边界层理论（第九版）核心内容与方程详解

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边界层理论（第九版）核心内容与方程详解（2017_Book_Boundary-LayerTheory）

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Boundary-Layer Theory

Hermann Schlichting (Deceased) Klaus Gersten

Boundary-Layer Theory With contributions from Egon Krause and Herbert Oertel Jr.

Translated by Katherine Mayes

Ninth Edition

Hermann Schlichting (Deceased)

Institute of Fluid Mechanics

Technical University of Braunschweig Braunschweig

Germany

Klaus Gersten

Institute of Thermodynamics and Fluid Mechanics

Ruhr-University Bochum

Bochum, Nordrhein-Westfalen Germany

ISBN 978-3-662-52917-1 ISBN 978-3-662-52919-5 (eBook)

DOI 10.1007/978-3-662-52919-5

Library of Congress Control Number: 2016944848

1st edition: © McGraw-Hill New York 1955

2nd edition: © Pergamon London 1955

4th edition: © McGraw-Hill New York 1960

6th edition: © McGraw-Hill New York 1968

7th edition: © McGraw-Hill New York 1975

8th edition: © Springer-Verlag Berlin Heidelberg 2000

9th edition: © Springer-Verlag Berlin Heidelberg 2017

This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, speciﬁcally the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microﬁlms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed.

The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a speciﬁc statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made.

Typesetting: Katherine Mayes, Darmstadt and LE-TEX, Leipzig

Cover design: de ’blik, Berlin Printed on acid-free paper

This Springer imprint is published by Springer Nature

The registered company is Springer-Verlag GmbH Berlin Heidelberg

For this edition corrections have been carried out and additional impor- tant literature published in recent years have been included (66 additional references). Section 22.8 on plane turbulent wall jets has been completely rewritten. I am very thankful for valuable assistance to Prof. Dr. E. Krause, Prof. Dr. H. Oertel, Prof. Dr. W. Schneider, Prof. Dr. M. Breuer, Prof. Dr. H.-D. Papenfuß and last but not least Gertraude Odemar.

Bochum, March 2016 Klaus Gersten

According to the tradition of this book, a German edition has always been soon followed by the English translation. I am very grateful to Springer– Verlag for undertaking this version and for securing a translator. My partic- ular thanks go to Katherine Mayes for this excellent translation. In the course of the translation, some errors in the German edition were corrected and a number of additions carried out. In this connection I am very thankful to Prof. Dr. W. Schneider, Vienna, for several suggestions and improvements. I would like to thank Ursula Beitz again for her careful checking of the biblio- graphy. I hope that the English edition will attain the same positive resonance as the ninth German edition.

Bochum, May 1999 Klaus Gersten

There is no doubt that Boundary–Layer Theory by Hermann Schlichting is one of most important books within the sphere of ﬂuid mechanics to appear in the last decade. Shortly before his death, Hermann Schlichting brought out the eighth edition which he revised together with his friend and former colleague Wilhelm Riegels.

When this edition went out of print and a new edition was desired by the publishers, I was very glad to take on the task. During the ﬁfteen years I spent at the institute of my highly respected teacher Hermann Schlichting, I had already been involved with earlier editions of the book and had revised some chapters. The burden was also eased by the fact that boundary–layer theory in its widest sense has been my preferred direction of research for many years.

It quickly became clear that a complete revision was necessary; indeed this was also known to Hermann Schlichting. In the preface to the eighth edition he wrote: “Noting the systematic of our knowledge of today, it would have been desirable to fully revise this work; however such a process would have pushed back the appearance of this book by years.” Compared to the eighth edition, the literature of the last 15 years had to be taken into account and recent developments, in turbulence models for example, had to be incor- porated. In order to keep the size of the book tractable, some results – those which no longer seem so important with today’s computing potential – had to be curtailed, or in some cases, left out altogether.

Thus the necessity to completely rewrite the text emerged. The funda- mental divisions within the book were retained; as before it consists of the four major sections: basic laws of the ﬂows of viscous ﬂuids, laminar bound- ary layers, the onset of turbulence, turbulent boundary layers. However a new ﬁfth section on numerical methods in boundary–layer theory has been added.

