Turbulent Kinetic Dissipation Research Articles

A length scale for non-local multi-scale gradient interactions in isotropic turbulence

Three-dimensional turbulent flows enhance velocity gradients via strong nonlinear interactions of the rate-of-strain tensor with the vorticity vector, and with itself. For statistically homogeneous flows, their total contributions to gradient production are related to each other by conservation of mass, and so are the total enstrophy and total dissipation. However, locally, they do not obey this relation and have different (often extreme) values, and for this reason both production mechanisms have been subject to numerous studies, often decomposed into multi-scale interactions. In general lines, their dynamics and contributions to the cascade processes and turbulent kinetic dissipation are different, which poses a difficulty for turbulence modelling. In this paper, we explore the consequence of the ‘Betchov’ relations locally, and show that they implicitly define a length scale. This length scale is found to be approximately three times the size of the turbulent structures and their interactions. It is also found that, while the non-locality of the dissipation and enstrophy at a given scale comes mostly from larger scales that do not cancel, the non-local production of strain and vorticity comes from multi-scale interactions. An important consequence of this work is that isotropic cascade models need not distinguish between vortex stretching and strain self-amplification, but can instead consider both entities as part of a more complex transfer mechanism, provided that their detailed point value is not required and a local average of reasonable size is sufficient.

Turbulent kinetic dissipation analysis for residual-based large eddy simulation of incompressible turbulent flow by variational multiscale method

The underlying physical mechanism of the residual-based large eddy simulation (LES) based on the variational multiscale (VMS) method is clarified. Resolved large-scale energy transportation equation is mathematically derived for turbulent kinetic energy budget analysis. Firstly, statistical results of benchmark turbulent channel flow at Reτ=180 obtained using a coarse mesh are compared with the results obtained by the classical LES with the Smagorinsky and dynamic subgrid stress (SGS) model. The present LES shows an advantage in predicting the statistical results of the incompressible turbulent flows. Secondly, the contributions of the unresolved small-scale presentation terms (Term I-IV in Eq. (10)) to the turbulent kinetic dissipation are analysed for the VMS method. The results show that the turbulent kinetic dissipation provided by the numerical diffusion in the VMS method is smaller in the inner layer, larger in the outer layer of the channel flow than those by the Smagorinsky and dynamic SGS model. The turbulent kinetic dissipation in the VMS method is mainly given by the numerical diffusion provided by one of the “cross-stress” terms (Term I, same as the stabilization term in the SUPG method) and LSIC term (Term IV). The other one of the “cross-stress” terms (Term II) gives rise to the positive turbulent kinetic energy budget, and does not dissipate the turbulent kinetic energy. The so-called “Reynolds stress” term (Term III) dissipates the turbulent energy but provides a very small numerical diffusion. Finally, on the basis of the turbulent kinetic energy dissipation analysis, a new residual-based stabilized finite element formulation is proposed by modifying the large-scale equation in the VMS method. Numerical experiments of 2D lid-driven cavity flow and 3D incompressible turbulent channel flow are tested to validate the proposed formulation. It is shown that all the stabilization terms in the proposed formulation produce additional numerical diffusions and physically increase the total turbulent kinetic dissipation. Consequently, an apparent improvement in both the first-order and second-order statistical quantities are pursued by the new stabilized finite element formulation.

Numerical investigation of internal flow characteristics in a mixed-flow pump with eccentric impeller

