Fluctuating Velocity Field Research Articles

抵抗低減乱流境界層流れにおける大規模乱流構造と壁面せん断応力との関係

We have performed PIV measurements for the drag-reducing turbulent boundary layer flows by injecting surfactant aqueous solution. For the case of the high drag reduction ratio, large-scale turbulence structures were often observed in the fluctuating velocity field. However, the interaction between large-scale turbulence structures and wall-shear stress has not been investigated. In this study, we performed wide-range and high-magnification PIV measurements in order to obtain large-scale turbulence structures and wall-shear stress simultaneously. Decreasing and increasing of wall-shear stress correspond to passing turbulence structures which consist of low and high fluctuation velocities, respectively. This indicates that there would be the correlation between large-scale turbulence structures and instantaneous wall shear stress.

Shell model of turbulent viscosity for the boundary layer

The problem of numerical simulation of developed turbulent flows is usually reduced to the choice of one or another closure of the mean field equations. It is hardly possible to find a universal solution to this issue; nevertheless, the development of an approach based on general principles remains an active research topic. This paper proposes a model of turbulent viscosity described in terms of the characteristics of velocity field fluctuations calculated on the basis of shell models. These models reproduce correctly the scale distribution of the turbulent energy and the spectral energy fluxes for hydrodynamic flows of various physical nature. Shell models are constructed using symmetry properties and conservation laws of the complete system of equations, as well as an assumption on homogeneity and isotropy of turbulence. Phenomenological relations implying specific spectral laws are not involved. In the developed approach, we did an attempt to determine the turbulent viscosity, while maintaining the universality and flexibility of shell models. The resulting mathematical formulation is a set of models for large (mean field equation) and small (cascade model) scales, as well as closing relations. The model implements energy conjugation of variables of different scales, which provides a nonlinear relation of fields at different levels. Taking into account the influence of the mean field on the energy distribution of turbulent fluctuations is a distinctive feature of the proposed approach. Numerical solutions are obtained for the flow in a plane infinite channel at various Reynolds numbers. It is shown that the obtained results are consistent with modern concepts of the logarithmic profile of the velocity field in the boundary layer. The physical meaning of model parameters is substantiated. Asymptotic solutions that qualitatively correspond to the Prandtl model are found.

Spectra of Temperature Fluctuations in the Solar Wind

Turbulent cascade transferring the free energy contained within the large scale fluctuations of the magnetic field, velocity and density into the smaller ones is probably one of the most important mechanisms responsible for heating of the solar corona and solar wind, thus the turbulent behavior of these quantities is intensively studied. The temperature is also highly fluctuating quantity but its variations are studied only rarely. There are probably two reasons, first the temperature is tensor and, second, an experimental determination of temperature variations requires knowledge of the full velocity distribution with an appropriate time resolution but such measurements are scarce. To overcome this problem, the Bright Monitor of the Solar Wind (BMSW) on board Spektr-R used the Maxwellian approximation and provided the thermal velocity with a 32 ms resolution, investigating factors influencing the temperature power spectral density shape. We discuss the question whether the temperature spectra determined from Faraday cups are real or apparent and analyze mutual relations of power spectral densities of parameters like the density, parallel and perpendicular components of the velocity and magnetic field fluctuations. Finally, we compare their spectral slopes with the slopes of the thermal velocity in both inertial and kinetic ranges and their evolution in course of solar wind expansion.

Analysis of unsteady flow in compressor cascade based on modal POD methods

There are complex secondary flow structures in the compressor cascade passage, which seriously suppresses the performance of the compressor. The flow structures are highly unstable, especially for highly loaded compressor cascades. The reduced-order model based on the modal decomposition method can capture the main characteristics of the flow field and offer a reference for the application of unsteady flow control methods. In this study, the POD methods are used to analyze the flow in a high-speed compressor cascade. The methods can extract the mode that reflects the main energy of the flow field. Both the design and off-design conditions are analyzed. The decomposition methods can obtain the global energy, time coefficient and spatial characteristics of the flow field. The result showed that the flow field of the cascade has high steadiness and regularity. The zeroth POD mode under design conditions occupies over 99% of the energy of the flow field. The fluctuation velocity of off-design conditions is larger. The first five POD modes can contain over 90% of the energy of the fluctuation velocity field.

