turbulence theory and modelingbc%ad%b7%d0.pdf공학적인문제에서의난류유동 기계,...
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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
~
CFD & Turbulence Lab. http://cfd.kookmin.ac.kr
School of Mechanical Engineering Copyright ⓒ 2009 Hyon Kook MYONG
Contents
서론
기초방정식
난류의 발생
난류의 생성 및 소산
와동(Vortex) Dynamics난류 스케일
상관
난류 스펙트럼
난류모델
난류 현상의 예측 예
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
~
CFD & Turbulence Lab. http://cfd.kookmin.ac.kr
School of Mechanical Engineering Copyright ⓒ 2009 Hyon Kook MYONG
Contents
서론
기초방정식
난류의 발생
난류의 생성 및 소산
와동(Vortex) Dynamics난류 스케일
상관
난류 스펙트럼
난류모델
난류 현상의 예측 예
CFD & Turbulence Lab. http://cfd.kookmin.ac.kr
School of Mechanical Engineering Copyright ⓒ 2009 Hyon Kook MYONG
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
CFD & Turbulence Lab. http://cfd.kookmin.ac.kr
School of Mechanical Engineering Copyright ⓒ 2009 Hyon Kook MYONG
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, ….
CFD & Turbulence Lab. http://cfd.kookmin.ac.kr
School of Mechanical Engineering Copyright ⓒ 2009 Hyon Kook MYONG
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, ….
CFD & Turbulence Lab. http://cfd.kookmin.ac.kr
School of Mechanical Engineering Copyright ⓒ 2009 Hyon Kook MYONG
Characteristics of Turbulent Flowin Engineering Field
Increase of skin friction
Increase of heat transfer
Increase of mixing
Dissipation
Turbulence induced random vibration
etc.
CFD & Turbulence Lab. http://cfd.kookmin.ac.kr
School of Mechanical Engineering Copyright ⓒ 2009 Hyon Kook MYONG
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 ≈
CFD & Turbulence Lab. http://cfd.kookmin.ac.kr
School of Mechanical Engineering Copyright ⓒ 2009 Hyon Kook MYONG
Physics of Turbulence-2
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
CFD & Turbulence Lab. http://cfd.kookmin.ac.kr
School of Mechanical Engineering Copyright ⓒ 2009 Hyon Kook MYONG
Physics of Turbulence-3
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!
CFD & Turbulence Lab. http://cfd.kookmin.ac.kr
School of Mechanical Engineering Copyright ⓒ 2009 Hyon Kook MYONG
Physics of Turbulence-4
Mean Flow withTurbulent energy
Laminar
Energy Cascade
ViscousDissipation
Large ScaleTurbulence . . . Small Scale
Turbulence
CFD & Turbulence Lab. http://cfd.kookmin.ac.kr
School of Mechanical Engineering Copyright ⓒ 2009 Hyon Kook MYONG
Physics of Turbulence-5
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 !
CFD & Turbulence Lab. http://cfd.kookmin.ac.kr
School of Mechanical Engineering Copyright ⓒ 2009 Hyon Kook MYONG
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, ,
CFD & Turbulence Lab. http://cfd.kookmin.ac.kr
School of Mechanical Engineering Copyright ⓒ 2009 Hyon Kook MYONG
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
CFD & Turbulence Lab. http://cfd.kookmin.ac.kr
School of Mechanical Engineering Copyright ⓒ 2009 Hyon Kook MYONG
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
CFD & Turbulence Lab. http://cfd.kookmin.ac.kr
School of Mechanical Engineering Copyright ⓒ 2009 Hyon Kook MYONG
Validity of Continuum Concept-2
CFD & Turbulence Lab. http://cfd.kookmin.ac.kr
School of Mechanical Engineering Copyright ⓒ 2009 Hyon Kook MYONG
Why we need turbulence theory ?
Impracticability of solving N-S eq. need turbulence theory
CFD & Turbulence Lab. http://cfd.kookmin.ac.kr
School of Mechanical Engineering Copyright ⓒ 2009 Hyon Kook MYONG
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
CFD & Turbulence Lab. http://cfd.kookmin.ac.kr
School of Mechanical Engineering Copyright ⓒ 2009 Hyon Kook MYONG
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.
CFD & Turbulence Lab. http://cfd.kookmin.ac.kr
School of Mechanical Engineering Copyright ⓒ 2009 Hyon Kook MYONG
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
CFD & Turbulence Lab. http://cfd.kookmin.ac.kr
School of Mechanical Engineering Copyright ⓒ 2009 Hyon Kook MYONG
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
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