Stochastic models for the droplet motion and evaporation in under-resolved turbulent flows at a large Reynolds number

2021 ◽  
Vol 932 ◽  
Author(s):  
M.A. Gorokhovski ◽  
S.K. Oruganti
Keyword(s):  
Reynolds Number ◽  
Energy Dissipation ◽  
Stochastic Models ◽  
Dissipation Rate ◽  
High Speed ◽  
Evaporation Rate ◽  
Energy Dissipation Rate ◽  
Large Reynolds Number ◽  
Small Scale ◽  
Droplet Motion

In this work we introduce a Lagrangian stochastic model for particle motion and evaporation to be used in large-eddy simulations (LES) of turbulent liquid sprays. Effects of small-scale intermittency, usually under-resolved in LES, are explicitly included via modelling of the energy dissipation rate seen by a droplet along its trajectory. Namely, the dissipation rate is linked to the norm of the droplet sub-filtered acceleration which is included in the droplet motion equation. This norm, along with the direction of the droplet sub-filtered acceleration, is simulated as a stochastic process. With increasing Reynolds number, the distribution of the sub-filtered acceleration develops longer tails, with a slower decay in auto-correlation functions of the norm and direction of this acceleration. The stochastic models are specified for particles larger and smaller the Kolmogorov length scale. The assumption of the droplet evaporation model is similar, i.e. the evaporation rate is strongly enhanced when a droplet is subjected to very localized zones of intense velocity gradients. Thereby, the overall evaporation process is assumed to be a succession of two steady-state sub-processes with equal intensities, i.e. evaporation and vapour mixing. Then the stochastic properties of the overall evaporation rate are also controlled by fluctuations of the energy dissipation rate along the droplet path, and with increasing Reynolds number, the intensity of fluctuations of this rate is also increasing. The assessment of the presented stochastic models in LES of high-speed non-evaporating and evaporating sprays show the accurate prediction of experimental data on relatively coarser grids along with a remarkably weaker sensitivity to the grid spacing. The joint statistics and Voronoi tessellations exhibit strong intermittency of evaporation rate. The intensity of turbulence along the droplet pathway substantially promotes the vaporization rate.

Evaluation of Turbulent Kinetic Energy Dissipation Rate in a Free Jet Flow from PIV Measurements

2012 ◽  
Vol 7 (1) ◽  
pp. 53-69
Author(s):  
Vladimir Dulin ◽  
Yuriy Kozorezov ◽  
Dmitriy Markovich
Keyword(s):  
Energy Dissipation ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Dissipation Rate ◽  
Energy Dissipation Rate ◽  
Turbulent Velocity ◽  
Small Scale ◽  
Velocity Fluctuations ◽  
Piv Measurements ◽  
Free Jet

The present paper reports PIV (Particle Image Velocimetry) measurements of turbulent velocity fluctuations statistics in development region of an axisymmetric free jet (Re = 28 000). To minimize measurement uncertainty, adaptive calibration, image processing and data post-processing algorithms were utilized. On the basis of theoretical analysis and direct measurements, the paper discusses effect of PIV spatial resolution on measured statistical characteristics of turbulent fluctuations. Underestimation of the second-order moments of velocity derivatives and of the turbulent kinetic energy dissipation rate due to a finite size of PIV interrogation area and finite thickness of laser sheet was analyzed from model spectra of turbulent velocity fluctuations. The results are in a good agreement with the measured experimental data. The paper also describes performance of possible ways to account for unresolved small-scale velocity fluctuations in PIV measurements of the dissipation rate. In particular, a turbulent viscosity model can be efficiently used to account for the unresolved pulsations in a free turbulent flow

Shape optimization of a split-and-recombine micromixer by the local energy dissipation rate

2020 ◽  
Vol 234 (3) ◽  
pp. 243-251
Author(s):  
Eshaq Ebnereza ◽  
Kamran Hassani ◽  
Mahmoud Seraj ◽  
Katayoun Gohari Moghaddam
Keyword(s):  
Reynolds Number ◽  
Energy Dissipation ◽  
Objective Function ◽  
Dissipation Rate ◽  
Computation Time ◽  
Energy Dissipation Rate ◽  
Local Energy ◽  
Number Range ◽  
Design Variables ◽  
Wide Range

