An Investigation of Velocity and Temperature Fields in Taylor-Couette Flows

Citation

Kedia, Rajesh (1997) An Investigation of Velocity and Temperature Fields in Taylor-Couette Flows. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/0AAS-AW20. https://resolver.caltech.edu/CaltechETD:etd-01102008-131126

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. In many experiments, especially those investigating aspects of fluid flow, it is common to observe time series data exhibiting chaos. Chaos lies in the realm of nonlinear dynamics, and specialized methods are available for the analysis of nonlinear time series. One particular method, called time delay analysis, is particularly useful for extracting information from time series representing measurements at a single point in space. In this thesis, hot-wire anemometry is used to obtain velocity time series from experiments on isothermal Taylor-Couette flow. For R/R[subscript c]=1.6, a simple limit cycle is observed, yielding an attractor of dimension of 1. For R/R[subscript c]=11.1, the attractor dimension increases, and the reconstructed attractor exhibits features characteristic of a transition to turbulence. In addition, various other states and transitions of the Taylor-Couette system are studied as well. Direct numerical simulations (DNS) have also been performed to study the effects of the gravitational and the centrifugal potentials on the stability of heated, incompressible Taylor-Couette flow. The flow is confined between two differentially heated, concentric cylinders and the inner cylinder is allowed to rotate. The Navier-Stokes equations and the coupled energy equation are solved using a spectral method. To validate the code, comparisons are made with existing linear stability analysis and with experiments. The code is used to calculate the local and average heat transfer coefficients for a fixed Reynolds number (R=100) and a range of Grashof numbers. The variation of the local coefficients of heat transfer on the cylinder surface is investigated, and maps showing different stable states of the flow are presented. Calculations of the time and space averaged equivalent conductivity show that the heat transfer decreases with Grashof number in axisymmetric Taylor vortex flow regime and increases with Grashof number after the flow becomes non-axisymmetric. The numerical simulations also demonstrate the existence of a hysteresis loop in heated Taylor-Couette flow, obtained by slowly varying the Grashof number. Two different stable states with same heat transfer are found to exist at the same Grashof number. The validity of Colburn's correlation is investigated as well; the Prandtl number dependence is found to be slightly different from Pr[...] for the range of Reynolds number investigated. Finally, a time delay analysis of the radial velocity and the local heat transfer coefficient time series obtained from the numerical simulation of the radially heated Taylor-Couette flow is performed. The two-dimensional projection of the reconstructed attractor shows a limit cycle for Gr[...]-1700. The limit cycle behavior disappears at Gr[...]-2100, and the reconstructed attractor becomes irregular. The attractor dimension increases to about 3.2 from a value of 1 for the limit cycle case.

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