster than the standard MHD turbulent dynamo that operates at timescales τ ~ L/vL. The signatures of the increased power at small scales and the increase of magnetic field intensity from CGL-MHD models could be observed at radio wavelengths. A comparison of the structure function of the synchrotron emission, as well as the statistics of Faraday rotation effects on the synchrotron polarization, for both the MHD and CGL-MHD models is provided.

Confinement Effects in Shallow-Water Jets

This paper documents measurements of the mean velocity field and turbulence statistics of an isothermal, round jet entering a shallow layer of water. The lower boundary of the jet was a solid wall and the upper boundary a free surface. The jet axis was midway between the solid wall and the free surface in all cases. Experiments were performed at a Reynolds number of 22,500 for water layer depths 15, 10, and 5 times the jet exit diameter (9 mm). Particle image velocimetry measurements were made on vertical and horizontal planes—both containing the axis of the jet. The measurements were taken from 10 to 80 jet diameters downstream. Results showed that, for the highly confined cases at downstream locations, the axial velocity was quite uniform over the depth, with a mild peak below the jet axis. In the horizontal plane, the velocity profiles were slightly narrower than the free jet profile, but in the vertical plane, they were wider. The mean vertical velocity profiles showed that entrainment was suppressed in the vertical direction. At the same time, the lateral velocity profiles indicate that fluid flows from the sides toward the jet centerline. For the shallow cases, the mean vertical velocity becomes negative over most of the depth at downstream locations, indicating that this inflow from the sides is directed downward toward the solid wall. The relative turbulence intensity results were suppressed in the axial and vertical directions and mildly enhanced in the lateral direction. As well, the Reynolds shear stress in the vertical plane was significantly reduced by the vertical confinement, while in the horizontal plane it was only slightly affected by the confinement.

Large eddy simulations of wall heat transfer and coherent structures in mixed convection over a wavy wall

In this numerical study the mixed convective flow of water over a heated wavy surface over a range of Reynolds and Richardson numbers, including transitional and turbulent flow regimes (20 ≤ Re ≤ 2000 and 0.5 ≤ Ri ≤ 5000) is investigated. A dynamic Large Eddy Simulation (LES) approach is applied where the thermal buoyancy effects are represented by the Boussinesq approximation. The LES results show good agreement with available measurements including first and second order statistics of velocity and thermal fields. We focus our investigation on the thermal buoyancy effects on the wall heat transfer and the spatial reorganisation of the vortical flow structures. In order to characterise the reorganisation of the mean flow features, the vortical coherent structures are identified and extracted according to the swirling strength criteria. Interesting reorganisation of flow structures takes place between Re = 20 and Re = 200 where the initially spanwise oriented large coherent structures start to be streamwise oriented. With further increase of Re, these large structures disappear from the central part of the simulated domain and reappear in the proximity of the horizontal wavy wall for Re ≥ 1000. The imprints of this flow reorganisation are clearly visible in the distributions of the local heat transfer coefficient (Nusselt number) along the horizontal wavy wall. The integral heat transfer for the wavy wall configuration is significantly enhanced (≈2.5 times) for Re = 1000, 2000 in comparison with the standard flat horizontal wall configuration.

Large-Eddy Simulation of Turbulence-Radiation Interactions in a Turbulent Planar Channel Flow

Large-eddy simulation (LES) has been performed for planar turbulent channel flow between two infinite, parallel, stationary plates. The capabilities and limitations of the LES code in predicting correct turbulent velocity and passive temperature field statistics have been established through comparison to direct numerical simulation data from the literature for nonreacting cases. Mixing and chemical reaction (infinitely fast) between a fuel stream and an oxidizer stream have been simulated to generate large composition and temperature fluctuations in the flow; here the composition and temperature do not affect the hydrodynamics (one-way coupling). The radiative transfer equation is solved using a spherical harmonics (P1) method, and radiation properties correspond to a fictitious gray gas with a composition- and temperature-dependent Planck-mean absorption coefficient that mimics that of typical hydrocarbon-air combustion products. Simulations have been performed for different optical thicknesses. In the absence of chemical reactions, radiation significantly modifies the mean temperature profiles, but temperature fluctuations and turbulence-radiation interactions (TRI) are small, consistent with earlier findings. Chemical reaction enhances the composition and temperature fluctuations and, hence, the importance of TRI. Contributions to emission and absorption TRI have been isolated and quantified as a function of optical thickness.