The partition into chapters had to be somewhat modiﬁed in order to improve the style of presentation of the material. Because of the necessary restrictions on the material, the aim was to concentrate on boundary–layer theory as the theory of high Reynolds number ﬂows. Accordingly the chap- ter on “creeping ﬂows”, that is ﬂows at very small Reynolds numbers, was omitted.

It seemed natural to steer towards the style and level of presentation with the same target audience as with Hermann Schlichting.

The research area of boundary–layer theory is continuously growing, and it has become so extensive that no single person can possess a complete overview. Consequently I am extremely grateful to two colleagues who sup- ported me actively. Professor E. Krause wrote the new additional chapter on numerical methods in boundary–layer theory, and Professor H. Oertel pro- vided the revision of the section on the onset of turbulence (stability theory).

Further assistance was furnished from diﬀerent sources. I am indebted to Dr.-Ing. Peter Scha…fer and Dr.-Ing. Detlev Vieth for a great many new sample calculations. Dr. Vieth also read the entire text discerningly. I am grateful to him for numerous improving suggestions. Renate Go…lzenleuchtner deserves particular thanks for generating the ﬁgures which almost all had to be newly drawn up. I would like to thank Ursula Beitz particularly for her careful and exhaustive checking of the bibliography, while Marianne Ferdinand and Eckhard Schmidt were of ﬁrst class assistance. It was by far impossible to adopt all citations, so that it may be necessary to revert to the eighth edition for speciﬁc references to earlier pieces of work.

The printing ﬁrm of Jrg Steﬀenhagen is due particular praise for an extremely fruitful collaboration. My thanks also go to Springer–Verlag for our most agreeable work together.

I hope we have been able to carry on the work of Hermann Schlichting as he would have wished.

Bochum, October 1996 Klaus Gersten

Introduction

Short historical review

At the end of the 19th century, ﬂuid mechanics had split into two diﬀerent directions which hardly had anything more in common. On one side was the science of theoretical hydrodynamics, emanating from Euler’s equations of motion and which had been developed to great perfection. However this had very little practical importance, since the results of this so–called classical hydrodynamics were in glaring contradiction to everyday experience. This was particularly true in the very important case of pressure loss in tubes and channels, as well as that of the drag experienced by a body moved through a ﬂuid. For this reason, engineers, on the other side, confronted by the practical problems of ﬂuid mechanics, developed their own strongly empirical science, hydraulics. This relied upon a large amount of experimental data and diﬀered greatly from theoretical hydrodynamics in both methods and goals.

It is the great achievement of Ludwig Prandtl which, at the beginning of this century, set forth the way in which these two diverging directions of ﬂuid mechanics could be uniﬁed. He achieved a high degree of correlation between theory and experiment, which, in the ﬁrst half of this century, has led to unimagined successes in modern ﬂuid mechanics. It was already known then that the great discrepancy between the results in classical hydrodynamics and reality was, in many cases, due to neglecting the viscosity eﬀects in the theory. Now the complete equations of motion of viscous ﬂows (the Navier Stokes equations) had been known for some time. However, due to the great mathematical diﬃculty of these equations, no approach had been found to the mathematical treatment of viscous ﬂows (except in a few special cases). For technically important ﬂuids such as water and air, the viscosity is very small, and thus the resulting viscous forces are small compared to the remaining forces (gravitational force, pressure force). For this reason it took a long time to see why the viscous forces ignored in the classical theory should have an important eﬀect on the…motion of the ﬂow.

