Rotating Split-Cylinder Flows

abstract: The three-dimensional flow contained in a rapidly rotating circular split cylinder is studied numerically solving the Navier--Stokes equations. The cylinder is completely filled with fluid and is split at the midplane. Three different types of boundary conditions were imposed, leading to a variety of instabilities and complex flow dynamics. The first configuration has a strong background rotation and a small differential rotation between the two halves. The axisymmetric flow was first studied identifying boundary layer instabilities which produce inertial waves under some conditions. Limit cycle states and quasiperiodic states were found, including some period doubling bifurcations. Then, a three-dimensional study was conducted identifying low and high azimuthal wavenumber rotating waves due to G\"ortler and Tollmien–-Schlichting type instabilities. Over most of the parameter space considered, quasiperiodic states were found where both types of instabilities were present. In the second configuration, both cylinder halves are in exact counter-rotation, producing an O(2) symmetry in the system. The basic state flow dynamic is dominated by the shear layer created in the midplane. By changing the speed rotation and the aspect ratio of the cylinder, the flow loses symmetries in a variety of ways creating static waves, rotating waves, direction reversing waves and slow-fast pulsing waves. The bifurcations, including infinite-period bifurcations, were characterized and the flow dynamics was elucidated. Additionally, preliminary experimental results for this case are presented. In the third set up, with oscillatory boundary conditions, inertial wave beams were forced imposing a range of frequencies. These beams emanate from the corner of the cylinder and from the split at the midplane, leading to destructive/constructive interactions which produce peaks in vorticity for some specific frequencies. These frequencies are shown to be associated with the resonant Kelvin modes. Furthermore, a study of the influence of imposing a phase difference between the oscillations of the two halves of the cylinder led to the interesting result that different Kelvin modes can be excited depending on the phase difference.Dissertation/ThesisDoctoral Dissertation Applied Mathematics 201

On the transition from two- to three-dimensional turbulence in the presence of background rotation

We explore the transition from three-dimensional to two-dimensional turbulence in rotating turbulent flows. Inertial waves are thought of as the main mechanism driving physical processes in rotating turbulent flows. However, they can only exist in a limited flow regime and some steady anisotropic phenomena, such as Taylor columns, are driven by wave-free mechanisms. We identify these flow regimes and conditions under which inertial waves play no part with regards to formation of columnar structures, the promotion of anisotropy and the development of a transient turbulent flow field. A new mechanism is proposed by which columnar structures and anisotropy in general develop in rotating flows, which is based on a balance between the Coriolis force and the viscous or inertial forces operating in the flow field. These theories are validated experimentally using a setup where turbulence is forced through fluid injection/withdrawal and both 3D and quasi-2D flow structures develop. In line with the proposed mechanism, the columnar structures are found to scale as _ R

Flow and heat transfer investigations in swirl tubes for gas turbine blade cooling

A swirl tube is a very effective cooling technique for high thermal loaded components like gas turbine blades. Such a tube consists of one or more tangential inlet jets, which induce a highly 3D swirling flow. This swirling flow is characterized by large velocities near the wall and an enhanced turbulence in the tube which both increase the convective heat transfer. In the present work, the flow phenomena and the heat transfer in swirl tubes are studied experimentally and numerically. Therefore, a generic swirl tube with tangential inlets at the upstream end of the tube and a novel application-oriented swirl tube geometry with multiple tangential inlet jets in axial direction are investigated in detail. In strong swirling flows, the flow field is dominated by the circumferential velocity which is characterized by a Rankine vortex with a solid body vortex in the tube center and a potential vortex in the outer region. A stability analysis reveals that the solid body vortex is unstable and hence explains the transformation of the solid body vortex into a stable potential vortex towards the tube outlet. In addition, the axial velocity shows a backflow region (vortex breakdown) in the tube center over the entire tube length. It is shown that a vortex breakdown occurs in swirl dominated flows. The measurements indicate that the heat transfer in swirl tubes increases with increasing Reynolds number and swirl number, respectively. Near the inlet, the maximum heat transfer occurs due to the large circumferential velocity component. With decreasing swirl and velocity towards the tube outlet, also the heat transfer decreases continuously. The investigation of the swirl tube with multiple tangential inlet jets reveals a very complex axial velocity which changes after each inlet due to the additional mass flow. However, the circumferential velocity stays almost constant since the swirl strength is re-enhanced with each inlet jet, respectively. For each inlet jet, a high heat transfer can be observed. However, the maximum heat transfer is lower than for the swirl tube with only one inlet because of the lower inlet jet velocities. On the other hand, the heat transfer distribution is more homogeneous over the entire tube length at a much lower pressure loss. For the investigated swirl tubes with one, three or five inlets, the thermal performance is in the same order of magnitude and hence all swirl tube configurations are suitable for cooling

