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2.27 紊流與傳輸(2002年春季)

2.27 Turbulent Flow and Transport, Spring 2002

 

翻譯:陳懿

編輯:洪曉慧、陳盈


Ocean waves breaking on a beach.

拍打沙灘的海浪。(圖片由加州環境資源評估服務處提供)

 

課程重點

這門課程包含了課程大綱,習題集範例以及閱讀書目。

 

課程描述

紊流,強調工程方法。動量、能量以及物種傳輸的控制方程。


課程第一天的資訊──紊流:產生,消散,以及比例定律。動量、能量以及物種傳輸的雷諾平均方程。自由與受限剪切紊流的簡單封閉方法。射流、管流和槽流,邊界層,浮力驅動的卷流與熱流,以及Taylor散佈的應用等等,包括熱量以及物種輸運還有流場本身。對更加複雜的封閉格式的介紹,包括紊流中的k-epsilon方法和統計方法。

 

評分

家庭作業

期中測驗(課堂外)

個人項目

期末測驗(課堂外)

 

課堂講稿

以下檔案為每節課中所涉及主題的概要,並且附有當天的閱讀作業。

1.   基礎定律和基本方程的回顧 Review of Fundamental Laws and Constitutive Equations (英PDF)

2.   紊流中的一些概念Concepts in Turbulence (英PDF)

3.   自由剪切流:射流,尾流,等等。基於對流動平均化並採用簡單封閉格式的解Free Shear Flows I: Jets, Wakes, etc.- Solutions Based on Simple Mean-Flow Closure Schemes

4.   有邊界流:一般近壁比例定律;管內流動,槽內流動,等等.Bounded flows I: General Near-Wall Scaling Laws; Flows in Pipes, Channels, etc. (英PDF)

5.   紊流邊界層介紹Introduction to Turbulent Boundary Layers (英PDF)

6.   浮力驅動的卷流,熱流,等等Buoyant Plumes, Thermals, etc. (英PDF)

7.   紊流模型介紹 Introduction to Turbulence Models (英PDF)

8.   管內流動和槽內流動的消散Dispersion in Pipe and Channel Flow (英PDF)  

 

教學時程

此教學時程只是概要性的課程進度。主題講述的順序如下所示,但是我們故意把時程表設計得具有彈性,以便或多或少按學生需要為某一主題留有時間。

以下閱讀資料是為了補充課堂講稿的主題。

 

相關閱讀資料  

1            

回顧流場與輸運方程,特別強調能量方程及其在黏性耗散中所起作用

Review of Flow and Transport Equations, with Particular Emphasis on the Energy Equation and the Role of Viscous Dissipation

 

1.1-1.4節

Sonin.《運動的基本定律:顆粒,物質體積,以及控制體積》Fundamental Laws of Motion: Particles, Material Volumes, And Control Volumes

Sonin.《黏性流體的運動方程》The Equation of Motion for Viscous Fluids.

White.《黏性流體流動》Viscous Fluid Flow. 2nd ed. 1991, pp. 59-89, 96-100.;或其他參考書.  

 

1.4-1.6節

Sonin分發課堂筆記以及總結  

 

1.7-1.8節

Sonin.《熱力學基本方程組以及溫度方程》"The Thermodynamic Constitutive Equations and the Equation for Temperature."  

 

1.10節:

課堂筆記  

 

1.11節

Bird, Curtis, and Hirschfelder.《氣體與液體的分子理論》Molecular Theory of Gases and Liquid. 1954, pp. 8-16.

Vincenti & Kruger.《物理氣體動力學導論》 Introduction to Physical Gas Dynamics.1965, pp.15-20.

2

不穩定性與轉換

Instability and Transition

3

紊流中的基本概念,封閉方程的方法和紊流建模

Fundamental Concepts in Turbulence, Approaches to Closure, and Turbulence Modeling

  3.3節
Pope. .第三、四章
Tennekes & Lumley. 第一、二章,pp. 19-24.

3.5-3.7節
White.第二版, pp. 402-409.

3.8節
Schlichting.第七版,pp. 578-586
White. pp. 436-440.