In his lecture on “Uber Flu… ssigkeitbewegung bei sehr kleiner Reibung” (On Fluid Motion with Very Small Friction) at the Heidelberg mathemati- cal congress in 1904, L. Prandtl (1904) showed how a theoretical treatment could be used on viscous ﬂows in cases of great practical importance. Using theoretical considerations together with some simple experiments, Prandtl showed that the ﬂow past a body can be divided into two regions: a very thin layer close to the body (boundary layer) where the viscosity is important, and the remaining region outside this layer where the viscosity can be ne- glected. With the help of this concept, not only was a physically convincing explanation of the importance of the viscosity in the drag problem given, but simultaneously, by hugely reducing the mathematical diﬃculty, a path was set for the theoretical treatment of viscous ﬂows. Prandtl supported his theoretical work by some very simple experiments in a small, self–built water channel, and in doing this reinitiated the lost connection between theory and practice. The theory of the Prandtl boundary layer or the frictional layer has proved to be exceptionally useful and has given considerable stimulation to research into ﬂuid mechanics since the beginning of this century. Under the inﬂuence of a thriving ﬂight technology, the new theory developed quickly and soon became, along with other important advances – airfoil theory and gas dynamics – a keystone of modern ﬂuid mechanics.

One of the most important applications of boundary–layer theory is the calculation of the friction drag of bodies in a ﬂow, e.g. the drag of a ﬂat plate at zero incidence, the friction drag of a ship, an airfoil, the body of an airplane, or a turbine blade. One particular property of the boundary layer is that, under certain conditions, a reverse ﬂow can occur directly at the wall. A separation of the boundary layer from the body and the formation of large or small eddies at the back of the body can then occur. This results in a great change in the pressure distribution at the back of the body, lead- ing to the form or pressure drag of the body. This can also be calculated using boundary–layer theory. Boundary–layer theory answers the important question of what shape a body must have in order to avoid this detrimental separation. It is not only in ﬂow past a body where separation can occur, but also in ﬂow through a duct. In this way boundary–layer theory can be used to describe the ﬂow through blade cascades in compressors and turbines, as well as through diﬀusers and nozzles. The processes involved in maximum lift of an airfoil, where separation is also important, can only be understood using boundary–layer theory. The boundary layer is also important for heat transfer between a body and the ﬂuid around it.

Initially boundary–layer theory was developed mainly for the laminar ﬂow of an incompressible ﬂuid, where Stokes law of friction could be used as an ansatz for the viscous forces. This area was later researched in very many pieces of work, so that today it can be considered to be fully understood. Later the theory was extended to the practically important turbulent in- compressible boundary–layer ﬂows. Around 1890, O. Reynolds (1894) had already introduced the fundamentally important concept of apparent turbu- lent stresses, but this did not yet permit the theoretical treatment of tur- bulent ﬂows. The introduction of the concept of the Prandtl mixing length, cf. L. Prandtl (1925), contributed considerable advances and, together with systematic experiments, allowed turbulent ﬂows to be treated theoretically with the help of boundary–layer theory. Even today a rational theory of fully developed turbulent flows remains to be found. Thanks to the great increase of velocities in flight technology, boundary layers in compressible flows weresubsequently also thoroughly examined. As well as the boundary layer in the velocity field, a thermal boundary layer also forms; this is of great importance for the heat transfer between the flow and the body. Because of internal friction (dissipation) at high Mach numbers, the body surface heats up greatly. This causes many problems, particularly in flight technology and satellite flights (“thermal barrier”).

The transition from laminar to turbulent flow, important for all of fluid mechanics, was first examined in pipe flow at the end of the last century by O. Reynolds (1883). Using the flow about a sphere, in 1914 Prandtl was able to show experimentally that the boundary layer also can be both laminar or turbulent and that the process of separation and thus the drag problem are controlled by this laminar–turbulent transition, cf. L. Prandtl (1914) The theoretical investigations into this transition assume Reynolds’ idea of the instability of the laminar flow. This was treated by Prandtl in 1921. After some futile attempts, W. Tollmien (1929) and H. Schlichting (1933) were able to theoretically calculate the indifference Reynolds number for the flat plate at zero incidence. However it took more than ten years before the theory could be confirmed by careful experiments by H.L. Dryden (1946–1948) and his coworkers. The effect of other parameters on the transition (pressure gradient, suction, Mach number, heat transfer) were clarified using the stability theory of the boundary layer. This theory has found important application with, among other things, airfoils with very low drag (laminar airfoils).

