Homogeneous Turbulent Field Research Articles

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.

On the generation of synthetic divergence-free homogeneous anisotropic turbulence

It is well known that the generation of appropriate unsteady boundary conditions represents an important component of successful Large Eddy Simulations in turbulent flows. In particular, when Computational Wind Engineering applications are considered, a recurrent problem consists in imposing turbulent fluctuations characterized by given spectra and length scales at the inlet boundary. In the present contribution, firstly, currently available techniques for the generation of synthetic turbulence are revised with a focus on their mathematical formulation. Then, two new approaches for the generation of homogeneous turbulence are proposed. The first one can be seen as a correction over existing techniques which allows to control the obtained length scales. The second method, conceived to generate anisotropic turbulence characterized by arbitrary harmonic content in both time and space, is designed to be computationally efficient, to guarantee the divergence-free condition and to ensure a good approximation of the resulting turbulence integral scales. Finally, the procedure is validated by synthesizing a homogeneous turbulent field characterized by time and length scales typical of the atmospheric boundary layer showing good results.

Estimation of turbulence characteristics from PIV in a high-pressure fan-stirred constant volume combustion chamber

In this paper, a systematic experimental study was conducted to clarify characteristics of turbulence field generated by two opposite fans in a cubic constant volume combustion bomb (CVCB). The effect of the fan speed (1000–2900rpm) and ambient pressure (0.1–3.0MPa) on root-mean-square fluctuations, probability density functions, integral length scales and energy spectra was investigated. To overcome the limitation of the 2D-PIV, three sheet velocity fields were measured to reconstruct the three-dimensional boundary of the homogeneous region. Experimental results showed that a nearly homogeneous turbulence field in a flat region around the center of the CVCB was generated while a slight departure from isotropy was unavoidable in the current configuration. The turbulence intensity was independent of the ambient pressure, but positively proportional to the fan speed. Absence of both fan speed and ambient pressure’s effect was observed for the integral length scales. Analysis of the turbulent energy spectra implied that the increase of fan speed and ambient pressure resulted in a smaller critical eddy scale where the viscosity dissipation effect started emerging.

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.

Sensitivity of the two-dimensional shearless mixing layer to the initial turbulent kinetic energy and integral length scale.

The shearless mixing layer is generated from the interaction of two homogeneous isotropic turbulence (HIT) fields with different integral scales ℓ_{1} and ℓ_{2} and different turbulent kinetic energies E_{1} and E_{2}. In this study, the sensitivity of temporal evolutions of two-dimensional, incompressible shearless mixing layers to the parametric variations of ℓ_{1}/ℓ_{2} and E_{1}/E_{2} is investigated. The sensitivity methodology is based on the nonintrusive approach; using direct numerical simulation and generalized polynomial chaos expansion. The analysis is carried out at Re_{ℓ_{1}}=90 for the high-energy HIT region and different integral length scale ratios 1/4≤ℓ_{1}/ℓ_{2}≤4 and turbulent kinetic energy ratios 1≤E_{1}/E_{2}≤30. It is found that the most influential parameter on the variability of the mixing layer evolution is the turbulent kinetic energy while variations of the integral length scale show a negligible influence on the flow field variability. A significant level of anisotropy and intermittency is observed in both large and small scales. In particular, it is found that large scales have higher levels of intermittency and sensitivity to the variations of ℓ_{1}/ℓ_{2} and E_{1}/E_{2} compared to the small scales. Reconstructed response surfaces of the flow field intermittency and the turbulent penetration depth show monotonic dependence on ℓ_{1}/ℓ_{2} and E_{1}/E_{2}. The mixing layer growth rate and the mixing efficiency both show sensitive dependence on the initial condition parameters. However, the probability density function of these quantities shows relatively small solution variations in response to the variations of the initial condition parameters.

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.

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.

