1. 유체역학 강의 시간: 화 2, 목 2-3교시 (공학관 166호)
강의 시간: 화 2, 목 2-3교시 (공학관 166호)
안동준 , 공학관 701호
조교: 최열교, , 공학관 732호
강의 목표: 화공생명공학의 기본이 되는 유체 이동의 미시적, 거시적 원리 이해/응용
강의 교재 및 참고 교재:
“Process Fluid Mechanics,” Morton M. Denn, Prentice-Hall (1980)
“Introduction to Fluid Dynamics,” Stanley Middleman (1997)
“Transport Phenomena,” Bird et al. (2001)
“Analysis of Transport Phenomena,” Deen (1998)
“Incompressible Flow,” Panton (1996)
“Fundamentals of Momentum, Heat, and Mass Transfer,” Welty et al. (2000)

2. Fluids: Liquids ? 한강

3. Fluids: Gases ?
Vincent van Gogh, 1889

4. Fluids: Solids ?
설악산

5. Deborah’s Viewpoints
The Deborah number is a dimensionless number, used in rheology to characterize how "fluid" a material is. Even some apparent solids "flow" if they are observed long enough; the origin of the name, coined by Prof. Markus Reiner, is the line "The mountains flowed before the Lord" in a song by prophetess Deborah recorded in the Bible (Judges 5:5).
Formally, the Deborah number is defined as the ratio of a relaxation time, characterizing the intrinsic fluidity of a material, and the characteristic time scale of an experiment (or a computer simulation) probing the response of the material. The smaller the Deborah number, the more fluid the material appears.
The equation is thus:
      
where tc refers to the characteristic timeframe and tp refers to the timeframe of the phenomenon.

6. Flow past closer spheres
Album of Fluid Motion
M. Van Dyke (1982)
Creeping flow
Flow in a wedge (Moffat effect)
Hele-Shaw flow past a circle
Flow over a rectangular cavity
Flow past closer spheres

7. Laminar flow
Separation flow
Secondary streaming induced by an
oscillating cylinder
Laminar separation from a curved wall
Symmetric plane flow past an airfoil
Cylinder at Re= R=10,000

8. Vortices
Starting vortex on a wedge
Karman vortex street behind a circular
cylinder at Re=140

9. Instability
Capillary instability of a liquid jet
Axisymmetric laminar Taylor vortex
Convection in a rotating annulus

10. Instability
Turbulence
Hexagonal Benard convection
Turbulent water jet
Kelvin-Helmoltz instability of
stratified shear flow

11. Turbulence
Free-surface flow
Wake of a grounded tankship
Spilling breaking waves
Atomization from a nozzle

12. Example 1: Transient simulation of complex chemical processes
Schematic diagram of spinning process
Flow
direction
Spinneret
Take-up
Diameter
Spinline distance
Modeling and Simulation
Equation of continuity
+ Equation of motion
+ Constitutive equation
+ Energy equation
+ etc.

13. Example 2: Transient simulation of complex chemical processes
Schematic diagram
Die
Cast film
Neck-in
Edge bead
Cross-section of the film
Chill roll

14. Example 3: Transient simulation of a complex chemical processes

15. Example 4: Curtain coating flow
(APPROACH TO
EXTENSIONAL FLOW)
FILM FORMING ZONE
TAKE-AWAY ZONE
(AFTER KISTLER (1983))
CURTAIN FORMING ZONE
CURTAIN FLOW ZONE
IMPINGEMENT ZONE
DYNAMIC
CONTACT LINE
STATIC

16. Part I. Introduction Chap. I: Process Fluid Mechanics Fluid mechanics
Morton M. Denn, Process Fluid Mechanics (1980)
Chap. I: Process Fluid Mechanics
1. Introduction
Fluid mechanics
• ~ concerned with the motion of fluids (liquid or gas) and the forces
associated with the motion
• ~ can explain the nature of physical phenomena involving the fluid flows
• One of fundamental transport phenomena
- Momentum, heat, and mass transfer

17. ~ focused on some overall characteristics of the motion itself
2. Macro-problems
~ focused on some overall characteristics of the motion itself
(No detailed structure of the flow filed)
Pipeline flow
• Power to pump the fluid  Decision for optimal pipe size …
Packed reactor
Pressure drop …
Fiber drawing (fiber spinning)
• Torque required to turn the screw
• Extruder screw speed
• Pressure build-up along the screw
• Drawing speed & tension …

