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fbtwitterlinkedinvimeoflicker grey 14rssslideshare1
Kopera, Michal Andrzej
Languages: English
Types: Doctoral thesis
Subjects: QA

Classified by OpenAIRE into

arxiv: Physics::Fluid Dynamics
A three-dimensional, turbulent \ud flow in a channel with a sudden expansion\ud was studied by direct numerical simulation of the incompressible Navier-Stokes\ud equations. The objective of this study was to provide statistical data of backwardfacing\ud step \ud flow for turbulence modelling. Additionally, analysis of the statistical\ud and dynamical properties of the \ud flow is performed.\ud The Reynolds number of the main simulation was Reh = 9000, based on the\ud step height and mean inlet velocity, with the expansion ratio ER = 2:0. The discretisation\ud is performed using the spectral/hp element method with stiffly-stable\ud velocity correction scheme for time integration. The inlet boundary condition is\ud a fully turbulent velocity and pressure field regenerated from a plane downstream\ud of the inlet. A constant \ud flowrate was ensured by applying Stokes \ud flow correction\ud in the inlet regeneration area.\ud Time and spanwise averaged results revealed, apart from the primary recirculation\ud bubble, secondary and tertiary corner eddies. Streamlines show an additional\ud small eddy at the downstream tip of the secondary corner eddy, with the\ud same circulation direction as the secondary vortex. The analysis of the 3D, timeonly\ud average shows the wavy spanwise structure of both primary and secondary\ud recirculation bubble, that results in spanwise variations of the mean reattachment\ud location. The visualisation of spanwise averaged pressure \ud uctuations and\ud streamwise velocity showed that the interaction of vortices with the recirculation\ud bubble is responsible for the \ud apping of the reattachment position. The\ud characteristic frequency St = 0:078 was found.\ud The analysis of small-scale energy transfer was performed to reveal large\ud backscatter regions in strong Reynolds stress areas in the mixing layer. High\ud correlation of small-scale transfer with non-linear interaction of large-scale velocity\ud and small-scale vorticity was found.\ud The data of the \ud flow fields was archived. It contains the averages for velocities,\ud pressure and Reynolds stress tensor, as well as 3D instantaneous pressure and\ud velocity history.
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    • 1 Introduction 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Survey of Previous Work . . . . . . . . . . . . . . . . . . . . . . . 3 1.2.1 Experimental Investigations . . . . . . . . . . . . . . . . . 3 1.2.2 First Numerical Experiments . . . . . . . . . . . . . . . . 9 1.2.3 Direct Numerical Simulations . . . . . . . . . . . . . . . . 10 1.3 Outline of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . 11
    • 2 Numerical Methods 13 2.1 Governing Equations . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2 Geometry and Mesh . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2.1 Domain de nition and boundary conditions . . . . . . . . 15
    • 3 Code Validation and Preliminary Simulations 54 3.1 Code Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.2 Preliminary Simulations . . . . . . . . . . . . . . . . . . . . . . . 60 3.2.1 Turbulent channel ow simulation . . . . . . . . . . . . . . 60 3.2.2 Laminar in ow backward-facing step ow simulation . . . 63 Abbot, D.E. & Kline, S.J. (1962). Experimental investigations of subsonic turbulent ow over single and double backward-facing steps. Transactions of the ASME. Series D, Journal of Basic Engineering, 84.
    • Armaly, B.F., Durst, F., Pereira, J.C.F. & Schonung, B. (1983). Experimental and theoretical investigation of backward-facing step ow. Journal of Fluid Mechanics Digital Archive, 127, 473{496.
    • Blackburn, H. & Sherwin, S. (2004). Formulation of a galerkin spectral element fourier method for three-dimensional incompressible ows in cylindrical geometries. Journal of Computational Physics, 197, 759{778.
    • Jovic, S. & Driver, D. (1994). Backward-facing step measurements at low reynolds number. NASA Tech. Mem., 108807.
    • Kaikstis, L., Karniadakis, G.E. & Orszag, S.A. (1991). Onset of threedimensionality, equilibria, and early transition in ow over a backward-facing step. Journal of Fluid Mechanics, 231, 501{538.
    • Kim, J., Kline, S.J. & Johnston, J.P. (1980). Investigation of a reattaching turbulent shear layer: Flow over a backward-facing step. Transactions of the ASME. Journal of Fluid Engineering , 102, 302{308.
    • Sherwin, S. & Blackburn, H. (2005). Three-dimensional instabilities and transition of steady and pulsatile axisymmetric stenotic ows. Journal of Fluid Mechanics, 533, 297{327.
    • Silveira Neto, A., Grand, D., Metais, O. & Lesieur, M. (1993). A numerical investigation of the coherent vortices in turbulence behind a backwardfacing step. Journal of Fluid Mechanics, 256, 1{25.
    • Spazzini, P., Iuso, G., Oronato, M., Zurlo, N. & Di Cicca, G. (2001). Unsteady behaviour of back-facing step ow. Experiments in Fluids, 30, 551{ 561.
    • Walsh, M. (1980). Drag characteristics of v-groove and transverse curvature riblets. Prog. Astronaut. Aeronaut., 72, 168.
    • Wei, T. & Willmarth, W. (1989). Reynolds-number e ects on the structure of a turbulent channel ow. Journal of Fluid Mechanics, 204, 57{95.
    • Westphal, R.V., Johnston, J.P. & Eaton, J.K. (1984). Experimental study of ow reattachment in a single-sided sudden expansion. NASA STI/Recon Technical Report N , 84, 18571{+.
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