Comparison of specific energy dissipation rate calculation methodologies utilising 2D PIV velocity measurement

It is critical to have an efficient energy budget in all the industrial process applications involving multiphase flow system where a significant amount of power is invested to achieve a desired outcome such as valuable particle collection and recovery in mineral flotation circuits. In order to achieve this aim there needs to be an ability to properly characterise the energy dissipation in the system; and from this knowledge to develop methodologies so that the supplied energy is distributed suitably among the eddies of different sizes which are responsible for enhancing different transport events such heat/mass transfer, mixing etc. The aim of the study was to obtain the 2D instantaneous velocity field in a homogeneous near isotropic turbulence field using particle image velocimetry (PIV) and then compute the space and time averaged specific energy dissipation rate from velocity field using four different methods, namely: (1) dimensional analysis, (2) velocity gradient, (3) structure function, and (4) energy spectrum. The system was studied in the Taylor Reynolds number range of 24–60, where it was found that the difference between the computed specific energy dissipation rates could be as much as 100 percent. Whilst it was found that there were uncertainties in all four methodologies, it is argued that the energy spectrum method is likely to give the most realistic quantification of the specific energy dissipation rate value since it was shown to satisfy the system energy balance which was not possible to do so for the other three methods. The energy spectrum method also had the added benefit of incorporating integral scale, Taylor microscale and Kolmogorov length scales in the quantification of the specific energy dissipation rate; whereas the other three methods are limited to either integral scale or Taylor microscale only. The limitation of the energy spectrum method, however, is the resolution of the energy spectrum down to the Kolmogorov length scale due to the noise in the measurement; and to resolve this problem a filter was applied to denoise in the dissipation range.

Clustering of vertically constrained passive particles in homogeneous isotropic turbulence.

We analyze the dynamics of small particles vertically confined, by means of a linear restoring force, to move within a horizontal fluid slab in a three-dimensional (3D) homogeneous isotropic turbulent velocity field. The model that we introduce and study is possibly the simplest description for the dynamics of small aquatic organisms that, due to swimming, active regulation of their buoyancy, or any other mechanism, maintain themselves in a shallow horizontal layer below the free surface of oceans or lakes. By varying the strength of the restoring force, we are able to control the thickness of the fluid slab in which the particles can move. This allows us to analyze the statistical features of the system over a wide range of conditions going from a fully 3D incompressible flow (corresponding to the case of no confinement) to the extremely confined case corresponding to a two-dimensional slice. The background 3D turbulent velocity field is evolved by means of fully resolved direct numerical simulations. Whenever some level of vertical confinement is present, the particle trajectories deviate from that of fluid tracers and the particles experience an effectively compressible velocity field. Here, we have quantified the compressibility, the preferential concentration of the particles, and the correlation dimension by changing the strength of the restoring force. The main result is that there exists a particular value of the force constant, corresponding to a mean slab depth approximately equal to a few times the Kolmogorov length scale η, that maximizes the clustering of the particles.

Preferential concentration of heavy particles in turbulence

Particle-laden flows are of relevant interest in many industrial and natural systems. When the carrier flow is turbulent, a striking feature is the phenomenon called preferential concentration: particles denser than the fluid have the tendency to inhomogeneously distribute in space, forming clusters and depleted regions. We present an investigation of clustering of small water droplets in homogeneous and isotropic active-grid-generated turbulence. We investigate the effect of Reynolds number (Rλ) and Stokes number (St) on particles clustering in the range Rλ ∼ 200−400 and St ∼ 2−10. Using Voronoï diagrams, we characterise clustering level and cluster properties (geometry, typical dimension and fractality). The exact same Voronoï analysis is then applied to investigate clustering properties of specific topological points of the velocity field of homogeneous isotropic turbulence obtained from direct numerical simulations at Rλ ∼ 220 and 300. The goal is to compare clustering properties of actual particles with those of such points in order to explore the relevance of possible clustering mechanisms, including centrifugal effects (heavy particles sampling preferentially low-vorticity regions) and sweep-stick mechanisms (heavy particles preferentially sticking to low-acceleration points). Our study points towards a leading role of zero-acceleration points and sweep-stick effects, at least for the experimental conditions considered in this study.

Development of a two zone turbulence model and its application to the cycle-simulation

The development of a two zone k-? turbulence model for the cycle-simulation software is presented. The in-cylinder turbulent flow field of internal combustion engines plays the most important role in the combustion process. Turbulence has a strong influence on the combustion process because the convective deformation of the flame front as well as the additional transfer of the momentum, heat and mass can occur. The development and use of numerical simulation models are prompted by the high experimental costs, lack of measurement equipment and increase in computer power. In the cycle-simulation codes, multi zone models are often used for rapid and robust evaluation of key engine parameters. The extension of the single zone turbulence model to the two zone model is presented and described. Turbulence analysis was focused only on the high pressure cycle according to the assumption of the homogeneous and isotropic turbulent flow field. Specific modifications of differential equation derivatives were made in both cases (single and two zone). Validation was performed on two engine geometries for different engine speeds and loads. Results of the cyclesimulation model for the turbulent kinetic energy and the combustion progress variable are compared with the results of 3D-CFD simulations. Very good agreement between the turbulent kinetic energy during the high pressure cycle and the combustion progress variable was obtained. The two zone k-? turbulence model showed a further progress in terms of prediction of the combustion process by using only the turbulent quantities of the unburned zone.

