Effect of Impeller Speed Perturbation in a Rushton Impeller Stirred Tank

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Somnath Roy ◽  
Sumanta Acharya
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Rotational Speed ◽  
Stirred Tank ◽  
Azimuthal Direction ◽  
Mean Flow ◽  
Eddy Simulation ◽  
Large Eddy ◽  
The Mean ◽  
Rushton Impeller

Flow inside an unbaffled Rushton-impeller stirred tank reactor (STR) is perturbed using a time dependent impeller rotational speed. Large eddy simulation (LES) revealed that the perturbation increased the width of impeller jet compared to the constant rotational speed cases. The turbulent fluctuations were also observed to be enhanced in the perturbed flow and showed higher values of production and convection of turbulent kinetic energy. Changes in the mean flow-field during the perturbation cycle are investigated. The trailing edge vortices were observed to propagate farther both in the radial and azimuthal direction in the perturbed case. Production of turbulent kinetic energy is observed to be related to the breakup of the impeller jet in the perturbed case. Dissipation of turbulent kinetic energy is augmented due to the perturbation ensuring a better mixing at the molecular scale.

On the interactions between large-scale structure and fine-grained turbulence in a free shear flow I. The development of temporal interactions in the mean

1976 ◽  
Vol 352 (1669) ◽  
pp. 213-247 ◽  
Keyword(s):  
Energy Transfer ◽  
Kinetic Energy ◽  
Shear Layer ◽  
Turbulent Kinetic Energy ◽  
Viscous Dissipation ◽  
Mean Flow ◽  
Fine Grained ◽  
Large Eddy ◽  
The Mean ◽  
Three Components

In this problem a mean turbulent shear layer originally exists, homogeneous in the streamwise direction, formed perhaps by previous instabilities, but in equilibrium with the fine-grained turbulence. At a given time, a large eddy of a fixed horizontal wavenumber is initiated. We study the subsequent time development of the non-equilibrium interactions between the three components of flow as they adjust towards ultimate simultaneous equilibrium, using the integrated energy-balance conservation equations to derive the amplitude equations. This necessarily involves the usual averaging procedure and a conditional or phase-averaging procedure by which the large structure motion is educed from the total fluctuations. In general, the mean flow growth is due to the energy transfer to both fluctuating components, the large eddy gains energy from the mean motion and exchanges energy with the fine-grained turbulence, while the fine-grained turbulence gains energy from the mean flow and exchanges with the large eddy and converts its energy to heat through viscous dissipation of the smallest scales. The closure problem is obtained via the shape assumptions which enter into the interaction integrals. The situation in which the fine-grained turbulent kinetic energy production and viscous dissipation are in local balance is considered, the displacement from equilibrium being due only to the energy transfer from the large eddy. The large eddy shape is taken to be two-dimensional, instability-wavelike, with its vorticity axis perpendicular to the direction of the mean outer stream. Prior to averaging, detailed but approximate calculations of the wave-induced turbulent Reynolds stresses are obtained; the product of these stresses with the appropriate large-eddy rates of strain give the energy transfer mechanism between the two disparate scales of fluctuations. Coupled, nonlinear amplitude or energy density equations for the three components of motion are obtained, the coefficients of which are the interaction integrals guided by the shape assumptions. It is found that for the special case of parallel flow, the energy of the large eddy first undergoes a hydrodynamic-instability type of amplification but eventually decays due to the energy transfer to the fine-grained turbulence, while the turbulent kinetic energy is displaced from an original level of equilibrium to a new one because of the ability of the large eddy to negotiate an indirect energy transfer from the mean flow. For the growing shear layer, approximate considerations show that if the mechanism of energy transfer from the large to the small scale is eventually weakened by the shear layer growth compared to the large-eddy production mechanism so that the amplification and decay process repeats, ‘bursts’ of the remnant of the same large eddy will occur repeatedly until an ultimate equilibrium is reached among the three interacting components of motion. However, for the large eddy whose wavenumber corresponds to that of the initially most amplified case, the ‘bursting’ phenomenon is much less pronounced and equilibrium is very nearly reached at the end of the very first ‘burst’.

scholarly journals Resolved and subgrid dynamics of Rayleigh–Bénard convection

2019 ◽  
Vol 867 ◽  
pp. 906-933 ◽  
Author(s):  
Riccardo Togni ◽  
Andrea Cimarelli ◽  
Elisabetta De Angelis
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Theoretical Framework ◽  
Temperature Fields ◽  
Temperature Variance ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Subgrid Scales ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

