Coupled Momentum and Heat Transport in Laminar Axisymmetric Pipe - - PowerPoint PPT Presentation

▶
coupled momentum and heat transport
SMART_READER_LITE
LIVE PREVIEW

Coupled Momentum and Heat Transport in Laminar Axisymmetric Pipe - - PowerPoint PPT Presentation

Sep 18, 2022 18 likes •533 views

Coupled Momentum and Heat Transport in Laminar Axisymmetric Pipe Flow of Ferrofluids in Non-Uniform Magnetic Fields: Theory and Simulation MS Candidate: Carlos F. Cruz-Fierro Advisor: Dr. Goran N. Jovanovic Chemical Engineering Department

slide-1
SLIDE 1

Coupled Momentum and Heat Transport in Laminar Axisymmetric Pipe Flow of Ferrofluids in Non-Uniform Magnetic Fields: Theory and Simulation

MS Candidate: Carlos F. Cruz-Fierro Advisor: Dr. Goran N. Jovanovic

Chemical Engineering Department Oregon State University April 2, 2003

Revision 1 33680.05

slide-2
SLIDE 2

2

Presentation Overview

  • Objectives
  • General concepts
  • Transport in the presence of EM fields
  • Simulation
  • Results
  • Conclusions
slide-3
SLIDE 3

3

Objectives

  • Show the necessary additions to conservation

equations when a fluid is subject to electromagnetic fields

  • Evaluate and interpret the effect of these fields in

the particular case of transport of momentum and heat in the axisymmetric pipe flow of a water-based ferrofluid

  • Extrapolate the simulation to predict the behavior of

an hypothetical liquid metal-based ferrofluid under similar flow conditions

slide-4
SLIDE 4

4

Transport Phenomena

  • Physical quantity A moved through space and

generated from or transformed into other physical quantities by known mechanisms

  • Conservation equation - represents a balance
  • f A in a control volume
  • Constitutive relation - associates quantities of

different nature; relates transport or generation with one or more driving forces

slide-5
SLIDE 5

5

Maxwell Equations

q

 D

t B E B t D H J

  • Set of four partial differential equations relating

fields (E, D, B, H) and their sources.

slide-6
SLIDE 6

6

Ferrofluid

  • Colloidal suspension of

nanosize ferromagnetic particles, stabilized by surfactant

  • High magnetic susceptibility
  • Remains fluid at high fields
  • Carrier fluid: water or

hydrocarbon

  • Current research in liquid-

metal ferrofluids

magnetic particle surfactant layer

slide-7
SLIDE 7

7

Presentation Overview

  • Objectives
  • General concepts
  • Transport in the presence of EM fields
  • Simulation
  • Results
  • Conclusions
slide-8
SLIDE 8

8

Mass Conservation Equation

t  u No change in the presence of electromagnetic fields

slide-9
SLIDE 9

9

Momentum Conservation Equation

P t     u uu g

EM

t t P     D u u g B u T D B

EM

T

Electromagnetic momentum Maxwell stress tensor

slide-10
SLIDE 10

10

Maxwell Stress Tensor

EM

d d    

D H

E DE D E E D B BH B H B H T I I Together with EM momentum can be transformed into Lorentz force density

q

 f E J B

slide-11
SLIDE 11

11

Thermal Energy Conservation Equation

ˆ ˆ : U U P t    u q u u

1 1 2 2

ˆ ˆ : U U t P t    u q u D H S u E B

1 1 2 2

D E B H

S

Electromagnetic energy Poynting vector

slide-12
SLIDE 12

12

Poynting Vector

S E H

Together with EM energy can be transformed into Joule heating

EM

w J E

slide-13
SLIDE 13

13

Ferrofluid Viscosity

, , , , ,

h h h

T T T       B B

2

tanh 1.5 sin tanh

h

       

2

1 1

c h h

a b    

3

6 1

M

mH M Bd T T       Viscosity at zero field plus effect of magnetic field

slide-14
SLIDE 14

14

Vortex Viscosity

B u u   m

particle rotation

slide-15
SLIDE 15

15

Vortex Viscosity

B u m u  

particle rotation Particle rotation causes magnetic misalignment

slide-16
SLIDE 16

16

Presentation Overview

  • Objectives
  • General concepts
  • Transport in the presence of EM fields
  • Simulation
  • Results
  • Conclusions
slide-17
SLIDE 17