18. Detailed structure of the flow field
3. Micro-problems
Detailed structure of the flow field
Analogy with heat and mass transports
Heat transfer coefficient
Particle-fluid mass transfer

19. Chap 2. Physical Properties
1. Introduction
• Density (): related to inertia & incompressible flow
• Viscosity ( or ): resistance to flow
2. Units
• Characteristic dimensions: length (L), mass (M), time ()
ex) velocity: L/ (m/s in SI units)
• SI units: length (m), mass (kg), time (s)
Table 2-2

20. 3. Continuum hypothesis • Density = mass / unit volume: Chap.7
Continuum hypothesis: mathematical limits for volumes tending to zero are
reached over a scale that remains large compared to molecular dimensions.
- Fluid elements dimension >> molecular dimension
- Meaningful for any volume, no matter how small

21. 4. Viscosity
• Fluid: material that cannot sustain a shearing in the absence of motion
• Viscosity measures the ease with which a fluid will flow
Operational definition of viscosity
Infinite parallel plates
• For const. U and H,
• For const. A, F=F(U/H) monotonically,
Shear stress:
Shear rate:
Shear stress ~ unique function of shear rate
Monotonically increasing

22. • Viscosity,
1 Pa.s = 10 p (g/cm.s) = 103 cp (e.g., water = 1 cp)
Newtonian fluids
• Constant viscosity () with varying shear rate (s)
e.g., low molecular weight liquids, all gases, …
• Effect of temp. on : For gases, T     (See Figs. 2-5, 2-6)
For liquids, T    

23. • e.g., high molecular weight liquids, slurries, suspensions, …
Non-Newtonian fluids
• e.g., high molecular weight liquids, slurries, suspensions, …
on log-log scale, viscosity function cannot drop off faster than slope -1
Bingham Plastic
Viscosity vs. shear rate?
Newtonian Fluid

24. Shear thinning fluids (pseudoplastic)
Shear thickening fluids (dilatant)
Bingham plastic (has yield stress)
e.g., Mayonnaise, blood, some paints, …

25. Difficult to measure two limiting values !
Upper Newtonian region
Power-law region
Lower Newtonian region
Difficult to measure two limiting values !
Power-law equation:
K: consistency factor, n: power-law index (n>0)
n  1 : Newtonian case
- Many processes are in power-law region, fitting data very well.
- Convenient equation for difference and integration.

26. Carreau model:
Time-dependent viscosity functions:
• e.g. some suspensions are time-dependent
• Viscosity changes in time with steady shearing (due to the structure change)
• Rheopectic: the longer the fluid undergoes shear, the higher its viscosity
(e.g., lubricants…)
Thixotropy: become less viscous, the longer the fluid undergo shear
Kinematic viscosity
Thermal diffusivity:
• Kinematic viscosity:
= Momentum diffusivity
Mass diffusivity:

27. Measurement
Merit compared with parallel plate flow ?
Linear velocity:
Shear rate:
Couette viscometer

28. 5. Viscoelasticity 6. Interfacial tension Skip… Chap. 19
Property of a liquid-gas or liquid-liquid interface
Giving rise to pressure difference (P) across an interface R1 R2
ds1
ds2 n
ds1
ds2
F2= ds2
F1= ds1
: force/unit length
acting across a line element in a surface
Normal to line, tangential to surface
Components of four forces in the direction of normal n to the surface

29. n component of these forces along ds2
Net n component of force due to interfacial tension
- for static fluids

30. Surface tension induces a pressure drop across a curved interface
Liquid
Air
P < PA
Fictitious Pressure Tank
Flat Interface (No Curvature)
Wall
P = PA PA

31. Interface Having Surface Tension
Qualitative pressures are as indicated in liquid for wavy interface shown
Pressure-Induced
Flow
Air
Liquid
Interface Having Surface Tension
Wall
P < PA
P > PA PA
Interfacial curvatures  Pressure drops  Flow
1. If there is no σ, the pressures are precisely atmospheric in the fluid at the
interface
2. The mechanism above is partially responsible for the healing of streaks