Stochastic analysis of bounded unsaturated flow in heterogeneous aquifers: Spectral/perturbation approach

This paper describes a stochastic analysis of steady state flow in a bounded, partially saturated heterogeneous porous medium subject to distributed infiltration. The presence of boundary conditions leads to non-uniformity in the mean unsaturated flow, which in turn causes non-stationarity in the statistics of velocity fields. Motivated by this, our aim is to investigate the impact of boundary conditions on the behavior of field-scale unsaturated flow. Within the framework of spectral theory based on Fourier–Stieltjes representations for the perturbed quantities, the general expressions for the pressure head variance, variance of log unsaturated hydraulic conductivity and variance of the specific discharge are presented in the wave number domain. Closed-form expressions are developed for the simplified case of statistical isotropy of the log hydraulic conductivity field with a constant soil pore-size distribution parameter. These expressions allow us to investigate the impact of the boundary conditions, namely the vertical infiltration from the soil surface and a prescribed pressure head at a certain depth below the soil surface. It is found that the boundary conditions are critical in predicting uncertainty in bounded unsaturated flow. Our analytical expression for the pressure head variance in a one-dimensional, heterogeneous flow domain, developed using a nonstationary spectral representation approach [Li S-G, McLaughlin D. A nonstationary spectral method for solving stochastic groundwater problems: unconditional analysis. Water Resour Res 1991;27(7):1589–605; Li S-G, McLaughlin D. Using the nonstationary spectral method to analyze flow through heterogeneous trending media. Water Resour Res 1995; 31(3):541–51], is precisely equivalent to the published result of Lu et al. [Lu Z, Zhang D. Analytical solutions to steady state unsaturated flow in layered, randomly heterogeneous soils via Kirchhoff transformation. Adv Water Resour 2004;27:775–84].

Statistics of Velocity Field in Laboratory-Simulated Downburst

As a laboratory model of downburst, the statistics of a turbulent velocity field of a vertical gravitational flow is investigated. By mechanically breaking a thin film fixed at the bottom of a cylindrical container, a finite mass of a high-density liquid begins to fall into a stationary low-density liquid, forming a vertical thermal. It impinges onto the horizontal ground and then diverges radially outward. By employing particle image velocimetry, the ensemble-averaged maps of velocity vectors, azimuthal vorticity, and turbulent stresses in a meridian plane are obtained. The statistical characteristics in the downdraft stage, impinging stage and diverging stage are examined. The nature and the role of the circulatory flow are demonstrated. The results show reasonable agreement with the actual downbursts observed in the atmosphere. Based on these results, the windshear hazard index for aircraft encountering a downburst is evaluated.

Prediction of velocity statistics in three‐dimensional multi‐Gaussian hydraulic conductivity fields

To study statistics of velocity fields in three‐dimensional heterogeneous multi‐Gaussian saturated hydraulic conductivity fields and the accuracy of their prediction, we performed high‐resolution Monte Carlo (MC) analyses. The MC analyses included variances of the log hydraulic conductivity in the range of 0.5 ≤ σY2 ≤ 3.0 and anisotropy ratios in the range of 0.017 ≤ e ≤ 1. The statistics of the velocity fields from the MC analyses are compared with analytical solutions of the first‐ and second‐order approximations of the stochastic flow equation. This paper shows that the second‐order approximations fit significantly better to the univariate statistics of the Darcy velocity from the MC analyses. For isotropic cases the second‐order approximations correspond fairly well to the univariate statistics of the velocity. For anisotropic cases the accordance is given only for the mean velocity and the variance of the transverse vertical component of the velocity. The MC analyses show that the spatial correlation of the velocity decreases more rapidly with increasing σY2. This was more pronounced for the anisotropic than for the isotropic case. The negative correlations, in absolute terms, of the transverse velocity components simultaneously decrease with increasing σY2. This is in contrast to the first‐order approximation of the spatial correlations of the velocity. It is assumed that the discrepancies between approximate solutions of the stochastic flow equation and the results of the MC analyses are strongly dependent on the nonnormality of the probability density distributions of the velocity.

