Ship Hydrodynamics - fincl.cnu.ac.krfincl.cnu.ac.kr/lecture/shiphydrodynamics/Lecture_Introduction_2017… · Ship Hydrodynamics Prof. Byoung-Kwon Ahn [email protected] http//fincl.cnu.ac.kr

Ship Hydrodynamics

Prof. Byoung-Kwon Ahn

[email protected] http//fincl.cnu.ac.kr

Dept. of Naval Architecture & Ocean Engineering

College of Engineering, Chungnam National University

Chapter 0: IntroductionShip Hydrodynamics 2

Lecture Information

Textbook: Fluid Mechanics: Fundamentals and Applications + Additional materials

by Yunus A. Cengel & John M. Cimbala (McGraw-Hill)

Time: Monday(13:30/75m), Wednesday(13:30/75m)

Structure: 15 weeks with two exams

Homework: selected problems at each chapter

Lecture materials: http//fincl.cnu.ac.kr

Grading: Midterm Exam(40%) + Final Exam(40%)

+ Homework(10%) + Attendance(10%)= Total(100%)

Reference Books:

선박의 저항과 추진 [대한조선학회/인터비전]

Preliminary subject: Fluid Mechanics (Y2)

Inquiry: 18:00~18:30 on every Monday (3-102)

Email: [email protected] Tel: 821- 6625

mailto:[email protected]


Contents

Chapter 0. Introduction

Chapter 1. Basic Concepts

Chapter 2. Properties of Fluids

Chapter 3. Fluid Statics

Chapter 4. Fluid Kinematics

Chapter 5. Fluid Dynamics: Conservation Principles

Chapter 6. Fluid Dynamics: Large Scale Analysis - Control Volume Analysis

Chapter 7. Fluid Dynamics: Experimental Analysis - Dimensional Analysis

Chapter 9. Fluid Dynamics: Small Scale Analysis - Differential Analysis

Chapter 8. Pipe Flows (Laminar and Turbulent Flows)

Chapter 9. Fluid Dynamics (Navier-Stokes Equation)

Chapter 10. Potential Flows

Chapter 11. Flow Over Bodies: Lift & Drag

Chapter 12. Compressible Flows

Chapter 13. Open Channel Flow → Chapter 12. Surface Waves

Chapter 14. Turbomachinery

Chapter 13. Computational Fluid Mechanics(CFD)

Chapter 14. Extra Topics: Practical Ship Hydrodynamics

Fluid Mechanics

(Y2)

Ship

Hydrodynamics

(Y3)


Fluid Mechanics Review

Chapter 1. Introduction and Basic Concepts

1) What is a Fluid and Fluid Mechanics?

2) Dimensions and Units


Fluid & Dynamics

Continuum Mechanics연속체역학

Rigid Body Mechanics강체역학

Deformable Body Mechanics가변체역학

Solid Mechanics고체역학

Fluid Mechanics유체역학

Fluid Statics

- Liquid (water): Hydrostatics- Gas (Air): Aerostatics

Fluid Dynamics

-Liquid (water): Hydrodynamics- Gas (Air): Aerodynamics

Ship Hydrodynamics



Chapter 2. Properties of Fluids

1) Basic properties of fluids: density, specific gravity,

specific weight etc

2) Compressibility

3) Shear Stress

4) Dynamic and Kinematic Viscosity

5) Surface Tension and Capillary Effect


Shear Stress

전단응력(shear stress): τ = F/A

유체 요소 AD의 각변형 속도 또는 변형률 (strain rate)

유체 요소의 변형률 (strain rate)은 속도구배

(velocity gradient)와 같다

5) 대부분의 유체의 전단응력은 유체 요소의 변형률 즉속도구배에 비례 함 (Hooke’s Law)

y

BA

C C’D D’

duy t

dy

u

duu ydy

d = dt

du/dy ytan(d ) tan( dt) dt=

d

dt

t dudt

y dy

d du

dt dy

d du

dt dy


Dynamic Viscosity

Newtonian fluids: 변형률이 전단응력에 비례하는 유체

- 물, 가솔린, 기름 등 대부분의 유체

2) Non-newtonian fluids: 변형률이 전단응력에 비례하지않는 유체 - 혈액, 액체 플라스틱 등

3) 뉴턴유체의 전단응력 (선형적인 관계식)

