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Fliud-solid interactions - Coggle Diagram
Fliud-solid interactions
Week 1. Основы
W1-1. Связь механики жидкости и механики твердого тела
solid mechanic
FLUID AND SOLID MECHANICS
A FUNDAMENTAL ISSUE
COUPLED FLUID AND SOLID MECHANICS
fluid mechanic
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
STIFFNESS AND DENSITY
FLUID ALONE
SOLID ALONE
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
FLUID AND SOLID
AT THE INTERFACE
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EQUATIONS IN THE SOLID DOMAIN
SINGLE MODE APPROXIMATION IN THE SOLID DOMAIN
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W1-6 Безразмерные уравнения сопряжения
DIMENSIONLESS QUANTITIES IN THE FLUID
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DIMENSIONLESS QUANTITIES IN THE SOLID
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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
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COUPLING WITH A STILL FLUID
Fast
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Slow
GENERAL CASE
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(nabl
U+nabl't'
U)]n
}phi
dS=D
f
Pure interface
Mphi_
f
[-PI+1/St(nabl
U+nabl't'
U)]n_dS=D*f
P(X_
+Dqphi
)=P0(X
+Dqphi
)+Dp(X
+Dqphi
)+...
=P0(X_)+Dqphi_nabl
P0+Dp(X
)+...
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u
= qd/dtphi _
M
f
phi
[-pI+1/St(nablu+nabl't'u)]n
dS-Mq
f
(nablPphi
)(phi
n
)dS=f
W2-4.Добавленная жесткость
SMALL REDUCED VELOCITY, SMALL MOTION
M
f
phi_[...]n_dS-Mq
f
(nablP0phi)(phin)dS=f
M - mass number
q - Modal displacement
P0 - static pressure
(nablP0phi)(phin)dS - modal shape
phin_ - Geometry
FLUID-INDUCED STIFFNESS
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Linearized fluid dynamics
Hydrostatics
W2-5. Добавленная масса
FLUID AND SOLID
FLUID LOADING : MOTION INDUCED STRESS
Fluid boundary
conditions
STOKES NUMBER
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Boundary conditions
W2-6.Вычисление добавленной массы
Added mass
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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
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Added damping effect
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