Signatures of primordial non-Gaussianity in the large-scale structure of the universe

We discuss how primordial (e.g. inflationary) non-Gaussianity in the cosmologicalperturbations is left imprinted in the large-scale structure of the universe. Our findingsshow that the information on the primordial non-Gaussianity set on super-Hubble scalesflows into post-Newtonian terms, leaving an observable imprint in the large-scale structure.Future high-precision measurements of the statistics of the dark matter density andpeculiar velocity fields will allow us to pin down the primordial non-Gaussianity, thusrepresenting a tool complementary to studies of the cosmic microwave backgroundanisotropies.

Simultaneous measurement of turbulent velocity field and surface wave amplitude in the initial stage of an open-channel flow by PIV

Particle image velocimetry (PIV) was employed to measure the two components of the turbulent velocity field in the initial stage of an open-channel flow in a streamwise-wall-normal plane, and the free-surface level was discriminated from the PIV image. The details of this technique was described and demonstrated by showing the instantaneous velocity field together with the free-surface shape, statistics of velocity field, and the wave-turbulence interaction terms. Preliminary experimental results showed that the turbulence intensity of the streamwise velocity fluctuations (u′) decreased, whereas that of the wall-normal velocity (v′) increased near the bottom wall with downstream distance in the initial stage of an open-channel flow; \(\overline {ug}\) (g is the fluctuation of free-surface level) had a negative value, \(\overline {vg}\) had a positive value near the free surface, and the surface-wave-affected depth deepened with downstream distance.

Wave-turbulence interaction of a low-speed plane liquid wall-jet investigated by particle image velocimetry

The surface-wave amplitude (free-surface level) and the turbulent velocity field of the liquid phase of a plane wall-jet flow have been simultaneously measured by means of particle image velocimetry, which allows for the investigation of surface waves and wave-turbulence interaction. The Reynolds number, Weber number, and Ohnesorge number of the tested flow, based on the bulk velocity, height of the closed channel, and physical properties of water, were 3.6×104, 1.2×103, and 9.5×10−4, respectively. Based on the measured datasets of the velocity field and free-surface level, the characteristics of the wave-turbulence interaction as well as the statistics of surface waves and turbulent velocity field were studied. The characteristics of the turbulent velocity field near the wavy free surface obtained in this study were different from those obtained previously for open-channel flows with no shear at the interface or negligible deformation of the free surface. It was found that reverse vortex motion was predominant beneath the wave crest to a depth of about 2mm under the tested flow condition at the near field of the wall jet, which was conjectured to be the main feature before the onset of breakup of the free surface.

Direct numerical simulation and large-eddy simulation of a shear-free mixing layer

High resolution direct numerical simulation (DNS) (512×1024×512) and large-eddy simulation (LES) of a shear-free mixing layer are presented. The geometry of the flow consists of two layers with different turbulence intensities that are in contact and interact through a fairly thin mixing layer. This geometry is used to explore the influence of inhomogeneities in the characteristic length scales, times scales and energy scales on the turbulence properties. Comparison of DNS results is made with the Veeravalli & Warhaft (J. Fluid Mech.207, 191–229, 1989) experiment. The LES is performed on a 32×64×32 grid using an eddy-viscosity model. The use of such a model appears to be justified by the very weak departures from isotropy that are observed in the shear-free mixing layer. The LES predictions are compared with the filtered DNS data and show that the eddy viscosity model performs very well in predicting the energy profile as well as the deviation from Gaussianity in the turbulent velocity field statistics.

Comment on “Velocity field statistics in homogeneous steady turbulence obtained using a high-resolution direct numerical simulation” [Phys. Fluids 14, 1065 (2002)

Comment on “Velocity field statistics in homogeneous steady turbulence obtained using a high-resolution direct numerical simulation” [Phys. Fluids 14, 1065 (2002)

Response to “Comment on ‘Velocity field statistics in homogeneous steady turbulence obtained using a high-resolution direct numerical simulation’ ” [Phys. Fluids 15, 1815 (2003)

Abstract

Small-scale statistics of turbulence at high Reynolds numbers by massive computation

Velocity field statistics in the inertial and dissipation ranges of three-dimensional, homogeneous, steady turbulent flow are studied using high-resolution direct numerical simulation (DNS) with up to N =1024 3 grid points. The Taylor microscale Reynolds number is between 38 and 460. The Kolmogorov spectrum E(k)=K ϵ ̄ 2/3 k −5/3 is observed clearly, and the value of the constant K is K =1.64. The structure functions and their scaling exponents are measured and found to be anomalous. The statistics of the volume-averaged energy dissipation rate per unit mass are also examined.