An Investigation of Droplet Diffusion in Isotropic Turbulence With Digital Holographic PIV

Volume 3 ◽  
2004 ◽  
Author(s):  
Edwin Malkiel ◽  
Jian Sheng ◽  
David Garber ◽  
Joseph Katz
Keyword(s):  
Time Series ◽  
Isotropic Turbulence ◽  
Diffusion Rate ◽  
Density Ratio ◽  
Digital Camera ◽  
Stokes Number ◽  
Sample Volume ◽  
Tracer Particles ◽  
Fluid Velocities ◽  
Digital Holograms

In-line digital holography is utilized to measure the Lagrangian trajectory of droplets in locally isotropic turbulence. The objective of these measurements is to determine the diffusion rate of these droplets as a function of density ratio between the continuous and dispersed phases, Stokes number and turbulence level relative to the quiescent settling/rise velocity of the droplets. The present experiments are conducted using diesel fuel with diameters of 0.5–2 mm, specific gravity of 0.85 and Stokes number in the 0.2 to 5 range. The droplets are injected into a 50 × 50 × 50 mm sample volume located in the center of a 160 1 tank. The turbulence is generated by four spinning grids, located symmetrically in the corners of the tank. Planar PIV has been used to characterize the turbulence prior to the experiments. A time series of in-line digital holograms is recorded at 2000 frames per second using a 1000×1000 pixel digital camera by back illuminating the sample volume with a collimated laser beam. Numerical reconstruction generates a time series of high-resolution images of the droplets and tracer particles throughout the sample volume. Subsequent analysis is used to obtain the velocity along the droplet trajectory. Lagrangian correlations can then be used for calculating the diffusion rate of these droplets. In a smaller sample volume, with a 15×15 mm cross section, and by using localized seeding, we can also simultaneously measure the droplet velocity along with the velocity of the fluid in the vicinity of this droplet. The results provide statistics on the correlations between the droplet and fluid velocities.

Diesel Droplet Diffusion in Isotropic Turbulence With Digital Holographic Cinematography

2005 ◽  
Author(s):  
Balaji Gopalan ◽  
Edwin Malkiel ◽  
Jian Sheng ◽  
Joseph Katz
Keyword(s):  
Time Series ◽  
High Speed ◽  
Isotropic Turbulence ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Time History ◽  
Sample Volume ◽  
Velocity Autocorrelation Function ◽  
Digital Cameras ◽  
Velocity Autocorrelation

High-speed in-line digital holographic cinematography was used to investigate the diffusion of droplets in locally isotropic turbulence. Droplets of diesel fuel (0.3–0.9mm diameter, specific gravity of 0.85) were injected into a 37×37×37mm3 sample volume located in the center of a 160-liter tank. The turbulence was generated by 4 spinning grids, located symmetrically in the corners of the tank, and was characterized prior to the experiments. The sample volume was back illuminated with two perpendicular collimated beams of coherent laser light and time series of in-line holograms were recorded with two high-speed digital cameras at 500 frames/sec. Numerical reconstruction generated a time series of high-resolution images of the droplets throughout the sample volume. We developed an algorithm for automatically detecting the droplet trajectories from each view, for matching the two views to obtain the three-dimensional tracks, and for calculating the time history of velocity. We also measured the mean fluid motion using 2-D PIV. The data enabled us to calculate the Lagrangian velocity autocorrelation function.

scholarly journals Modelling of turbulence modulation in particle- or droplet-laden flows

2012 ◽  
Vol 706 ◽  
pp. 251-273 ◽  
Author(s):  
Daniel W. Meyer
Keyword(s):  
Isotropic Turbulence ◽  
Density Ratio ◽  
Joint Probability ◽  
Stokes Number ◽  
Navier Stokes ◽  
Grid Turbulence ◽  
Heavy Particles ◽  
Turbulence Modulation ◽  
Modelling Framework ◽  
Liquid Flows

