Quantum Mechanics and the Cool Science of Hydrogen · 2017-05-11 · Quantum Mechanics and the Cool...

Jacob Leachman • School of Mechanical and Materials Engineering HYPER

Jacob Leachman, Associate ProfessorSchool of Mechanical & Materials Engineering

[email protected] (509) 335-7711http://hydrogen.wsu.edu @hydrogenprof

Quantum Mechanics and the Cool Science of Hydrogen

HYPER

drogenroperties fornergyesearch

H

In this talk:

1. An introduction

2. Why hydrogen?

3. Quantum Mechanics

4. Equations of State

5. Mixtures

http://hydrogen.wsu.edu/


1. Intro: My Norwegian Heritage:

2


1. Intro: Washington State University – Est. 1890

3

Land Grant:

Agriculture &

Engineering

emphasis

30,000 students

1,000 Mechanical &

Materials Engineers


H1.00794

1

ydrogen:2. Why the Swiss Army knife of energy.

Kardeshev Level 0:

Fossil & Organic energy

Kardeshev Level 1:

Sustainable planetary energy

Kardeshev Level 2:

Solar system energy

Kardeshev Level 3:

Galactic energy

4


3. Quantum Mechanics: The Hydrogen FamilyHydrogen

Atoms

Protium

Deuterium

Tritium

Isotopic Molecules

Hydrogen

Deuterium

Tritium

Non-isotopic Molecules

Hydrogen-Deuteride

Hydrogen-Tritide

Deuterium-Tritide

= Electron and orbit

= Proton = Neutron = Covalent bond

Allotropes (spin – isomers)

ParahydrogenOrthohydrogen

Paradeuterium Orthodeuterium

ParatritiumOrthotritium

= Nuclear spin

5


3. Quantum Mechanics: Nuclear-Spin IsomersIn 1932, Werner Heisenberg won the Nobel Prize:

“for the creation of quantum mechanics, the application of which has, inter alia, led to the discovery of the

allotropic forms of hydrogen.”1

1Nobelprize.org accessed 2010

6

Orthohydrogen Parahydrogen

Normal Hydrogen

3:1

/2 1 vJE kTn

n vJ

v J

Z i J E e

,0

,0

ortho

op

para

ZK

Z

2

20 2 1

0 0

5

2P B

Z ZC R k T

Z Z

2 2

2,2 ,1 ,2 ,10

,

,0 ,0 ,0 ,0

5

2

para para ortho ortho

P mix para ortho B

para para ortho ortho

Z Z Z ZC R y y k T

Z Z Z Z

Partition function:

Equilibrium ratio: Equilibrium Cp0:

All other ortho-para composition Cp0:


3. Quantum Mechanics: Ortho-para effects on properties

7

Latent heat of

vaporization

• 30% difference in ideal-gas properties• 5% difference in near-critical real-fluid properties• Largest, controllable “phase-change” of any cryogenic material


3. Quantum Mechanics: Thermal deBroglie Wavelength

8

• Lennard-Jones 6-12 Potential:

Repulsion

Attraction

RadiusU E

ner

gy

0 σ

-ε

12 6

4Ur r

AttractionRepulsion

3

AN PP

3

AN

RTT

• deBoer non-dimensionalized:

