The principal objectives of the work described in this thesis were: 1. To develop an improved multiphase CFD model for classifying cyclones and further improve understanding of the separation mechanism based on fluid flow and turbulence inside the cyclone. 2. To develop an improved Empirical model of classifying cyclones, covering a wide range of design and operating conditions. The multi-phase CFD model developed in this work is based on the approach reported by Brennan et al (2002) and Brennan (2003) using Fluent, and involves individual models for the air-core, turbulence, and particle classification. Two-phase VOF and mixture models for an air/water system were used to predict the air-core and the pressure and flow fields on 3D fitted fine grids. The turbulence was resolved using both DRSM (QPS) and LES turbulence models. The predicted mean and turbulent flow field from the LES and DRSM turbulence models were compared with the LDA measurements of Hsieh (1988). The LES model predicts the experimental data more accurately than the DRSM model. The standard mixture model (Manninnen et al, 1996) and the modified mixture model for a water/air/solids system were used to predict cyclone performance. The standard mixture model was able to predict classification efficiency reasonably at low solids concentrations, but under-predicts the recovery of coarse size fractions to underflow. To improve the predictions at moderate to high feed solids, the author modified the slip velocity with additional Bagnold dispersive forces, Saffman lift forces, and a hindered settling correction for particle drag in the mixture model superimposed on an LES turbulence model. Several cyclone geometries were used for validating the multiphase CFD model. The modified mixture model improves prediction of the separation of coarse size particles, and the predicted closely matches the experimental in various cyclones. The particle classification mechanism has been further elucidated using the simulated particle concentration distributions. At high solids concentrations, the modified CFD model predicts the efficiency curve reasonably well, especially the cut-size of the cyclone, but prediction of fine particle recovery to overflow is poor compared to the experimental data. It appears that the fines are significantly affected by turbulent dispersion and the flow resistance due to the high viscosity of the slurry at the apex is not sufficiently accounted for in the modified Mixture model. The improved multi-phase CFD model was validated against two sets of experimental data available in the literature: particle concentrations measured by gamma ray tomography data in a dense medium cyclone (Subramanian, 2002), and particle size distribution inside a hydrocyclone (Renner, 1976). Large eddy simulation (LES) with the modified Mixture model, including medium with a feed size distribution appears to be promising in predicting medium segregation inside a dense medium cyclone. The CFD predicted sample size distributions at different positions are reasonably comparable with Renner’s (1976) experimental data near the wall and in the bottom cone, but differ considerably near the forced vortex region, and also near the tip of the vortex finder wall. The CFD model shows no air-core formation at the low operating pressure used by Renner, which suggests his experiments involved an unusual/unstable forced vortex based cyclone separation. The effect of turbulence on fluid and solid particle motion was also studied in this thesis. The resolved turbulent fluctuations from LES of the hydrocyclone at steady flow were analysed using ensemble averaging. The ratio of the effective turbulent acceleration of each particle size to the centrifugal acceleration was calculated for various cyclones, which showed that turbulent mixing becomes less important with larger particles. The trends in this ratio correlate with the equilibrium positions of the particles from the multiphase LES. The analysis indicates that the short-circuiting might be aggravated by turbulent mixing across the locus of zero vertical velocity (LZVV) against the classification force, and along the vortex finder wall into the inner upflow region of the cyclone. An experimental study of the “fish-hook” effect was pursued in various industrial scale cyclones to evaluate the effect of various cyclone parameters. The observed diameter at which fine particle recovery starts to increase is mainly affected by feed solids content and spigot diameter, but less influenced by feed pressure. The observed particle recovery to the underflow at the fishhook dip size, the bypass, is always higher than the underflow water split. Any cyclone variable that affects the underflow water split, will also affect the bypass value. CFD studies showing high particle Reynolds numbers for coarse particles were used to provide a qualitative mechanism for fines reporting to the underflow in the wakes behind the larger particles (Tang et all. 1992). The Frachon and Cilliers (1999) model was used to fit and evaluate the fishhook parameters. The variations of these fishhook parameters were quantified for changes in cyclone design and operating conditions. The development of an improved empirical hydrocyclone model was attempted by collecting extensive historical data covering a wide range of cyclones. Additional experiments on 10 and 20 inch Krebs cyclones were performed to fill the gaps in the database, especially at low to moderate feed solids concentration and with different cone sections. Tangential velocity, turbulent diffusion, slurry viscosity and particle hindered settling correlations were identified from CFD as the key inputs to the particle classification mechanism for the empirical model. A new cyclone model structure based on a dimensionless approach has been developed. The model for , , Q gives a very good fit to the data, while the model for separation sharpness gave reasonable correlations with the cyclone design and operating conditions. 208 additional data sets were used to validate the new hydrocyclone model.

Thesis (M.S.)--Rochester Institute of Technology, 1996. / Typescript. Includes bibliographical references (leaves [159]-[161]).

