Moukalled F., Mangani L., Darwish M. The finite volume method in computational fluid dynamics. An advanced introduction with OpenFOAM and Matlab (Moukalled F., Mangani L., Darwish M. The finite volume method in computational fluid dynamics. An advanced introduction with OpenFOAM and Matlab.pdf), страница 5

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .17.1 Turbulence Modeling. . . . . . . . . . . . . . . . . . . . . . . . . .17.2 Reynolds Averaging . . . . . . . . . . . . . . . . . . . . . . . . . .17.2.1Time Averaging . . . . . . . . . . . . .

. . . . . . . . .17.2.2Spatial Averaging . . . . . . . . . . . . . . . . . . . . .17.2.3Ensemble Averaging . . . . . . . . . . . . . . . . . . .17.2.4Averaging Rules . . . . . . . . . . . . . . . . . . . . . .17.2.5Incompressible RANS Equations . . . . . . . . . . .17.3 Boussinesq Hypothesis. . . .

. . . . . . . . . . . . . . . . . . . . .17.4 Turbulence Models . . . . . . . . . . . . . . . . . . . . . . . . . . .17.5 Two-Equation Turbulence Models . . . . . . . . . . . . . . . . .17.5.1Standard k − ɛ Model . . . . . . . . . . . . . . . . . .17.5.2The k − ω Model . . . . . . . . . . . . . .

. . . . . . .17.5.3The Baseline (BSL) k − ω Model . . . . . . . . . .17.5.4The Shear Stress Transport (SST) k − ω Model17.6 Summary of Incompressible Turbulent Flow Equations . .17.7 Discretization of the Turbulent Flow Equations . . . .

. . . .17.7.1The Discretized Form of the k Equation . . . . . .17.7.2The Discretized Form of the ɛ Equation . . . . . .17.7.3The Discretized Form of the ω Equation . . . . .17.8 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . .17.8.1Modeling Flow Near the Wall. . . . . . . . .

. . . .17.8.2Standard Wall Functions . . . . . . . . . . . . . . . .17.8.3Improved Wall Functions . . . . . . . . . . . . . . . .17.8.4Scalable Wall Functions . . . . . . . . . . . . . . . . .17.8.5Wall Boundary Conditions for LowReynolds Number Models . . . . . . . . . . . . . .

.17.8.6Automatic Near-Wall Treatment . . . . . . . . . . .17.8.7Near-Wall Heat Transfer . . . . . . . . . . . . . . . .17.8.8Other Boundary Conditions . . . . . . . . . . . . . .17.9 Calculating Normal Distance to the Wall . . . . . . . . . . . .17.10 Computational Pointers . . . . .

. . . . . . . . . . . . . . . . . . .17.10.1 The k − ɛ Model . . . . . . . . . . . . . . . . . . . . . .17.10.2 The SST k – ω Model . . . . . . . . . . . . . . . . . .17.10.3 simpleFoamTurbulent. . . . . . . . . . . . . . . . . . .17.11 Closure . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . .17.12 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................693693696696696697697697699700700700702704705707707708708709710710711716718....................................71972072172272372572773473874074074218 Boundary Conditions in OpenFOAM® and uFVM .

. . . . . . . . . . .18.1 Boundary Conditions in OpenFOAM® . . . . . . . . . . . . . . . . .18.2 Boundary Condition Customization . . . . . . . . . . . . . . . . . . .745745747Contentsxxi18.3 Development of a New BC: No Slip Wall Condition .18.4 The No-Slip Boundary Condition in uFVM . . . . . . .18.5 Closure . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . .Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .........................752756759759......................................................76176176176376877077377677620 Closing Remarks . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . .777Appendix: uFVM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .77919 An OpenFOAM® Turbulent Flow Application .19.1 Introduction . . . . . . . . . . . . . . . . . . . . .19.2 The Ahmed Bluff Body . . . . . . . . . . . .

.19.3 Domain Discretization . . . . . . . . . . . . . .19.3.1Initial and Boundary Conditions19.3.2Systems Files . . . . . . . . . . . . .19.3.3Running the Solver . . . . . . . . .19.4 Conclusion . . . . . . . . . . . . . . . . . . . . . .References. .

. . . . . . . . . . . . . . . . . . . . . . . . . .........................................................................About the AuthorsFadl Moukalled received his Ph.D. in Mechanical Engineering from LouisianaState University in 1987. During that same year, he joined the MechanicalEngineering Department at the American University of Beirut where currently heserves as a professor. His research interests cover several aspects of the finitevolume method and its use in computational fluid dynamics.

