Isotropic Turbulent Field Research Articles

Uniform-momentum zones in a turbulent boundary layer subjected to freestream turbulence

Abstract

Numerical Study of Hydrogen Auto-Ignition Process in an Isotropic and Anisotropic Turbulent Field

The physical mechanisms underlying the dynamics of the flame kernel in stationary isotropic and anisotropic turbulent field are studied using large eddy simulations (LES) combined with a pdf approach method for the combustion model closure. Special attention is given to the ignition scenario, ignition delay, size and shape of the flame kernel among different turbulent regimes. Different stages of ignition are analysed for various levels of the initial velocity fluctuations and turbulence length scales. Impact of these parameters is found small for the ignition delay time but turns out to be significant during the flame kernel propagation phase and persists up to the stabilisation stage. In general, it is found that in the isotropic conditions, the flame growth and the rise of the maximum temperature in the domain are more dependent on the initial fluctuations level and the length scales. In the anisotropic regimes, these parameters have a substantial influence on the flame only during the initial phase of its development.

An experimental assessment of the enhancement of fuel droplet vaporization in a very high turbulence intensity environment

A zero-mean flow fan-stirred chamber is used to gather data on suspended fuel droplet evaporation at turbulence intensities, q1/2, approaching 4.30 m/s. This research is driven by the oft-cited but unconfirmed belief that the droplet evaporation rate, K, eventually plateaus with increasing turbulence kinetic energy. Further motivation comes from numerous real-world examples, including combustion systems, where droplets are exposed to turbulence intensities far beyond the experimental capabilities reported in the literature to date. Decane, ethanol, and heptane fuels are selected and grouped into two categories based on the similarity of their vapor pressures, Pv, and mass diffusivity coefficients, DAB, in an effort to discern which thermophysical properties are important to vaporization enhancement, or lack thereof, in high turbulence. Individual droplets with constant initial diameters, d0, of 500 µm are placed in the central region of a highly homogeneous and isotropic turbulent flow field using a novel multi-fiber intersection technique. Neither alkane fuel exhibits any sign of reduced effect of turbulence, as K/K0 remains a strongly linear function of turbulence intensity throughout the test conditions. Conversely, the normalized evaporation rate of ethanol begins to plateau at the higher levels of intensity. Although equalizing the vapor pressures of ethanol and heptane was sufficient to match K/K0 values at low intensity, their divergence as q1/2 increases implies that the thermodynamically-predicted vapor quantity at the droplet surface does not enforce an upper limit on turbulence effectiveness at moderately elevated temperatures. This is confirmed by decane, which has the lowest volatility and yet experiences the greatest improvement in evaporation rate at the highest levels of turbulence.

Revisiting turbulence small-scale behavior using velocity gradient triple decomposition

Turbulence small-scale behavior has been commonly investigated in literature by decomposing the velocity-gradient tensor (Aij) into the symmetric strain-rate (Sij) and anti-symmetric rotation-rate (Wij) tensors. To develop further insight, we revisit some of the key studies using a triple decomposition of the velocity-gradient tensor. The additive triple decomposition formally segregates the contributions of normal-strain-rate (Nij), pure-shear (Hij) and rigid-body-rotation-rate (Rij). The decomposition not only highlights the key role of shear, but it also provides a more accurate account of the influence of normal-strain and pure rotation on important small-scale features. First, the local streamline topology and geometry are described in terms of the three constituent tensors in velocity-gradient invariants’ space. Using direct numerical simulation (DNS) data sets of forced isotropic turbulence, the velocity-gradient and pressure field fluctuations are examined at different Reynolds numbers. At all Reynolds numbers, shear contributes the most and rigid-body-rotation the least toward the velocity-gradient magnitude (A2 ≡ AijAij). Especially, shear contribution is dominant in regions of high values of A2 (intermittency). It is shown that the high-degree of enstrophy intermittency reported in literature is due to the shear contribution toward vorticity rather than that of rigid-body-rotation. The study also provides an explanation for the non-intermittent nature of pressure-Laplacian, despite the strong intermittency of enstrophy and dissipation fields. The study further investigates the alignment of the rotation axis with normal strain-rate and pressure Hessian eigenvectors. Overall, it is demonstrated that triple decomposition offers unique and deeper understanding of velocity-gradient behavior in turbulence.

