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A numerical method based on b-spline polynomials was developed to study incompressible flows in cylindrical geometries. A b-spline method has the advantages of possessing spectral accuracy and the flexibility of standard finite element methods. Using this method it was possible to ensure regularity of the solution near the origin, i.e. smoothness and boundedness. Because b-splines have compact support, it is also possible to remove b-splines near the center to alleviate the constraint placed on the time step by an overly fine grid. Using the natural periodicity in the azimuthal direction and approximating the streamwise direction as periodic, so-called time evolving flow, greatly reduced the cost and complexity of the computations. A direct numerical simulation of pipe flow was carried out using the method described above at a Reynolds number of 5600 based on diameter and bulk velocity. General knowledge of pipe flow and the availability of experimental measurements make pipe flow the ideal test case with which to validate the numerical method. Results indicated that high flatness levels of the radial component of velocity in the near wall region are physical; regions of high radial velocity were detected and appear to be related to high speed streaks in the boundary layer. Budgets of Reynolds stress transport equations showed close similarity with those of channel flow. However contrary to channel flow, the log layer of pipe flow is not homogeneous for the present Reynolds number. A topological method based on a classification of the invariants of the velocity gradient tensor was used. Plotting iso-surfaces of the discriminant of the invariants proved to be a good method for identifying vortical eddies in the flow field. Loulou, Patrick and Moser, Robert D. and Mansour, Nagi N. and Cantwell, Brian J. Ames Research Center DIGITAL SIMULATION; COMPUTERIZED SIMULATION; COMPUTATIONAL FLUID DYNAMICS; INCOMPRESSIBLE FLOW; PIPE FLOW; FINITE ELEMENT METHOD; TURBULENT FLOW; ...
In this thesis, the effects of computational domain size and radius ratio on fully developed turbulent flow and heat transfer in a concentric annular pipe are investigated using direct numerical simulation (DNS). To perform DNS, a new parallel computer code based on the pseudo-spectral method was developed using the FORTRAN 90/95 programing languages and the message passing interface (MPI) libraries. In order to study the effects of computational domain size on the turbulence statistics, twelve test cases of different domain sizes are compared. The effects of radius ratio are investigated through a systematic study based on four radius ratios of a concentric pipe. The characteristics of the velocity and temperature fields are examined at two Reynolds number of Re_(D_h ) =8900$ and 17700. The radius ratio affects the interaction of two boundary layers of the concentric annular pipe and has a significant impact on the turbulent flow structures and dynamics. The characteristics of the flow and temperature fields are investigated in both physical and spectral spaces, which include the analyses of the first- and second-order statistical moments, budget balance of the transport equation of Reynolds stresses, two-point correlation coefficients, and premultiplied spectra of velocity, vorticity, and temperature fluctuations. It is observed that the scales and dynamics of turbulence structures vary with the radius ratio as well as the surface curvature of the concave and convex walls. The characteristic length scales of the turbulence structures are identified through a spectral analysis.
In this thesis, direct numerical simulations have been preformed with a high-order spectral element method computer code to investigate the Coriolis force effect on a fully-developed turbulent flow confined within a circular pipe subjected to radial system rotations. In order to study the radially rotating effects on the flow, a wide range of rotation numbers have been tested. In response to the system rotation imposed, large-scale secondary flows appear as streamwise counter-rotating vortices, which highly interact with the boundary layer and have a significant impact on the turbulent flow structures and dynamics. A quasi Taylor-Proudman region occurs at low rotation numbers, where the mean axial velocity is invariant along the rotating axis. As the rotation number increases, laminarization occurs near the bottom wall of the pipe, and the flow become fully laminarized when the rotation number approaches one. The characteristics of the flow field are investigated in both physical and spectral spaces, which include the analyses of the first- and second-order statistical moments, pre-multiplied spectra of velocity fluctuations, budget balance of the transport equation of Reynolds stresses, and coherent flow structures.