New Horizons for Optimization in Fluid
Mechanics

Cameron Tropea
Institute of Fluid Mechanics and Aerodynamics
Center of Smart Interfaces
Technische Universität Darmstadt, Germany
International Research Training Group (IGK 1529)
9th Japanese-German International Workshop on
Mathematical Fluid Dynamics
Novemeber 5-8, 2013, Waseda University
Cameron Tropea | Center of Smart Interfaces | Technische Universität Darmstadt

1Personnel

Felix Loosmann
 PhD student Graduate School ofComputational Engineering Enhanced compact heatexchangers

Florian Wassermann
 PhD student
 Center of Smart Interfaces Magnetic Resonance
Thermometry

Cameron Tropea | Center of Smart Interfaces | Technische Universität Darmstadt

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Cooperative Research

Fluid Mechanics and Aerodynamics
Cameron Tropea | Center of Smart Interfaces | Technische Universität Darmstadt

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VisionRapid-Prototyping offers unlimited degrees of freedom in design andmanufacturing of complex components.
This introduces new challenges for the mechanical engineer,
perhaps surpassing his formal education in the areas of optimization
A vision of new possibilities can be illustrated using the field ofinternal heat exchangers.

Cameron Tropea | Center of Smart Interfaces | Technische Universität Darmstadt4

General Design Objectives
Minimize both size of the heat exchanger and thework required to pump fluid through it
Direct Laser Sintering
Technology
 Manufacture 3D objects insingle step directly from CAD
 No bonding issues
 Arbitrary internal structure
Optimize shape of passages for
fluid flow to maximize heattransfer while reducing pressure
lossesCameron Tropea | FG Strömungslehre und Aerodynamik | Center of Smart Interfaces |5Forced convection flows in heat exchanger
Pin Fin Array(simple geometry)

Tetadecahedron(advanced geometry)

Stochastic FoamSource: Onstad et al. 2010
Cameron Tropea | Center of Smart Interfaces | Technische Universität Darmstadt

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Conventional Heat Exchangers

Source: T.J. Lu et al.

Cameron Tropea | Center of Smart Interfaces | Technische Universität Darmstadt

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New horizons, new structures

Source: www.inhabitat.com

Tetradecahedral Lord Kelvin 1887
 Found in aluminium foams
 Isoperimetric quotient = 0.75

Weaire Phelan structure (1993)
 Olympic swimming stadium inBeijing
 8 irregular tetradecahedrons + 2
dodecahedron Isoperimetric quotient = 0.76

Cameron Tropea | Center of Smart Interfaces | Technische Universität Darmstadt

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Magnetic Resonance Imaging (MRI) in MedicalApplications
MRI encompasses different measurement principles
 Magnetic Resonance Imaging (MRI): visualization of tissue Magnetic Resonance Velocimetry (MRV): extracting fluid flow of blood vessels

MRI-scanner

Source: www.siemens.de
Cameron Tropea | Center of Smart Interfaces | Technische Universität Darmstadt

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4D MRV by Markl et al.: A Living, Beating Heartlinker Herzkammer und Aorta
linke Lungenvene
rechte Lungenvene
Untere Hohlvene
Obere Hohlvene

Source: WikipediaCameron Tropea | Center of Smart Interfaces | Technische Universität Darmstadt

10Magnetic Resonance Tomograph in the Clinic

Source: www.siemens.de
Cameron Tropea | Center of Smart Interfaces | Technische Universität Darmstadt

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MRI – Possibilities and Limitations

Possibilities

Limitations

 Non-invasive No optical access necessary
 No post-processing 3-dimensional data
 3 velocity component data Experiments with water flow
 No metal material
 FOV: cubical (500mm)^3
 MRV – „just“ velocities
 Velocity range: 1cm/day up to 10 m/s
 Steady flow But: CineMRV, Reynolds stresses,concentration, thermometry
measurements possible

 Resolution: ~0.7mm iso-volume(decreasing SNR)

Cameron Tropea | Center of Smart Interfaces | Technische Universität Darmstadt

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Basic principle: NMR
 NMR = Nuclear Magnetic Resonance

Simple atomic modelelectrons

 Using quantum mechanical features of the atomic nucleus

 Focus on Hydrogen nucleus
 Reason: It is present in the human body!
 1 proton  charge
 Spin = ½  rotation
“Spin Magnet”

nucleus Spin Magnet can interact with magnetic fields  measurement signal
 Static field (B0-field, 3 Tesla)  Spin magnet precesses
 Dynamic fields:
 RF pulses  stimulation
 Gradient fields  imaging, fluid velocities

Cameron Tropea | Center of Smart Interfaces | Technische Universität Darmstadt

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Simple Geometry: Pin Fin Array Re=10,000
 Ercoftac SIG 15 Testcase 2

Recirculation zones,
hot spot(blue)
High speed jets(green)

