Direct Numerical Simulation Of Turbulent Flow In A Curved Channel

This book provides students and researchers in fluid engineering with an up-to-date overview of turbulent flow research in the areas of simulation and modeling. A key element of the book is the systematic, rational development of turbulence closure models and related aspects of modern turbulent flow theory and prediction. Starting with a review of the spectral dynamics of homogenous and inhomogeneous turbulent flows, succeeding chapters deal with numerical simulation techniques, renormalization group methods and turbulent closure modeling. Each chapter is authored by recognized leaders in their respective fields, and each provides a thorough and cohesive treatment of the subject.

This book allows readers to tackle the challenges of turbulent flow problems with confidence. It covers the fundamentals of turbulence, various modeling approaches, and experimental studies. The fundamentals section includes isotropic turbulence and anistropic turbulence, turbulent flow dynamics, free shear layers, turbulent boundary layers and plumes. The modeling section focuses on topics such as eddy viscosity models, standard K-E Models, Direct Numerical Stimulation, Large Eddy Simulation, and their applications. The measurement of turbulent fluctuations experiments in isothermal and stratified turbulent flows are explored in the experimental methods section. Special topics include modeling of near wall turbulent flows, compressible turbulent flows, and more.

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.

obtained are still severely limited to low Reynolds numbers (about only one decade better than direct numerical simulations), and the interpretation of such calculations for complex, curved geometries is still unclear. It is evident that a lot of work (and a very significant increase in available computing power) is required before such methods can be adopted in daily's engineering practice. I hope to l"Cport on all these topics in a near future. The book is divided into six chapters, each· chapter in subchapters, sections and subsections. The first part is introduced by Chapter 1 which summarizes the equations of fluid mechanies, it is developed in C~apters 2 to 4 devoted to the construction of turbulence models. What has been called "engineering methods" is considered in Chapter 2 where the Reynolds averaged equations al"C established and the closure problem studied (§1-3). A first detailed study of homogeneous turbulent flows follows (§4). It includes a review of available experimental data and their modeling. The eddy viscosity concept is analyzed in §5 with the l"Csulting ~alar-transport equation models such as the famous K-e model. Reynolds stl"Css models (Chapter 4) require a preliminary consideration of two-point turbulence concepts which are developed in Chapter 3 devoted to homogeneous turbulence. We review the two-point moments of velocity fields and their spectral transforms (§ 1), their general dynamics (§2) with the particular case of homogeneous, isotropie turbulence (§3) whel"C the so-called Kolmogorov's assumptions are discussed at length.

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.