AbstractAddition of particles or droplets to turbulent liquid flows or addition of droplets to turbulent gas flows can lead to modulation of turbulence characteristics. Corresponding observations have been reported for very small particle or droplet volume loadings ${\Phi }_{v} $ and therefore may be important when simulating such flows. In this work, a modelling framework that accounts for preferential concentration and reproduces isotropic and anisotropic turbulence attenuation effects is presented. The framework is outlined for both Reynolds-averaged Navier–Stokes (RANS) and joint probability density function (p.d.f.) methods. Validations are performed involving a range of particle and flow-field parameters and are based on the direct numerical simulation (DNS) study of Boivin, Simonin & Squires (J. Fluid Mech., vol. 375, 1998, pp. 235–263) dealing with heavy particles suspended in homogeneous isotropic turbulence (Stokes number $\mathit{St}= O(1{\unicode{x2013}} 10)$, particle/fluid density ratio ${\rho }_{p} / \rho = 2000$, ${\Phi }_{v} = O(1{0}^{- 4} )$) and the experimental investigation of Poelma, Westerweel & Ooms (J. Fluid Mech., vol. 589, 2007, pp. 315–351) involving light particles ($\mathit{St}= O(0. 1)$, ${\rho }_{p} / \rho \gtrsim 1$, ${\Phi }_{v} = O(1{0}^{- 3} )$) settling in grid turbulence. The development in this work is restricted to volume loadings where particle or droplet collisions are negligible.

scholarly journals Optimal Homotopy Asymptotic Method for a thin film flow of a pseudo plastic fluid draining down or lifting up on a cylindrical surface

2013 ◽  
Vol 19 (4) ◽  
pp. 513-527
Author(s):  
Kamran Alam ◽  
M.T. Rahim ◽  
S. Islam ◽  
A.M. Sidiqqui
Keyword(s):  
Thin Film ◽  
Asymptotic Method ◽  
Cylindrical Surface ◽  
Film Flow ◽  
Vertical Cylinder ◽  
Stokes Number ◽  
Velocity Shear ◽  
Thin Film Flow ◽  
Fluid Velocities ◽  
Optimal Homotopy Asymptotic Method

In this study, the pseudo plastic model is used to obtain the solution for the steady thin film flow on the outer surface of long vertical cylinder for lifting and drainage problems. The non-linear governing equations subject to appropriate boundary conditions are solved analytically for velocity profiles by a modified homotopy perturbation method called the Optimal Homotopy Asymptotic method. Expressions for the velocity profile, volume flux, average velocity, shear stress on the cylinder, normal stress differences, force to hold the vertical cylindrical surface in position, have been derived for both the problems. For the non-Newtonian parameter ?=0, we retrieve Newtonian cases for both the problems. We also plotted and discussed the affect of the Stokes number St, the non-Newtonian parameter ? and the thickness ? of the fluid film on the fluid velocities.

Snowflakes in the atmospheric surface layer: observation of particle–turbulence dynamics

2017 ◽  
Vol 814 ◽  
pp. 592-613 ◽  
Author(s):  
Andras Nemes ◽  
Teja Dasari ◽  
Jiarong Hong ◽  
Michele Guala ◽  
Filippo Coletti
Keyword(s):  
Large Scale ◽  
Isotropic Turbulence ◽  
Volume Fraction ◽  
Response Times ◽  
Field Measurements ◽  
Stokes Number ◽  
Inertial Particles ◽  
Natural Setting ◽  
Scale Particle ◽  
Particle Imaging

We report on optical field measurements of snow settling in atmospheric turbulence at $Re_{\unicode[STIX]{x1D706}}=940$. It is found that the snowflakes exhibit hallmark features of inertial particles in turbulence. The snow motion is analysed in both Eulerian and Lagrangian frameworks by large-scale particle imaging, while sonic anemometry is used to characterize the flow field. Additionally, the snowflake size and morphology are assessed by digital in-line holography. The low volume fraction and mass loading imply a one-way interaction with the turbulent air. Acceleration probability density functions show wide exponential tails consistent with laboratory and numerical studies of homogeneous isotropic turbulence. Invoking the assumption that the particle acceleration has a stronger dependence on the Stokes number than on the specific features of the turbulence (e.g. precise Reynolds number and large-scale anisotropy), we make inferences on the snowflakes’ aerodynamic response time. In particular, we observe that their acceleration distribution is consistent with that of particles of Stokes number in the range $St=0.1{-}0.4$ based on the Kolmogorov time scale. The still-air terminal velocities estimated for the resulting range of aerodynamic response times are significantly smaller than the measured snow particle fall speed. This is interpreted as a manifestation of settling enhancement by turbulence, which is observed here for the first time in a natural setting.