17

Simulation

Flow Flow

R R c min Rc max

slide-18
SLIDE 18

18

FiRMA code

  • FiRMa: Flow in Response to a Magnetic field
  • Visual Basic code serves as simulation solver and

visualization tool for the output

slide-19
SLIDE 19

19

Magnetic Field Simulation

pipe wall

1 2 3 ... LI LI+1 ... ... NI 1 2 3 4 ... NJ=LJ ... ...

-direction

symmetry

  • Find vector potential A,

then B = A

  • First order triangular

finite element

  • Mesh extends radially

beyond pipe to include coil(s) and to allow fields lines to close

  • Potential fixed at

boundary nodes A = 0

slide-20
SLIDE 20

20

Fluid Flow Simulation

  • SIMPLE Method,

solution of momentum and mass conservation

  • Upwind scheme
  • Rectangular grid,

staggered cells for momentum equation

  • Additional cells around

to include boundary conditions

pipe wall

1 2 3 ... ... LI LI+1 1 j=0 2 3 4 ... LJ LJ+1 ... ... i=0

slide-21
SLIDE 21

21

Heat Transfer Simulation

  • Same grid as pressure
  • Two types of wall cells: constant

temperature and adiabatic

  • Upwind scheme
slide-22
SLIDE 22

22

Presentation Overview

  • Objectives
  • General concepts
  • Transport in the presence of EM fields
  • Simulation
  • Results
  • Conclusions
slide-23
SLIDE 23

23

Vector Potential - Single Coil

— 0.002 T·m — 0 — -0.002

slide-24
SLIDE 24

24

Br - Single Coil

— 0.073 T — 0 — -0.073

slide-25
SLIDE 25

25

Bz - Single Coil

— 0.410 T — 0 — -0.410

slide-26
SLIDE 26

26

Magnitude of B - Single Coil

— 0.410 T — 0

slide-27
SLIDE 27

27

Vector Potential - Double Coil

— 0.002 T·m — 0 — -0.002

slide-28
SLIDE 28

28

Br - Double Coil

— 0.115 T — 0 — -0.115

slide-29
SLIDE 29

29

Bz - Double Coil

— 0.18 T — 0 — -0.18

slide-30
SLIDE 30

30

Magnitude of B - Double Coil

— 0.18 T — 0

slide-31
SLIDE 31

31

Velocity components

Water-based ferrofluid, single coil (run W-04s)

— 1×10–5 m/s — 0 — -1×10–5 m/s — 0.020 m/s — 0

ur uz

slide-32
SLIDE 32

32

Velocity components

Water-based ferrofluid, double coil (run W-04d)

— 3.8×10–5 m/s — 0 — -3.8×10–5 m/s — 0.020 m/s — 0

ur uz

slide-33
SLIDE 33

33

Velocity components

Mercury-based ferrofluid, single coil (run M-04s)

— 7.5×10–4 m/s — 0 — -7.5×10–4 m/s — 0.020 m/s — 0

ur uz

slide-34
SLIDE 34

34

Velocity components

Mercury-based ferrofluid, single coil (run M-04s)

— 1.8×10–3 m/s — 0 — -1.8×10–3 m/s — 0.019 m/s — 0

ur uz

slide-35
SLIDE 35

35

Apparent Viscosity

Water-based ferrofluid

— 0.032 Pa·s — 0 — 0.036 Pa·s — 0

single coil double coil

slide-36
SLIDE 36

36

Apparent Viscosity

Mercury-based ferrofluid

— 0.035 Pa·s — 0 — 0.037 Pa·s — 0

single coil double coil

slide-37
SLIDE 37

37 — 0.020 m/s — 0

0.005 0.010 0.015 0.020 0.025

  • 0.010
  • 0.005

0.005 0.010

r [m] Uz [m/s]