A vortex identification method based on strain and enstrophy production invariants

A new vortex identification method is proposed for extracting vortical structures from homogeneous isotropic turbulence. The method is compared with other identification schemes such as the high rotational method ([Formula: see text]), the vorticity magnitude method ([Formula: see text]), the negative eigenvalue method ([Formula: see text]) and the normalized vorticity method ([Formula: see text]). A new normalization method based on the probability distribution function (PDF) of the identification invariants is also introduced. In addition, a modification for the discriminant criterion known as the [Formula: see text] method is carried out and it is denoted as the modified delta method ([Formula: see text]). The velocity of the isotropic turbulent field is simulated using the lattice Boltzmann method with resolution [Formula: see text]. The new identification method depends on the higher-orders of the invariants of the velocity gradient tensor as well as the strain rate and the enstrophy production terms. The elongated tube-like vortices are extracted successfully using the new method and several features of the vortices are demonstrated and compared with the vortical structures that are extracted using the [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] identification methods. The recommended normalization method enabled the justification of the visualization threshold value to be within the order of unity and the threshold value [Formula: see text] is used in all identification methods. A remarkably similar geometrical worm-like vortices are extracted and a high similarity between the identification methods is observed and statistically studied.

Kappa Distributions and Isotropic Turbulence

In this work, the two-point probability density function (PDF) for the velocity field of isotropic turbulence is modeled using the kappa distribution and the concept of superstatistics. The PDF consists of a symmetric and an anti-symmetric part, whose symmetry properties follow from the reflection symmetry of isotropic turbulence, and the associated non-trivial conditions are established. The symmetric part is modeled by the kappa distribution. The anti-symmetric part, constructed in the context of superstatistics, is a novel function whose simplest form (called “the minimal model”) is solely dictated by the symmetry conditions. We obtain that the ensemble of eddies of size up to a given length r has a temperature parameter given by the second order structure function and a kappa-index related to the second and the third order structure functions. The latter relationship depends on the inverse temperature parameter (gamma) distribution of the superstatistics and it is not specific to the minimal model. Comparison with data from direct numerical simulations (DNS) of turbulence shows that our model is applicable within the dissipation subrange of scales. Also, the derived PDF of the velocity gradient shows excellent agreement with the DNS in six orders of magnitude. Future developments, in the context of superstatistics, are also discussed.

Lagrangian statistics of pressure fluctuation events in homogeneous isotropic turbulence

Homogeneous and isotropic turbulent fields obtained from two direct numerical simulation databases (with Reλ equal to 150 and 418) were seeded with point particles that moved with the local fluid velocity to obtain Lagrangian pressure histories. Motivated by cavitation inception modeling, the statistics of events in which such particles undergo low-pressure fluctuations were computed, parameterized by the amplitude of the fluctuations and by their duration. The main results are the average frequencies of these events and the probabilistic distribution of their duration, which are of predictive value. A connection is also established between these average frequencies and the pressure probability density function, thus justifying experimental methods proposed in the literature. Further analyses of the data show that the occurrence of very-low-pressure events is highly intermittent and is associated with wormlike vortical structures of length comparable to the integral scale of the flow.

Turbulent wind field representation and conditional mean-field simulation.

The covariance structure of a homogeneous isotropic turbulent wind velocity field is derived in terms of modified Bessel functions for an extended form of the Kàrmàn velocity spectrum, including explicit expressions for the transverse coherence functions. A concept of transformed isotropic turbulence is introduced to account for differences in the axial, transverse and vertical fluctuating wind velocities and length scales in natural wind. A special form of the auto-regressive simulation format is developed for convected turbulence with exponentially increasing intervals to the regression planes. In each step, the wind velocity field in a transverse plane is represented by a conditional mean field and a stochastic contribution determined explicitly by the time-space covariances. Simulation results are presented for a square area of dimension less than the integral length scale, representative of buildings and wind turbines, and a horizontal line of length six times the length scale, representative of a long-span bridge. The simulations demonstrate high accuracy of simulated spectral densities, covariance functions and transverse coherence functions. The simulated results do not show visible dependence on the specific points used for the simulated records. The efficiency and the free simulation point configuration suggest high competitiveness compared to fast Fourier transform-based spectral methods.

