Download or read book Modeling of Scalar Probability Density Functions in Turbulent Flows written by Ashok Kumara Varma and published by . This book was released on 1978 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt: Turbulent flows involving chemical reactions are a basic feature of many combustion and propulsion systems. The development of calculation procedures for turbulent reacting flows requires the understanding and modeling of the coupling between turbulence and combustion. Second-order closure modeling of turbulent flows provides a convenient framework for studying these interactions between turbulence and chemical reactions. Models for the scalar probability density function (pdf) have to be developed to achieve closure of turbulent transport equations for mixing and reacting flows. A delta function 'typical eddy' model has been developed for the joint pdf of the scalar variables. It has been demonstrated that delta functions are a necessary part of pdf's in order to attain the extremums of the statistical constraints on the moments. The statistical bounds on a number of moments of interest have been derived. It has been proven that a rational pdf composed of a set of delta functions alone can always be constructed at any point within the statistically valid moment space. The model provides a good representation of actual pdf's in two-species, variable-density mixing flows. The model has been directly compared to experimental pdf measurements and good agreement for higher-order moments has been demonstrated. It can be shown that the delta function pdf model is significantly simpler than other proposed pdf models and is more than adequate for the closure of the transport equations. (Author).

Download or read book Modelling of Scalar Probability Density Functions in Turbulent Flows written by Ashok K.. Varma and published by . This book was released on 1978 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Second Order Closure Modeling of Variable Density Turbulent Flows written by Ashok Kumara Varmer and published by . This book was released on 1979 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mixing and Chemical reactions under turbulent flow conditions are a basic feature of the energy release processes in many combustion and propulsion systems. The development of predictive calculation procedures for these systems requires the understanding and modeling of coupling between turbulence and various physical and chemical processes. Second-order closure modeling of turbulent flows provides a rational framework for studying these interactions. Models for the scalar probability density function (pdf) have to be developed to achieve closure of turbulent transport equations for mixing and reacting flows. A delta function 'typical eddy' pdf model for two species flows has been developed and incorporated into a complete second-order closure computer program. The program has been used to study uniform and variable density flowfields and the model predictions have been compared to experimental measurements. The modeling of turbulence dynamics for variable density flows requires further improvement. However, the importance of modeling the higher-order scalar correlations has been demonstrated. A number of statistical constraints on three species flowfields have also been derived. These will be useful in the development of the 'typical eddy' pdf modelfor reacting flows. (Author).

Download or read book The Statistical Dynamics of Turbulence written by Jovan Jovanovic and published by Springer Science & Business Media. This book was released on 2004-02-09 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: This short but complicated book is very demanding of any reader. The scope and style employed preserve the nature of its subject: the turbulence phe nomena in gas and liquid flows which are believed to occur at sufficiently high Reynolds numbers. Since at first glance the field of interest is chaotic, time-dependent and three-dimensional, spread over a wide range of scales, sta tistical treatment is convenient rather than a description of fine details which are not of importance in the first place. When coupled to the basic conserva tion laws of fluid flow, such treatment, however, leads to an unclosed system of equations: a consequence termed, in the scientific community, the closure problem. This is the central and still unresolved issue of turbulence which emphasizes its chief peculiarity: our inability to do reliable predictions even on the global flow behavior. The book attempts to cope with this difficult task by introducing promising mathematical tools which permit an insight into the basic mechanisms involved. The prime objective is to shed enough light, but not necessarily the entire truth, on the turbulence closure problem. For many applications it is sufficient to know the direction in which to go and what to do in order to arrive at a fast and practical solution at minimum cost. The book is not written for easy and attractive reading.