scholarly journals Improved Turbulence Profiling with Field-Adapted Acoustic Doppler Velocimeters Using a Bifrequency Doppler Noise Suppression Method

2008 ◽  
Vol 25 (3) ◽  
pp. 452-463 ◽  
Author(s):  
D. Hurther ◽  
U. Lemmin
Keyword(s):  
Noise Reduction ◽  
Carrier Frequency ◽  
Noise Suppression ◽  
Isotropic Turbulence ◽  
Field Studies ◽  
Sample Volume ◽  
Grid Turbulence ◽  
Electronic Circuitry ◽  
Reduction Methods ◽  
Velocity Spectra

Abstract A novel noise reduction method and corresponding technique are presented for improving turbulence measurements with acoustic Doppler velocimeters (ADVs) commonly used in field studies of coastal and nearshore regions, rivers, lakes, and estuaries. This bifrequency method is based on the decorrelation of the random and statistically independent Doppler noise terms contained in the Doppler signals at two frequencies. It is shown through experiments in an oscillating grid turbulence (OGT) tank producing diffusive isotropic turbulence that a shift in carrier frequency of less than 10% is sufficient to increase the resolved frequency range by a decade in the turbulent velocity spectra. Over this spectral range, the slope of the velocity spectra agrees well with the universal inertial range value of −5/3. The limit due to spatial averaging effects over the sample volume can be determined from the abrupt deviation of the spectral slope from the −5/3 value. As a result, the relative error of the turbulent intensity estimate and the turbulent kinetic energy (TKE) dissipation rate, measured by two different methods, does not exceed 10% in the case of isotropic turbulence. Furthermore, the bifrequency method allows accurate estimates of the turbulent microscales as shown by the good agreement of the ratio between the Taylor and Kolmogorov microscales and an Re1/4t power law. Compared to previous Doppler noise reduction methods (Garbini et al.), an increase in time resolution by a factor of 4 is achieved. The proposed method also avoids the loss of TKE energy contained in isotropic flow structures of size equal to and smaller than the sample volume. Different from Doppler noise methods proposed by Hurther and Lemmin and Blanckaert and Lemmin, this method does not require additional hardware components, electronic circuitry, or sensors because the redundant instantaneous velocity field information is captured with the same transducer. The required shift in carrier frequency is small enough for the bifrequency method to be easily implemented in commercial ADVs.

scholarly journals Instrumental setup for high-throughput small- and wide-angle solution scattering at the X33 beamline of EMBL Hamburg

2012 ◽  
Vol 45 (3) ◽  
pp. 489-495 ◽  
Author(s):  
Clement E. Blanchet ◽  
Alexey V. Zozulya ◽  
Alexey G. Kikhney ◽  
Daniel Franke ◽  
Peter V. Konarev ◽  
...  
Keyword(s):  
High Throughput ◽  
Digital Camera ◽  
Sample Volume ◽  
Wide Angle ◽  
Pixel Detector ◽  
Fully Integrated ◽  
X Ray Scattering ◽  
Angle Scattering ◽  
Rapid Switching ◽  
User Friendly

A setup is presented for automated high-throughput measurements of small-angle X-ray scattering (SAXS) from macromolecular solutions on the bending-magnet beamline X33 of EMBL at the storage ring DORIS-III (DESY, Hamburg). A new multi-cell compartment allows for rapid switching between in-vacuum and in-air operation, for digital camera assisted control of cell filling and for colour sample illumination. The beamline is equipped with a Pilatus 1 M-W pixel detector for SAXS and a Pilatus 300 k-W for wide-angle scattering (WAXS), and results from the use of the Pilatus detectors for scattering studies are reported. The setup provides a broad resolution range from 100 to 0.36 nm without the necessity of changing the sample-to-detector distance. A new optimized robotic sample changer is installed, permitting rapid and reliable automated sample loading and cell cleaning with a required sample volume of 40 µl. All the devices are fully integrated into the beamline control software system, ensuring fully automated and user-friendly operation (attended, unattended and remote) with a throughput of up to 15 measurements per hour.