Reconciling cosmic ray diffusion with Galactic magnetic field models

We calculate the diffusion coefficients of charged cosmic rays (CR) propagating in regular and turbulent magnetic fields. If the magnetic field is dominated by an isotropic turbulent component, we find that CRs reside too long in the Galactic disc. As a result, CRs overproduce secondary nuclei like boron for any reasonable values of the strength and the coherence length of an isotropic turbulent field. We conclude therefore that the propagation of Galactic CRs has to be strongly anisotropic because of a sufficiently strong regular field and/or of an anisotropy in the turbulent field. As a consequence, the number of sources contributing to the local CR flux is reduced by a factor \U0001d4aa(100) compared to the case of isotropic CR diffusion.

Interaction of a planar reacting shock wave with an isotropic turbulent vorticity field.

Linear interaction analysis (LIA) is employed to investigate the interaction of reactive and nonreactive shock waves with isotropic vortical turbulence. The analysis is carried out, through Laplace-transform technique, accounting for long-time effects of vortical disturbances on the burnt-gas flow in the fast-reaction limit, where the reaction-region thickness is significantly small in comparison with the most representative turbulent length scales. Results provided by the opposite slow-reaction limit are also recollected. The reactive case is here restricted to situations where the overdriven detonation front does not exhibit self-induced oscillations nor inherent instabilities. The interaction of the planar detonation with a monochromatic pattern of perturbations is addressed first, and then a Fourier superposition for three-dimensional isotropic turbulent fields is employed to provide integral formulas for the amplification of the kinetic energy, enstrophy, and anisotropy downstream. Transitory evolution is also provided for single-frequency disturbances. In addition, further effects associatedtothe reaction rate, which have not been included in LIA, are studied through direct numerical simulations. The numerical computations, based on WENO-BO4-type scheme, provide spatial profiles of the turbulent structures downstream for four different conditions that include nonreacting shock waves, unstable reacting shock (sufficiently high activation energy), and stable reacting shocks for different detonation thicknesses. Effects of the propagation Mach number, chemical heat release, and burn rate are analyzed.

Experimental investigation of the effect of droplet size on the vaporization process in ambient turbulence

This paper presents the results of an experimental investigation of the effect of droplet size on the fuel vaporization process in a turbulent atmosphere at standard ambient conditions. Single droplets of n-heptane and n-decane are formed and evaporated at the intersection point of two micro-fibers placed in the center of a fan-stirred spherical vessel which is maintained at room temperature and pressure. The droplet initial diameter varies in the range between 145 and 730µm. A controlled isotropic and homogeneous turbulent flow field with nearly zero mean velocity and intensity ranging between 0.25 and 1.5m/s is generated inside the vessel by means of eight axial fans. The results indicate that the droplet normalized squared diameter varies quasi-linearly with time, suggesting the applicability of the d2 law at all examined conditions. More importantly, the results reveal that the droplet initial diameter becomes a significant contributing factor in determining the evaporation rate in a turbulent environment, as the rate of vaporization is found to increase with both turbulent intensity and droplet size. However, droplet size produces no effect on the vaporization rate in quiescent (no flow) surroundings. The results also emphasize that as the ratio of the Kolmogorov length scale over droplet initial diameter approaches unity, the effect of turbulence becomes negligible, illustrating the importance of the small-scale eddies, and their relation to droplet size, in the transport/transfer of mass. The coupled effect of droplet size and turbulence on the vaporization rate is correlated in terms of either a turbulent Reynolds number or a vaporization Damköhler number.

Charged Particle Diffusion in Isotropic Random Magnetic Fields

Abstract The investigation of the diffusive transport of charged particles in a turbulent magnetic field remains a subject of considerable interest. Research has most frequently concentrated on determining the diffusion coefficient in the presence of a mean magnetic field. Here we consider the diffusion of charged particles in fully three-dimensional isotropic turbulent magnetic fields with no mean field, which may be pertinent to many astrophysical situations. We identify different ranges of particle energy depending upon the ratio of Larmor radius to the characteristic outer length scale of turbulence. Two different theoretical models are proposed to calculate the diffusion coefficient, each applicable to a distinct range of particle energies. The theoretical results are compared to those from computer simulations, showing good agreement.

