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
*A. Bejan and S. Lorente, Design with Constructal Theory (Wiley, 2008)
www.constructal.org
Adrian BejanJ. A. Jones Distinguished Professor
Duke University
Constructal Theory and Applications
Sylvie LorenteUniversity of Toulouse
France
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 accessto its currents”.
Time
The sense of the movie tape of design in nature
3
00
L
WW 21+
00
V
Larger animals
travel faster, V ~ M1/6
wave less frequently, t–1 ~ M–1/6
and are stronger, F = 2gM
move more mass to greater distances, W ~ MgL
Flying
5
Vertical loss: W1 ~ MgLb
Horizontal loss: W2 ~ FdragL
Constructal Flow of Animal Mass
A. Bejan, Shape and Structure, from Engineering to Nature,
Cambridge Univ. Press, 2000.
Constructal animals, “human & machine species”, technology evolution
6
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.
The evolution of speed, size and shape in modern athleticsJ. D. Charles and A. Bejan, The Journal of Experimental Biology 212 (2009), 2419-2425
8
Fig. 1. Swimming world records for 100 m freestyle, men: (A) speed (V) vs time (t); (B) body mass (M) vst; (C) V vs M. The world record data for all the figures cover the period 1912–2008.
9
Constructal origin of “characteristic sizes”
10
Fixed mass: flying with less fuel
Fixed fuel: flying more mass, farther
More mass = faster
11
The size of every component that functions inside a complex flow system
2
P 32 = U
L D
∆ µ
Round duct with specified flow rate
is the mean fluid velocity,U ( )2m / D / 4ρπ&
1
p
W m P =
L p L
∆η
& &2W m
2 gVL L
≅&
21 2 124
W W c + c D
L D
+≅
& &
( )2 21 pc 128 m /= µ πη ρ& 2 wc 2 gV= περ
1/ 61/ 6 21
opt 2 22 p w
c 128 mD 2
c gV
⎛ ⎞⎛ ⎞ µ= = ⎜ ⎟⎜ ⎟ ⎜ ⎟π η ρ ρ⎝ ⎠ ⎝ ⎠
&
0 0
0 1
0 1
H V= 2
L V
t = t
Constructal Flow of People and Goods
~5 minutes Atlanta airport
V0: walking
V1: riding
12
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 accessto its currents”.
Time
The sense of the movie tape of design in nature
15
Constructal law: The time direction of the movie tape ofgeneration of design in nature,
not about optimality, min, max, “entropy”, destiny, or end-design.
Ad-hoc optimality principles, whose results were also deduced from
Minimization of entropy generation (EGM)Maximization of entropy generation (MEP)Minimization of flow resistanceMaximization of flow resistanceMinimum time, costMinimum weightOptimal organ sizeUniform stressesSurvival of the fittestSurvival of the most adaptableMaximum growth rate of disturbances : hydrodynamic instability
the constructal law:
16
Thermodynamics: systems viewed as black boxes, without configuration:
“Energy” defined
“Entropy” defined
Carnot limit, exergy, 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.
System: closed, cycles (or steady).
18
L H
L H
Q Q0
T T− ≥
H LQ Q W 0− − =
Lrev H
H
TW Q 1
T
⎛ ⎞= −⎜ ⎟
⎝ ⎠
st1 law :
nd2 law :
Derived :
Q: What happened to the produced work?
