Turbulence Theory and ModelingBC%AD%B7%D0.pdf공학적인문제에서의난류유동 기계, 구조물내외부에서의난류: 유체기계, 수송기계, 공작기계, 컴퓨터기기,

CFD & Turbulence Lab. http://cfd.kookmin.ac.kr

School of Mechanical Engineering Copyright ⓒ 2009 Hyon Kook MYONG

Turbulence Theory and Modeling

Hyon Kook MYONG

School of Mechanical Engineering

http://cfd.kookmin.ac.kr

~



Contents

서론

기초방정식

난류의 발생

난류의 생성 및 소산

와동(Vortex) Dynamics난류 스케일

상관

난류 스펙트럼

난류모델

난류 현상의 예측 예



Turbulence Theory and Modeling

Hyon Kook MYONG

School of Mechanical Engineering

http://cfd.kookmin.ac.kr

~



Contents

서론

기초방정식

난류의 발생

난류의 생성 및 소산

와동(Vortex) Dynamics난류 스케일

상관

난류 스펙트럼

난류모델

난류 현상의 예측 예



Definition of Turbulence(Taylor and von Karman, 1937)

Turbulence is an irregular motionwhich in general makes its appearance in fluids, gaseous or liquid, when they flow past solid surface or even when neighboring streams of the same fluid flow

past or over one another.

유체의 속도, 온도, 밀도, 압력 등이 시간과 장소에 따라 불규칙적으로 매우 빠르

게 변동(요동)하는 유동 형태



공학적인 문제에서의 난류유동

기계, 구조물 내외부에서의 난류:유체기계, 수송기계, 공작기계, 컴퓨터 기기, 열기관, 에너지 플랜트, 화학

플랜트, 공조, 건축, metal processing, 윤활, …...

자연계에서의 난류:기상, 대기, 해양, 하천, 맨틀, 우주, …..

생체 내에서의 난류:혈액, 체액의 유동, ….



난류현상의 문제점

유체 공학적 문제:저항, 마찰계수, 날개 성능, 유동 패턴, 유체 진동, 소음 발생, …...

전열 공학적 문제:열전달율, 전열온도, 물질전달율, 열(물질)확산, …..

이론 물리학적 문제:Chaos 또는 난류의 발생, 불안정성, 천이, 수리 통계, ….



Characteristics of Turbulent Flowin Engineering Field

Increase of skin friction

Increase of heat transfer

Increase of mixing

Dissipation

Turbulence induced random vibration

etc.



Physics of Turbulence-1

Irregularity :

Rely on statistical method due to random motion.

Large Reynolds Number :

Turbulence develops as an instability of laminar flows if the Reynolds number becomes too large.

The instabilities are related to the interaction of viscous terms and nonlinear inertia terms in the equations of motion.

Pipe flow b. l. flowJet flowL

UUUL

μ

ρν

2

Re == 2300Re ≈510Re≈

30~10Re ≈




Diffusivity :It cause rapid mixing and increased rates of momentum, heat and mass transfer. 박리(separation) 방지

3-D Vorticity Fluctuations :Rotational and three-dimensional. 와도변동은 와동의 신장(stretching)에 의해발생(2차원 난류는 존재할 수 없다!!)

Laminar Flow Turbulent Flow

( )urot=ω




Dissipation :Turbulence features a cascading process whereby, as the turbulence decays, its kinetic energy transfers from large eddies to smaller eddies.

Ultimately, the smallest eddies dissipate into heat through the action of molecular viscosity.

~~

e.g.

cycloneNo turbulence!




Mean Flow withTurbulent energy

Laminar

Energy Cascade

ViscousDissipation

Large ScaleTurbulence . . . Small Scale

Turbulence




Continuum :Turbulence consists of a continuous spectrum of scales ranging from largest to smallest, but even the smallest scales occurring in a turbulent flow are ordinarily far large than any molecular length scale.

Turbulence flows are flows :Turbulence is not a feature of liquids but of fluid flows.

Since the equations of motion are nonlinear, each individual flow pattern has certain unique characteristics that are associated with its initial and boundary conditions.

cf) Karman vortex

No dissipation !Not diffuse !



Turbulence Scale

Small Scale

UniversalVery short lifetimeIsotropicMost dissipation of energyIneffective in transport phenomena

Large Scale

Largely depend on geometric b.c. Long lifetimeDirectionalMost turbulent energy

Effective in transport phenomena

u t, , η υ τ, ,



Smallest Eddy Scale

where

Kolmogorov scales

Thus, turbulence theory is needed ! ! !

( )η ε ν≈ f ,

[ ][ ]

ε

ν

: :

: :

L T dissipation rate of turbu lence

L T kinem atic vis ity

2 3

2 cos

( )ην≈ ≈

− −u 3 4 3 4R e

( )η ν ε≡ 3 1 4/

/ ( )τ ν ε≡ / /1 2

( )v ≡ νε 1 4/ vην

≡ 1



Validity of Continuum Concept-1

: molecular mean free pathλ

ν λ≈ c where c speed of sound:

λη

νη

νη

νη

ν~ ~ ~ ~Re

~Rec u

uc u

MauMa Ma

−34

14

=μ



Validity of Continuum Concept-2



Why we need turbulence theory ?

Impracticability of solving N-S eq. need turbulence theory



난류를 다루는 방법-1

난류는 초기조건 또는 경계조건에 크게 의존하는 비선형으로, 일반적인 해

는 존재하지 않고 엄밀하게는 하나하나 모두 다르다. 따라서, 어떤 종류

의 그룹 난류에 적절한 공통적 해석 또는 법칙을 찾아내는 것이 난류를 다

루는 기본적인 목적으로 된다.(예1) Internal flows; pipe flow, channel flow

External flows; b.l. flow, jet

(예2) Free turbulenceWall turbulence



난류를 다루는 방법-2

(예3) Homogeneous turbulence; 난류의 모든 통계량이 어느 방향으로

도 변하지 않음. 즉, 좌표계의 평행이동에 대해 불변!!

(예4) Isotropic turbulence; 난류의 모든 통계량 기술이 좌표회전에 대해

서 불변.

(예5) Shear turbulence; 평균속도분포에 변형이 있음. 난동량 생성이 있

음.



Inviscid Estimate for Dissipation Rate

Rate of energy supply (=Production rate)

Production rate = Dissipation rate

Viscous dissipation of energy can be estimated from the large-scale dynamics, which do not involve viscosity.

≈ =u u u2 3

ε ~ u3



Methods of Analysis

Mathematical modeling; ①correlation method ②spectral method

Dimensional analysis – e.g.) Inertial subrange

Order of Magnitude – e.g.) Asymptotic invariance

Scale Analysis – e.g.) Local invariance

Documents

Turbulence Theory and ModelingBC%AD%B7%D0.pdf공학적인문제에서의난류유동 기계, 구조물내외부에서의난류: 유체기계, 수송기계, 공작기계, 컴퓨터기기,