유체역학및열전달 chapter 3. fluid flow phenomena -...

부산대학교 현규유체역학및열전달 1

유체역학및열전달

Chapter 3. Fluid flow phenomena

부산대학교 화공생명공학부현 규 (Kyu Hyun)

부산대학교 현규

Chapter 3. Fluid flow phenomena (1)

유체역학및열전달 2

• The behavior of a flowing fluid depends strongly on whether the fluid is under the influence of solid boundaries

• Potential flow : 벽의 영향이 적은 지역 (전단 응력 무시 가능)• Incompressible & zero viscosity인 ideal fluid 거동으로 해석• Newton 역학으로 기술가능• (1) Circulation 나 eddies가 없는 irrotational flow (2) friction이 없어 heat

dissipation이 없음

• Boundary layer flow : 고체 경계의 영향 하에 있는 유체의 흐름• (1) the coupling of velocity gradient and shear stress filed (속도 구배와

전단응력장의 결합)• (2) the onset of turbulence (난류의 발생)• (3) the formation and growth of boundary layers (경계층의 형성과 성장)• (4) the separation of boundary layers from contact with the solid boundary

(고체 경계와의 접촉면으로부터 경계층의 분리).




• Most technical flow processes are best studied by considering the fluid stream as two parts, the boundary layer and the remaining fluid.




• Velocity field (속도장)• The fluid adheres to the solid at the actual interface between solid and

fluid• If therefore, the wall is at rest in the reference frame chosen for the

solid-fluid system, the velocity of the fluid at the interface is zero (= no-slip boundary condition).

• When the velocity at each location is constant, the field is invariant with time the flow is said to be steady.

• One-dimensional flow (일차원 흐름)• A flow that has only one-velocity component (In general velocity is

vector).

- Velocity field- Steady flow


Laminar flow, shear rate and shear stress


• Laminar flow (층류)• At low velocities fluids tend to flow without lateral mixing, cross-current

and eddies.• Velocity gradient: 속도 기울기 전단 속도

• Shear stress (전단 응력)• This force is exerted by the fluid above plane C on the fluid between

plane C and the wall

Velocity

Velocity gradient

][)( 1-= sdydu g&

][ 2-×== mNPaAF

s

st


Rheological Properties of fluids (1)


• Newtonian and non-newtonian fluids• The relationships between the shear stress and shear rate in a real

fluid are part of the science of rheology.

dydumt =

l μ is constant (Newtonian)l μ is function of shear rate (Non-newtonian)

Bingham fluid (치약)

Shear thickening

Newtonian (꿀)Shear thinning (고분자)




• Time-dependent flow

• Viscoelastic fluids (점탄성) : viscous and elastic properties

Designation Effect of increasing shear rate

Time-dependent?

Examples

Pseudoplastic(유사가소성)

Thins No Polymer solutions, starchsuspensions, mayonnaise, paints

Thixotropic(요변성)

Thins Yes Some polymer solutions, some paints(시간에 따라 점도 감소)

Newtonian None No Gases, most simple liquidsDilantant(팽창성)

Thickens No Corn flour-sugar solutions, starch in water

Rheopectic Thickens Yes Bentonite clay suspensions(시간에 따라 점도 증가)


Viscoelatic fluids (1)


• What is viscoelasticity?

SUPER BALL

TENNISBALL

STORAGE = Elastic part

LOSS = Viscous part


Viscoelatic fluids (2)


l 대부분의 유체는점탄성을 가지고 있다.

l 하지만, 점성과 탄성이라는것은 한꺼번에 나타나지않는다.

l 점탄성에서 가장 중요한개념은 “시간”이다.

슬로 모션으로 촬영한 물방울


데보라 (Deborah number)


“The Mountains flowed before the Lord”

“산은신앞에서는흘러내린다 ”

l데보라 (Deborah) : 구약성경에나오는이스라엘의예언자

-산도 흘러 내릴 수 있다

-하지만 사람이 아니라 신 앞에서만 흘러 내린다

이문장에는두가지뜻이들어있다.

l왜냐하면, 사람이사는동안(아주짧은시간대충 60년)에는산이흘러내리는것을볼수없기때문에.

-De= 물질의 시간/ 관찰자의 시간

-De >>1 : 탄성체, De << 1 : 점성체




• Viscosity : shear stress와 shear rate간의 비례상수

• Gas viscosities increase with temperature increasing• Liquid viscosities decrease with temperature increasing

• Kinematic viscosity (동점도)

dydumt =

rmn =




• What is dynamic oscillatory shear test?