A passive split-and-recombine micromixer was developed based on the concept of lamellar structure and advection mixing type for a serpentine structure. The flow patterns and mixing performance were analyzed using numerical simulation in Reynolds number range of 10≤ Reynolds ≤170. Two design variables, defining the shape of the split-and-recombine branch, were optimized by the local energy dissipation rate as the objective function. The reduction of computation time and the absence of numerical diffusion were the advantages of using the energy dissipation rate as the objective function. At each Reynolds number, 64 sample data was generated on the design space uniformly. Then a model was used based on the Radial basis neural network for the prediction of the objective function. The optimum values of the design variables within the constraint range were found on the response surface. The optimization study was performed at five Reynolds numbers of 10, 50, 90, 130, 170 and the mixing index was improved 0.156, 0.298, 0.417, 0.506, and 0.57, respectively. The effect of design variables on the objective function and the concentration pattern was presented and analyzed. Finally, the mixing characteristic of the split-and-recombine micromixer was studied in a wide range of Reynolds number and the flow was categorized to stratify and show the vortex regime based on the Reynolds number. The optimized split-and-recombine micromixer could be integrated by any system depending on the desired velocity and Reynolds number.

scholarly journals Spectrally Resolved Energy Dissipation Rate and Momentum Flux of Breaking Waves

2008 ◽  
Vol 38 (6) ◽  
pp. 1296-1312 ◽  
Author(s):  
Johannes R. Gemmrich ◽  
Michael L. Banner ◽  
Chris Garrett
Keyword(s):  
Energy Dissipation ◽  
Wave Field ◽  
Wave Energy ◽  
Dissipation Rate ◽  
Momentum Flux ◽  
Phase Speed ◽  
Breaking Waves ◽  
Energy Dissipation Rate ◽  
Small Scale ◽  
Breaking Wave

Abstract Video observations of the ocean surface taken from aboard the Research Platform FLIP reveal the distribution of the along-crest length and propagation velocity of breaking wave crests that generate visible whitecaps. The key quantity assessed is Λ(c)dc, the average length of breaking crests per unit area propagating with speeds in the range (c, c + dc). Independent of the wave field development, Λ(c) is found to peak at intermediate wave scales and to drop off sharply at larger and smaller scales. In developing seas breakers occur at a wide range of scales corresponding to phase speeds from about 0.1 cp to cp, where cp is the phase speed of the waves at the spectral peak. However, in developed seas, breaking is hardly observed at scales corresponding to phase speeds greater than 0.5 cp. The phase speed of the most frequent breakers shifts from 0.4 cp to 0.2 cp as the wave field develops. The occurrence of breakers at a particular scale as well as the rate of surface turnover are well correlated with the wave saturation. The fourth and fifth moments of Λ(c) are used to estimate breaking-wave-supported momentum fluxes, energy dissipation rate, and the fraction of momentum flux supported by air-entraining breaking waves. No indication of a Kolmogorov-type wave energy cascade was found; that is, there is no evidence that the wave energy dissipation is dominated by small-scale waves. The proportionality factor b linking breaking crest distributions to the energy dissipation rate is found to be (7 ± 3) × 10−5, much smaller than previous estimates.

Estimation of Small-Scale Vertical Diffusivity for CO2 Injected in the Deep Ocean

2009 ◽  
Author(s):  
Shinichiro Hirabayashi ◽  
Toru Sato
Keyword(s):  
Spectral Analysis ◽  
Energy Dissipation ◽  
Dissipation Rate ◽  
Spatial Information ◽  
Measurement Data ◽  
Deep Ocean ◽  
Energy Dissipation Rate ◽  
Small Scale ◽  
Computational Domain ◽  
Vertical Diffusivity

In this study, vertical diffusivity, the scale of which was O (10 m), at a particular site in the deep ocean was estimated by using numerical simulations with forcing low-wavenumber components, which had been reproduced from measurement data. Spatial information of velocity field was reproduced by spectral analysis of 4 sets of time-series measured simultaneously at different places in the real ocean. In order to estimate finer-scale structures, which are necessary to obtain statistical quantities such as energy dissipation rate, large eddy simulations were carried out with forcing low-wavenumber components of velocity reproduced in the spectral analysis. The low-wavenumber components generated by the nonlinear interaction of forced components and resolved components were successfully removed from the computational domain by introducing a partial spectral filter in place of the conventional FFT filter. Vertical diffusivity was estimated by using the energy dissipation rate of the reproduced flow field, which was 3.3×10−5 m2s−1 on the time average.

