Fliud-solid interactions
Week 1. Основы
W1-1. Связь механики жидкости и механики твердого тела
solid mechanic
fluid mechanic
FLUID AND SOLID MECHANICS
A FUNDAMENTAL ISSUE
COUPLED FLUID AND SOLID MECHANICS
FLUID-SOLID INTERACTIONS
W1-2 Инструмент анализа размерностей
FLOW AROUND A SPHERE : DIMENSIONAL QUANTITIES
FLOW AROUND A SPHERE : THE DIMENSIONLESS REYNOLDS NUMBER
PHYSICAL LAWS
EXAMPLE : DRAG ON A SPHERE
MEANING OF DIMENSIONLESS PARAMETERS
W1-3 Безразмерные числа
FLUID ALONE
SOLID ALONE
STIFFNESS AND DENSITY
DECOUPLED FLUID-SOLID INTERACTIONS
W1-4 Размерный анализ взаимодействий
DIMENSIONLESS PARAMETERS
FLUID AND SOLID
A NEW DIMENSIONLESS QUANTITY
THE MASS NUMBER
THE REDUCED VELOCITY
THE CAUCHY NUMBER
CLASSIFYING PROBLEMS USING DIMENSIONLESS NUMBERS
W1-5 Объединенные уравнения для жидкостей и твердых тел
EQUATIONS IN THE FLUID DOMAI
EQUATIONS IN THE SOLID DOMAIN
SINGLE MODE APPROXIMATION IN THE SOLID DOMAIN
FLUID AND SOLID
AT THE INTERFACE
Kinematic condition
Dynamic condition
AT THE INTERFACE
Fluid boundary
conditions
Solid boundary conditions
W1-6 Безразмерные уравнения сопряжения
DIMENSIONLESS QUANTITIES IN THE FLUID
DIMENSIONLESS QUANTITIES IN THE SOLID
DIMENSIONLESS TIME
DIMENSIONLESS EQUATIONS AT THE INFERFACE
Kinematic conditio
Dynamic condition
Fluid boundary
conditions
Solid boundary
conditions
Week 2. Твердое тело с неподвижной жидкостью
W2-1 Небольшие пониженные скорости
EFFECT OF THE REDUCED VELOCITY
BOUNDARY CONDITIONS ON THE FLUID DOMAIN
SMALL REDUCED VELOCITY
GENERAL CASE
COUPLING WITH A STILL FLUID
Fast
Slow
W2-2. Адаптированные безразмерные числа
NEW DIMENSIONLESS NUMBERS
Reynolds
Froude
Cauch
Stokes
Dynamic Froude
Mass
CHOICE OF DIMENSIONLESS NUMBERS
DIMENSIONLESS VARIABLES
FLUID AND SOLID
Fluid boundary
conditions
Solid boundary
conditions
Boyndary conditions
W2-3. Малое движение твердого тела
Displacement number
EXPANSION OF ALL VARIABLES
EQUATIONS AT THE ORDER ZERO IN D
Hydrostatics !
Kinematic condition
Dynamic condition
EQUATIONS AT THE INTERFACE
f{M[-PI+1/St(nablU+nabl't'U)]n}phidS=Df
Pure interface
Mphi_f[-PI+1/St(nablU+nabl't'U)]n_dS=D*f
P(X_+Dqphi)=P0(X+Dqphi)+Dp(X+Dqphi)+...
=P0(X_)+Dqphi_nablP0+Dp(X)+...
-
TWO KINDS OF FORCES
u= qd/dtphi _
Mfphi[-pI+1/St(nablu+nabl't'u)]ndS-Mqf(nablPphi)(phin)dS=f
W2-4.Добавленная жесткость
SMALL REDUCED VELOCITY, SMALL MOTION
Mfphi_[...]n_dS-Mqf(nablP0phi)(phin)dS=f
M - mass number
q - Modal displacement
P0 - static pressure
(nablP0phi)(phin)dS - modal shape
phin_ - Geometry
FLUID-INDUCED STIFFNESS
EXAMPLE : ICEBERGS AND ICE CUBES
Linearized fluid dynamics
Hydrostatics
W2-5. Добавленная масса
FLUID AND SOLID
FLUID LOADING : MOTION INDUCED STRESS
Fluid boundary
conditions
Boundary conditions
STOKES NUMBER
HIGH STOKES NUMBER
Negligible viscous effects
HIGH STOKES NUMBER : A SINGLE MODE SOLUTION
ADDED MASS
The fluid response is instantaneous
The fluid force is an inertia force.
Initial choice
New choice
Small reduced velocity
Small amplitude
Small viscosity
W2-6.Вычисление добавленной массы
Added mass
A CYLINDER IMMERSED IN AN INFINITE FLUID DOMAIN
Dimensionless
Dimensional
Apparent mass ~ double mass
(in that case !)
KINETIC ENERGY OF THE FLUID
DIRECTIONAL ADDED MASS
W3 Вязкость и гравитационный эффект
W3.1 Добавленное демпфирование
FLUID AND SOLID
Solid boundary
conditions
Fluid boundary
conditions
STOKES NUMBER
LOW STOKES NUMBER
Dominant viscous effects
LOW STOKES NUMBER :
A SINGLE MODE SOLUTION
interface
ADDED DAMPING
The fluid force is a damping force
The fluid response is instantaneous
ADDED DAMPING AND ADDED MASS
Added mass effect
Added damping effect