In order to study the internal flow fields of mixed-flow pump with eccentric impeller, the numerical simulation and experiment have been conducted based on the dynamic sliding multi-region method. During simulation, the impeller domain has been separated by three sub-domains to apply the whirl effect. The pressure, turbulent kinetic dissipation and streamline distribution in the tip clearance were analyzed. The results show that the energy performance of calculation is basically consistent with the experimental results, which indicates the accuracy of energy performance prediction. The efficiency and head at the design flow condition drop about 20% and 11%, respectively, when e = 0.5 mm. The circumferential pressure distribution of impeller inlet and outlet is influenced greatly by the eccentric impeller, but the middle part of impeller suffered little effects as a result of the rotation effect of impeller. When the impeller is eccentric, the tip leakage flow and tip leakage vortex (TLV) are restrained at small tip clearance but enhance at large tip clearance. The angle between the TLV core and blade rim also increases at large tip clearance but decreases at small tip clearance. More energy has dissipated in the first half part of impeller channel within tip region, and the impacting depth increases with the increase in eccentricity, which affect the inlet flow fields of impeller at large eccentricity. The turbulent kinetic dissipation and hydraulic losses increase with the increase in eccentricity, which is the main factor for the decrease in pump efficiency.

Turbulence characteristics in a rough open channel under unsteady flow conditions

ABSTRACT Most open channel flows are generally unsteady in nature. Very few studies have been carried out in the past to investigate the turbulence characteristics in unsteady open channel flows over a rough bed at different test reaches. In the present study, experiments are conducted for two different flow depths over a rough bed and hydrographs are passed at the inlet of a rectangular flume. With consideration of laboratory constraints, the present study characterizes the unsteady flow as high catchment with long duration flood. The behavior of velocities in both the rising limb and falling limb for same flow depth is observed. Classical hysteresis effect of stage-discharge (h ~ Q) rating curve is illustrated. The present study investigates the turbulent intensities and Reynolds stresses under unsteady flow conditions. The turbulence intensities and Reynolds stresses in the rising limb are higher than that of the falling limb at same flow depth. Turbulence characteristics, i.e. turbulent kinetic energy (TKE), mean kinetic energy (MKE) and turbulent kinetic dissipation rate are also analyzed. It is found that the turbulence intensities, Reynolds stresses, and Turbulence characteristics are gradually decreased towards the downstream reaches.

Comparison of Euler‐Euler Approach and Euler–Lagrange Approach to Model Gas Injection in a Ladle

The gas injection in a ladle using a porous plug is simulated using both the Euler‐Euler and Euler‐Lagrange approaches. The effects of various forces, bubble sizes, and bubble injection frequencies on the flow pattern are modeled. For predicting axial velocity and turbulent kinetic energy, the Euler‐Lagrange approach fits better than Euler‐Euler approach with the measured data. In the Euler‐Euler approach, differences in axial velocities and turbulent kinetic energies for various bubble sizes mainly appears in the plume zone. In the Euler‐Lagrange approach, different bubble sizes with the same injection frequency have a small impact on the turbulence dissipation. Furthermore, the turbulent dispersion from the gas phase to the liquid phase has an important effect on the plume structure and spout eye formation. For both modeling, the smaller the bubble diameter is, the larger the axial velocity and turbulent kinetic dissipation are in the central zone. For the bubble coalescence and breakup, according to the comparison of two modeling approaches, the Euler‐Lagrange approach is more accurate in predicting the flow pattern for gas injection with a porous plug in the ladle.

CFD modeling of turbulent reacting flow in a semi-batch stirred-tank reactor

Abstract For the mixing-sensitive reactions, both chemical kinetics and mixing conditions of the reactants determine the distributions of products. The direct quadrature method of moments combining with the interaction by exchange with the mean micro-mixing model (DQMOM-IEM) has been validated for the chemical reacting flows in micro-reactors. Quite encouraging simulation results offer great promise, but the applicability of this method is needed to be explored furthermore, such as in stirred reactors. In this work, the two-environment DQMOM-IEM model was created with C language and used to customize Fluent through the user-defined functions. The mixing effects on the course of parallel competing chemical reactions carried out in a semi-batch single-phase stirred reactor were predicted. The simulation results show that the rising feed velocity enlarges the volume of reaction zone and maximize the yield of the by-product, which also indicates that the feed stream is more difficultly dispersed into the main stream and the zone surrounding feedpipe exit with high turbulent kinetic dissipation rate cannot be efficiently used.

