Constructal Theory and Its Applications by Prof. Adrian Bejan and

A talk “Constructal Theory and Its Applications” by renowned Professors
A Faculty Based Seminar was presented by Professor Adrian Bejan and Professor Sylvie Lorente on
27 January 2010. Over 140 audiences attended.
Power point file of Prof. Bejan
Power point file of Prof. Lorente
The last two decades have marked important changes in how thermodynamics is taught, researched
and practiced. The generation of flow configuration was identified as a natural phenomenon. The new
physics principle that covers this phenomenon is the constructal law, which was formulated in 1996:
“For a finite-size flow system to persist in time (to survive) its configuration must evolve (morph) in
time in such a way that it provides easier flow access to its currents.” The geometric structures derived
from this principle for engineering applications have been named constructal designs. The thought that
the same principle serves as basis for the occurrence of geometric form in natural flow systems is
constructal theory. The origin of the generation of geometric form rests in the balancing (or
distributing) of the various flow resistances through the system. A real system owes its irreversibility
to several mechanisms, most notably the flow of fluid, heat and electricity. The effort to improve the
performance of an entire system rests on the ability to balance all its internal flow resistances, together
and simultaneously, in an integrative manner. This seminar will present Professor Bejan’s recent work
and breakthrough on this subject area.
The Speakers :
Professor Adrian Bejan, Duke University
Professor Bejan got his BS, MS and PhD from Massachusetts Institute of Technology (MIT). He is
now the J.A. Jones Professor of
Mechanical Engineering. His
research covers a wide range of
topics in thermodynamics, heat
transfer,
fluid
mechanics,
convection and porous media.
More recently, he developed the
constructal law of design in
nature. He is ranked among the
100 most highly cited authors
worldwide in engineering (all
fields, all countries), the
Institute
of
Scientific
Information, 2001. Professor
Bejan has received 15 honorary
doctorates from universities in
10 countries.
Lecture by Professor Bejan
Professor Sylvie Lorente, INSA Toulouse, France
Professor Lorente got her BS, MS
and PhD from INSA Toulouse,
France. She is at Laboratory of
Materials and Durability of
Constructions,
INSA-UPS,
Department of Civil Engineering,
Nathional Institute of Applied
Science, Touloue, France. Her
research interests encompass
vascularized
materials,
constructal theory, porous media,
fluid mechanics, heat and mass
transfer.
Lecture by Professor Lorente
Presentation of Souvenir
Constructal Theory and
Applications
Adrian Bejan
Sylvie Lorente
J. A. Jones Distinguished Professor
Duke University
University of Toulouse
France
www.constructal.org
*A. Bejan and S. Lorente, Design with Constructal Theory (Wiley, 2008)
“The design” vs. “to design”
“Design in Nature” is flow
Inanimate
Animate
2
1. The generation of “design” is a physics phenomenon.
2. The phenomenon is summarized by the constructal law (1996)
“For a finite-size flow system to persist in time (to live) it must
evolve in such a way that it provides greater and greater access
to its currents”.
The sense of the movie tape of design in nature
Time
3
Nature flows with design (configuration)
Animate + inanimate
Geo + Bio + Socio
4
Constructal Flow of Animal Mass
Flying
Vertical loss:
W1 ~ MgLb
Horizontal loss:
W2 ~ FdragL
W1 + W 2
L
Larger animals
travel faster, V ~ M1/6
wave less frequently, t–1 ~ M–1/6
00
0
0
V
and are stronger, F = 2gM
move more mass to greater distances, W ~ MgL
5
A. Bejan, Shape and Structure,
from Engineering to Nature,
Cambridge Univ. Press, 2000.
Constructal animals, “human & machine species”, technology evolution
6
J. Exp. Biol. 209 (2006) 238-248.
Pour la Science, August 2006.
7
The evolution of speed, size and shape in modern athletics
J. D. Charles and A. Bejan, The Journal of Experimental Biology 212 (2009), 2419-2425
Fig. 2. Running world records for 100 m dash, men:
(A) speed (V) vs time (t); (B) body mass (M) vs t; (C)
V vs M. The world record data for all the figures
cover the period 1929–2008.
8
Fig. 1. Swimming world records for 100 m freestyle,
men: (A) speed (V) vs time (t); (B) body mass (M) vs
t; (C) V vs M. The world record data for all the figures
cover the period 1912–2008.