- 점성계수는 속도 구배에 독립적

4) 점성계수(coefficient of viscosity) 또는동역학적 점성계수 (dynamic viscosity)

2 N/m du

dy

2

2

m N s kgunit: N/m = = =Pa s (poise)

m/s m m s

dy

du

(Newtonian fluids)

(Non-newtonian fluids)


Kinematic Viscosity

동점성계수 (kinematic viscosity): 밀도에 대한 동역학적 점성계수의 비율

운동학(kinematics)적 차원을 가짐: Stoke [cm2/s]

Reynolds number:

2 2

2 4

/ unit: =

/

N s m m

N s m s

The viscosity of liquids decreases and the viscosity of gases increase with temperature

Fluid

(15ºC, 1atm)Density(ρ) Viscosity(μ)

Kinematic

Viscosity(ν)

Water999.1

[kg/m3]

1.144x10-3

[kg/ms]1.144x10-6

[m2/s]

Air 1.224

[kg/m3]

1.785x10-5

[kg/ms]

1.458x10-5

[m2/s]

e

VLR VL



Chapter 3. Fluid Statics

1) Pressure and variation of pressure with depth

2) Manometer and Barometer

3) Hydrostatic Forces on Submerged Body


유체 정역학(Fluid Statics): 유체입자의 상대 운동이 없을 때(정지상태) 또는 관성

좌표계 (inertial reference)에 대하여 등속운동을 하는 정적 평형상태에 있을 때

유체에 의해 작용하는 힘의 평형관계를 다루는 역학

- 정지상태에 있는 (물체 속의) 유체

- 등속 운동하는 (물체 속의) 유체

유체에 작용하는 힘

표면력(Surface Force) or 표면응력 – 표면에 직접 접촉하여 작용하는 힘

수직응력(Normal Stress, σ)

압축응력(Compressible Stress) – 압력(Pressure)

인장응력(Tensile Stress)

전단(접선)응력(Shear Stress, τ)

체적력(Body Force) – 표면에 접촉하지 않고 작용하는 힘

- 중력(Gravity), 전/자기력(Electro/Magnetic Force)

유체정역학에서는 유체의 상대 운동이 없는 상태(du/dy=0), 즉 전단응력이

작용하지 않는 상태에서 수직응력(σ - 압력)과 체적력(Gravity)만을 고려

Forces Acting on Fluid


유체요소의 관성력: (관성적으로 정지상태)

운동량 보존법칙:

정지상태의 압력(p)은 중력장에서 단지수직방향(z)만의 함수임

F 0

( ) 0

( )

ma

P dxdydz gdxdydz k

P g k

Pg

z

0 ma adxdydz

1 1

1 0 1 0 1

0 0

(ODE)

( ) atm atm

P dP

z dz

dP dz P P z z P h P gh P

z

x

y P0 = Patm

P1 = Patm + ρgh

h = z0 - z1

①

ⓞ

Fluid Statics; Pressure w/ Depth



Chapter 4. Fluid Kinematics

1) Lagrangian & Eulerian Descriptions of Fluid Motion

2) Material Derivative

3) Flow Visualization

4) Motion and Deformation of Fluid Elements: Stress

Tensor

5) Vorticity and Rotationality

6) Reynolds Transport Theorem (RTT)


Material Derivative

Material (total, particle & substantial) Derivative:

물질가속도(Material acceleration):

국소가속도

대류가속도

압력의 물질 도함수(Material derivative of pressure):

국소압력

대류압력

D dV

Dt dt t

Material

Derivative

Local

Term

Convective

Term

P

t

D

DtP

PV

( , , , )DV

a x y z tD

V

tV

tV


Flow Visualization

유동가시화를 통해 유동의 정성적, 정량적인 정보를 얻음

유동가시화는 물리적 실험 뿐만 아니라 수치해석(CFD)에도 유용하게 이용

유동가시화의 다양한 방법:

유선(Streamline)

유적선(Pathline)

유맥선(Streakline)

시간선(Timeline)

굴절 유동가시화 기법(Refractive flow visualization technique)

표면 유동가시화 기법(Surface flow visualization technique)