The speed and efficiency of stratified turbulent mixing in homogenising temperatures, chemical composition and flow speeds makes it one of farthest reaching fluid mechanical phenomenon for life on earth. It is an aesthetically beautiful phenomenon, rich in complex physical behaviours and extremely challenging to model mathematically. Laboratory experiments have a valuable role to play to guide theoretical and numerical work towards a better understanding of this phenomenon by providing insight into real flows under controlled conditions. This dissertation addresses some aspects of the laboratory buoyancy-driven exchange flows through an inclined duct connecting two reservoirs containing fluids of different densities. We employ a novel experimental technique to perform near-instantaneous, volumetric measurements of the three-component velocity field and density field simultaneously, providing an unprecedented quantitative picture of these sustained stratified shear flows. We start by characterising the variety of observed behaviours, or flow regimes, as we vary the density difference between the two reservoirs, the angle of inclination of the duct with respect to the horizontal, the way the density difference is achieved (solutions of salt/fresh water or cold/warm water) and the geometry of the duct. These empirical observations allow us to formulate a number of specific research questions, guiding the work of the next chapters. We then focus on the regime in which Holmboe waves are observed, and demonstrate that these well-known interfacial travelling disturbances have a distinct structure when confined by solid boundaries. We characterise this structure and identify the physical mechanisms at its origin by means of linear stability theory. Since Holmboe waves are found in the intermediate, transitional regime between laminar and turbulent flows, we conjecture that their structure may be relevant to more turbulent flows, where resembling structures are indeed observed. Next, we tackle the quantitative analysis of universal transition curves separating the observed flow regimes (laminar, waves, intermittently turbulent or fully turbulent) as well and the net mass flow rate exchanged by the reservoirs. We show that these long-lasting questions in the study of exchange flows can be addressed in the framework of frictional hydraulic theory, and we derive detailed scaling laws involving only a few nondimensional parameters. Finally, we overcome some of the limitations of hydraulic theory by performing a more detailed, time-resolved, three-dimensional analysis of the energetics of the wave, intermittent and turbulent regimes. We identify and quantify the sources and sinks of energy in each regime, and identify some of the structures responsible for viscous energy dissipation and mixing. We also suggest possible future directions for the present work given recent progress in the literature.

The turbulent boundary layer is an aspect of fluid flow which dominates the performance of many engineering systems - yet the analytic solution of such flows is intractable for most applications. Our understanding of boundary layers is therefore limited by our ability to simulate and measure them. Tomographic Particle Image Velocimetry (TPIV) is a recently developed technique for direct measurement of fluid velocity within a 3D region. This allows new insight into the topological structure of turbulent boundary layers. Increasing Reynolds Number increases the range of scales at which turbulence exists; a measurement technique must have a larger 'dynamic range' to fully resolve the flow. Tomographic PIV is currently limited in spatial dynamic range (which is also linked to the spatial and temporal resolution) due to a high degree of noise. Results also contain significant bias error. This work proposes a modification of the technique to use more than two exposures in the PIV process, which (for four exposures) is shown to improve random error by a factor of 2 to 7 depending on experimental setup parameters. The dynamic range increases correspondingly and can be doubled again in highly turbulent flows. Bias error is reduced by up to 40%. An alternative reconstruction approach is also presented, based on application of a reduction strategy (elimination of coefficients based on a first guess) to the tomographic weightings matrix Wij. This facilitates a potentially significant increase in computational efficiency. Despite the achieved reduction in error, measurements contain non-zero divergence due to noise and sampling errors. The same problem affects visualisation of topology and coherent fluid structures. Using Projection Onto Convex Sets, a framework for post-processing operators is implemented which includes a divergence minimisation procedure and a scale-limited denoising strategy which is resilient to 'false' vectors contained in the data. Finally, developed techniques are showcased by visualisation of topological information in the inner region of a high Reynolds Number boundary layer (δ+ = 1890, Reθ = 3650). Comments are made on the visible flow structures and tentative conclusions are drawn.

No description available.

The work presented here is part of an ongoing effort to develop a highly accurate and numerically efficient turbulence simulation technique. The paper consists of four main parts, viz., the general discussion of the procedure known as Additive Turbulent Decomposition, the derivation of the "synthetic velocity" subgrid-scale model of the high wavenumber turbulent fluctuations necessary for its implementation, the numerical investigation of this model and a priori tests of said models physical validity. Through these investigations we have demonstrated that this procedure, coupled with the use of the "Poor Mans Navier-Stokes" equation subgrid-scale model, has the potential to be a faster, more accurate replacement of currently popular turbulence simulation techniques since: 1. The procedure is consistent with the direct solution of the Navier-Stokes equations if the subgrid-scale model is valid, i.e, the equations to be solved are never filtered, only solutions. 2. Model parameter values are "set" by their relationships to N.S. physics found from their derivation from the N.S. equation and can be calculated "on the fly" with the use of a local high-pass filtering of grid-scale results. 3. Preliminary studies of the PMNS equation model herein have shown it to be a computationally inexpensive and a priori valid model in its ability to reproduce high wavenumber fluctuations seen in an experimental turbulent flow.