Particle Dispersion in Fine Scales of Homogeneous Isotropic Turbulence

2007 ◽  
Author(s):  
M. Sato ◽  
M. Tanahashi ◽  
T. Miyauchi
Keyword(s):  
Isotropic Turbulence ◽  
Major Axis ◽  
Stokes Number ◽  
High Energy ◽  
Energy Dissipation Rate ◽  
Particle Dispersion ◽  
Fine Scale ◽  
Number Density ◽  
Homogeneous Isotropic Turbulence ◽  
Preferential Concentration

Direct numerical simulations of homogeneous isotropic turbulence laden with particles have been conducted to clarify the relationship between particle dispersion and coherent fine scale eddies in turbulence. Dispersion of 106 particles are analyzed for several particle Stokes numbers. The spatial distributions of particles depend on their Stokes number, and the Stokes number that causes preferential concentration of particles is closely related to the time scale of coherent fine scale eddies in turbulence. On the plane perpendicular to the rotating axes of fine scale eddies, number density of particle with particular Stokes number is low at the center of the fine scale eddy, and high in the regions with high energy dissipation rate around the eddy. The maximum number density can be observed at about 1.5 to 2.0 times the eddy radius on the major axis of the fine scale eddy.

An Investigation of Crossing Trajectory Effects in Turbulent Shear Flow (Keynote)

2005 ◽  
Author(s):  
Lionel Thomas ◽  
Benoiˆt Oesterle´
Keyword(s):  
Shear Flow ◽  
Isotropic Turbulence ◽  
Fluid Velocity ◽  
Stokes Number ◽  
Turbulent Shear ◽  
Inertial Particles ◽  
Turbulent Shear Flow ◽  
Velocity Magnitude ◽  
Dispersed Particles ◽  
Lagrangian Tracking

The dispersion of small inertial particles moving in a homogeneous, hypothetically stationary, shear flow is investigated using both theoretical analysis and numerical simulation, under one-way coupling approximation. In the theoretical approach, the previous studies are extended to the case of homogeneous shear flow with a corresponding anisotropic spectrum. As it is impossible to obtain a closed theoretical solution without some drastic simplifications, the motion of dispersed particles is also investigated using kinematic simulation where random Fourier modes are generated according to a prescribed anisotropic spectrum with a superimposed linear mean fluid velocity profile. The combined effects of particle Stokes number and dimensionless drift velocity (magnitude and direction) are investigated by computing the statistics from Lagrangian tracking of a large number of particles in many flow field realizations, and comparison is made between the observed effects in shear flow and in isotropic turbulence.

Stochastic theory and direct numerical simulations of the relative motion of high-inertia particle pairs in isotropic turbulence

2017 ◽  
Vol 813 ◽  
pp. 205-249 ◽  
Author(s):  
Rohit Dhariwal ◽  
Sarma L. Rani ◽  
Donald L. Koch
Keyword(s):  
Numerical Simulations ◽  
Relative Motion ◽  
Relative Velocity ◽  
Isotropic Turbulence ◽  
Stochastic Theory ◽  
Stokes Number ◽  
Time Correlation ◽  
Direct Numerical Simulations ◽  
Time Integral ◽  
Particle Pairs