Generalized acoustic Helmholtz equation and its boundary conditions in a quasi 1-D duct with arbitrary mean properties and mean flow

We derive the generalized Helmholtz equation governing the acoustic pressure field in a quasi one-dimensional duct with axially varying cross-section and arbitrary (axially inhomogeneous) mean properties such as the velocity, temperature, density and pressure. To express the Helmholtz equation exclusively in terms of the fluctuating pressure field pˆ, we developed an expression relating density and pressure fluctuations, which is a differential equation for the generalized case of a duct with arbitrary mean properties. The “classical” algebraic expression for the density fluctuation field, ρˆ=pˆ/c̄2, is strictly valid for a constant cross-section duct with uniform mean properties and uniform or zero mean flow (c̄ is the mean sound speed). We show that using the classical ρˆ–pˆ relation in deriving the Helmholtz equation may lead to significant errors in both the phase and amplitude of the acoustic field pˆ. These errors arise because the Helmholtz equation thus obtained fails to account for the boundary condition on density fluctuations at the duct inlet. Furthermore, a linearly-exact derivative boundary condition to the Helmholtz equation of the form dpˆdx=f(pˆ,uˆ,ρˆ;ω) is developed, where uˆ is the velocity fluctuation field and ω is the angular frequency. The pˆ field obtained by solving the generalized Helmholtz equation in conjunction with the derivative boundary condition shows excellent agreement with that obtained through the solution of the linearized Euler equations.

Unsteady flow structures behind a shark denticle replica on the wall: Time-resolved particle image velocimetry measurements

Experiments were performed to determine the unsteady flow structures of a shark denticle replica with three longitudinal ridges of different elevations and sharp trailing edges. Time-resolved particle image velocimetry measurements were conducted to capture the time-varying flow fields behind a shark denticle replica and contoured denticle, using the latter as a benchmark configuration for comparison. The flow fields in the streamwise and spanwise planes were obtained experimentally to determine the highly three-dimensional flow behavior. The flow dynamics of the unsteady superimposed flow structures behind the denticle replica are illustrated in terms of the time-averaged flow fields, statistical flow quantities, dominant vortex structures, and their phase-dependent evolution processes. The findings demonstrate that the denticle replica reduces the size and stability of the recirculation zone, suppressing flow separation. The velocity fluctuations and Reynolds shear stresses of the denticle replica are higher than those of the contoured denticle. Proper orthogonal decomposition analysis on the fluctuating velocity fields reveals alternating clockwise and counterclockwise vortices that convect along the streamwise direction, which correspond to decomposed flow structures, such as counter-rotating vortex pairs in the spanwise plane. These aspects are considered to be signatures of a hairpin-shaped vortex based on the phase-averaging analysis of the unsteady three-dimensional behavior. A hairpin-shaped vortex makes a concerted contribution to fluid mixing between the central wake region and surrounding area. As the fluid flows downstream, fast detachment of the hairpin-shaped vortex is recognized away from the wall to the main stream, which in turn attenuates the flow structure signatures in the spanwise plane. A low-frequency swinging motion of the fluid is also identified in the central wake region, which enhances fluid mixing on the two sides of the wake.

Experimental investigation on drag reduction in a turbulent boundary layer with a submerged synthetic jet

This work investigates the active control of a fully developed turbulent boundary layer by a submerged synthetic jet actuator. The impacts of the control are explored by measuring the streamwise velocities using particle image velocimetry, and reduction of the skin-friction drag is observed in a certain range downstream of the orifice. The coherent structure is defined and extracted using a spatial two-point correlation function, and it is found that the synthetic jet can efficiently reduce the streamwise scale of the coherent structure. Proper orthogonal decomposition analysis reveals that large-scale turbulent kinetic energy is significantly attenuated with the introduction of a synthetic jet. The conditional averaging results show that the induction effect of the prograde vortex on the low-speed fluid in a large-scale fluctuation velocity field is deadened, thereby suppressing the bursting process near the wall.

