Statistical theory and modeling for turbulent flows (2000)
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Flow Measurement and Instrumentation 13 (2002) 53–54 www.elsevier.com/locate/flowmeasinst Book review Statistical theory and modeling for turbulent flows (2000) By P.A. Durbin and B.A. Pettersson Reif. Wiley, Chich- ester, ISBN 0471497444, £29.95 A number of new texts on turbulent flows have appeared in the last five years or so, each with its own particular slant and objectives. In this book, one of the most recent, the authors’ declared, and rather unique objective is to provide ‘a solid background for those working’ in the field of computational fluid dynamics, enabling them to determine ‘whether a particular (turbulence) model is suited to computing given flow phenomena’. With the exploding use of Computational Fluid Dynamics (CFD) in industry and the often crucial importance of turbulence in the particular flow being computed, this is a splendid objective. Too often, such codes are used rather like black boxes, with little thought being given to the possible effects of inadequacies in the turbulence model. Given the authors’ objective, it is no surprise that the text differs from most, in that the emphasis is on the bases and, importantly, the failings of the more common turbulence models. But they provide plenty of physical insight and succeed well in avoiding the pitfall of a dry exposition. Perhaps this is partly because, like many books of its kind, it grew out of lec- ture notes for graduate courses — in this case at Stanford University; students often provide feedback crucial to honing ones arguments and adjusting ones material! Attention is concentrated particularly on the single-point statistical closures which are so ubiquitous in practice and the authors make only passing reference to the more research-oriented turbulence simulation techniques like Direct and Large Eddy Simulation. The book is split helpfully into three major sections. After an initial chapter containing a largely qualitative introduction on the nature of turbulence and the closure problem, Part I — about 40% of the total — starts with a chapter on the necessary mathematical and statistical tools. This includes a review of tensors and, unusually, a section on co-ordinate transformation. The former is a useful precurser to much of the rest of the book, but the latter is presumably only included for completeness, recognising perhaps that some readers might actually want to implement turbulence models into codes of their own. Later chapters cover Reynolds averaging, a review of parallel and self-similar shear flows (including some material on heat and mass transfer) and a discussion of structures, vorticity and dissipation. Overall, Part I is much less complete than corresponding discussions in other recent texts, but provides a satisfactory basis for Part II, which is really the central thrust of the book. Single point closure modelling is discussed in the three chapters comprising Part II — roughly the next 40% of the book. There are now over 100 available tur- bulence models so it is not surprising that the authors make no attempt to review even a significant subset of these. After an initial brief summary of integral and mix- ing length models, they concentrate rather on a full expo- sition of the k-e model (14 pages) and the basics of second moment closures (SMCs, 32 pages), with brief mention of some popular variants (e.g. the k-e and the Spalart–Allmaras eddy-viscosity transport models or, in the case of SMCs, the v 2 f model). Their approach is to underline the theoretical bases and consequent weak- nesses of the models; this is done in much more detail than is usual and includes illuminating illustrations via analytical solutions and/or comparisons between compu- tation and experiment. Some of the more common engin- eering ‘fix-ups’ to the cruder models are described and chapter 7 concludes with a number of examples of SMC computations for flows which could not be adequately predicted with standard eddy-viscosity closures. Part II closes with a chapter on what the authors term ‘Advanced Topics’. This includes further discussion of some of the basic modelling principles (e.g. Galilean invariance and realizability), a fuller exposition of mov- ing equilibrium solutions of second moment closures (i.e. solutions in which the rates of change of all compo- nents of the Reynolds stress tensor are proportional to the rate of change of total turbulence energy) and con- sideration of active and passive scalar flux modelling. Throughout this second part of the book, some of the authors’ particular interests are more clearly seen. It is perhaps here that, in their own words in the Preface, the ‘authors (will) put their own slant on the contents’. So, for example, presentation (in Chapter 6) of the well- known failure of the k-e model to respond appropriately to strong normal strains — what the authors here call ‘the stagnation point anomaly’—the unusually full dis- cussion of how models should embody the various influences of wall effects (in Chapter 7) and the demon- stration of bifurcation behaviour in solutions from non- linear eddy viscosity models (in Chapter 8) are all clearly influenced by the authors’ previous thought on these top- ics. Other authors might have emphasised different
Transcript of Statistical theory and modeling for turbulent flows (2000)
Flow Measurement and Instrumentation 13 (2002) 53–54www.elsevier.com/locate/flowmeasinst
Book review
Statistical theory and modeling for turbulent flows(2000)By P.A. Durbin and B.A. Pettersson Reif. Wiley, Chich-ester, ISBN 0471497444, £29.95
A number of new texts on turbulent flows haveappeared in the last five years or so, each with its ownparticular slant and objectives. In this book, one of themost recent, the authors’ declared, and rather uniqueobjective is to provide ‘a solid background for thoseworking’ in the field of computational fluid dynamics,enabling them to determine ‘whether a particular(turbulence) model is suited to computing given flowphenomena’. With the exploding use of ComputationalFluid Dynamics (CFD) in industry and the often crucialimportance of turbulence in the particular flow beingcomputed, this is a splendid objective. Too often, suchcodes are used rather like black boxes, with little thoughtbeing given to the possible effects of inadequacies in theturbulence model. Given the authors’ objective, it is nosurprise that the text differs from most, in that theemphasis is on the bases and, importantly, the failings ofthe more common turbulence models. But they provideplenty of physical insight and succeed well in avoidingthe pitfall of a dry exposition. Perhaps this is partlybecause, like many books of its kind, it grew out of lec-ture notes for graduate courses — in this case at StanfordUniversity; students often provide feedback crucial tohoning ones arguments and adjusting ones material!Attention is concentrated particularly on the single-pointstatistical closures which are so ubiquitous in practiceand the authors make only passing reference to the moreresearch-oriented turbulence simulation techniques likeDirect and Large Eddy Simulation.