9
Constructal origin of “characteristic sizes”
Fixed mass: flying with less fuel
Fixed fuel: flying more mass, farther
More mass = faster
10
The size of every component that functions inside a complex flow system
&
& ∆P
W
m
1
=
ηp p L
L
&
W
m
2
≅ 2 gV
L
L
& +W
&
W
c
1
2
≅ 14 + c2 D2
L
D
Round duct with specified flow rate
(
& 2 / πηpρ2
c1 = 128µm
∆P
32µ
= 2 U
L
D
(
& / ρπD 2 / 4
U is the mean fluid velocity, m
)
1/ 6
⎛ c ⎞
Dopt = ⎜ 2 1 ⎟
⎝ c2 ⎠
)
c2 = 2περ w gV
1/ 6
⎛ 128µm
&2 ⎞
=⎜ 2
⎟
⎜ π ηpρ2ρw gV ⎟
⎝
⎠
11
Constructal Flow of People and Goods
V0: walking
V1: riding
H0
V0
=2
L0
V1
t 0 = t1
~5 minutes
Atlanta
airport
12
LONDON
PARIS
NICE
13
2002
2050
14
1. The generation of “design” is a physics phenomenon.
2. The phenomenon is summarized by the constructal law (1996)
“For a finite-size flow system to persist in time (to live) it must
evolve in such a way that it provides greater and greater access
to its currents”.
The sense of the movie tape of design in nature
Time
15
Constructal law: The time direction of the movie tape of
generation of design in nature,
not about optimality, min, max, “entropy”, destiny, or end-design.
Ad-hoc optimality principles, whose results were also deduced from
the constructal law:
Minimization of entropy generation (EGM)
Maximization of entropy generation (MEP)
Minimization of flow resistance
Maximization of flow resistance
Minimum time, cost
Minimum weight
Optimal organ size
Uniform stresses
Survival of the fittest
Survival of the most adaptable
Maximum growth rate of disturbances : hydrodynamic instability
16
A. Bejan and S. Lorente, Design with Constructal Theory, Wiley, 2008
www.constructal.org
17
Thermodynamics: systems viewed as black boxes, without configuration:
System: closed, cycles (or steady).
1st law :
QH − QL − W = 0
QL QH
−
≥0
2 law :
TL TH
nd
Derived : Wrev
“Energy” defined
“Entropy” defined
⎛ TL ⎞
= Q H ⎜ 1 − ⎟ Carnot limit, exergy,
⎝ TH ⎠ availability
Gouy & Stodola theorem
stability (U min, S max)
Note: Entropy generation minimization (EGM or maximization of efficiency) is not one
of the derived statements. It is a self-standing ad-hoc statement.
18
Open system,
steady state :
Engine, on
vehicle
Animal
19
Evolution, in time:
Configuration
Performance
20
Q: What happened to the produced work?
A: Mass was
moved to
a distance
= Mixing
Work = (“friction factor”) (weight) (distance)
water
W
land
Mg
L
air
21
The whole Earth is an “engine + brake” system
22
System:
Animal
Human & machine
Earth
23
24
Constructal Design of Roots, Trunk and Canopy:
Water flow + flow of stresses
h
= constant
x
Leonardo da Vinci’s rule
Fibonacci sequence
A. Bejan, S. Lorente and J. Lee,
Journal of Theoretical Biology,
Vol. 254 (3), 7 October 2008 25
Constructal Design of the Forest
Tree mass flow rate ~ tree length scale
(b)
(a)
Zipf’s distribution, predicted,
predicted earlier for
city size vs. rank (2006)
26
The Pyramids,
from Egypt to
Central America
W = W12 + W23
(
= µ1N ( R − r ) + ( µ 2 N cos α + N sin α ) H + r
⎡1
⎤
αopt = tan-1 ⎢ ( µ 2 - µ1 )⎥
⎣2
⎦
2
2
)
1/ 2
27
Design with Constructal
Theory, Vascularization
Sylvie Lorente, Adrian Bejan
Université de Toulouse,
INSA Toulouse, France.
Duke University, Durham, USA
1
Adrian Bejan, Duke University, North
Carolina, USA
1996
“For a finite-size open system to persist in
time (to survive) it must evolve in such a
way that it provides easier and easier
access to the currents that flow through it ”.