Applicability of Taylor’s hypothesis during Parker Solar Probe perihelia

We investigate the validity of Taylor’s hypothesis (TH) in the analysis of velocity and magnetic field fluctuations in Alfvénic solar wind streams measured by Parker Solar Probe (PSP) during the first four encounters. The analysis is based on a recent model of the spacetime correlation of magnetohydrodynamic (MHD) turbulence, which has been validated in high-resolution numerical simulations of strong reduced MHD turbulence. We use PSP velocity and magnetic field measurements from 24 h intervals selected from each of the first four encounters. The applicability of TH is investigated by measuring the parameterϵ = δu0/√2V⊥, which quantifies the ratio between the typical speed of large-scale fluctuations,δu0, and the local perpendicular PSP speed in the solar wind frame,V⊥. TH is expected to be applicable forϵ≲ 0.5 when PSP is moving nearly perpendicular to the local magnetic field in the plasma frame, irrespective of the Alfvén Mach numberMA=VSW∕VA, whereVSWandVAare the local solar wind and Alfvén speed, respectively. For the four selected solar wind intervals, we find that between 10 and 60% of the time, the parameterϵis below 0.2 and the sampling angle (between the spacecraft velocity in the plasma frame and the local magnetic field) is greater than 30°. For angles above 30°, the sampling direction is sufficiently oblique to allow one to reconstruct the reduced energy spectrumE(k⊥) of magnetic fluctuations from its measured frequency spectra. The spectral indices determined from power-law fits of the measured frequency spectrum accurately represent the spectral indices associated with the underlying spatial spectrum of turbulent fluctuations in the plasma frame. Aside from a frequency broadening due to large-scale sweeping that requires careful consideration, the spatial spectrum can be recovered to obtain the distribution of fluctuation’s energy across scales in the plasma frame.

Quantifying eddy structures and very-large-scale motions in turbulent round jets

Abstract

Scaling of Droplet Breakup in High-Pressure Homogenizer Orifices. Part I: Comparison of Velocity Profiles in Scaled Coaxial Orifices

Properties of emulsions such as stability, viscosity or color can be influenced by the droplet size distribution. High-pressure homogenization (HPH) is the method of choice for emulsions with a low to medium viscosity with a target mean droplet diameter of less than 1 µm. During HPH, the droplets of the emulsion are exposed to shear and extensional stresses, which cause them to break up. Ongoing work is focused on better understanding the mechanisms of droplet breakup and relevant parameters. Since the gap dimensions of the disruption unit (e.g., flat valve or orifice) are small (usually below 500 µm) and the droplet breakup also takes place on small spatial and time scales, the resolution limit of current measuring systems is reached. In addition, the high velocities impede time resolved measurements. Therefore, a five-fold and fifty-fold magnified optically accessible coaxial orifice were used in this study while maintaining the dimensionless numbers characteristic for the droplet breakup (Reynolds and Weber number, viscosity and density ratio). Three matching material systems are presented. In order to verify their similarity, the local velocity profiles of the emerging free jet were measured using both a microparticle image velocimetry (µ-PIV) and a particle image velocimetry (PIV) system. Furthermore, the influence of the outlet geometry on the velocity profiles is investigated. Similar relationships were found on all investigated scales. The areas with the highest velocity fluctuations were identified where droplets are exposed to the highest turbulent forces. The Reynolds number had no influence on the normalized velocity fluctuation field. The confinement of the jet started to influence the velocity field if the outlet channel diameter is smaller than 10 times the diameter of the orifice. In conclusion, the scaling approach offers advantages to study very fast processes on very small spatial scales in detail. The presented scaling approach also offers chances in the optimization of the geometry of the disruption unit. However, the results also show challenges of each size scale, which can come from the respective production, measurement technology or experimental design. Depending on the problem to be investigated, we recommend conducting experimental studies at different scales.