Download or read book PDF Modeling of Turbulent Flows on Unstructured Grids written by József Bakosi and published by . This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In probability density function (PDF) methods of turbulent flows, the joint PDF of several flow variables is computed by numerically integrating a system of stochastic differential equations for Lagrangian particles. Because the technique solves a transport equation for the PDF of the velocity and scalars, a mathematically exact treatment of advection, viscous effects and arbitrarily complex chemical reactions is possible; these processes are treated without closure assumptions. A set of algorithms is proposed to provide an efficient solution of the PDF transport equation modeling the joint PDF of turbulent velocity, frequency and concentration of a passive scalar in geometrically complex configurations. An unstructured Eulerian grid is employed to extract Eulerian statistics, to solve for quantities represented at fixed locations of the domain and to track particles. All three aspects regarding the grid make use of the finite element method. Compared to hybrid methods, the current methodology is stand-alone, therefore it is consistent both numerically and at the level of turbulence closure without the use of consistency conditions. Since both the turbulent velocity and scalar concentration fields are represented in a stochastic way, the method allows for a direct and close interaction between these fields, which is beneficial in computing accurate scalar statistics. Boundary conditions implemented along solid bodies are of the free-slip and no-slip type without the need for ghost elements. Boundary layers at no-slip boundaries are either fully resolved down to the viscous sublayer, explicitly modeling the high anisotropy and inhomogeneity of the low-Reynolds-number wall region without damping or wall-functions or specified via logarithmic wall-functions. As in moment closures and large eddy simulation, these wall-treatments provide the usual trade-off between resolution and computational cost as required by the given application. Particular attention is focused on modeling the dispersion of passive scalars in inhomogeneous turbulent flows. Two different micromixing models are investigated that incorporate the effect of small scale mixing on the transported scalar: the widely used interaction by exchange with the mean and the interaction by exchange with the conditional mean model. An adaptive algorithm to compute the velocity-conditioned scalar mean is proposed that homogenizes the statistical error over the sample space with no assumption on the shape of the underlying velocity PDF. The development also concentrates on a generally applicable micromixing timescale for complex flow domains. Several newly developed algorithms are described in detail that facilitate a stable numerical solution in arbitrarily complex flow geometries, including a stabilized mean-pressure projection scheme, the estimation of conditional and unconditional Eulerian statistics and their derivatives from stochastic particle fields employing finite element shapefunctions, particle tracking through unstructured grids, an efficient particle redistribution procedure and techniques related to efficient random number generation. The algorithm is validated and tested by computing three different turbulent flows: the fully developed turbulent channel flow, a street canyon (or cavity) flow and the turbulent wake behind a circular cylinder at a sub-critical Reynolds number. The solver has been parallelized and optimized for shared memory and multi-core architectures using the OpenMP standard. Relevant aspects of performance and parallelism on cache-based shared memory machines are discussed and presented in detail. The methodology shows great promise in the simulation of high-Reynolds-number incompressible inert or reactive turbulent flows in realistic configurations.

Download or read book Developments in the Probability Density Function Method for Turbulent Flows written by Daniel Connell Haworth and published by . This book was released on 1986 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Velocity wave vector Probability Density Function Models for Inhomogeneous Turbulent Flows written by Paul Richard Van Slooten and published by . This book was released on 1998 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: Constructs and implements turbulence models for probability density function (PDF) methods for the computation of turbulent reacting flows. Treats the processes of convection and reaction without further assumptions at this level of closure, while the effects of the fluctuation pressure gradient and the diffusion of the fluctuating velocity by molecular viscosity require modeling. Effects correspond to the pressure-rate-of-strain correlations, the pressure transport, and the dissipation tensor in the Reynolds stress equation. Investigates models for each of these variables.

Download or read book Turbulent Combustion Modeling written by Tarek Echekki and published by Springer Science & Business Media. This book was released on 2010-12-25 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: Turbulent combustion sits at the interface of two important nonlinear, multiscale phenomena: chemistry and turbulence. Its study is extremely timely in view of the need to develop new combustion technologies in order to address challenges associated with climate change, energy source uncertainty, and air pollution. Despite the fact that modeling of turbulent combustion is a subject that has been researched for a number of years, its complexity implies that key issues are still eluding, and a theoretical description that is accurate enough to make turbulent combustion models rigorous and quantitative for industrial use is still lacking. In this book, prominent experts review most of the available approaches in modeling turbulent combustion, with particular focus on the exploding increase in computational resources that has allowed the simulation of increasingly detailed phenomena. The relevant algorithms are presented, the theoretical methods are explained, and various application examples are given. The book is intended for a relatively broad audience, including seasoned researchers and graduate students in engineering, applied mathematics and computational science, engine designers and computational fluid dynamics (CFD) practitioners, scientists at funding agencies, and anyone wishing to understand the state-of-the-art and the future directions of this scientifically challenging and practically important field.