MULTIRESOLUTION AND NONLINEAR DIFFUSION FILTERING OF HOMOGENEOUS ISOTROPIC TURBULENCE

The multiresolution (Gabor and wavelet transforms) and nonlinear diffusion filtering (NDF) methods are investigated to extract the coherent and incoherent parts of a forced homogeneous isotropic turbulent field. The aim of this paper is to apply two different analyses to decompose the turbulent field into organized coherent and random incoherent parts. The first analysis filtering process (Gabor and wavelet transforms) is based on the frequency domain; however the second NDF filtering analysis is implemented in the spatial domain. The turbulent field is generated using the Lattice Boltzmann method (LBM) with a resolution of 1283, and the Q-identification method is used to extract the elongated vortical structures. The three filtering methods are applied against the scalar Q-field rather than a vector field (velocity or vorticity fields). The Gabor transform and the orthogonal wavelet with approximately symmetric basis are applied to filter out incoherent noise. Filtering in the Gabor domain is done in the highest quarter frequency values, whereas filtering in the wavelet domain is done using sub-band dependent thresholding. The NDF method is based on explicit finite-difference discretization in the spatial domain. Results indicate that the three filtering methods smoothly identify the coherent and incoherent parts. Although the NDF method isolates the incoherent part more smoothly, the cross sections of the vortices in the coherent part are changed. Also, the Gabor filtering method can remove few incoherent points from the flow field, compared with the other two methods. The wavelet method tends to identify the coherent vortices and remove the incoherent noise without any change in the physical structure of the turbulent field.

Numerical modelling of horizontal sediment-laden jets

Sediment-laden turbulent flows are commonly encountered in natural and engineered environments. It is well known that turbulence generates fluctuations to the particle motion, resulting in modulation of the particle settling velocity. A novel stochastic particle tracking model is developed to predict the particle settling out and deposition from a sediment-laden jet. Particle velocity fluctuations in the jet flow are modelled from a Lagrangian velocity autocorrelation function that incorporates the physical mechanism leading to a reduction of settling velocity. The model is first applied to study the settling velocity modulation in a homogeneous turbulence field. Consistent with basic experiments using grid-generated turbulence and computational fluid dynamics (CFD) calculations, the model predicts that the apparent settling velocity can be reduced by as much as 30 % of the stillwater settling velocity. Using analytical solution for the jet mean flow and semi-empirical RMS turbulent velocity fluctuation and dissipation rate profiles derived from CFD predictions, model predictions of the sediment deposition and cross-sectional concentration profiles of horizontal sediment-laden jets are in excellent agreement with data. Unlike CFD calculations of sediment fall out and deposition from a jet flow, the present method does not require any a priori adjustment of particle settling velocity.

Partial differential equations filtering of forced and decaying homogeneous isotropic turbulent fields

The non-linear diffusion and the fourth order partial differential equations (PDEs) are used to decompose a turbulent flow field into coherent and incoherent fields. The methods are applied against the velocity fields for both forced and decaying homogeneous isotropic turbulence. The aim of this paper is to examine the ability of the partial differential equations in extracting coherent vortices from a turbulent flow field in the spatial domain without transforming the turbulent velocity field into frequency domain. The comparison against the standard methods such as the wavelet and Fourier decompositions are also considered. The three dimensional velocity fields with a resolution of 1283 are generated using the Lattice Boltzmann method (LBM) where the Taylor micro-scale Reynolds numbers are 72 and 29 for forced and decaying fields, respectively. Results show that the coherent field and the random incoherent part contribute to all scales in the inertial range. The two filtering methods approximately identify the coherent fields without any loss of the geometrical structure of the vortices. The statistical properties such as flatness, skewness and spectrum of the extracted fields (coherent and incoherent parts) are also investigated for each filtering method.

Clustering of inelastic soft spheres in homogeneous turbulence

In this paper we numerically investigate the influence of dissipation during particle collisions in an homogeneous turbulent velocity field by coupling a discrete element method to a lattice-Boltzmann simulation with spectral forcing. We show that even at moderate particle volume fractions the influence of dissipative collisions is important. We also investigate the transition from a regime where the turbulent velocity field significantly influences the spatial distribution of particles to a regime where the distribution is mainly influenced by particle collisions.