In this work we present and demonstrate the reliability of a theoretical framework for the study of thermally driven turbulence. It consists of scale-by-scale budget equations for the second-order velocity and temperature structure functions and their limiting cases, represented by the turbulent kinetic energy and temperature variance budgets. This framework represents an extension of the classical Kolmogorov and Yaglom equations to inhomogeneous and anisotropic flows, and allows for a novel assessment of the turbulent processes occurring at different scales and locations in the fluid domain. Two relevant characteristic scales, $\ell _{c}^{u}$ for the velocity field and $\ell _{c}^{\unicode[STIX]{x1D703}}$ for the temperature field, are identified. These variables separate the space of scales into a quasi-homogeneous range, characterized by turbulent kinetic energy and temperature variance cascades towards dissipation, and an inhomogeneity-dominated range, where the production and the transport in physical space are important. This theoretical framework is then extended to the context of large-eddy simulation to quantify the effect of a low-pass filtering operation on both resolved and subgrid dynamics of turbulent Rayleigh–Bénard convection. It consists of single-point and scale-by-scale budget equations for the filtered velocity and temperature fields. To evaluate the effect of the filter length $\ell _{F}$ on the resolved and subgrid dynamics, the velocity and temperature fields obtained from a direct numerical simulation are split into filtered and residual components using a spectral cutoff filter. It is found that when $\ell _{F}$ is smaller than the minimum values of the cross-over scales given by $\ell _{c,min}^{\unicode[STIX]{x1D703}\ast }=\ell _{c,min}^{\unicode[STIX]{x1D703}}Nu/H=0.8$, the resolved processes correspond to the exact ones, except for a depletion of viscous and thermal dissipations, and the only role of the subgrid scales is to drain turbulent kinetic energy and temperature variance to dissipate them. On the other hand, the resolved dynamics is much poorer in the near-wall region and the effects of the subgrid scales are more complex for filter lengths of the order of $\ell _{F}\approx 3\ell _{c,min}^{\unicode[STIX]{x1D703}}$ or larger. This study suggests that classic eddy-viscosity/diffusivity models employed in large-eddy simulation may suffer from some limitations for large filter lengths, and that alternative closures should be considered to account for the inhomogeneous processes at subgrid level. Moreover, the theoretical framework based on the filtered Kolmogorov and Yaglom equations may represent a valuable tool for future assessments of the subgrid-scale models.

scholarly journals The Process of the Intensification of Coal Fly Ash Flotation Using a Stirred Tank

Minerals ◽  
2018 ◽  
Vol 8 (12) ◽  
pp. 597 ◽  
Author(s):  
Lu Yang ◽  
Zhenna Zhu ◽  
Xin Qi ◽  
Xiaokang Yan ◽  
Haijun Zhang
Keyword(s):  
Fly Ash ◽  
Kinetic Energy ◽  
Large Eddy Simulation ◽  
Rotation Speed ◽  
Coal Fly Ash ◽  
Stirred Tank ◽  
Turbulent Length Scale ◽  
Mineral Particles ◽  
Eddy Simulation ◽  
Large Eddy

Pulp preconditioning using a stirred tank as a pretreatment process is vital to the flotation system, which can be used to improve the flotation efficiency of mineral particles. The kinetic energy that is dissipated in the stirred tank could strengthen the interaction process between mineral particles and flotation reagents to improve the flotation efficiency in the presence of the preconditioning. In this paper, the effect of the conditioning speed on the coal fly ash flotation was investigated using numerical simulations and conditioning-flotation tests. The large eddy simulation coupled with the Smagorinsky-Lilly subgrid model was employed to simulate the turbulence flow field in the stirred tank, which was equipped with a six blade Rushton turbine. The impeller rotation was modelled using the sliding mesh. The simulation results showed that the large eddy simulation (LES) well matched the previous experimental data. The turbulence characteristics, such as the mean velocity, turbulent kinetic energy, power consumption and instantaneous structures of trailing vortices were analysed in detail. The turbulent length scale (η) decreased as the rotation speed increased, and the minimum value of η was almost unchanged when the rotation speed was more than 1200 rpm. The conditioning-flotation tests of coal fly ash were conducted using different conditioning speeds. The results showed that the removal of unburned carbon was greatly improved due to the strengthened turbulence in the stirred tank, and the optimal results were obtained with an LOI of 3.32%, a yield of 78.69% and an RUC of 80.89% when the conditioning speed was 1200 rpm.

