Niranjan S. Ghaisas

Cage Instabilities in Cylindrical Roller Bearings

A six-degree-of-freedom model was developed and used to simulate the motion of all elements in a cylindrical roller bearing. Cage instability has been studied as a function of the roller-race and roller-cage pocket clearances for light-load and high-speed conditions. The effects of variation in inner race speed, misalignment, cage asymmetry, and varying size of one of the rollers have been investigated. In addition, three different roller profiles have been used to study their impact on cage dynamics. The results indicate that the cage exhibits stable motion for small values of roller-race and roller-cage pocket clearances. A rise in instability leads to discrete cage-race collisions with high force magnitudes. Race misalignment leads to a rise in instability for small roller-cage pocket clearances since skew control is provided by the sides of the cage pocket. One roller of larger size than the others causes inner race whirl and leads to stable cage motion for small roller-race clearances without any variation in roller-cage pocket clearance. Cage asymmetry and different roller profiles have a negligible impact on cage motion.

Geometry-Based Models for Studying the Effects of Wind Farm Layout

AbstractLayout studies are critical in designing large wind farms, since wake effects can lead to significant reductions in power generation. Optimizing wind farm layout using computational fluid dynamics is practically unfeasible today because of their enormous computational requirements. Simple statistical models, based on geometric quantities associated with the wind farm layout, are therefore attractive because they are less demanding computationally. Results of large-eddy simulations of the Lillgrund (Sweden) offshore wind farm are used here to calibrate such geometry-based models. Several geometric quantities (e.g., blockage ratio, defined as the fraction of the swept area of a wind turbine that is blocked by upstream turbines) and their linear combinations are found to correlate very well (correlation coefficient of ~0.95) with the power generated by the turbines. Linear models based on these geometric quantities are accurate at predicting the farm-averaged power and are therefore used here to stud...

Large eddy simulation of turbulent horizontal buoyant jets

Large eddy simulations (LESs) of turbulent horizontal buoyant jets are carried out using a high-order numerical method and Sigma subgrid-scale (SGS) eddy-viscosity model, for a number of different Reynolds (Re) and Richardson (Ri) numbers. Simulations at previous experimental flow conditions (Re = 3200, 24, 000 and Ri = 0, 0.01) are carried out first, and the results are found to be qualitatively and quantitatively similar to the experimental results, thus validating the numerical methodology. The effect of varying Ri (values 2×10−4, 0.001, 0.005, and 0.01) and Re (3200 and 24, 000) is studied next. The presence of stable stratification on one side and unstable stratification on the other side of the jet centreline leads to an asymmetric development of horizontal buoyant jets. It is found that this asymmetry, the total radial spread and the vertical deflection are significantly affected by Ri, while Re affects only the radial asymmetry. The need for developing improved integral models, accounting for this asymmetry, is pointed out. Turbulent production and dissipation rates are investigated, and are found to be symmetric in the horizontal plane, but asymmetric in the mid-vertical plane. A previously proposed model, for correlation between the vertical component of the fluctuating scalar flux vector and the vertical cross-correlation component of the Reynolds tensor, is modified based on the current LES results. Instantaneous scalar and velocity fields are analysed to reveal the structure of horizontal buoyant jets. Similar to the developed turbulent jet, the flow close to the nozzle too is found to be markedly different in the stable and unstable stratification regions. Persistent coherent vortex rings are found in the stable stratification region, while intermittent breakdown of vortex rings into small-scale structures is observed in the unstable stratification region. Similarities and differences between the flow structures in the horizontal buoyant jet configuration and those in the jet in crossflow configuration are discussed. Finally, a dynamic mode decomposition analysis is carried out, which indicates that the flow in the unstable stratification region is more energetic and prone to instabilities, as compared to the flow in the stable stratification region.

Sensitivity Issues in Finite-Difference Large-Eddy Simulations of the Atmospheric Boundary Layer with Dynamic Subgrid-Scale Models

The neutral atmospheric boundary layer (ABL) is simulated by finite-difference large-eddy simulations (LES) with various dynamic subgrid-scale (SGS) models. The goal is to understand the sensitivity of the results to several aspects of the simulation set-up: SGS model, numerical scheme for the convective term, resolution, and filter type. Three dynamic SGS models are tested: two scale-invariant models and the Lagrangian-averaged scale-dependent (LASD) model. The results show that the LASD model has the best performance in capturing the law-of-the-wall, because the scale invariance hypothesis is violated in finite-difference LES. Two forms of the convective term are tested, the skew-symmetric and the divergence forms. The choice of the convective term is more important when the LASD model is used and the skew-symmetric scheme leads to better simulations in general. However, at fine resolutions both in space and time, the sensitivity to the convective scheme is reduced. Increasing the resolution improves the performance in general, but does not better capture the law of the wall. The box and Gaussian filters are tested and it is found that, combined with the LASD model, the Gaussian filter is not sufficient to dissipate the small numerical noises, which in turn affects the large-scale motions. In conclusion, to get the most benefits of the LASD model within the finite-difference framework, the simulations need to be set up properly by choosing the right combination of numerical scheme, resolution, and filter type.