Velocity-gradient dynamics in compressible turbulence: influence of Mach number and dilatation rate

The onset of compressibility effects brings about profound changes in the nature of pressure and its consequent influence on velocity-gradient evolution in turbulent flows. In this work we examine the changing action of pressure on velocity-gradient evolution with varying levels of compressibility in decaying isotropic turbulence. The degree of departure from incompressibility is characterized in one of the following three ways: (1) local turbulent Mach number, which is indicative of local balance between inertial and pressure effects; (2) local relative dilatation, which is a measure of the level of compression/expansion rate of a fluid element and (3) global turbulent Mach number, which is a global measure of compressibility of a homogeneous turbulent flow field. It is found that the pressure-Hessian inhibits velocity-gradient steepening at incompressible and subsonic local Mach numbers. In contrast, at higher local Mach numbers, the pressure-Hessian becomes the dominant driver of gradient steepening. Expanding fluid elements (positive dilatation) are generally associated with gentler overall gradients than contracting (negative dilatation) elements. With increasing local turbulent Mach number, the disparity increases as the gradients of contracting elements become steeper. Overall, this work provides important insight into the velocity-gradient dynamics in compressible flows.

Extraction of coherent vortices from homogeneous turbulence using curvelets and total variation filtering methods

Most filtering methods for turbulent flow depend on wavelet and Fourier decompositions; however, this paper employs curvelets and total variation (TV) filtering methods. These two methods are investigated to extract the coherent and incoherent parts of a forced homogeneous isotropic turbulent field. The Lattice Boltzmann method with resolutions of 1283 and 2563 is used to simulate the turbulent fields, and the Q-identification method is applied to extract the elongated vortical structures. Most of the previous efforts apply filtering techniques to the velocity or vorticity fields; however, this paper applies the two filtering methods to the Q-field. 3D curvelet filtering is applied using a nonlinear thresholding technique. The 3D total variation method is applied using the split Bregman regularization method. The results indicate that the two filtering methods identify the coherent and incoherent parts smoothly. The results of the two filtering methods tend to identify coherent vortices and remove incoherent noise without any change in the physical structure of the turbulent fields. The results are compared with previous efforts using wavelet and Fourier decompositions.

Towards a stochastic multi-point description of turbulence

In previous work it was found that the multi-scale statistics of homogeneous isotropic turbulence can be described by a stochastic "cascade" process of the velocity increment from scale to scale, which is governed by a Fokker-Planck equation. We now show how this description for increments can be extended in order to obtain the complete multi-point statistics in real space of the turbulent velocity field (Stresing & Peinke, 2010). We extend the stochastic cascade description by conditioning on an absolute velocity value itself, and find that the corresponding conditioned process is also governed by a Fokker-Planck equation, which contains as a leading term a simple additional velocity-dependent coefficient, d10, in the drift function. Taking the velocity-dependence of the Fokker-Planck equation into account, the multi-point statistics in the inertial range can be expressed by two-scale statistics of velocity increments, which are equivalent to three-point statistics of the velocity field. Thus, we propose a stochastic three-point closure for the velocity field of homogeneous isotropic turbulence. Investigating the coefficient d10 for different flows, we find clear evidence that the multipoint structure of small scale turbulence is not universal but depends on the type of the flow.

Random vectorial fields representing the local structure of turbulence

We propose a method to build up a random homogeneous, isotropic and incompressible turbulent velocity field that mimics turbulence in the inertial range. The underlying Gaussian field is given by a modified Biot-Savart law. The long range correlated nature of turbulence is then incorporated heuristically using a non linear transformation inspired by the recent fluid deformation imposed by the Euler equations. The resulting velocity field shows a non vanishing mean energy transfer towards the small scales and realistic alignment properties of vorticity with the eigenframe of the deformation rate.

A model for predicting the acceleration variance of arbitrary-density finite-size particles in isotropic turbulence

The paper concerns the effects of particle inertia, density, and size on acceleration statistics. A simple analytical model for estimating the acceleration variance of particles suspended in an isotropic homogeneous turbulent flow field is developed. This model is capable of qualitative describing the particle acceleration variance over the entire range of the particle-to-fluid density ratio. Comparisons of model predictions with numerical simulations and experimental data are presented.