Influence of cavity flow on turbine aerodynamics

In order to deal with high temperatures faced by the components downstream of the combustion chamber, some relatively cold air is bled at the compressor. This air feeds the cavities under the turbine main annulus and cool down the rotor disks ensuring a proper and safe operation of the turbine. This thesis manuscript introduces a numerical study of the effect of the cavity flow close to the turbine hub on its aerodynamic performance. The interaction phenomena between the cavity and main annulus flow are not currently fully understood. The study of these phenomena is performed based on different numerical approaches (RANS, LES and LES-LBM) applied to two configurations for which experimental results are available. A linear cascade configuration with an upstream cavity and various rim seal geometries (interface between rotor and stator platform) and cavity flow rate available. A rotating configuration that is a two stage turbine including cavities close to realistic industrial configurations. Additional losses incurred by the cavity flow are measured and studied using a method based on exergy (energy balance in the purpose to generate work)

Meshless Direct Numerical Simulation of Turbulent Incompressible Flows

A meshless direct pressure-velocity coupling procedure is presented to perform Direct Numerical Simulations (DNS) and Large Eddy Simulations (LES) of turbulent incompressible flows in regular and irregular geometries. The proposed method is a combination of several efficient techniques found in different Computational Fluid Dynamic (CFD) procedures and it is a major improvement of the algorithm published in 2007 by this author. This new procedure has very low numerical diffusion and some preliminary calculations with 2D steady state flows show that viscous effects become negligible faster that ever predicted numerically. The fundamental idea of this proposal lays on several important inconsistencies found in three of the most popular techniques used in CFD, segregated procedures, streamline-vorticity formulation for 2D viscous flows and the fractional-step method, very popular in DNS/LES. The inconsistencies found become important in elliptic flows and they might lead to some wrong solutions if coarse grids are used. In all methods studied, the mathematical basement was found to be correct in most cases, but inconsistencies were found when writing the boundary conditions. In all methods analyzed, it was found that it is basically impossible to satisfy the exact set of boundary conditions and all formulations use a reduced set, valid for parabolic flows only. For example, for segregated methods, boundary condition of normal derivative for pressure zero is valid only in parabolic flows. Additionally, the complete proposal for mass balance correction is right exclusively for parabolic flows. In the streamline-vorticity formulation, the boundary conditions normally used for the streamline function, violates the no-slip condition for viscous flow. Finally, in the fractional-step method, the boundary condition for pseudo-velocity implies a zero normal derivative for pressure in the wall (correct in parabolic flows only) and, when the flows reaches steady state, the procedure does not guarantee mass balance. The proposed procedure is validated in two cases of 2D flow in steady state, backward-facing step and lid-driven cavity. Comparisons are performed with experiments and excellent agreement was obtained in the solutions that were free from numerical instabilities. A study on grid usage is done. It was found that if the discretized equations are written in terms of a local Reynolds number, a strong criterion can be developed to determine, in advance, the grid requirements for any fluid flow calculation. The 2D-DNS on parallel plates is presented to study the basic features present in the simulation of any turbulent flow. Calculations were performed on a short geometry, using a uniform and very fine grid to avoid any numerical instability. Inflow conditions were white noise and high frequency oscillations. Results suggest that, if no numerical instability is present, inflow conditions alone are not enough to sustain permanently the turbulent regime. Finally, the 2D-DNS on a backward-facing step is studied. Expansion ratios of 1.14 and 1.40 are used and calculations are performed in the transitional regime. Inflow conditions were white noise and high frequency oscillations. In general, good agreement is found on most variables when comparing with experimental data

Thermal Flows

Flows of thermal origin and heat transfer problems are central in a variety of disciplines and industrial applications. The present book entitled Thermal Flows consists of a collection of studies by distinct investigators and research groups dealing with different types of flows relevant to both natural and technological contexts. Both reviews of the state-of-the-art and new theoretical, numerical and experimental investigations are presented, which illustrate the structure of these flows, their stability behavior, and the possible bifurcations to different patterns of symmetry and/or spatiotemporal regimes. Moreover, different categories of fluids are considered (liquid metals, gases, common fluids such as water and silicone oils, organic and inorganic transparent liquids, and nanofluids). This information is presented under the hope that it will serve as a new important resource for physicists, engineers and advanced students interested in the physics of non-isothermal fluid systems; fluid mechanics; environmental phenomena; meteorology; geophysics; and thermal, mechanical and materials engineering