Evaluation of the turbulent kinetic dissipation rate in an agitated vessel

The design of agitated tanks depends on operating conditions and processes for that are used for. An important parameter for the scale-up modelling is the dissipation rate of the turbulent kinetic energy. The dissipation rate is commonly assumed to be a function of the impeller power input. But this approach gives no information about distribution of the dissipation rate inside the agitated volume. In this paper the distributions of the dissipation rate inside the agitated vessels are estimated by evaluations of the CFD (Computational Fluid Dynamics). The results obtained from RANS (Reynolds Averaged Navier-Stokes equations) k-e turbulent model and LES (Large Eddy Simulations) with Smagorinsky SGS (Sub Grid Scale) model are compared. The agitated vessels with standard geometry equipped with four baffles and stirred by either a standard Rushton turbine or a high shear impeller were investigated. The results are compared with mean dissipation rate estimated from the total impeller power input.

Overlooked Role of Mesoscale Winds in Powering Ocean Diapycnal Mixing.

Diapycnal mixing affects the uptake of heat and carbon by the ocean as well as plays an important role in global ocean circulations and climate. In the thermocline, winds provide an important energy source for furnishing diapycnal mixing primarily through the generation of near-inertial internal waves. However, this contribution is largely missing in the current generation of climate models. In this study, it is found that mesoscale winds at scales of a few hundred kilometers account for more than 65% of near-inertial energy flux into the North Pacific basin and 55% of turbulent kinetic dissipation rate in the thermocline, suggesting their dominance in powering diapycnal mixing in the thermocline. Furthermore, a new parameterization of wind-driven diapycnal mixing in the ocean interior for climate models is proposed, which, for the first time, successfully captures both temporal and spatial variations of wind-driven diapycnal mixing in the thermocline. It is suggested that as mesoscale winds are not resolved by the climate models participated in the Coupled Model Intercomparison Project Phase 5 (CMIP5) due to insufficient resolutions, the diapycnal mixing is likely poorly represented, raising concerns about the accuracy and robustness of climate change simulations and projections.

Estimation of turbulence dissipation rate by Large eddy PIV method in an agitated vessel

The distribution of turbulent kinetic energy dissipation rate is important for design of mixing appa- ratuses in chemical industry. Generally used experimental methods of velocity measurements for measurement in complex geometries of an agitated vessel disallow measurement in resolution of small scales close to turbu- lence dissipation ones. Therefore, Particle image velocity (PIV) measurement method improved by large eddy PIV approach was used. Large eddy PIV method is based on modeling of smallest eddies by a sub grid scale (SGS) model. This method is similar to numerical calculations using Large Eddy Simulation (LES) and the same SGS models are used. In this work the basic Smagorinsky model was employed and compared with power law approximation. Time resolved PIV data were processed by Large Eddy PIV approach and the obtained results of turbulent kinetic dissipation rate were compared in selected points for several operating conditions (impeller speed, operating liquid viscosity).

Measurements of Form and Frictional Drags over a Rough Topographic Bank

AbstractPressure differences across topography generate a form drag that opposes the flow in the water column, and viscous and pressure forces acting on roughness elements of the topographic surface generate a frictional drag on the bottom. Form drag and bottom roughness lengths were estimated over the East Flower Garden Bank (EFGB) in the Gulf of Mexico by combining an array of bottom pressure measurements and profiles of velocity and turbulent kinetic dissipation rates. The EFGB is a coral bank about 6 km wide and 10 km long located at the shelf edge that rises from 100-m water depth to about 18 m below the sea surface. The average frictional drag coefficient over the entire bank was estimated as 0.006 using roughness lengths that ranged from 0.001 cm for relatively smooth portions of the bank to 1–10 cm for very rough portions over the corals. The measured form drag over the bank showed multiple time-scale variability. Diurnal tides and low-frequency motions with periods ranging from 4 to 17 days generated form drags of about 2000 N m−1 with average drag coefficients ranging between 0.03 and 0.22, which are a factor of 5–35 times larger than the average frictional drag coefficient. Both linear wave and quadratic drag laws have similarities with the observed form drag. The form drag is an important flow retardation mechanism even in the presence of the large frictional drag associated with coral reefs and requires parameterization.