scholarly journals High-Resolution In Situ Profiling through the Stable Boundary Layer: Examination of the SBL Top in Terms of Minimum Shear, Maximum Stratification, and Turbulence Decrease

2006 ◽  
Vol 63 (4) ◽  
pp. 1291-1307 ◽  
Author(s):  
B. B. Balsley ◽  
R. G. Frehlich ◽  
M. L. Jensen ◽  
Y. Meillier
Keyword(s):  
Boundary Layer ◽  
Energy Dissipation ◽  
High Resolution ◽  
Stable Boundary Layer ◽  
Dissipation Rate ◽  
Energy Dissipation Rate ◽  
Horizontal Wind ◽  
Small Scale ◽  
Stable Boundary ◽  
Stable Conditions

Abstract Some 50 separate high-resolution profiles of small-scale turbulence defined by the energy dissipation rate (ɛ), horizontal wind speed, and temperature from near the surface, through the nighttime stable boundary layer (SBL), and well into the residual layer are used to compare the various definitions of SBL height during nighttime stable conditions. These profiles were obtained during postmidnight periods on three separate nights using the Tethered Lifting System (TLS) during the Cooperative Atmosphere–Surface Exchange Study (CASES-99) campaign in east-central Kansas, October 1999. Although the number of profiles is insufficient to make any definitive conclusions, the results suggest that, under most conditions, the boundary layer top can be reasonably estimated in terms of a very significant decrease in the energy dissipation rate (i.e., the mixing height) with height. In the majority of instances this height lies slightly below the height of a pronounced minimum in wind shear and slightly above a maximum in N 2, where N is the Brunt–Väisälä frequency. When combined with flux measurements and vertical velocity variance data obtained from the nearby 55-m tower, the results provide additional insights into SBL processes, even when the boundary layer, by any definition, extends to heights well above the top of the tower. Both the TLS profiles and tower data are then used for preliminary high-resolution studies into various categories of SBL structure, including the so-called upside-down boundary layer.

The multifractal lagrangian nature of turbulence

1993 ◽  
Vol 342 (1665) ◽  
pp. 379-411 ◽  
Keyword(s):  
Fixed Point ◽  
Energy Dissipation ◽  
Turbulent Flows ◽  
Dissipation Rate ◽  
Small Volume ◽  
Energy Dissipation Rate ◽  
Small Scale ◽  
Fractal Curve ◽  
Multifractal Formalism ◽  
Lagrangian Statistics

The multifractal formalism for the eulerian statistics of small-scale dynamics in turbulent flows is reviewed. Theoretical extensions of these results (the statistics of small volume averages of the energy dissipation rate) are used to predict properties of the probability distribution of the local energy dissipation rate at a fixed point. The improved parametrization of the eulerian statistics allows the lagrangian statistics (those for a fixed fluid particle in contrast to the eulerian statistics at a fixed point) to be determined exactly by using results derived as a consequence of incompressibility. Several properties of particle trajectories in a turbulent flow can be predicted with these new lagrangian statistics. In particular, a trajectory is typically smooth and generally unremarkable in its features. This contrasts the often suggested description: that of a highly convoluted and intricately structured ‘fractal’ curve. Some of the traditional dispersion results, which depend on the lagrangian statistics, are shown to be only weakly influenced by the intermittency inherent in the multifractal character of turbulence.

Transport equation for the mean turbulent energy dissipation rate in low- grid turbulence

2014 ◽  
Vol 747 ◽  
pp. 288-315 ◽  
Author(s):  
L. Djenidi ◽  
R. A. Antonia
Keyword(s):  
Reynolds Number ◽  
Energy Dissipation ◽  
Transport Equation ◽  
Power Law ◽  
Dissipation Rate ◽  
Low Reynolds Number ◽  
Energy Dissipation Rate ◽  
Grid Turbulence ◽  
Power Law Decay ◽  
The Mean