On the structure of shear stress and turbulent kinetic energy flux across the roughness layer of a gravel-bed channel flow

2009 ◽  
Vol 638 ◽  
pp. 423-452 ◽  
Author(s):  
EMMANUEL MIGNOT ◽  
D. HURTHER ◽  
E. BARTHELEMY
Keyword(s):  
Shear Stress ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Channel Flow ◽  
Mean Flow ◽  
Local Flow ◽  
Gravel Bed ◽  
Wall Flows ◽  
The Mean ◽  
Conditional Statistics

This study examines the structure of shear stress and turbulent kinetic energy (TKE) flux across the roughness layer of a uniform, fully rough gravel-bed channel flow (ks+ ≫ 100, δ/k = 20) using high-resolution acoustic Doppler velocity profiler measurements. The studied gravel-bed roughness layer exhibits a complex random multi-scale roughness structure in strong contrast with conceptualized k- or d-type roughness in standard rough-wall flows. Within the roughness layer, strong spatial variability of all time-averaged flow quantities are observed affecting up to 40% of the boundary layer height. This variability is attributed to the presence of bed zones with emanating bed protuberances (or gravel clusters) acting as local flow obstacles and bed zones of more homogenous roughness of densely packed gravel elements. Considering the strong spatial mean flow variability across the roughness layer, a spatio-temporal averaging procedure, called double averaging (DA), has been applied to the analysed flow quantities. Three aspects have been addressed: (a) the DA shear stress and DA TKE flux in specific bed zones associated with three classes of velocity profiles as previously proposed in Mignot, Barthélemy & Hurther (J. Fluid Mech., vol. 618, 2009, p. 279), (b) the global and per class DA conditional statistics of shear stress and associated TKE flux and (c) the contribution of large-scale coherent shear stress structures (LC3S) to the TKE flux across the roughness layer. The mean Reynolds and dispersive shear structure show good agreement between the protuberance bed zones associated with the S-shape/accelerated classes and recent results obtained in standard k-type rough-wall flows (Djenidi et al., Exp. Fluids, vol. 44, 2008, p. 37; Pokrajac, McEwan & Nikora, Exp. Fluids, vol. 45, 2008, p. 73). These gravel-bed protuberances act as local flow obstacles inducing a strong turbulent activity in their wake regions. The conditional statistics show that the Reynolds stress contribution is fairly well distributed between sweep and ejection events, with threshold values ranging from H = 0 to H = 8. However, the TKE flux across the roughness layer primarily results from the residual shear stress between ejection and sweep of very high magnitude (H = 10–20) and of small turbulent scale. Although LC3S are seen to penetrated the interfacial roughness layer, their TKE flux contribution is found to be negligible compared to the very energetic small-scale sweep events. These sweeps are dominantly produced in the bed zones of local gravel protuberances where the velocity profiles are inflexional of S-shape type and the mean flow properties are of mixing-layer flow type as previously shown in Mignot et al. (2009).

Large Eddy Simulation of Francis Turbine Flow Fields under Small Opening Condition

2013 ◽  
Vol 444-445 ◽  
pp. 281-285 ◽  
Author(s):  
Tao Guo ◽  
Jun Zhou ◽  
Xiao Nan Liu
Keyword(s):  
Kinetic Energy ◽  
Large Eddy Simulation ◽  
Turbulent Kinetic Energy ◽  
Guide Vane ◽  
Francis Turbine ◽  
Scale Model ◽  
Unstable Flow ◽  
Small Opening ◽  
Eddy Simulation ◽  
Large Eddy

The vibration intensity is strong in Francis turbine occurred under the small opening conditions, such as Lijia Gorges and Three Gorges project. In paper we use large eddy simulation (LES) method base on Vreman SubGrid-Scale model to study the generation and evolution process of turbulence flow, capturing the details of the flow structures and the dissipation of the turbulent kinetic energy. The SIMPIEC algorithm is applied to solve the coupled equation of velocity and pressure. The result shows that the small guide vane opening conditions deviate the optimal conditions most. So some unstable flow characters been induced. Such as the turbulent kinetic energy of fluid in guide vanes zone, the blade passage and the draft tube are very strong. The unstable flow phenomenon including the swirl, flow separation, interruption and vortex strip. It can be deduced that the vibration of unit is induced by these flow characteristic.

Large-eddy simulation of the Richtmyer–Meshkov instability

2015 ◽  
Vol 93 (10) ◽  
pp. 1124-1130 ◽  
Author(s):  
T. Wang ◽  
P. Li ◽  
J.S. Bai ◽  
G. Tao ◽  
B. Wang ◽  
...  
Keyword(s):  
Kinetic Energy ◽  
Flow Field ◽  
Large Eddy Simulation ◽  
Turbulent Kinetic Energy ◽  
Interface Instability ◽  
Simulation Code ◽  
Interface Evolution ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Turbulence Mixing