Mass was moved to a distance = Mixing
A:
Work = (“friction factor”) (weight) (distance)water
W land Mg Lair
21
Water flow + flow of stresses
Leonardo da Vinci’s ruleh constant
x=
A. Bejan, S. Lorente and J. Lee, Journal of Theoretical Biology, Vol. 254 (3), 7 October 2008
Constructal Design of Roots, Trunk and Canopy:
Fibonacci sequence 25
Tree mass flow rate ~ tree length scale
Zipf’s distribution, predicted,
predicted earlier for city size vs. rank (2006)
Constructal Design of the Forest
26
(b)
(a)
The Pyramids, from Egypt to Central America
( ) ( )( )12 23
1/ 22 21 2
W W W
N R r N cos N sin H r
= +
= µ − + µ α + α +
( )⎡ ⎤⎢ ⎥⎣ ⎦
-1opt 2 1
1α = tan µ - µ2 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, USA1996
“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
Two visions
• Understand and predict natural phenomena (river basin, circulation in atmosphere, swimming, flying…)
• Design for the engineers
Constructal Theory :
Minimization of flow resistances Geometry
3
4
Tree-shaped networks in a disc-shaped body
Line-to-line tree flow
Vascularized materials for self healing
Vascularized materials for self cooling
Outline
Micro-channelsElectronics cooling
objectives
constraints Disc-shaped area Number of outletsTotal volume of the tubes
To deliver a fluid from a source to a given number of outlets (users)
Minimum ∆P
Tree-shaped networks in a disc-shaped body
5
We obtain the connecting angles by minimizing the function ‘overall pression’
(48 outlets)
The shape of the network is the result.It is « given » by the angles.
6
When optimized complexity is beneficial
N = constantpairing is a useful feature if N sufficiently large
N increases the level of pairing increases
complexity increasesN constant
7
Laminar flow, pressure drop
4D
LPo
8mP νπ
=∆ &
Poiseuille constant, 16 for
round tube
n, bifurcation levelα =45°
10 L2L =21 L2L =
etc, etc…
1ii m2m += &&
11
nref 2
14
P
P≅
∆∆
1P
P
ref
<∆∆
When are tree-shaped flows better than parallel flows?
Level of bifurcation: n > 4
refP / P 0.1∆ ∆ < n 7>12
Vascularized materials for self healing
• Objective: Recover the initial strength after healing
• First attempt: micro capsules or tubes embedded in the material. Today: vascular structures
• Cracks loss of mechanical performances
13
14
Pressurized network
( )dV m m m mi, j i, j N W S E
dtρ = + − −& & & &
Objective: to minimize the discharge time of the network
Pressurized network
0
0,4
0,8
1,2
8*8 20*20 40*40Grid
t_m
in /
t_1D
15
16
17
Result: D2/D1 optimal leading to a discharge time divided by 2
15
Direct injection of the fluid in the network
Trees matched canopy to canopy
trunk
canopy
trunk
canopy
16
17
Example of 6 elements
• Diameter ratio corresponding to a minimum flow resistance • Choice of the most performing network
Optimal diameter ratio and optimal aspect ratio
Systematic study: trend?
0
10
20
30
40
50
0 10 20 30 40 50 60
number of elements
redu
ctio
n of
the
flow
resi
stan
ce
Optimal aspect ratio: close to 1
D1/D2 optimizedvs single D
18
L = nd1P∆
H
m&
m&
d
p
L
py
3P∆
3D
Hm&
m&
1D
H
p
L r
py
1
2
r
3D
py3D
1D
1
2
r
3D4D
4D
m&
m&
First construct: one-dimensional stack
Second construct, 3D
Third construct, 3D
Trees matched canopy to canopy:the superiority of vascular design
19
First construct (1D stack) and second construct
Growth & transitions: larger and more complex vasculatures
610
1
210
1 10 310210
3P~∆
1p =
1P~∆
410
2
3
10
20
30
y
dN
1
210
1 10 210
P~∆
410
1P~∆
( )envP~
3∆
( )envP~
4∆
5p ≅
1p =
2p =
3p =
4p = 3r ≅
y
dN
First, second, and third constructs
Scaling up: not an enigma when the principle of configuration generation is known
20
23
For a given pumping power, increasing n increases the thermal performance.
If n>4, trees are better.
Conclusion
• Optimal micro-vascularization through constructal theory designed porous media
• Application to different scales
26