1 2 1 2 parabolic

Velocity Profiles

Mercury-based ferrofluid, single coil

slide-38
SLIDE 38

38

Velocity Profiles

Mercury-based ferrofluid, single coil

0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020

  • 0.010
  • 0.005

0.005 0.010

r/R [-] Uz [m/s]

1 2 1 2 parabolic — 0.019 m/s — 0

slide-39
SLIDE 39

39

0.005 0.010 0.015 0.020 2.5E+6 5.0E+6 7.5E+6 1.0E+7

Coil current density [A/m²] Average velocity [m/s]

Single coil without heating Single coil with heating Double coil without heating Double coil with heating

Average Velocity

Water-based ferrofluid

slide-40
SLIDE 40

40 0.005 0.010 0.015 2.5E+6 5.0E+6 7.5E+6 1.0E+7

Coil current density [A/m²] Average velocity [m/s]

Single coil without heating Single coil with heating Double coil without heating Double coil with heating

Average Velocity

Mercury-based ferrofluid

slide-41
SLIDE 41

41

Temperature Profiles

Water-based ferrofluid No field Single coil Double coil

— 100 °C — 20

slide-42
SLIDE 42

42

Temperature Profiles

Mercury-based ferrofluid No field Single coil Double coil

— 100 °C — 20

slide-43
SLIDE 43

43

500 1000 1500 2000 0.025 0.050 0.075 0.100 0.125 0.150

Axial distance from bottom [m] Local heat transfer coefficient [W/m²·K]

W-00-h W-04s-h W-04d-h Heated region

Local Heat Transfer Coefficient

Water-based ferrofluid

slide-44
SLIDE 44

44

500 1000 1500 2000 2500 3000 3500 4000 0.025 0.050 0.075 0.100 0.125 0.150

Axial distance from bottom [m] Local heat transfer coefficient [W/m²·K]

M-00-h M-04s-h M-04d-h Heated region

Local Heat Transfer Coefficient

Mercury-based ferrofluid

slide-45
SLIDE 45

45

600 620 640 660 680 700 720 740 760 780 800 2.5E+6 5.0E+6 7.5E+6 1.0E+7

Coil current density [A/m²]

Average heat transfer coefficient [W/m²·K]

Single coil with heating Double coil with heating

Average Heat Transfer Coefficient

Water-based ferrofluid

slide-46
SLIDE 46

46

1100 1120 1140 1160 1180 1200 1220 1240 1260 1280 1300 2.5E+6 5.0E+6 7.5E+6 1.0E+7

Coil current density [A/m²]

Average heat transfer coefficient [W/m²·K]

Single coil with heating Double coil with heating

Average Heat Transfer Coefficient

Mercury-based ferrofluid

slide-47
SLIDE 47

47

Presentation Overview

  • Objectives
  • General concepts
  • Transport in the presence of EM fields
  • Simulation
  • Results
  • Conclusions
slide-48
SLIDE 48

48

Conclusions

  • Very small effect on velocity profile in water-based

ferrofluid (vortex viscosity only); much larger effect in mercury-based ferrofluid (Lorentz forces)

  • Increased viscosity caused reduction in average

velocity

  • No change in temperature profile of water-based

ferrofluid; large changes for mercury-based ferrofluid

  • Peak in local heat transfer coefficient coincides with

region of higher radial velocities induced by stronger field gradients

slide-49
SLIDE 49

49

Future Work

  • Search for other flow conditions with larger

magnetic field effect in momentum and heat transport

  • Examine other geometric configurations
  • Extend simulation to cases without axial symmetry

assumption

  • Work into expanding current vision of

transport theory

slide-50
SLIDE 50

50

Acknowledgments

FINANCIAL SUPPORT Consejo Nacional de Ciencia y Tecnología (CONACYT, México) COMMITTEE MEMBERS

  • Dr. Goran Jovanovic
  • Dr. Chih-hung Chang
  • Dr. Ronald Guenther
  • Dr. Ronald Miner

ChE FACULTY AND STAFF specially to

  • Dr. Levenspiel

Dawn Jordana Nick

  • Dr. Rorrer
slide-51
SLIDE 51

51

Acknowledgments

ChE GRADUATE STUDENTS