Jet impingement
 high convective
heat transfer
Cameron Tropea | Center of Smart Interfaces | Technische Universität Darmstadt

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Laser Sintered Structures

Cubic array

Cameron Tropea | Center of Smart Interfaces | Technische Universität Darmstadt

Tetradecahedral array

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Experimental Facility (U of Toronto)

Cameron Tropea | Center of Smart Interfaces | Technische Universität Darmstadt

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Measurement Data
10240

kW/m² 3.2 2.3 1.5 0.8

Cubic
Tetradecahedral
Eq. (4)Eq. (5)Structure
Tetradecahedral
Cubic
Empty Channel
Laser Sintered Empty Channel

Nusselt Number, NuH

200

fDa0.5

10.1

160

×+120

80

400.01

01

10100

1000

ReK

2000
3000
Reynolds Number, ReH

Pressure Loss

Heat Transfer

Cameron Tropea | Center of Smart Interfaces | Technische Universität Darmstadt

01000

4000

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Heat Transfer Coefficient, h [W/m2K]

Infrared Visualization
25080 L/min
20060 L/min
40 L/min15020 L/min

100500050 100 150 200 250 300
Axial Distance from Inlet, x [mm]IR Camera

Cameron Tropea | Center of Smart Interfaces | Technische Universität Darmstadt

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Conduction vs. Convection
Cubic Array

Tetradecahedral Array

2.3 kW/m²: 20, 40, 60, 80 L/min
Cameron Tropea | Center of Smart Interfaces | Technische Universität Darmstadt

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Heat Exchanger Efficiency
Peclet Number

QconvPe 
Qcond k s 1    H
Increase of enthalpy

Q  mc p ,a Tin  Tout For given flow rate Pe smaller for
cubic array because  is lower.
Convection more dominant for
tetradecahedral than cubis array.

100Heat Exchanger Efficiency, η [%]mc p ,a806040kW/m²Structure
Tetradecahedral
Cubic

203.2

2.3

1.5

2030
Peclet Number, Pe

40

0.8

00Cameron Tropea | Center of Smart Interfaces | Technische Universität Darmstadt

105020More complexity: Tetradecahedral grid Flow rate = 62 l/min @ 30°C, Ubulk=0.109m/s
 MRV parameters Field of view (FOV): 158x100x100mm3, 1x1x1mm3 resolution
 1.58mio vectors
 3 scans averaged (improved SNR), 17 min/scan
FOV - MRV

Domain - CFD

Cameron Tropea | Center of Smart Interfaces | Technische Universität Darmstadt

MRV – Data centered21

Similar flow features as in the Pin Fin Arrayflow through the element center

flow at the element surroundings

Recirculation zones,
hot spot

High speed jets

Cameron Tropea | Center of Smart Interfaces | Technische Universität Darmstadt

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Development of flow field Flow fully developed after 3 tetradecahedral elementsCameron Tropea | Center of Smart Interfaces | Technische Universität Darmstadt

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Flow field development

Cameron Tropea | Center of Smart Interfaces | Technische Universität Darmstadt

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CFD simulation
Notes on numerical methods
 Scaling of model: MRV:SIM = 3.9 : 1
 Constant Reynolds Number Velocity ratio: MRV:SIM = 0.109 : 0.4251 [m/s] Numerical Method: FVM, laminar, steady state (SIMPLE algorithm)
 Numerical Software: OpenFOAM 2.2.x / 2.2.1
CFD Domain
 Gradient schemes: Linear Divergence schemes: Upwind Symmetry (reduced CFD domain)

Mesh Type: unstructured
 Generator: snappyHexMesh
 Cell Count: 29,619,795
 Max Skewness: 1.16
Cameron Tropea | Center of Smart Interfaces | Technische Universität Darmstadt

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MRV vs. CFD

Cameron Tropea | Center of Smart Interfaces | Technische Universität Darmstadt

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Optimization Strategy
 Overall concept
 Appropriate indicator functions
 Objective functions (global/local)
 CFD/MRV validation
 Optimization strategy
Design factors
 Strut geometry
 …..

Goodness factor:

i Nu Pr 1/3
jf ReCameron Tropea | Center of Smart Interfaces | Technische Universität Darmstadt

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Streamlines
 Streamlines in center of structure (blue) stay in line maybe disadvantegeous for heat transfer

 Streamlines off center of structure (red) diverge
 increased diffusion (and heat transfer)

Cameron Tropea | Center of Smart Interfaces | Technische Universität Darmstadt

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New horizons: Three-dimensional temperature
mapping using MR Thermometry
To recall: Important for MRI is the magnetic reaction ofthe Hydrogen core (proton) of the H2O molecule H2O = dipol Liquid H2O = Varying hydrogen bonds
 Increased water temperature leads to less strongerhydrogen bonds (bonds bend, stretch and break)The free electron can screen the hydrogen more
efficiently
This reduces the local effective magnetic fieldLarmor frequency decreases
 |ω50°C – ω20°C| = 38.3Hz (only!) Only measurable in the MR signal phase Phase-difference Δ𝜙 is proportional to watertemperature difference to a reference scanCameron Tropea | Center of Smart Interfaces | Technische Universität Darmstadt