A study on flow characteristics around a hemispherical dome

Large eddy simulation (LES) is used to investigate the unsteady flow around a hemispherical dome. The Reynolds number based on the diameter of the hemisphere is 2.4 × 104. The mean velocity field and fluctuation velocity field were systematically studied. By means of the distribution of mean pressure coefficient, the vulnerable position on the hemispherical dome was found. By means of mean velocity profile, three regions of different properties were divided, and their effects on other creatures and buildings were considered. The probability density function (PDF), joint probability density function (JPDF) and Lumley triangle are further studied. The different intensity of the intermittency of turbulence, the different proportion of ejection (Q2) and sweeping (Q4) events and the anisotropy of Reynolds stress are explained respectively in these three regions.

Energetic motions in turbulent partially filled pipe flow

Turbulent partially filled pipe flow was investigated using stereoscopic particle imaging velocimetry in the cross-stream plane for a range of flow depths at a nominally constant Reynolds number of 30 000 (based on the bulk velocity and hydraulic diameter). Unlike full pipe flow, which is axisymmetric, the turbulent kinetic energy exhibits significant azimuthal (and radial) variation. Proper orthogonal decomposition (POD) of the fluctuating velocity field indicates that the leading-order POD modes occupy the “corners” where the free surface meets the pipe wall and that these modes, which are closely linked to the instantaneous cellular structure, contribute nearly a quarter of the overall turbulent kinetic energy. Spatial distributions of the large- and very-large-scale motions (LSMs/VLSMs) estimated from pseudo-instantaneous three-dimensional velocity fields reveal a preference for the sides (in close proximity to the free surface) and bottom quadrant of the pipe. That the LSMs and VLSMs are shown to populate a region spanning the width of the free surface, as well as the corners, strongly suggests that there is a dynamical connection between LSMs/VLSMs and the instantaneous cellular structures in turbulent partially filled pipe flow, which can explain the spatial redistribution of the turbulent kinetic energy.

A comparative study of machine learning models for predicting the state of reactive mixing

Mixing phenomena are important mechanisms controlling flow, species transport, and reaction processes in fluids and porous media. Accurate predictions of reactive mixing are critical for many Earth and environmental science problems such as contaminant fate and remediation, macroalgae growth, and plankton biomass growth. To investigate the evolution of mixing dynamics under different scenarios (e.g., anisotropy, fluctuating velocity fields), a finite-element-based numerical model was built to solve the fast, irreversible bimolecular reaction-diffusion equations to simulate a range of reactive-mixing scenarios. A total of 2,315 simulations were performed using different sets of model input parameters comprising various spatial scales of vortex structures in the velocity field, time-scales associated with velocity oscillations, the perturbation parameter for the vortex-based velocity, anisotropic dispersion contrast (i.e., ratio of longitudinal-to-transverse dispersion), and molecular diffusion. The outputs comprised concentration profiles of reactants and products. The inputs and outputs from these simulations were concatenated into feature and label matrices, respectively, to train 20 different machine learning (ML) models intended to emulate system behavior. These 20 ML emulators, based on linear methods, Bayesian methods, ensemble learning methods, and multilayer perceptrons (MLPs), were trained to classify the state of mixing and predict three quantities of interest (QoIs) characterizing species production, decay (i.e., average concentration, square of average concentration), and degree of mixing (i.e., variances of species concentration). Unsurprisingly, linear classifiers and regressors failed to reproduce the QoIs; however, ensemble methods (classifiers and regressors) and the MLP model accurately classified the state of reactive mixing and the QoIs. Among ensemble methods, random forest and decision-tree-based AdaBoost faithfully predicted the QoIs. At run time, trained ML emulators produced results ≈105 times faster than the finite-element simulations. Due to their low computational expense and high accuracy, ensemble and MLP models are excellent emulators for these numerical simulations and great utilities in uncertainty quantification exercises, which can require 1,000s of forward model runs.