An important characteristic of modern research into fluid mechanics in general and more specifically into the branch of boundary–layer theory is the close connection between theory and experiment. The most crucial advances have been achieved through a few fundamental experiments together with theoretical considerations. Many years ago, A. Betz (1949) produced a review of the development of boundary–layer theory, with particular emphasis on the mutual fructification of theory and experiment. Research into boundary layers, inspired by Prandtl from 1904, were, in the first 20 years up until Prandtl’s Wilbur Wright memorial lecture at the Royal Aeronautical Society in London, (L. Prandtl (1927)) almost exclusively confined to Prandtl’s institute in G¨ottingen. It is only since 1930 that other researchers have been involved in the further expansion of boundary–layer theory, initially in England and the USA. Today boundary–layer theory has spread over the whole world; together with other branches it forms one of the most important pillars of fluid mechanics.

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基于DEFORM3D二次开发的塑性成形过程组织演化模拟【文献】

摘要:金属热成形方法可以有效改善产品的综合机械性能,利用有限元模拟可以为控制锻造和产品质量提供理论依据。在Deform3D的热力耦合刚粘塑性有限元模拟技术的基础上,进行了微观组织演化的二次开发,可以扩展有限元软件的组织模拟能力,并利用该方法对20CrMnTi钢镦锻热成形过程进行了计算机模拟,得到了热力参数的分布状况和内部晶粒度变化的规律。通过摇臂轴的镦锻成形模拟证明了组织模拟能够为工艺改进提供理论依据。关键词:刚粘塑性;有限元;晶粒尺寸;显微组织演化;热镦锻中图分类号:TG111.7文献标识码:A文章编号:1007-2012(2005)Sup-0040-041引言高温成形过程中，金属将发生动态和静态再结晶，产生新的晶粒。这种微观组织的演变在很大程度上决定了产品的宏观力学性能\(^{[1-2]}\)。利用热加工过程控制晶粒大小，细化微观组织，是提高产品力学性能的重要手段。因此，研究材料在热成形过程中的宏观力学行为和微观组织的变化，揭示其相互之间的关系，并依据优化工艺参数、设计塑性成形工艺和锻后冷却方案，对解决目前的工艺问题，提高产品质量是很有意义的，同时也是变形过程全面模拟的前沿课题\(^{[3]}\)。有限元数值模拟技术是随着物理模拟设备的完善以及计算机技术的发展而发展起来的。鉴于有限元法是目前唯一能对塑性加工过程给出全面且较为精确数值解的分析方法，本文对材料组织性能所进行的数值模拟均采用该分析方法。数值模拟软件是求解塑性加工问题的一个基本工具。现在市场上已有许多成熟的用于金属塑性加工的商业软件。如DEFORM，MSC.MARC，MSC.SUPERFORM，Dynaform等，但这些软件都只进行宏观变形和温度的分析计算，没有考虑宏观与微观耦合，不具备微观组织演化的模拟和预测功能，或者只具有简单的预测能力，其模型并不一定适合于所考察的问题。本文通过对Deform3D二次开发，将适合于材料的组织模型与成形的热力耦合计算结合，模拟热成形过程中的组织演化。