Renormalized cumulants and velocity derivative skewness in Kolmogorov turbulence

We apply a renormalized perturbative scheme to the Navier–Stokes equation for an incompressible isotropic turbulent velocity field. This allows us to obtain the renormalized expressions for second- and third-order cumulants of the velocity derivative directly from the corresponding Feynman diagrams. The resulting expressions are integrated numerically by excluding and including the dissipation range assuming Kolmogorov and Pao’s phenomenological expressions for the energy spectrum. The ensuing values for skewness are found to be S = −0.647 (when the dissipation range is excluded) and (when the dissipation is included). These estimated values are compared with various experimental, numerical and theoretical results.

Towards improved numerical schemes of turbulent lateral dispersion

This paper focuses on an alternative approach of lateral turbulent dispersion, proposed by Benoit Cushman-Roisin in 2008, that is based on a linear increase of the width of dispersing patches in a field of isotropic horizontal turbulence. In the open ocean, this Richardson-like dispersion regime is a well-observed feature on sub-mesoscale length scales from 10 to 100km. In this work, we successfully validate and calibrate the new diffusion scheme using Lagrangian particles and Eulerian tracer in turbulent velocity fields simulated with the shallow-water equations. In discretized form, the new diffusion scheme exclusively relies on specification of a turbulent velocity scale that, unlike the turbulent diffusivity of Fickian approaches, is well defined through statistical properties of the turbulent flow.

Assessment of the rain drop inertia effect for radar-based turbulence intensity retrievals

A new model is proposed on how to account for the inertia of scatterers in radar-based turbulence intensity retrieval techniques. Rain drop inertial parameters are derived from fundamental physical laws, which are gravity, the buoyancy force, and the drag force. The inertial distance is introduced, which is a typical distance at which a particle obtains the same wind velocity as its surroundings throughout its trajectory. For the measurement of turbulence intensity, either the Doppler spectral width or the variance of Doppler mean velocities is used. The relative scales of the inertial distance and the radar resolution volume determine whether the variance of velocities is increased or decreased for the same turbulence intensity. A decrease can be attributed to the effect that inertial particles are less responsive to the variations of wind velocities. An increase can be attributed to inertial particles that have wind velocities corresponding to an average of wind velocities over their backward trajectories, which extend outside the radar resolution volume. Simulations are done for the calculation of measured radar velocity variance, given a 3-D homogeneous isotropic turbulence field, which provides valuable insight in the correct tuning of parameters for the new model.

DNS of a turbulent flow past two fully resolved aligned spherical particles

Direct numerical simulation with fully resolved immersed boundary method is employed to study a turbulent flow past two aligned spherical particles with different distances. A homogeneous isotropic turbulence field is generated as the inflow boundary condition and is kept developing throughout the simulation to avoid periodicity. The particle radius is about 4.7–7.9 times the Kolmogorov length and the turbulent intensities are about 12.9%, 24% and 36%. Validation is made comparing with former researchers and the distance effect is studied by comparing the hydrodynamic forces, particle induced extra dissipation, turbulent kinetic energy, and the synchronous rate of the cross-stream forces. It is shown that, under a mean flow with turbulent intensities, with enlarging the particle distances, the wake shedding behind the upstream particle is longer; the magnitudes of the stream-wise hydrodynamic forces exerted on both particles are higher. Increased turbulent intensity of the inlet condition or increased particle Reynolds number contributes to the particle induced kinetic energy and the increase of Reynolds number diminishes the difference on the particle boundary at its lateral sides. The monotonic decrease of synchronous rate of the cross-stream forces is observed with increasing particle distances when Rep=80, while it fails under higher Reynolds number.

Comparison of surface wind noise predictions from mirror flow and rapid-distortion models of atmospheric turbulence

For atmospheric acoustic measurements at the ground surface, the principal source of the intrinsic wind noise is shearing of the turbulence by the mean flow. The pressure spectra from this turbulence-shear mechanism depend on two-point statistics of the anisotropic, inhomogeneous atmospheric turbulence. The inhomogeneity of the surface-normal velocity component can be realistically modeled by the mirror flow, which is a superposition of two correlated isotropic turbulent fields in transformed coordinates. Another analytical framework is rapid-distortion theory, which approximates the turbulence as the result of linearized distortion of an initially homogeneous field by the mean flow. This study compares turbulence-shear spectra calculated with the mirror flow model and rapid-distortion models for both surface blocking effects and mean shear distortion. For each case, the model parameters are estimated by fits to the single-point velocity spectra recorded in a recent experiment near Laramie, Wyoming. The s...