On the direction of the velocity and magnetic field fluctuations in undisturbed solar wind

Abstract Measurements of velocity and magnetic field in near-Earth heliosphere is analized in order to investigate systematical deflection from transversality of the velocity and magnetic field fluctuations in undisturbed solar wind. Fluctuations occurred in the meridional plain of heliosphere (RN plain of the RTN reference system) are transversal with respect to mean magnetic field during periods of high solar activity, but they become non-transversal close to solar cycle minima. This phenomenon is investigated focusing on a role of Alfvén waves. It is shown that deflections from transversality is mostly expressed by fluctuations in slow solar wind streams with low contribution of Alfvén waves, whereas strongly Alfvénic turbulence undergo such deflection in a less degree. In addition, we consider orientation of velocity fluctuations in the azimuthal (RT) plain of heliosphere, which also indicates some interesting features.

Вихрова динаміка сполучених течій

Group constructions of bluff bodies are widely used in bridge construction practice. The junction flows of such structures are characterized by considerable complexity, nonstationarity and instability. In the vicinity of bluff bodies, systems of horseshoe vortex structures, shear layers, separated regions, jet flows, wake vortices and vortex Karman’s streets are formed. The study of the features of the generation and evolution of vortex and jet flows, the mechanisms of interaction of these flows with streamlined surfaces requires considerable effort during numerical and physical modeling. The purpose of the work is to determine the features of vortex and jet flow in the region of junction of three-row pile grillage with a rigid flat surface. Experimental studies were carried out in laboratory conditions in a hydrodynamic channel, where the three-row group of cylinders was installed on the hydraulically smooth rigid surface. Visual investigations and measurements of the velocity field were carried out inside and around the three-row grillage. The features of the formation and evolution of vortex and jet flows inside and near the cylindrical group were established. Integral and spectral characteristics of the velocity fluctuation field were obtained.

Dynamic Phase Alignment in Inertial Alfvén Turbulence.

In weakly collisional plasma environments with sufficiently low electron beta, Alfvénic turbulence transforms into inertial Alfvénic turbulence at scales below the electron skin depth, k_{⊥}d_{e}≳1. We argue that, in inertial Alfvénic turbulence, both energy and generalized kinetic helicity exhibit direct cascades. We demonstrate that the two cascades are compatible due to the existence of a strong scale dependence of the phase alignment angle between velocity and magnetic field fluctuations, with the phase alignment angle scaling as cosα_{k}∝k_{⊥}^{-1}. The kinetic and magnetic energy spectra scale as ∝k_{⊥}^{-5/3} and ∝k_{⊥}^{-11/3}, respectively. As a result of the dual direct cascade, the generalized helicity spectrum scales as ∝k_{⊥}^{-5/3}, implying progressive balancing of the turbulence as the cascade proceeds to smaller scales in the k_{⊥}d_{e}≫1 range. Turbulent eddies exhibit a phase-space anisotropy k_{∥}∝k_{⊥}^{5/3}, consistent with critically balanced inertial Alfvén fluctuations. Our results may be applicable to a variety of geophysical, space, and astrophysical environments, including the Earth's magnetosheath and ionosphere, solar corona, and nonrelativistic pair plasmas, as well as to strongly rotating nonionized fluids.

Hairpin vortices in the largest scale of turbulent boundary layers

We have conducted direct numerical simulations of a turbulent boundary layer for the momentum-thickness-based Reynolds number Reθ = 180–4600. To extract the largest-scale vortices, we coarse-grain the fluctuating velocity fields by using a Gaussian filter with the filter width comparable to the boundary layer thickness. Most of the largest-scale vortices identified by isosurfaces of the second invariant of the coarse-grained velocity gradient tensor are similar to coherent vortices observed in low-Reynolds-number regions, that is, hairpin vortices or quasi-streamwise vortices inclined to the wall. We also develop a percolation analysis to investigate the threshold-dependence of the isosurfaces and objectively identify the largest-scale hairpin vortices in terms of the coarse-grained vorticity, which leads to the quantitative evidence that they never disappear even in fully developed turbulent regions. Hence, we conclude that hairpin vortices exist in the largest-scale structures irrespective of the Reynolds number.