射流,尾流,等等。通過簡單封閉格式建立模型,自由流動中的物理量為標量的輸運(溫度,濃度)


Jets, Wakes, etc. Modeled via Simple Closure Schemes. Scalar Transport in Free Flows (Temperature, Concentration)

 

關於層流Laminar Flow

White.第二版, pp. 253-260, 301-304, 470-481

Pope. 第四、五章.

Schlichting.第七版,第24章, pp.183-185.

關於紊流剪切層:

Champagne, Pao, and Wygnaski.《流體力學期刊》J. Fluid Mech., 74 (1976), pp. 209-250.

Hinze..第六章

Abramovich.《紊射流理論》The Theory of Turbulent Jets. pp. 103-113, 120-125.

Rajaratnam.〈紊射流〉"Turbulent Jets." Elsevier, 1976.

Rodi.《對流研究》Studies in Convection.. Edited by B. E. Launder. , 1975, Academic

Press, 1975, pp. 79 ff.

Townsend.《剪切紊流的結構》Chap. 6 in The Structure of Turbulent Shear Flow. 2nd ed. Cambridge, 1976.

講義:實驗資料與總結選讀

5

浮力驅動卷流與瞬態的熱流等等

Buoyant Plumes, Transient Thermals, etc.

  7.1-.7.2, 10.1-10.2
Pope.
White. 第二版, pp. 411-416, 421-429, 436-440.
Schlichting. 第19及20章

5.2- 5.5節
Monin & Yaglom I.第三章
Tennekes & Lumley. pp. 147-165, 171-176. 
 

掠壁紊流:一般近壁流動比例定律,管內流動,槽內流動,等等

Turbulent Flow over Walls: General Near-Wall Scaling Laws; Flows in Pipes, Channels, etc. 

 

Pope. pp. 298 ff.

White. pp. 409-421, 429-.443.

Schlichting.第二十一章.

Bradshaw.第二章.

Cebeci & Smith.《紊流邊界層分析》Analysis of Turbulent Boundary Layers. Academic, 1974.

6.7節
Bushnell & McGinley.〈壁面流動的紊流控制〉"Turbulence control in wall flows."《流體力學年鑒》Ann. Rev. Fluid Mech. Vol. 21 (1989), pp.1.

Hinze. 681-84.
Blackwelder & Haritonidis.《流體力學期刊》J. Fluid Mech., 132 (1983), pp. 87-103.

Walsh & Lindemann. AIAA.84.0347.
Gallagher & Thomas. AIAA.84.2185.
Bechert. AIAA.85.0546. 
 

 7

邊界層

Boundary Layers 
 

 

Morton, Taylor & Turner.《皇家學會學報》Proc. Roy. Soc. A, 234 (1956), pp. 1-23.
Turner.《流體中的浮力效應》Buoyancy Effects in Fluids. Cambridge, 1973, pp. 165-173, 194-200.

Chen & Rodi.〈實驗數據回顧〉"A Review of Experimental Data."《垂直方向浮力驅動紊射流》Vertical Turbulent Buoyant Jets. Pergamon Press, 1980.

Fay.〈浮力驅動卷流與尾流〉"Buoyant Plumes and Wakes."《流體力學年鑒》Ann. Rev. Fluid Mech., Vol. 5 (1973).

List.〈紊射流與紊卷流〉"Turbulent Jets and Plumes."《流體力學年鑒》 Ann. Rev. Fluid Mech., Vol. 14 (1982).

Rodi.《浮力驅動紊射流和紊卷流》Turbulent Buoyant Jets & Plumes. Pergamon Press, 1982. 
 

 8

剪切層流與剪切紊流中的過渡階段消散(Taylor消散)

Transient Dispersion in Laminar and Turbulent Shear Flows (Taylor Dispersion) 
 

 

Pope. Chap. 4, 10, 11.第四、十、十一章

Chen & Yaw.《紊流建模原理》Fundamentals of Turbulence Modeling. Taylor & Francis, 1998.

Libby.《紊流導論》Introduction to Turbulence. Taylor& Francis, 1996.

LaJones, and under.《熱傳遞物質國際期刊》Int. J. Heat Mass Transfer, 15 (1972): 301.

