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
Chapter 0: IntroductionShip Hydrodynamics 3
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)
Chapter 0: IntroductionShip Hydrodynamics 4
Fluid Mechanics Review
Chapter 1. Introduction and Basic Concepts
1) What is a Fluid and Fluid Mechanics?
2) Dimensions and Units
Chapter 0: IntroductionShip Hydrodynamics 5
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 0: IntroductionShip Hydrodynamics 6
Fluid Mechanics Review
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
Chapter 0: IntroductionShip Hydrodynamics 7
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
Chapter 0: IntroductionShip Hydrodynamics 8
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)
Chapter 0: IntroductionShip Hydrodynamics 9
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 0: IntroductionShip Hydrodynamics 10
Fluid Mechanics Review
Chapter 3. Fluid Statics
1) Pressure and variation of pressure with depth
2) Manometer and Barometer
3) Hydrostatic Forces on Submerged Body
Chapter 0: IntroductionShip Hydrodynamics 11
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
Chapter 0: IntroductionShip Hydrodynamics 12
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 0: IntroductionShip Hydrodynamics 13
Fluid Mechanics Review
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)
Chapter 0: IntroductionShip Hydrodynamics 14
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
Chapter 0: IntroductionShip Hydrodynamics 15
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)
Chapter 0: IntroductionShip Hydrodynamics 16
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
Chapter 0: IntroductionShip Hydrodynamics 17
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
Chapter 0: IntroductionShip Hydrodynamics 18
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
Chapter 0: IntroductionShip Hydrodynamics 19
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 0: IntroductionShip Hydrodynamics 20
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
Fluid Mechanics Review
Contents of Fluid Dynamics
Chapter 0: IntroductionShip Hydrodynamics 21
Fluid Mechanics Review
Chapter 5. Fluid Dynamics: Conservation Principles
1) Conservation of Mass
2) Conservation of Momentum
3) Conservation of Energy
4) Bernoulli Equation & its applications
Chapter 0: IntroductionShip Hydrodynamics 22
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
Chapter 0: IntroductionShip Hydrodynamics 23
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
Chapter 0: IntroductionShip Hydrodynamics 24
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 0: IntroductionShip Hydrodynamics 25
Fluid Mechanics Review
Chapter 6. Fluid Dynamics: Large Scale Analysis
1) Control Volume Analysis
2) Linear and Angular Momentum Equation
Chapter 0: IntroductionShip Hydrodynamics 26
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
Chapter 0: IntroductionShip Hydrodynamics 27
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 0: IntroductionShip Hydrodynamics 28
Fluid Mechanics Review
Chapter 7. Fluid Dynamics: Dimensional Analysis
1) Dimensional Homogeneity
2) Dimensional Analysis and Similarity
3) Buckinghanm Pi Theorem
4) Experimental Testing and Incomplete Similarity
Chapter 0: IntroductionShip Hydrodynamics 29
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
Chapter 0: IntroductionShip Hydrodynamics 30
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
Chapter 0: IntroductionShip Hydrodynamics 31
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
Chapter 0: IntroductionShip Hydrodynamics 32
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:
Chapter 0: IntroductionShip Hydrodynamics 33
Flows with Free Surfaces
Chapter 0: IntroductionShip Hydrodynamics 34
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