𝜔(𝑇) = 𝛾𝐵𝑒𝑓𝑓 (𝑇)Δ𝜙 = 𝜙𝑟𝑒𝑓 𝑇𝑟𝑒𝑓 − 𝜙 𝑇𝑖29

Thanks for your attentionCameron Tropea | Center of Smart Interfaces | Technische Universität Darmstadt

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A first shot…
 Heated bottle filled with concentrated
water inside a heat exchanger Concentrated water prevents freeconvection flow

 MR Thermometry sequence:TMRT,mean = 19.06+/-0,39°C

 Fibre optical temperature transducer:

Measured temperature field (2D)

TLuxtron = 19.10°C

 Goal of DFG funded project:

T [°C]

 Measuring 3D temperature fields
together with 3D velocity fields

Cameron Tropea | Center of Smart Interfaces | Technische Universität Darmstadt

31Spin The spin is a quantum-mechanical characteristic of atomic particles.
 Uneven mass number  net spin!
 A rotating charge is always magnetic.
 Spins are distributed in the field An ensemble of spins in a small volume = VOXEL
Spin of a proton

Source: Hendrix 2008

Cameron Tropea | Center of Smart Interfaces | Technische Universität Darmstadt

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Spin in a magnetic field In the presence of a strong external magnetic field the nuclei align along
the field direction.
 More up-spins than down-spins  net magnetization

Source: Hendrix 2008

Cameron Tropea | Center of Smart Interfaces | Technische Universität Darmstadt

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Spin precession
 The spin magnets do not align steadily. Theyprecess.
 The spin precession takes place at a fixed
frequency depending on the magnetic fieldstrength.
 Lamor frequency
𝜔0 = 𝛾𝐵0
 All spin magnets precess with same
frequency but different phase no resulting magnetization!

Source: Hendrix 2008

Cameron Tropea | Center of Smart Interfaces | Technische Universität Darmstadt

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Measuring the Spin
 No magnetization can be measured!
However all spins precess out of phase…

HF-Puls HF pulses (circular polarized wave) at theprecession frequency disturb the equilibrium of thespins.
 The spin flips at angle α A transverse magnetization is achievedH This produces a magnetization vector M with
 Longitudinal component (M_z)
 Transverse component (M_xy)
H[1]Source: Hendrix 2008

Cameron Tropea | Center of Smart Interfaces | Technische Universität Darmstadt

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Relaxation and Decay
 Spin-lattice relaxation (or T1 relax.) of M_z
 Time constant T1
 Due to interactions with surrounding atomicneighborhood

 Decay of transversal magnetization (or T2*relaxation)
 Time constant T2*
 Local precession frequency
differences lead to spin-spin
phase dispersion
Source: Hendrix 2008

 Different relaxation types lead to different
contrast of tissue

Cameron Tropea | Center of Smart Interfaces | Technische Universität Darmstadt

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MR-Signal
 90°-rf pulse All spins in phase M_z=0
 M_xy rotates with Larmor frequency

 Transverse magnetization is equal to a rotating
magnet Dynamo principle
 induces electric current in a coil

HF-PulsH MR-Signal=Free induction decay of M_xy

Source: Hendrix 2008

Cameron Tropea | Center of Smart Interfaces | Technische Universität Darmstadt

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Measuring volume in 3D
The precession frequency is depending on themagnetic field strength

By applying gradients to the field strength slices of the volume can be selected during excitation(slice selection)

 Local precession frequencies can be modified (xcoordinate/frequency encoding) Phase differences can be obtained by temporal
gradients (y-coordinate/phase encoding)

Source: Hendrix 2008

Cameron Tropea | Center of Smart Interfaces | Technische Universität Darmstadt

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From the signal to the image
The complex signal is stored in k-space.
Two Fourier Transforms reconstruct the original
magnitude of the signal in every voxel. That gives theimage.

FTSource: www.siemens.de

Cameron Tropea | Center of Smart Interfaces | Technische Universität Darmstadt

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Phase Contrast Imaging
 Not used so far is the original phase 𝜙 of the signal in every voxel=> Phase Contrast Imaging  Velocities

Cameron Tropea | Center of Smart Interfaces | Technische Universität Darmstadt

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Measuring Velocities 3C
The phase of the MR-signal is sensitivefor fluid motion.

By applying a bipolar gradient pulse, Static spins acquire phase and lose itagain
 Moving spins acquire less phase thanthey loose
One measurement per direction (3C)
necessary.

Source: Markl et al.

Cameron Tropea | Center of Smart Interfaces | Technische Universität Darmstadt

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