LaJones, and under.《熱傳遞物質國際期刊》Int. J. Heat Mass Transfer, 16 (1973): 1119.

Bradshaw, Cebeci, and Whitelaw.《紊流的工程計算方法》Engineering Calculation Methods for Turbulent Flow. Academic Press, 1981.

Rodi.《水力學中的紊流模型及其應用》——〈最新進展回顧〉Turbulence models and their applications in Hydraulics-- "a state of the art review,",水力學國際協會. Int. Assoc. for Hydraulics.Research, Delft, 1984.

Rodi.《工程中紊流建模與實驗》Engineering Turbulence Modelling and Experiments 3, Elsevier (1996).

《紊流》Turbulence第一、五章,Bradshaw. Springer編輯,1978
Monin & Yaglom. Vol. 1. MIT Press, 1979, pp. 373-393, 393 ff. 
 

9

紊流模型及其應用

Turbulence Models and Their Application

 

Taylor, G. I.《皇家學會學報》Proc. Roy. Soc.. A, 219 (1953), pp. 186-203 (層流)(Laminar). ;223 (1954), pp. 446-468 (紊流). (Turbulent).

Aris. R.《皇家學會學報》Proc. Roy. Soc. A. 235 (1956), pp. 67-77.

Probstein, R. F.《物理化學水動力學》Physicochemical Hydrodynamics. 2nd ed. Wiley, 1994, pp. 87, 93.

Levich,《物理化學水動力學》Physicochemical Hydrodynamics, Prentice Hall, 1962, pp. 116-120.

Fischer, H. B.〈開放式槽流中的縱向消散與紊流混合層〉"Longitudinal dispersion and turbulent mixing in open channel flow."《流體力學年鑒》Ann. Rev. Fluid Mech., Vol. 5 (1973), pp. 59-78.

Chatwin, P. C., and P. J. Sullivan.《流體力學期刊》J. Fluid Mech., 120 (1982), pp. 347-358.

Smith, R.《流體力學期刊》J. Fluid Mech., 215 (1990), pp. 195-207.

Monin & Yaglom,《統計流體力學》Statistical Fluid Mechanics. Vol. 1. MIT, 1973, pp. 617-627.《物理協會學報》. 67, 12.B (1955), pp. 857-869. 
 

10

附加主題

Additional Topics  

 

作業

以下習題集作為閱讀資料與講義的補充。

習題 1 (英PDF)

習題2 (英PDF)

習題3 (英PDF)

 

以下為系統擷取之英文原文

2.27 Turbulent Flow and Transport

Spring 2002


Ocean waves breaking on a beach. Ocean waves breaking on a beach. (Image courtesy of California Environmental Resource Evaluation Service.)

Course Highlights

This course includes lecture outlines, sample problem sets and reading lists.



Course Description

Turbulent flows, with emphasis on engineering methods. Governing equations for momentum, energy, and species transfer.

Turbulence: its production, dissipation, and scaling laws. Reynolds averaged equations for momentum, energy, and species transfer. Simple closure approaches for free and bounded turbulent shear flows. Applications to jets, pipe and channel flows, boundary layers, buoyant plumes and thermals, and Taylor dispersion, etc., including heat and species transport as well as flow fields. Introduction to more complex closure schemes, including the k-epsilon, and statistical methods in turbulence.





Syllabus

The syllabus outlines the information covered in the first day of class.

Topics Review of flow and transport equations, with particular emphasis on the energy equation and the role of viscous dissipation. Instability and transition. Fundamental concepts in turbulence; approaches to closure and turbulence modeling. Jets, wakes, etc. modeled via simple closure schemes. Scalar transport in free flows (temperature, concentration). Buoyant plumes, transient thermals, etc. Turbulent flow over walls: general near-wall scaling laws; flows in pipes, channels, etc. Boundary layers. Transient dispersion in laminar and turbulent shear flows (Taylor dispersion). Turbulence models and their application. Additional topics.

Grading

Homework Problems
Midterm Quiz (take-home)
Individual Project
Take-home Final Exam

 



Calendar

This calender is only a broad outline of the schedule for the course. Topics are covered in the order shown below, but the schedule is deliberately dynamic so that more, or less, time may be devoted to a particular topic as needed by the students.