Low-Frequency Modulation of Turbulent Diapycnal Mixing by Anticyclonic Eddies Inferred from the HOT Time Series

Abstract Profiles of potential density obtained from CTD measurements during the Hawaii Ocean Time series (HOT) program in the vicinity of the island of Oahu, Hawaii, are used to evaluate low-frequency variability of turbulent kinetic dissipation rates based on a finescale parameterization method. A distinct seasonal cycle, as well as an increasing trend of dissipation rates, is found in the upper 300–600 m. The trend is mainly due to the much weaker diapycnal mixing in the first four years of the record, that is, 1988–92. In the upper 300–600 m, enhanced diapycnal mixing is found under anticyclonic eddies with the mean dissipation rate about 53% larger than that under eddy-free conditions. The modulation of dissipation rates by anticyclonic eddies becomes more evident with increasing eddy strength. The role of cyclonic eddies in modulating diapycnal mixing is almost negligible compared with that of anticyclonic eddies. The mean dissipation rate under cyclonic eddies is comparable to that under eddy-free conditions with a difference of less than 10%. Seasonality of the dissipation rates is partly modulated by the seasonal variation of anticyclonic eddies.

CFD simulation of effects of the configuration of gas distributors on gas–liquid flow and mixing in a bubble column

Abstract Numerical simulations of gas–liquid flow in a cylindrical bubble column of 400 mm in diameter at the superficial gas velocity U g = 0.10 m s - 1 were conducted to investigate effects of the configuration of gas distributors on hydrodynamic behaviour, gas hold-up and mixing characteristics. Eight different gas distributors were adopted in the simulation. The simulation results clearly show that the configuration of gas distributor have an important impact on liquid velocity and local gas hold-up in the vicinity of the gas distributor. Comparisons of the overall gas holdup and mixing time among different gas distributors have demonstrated that none of the adopted gas distributors was able to produce the highest interfacial area and also yield the shortest mixing time. The CFD modelling results reveal that an increase in the number of gas sparging pipes used in gas distributors is beneficial in improving the gas hold-up but is disadvantageous in reducing bubble size due to a decrease in turbulent kinetic dissipation. It has been demonstrated from the simulations that the appearance of asymmetrical flow patterns in the bubble column and the adoption of smaller gas sparging pipes for gas distributors are effective in improving the mixing characteristics.

ONE- and TWO-Equation Models for Canopy Turbulence

The predictive skills of single- and two-equation (or K-e) models to compute pro- files of mean velocity (U), turbulent kinetic energy (K), and Reynolds stresses ðu 0 w 0 Þ are compared against datasets collected in eight vegetation types and in a flume experiment. These datasets range in canopy height h from 0.12 to 23 m, and range in leaf area index (LAI) from 2 to 10 m 2 m � 2 . We found that for all datasets and for both closure models, measured and modelled U, K, and u 0 w 0 agree well when the mixing length (lm )i sa priori specified. In fact, the root-mean squared error between measured and modelled U, K, and u 0 w 0 is no worse than published values for second- and third-order closure approaches. Within the context of one- dimensional modelling, there is no clear advantage to including a turbulent kinetic dissipation rate (e) budget when lm can be specified instead. The broader implication is that the added complexity introduced by the e budget in K-e models need not translate into improved pre- dictive skills of U, K, and u0w0 profiles when compared to single-equation models.

Fractal dimension as an indicator for turbulent mixing in the thermocline

The complexity of small‐scale density fluctuations is investigated experimentally, with special emphasis on their scale‐similar (fractal) facets. Using empirical observations, it is shown that the fractal dimension of density at scales between 0.1 and 3 m is closely related to the turbulent kinetic dissipation rate ε, the local buoyancy frequency N, and the buoyancy Reynolds number ε/νN2 in the upper equatorial Pacific thermocline.