AbstractA direct numerical simulation (DNS) based on the lattice Boltzmann method (LBM) is carried out in low-Reynolds-number grid turbulence to analyse the mean turbulent kinetic energy dissipation rate, $\overline{\epsilon }$, and its transport equation during decay. All the components of $\overline{\epsilon }$ and its transport equation terms are computed, providing for the first time the opportunity to assess the contribution of each term to the decay. The results indicate that although small departures from isotropy are observed in the components of $\overline{\epsilon }$ and its destruction term, there is sufficient compensation among the components for these two quantities to satisfy isotropy to a close approximation. A short distance downstream of the grid, the transport equation of $\overline{\epsilon }$ simplifies to its high-Reynolds-number homogeneous and isotropic form. The decay rate of $\overline{\epsilon }$ is governed by the imbalance between the production due to vortex stretching and the destruction caused by the action of viscosity, the latter becoming larger than the former as the distance from the grid increases. This imbalance, which is not constant during the decay as argued by Batchelor & Townsend (Proc. R. Soc. Lond. A, vol. 190, 1947, pp. 534–550), varies according to a power law of $x$, the distance downstream of the grid. The non-constancy implies a lack of dynamical similarity in the mechanisms controlling the transport of $\overline{\epsilon }$. This is consistent with the fact that the power-law-decay ($\overline{q^2} \sim x^n$) exponent $n$ is not equal to $-$1. It is actually close to $-$1.6, a value in keeping with the relatively low Reynolds number of the simulation. These results highlight the importance of the imbalance in establishing the value of $n$. The $\overline{\epsilon }$-transport equation is also analysed in relation to the power-law decay. The results show that the power-law exponent $n$ is controlled by the imbalance between production and destruction. Further, a relatively straightforward analysis provides information on the behaviour of $n$ during the entire decay process and an interesting theoretical result, which is yet to be confirmed, when $R_{\lambda } \rightarrow 0 $, namely, the destruction coefficient $G$ is constant and its value must lie between $15/7$ and $30/7$. These two limits encompass the predictions for the final period of decay by Batchelor & Townsend (1947) and Saffman (J. Fluid Mech., vol. 27, 1967, pp. 581–593).

Characteristics of the turbulent energy dissipation rate in a cylinder wake

2017 ◽  
Vol 835 ◽  
pp. 271-300 ◽  
Author(s):  
J. G. Chen ◽  
Y. Zhou ◽  
R. A. Antonia ◽  
T. M. Zhou
Keyword(s):  
Reynolds Number ◽  
Energy Dissipation ◽  
Dissipation Rate ◽  
Turbulent Energy ◽  
Energy Dissipation Rate ◽  
Vortex Street ◽  
Local Isotropy ◽  
Similarity Hypothesis ◽  
Turbulent Energy Dissipation Rate ◽  
Karman Vortex

This work aims to improve our understanding of the turbulent energy dissipation rate in the wake of a circular cylinder. Ten of the twelve velocity derivative terms which make up the energy dissipation rate are simultaneously obtained with a probe composed of four X-wires. Measurements are made in the plane of mean shear at$x/d=10$, 20 and 40, where$x$is the streamwise distance from the cylinder axis and$d$is the cylinder diameter, at a Reynolds number of$2.5\times 10^{3}$based on$d$and free-stream velocity. Both statistical and topological features of the velocity derivatives as well as the energy dissipation rate, approximated by a surrogate based on the assumption of homogeneity in the transverse plane, are examined. The spectra of the velocity derivatives indicate that local axisymmetry is first satisfied at higher wavenumbers while the departure at lower wavenumbers is caused by the Kármán vortex street. The spectral method proposed by Djenidi & Antonia (Exp. Fluids, vol. 53, 2012, pp. 1005–1013) based on the universality of the dissipation range of the longitudinal velocity spectrum normalized by the Kolmogorov scales also applies in the present flow despite the strong perturbation from the Kármán vortex street and violation of local isotropy at small$x/d$. The appropriateness of the spectral chart method is consistent with Antoniaet al.’s (Phys. Fluids, vol. 26, 2014, 45105) observation that the two major assumptions in Kolmogorov’s first similarity hypothesis, i.e. very large Taylor microscale Reynolds number and local isotropy, can be significantly relaxed. The data also indicate that vorticity spectra are more sensitive, when testing the first similarity hypothesis, than velocity spectra. They also reveal that the velocity derivatives$\unicode[STIX]{x2202}u/\unicode[STIX]{x2202}y$and$\unicode[STIX]{x2202}v/\unicode[STIX]{x2202}x$play an important role in the interaction between large and small scales in the present flow. The phase-averaged data indicate that the energy dissipation is concentrated mostly within the coherent spanwise vortex rollers, in contrast with the model of Hussain (J. Fluid Mech., vol. 173, 1986, pp. 303–356) and Hussain & Hayakawa (J. Fluid Mech., vol. 180, 1987, p. 193), who conjectured that it resides mainly in regions of strong turbulent mixing.

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