        WEEK #       TOPICS        
     
  1       Review of Flow and Transport Equations, with Particular Emphasis on the Energy Equation and the Role of Viscous Dissipation  
     
     
  2       Instability and Transition  
     
     
  3       Fundamental Concepts in Turbulence, Approaches to Closure, and
Turbulence Modeling
 
     
     
  4       Jets, Wakes, etc. Modeled via Simple Closure Schemes. Scalar Transport in Free Flows (Temperature, Concentration)  
     
     
  5       Buoyant Plumes, Transient Thermals, etc.  
     
     
  6       Turbulent Flow over Walls: General Near-Wall Scaling Laws; Flows in Pipes, Channels, etc.  
     
     
  7       Boundary Layers  
     
     
  8       Transient Dispersion in Laminar and Turbulent Shear Flows (Taylor Dispersion)  
     
     
  9       Turbulence Models and Their Application  
     
     
  10       Additional Topics  
     






 

 

 



Readings

The readings listed below are intended to supplement the topics covered in the lecture notes.

        SECTION       READINGS        
 
  Lecture 1  
 
     
  Sec.1.1-1.4       Sonin. Fundamental Laws of Motion: Particles, Material Volumes, And Control Volumes.
Sonin. The Equation of Motion for Viscous Fluids.
White. Viscous Fluid Flow. 2nd ed. 1991, pp. 59-89, 96-100.
Pope. Chap. 2; or other books.
 
     
     
  Sec 1.4-1.6       Class notes plus summaries handed out by Sonin  
     
     
  Sec.1.7-1.8       Handout:
Sonin. "The Thermodynamic Constitutive Equations and the Equation for Temperature."
 
     
     
  Sec.1.10       Class notes  
     
     
  Sec. 1.11       Bird, Curtis, and Hirschfelder. Molecular Theory of Gases and Liquid.  1954, pp. 8-16.
Vincenti & Kruger. Introduction to Physical Gas Dynamics.1965, pp.15-20.
 
     
 
  Lecture 3  
 
     
          Pope. Chap. 3 and 4.  
     
     
  Sec. 3.3       Tennekes & Lumley. Chap. 1 and 2, pp. 19-24.  
     
     
  Sec. 3.5-3.7       White. 2nd ed., pp. 402-409.  
     
     
  Sec. 3.8       Schlichting. 7th ed., pp. 578-586.
White. pp. 436-440.
 
     
 
  Lecture 4  
 
     
          For Laminar Flow:
White. 2nd ed., pp. 253-260, 301-304, 470-481.
Pope. Chap. 4 & 5.
Schlichting. 7th ed. Chap. 24, pp.183-185.

For Turbulent Shear Layer:
Champagne, Pao, and Wygnaski. J. Fluid Mech., 74 (1976), pp. 209-250.

Further Reading:
Hinze. Chap. 6.
Abramovich. The Theory of Turbulent Jets. pp. 103-113, 120-125. 
Rajaratnam. "Turbulent Jets." Elsevier, 1976.
Rodi. Studies in Convection. Edited by B. E. Launder. Academic Press, 1975, pp. 79 ff.
Townsend. Chap. 6 in The Structure of Turbulent Shear Flow. 2nd ed. Cambridge, 1976.

Handouts:
Selected experimental data and summaries.
 
     
 
  Lecture 5  
 
     
  Sec. 7.1-.7.2, 10.1-10.2       Pope.
White. 2nd ed., pp. 411-416, 421-429, 436-440.
Schlichting. Chap. 19 & 20.
 
     
     
  Sec. 5.2- 5.5       Monin & Yaglom I. Chap. 3.
Tennekes & Lumley. pp. 147-165, 171-176.
 
     
 
  Lecture 6  
 
     
          Pope. pp. 298 ff.
White. pp. 409-421, 429-.443.
Schlichting. Chap. 21.
Bradshaw. Chap. 2.
Cebeci & Smith. Analysis of Turbulent Boundary Layers. Academic, 1974.
 