2模型建立材料在热塑性变形中除了应力和应变的变化外，还要发生复杂的微观组织变化，即动态再结晶、静态再结晶、晶粒生长等。研究表明，再结晶的晶粒尺寸和再结晶晶粒百分比，除了和原始晶粒尺寸与微量元素含量有关外，主要取决于变形及冷却过程的温度、应变和应变速率。由于热成形过程的复杂性，很难进行现场测试，而在实验室进行研究，只能得到简单条件下的显微组织与宏观热力参数间的定量关系。通过有限元模拟，可以十分方便经济地获得场量信息，因此可以将有限元用于组织演化的预报和控制。图1给出了用有限元模拟材料热变形过程中微观组织演化的计算流程。在实验室通过热力模拟试验，可以获得材料的准经验数学模型，其经验模型大都是通过试验数据回归获得Avrami形式的数学模型。在对有限元软件开发过程中，将组织模型离散，在每一迭代步中计算，其计算过程如图2所示。把再结晶模型与刚粘塑性有限元程序耦合，即在子程序计算时，首先分析变形过程中的动态再结晶，在实际计算中首先判断再结晶的体积百分数，当X＜0.95时，判断等效应变ε是否大于临界应变ε_c。如果等效应变大于临界应变，则开始计算动态再结晶过程；当动态再结晶分数\(X>0.95\)时，则直接转为晶粒长大的有关计算。把静态再结晶模型与热传导有限元耦合，可以分析卸载后的静态再结晶。Deform3D是由SFTC公司开发的一个体积成形有限元工艺模拟专用商业软件，其用户定义子程序的代码储存在def_usr.f中，有限元主程序通过调用该文件中的子程序，可以计算出用户自定义变量的值。所以关键问题在于该子程序的编写。其中USRMSH子程序包含了有限元计算中所有的变量。通过这个用户子程序，可以修改所有这些变量。该子程序申明如下：SUBROUTINEUSRMSH(RZ,DRZ,URZ,TEMP,DTMP,FRZA,FRZB,EFSTS,EFEPS,TEPS,RDTY,STS,EPS,DCRP,TSRS,DAMG,USRVE,USRVN,ATOM,HEATND,EPRE,VOLT,WEAR,DUM1,PRZA,DUM2,DUM3,HDNS,VF,DVF,VFN,TICF,GRN-SZ,CURTIM,DTMAbC,BCD,NBCDT,NOD,MATR,NBDRY,KOBJ,NUMEL,NUMNP,NDSTART,NDEND,NUMFAC,NUSRVE,NUSRND,NPHASE,ISTATUS,NROUTINE,NONP)其中TEMP为温度,DTMP为该迭代步的温度增量,EFEPS(NUMEL)是等效应变率,TEPS(NUMEL)是塑性应变增量。在子程序中需读入组织模拟需要的以上4个基本参量。对于组织模拟来说,通过USRMSH可以修改以下参量:VF(NPHASE,*):再结晶分数DFV(NPHASE,*):再结晶分数增量DFN(NPHASE,*):静态再结晶分数GRNSZ(*):晶粒尺寸3实例分析扇形齿轮摇臂轴广泛应用于汽车等各种机动车的发动机、转向系统、循环球方向系统。由于在工作时受力复杂,工作环境恶劣,要求摇臂轴有较高的力学性能。因此对其热成形过程中的组织演化过程进行模拟,指导工艺有着重要的意义[4,5]。摇臂轴采用一步成形,材料采用20CrMnTi,模具材料为5CrNiMo。因为工件为平面对称,所以,取其1/2进行模拟,坯料划分为52111个六面体单元,共7085个节点,上模1918个单元,下模5823个单元。坯料的材料为20CrMnTi,其组织模型如下所示:将组织数学模型离散化,通过修改USRMSH子程序获得了模拟结果。图3是模拟使用的模型图。反映材料热成形过程的主要特征参量为温度场(见图4)、应变与应变速率分布(见图5、图6)等。而热成形过程中材料内部显微组织的变化,可由再结晶程度和晶粒度大小来说明(图7和图8)。图中坯料内的温度场与图中应变与应变率的等值线分布符合塑性加工过程中热力因素的变化规律。由图7可以看出,在这种等效应变分布条件下坯料内各区域都发生了不同程度的再结晶。4结论采用热力耦合刚粘性有限元微观组织模拟技术,对20CrMnTi结构钢摇臂轴镦锻成形进行了模拟研究,所得到的有关场量信息符合变形规律。数值模拟结果表明,有限元组织模拟可以为摇臂轴热成形工艺的实施及产品质量的控制,生产合格产品提供理论依据。原资料见附件免责声明：本页面/内容部分素材来源于互联网公开信息，旨在传递更多信息，不代表本平台立场。版权归原作者或机构所有，如涉及侵权，请通过平台联系我们，我们将在核实后第一时间处理。本平台对转载内容的真实性、准确性不作任何保证，用户需自行判断并承担使用风险。

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