The book is split helpfully into three major sections.After an initial chapter containing a largely qualitativeintroduction on the nature of turbulence and the closureproblem, Part I — about 40% of the total — starts witha chapter on the necessary mathematical and statisticaltools. This includes a review of tensors and, unusually,a section on co-ordinate transformation. The former is auseful precurser to much of the rest of the book, butthe latter is presumably only included for completeness,recognising perhaps that some readers might actuallywant to implement turbulence models into codes of theirown. Later chapters cover Reynolds averaging, a reviewof parallel and self-similar shear flows (including somematerial on heat and mass transfer) and a discussion of
structures, vorticity and dissipation. Overall, Part I ismuch less complete than corresponding discussions inother recent texts, but provides a satisfactory basis forPart II, which is really the central thrust of the book.
Single point closure modelling is discussed in thethree chapters comprising Part II — roughly the next40% of the book. There are now over 100 available tur-bulence models so it is not surprising that the authorsmake no attempt to review even a significant subset ofthese. After an initial brief summary of integral and mix-ing length models, they concentrate rather on a full expo-sition of the k-e model (14 pages) and the basics ofsecond moment closures (SMCs, 32 pages), with briefmention of some popular variants (e.g. thek-e and theSpalart–Allmaras eddy-viscosity transport models or, inthe case of SMCs, thev2�f model). Their approach isto underline the theoretical bases and consequent weak-nesses of the models; this is done in much more detailthan is usual and includes illuminating illustrations viaanalytical solutions and/or comparisons between compu-tation and experiment. Some of the more common engin-eering ‘fix-ups’ to the cruder models are described andchapter 7 concludes with a number of examples of SMCcomputations for flows which could not be adequatelypredicted with standard eddy-viscosity closures. Part IIcloses with a chapter on what the authors term‘Advanced Topics’. This includes further discussion ofsome of the basic modelling principles (e.g. Galileaninvariance and realizability), a fuller exposition of mov-ing equilibrium solutions of second moment closures(i.e. solutions in which the rates of change of all compo-nents of the Reynolds stress tensor are proportional tothe rate of change of total turbulence energy) and con-sideration of active and passive scalar flux modelling.
Throughout this second part of the book, some of theauthors’ particular interests are more clearly seen. It isperhaps here that, in their own words in the Preface, the‘authors (will) put their own slant on the contents’. So,for example, presentation (in Chapter 6) of the well-known failure of thek-e model to respond appropriatelyto strong normal strains — what the authors here call‘the stagnation point anomaly’—the unusually full dis-cussion of how models should embody the variousinfluences of wall effects (in Chapter 7) and the demon-stration of bifurcation behaviour in solutions from non-linear eddy viscosity models (in Chapter 8) are all clearlyinfluenced by the authors’ previous thought on these top-ics. Other authors might have emphasised different
54 Book review / Flow Measurement and Instrumentation 13 (2002) 53–54
points, but that by no means invalidates what is includedhere. Indeed, it could be argued that proper appreciationof these particular issues (and others discussed) is, infact, crucial in understanding when and why commonmodels fail.
The final 20% of the book, Part III, first summarises(in Chapter 9) basic Fourier Transform relationships andthen presents a fairly classical, albeit brief, description ofhomogenous, isotropic turbulence in terms of the three-dimensional energy spectrum (Chapter 10) and itsrelated functions. Some discussion of the causes of theenergy cascade, through consideration of the triad inter-actions made explicit in the spectral evolution equation,is given in Chapter 10 and the book closes with a chapteron rapid distortion theory (RDT). This latter, again, is anindication of the authors’ particular interests but containshelpful discussion which would not normally be con-sidered by CFD practitioners — of, for example, howRapid Distortion Theory (RDT) can be employed forstrongly inhomogeneous situations like wall turbulence.Like Part I, this part of the book is by no means compre-hensive; there is much that is missing, but it does providea sound basis for more deeper study if the reader sowishes.
Any text on turbulence which aims to provide genuineunderstanding cannot avoid mathematics. For this book,it would be particularly important for readers to perusethe Preface before attacking the body of the text. Theauthors state clearly that for a first course on turbulencefor engineering students certain sections would best beomitted; the more ‘advanced material is intended for pro-spective researchers’ . This is wise advice. Practitionersin industry, who are perhaps those who most clearly
often need an education enabling them to determine‘whether a particular (turbulence) model is suited tocomputing given flow phenomena’ are perhaps unlikelyto turn first to this book, particularly if they have noprior knowledge of turbulence. But it does, in fact, con-tain much that they would find illuminating providedthey are prepared to dig deep and select sections appro-priately.
It is much more likely that graduate students undertak-ing courses which include CFD elements will turn to thistext and, for them, it has much to commend it and shouldcertainly be on recommended reading lists. Each chapteris followed by a set of (usually some dozen or so)example questions, some of which require facility withtensors and many of which provide further physicalillumination. The reference list is reasonably compre-hensive, the book is generally well-written and well-illustrated, and it does not have enough typographicalerrors to annoy this reviewer.
In conclusion, although this book is not such a com-prehensive exposition of turbulence as can be found else-where, it provides an excellent introduction to single-point closure modelling. It should prove helpful to allstudents beginning to think about turbulence and itsmodelling and it will be especially valuable for thosewho want to understand the bases and the failings of theusual Reynolds-averaged one-point models.
Ian P. Castro,University of Southampton, School of EngineeringSciences, Highfield, Southampton SO17 1BJ, UK
PII: S0955-5986(02)00014-6
