Fluid dynamics và ứng dụng tính toán

Introduction to Fluid Mechanics*
Fred Stern, Tao Xing, Jun Shao, Surajeet Ghosh
8/26/2005

AFD

EFD

CFD

 U 0
DU
1 2
 p 
 U   ui u j
Dt
Re

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Fluid Mechanics
• Fluids essential to life
• Human body 65% water
• Earth’s surface is 2/3 water
• Atmosphere extends 17km above the earth’s surface
• History shaped by fluid mechanics
• Geomorphology
• Human migration and civilization

• Modern scientific and mathematical theories and methods
• Warfare
• Affects every part of our lives

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History
Faces of Fluid Mechanics

Archimedes

(C. 287-212 BC)

Navier

(1785-1836)

Newton

(1642-1727)

Stokes

(1819-1903)

Leibniz

(1646-1716)

Reynolds

(1842-1912)
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Bernoulli

Euler

(1667-1748)

(1707-1783)

Prandtl

Taylor

(1875-1953)

(1886-1975)
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Significance
• Fluids omnipresent
• Weather & climate
• Vehicles: automobiles, trains, ships, and
planes, etc.

• Environment
• Physiology and medicine
• Sports & recreation
• Many other examples!

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Weather & Climate
Tornadoes

Thunderstorm

Global Climate

Hurricanes

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Vehicles
Surface ships

Aircraft

High-speed rail

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Submarines

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Environment
Air pollution

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River hydraulics

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Physiology and Medicine
Blood pump

Ventricular assist device

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Sports & Recreation
Water sports

Cycling

Auto racing

Offshore racing

Surfing

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Fluids Engineering
Reality
Fluids Engineering System

EFD, U

D

 B2  P2

Components

Idealized

Mathematical Physics Problem Formulation

AFD, U m

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CFD,

2
2
U s  U SM
 U SN

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Analytical Fluid Dynamics
The theory of mathematical physics
problem formulation
• Control volume & differential analysis
• Exact solutions only exist for simple
geometry and conditions
• Approximate solutions for practical
applications
•

• Linear
• Empirical relations using EFD data
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Analytical Fluid Dynamics
•

Lecture Part of Fluid Class
•
•
•
•
•
•
•
•

Definition and fluids properties
Fluid statics
Fluids in motion
Continuity, momentum, and energy principles
Dimensional analysis and similitude
Surface resistance
Flow in conduits
Drag and lift

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Analytical Fluid Dynamics
• Example: laminar pipe flow

UD
 2000
Assumptions: Fully developed, Low Re 

Approach: Simplify momentum equation,
Schematic
integrate, apply boundary conditions to
determine integration constants and use
energy equation to calculate head loss
0
2
0
0
  u  2u 
Du
p

   2  2   gx
Dt
x
y 
 x

Exact solution :

u(r)  1 ( p)(R2  r 2)
4 x

8 du

8 w  dy w 64
f

Friction factor:
V 2 V 2 Re
p1
p2
L V 2 32  LV
hf  f

Head loss:   z1    z2  h f
D 2g
D2
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Analytical Fluid Dynamics
• Example: turbulent flow in smooth pipe( Re  3000)
Three layer concept (using dimensional analysis)

u u u


1.

y  yu 

u*   w 

0  y  5

Overlap layer (viscous and turbulent shear important)
1
u   ln y   B


3.

*



Laminar sub-layer (viscous shear dominates)

u y
2.

*

20  y   105

(=0.41, B=5.5)

Outer layer (turbulent shear dominates)

Assume log-law is valid across entire pipe:



Uu
r 
5

f
1


 y  10
*
u
r0 


u r
u*

*
1  r0  r  u
 ln
B



Integration for average velocity and using EFD data to adjust constants:
1
2log  Re f 1 2   .8
f
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Analytical Fluid Dynamics
• Example: turbulent flow in rough pipe
Both laminar sublayer and overlap
layer

Inner
layer:by uroughness
are
affected
u   y k 
Outer layer: unaffected
Overlap layer:

1 y
u   ln constant
 k

Three regimes of flow depending on k+
1. K+<5, hydraulically smooth (no effect of roughness)
2. 5 < K+< 70, transitional roughness (Re dependent)
3. K+> 70, fully rough (independent Re)

For 3, using EFD data to adjust constants:
1 y
u   ln  8.5  f  Re 
 k

Friction factor:

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1
k D
 2log
3.7
f

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Analytical Fluid Dynamics
• Example: Moody diagram for turbulent pipe flow
Composite Log-Law for smooth and rough pipes is given by the Moody diagram:

1
f

1

2

k D
2.51 
 2log 

12
 3.7 Re f 

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Experimental Fluid Dynamics (EFD)
Definition:
Use of experimental methodology and procedures for solving fluids engineering
systems, including full and model scales, large and table top facilities,
measurement systems (instrumentation, data acquisition and data reduction),
uncertainty analysis, and dimensional analysis and similarity.
EFD philosophy:
• Decisions on conducting experiments are governed by the ability of the expected
test outcome, to achieve the test objectives within allowable uncertainties.
• Integration of UA into all test phases should be a key part of entire experimental
program
• test design
• determination of error sources
• estimation of uncertainty
• documentation of the results

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Purpose
• Science & Technology: understand and investigate a

phenomenon/process, substantiate and validate a theory
(hypothesis)

• Research & Development: document a process/system,
provide benchmark data (standard procedures,
validations), calibrate instruments, equipment, and
facilities
• Industry: design optimization and analysis, provide data
for direct use, product liability, and acceptance
• Teaching: instruction/demonstration

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Applications of EFD

Application in science & technology

Application in research & development

Picture of Karman vortex shedding

Tropic Wind Tunnel has the ability to create
temperatures ranging from 0 to 165 degrees
Fahrenheit and simulate rain

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Applications of EFD (cont’d)

Example of industrial application
NASA's cryogenic wind tunnel simulates flight
conditions for scale models--a critical tool in
designing airplanes.
Application in teaching
Fluid dynamics laboratory
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