Download or read book Statistical Theory and Modeling for Turbulent Flows written by P. A. Durbin and published by John Wiley & Sons. This book was released on 2011-06-28 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing a comprehensive grounding in the subject of turbulence, Statistical Theory and Modeling for Turbulent Flows develops both the physical insight and the mathematical framework needed to understand turbulent flow. Its scope enables the reader to become a knowledgeable user of turbulence models; it develops analytical tools for developers of predictive tools. Thoroughly revised and updated, this second edition includes a new fourth section covering DNS (direct numerical simulation), LES (large eddy simulation), DES (detached eddy simulation) and numerical aspects of eddy resolving simulation. In addition to its role as a guide for students, Statistical Theory and Modeling for Turbulent Flows also is a valuable reference for practicing engineers and scientists in computational and experimental fluid dynamics, who would like to broaden their understanding of fundamental issues in turbulence and how they relate to turbulence model implementation. Provides an excellent foundation to the fundamental theoretical concepts in turbulence. Features new and heavily revised material, including an entire new section on eddy resolving simulation. Includes new material on modeling laminar to turbulent transition. Written for students and practitioners in aeronautical and mechanical engineering, applied mathematics and the physical sciences. Accompanied by a website housing solutions to the problems within the book.

Download or read book Probability Density Function Modeling of Turbulent Non reactive and Reactive Spray Flows written by Hai-Wen Ge and published by . This book was released on 2006 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book On the Coalescence dispersion Modeling of Turbulent Molecular Mixing written by Peyman Givi and published by . This book was released on 1987 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Novel Strategy for Numerical Simulation of High Speed Turbulent Reacting Flows written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-06-20 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: The objective of this research is to improve and implement the filtered mass density function (FDF) methodology for large eddy simulation (LES) of high-speed reacting turbulent flows. We have just completed Year 1 of this research. This is the Final Report on our activities during the period: January 1, 2003 to December 31, 2003. 2002. In the efforts during the past year, LES is conducted of the Sandia Flame D, which is a turbulent piloted nonpremixed methane jet flame. The subgrid scale (SGS) closure is based on the scalar filtered mass density function (SFMDF) methodology. The SFMDF is basically the mass weighted probability density function (PDF) of the SGS scalar quantities. For this flame (which exhibits little local extinction), a simple flamelet model is used to relate the instantaneous composition to the mixture fraction. The modelled SFMDF transport equation is solved by a hybrid finite-difference/Monte Carlo scheme. Sheikhi, M. R. H. and Drozda, T. G. and Givi, P. Langley Research Center

Download or read book Calculations of Turbulent Reacting Flows Using PDF Methods written by David Henry Rowinski and published by . This book was released on 2013 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents applications of the probability density function (PDF) method to several recently-developed turbulent flows, and the implementation and assessment of several sub-models. A series of lean piloted premixed jet flames (in order of lowest to highest jet bulk velocity: PM1-50, PM1-100, PM1150, and PM1-200) is first studied using a Reynolds-Averaged Navier-Stokes (RANS) based PDF method. These calculations use diagnostic testing and thorough parametric studies of models to show that the standard models overpredict the reaction rate in the flames PM1-150 and PM1-200. The nature of the combustion in these flames is examined through comparison to simpler combustion models, and it is found to be similar to laminar non-premixed flames. These same flames are then investigated further using both RANS-PDF and the recently developed Large Eddy Simulation (LES) PDF method. Simple models for molecular diffusion and combustion are tested and implemented in the RANS-PDF calculations. In the LES-PDF calculations, the effects of differential diffusion and the mixing model constant, C M, are both examined, and the calculations are found to be very sensitive to the value of C M . This study yields substantially improved calculations of all the flames. In particular, the study of C M shows strong evidence that larger values of C M are necessary for flames PM1-150 and PM1-200. The modeling of molecular mixing is investigated further through a study of a non-reacting turbulent jet flow with three inflowing streams. This study presents the unique opportunity to compare the scalar dissipation rate and conditional diffusion from the calculations to experimental data. In the RANS-PDF calculations of this flow, three classic mixing models are evaluated. The joint scalar PDF's are very sensitive to the choice of mixing model and show a wide variability from the measurements. Only the Euclidean Minimum Spanning Tree (EMST) produces compositions which lie very close to the slow manifold identified in the experimental work. LES calculations of the same flow are performed, and the dissipation rate and conditional diffusion are calculated. The resolved scalar dissipation rate is found to be in good agreement with the experimental data, but depends strongly on the resolution; the total dissipation rate from the RANS-PDF and LES calculations indicates significantly larger scalar dissipation rates than those measured experimentally. Lastly, LES-PDF calculations of the same flow yield joint-PDF's in very good agreement with the experimental data, and are far-improved from those of any mixing model studied with RANS-PDF. The attenuation of variance production model is introduced for LES-PDF and tested in this flow. This new model results in an additional dissipation of scalar variance and yields calculations of improved accuracy on coarse grids.