The relative velocities and positions of monodisperse high-inertia particle pairs in isotropic turbulence are studied using direct numerical simulations (DNS), as well as Langevin simulations (LS) based on a probability density function (PDF) kinetic model for pair relative motion. In a prior study (Rani et al., J. Fluid Mech., vol. 756, 2014, pp. 870–902), the authors developed a stochastic theory that involved deriving closures in the limit of high Stokes number for the diffusivity tensor in the PDF equation for monodisperse particle pairs. The diffusivity contained the time integral of the Eulerian two-time correlation of fluid relative velocities seen by pairs that are nearly stationary. The two-time correlation was analytically resolved through the approximation that the temporal change in the fluid relative velocities seen by a pair occurs principally due to the advection of smaller eddies past the pair by large-scale eddies. Accordingly, two diffusivity expressions were obtained based on whether the pair centre of mass remained fixed during flow time scales, or moved in response to integral-scale eddies. In the current study, a quantitative analysis of the (Rani et al. 2014) stochastic theory is performed through a comparison of the pair statistics obtained using LS with those from DNS. LS consist of evolving the Langevin equations for pair separation and relative velocity, which is statistically equivalent to solving the classical Fokker–Planck form of the pair PDF equation. Langevin simulations of particle-pair dispersion were performed using three closure forms of the diffusivity – i.e. the one containing the time integral of the Eulerian two-time correlation of the seen fluid relative velocities and the two analytical diffusivity expressions. In the first closure form, the two-time correlation was computed using DNS of forced isotropic turbulence laden with stationary particles. The two analytical closure forms have the advantage that they can be evaluated using a model for the turbulence energy spectrum that closely matched the DNS spectrum. The three diffusivities are analysed to quantify the effects of the approximations made in deriving them. Pair relative-motion statistics obtained from the three sets of Langevin simulations are compared with the results from the DNS of (moving) particle-laden forced isotropic turbulence for $St_{\unicode[STIX]{x1D702}}=10,20,40,80$ and $Re_{\unicode[STIX]{x1D706}}=76,131$. Here, $St_{\unicode[STIX]{x1D702}}$ is the particle Stokes number based on the Kolmogorov time scale and $Re_{\unicode[STIX]{x1D706}}$ is the Taylor micro-scale Reynolds number. Statistics such as the radial distribution function (RDF), the variance and kurtosis of particle-pair relative velocities and the particle collision kernel were computed using both Langevin and DNS runs, and compared. The RDFs from the stochastic runs were in good agreement with those from the DNS. Also computed were the PDFs $\unicode[STIX]{x1D6FA}(U|r)$ and $\unicode[STIX]{x1D6FA}(U_{r}|r)$ of relative velocity $U$ and of the radial component of relative velocity $U_{r}$ respectively, both PDFs conditioned on separation $r$. The first closure form, involving the Eulerian two-time correlation of fluid relative velocities, showed the best agreement with the DNS results for the PDFs.

Modulation of isotropic turbulence by particles of Taylor length-scale size

2010 ◽  
Vol 650 ◽  
pp. 5-55 ◽  
Author(s):  
FRANCESCO LUCCI ◽  
ANTONINO FERRANTE ◽  
SAID ELGHOBASHI
Keyword(s):  
Isotropic Turbulence ◽  
Volume Fraction ◽  
Density Ratio ◽  
Particle Diameter ◽  
Finite Size ◽  
Rate Of Change ◽  
Spherical Particles ◽  
Length Scale ◽  
Frequency Spectra ◽  
Scale Size

This study investigates the two-way coupling effects of finite-size solid spherical particles on decaying isotropic turbulence using direct numerical simulation with an immersed boundary method. We fully resolve all the relevant scales of turbulence around freely moving particles of the Taylor length-scale size, 1.2≤d/λ≤2.6. The particle diameter and Stokes number in terms of Kolmogorov length- and time scales are 16≤d/η≤35 and 38≤τp/τk≤178, respectively, at the time the particles are released in the flow. The particles mass fraction range is 0.026≤φm≤1.0, corresponding to a volume fraction of 0.01≤φv≤0.1 and density ratio of 2.56≤ρp/ρf≤10. The maximum number of dispersed particles is 6400 for φv=0.1. The typical particle Reynolds number is of O(10). The effects of the particles on the temporal development of turbulence kinetic energy E(t), its dissipation rate (t), its two-way coupling rate of change Ψp(t) and frequency spectra E(ω) are discussed.In contrast to particles with d < η, the effect of the particles in this study, with d > η, is that E(t) is always smaller than that of the single-phase flow. In addition, Ψp(t) is always positive for particles with d > η, whereas it can be positive or negative for particles with d < η.

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