Density stratification is one of the essential underlying physical mechanisms for atmospheric and oceanic flow. As a first step to investigating the mechanisms of stratified turbulence, linear stability plays a critical role in determining under what conditions a flow remains stable or unstable. In the study of transition to stratified turbulence, a common vortex model, known as the Lamb-Chaplygin dipole, is used to investigate the conditions under which stratified flow transitions to turbulence. Numerous investigations have determined that a critical length scale, known as the buoyancy length, plays a key role in the breakdown and transition to stratified turbulence. At this buoyancy length scale, an instability unique to stratified flow, the zigzag instability, emerges. However investigations into sub-buoyancy length scales have remained unexplored. In this thesis we discover and investigate a new instability of the Lamb-Chaplyin dipole that exists at the sub-buoyancy scale. Through numerical linear stability analysis we show that this short-wave instability exhibits growth rates similar to that of the zigzag instability. We conclude with nonlinear studies of this short-wave instability and demonstrate this new instability saturates at a level proportional to the cube of the aspect ratio.

In this thesis I study a variety of two-dimensional turbulent systems using a mixed analytical, phenomenological and numerical approach. The systems under consideration are governed by the two-dimensional Navier-Stokes (2DNS), surface quasigeostrophic (SQG), alpha-turbulence and magnetohydrodynamic (MHD) equations. The main analytical focus is on the number of degrees of freedom of a given system, defined as the least value $N$ such that all $n$-dimensional ($n$ ≥ $N$) volume elements along a given trajectory contract during the course of evolution. By equating $N$ with the number of active Fourier-space modes, that is the number of modes in the inertial range, and assuming power-law spectra in the inertial range, the scaling of $N$ with the Reynolds number $Re$ allows bounds to be put on the exponent of the spectrum. This allows the recovery of analytic results that have until now only been derived phenomenologically, such as the $k$[superscript(-5/3)] energy spectrum in the energy inertial range in SQG turbulence. Phenomenologically I study the modal interactions that control the transfer of various conserved quantities. Among other results I show that in MHD dynamo triads (those converting kinetic into magnetic energy) are associated with a direct magnetic energy flux while anti-dynamo triads (those converting magnetic into kinetic energy) are associated with an inverse magnetic energy flux. As both dynamo and anti-dynamo interacting triads are integral parts of the direct energy transfer, the anti-dynamo inverse flux partially neutralises the dynamo direct flux, arguably resulting in relatively weak direct energy transfer and giving rise to dynamo saturation. These theoretical results are backed up by high resolution numerical simulations, out of which have emerged some new results such as the suggestion that for alpha turbulence the generalised enstrophy spectra are not closely approximated by those that have been derived phenomenologically, and new theories may be needed in order to explain them.

This thesis presents the results of steady, Reynolds-averaged Navier-Stokes (RANS) computations for jet flow emanating from a generic turbofan engine exhaust. All computations were performed with commercial solver FLUENT v6.2.16. Different turbulence models were evaluated. In addition to turbulence modeling issues, a parametric study was considered. Different modeling approaches for turbulent jet flows were explained in brief, with specific attention given to the Reynolds-averaged Navier-Stokes (RANS) method used for the calculations. First, a 2D ejector problem was solved to find out the most appropriate turbulence model and solver settings for the jet flow problem under consideration. Results of one equation Spalart-Allmaras, two-equation standart k-&amp / #949 / , realizable k-&amp / #949 / , k-&amp / #969 / and SST k-&amp / #969 / turbulence models were compared with the experimental data provided and also with the results of Yoder [21]. The results of SST k-&amp / #969 / and Spalart-Allmaras turbulence models show the best agreement with the experimental data. Discrepancy with the experimental data was observed at the initial growth region of the jet, but further downstream calculated results were closer to the measurements. Comparing the flow fields for these different turbulence models, it is seen that close to the onset of mixing section, turbulence dissipation was high for models other than SST k-&amp / #969 / and Spalart-Allmaras turbulence models. Higher levels of turbulent kinetic energy were present in the SST k-&amp / #969 / and Spalart-Allmaras turbulence models which yield better results compared to other turbulence models. The results of 2D ejector problem showed that turbulence model plays an important role to define the real physics of the problem. In the second study, analyses for a generic, subsonic, axisymmetric turbofan engine exhaust were performed. A grid sensitivity study with three different grid levels was done to determine grid dimensions of which solution does not change for the parametric study. Another turbulence model sensitivity study was performed for turbofan engine exhaust analysis to have a better understanding. In order to evaluate the results of different turbulence models, both turbulent and mean flow variables were compared. Even though turbulence models produced much different results for turbulent quantities, their effects on the mean flow field were not that much significant. For the parametric study, SST k-&amp / #969 / turbulence model was used. It is seen that boundary layer thickness effect becomes important in the jet flow close to the lips of the nozzles. At far downstream regions, it does not affect the flow field. For different turbulent intensities, no significant change occurred in both mean and turbulent flow fields.