Motion & Deformation

유체요소의 운동과 변형의 기본 형태:

a) 이동(Translation)

b) 회전(Rotation)

c) 선형변형(Linear strain)

d) 전단변형(Shear strain)

유체역학에서는 운동과 변형이 동시에 발생하여복잡하므로 이들을 율(rate)의 형태로 표현하는것이 필요

a) 속도(velocity): rate of translation

b) 각속도(angular velocity): rate of rotation

c) 선형변형률(linear strain rate): rate of linear strain

d) 전단변형률(shear strain rate): rate of shear strain

변형률(deformation rates)을 속도와 속도의도함수로 표현


Shear Strain Rate Tensor

텐서량(Tensor Quantities):

0계텐서(0th order tensor)–스칼라(Scalar)량(n0): 크기만으로 정의되는 물리량 - Speed

1계텐서(1st order tensor)–벡터(Vector)량(n1): 크기와 방향으로 정의되는 물리량 - Velocity

2계텐서(2nd order tensor)–텐서(Tensor)량(n2): 크기/방향/작용면으로 정의되는 물리량 - Stress

응력텐서(Stress Tensor): 선형/전단 변형률 텐서(Shear strain rate tensor)와의 관계:

1 1

2 2

1 1

2 2

1 1

2 2

xx xy xz

ij yx yy yz

zx zy zz

u v u w u

x x y x z

u v v w v

y x y y z

u w v w w

z x z y z

ij ij


Vorticity

각속도

와도(Vorticity): 유체 입자의 각속도의 2배

비회전 유동(Irrotational Flow):

회전 유동(Rotational Flow):

2V

1

2

1 1curl( )

2 2

x y zi j k

w v u w v ui j k

y z z x x y

V V

0

w v u w v ui j k

y z z x x y

1 1z r z rr z

ruuu u u ue e e

r z z r r r


Material Derivative & RTT

( )Df f

V fDt t

Lagrangian

Description

Eulerian

Description

Differential Analysis

The Material Derivative is used to transform from Lagrangian to Eulerian

descriptions for Differential Analysis

MV

dDf

DtV ( )

CV

fV f

td V

System

Analysis

Control

Volume

Analysis

Integral Analysis

The Reynolds transport theorem (RTT) is used to transform from system to

control volume for Integral Anlaysis

nCV C

s

S

syddV

Bb bV dA

dt t



Chapter 6. Fluid Dynamics: Large Scale Analysis - Control Volume Analysis

Chapter 7. Fluid Dynamics: Experimental Analysis - Dimensional Analysis

Chapter 9. Fluid Dynamics: Small Scale Analysis - Differential Analysis


Contents of Fluid Dynamics




1) Conservation of Mass

2) Conservation of Momentum

3) Conservation of Energy

4) Bernoulli Equation & its applications


Conservation Laws

Conservation of Mass: mass of a system remains constant

Conservation of Momentum: momentum of a system remains constant when the net force acting on it is zero

Conservation of Linear Momentum

Conservation of Angular Momentum

Conservation of Energy: net energy transfer to or from a system during a process be equal to the change in the energy content of the system

0Dm

Dt

( )D mVF

Dt

( )D r mVM

Dt

DE Q W

Dt t t


Bernoulli Equation

Bernoulli Equation: relation between pressure and velocity and elevation in regions of steady, incompressible and inviscid flow.

2) Viscous effects are negligibly small compared to inertial, gravitational and pressure effects.

3) Conservation of linear momentum principle.

4) When the flow is steady, all particles that pass through the same point follow the same path, and the velocity vectors remain tangent to the path at every point.

5) Bernoulli Equation [J]: Sum of the kinetic, potential, and flow energies of a fluid particle is constant along a streamline of steady, incompressible and inviscid flow.