A priori evaluation of large eddy simulation subgrid-scale scalar flux models in isotropic passive-scalar and anisotropic buoyancy-driven homogeneous turbulence

Direct numerical simulation (DNS) of passive (non-buoyant) and active (buoyant) scalar homogeneous turbulence is carried out using a standard pseudo-spectral numerical method. The flow settings simulated include stationary forced and decaying passive-scalar turbulence, as well as decaying anisotropic active-scalar turbulence. The Schmidt number is unity in all cases. The results are compared with, and are found to be in very good agreement with, previous similar DNS studies. The well-validated DNS data are divided into 19 sets, and are employed to study different large eddy simulation (LES) subgrid-scale (SGS) models for the SGS scalar flux. The models examined include three eddy-viscosity-type models (Smagorinsky, Vreman and Sigma with a constant SGS Schmidt number), a Dynamic Structure model and two versions of the Gradient (Gradient and Modulated Gradient) model. The models are investigated with respect to their ability to predict the orientation, and the magnitude, of the SGS scalar flux. Eddy-viscosity models are found to predict the magnitude of the SGS scalar flux accurately, but are poor at predicting the orientation of the SGS scalar flux. The Dynamic Structure and Gradient models are better than eddy-viscosity models at predicting both the magnitude and direction. However, neither of them can be realised in an actual LES, without carrying additional transport equations. Based on these observations, four new models are proposed – combining directions from Dynamic Structure and Gradient models, and magnitudes from Smagorinsky and Vreman eddy-viscosity models. These models are expected to be better than eddy-viscosity and Modulated Gradient models, and this is confirmed by preliminary a posteriori tests.

Dynamic gradient models for the sub-grid scale stress tensor and scalar flux vector in large eddy simulation

ABSTRACTA number of dynamic variants of the modulated gradient model (MGM) for the sub-grid scale (SGS) stress tensor and the SGS scalar flux vector are developed and evaluated a posteriori in large eddy simulations of neutral and stably stratified turbulent channel flow. Two dynamic procedures are evaluated: one based on the local equilibrium hypothesis (called local-dynamic models) and one based on the global equilibrium and steady state hypotheses (global-dynamic models). These local-dynamic (LD) and global-dynamic (GD) versions of MGM are found to be much more accurate than the constant coefficient MGM in neutral turbulent channel flow at friction Reynolds numbers of 180 and 590. The constant coefficient MGM and GD-MGM are also found to yield the correct asymptotic behaviour close to the wall, which indicates the suitability of coupling the MGM kernel with the GD procedure. For the SGS scalar flux vector, LD and GD versions of the MGM are evaluated along with LD and GD versions of the recently propose...

A unified high-order Eulerian method for continuum simulations of fluid flow and of elastic–plastic deformations in solids

Abstract We develop a new high-order method for Eulerian simulations of solids undergoing large, elastic–plastic deformations. Thermodynamically consistent constitutive relations of classical hyperelasticity are used to describe the behavior of solids, liquids and gases in a unified manner. Two kinematic formulations, one based on the inverse deformation gradient tensor, and a second based on the symmetric Finger tensor, are used for tracking large deformations in solids. Simulations based on the Finger tensor are shown to be equivalent to those using the full inverse deformation gradient tensor at much lower computational expense. The numerical algorithm employs a 10th-order compact finite-difference scheme for spatial discretization and a 4th-order Runge–Kutta time-stepping scheme. An improved form of the Localized Artificial Diffusivity (LAD) method is used for numerical regularization of shocks and contact discontinuities. We show that this high-order numerical framework, previously used for simulations of fluid flows, is suitable for problems involving large deformations in elastic–plastic solids as well. Particular emphasis is laid on the choice of the artificial diffusivity parameters in order to sufficiently capture shocks and discontinuities in all the aforementioned continuum media with minimal added dissipation. Test cases in one and two dimensions are shown to demonstrate the feasibility and accuracy of the proposed approach. In particular, this choice of algorithms is shown to lead to excellent numerical resolution properties, and to preserve mass-consistency and curl/compatibility constraints with high order of accuracy. Potential extensions of this numerical framework include application to multi-material problems, involving compressible flow of fluids coupled to elastic–plastic deformations in solids, that are of significant engineering interest.

Dynamics of Bearing Shaft Systems

The objective of this study was to develop a bearing model which can be combined with shafts, gears etc. to virtually investigate the motion and loading of the elements in the bearing. Models for ball, cylindrical and tapered rolling bearing dynamics have been designed, developed and combined with rigid and flexible shafts subject to various loading conditions and eccentric masses. The results from this investigation demonstrated that for rotating shaft bearing systems, the motion and the loads on the rolling elements are significantly different than that predicted by static and / or quasi-static type analysis. Results from shaft bearing system, where shaft may be supported by combinations of ball and rolling element bearings will be demonstrated. Cage motion and stability under various load and speed combinations will be discussed.© 2005 ASME