A time-dependent Eulerian model of droplet diffusion in turbulent flow

Industrial sprays are common in many operations where liquid application to surfaces is required. Maximization of the spray process efficacy depends on accurate simulation of spray characteristics and surrounding flow conditions. Traditionally, droplet modeling has been performed using a Lagrangian approach which requires tracking a sufficient number of droplets to form statistical estimates of droplet deposition. Alternatively for this study, an Eulerian-based flow and droplet transport model using the Direct Quadrature Method of Moments (DQMOM) is applied to spray modeling and is coupled with the Reynolds Averaged Navier Stokes (RANS) equations and Shear Stress Transport (SST) turbulence model. A new turbulent diffusion model is developed for droplet transport which accounts for inertia and time-limit effects and covers a wide range of operational parameters associated with aerial spraying. The model is based on a full parametric study using Lagrangian particle tracking in a uniform, homogeneous and isotropic turbulent flow field and is subsequently implemented within the Eulerian DQMOM framework and compared to: 1) Lagrangian tracking predictions of a log-normal particle size distribution injected into a homogeneous, isotropic turbulent flow field, and 2) full-scale experimental wind tunnel measurements in the anisotropic, non-homogeneous wake of a hollow cone hydraulic nozzle.

Effect of Oscillation Structures on Inertial-Range Intermittence and Topology in Turbulent Field

AbstractUsing the incompressible isotropic turbulent fields obtained from direct numerical simulation and large-eddy simulation, we studied the statistics of oscillation structures based on local zero-crossings and their relation with inertial-range intermittency for transverse velocity and passive scalar. Our results show that for both the velocity and passive scalar, the local oscillation structures are statistically scale-invariant at high Reynolds number, and the inertial-range intermittency of the overall flow region is determined by the most intermittent structures characterized by one local zero-crossing. Local flow patterns conditioned on the oscillation structures are characterized by the joint probability density function of the invariants of the filtered velocity gradient tensor at inertial range. We demonstrate that the most intermittent regions for longitudinal velocity tend to lay at the saddle area, while those for the transverse velocity tend to locate at the vortex-dominated area. The connection between the ramp-cliff structures in passive scalar field and the corresponding saddle regions in the velocity field is also verified by the approach of oscillation structure classification.

Magnetic fields in spiral galaxies

Radio synchrotron emission is a powerful tool to study the strength and structure of magnetic fields in galaxies. Unpolarized synchrotron emission traces isotropic turbulent fields which are strongest in spiral arms and bars (20-30 \mu G) and in central starburst regions (50-100 \mu G). Such fields are dynamically important; they affect gas flows and drive gas inflows in central regions. -- Polarized emission traces ordered fields, which can be regular or anisotropic turbulent, where the latter originates from isotropic turbulent fields by the action of compression or shear. The strongest ordered fields (10-15 \mu G) are generally found in interarm regions. In galaxies with strong density waves, ordered fields are also observed at the inner edges of spiral arms. Ordered fields with spiral patterns exist in grand-design, barred and flocculent galaxies, and in central regions. Ordered fields in interacting galaxies have asymmetric distributions and are a tracer of past interactions between galaxies or with the intergalactic medium. In radio halos around edge-on galaxies, ordered magnetic fields with X-shaped patterns are observed. -- Faraday rotation measures of the diffuse polarized radio emission from galaxy disks reveal large-scale spiral patterns that can be described by the superposition of azimuthal modes; these are signatures of regular fields generated by mean-field dynamos. "Magnetic arms" between gaseous spiral arms may also be products of dynamo action, but need a stable spiral pattern to develop. Helically twisted field loops winding around spiral arms were found in two galaxies so far. Large-scale field reversals, like the one found in the Milky Way, could not yet be detected in external galaxies. -- The origin and evolution of cosmic magnetic fields will be studied with forthcoming radio telescopes like the Square Kilometre Array.