As a founding memberof the CFD Group at AUB, he worked on convection schemes, pressure-basedsegregated algorithms for incompressible and compressible flows, adaptive gridmethods, multigrid methods, transient schemes for free surface flows, multiphaseflows, and fully coupled pressure-based solvers for incompressible, compressible,and multiphase flows.Luca Mangani received his Ph.D. form the University of Florence in 2006, wherehe worked on the development of a state-of-the-art turbo machinery code inOpenFOAM® for heat transfer and combustion analysis. After three years ofpostdoc work, he joined the Lucerne University of Applied Sciences and Arts assenior research and chief engineer for CFD simulations.

Since 2014, he is serving asan associate professor at the Fluid Mechanics and Hydro-machines Department,where he manages a variety of projects with industrial partners aimed at developingadvanced and novel CFD tools. His research interests include pressure- and densitybased solvers, segregated and fully coupled algorithms, fluid-structure interaction(FSI), turbulence, and conjugate heat transfer modeling.Marwan Darwish received his Ph.D. in Materials Processing from BRUNELUniversity in 1991. He worked at the BICOM institute for one year as a postdocbefore joining the Mechanical Engineering Department at the American Universityof Beirut in 1992, where he currently serves as a professor. His research interestcovers a range of topics including solidification, advanced numerics, free surfaceflow, high-resolution schemes, multiphase flows, coupled algorithms, and algebraicmultigrid.

He is a founding member of the CFD Group at AUB.xxiiiPart IFoundationChapter 1IntroductionAbstract This chapter presents an overview of the book. It starts with a briefdescription of Computational Fluid Dynamics (CFD) and its use as a core designtool in a whole class of applications, and of the Finite Volume Method (FVM) andits role in the advancement of CFD.

The chapter ends with a discussion of the bookphilosophy, structure, and content.1.1What Is Computational Fluid Dynamics (CFD)“We are literally at a significant point in history. A third branch of the scientificmethod, computer simulation, is emerging as a day-to-day tool. It is taking its placenext to experimental development and mathematical theory as a way to new discoveries in science and engineering”. This was part of the speech of JohnRollwagen, chairman and CEO of Cray Research, to the opening session ofSupercomputing 89.While it is common to refer to this or similar statements about the importance ofsimulation tools and techniques to the advancement of science and technology ingeneral, it is now very clear that the use of simulation tools has become crucial tothe development of a wide range of everyday technologies.

In fact, numericalsimulation tools nowadays play the role of technology enablers.Computational Fluid Dynamics (CFD) is one such tool. Even though the impetusto its development was initially provided by some sections within the aeronauticsand aerospace industry, it has grown to become an essential tool in a range of otherdesign intensive industries such as the automotive, power generation, chemical,nuclear, and marine industries, to cite a few. Over the past decade newer industrieshave joined the ranks of heavy CFD users: for example in the electronics industryCFD is employed to optimize energy systems and heat transfer for the cooling ofelectronic devices, in the biomedical industry CFD is now a core development andvalidation tool for medical applications, and in the building industry CFD is used in© Springer International Publishing Switzerland 2016F.

Moukalled et al., The Finite Volume Method in Computational Fluid Dynamics,Fluid Mechanics and Its Applications 113, DOI 10.1007/978-3-319-16874-6_1341IntroductionHVAC (heating, ventilating, and air conditioning), in fire simulation, and in airquality assessment.This has happened in little over two decades since the statement of JohnRollwagen was made and over four decades since the development of the seminalSIMPLE algorithm by the CFD group of Brian Spalding at Imperial College in theearly 70s.Computational Fluid Dynamics is just one of the later Computer AidedEngineering tools that has gone mainstream. It has joined a well-established set oftools, such as the Finite Element Analysis (FEA) for Solid Mechanics and Vibrationthat has been part of the engineering design cycle since the mid 80s.

The reason forthis delay is the complexity of the equations that need to be solved. At their center isthe Navier-Stokes equation that amazingly enough models accurately a whole set offlow phenomena from turbulent or laminar single phase incompressible flows, tocompressible all-speed flows, and all the way to multiphase flows.Amongst the numerical methods used to implement CFD, the Finite VolumeMethod has come to play a unique role.1.2What Is the Finite Volume MethodThe Finite Volume Method (FVM) is a numerical technique that transforms thepartial differential equations representing conservation laws over differential volumes into discrete algebraic equations over finite volumes (or elements or cells).

Ina similar fashion to the finite difference or finite element method, the first step in thesolution process is the discretization of the geometric domain, which, in the FVM,is discretized into non-overlapping elements or finite volumes. The partial differential equations are then discretized/transformed into algebraic equations by integrating them over each discrete element. The system of algebraic equations is thensolved to compute the values of the dependent variable for each of the elements.In the finite volume method, some of the terms in the conservation equation areturned into face fluxes and evaluated at the finite volume faces.