     
     
  Sec. 6.7       Bushnell & McGinley. "Turbulence control in wall flows." Ann. Rev. Fluid Mech. Vol. 21 (1989), pp.1.
Hinze. 681-84.
Blackwelder & Haritonidis. J. Fluid Mech., 132 (1983), pp. 87-103.
Walsh & Lindemann. AIAA.84.0347.
Gallagher & Thomas. AIAA.84.2185.
Bechert. AIAA.85.0546.
 
     
 
  Lecture 7  
 
     
          Morton, Taylor & Turner. Proc. Roy. Soc. A, 234 (1956), pp. 1-23.
Turner. Buoyancy Effects in Fluids. Cambridge, 1973, pp. 165-173, 194-200.
Chen & Rodi. "A Review of Experimental Data." Vertical Turbulent  Buoyant Jets. Pergamon Press, 1980.
Fay. "Buoyant Plumes and Wakes." Ann. Rev. Fluid Mech., Vol. 5 (1973).
List. "Turbulent Jets and Plumes." Ann. Rev. Fluid Mech., Vol. 14 (1982).
Rodi. Turbulent Buoyant Jets & Plumes. Pergamon Press, 1982.
 
     
 
  Lecture 8  
 
     
          Pope. Chap. 4, 10, 11.
Chen & Yaw. Fundamentals of Turbulence Modeling. Taylor & Francis, 1998.
Libby. Introduction to Turbulence. Taylor& Francis, 1996.
LaJones, and under. Int. J. Heat Mass Transfer, 15 (1972): 301.
LaJones, and under. Int. J. Heat Mass Transfer, 16 (1973): 1119.
Bradshaw, Cebeci, and Whitelaw. Engineering Calculation Methods for Turbulent  Flow. Academic Press, 1981.
Rodi. Turbulence models and their applications in Hydraulics-- "a state of the art review," Int. Assoc. for Hydraulics.
Research, Delft, 1984.
Rodi. Engineering Turbulence Modelling and Experiments 3, Elsevier (1996).
Turbulence. Chap. 1 & 5. Edited by Bradshaw. Springer, 1978.
Monin & Yaglom. Vol. 1. MIT Press, 1979, pp. 373-393, 393 ff.
 
     
 
  Lecture 9  
 
     
          Taylor, G. I. Proc. Roy. Soc. A, 219 (1953), pp. 186-203 (Laminar).
                                     223 (1954), pp. 446-468 (Turbulent).
                                     225 (1954), pp. 473-477.
                  Proc. Phys. Soc. 67, 12.B (1955), pp. 857-869.
Aris. R. Proc. Roy. Soc. A. 235 (1956), pp.  67-77.
Probstein, R. F. Physicochemical Hydrodynamics. 2nd ed. Wiley, 1994,  pp. 87, 93.
Monin & Yaglom, Statistical Fluid Mechanics. Vol. 1. MIT, 1973, pp. 617-627.
Levich, Physicochemical Hydrodynamics, Prentice Hall, 1962, pp. 116-120.
Fischer, H. B. "Longitudinal dispersion and turbulent mixing in open channel flow." Ann. Rev. Fluid Mech., Vol. 5 (1973), pp. 59-78.
Chatwin, P. C., and P. J. Sullivan. J. Fluid Mech., 120 (1982), pp. 347-358.
Smith, R. J. Fluid Mech., 215 (1990), pp. 195-207.
 
     

 



Lecture Notes

The following files show the outline of the topics covered in each lecture, along with the reading assignments for that day.

Review of Fundamental Laws and Constitutive Equations (PDF) Concepts in Turbulence (PDF) Free Shear Flows I: Jets, Wakes, etc.- Solutions Based on Simple Mean-Flow Closure Schemes (PDF) Bounded flows I: General Near-Wall Scaling Laws; Flows in Pipes, Channels, etc. (PDF) Introduction to Turbulent Boundary Layers (PDF) Buoyant Plumes, Thermals, etc. (PDF) Introduction to Turbulence Models (PDF) Dispersion in Pipe and Channel Flow (PDF)


 


Assignments

The following problem sets are offered as supplements to the readings and lectures.

Problem 1 (PDF)
Problem 2 (PDF)
Problem 3 (PDF)

 


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