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The objectives of this study are as follows: (1) to conduct a direct numerical simulation of turbulent backward facing step flow using inflow and outflow conditions; and (2) to provide data in the form of Reynolds stress budgets for Reynolds averaged modeling. The report presents the basic statistical data and comparisons with the concurrent experiments of Jovic and Driver and budgets of turbulent kinetic energy. Le, Hung and Moin, Parviz Unspecified Center ...
A three-dimensional, turbulent flow in a channel with a sudden expansion was studied by direct numerical simulation of the incompressible Navier-Stokes equations. The objective of this study was to provide statistical data of backwardfacing step flow for turbulence modelling. Additionally, analysis of the statistical and dynamical properties of the flow is performed. The Reynolds number of the main simulation was Reh = 9000, based on the step height and mean inlet velocity, with the expansion ratio ER = 2:0. The discretisation is performed using the spectral/hp element method with stiffly-stable velocity correction scheme for time integration. The inlet boundary condition is a fully turbulent velocity and pressure field regenerated from a plane downstream of the inlet. A constant flowrate was ensured by applying Stokes flow correction in the inlet regeneration area. Time and spanwise averaged results revealed, apart from the primary recirculation bubble, secondary and tertiary corner eddies. Streamlines show an additional small eddy at the downstream tip of the secondary corner eddy, with the same circulation direction as the secondary vortex. The analysis of the 3D, timeonly average shows the wavy spanwise structure of both primary and secondary recirculation bubble, that results in spanwise variations of the mean reattachment location. The visualisation of spanwise averaged pressure uctuations and streamwise velocity showed that the interaction of vortices with the recirculation bubble is responsible for the apping of the reattachment position. The characteristic frequency St = 0:078 was found. The analysis of small-scale energy transfer was performed to reveal large backscatter regions in strong Reynolds stress areas in the mixing layer. High correlation of small-scale transfer with non-linear interaction of large-scale velocity and small-scale vorticity was found. The data of the flow fields was archived. It contains the averages for velocities, pressure and Reynolds stress tensor, as well as 3D instantaneous pressure and velocity history.
It is a truism that turbulence is an unsolved problem, whether in scientific, engin eering or geophysical terms. It is strange that this remains largely the case even though we now know how to solve directly, with the help of sufficiently large and powerful computers, accurate approximations to the equations that govern tur bulent flows. The problem lies not with our numerical approximations but with the size of the computational task and the complexity of the solutions we gen erate, which match the complexity of real turbulence precisely in so far as the computations mimic the real flows. The fact that we can now solve some turbu lence in this limited sense is nevertheless an enormous step towards the goal of full understanding. Direct and large-eddy simulations are these numerical solutions of turbulence. They reproduce with remarkable fidelity the statistical, structural and dynamical properties of physical turbulent and transitional flows, though since the simula tions are necessarily time-dependent and three-dimensional they demand the most advanced computer resources at our disposal. The numerical techniques vary from accurate spectral methods and high-order finite differences to simple finite-volume algorithms derived on the principle of embedding fundamental conservation prop erties in the numerical operations. Genuine direct simulations resolve all the fluid motions fully, and require the highest practical accuracy in their numerical and temporal discretisation. Such simulations have the virtue of great fidelity when carried out carefully, and repre sent a most powerful tool for investigating the processes of transition to turbulence.
This book contains a selection of the papers that were presented at the EUROMECH colloquium on particle-laden flow held at the University of Twente in 2006. The multiscale nature of this challenging field motivated the calling of the colloquium and reflects the central importance that the dispersion of particles in a flow has in various geophysical and environmental problems. The spreading of aerosols and soot in the air, the growth and dispersion of plankton blooms in seas and oceans, or the transport of sediment in rivers, estuaries and coastal regions are striking examples.
In this translation of the German edition, the authors provide insight into the numerical simulation of fluid flow. Using a simple numerical method as an expository example, the individual steps of scientific computing are presented: the derivation of the mathematical model; the discretization of the model equations; the development of algorithms; parallelization; and visualization of the computed data. In addition to the treatment of the basic equations for modeling laminar, transient flow of viscous, incompressible fluids - the Navier-Stokes equations - the authors look at the simulation of free surface flows; energy and chemical transport; and turbulence. Readers are enabled to write their own flow simulation program from scratch. The variety of applications is shown in several simulation results, including 92 black-and-white and 18 color illustrations. After reading this book, readers should be able to understand more enhanced algorithms of computational fluid dynamics and apply their new knowledge to other scientific fields.