2
Introduction
Constructal Theory :
Minimization of flow resistances
Geometry
Two visions
• Understand and predict natural
phenomena (river basin,
circulation in atmosphere,
swimming, flying…)
• Design for the engineers
3
Outline
‰ Tree-shaped networks in a disc-shaped
body
‰ Line-to-line tree flow
‰ Vascularized materials for self healing
‰ Vascularized materials for self cooling
4
Tree-shaped networks in
a disc-shaped body
Micro-channels
Electronics cooling
objectives
To deliver a fluid from a source
to a given number of outlets
(users)
Minimum ∆P
constraints
Disc-shaped area
Number of outlets
Total volume of the tubes
5
We obtain the connecting angles by minimizing
the function ‘overall pression’
The shape of the network is the result.
It is « given » by the angles.
(48 outlets)
6
When optimized complexity is beneficial
N = constant
pairing is a useful feature
if N sufficiently large
N increases
the level
of pairing increases
complexity increases
N constant
7
Line-to-line tree flow
8
Laminar flow
Optimal diameter ratio
D i / D i +1 = 2
1/ 3
Hess-Murray law
9
For a given mass flow rate
d
Or
We fix the volume of tubes
α = 45°
10
Laminar flow, pressure drop
8
L
& Po ν 4
∆P = m
π
D
Poiseuille
constant, 16 for
round tube
n, bifurcation level
α =45°
L 0 = 2L1
L1 = 2L 2
& i = 2m
& i +1
m
etc, etc…
11
∆P
14
≅ n
∆Pref 2
When are tree-shaped flows
better than parallel flows?
∆P
<1
∆Pref
∆P / ∆Pref < 0.1
Level of
bifurcation: n >
4
n>7
12
Vascularized materials for
self healing
• Cracks Æ loss of mechanical performances
• Objective: Recover the initial strength after
healing
• First attempt: micro capsules or tubes
embedded in the material. Today: vascular
structures
13
Pressurized network
Pressurized network
&N +m
&W −m
&S − m
&E
ρi, jVi, j ) = m
(
dt
d
Objective: to minimize the
discharge time of the network
14
1,2
t_min / t_1D
15
0,8
16
0,4
17
0
8*8
20*20
40*40
Grid
Result: D2/D1 optimal leading to a
discharge time divided by 2
15
Trees matched canopy to canopy
Direct injection of the fluid in the network
trunk
canopy
canopy
trunk
16
• Diameter ratio corresponding to
a minimum flow resistance
• Choice of the most performing
network
Optimal diameter ratio and
optimal aspect ratio
Example of 6 elements
17
D1/D2 optimized
vs single D
reduction of the flow resistance
Systematic study: trend?
50
40
30
20
10
0
0
10
20
30
40
50
60
number of elements
Optimal aspect ratio: close to 1
18
Trees matched canopy to canopy:
the superiority of vascular design
Second construct, 3D
∆P3
First construct: one-dimensional stack
∆P1
L = nd
&
m
D3
d
H
&
m
&
m
H
py
&
m
D1
L
p
&
m
1
r
py
D3
2
D3
D4
2
D1
&
m
1
H
D4
L
p
D3
r
py
r
Third construct, 3D
19
Growth & transitions: larger and more complex
vasculatures
Scaling up: not an enigma
when the principle of configuration generation is known
10 6
104
~
∆P1
~
∆P4 (env )
30
~
∆P
20
10
4
~
∆P3
10
p=3
102
3
102
p≅5
p=4 r≅3
~
∆P3 (env )
~
∆P1
2
p =1
p=2
p =1
1
1
1
10
N
d
y
102
103
First construct (1D stack)
and second construct
1
10
d
N
y
102
First, second, and third
constructs
20
Vascularized materials for
self cooling
21
Effect of the pumping power on the temperature distribution
Be = 1.3 × 109
Be = 1.7 × 1010
22
For a given pumping power,
increasing n increases the thermal
performance.
If n>4, trees are better.
23
Global thermal resistance vs pressure drop number, steady state
24
Time delay before the start of cooling
25
Conclusion
• Optimal micro-vascularization through
constructal theory Æ designed porous media
• Application to different scales
26
Toulouse
27
27