Download or read book Modeling of Turbulent Reacting Flows with Probability Density Functions for Scramjet Applications written by Robert A. Baurle and published by . This book was released on 1995 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Probability Density Functions in Turbulent Channel Flow written by Surya P. G. Dinavahi and published by . This book was released on 1992 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Advances in Modeling Mixing and Molecular Transport in Probability Density Function Methods of Turbulent Reacting Flows written by Sharadha Viswanathan and published by . This book was released on 2011 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modeling of turbulent reacting flow problems using Probability Density Function (PDF) methods yields transport and reaction in closed form while the processes related to the conditional dissipation of species compositions need to be closed using mixing models. First, we study the dispersion from line sources in decaying grid turbulence using a modified form of the Interaction by Exchange with the Conditional Mean (IECM) mixing model. These flows pose a significant challenge to statistical models, because the scalar length scale (of the initial plume) is much smaller than the turbulence integral scale. Consequently, this necessitates incorporating the effects of molecular diffusion in order to model laboratory experiments. The effects of molecular diffusion are modeled by adding a conditional mean scalar drift term and a laminar wake model is used to obtain an analytic expression for the mixing timescale at small times which is subsequently used as part of a general specification of the mixing timescale. Based on this modeling, PDF calculations are performed, and comparison is made primarily with existing experimental and numerical data on single and multiple line sources. A heated mandoline is also considered. This establishes the validity of the proposed model and the significant effect of molecular diffusion on the decay of scalar fluctuations. Next, various numerical implementations of mixing and molecular transport in LES/PDF studies of turbulent reacting flows are evaluated for accuracy using the Method of Manufactured Solutions (MMS). Mixing is modeled using the Interaction by Exchange with the Mean (IEM) model and the effects of molecular transport are incorporated as a mean drift term in the mixing step. This methodology avoids spurious production of scalar variance and also allows direct incorporation of differential diffusion effects. The implementation of the mixing model is shown to be successful in capturing the effects of differential diffusion accurately with the additional property of satisfying detailed conservation and realizability of species mass fractions. Additionally, we present a new variance reduction technique by way of an implicit smoothing methodology. This smoothing scheme is shown to satisfy conservation, boundedness and regularity criteria. Moreover, for an appropriate choice of the smoothing length scale, significant improvements in accuracy can be achieved for an incremental increase in computational cost. Also, it is shown that with smoothing, the bias and statistical errors due to finite number of particles in the Lagrangian Monte Carlo simulations now scale as N[-]1 and tot N[-]1/2 respectively, where Ntot is the total number of particles in the computatot tional domain. Finally, the numerical implementations described are applied to the study of a turbulent reacting jet flame (Sandia Flame D). It is shown that this implementation yields a consistent formulation between the LES and the PDF methods. Further, cross-validation is presented as a numerical technique to assist in the automatic choice of the smoothing length scale and the application of crossvalidation to smoothing of PDF fields is shown to improve the consistency between the LES and PDF fields.

Download or read book Closure Strategies for Turbulent and Transitional Flows written by Brian Edward Launder and published by Cambridge University Press. This book was released on 2002-02-21 with total page 774 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher Description