유체역학 강의 시간: 화 2, 목 2-3교시 (공학관 166호) 강의 시간: 화 2, 목 2-3교시 (공학관 166호) 안동준 (ahn@korea.ac.kr), 3290-3301, 공학관 701호 조교: 최열교, 3290-3729, 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)

Fluids: Liquids ? 한강

Fluids: Gases ? Vincent van Gogh, 1889

Fluids: Solids ? 설악산

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.

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

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=26 R=10,000

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

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

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

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

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.

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

Example 3: Transient simulation of a complex chemical processes

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

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

~ 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 …

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

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

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

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

• 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    

• 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

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

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.

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:

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

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

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

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

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