Propagation of perturbations and meandering in a free surface shallow water jet

A shallow water free-surface turbulent jet is investigated at Froude numbers variable between about 0.15 and 0.6 and a Reynolds number equal to 5000, with a jet height-to-width aspect ratio variable from 0.5 to 1.1. In these experimental conditions, the flow is unstable and develops local transverse instabilities, which are amplified to a global meandering motion, forcing the jet to oscillate orthogonally to its axis. Instantaneous and averaged velocity fields are obtained by means of high-density, correlation-based time-resolved Particle Tracking Velocimetry. From the average point of view, the present jet configuration resembles a confined jet condition similar to that of wall jets, but with additional relevant three-dimensional effects, retaining self-similar properties, with a net co-flow and some ambient fluid entrainment. For increasing Froude numbers, such configuration is moved downstream and the jet spreading is delayed. The high resolution in space and time of present measurements allows to locally detect and following perturbed patterns and to derive amplitude and frequency of oscillation of the global meandering motion, the former increasing with axial distance and decreasing with Froude number, the latter doing just the opposite. The velocity of propagation of perturbed patterns is also investigated in comparison to the jet mean velocity, the local celerity of propagation of fluctuating velocity fields being derived. Results indicate that axial fluctuations propagate downstream similarly to transverse fluctuations along the orthogonal direction, thus showing a close coupling among the two motions and the onset of a self-sustained mechanism driven by the mean flow, responsible for the generation of the macroscopic meandering motion. This effect is in agreement with numerical predictions and is emphasised as the Froude number increases.

Magnetic–Internal–Kinetic Energy Interactions in High-Speed Turbulent Magnetohydrodynamic Jets

Abstract The goal of this study is to investigate the interactions between turbulent kinetic, internal, and magnetic energies in planar magnetohydrodynamic (MHD) jets at different regimes of Mach and Alfvén Mach numbers. Toward this end, temporal simulations of planar MHD jets are performed, using two types of initial fluctuating velocity field: (i) single velocity perturbation mode with a streamwise wavevector and (ii) random, isotropic perturbations over a band of wavevectors. At low Mach numbers, magnetic tension work results in a reversible exchange of energy between fluctuating velocity and magnetic fields. At high Alfvén Mach numbers, this exchange results in the equipartition of turbulent kinetic and magnetic energies. At higher Mach numbers, dilatational kinetic energy is (reversibly) exchanged with internal and magnetic energies, by means of pressure-dilatation and magnetic-pressure-dilatation, respectively. Therefore, at high Mach and Alfvén Mach numbers, dilatational kinetic energy is seen to be in equipartition with the sum of turbulent internal and magnetic energies. In each of the regimes, the consequent effect of the interactions on the background Kelvin–Helmholtz vortex evolution is also identified.

A POD-Galerkin reduced-order model for two-dimensional Rayleigh-Bénard convection with viscoelastic fluid

Reduced-order model (ROM) based on proper orthogonal decomposition (POD) has been widely used in different fields, such as optimization design and flow control, etc., which needs to get calculation results quickly. Most of present studies about POD-ROM focus on the Newtonian fluid flows, whereas, few studies are related with viscoelastic fluid flows. In this paper, POD-ROM is the first time developed for viscoelastic fluid flow by considering a typical two-dimensional thermal fluid problem: Rayleigh-Bénard convection (RBC). Three different cases are chosen to simulate viscoelastic RBC flow at Rayleigh number of 108, Prandtl number of 7.0 and Weissenberg number of 0.1, 0.2 and 0.3, respectively. It is found that phase portraits under different POD modes share the same trend as that for DNS. By introducing ‘intrinsic stabilization scheme’ closure model, it shows that the relative errors of fluctuation velocity, temperature and conformation tensor fields decrease greatly, i.e., POD-ROM with closure model can perform better than POD-ROM without closure model for long-time prediction.