( ) 0 0cos Re[ ]i tt t e wg g w g= =

( ) ( )0 0cos( ) Re[ ]i tt t e w ds s w d s += + =

Input (strain)

Output (stress)

Phase angle 0° < d < 90°

0Re[ ( ) ]i tG e ww g*=

( ) ( ) ( )G G iGw w w* ¢ ¢¢º +

Strain

Stress

Pure “Elastic” material

d = 0°Strain

Stress

Pure “Viscous” material

d = 90°

“Viscoelastic” material

Oscillatory shear

Measuring stress

Rheometer

qSAOS (Small Amplitude Oscillatory Shear) test, it valid on linear regimeqSAOS (Small Amplitude Oscillatory Shear) test, it valid on linear regime




• Viscosity and Momentum flux• Flux = the rate of flow of any quantity per unit area• 벽에서 조금 떨어져서 흐르는 유체는 운동량을 가지지만, 벽에서는

유속이 0이므로 운동량도 0이다.• 따라서 움직이는 유체는 그보다 빨리 움직이는 유체층으로부터

차례로 운동량을 전달 받는다.• x 방향 운동량이 –y 방향으로 전달되어, u=0인 벽에 이르게 된다.

벽은 움직이지 않은므로, 운동량은 전단력으로 벽에 전달되는데, 이를벽전단 (wall shear)라 한다.

• 운동량은 유속이 빠른 부분에서 느린 부분으로 전달된다.• 이는 열이 고온에서 저온으로 흐르는것과 같다.• Momentum flux는 속도 구배 du/dy에 따라 달라진다.• 즉, 흐름방향에 수직인 방향으로의 momentum flux는 속도 구배에

비례하며 그 비례 상수가 점도가 된다.

dydumt =

dydTk

Aq

-=

부산대학교 현규유체역학및열전달 14

• Viscosity models• Newtonian fluids

• Bingham plastics

• Power-law fluids

dydumt =

dydu

dyduK

dyduK

nn 1-

=÷÷ø

öççè

æ=t

0

00

0 tt

tttt

<=

>=-

atdydu

atdyduK

l K: flow consistency indexl n: power-law index

n=1, Newtonian fluids (K=μ)n<1, pseudo-plastic (shear thinning) fluidsn>1, dilatant (shear thickening) fluids


Yield stress


우유 +식초 (Viscosity vs. Structure)


• Casein Protein

-Figure 1 : A casein micelle; A: a submicelle; B: protruding chain; C: Calcium phosphate; D: κ-casein; E: phosphate grou




• Viscosity as a function of shear rate


Turbulence (난류) (1)


• 난류는 여러 공학분야에서 중요하므로, 최근에 이에관한 연구가 많이 진행되었다.• 실제 난류중의 유속변동과 에디를 세부적으로 측정한결과 난류의 정성적 정량적 성질에 관해 많은 것을 알게되었다.



유체역학및열전달 Seminar 18

• Reynolds number

• In a pipe flow• Laminar region at Re < 2,100• Turbulent region at Re > 4,000• Transition region at 2,100 < Re < 4,000

nmr VDVD==Re

-Turbulent flow consist of eddies-Energy dissipation-Largest : dimension of stream-Smallest : 10-100 μm


• Deviating velocities (편차속도) in turbulent flow

• In one dimensional flow

u¢

iu u



wwvvuuu iii ¢=¢=¢+=l Although at first sight turbulence seems to be structureless and randomized.

lQuantitative characterization of turbulence is commonly done by statistical analysis of the frequency distributions

(random nature)


• Statistical nature of turbulence

• By measuring u’, v’, w’ at different places and over varying time periods, two kinds of data are obtained

(1) The three deviating velocity components at a single point can be measured, in general any two of them are found to be correlated. (same point at same time)(2) the values of single deviating velocity can be measured at different positions, (at station 1 and 2)

• Correlation coefficient



22 )()( vu

vuR vu¢¢

¢¢=¢¢

22

21

21

)()( uu

uuRu¢¢

¢¢=¢


• Reynolds stress (or turbulent shear stress), τt• 난류에서는 층류보다 훨씬 큰 shear force가 존재 (deviating velocity 때문).

따라서 점성응력외에 추가적인 난류 전단응력 (Reynolds stress)을고려하여야 함.

• Eddy viscosity, Ev• 난류전단응력과 전단속도와의 관계에서 정의되는 점도• Eddy viscosity, Ev 는 shear viscosity μ와 유사하게 정의됨

• Total shear stress in turbulent flow• Viscous stress와 turbulent stress의 합



dyduEvt =t

vut ¢¢= rt

dyduEvtv )( +=+= mttt


• Flow in boundary layers• The part of a moving fluid in which the fluid motion is influenced by

the presence of a solid boundary.

• 일반적으로 속도가 u∞ (bulk fluid velocity)의 99%가 되는지점을 연결한 line을 OL로 정의함

Boundary layers (경계층) (1)

Z= thickness of boundary layer

OL = outer limit of boundary layer



• Laminar and turbulent flow in boundary layers

• Laminar layer : very close to the wall• The viscous sublayer• The buffer layer• The turbulent zone




• Development of boundary layer flow in pipe

• The length of the entrance region of the tube necessary for fully developed flow to be established is called the transition length.

• Approximate transition length of straight pipe to reach fully developed flow, for laminar flow


-Fully developed flow (완전발달흐름): 속도분포가더이상변하지않는흐름

Re.050=Dxt



• Boundary layer separation and wake formation


Boundary layer separation:• When there is an abrupt change in the flow channel, such as a sudden expansion or contraction .


유체역학및열전달 chapter 3. fluid flow phenomena -...

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