Boundary Layer

(Inviscid region)

(Viscous region)

Wake

2 2

1 1 2 21 2

2 2

P V P Vgz gz


Conservation of Linear Momentum:

Acceleration along a streamline (s-direction):

Forces acting along a streamline:

Bernoulli Equation

( ) sinsF PdA P dP dA W

s sF ma

2 21 1 1( ) 0

2 2

dz dVdPdA gdAds dAds V

ds ds

dP gdz VdV

dPd V gdz dP dV g dz C

2

2

P Vgz C

s

V V dV V ds VdV ds dt

s t dt s dt t

dV V ds V dVa V V

dt s dt s ds

steady



Chapter 6. Fluid Dynamics: Large Scale Analysis

1) Control Volume Analysis

2) Linear and Angular Momentum Equation


Linear Momentum Equation

Newton’s second law for a system of mass m subjected to a force F is expressed as

Use RTT with b = V and B = mV to shift from system formulation of the control volume

formulation

sys

d mVVd V

dt t

r

CV CS

V V n dA

F Vd Vt

r

CV CS

V V n dA


Integral Analysis

Steady Flow

Mass flow rate (mass flux)

Momentum flow rate (momentum flux)

To account for error, use momentum-flux correction factor (

F Vd Vt

avg avg

out inCV

m V m V 1

C

C

C avgA

VdA

A V

( )

C

C avg C avg avg

A

V V n dA V A V mV

( )

C

C avg C

A

m V n dA V A

( )r

CS

F V V n dA



Chapter 7. Fluid Dynamics: Dimensional Analysis

1) Dimensional Homogeneity

2) Dimensional Analysis and Similarity

3) Buckinghanm Pi Theorem

4) Experimental Testing and Incomplete Similarity


Principle of Similarity

Geometric Similarity: the model must be the same shape as the prototype. Each dimension must be scaled by the same factor.

Kinematic Similarity: velocity as any point in the model must be proportional

Dynamic Similarity: all forces in the model flow scale by a constant factor to corresponding forces in the prototype flow.

Complete Similarity is achieved only if all three above conditions are met.

Geometric similarity

Kinematic similarity

Dynamic similarity


Dimension of the force

Consider all forces acting on a body in fluid flows

P V TG IEFF ma F FF FF 3 2

2 2

3

2 2 2

2

2

Inertial force ( )

Gravitational force ( )

Pressure force ( )

Viscous force ( )

Surface tension force ( )

Elastic force ( )

I

G

P

V

T

E

LVF ma V LL

F mg L g

F PA V A V L

VF A A VLL

F L V L

F A L


Nondimensional parameters

Common established nondimensional parameters:

2 2 2

3

2 2

Intertial forceGravitat

Intertial forceViscous fo

ional force

rceReyno

Froude number

l

Euler numb

ds number

er

I

G

I

V

Vr g

F V L VF gLgL

F V L VL

F VLVL

L

e

F

R

2

2 2 2

2 2 2

Pressure forceInertial force

Intertial forceSurf

Intertial forceElastic forc

ace tension force

e

Weber number

Mach num er

b

P

I

I

T

F PL Pu F V L V

F V L V L

e F L

E

W

2 2 2

2 2 I

E

F V L V Va F CL C

M

2where is a bulk modulus of elasticity c


Nondimensional parameters

2

Pressure-Vapor P

cDynamic pressure 1/2

Characteristic flow timePeriod of oscillation

Lift forceDynamic force

Cavitation number

Strouhal number

Lift coefficient

vP P

V

fL

t VS

2

2

2

1/2

Drag force

Dynamic force 1/2

Static pressure diff.

Dynamic pressure 1/2

Wal

Drag coefficient

Pressure coefficient

Friction coefficient

L

D

F

L V A

F

D V A

P P

p V

C

C

C

2

l friction forceDynamic pressure 1/2

fF

f V AC

Common established nondimensional parameters:


Flows with Free Surfaces


For ship hydrodynamics:

Complete similarity?:

To match both Re and Fr, viscosity in the model test is a function of scale ratio! This is not

feasible to change the kinematic viscosity each model test.

p m

e e m pm p m pm p

mr r m p pm p

pm p

LVL VLR R V V

L

LV VF F V V VgL gL L

3/ 2 3/ 2

m m mm p

p p p

L L

L L

( , , , , )

( , )

D

D e r

F f V L g

C f R F

Flows with Free Surfaces

Documents

Ship Hydrodynamics - fincl.cnu.ac.krfincl.cnu.ac.kr/lecture/shiphydrodynamics/Lecture_Introduction_2017… · Ship Hydrodynamics Prof. Byoung-Kwon Ahn [email protected] http//fincl.cnu.ac.kr