The subgrid-scale (SGS) terms of turbulence transport are modelled by the stretched-vortex SGS stress model, and a large-eddy simulation code multi-viscous fluid and turbulence (MVFT) is developed to investigate the MVFT problems. Then one AWE shock tube experiment of interface instability is simulated numerically by MVFT code, which reproduces the development process of the interface. The obtained numerical images of interface evolution and wave structures in flow field are consistent with the experimental results. The evolution of perturbed interface and propagation of shock waves in flow field and their interactions are analyzed in detail. The statistics features of turbulence mixing in the form of finer quantities, such as the turbulent kinetic energy, enstrophy, density variance, and turbulent mass flux are investigated, which also proves that the SGS model has a key role in large-eddy simulation. The turbulent kinetic energy and enstrophy decay with time as a power law.

scholarly journals The streamwise turbulence intensity in the intermediate layer of turbulent pipe flow

2015 ◽  
Vol 774 ◽  
pp. 324-341 ◽  
Author(s):  
J. C. Vassilicos ◽  
J.-P. Laval ◽  
J.-M. Foucaut ◽  
M. Stanislas
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Intermediate Layer ◽  
High Reynolds Number ◽  
Logarithmic Derivative ◽  
Turbulent Pipe Flow ◽  
Mean Flow ◽  
The Mean ◽  
High Reynolds

The spectral model of Perryet al. (J. Fluid Mech., vol. 165, 1986, pp. 163–199) predicts that the integral length scale varies very slowly with distance to the wall in the intermediate layer. The only way for the integral length scale’s variation to be more realistic while keeping with the Townsend–Perry attached eddy spectrum is to add a new wavenumber range to the model at wavenumbers smaller than that spectrum. This necessary addition can also account for the high-Reynolds-number outer peak of the turbulent kinetic energy in the intermediate layer. An analytic expression is obtained for this outer peak in agreement with extremely high-Reynolds-number data by Hultmarket al. (Phys. Rev. Lett., vol. 108, 2012, 094501;J. Fluid Mech., vol. 728, 2013, pp. 376–395). Townsend’s (The Structure of Turbulent Shear Flows, 1976, Cambridge University Press) production–dissipation balance and the finding of Dallaset al. (Phys. Rev. E, vol. 80, 2009, 046306) that, in the intermediate layer, the eddy turnover time scales with skin friction velocity and distance to the wall implies that the logarithmic derivative of the mean flow has an outer peak at the same location as the turbulent kinetic energy. This is seen in the data of Hultmarket al. (Phys. Rev. Lett., vol. 108, 2012, 094501;J. Fluid Mech., vol. 728, 2013, pp. 376–395). The same approach also predicts that the logarithmic derivative of the mean flow has a logarithmic decay at distances to the wall larger than the position of the outer peak. This qualitative prediction is also supported by the aforementioned data.

Large Eddy Simulation of Cylindrical Jet Breakup and Correlation of Simulation Results With Experimental Data

2017 ◽  
Vol 139 (10) ◽  
Author(s):  
Shashank S. Moghe ◽  
Scott M. Janowiak
Keyword(s):  
Experimental Data ◽  
Kinetic Energy ◽  
Large Eddy Simulation ◽  
Turbulent Kinetic Energy ◽  
Experimental Results ◽  
Eddy Simulation ◽  
Jet Breakup ◽  
Large Eddy ◽  
Oil Jet ◽  
Piston Cooling

Modern engines with increasing power densities have put additional demands on pistons to perform in incrementally challenging thermal environments. Piston cooling is therefore of paramount importance for engine component manufacturers. The objective of this computational fluid dynamics (CFD) study is to identify the effect of a given piston cooling nozzle (PCN) geometry on the cooling oil jet spreading phenomenon. The scope of this study is to develop a numerical setup using the open-source CFD toolkit OpenFoam® for measuring the magnitude of oil jet spreading and comparing it to experimental results. Large eddy simulation (LES) turbulence modeling is used to capture the flow physics that affects the inherently unsteady jet breakup phenomenon. The oil jet spreading width is the primary metric used for comparing the numerical and experimental results. The results of simulation are validated for the correct applicability of LES by evaluating the fraction of resolved turbulent kinetic energy (TKE) at various probe locations and also by performing turbulent kinetic energy spectral analysis. CFD results appear promising since they correspond to the experimental data within a tolerance (of ±10%) deemed satisfactory for the purpose of this study. Further generalization of the setup is underway toward developing a tool that predicts the aforementioned metric—thereby evaluating the effect of PCN geometry on oil jet spreading and hence on the oil catching efficiency (CE) of the piston cooling gallery. This tool would act as an intermediate step in boundary condition formulation for the simulation determining the filling ratio (FR) and subsequently the heat transfer coefficients (HTCs) in the piston cooling gallery.

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