1/ 2

aN h

M


3. Quantum Mechanics: Quantum Parameter

0

0.5

1

1.5

2

2.5

3

3.5

Xenon

Krypt

on

Argon

Oxy

gen

CO

Nitr

ogen

met

hane

Neo

n

Tritiu

m

Deu

teriu

mHD

Parah

ydro

gen

Nor

mal

Hyd

roge

n

Hel

ium

-4

Hel

ium

-3

Fluid

Qu

an

tum

Para

mete

r

He-4

H2

D2

Ne Reduced Pressures versus Quantum Parameter

0

2

4

6

8

10

12

14

0 0.5 1 1.5 2 2.5 3 3.5

Quantum Parameter

Red

uced

Pre

ssu

re

P_crit

P_tp

He-3

He-4

H2

HD

D2

T2Ne

Classical


4. Equations of State: The pre-2007 Hydrogen EOS

• 32-term, pressure explicit, modified Benedict-Webb-Rubin EOS

• Published in 1984 by B. Younglove and R. McCarty at NBS

• 121 MPa Pressure limit

• 400 K Temperature limit

• Unphysical regions

• Same EOS for normal & para

10

2

432

132

32

112

42

9

2

32

72

42

52

32

3

2

9

2

87

2

654

2

3

2

21

2

exp323130

exp2928

exp2726

exp2524

exp2322

exp212019

181716151413

121110

9876

54321

T

G

T

G

T

G

T

G

T

G

T

G

T

G

T

G

T

G

T

G

T

G

T

G

T

G

T

G

T

G

T

G

T

G

T

G

T

GG

T

GGTG

T

G

T

GGTG

T

G

T

GGTGTGRTP

PropertyUncertainty in the Normal Hydrogen and

Methane EOS

Liq.

H2

Vap.

H2

Super

H2 Methane

Density 0.1 % 0.25

%

0.2 % 0.03-0.07 %

Heat Capacity 3 % 3 % 3 % <1 %

Speed of Sound 2 % 1 % 1 % 0.03-0.3 %


4. Equations of State: Fundamental in Helmholtz Form

11

,

,

RT

Ta

0, , ,r T

Tcc

kk

i

k baa k exp1ln

lnln,0

1

2 2

, exp

exp

i i i i i

i i

yxd t d t pr

i i

i i x

zd t

i i i i i

i y

N N

N D

Ideal-gas function Real-fluid function


4. Equations of State: Properties in Helmholtz Form

12

1,0

rr

RTTh

rr

RTs

0

0

,

r

RTTP 1,

r

RT

PTZ 1,

r

RTTu0

,

rrRTTg 01,

2

2

2

022,

r

v RTc

2

22

22

21

1

,rr

rr

vp RcTc

2

2

2

022

22

2

22

1

21

,

r

rr

rr

M

RTTw

r

c

TB1

lim0

2

2

20

1lim

r

c

TC

meas calc

Tmeas

P PF

P

...222

vv ccPP FWFWFWS

meas calc

P

meas

P PF

P

v

vmeas vcalc

c

vmeas

c cF

c

• Non-linear fitting algorithm


4. Equations of State: The EOS development process

13

Comparison

Plots

Iteration

Function

limits

Data

file

EOS

terms


14

4. Equations of State: Parahydrogen vapor pressures

Le

ach

ma

n

et a

l.M

cC

arty

& Y

ou

ng

love


15

4. Equations of State: QLCS vapor pressure predictions


16

4. Equations of State: Parahydrogen sound speeds

Le

ach

ma

n

et a

l.M

cC

arty

& Y

ou

ng

love


17

4. Equations of State: Parahydrogen isochoric heat capacities

Le

ach

ma

n

et a

l.M

cC

arty

& Y

ou

ng

love


18

4. Equations of State: Hydrogen Densities vs. Pressure

McC

arty

& Y

ou

ng

love

Le

ach

ma

n

et a

l.


19

4. Equations of State: Hydrogen Densities vs. Temperature

McC

arty

& Y

ou

ng

love

Le

ach

ma

n

et a

l.


4. Equations of State: Parahydrogen Surface

20

, 1r

P T RT

2 0 2

2

2 2,

r

vc T R

Leachman et al.

Younglove & McCarty


4. Equations of State: 14-term hydrogen EOS

21

i Ni ti di pi

1 -7.33375 0.6855 1 0

2 0.01 1 4 0

3 2.60375 1 1 0

4 4.66279 0.489 1 0

5 0.682390 0.774 2 0

6 -1.47078 1.133 2 0

7 0.135801 1.386 3 0

8 -1.05327 1.619 1 1

9 0.328239 1.162 3 1

10 -0.0577833 3.96 2 --

11 0.0449743 5.276 1 --

12 0.0703464 0.99 3 --

13 -0.0401766 6.791 1 --

14 0.119510 3.19 1 --

i Phi Beta Gamma D

10 -1.7437 -0.194 0.8048 1.5487

11 -0.5516 -0.2019 1.5248 0.1785

12 -0.0634 -0.0301 0.6648 1.28

13 -2.1341 -0.2383 0.6832 0.6319

14 -1.777 -0.3253 1.493 1.7104

Temperature

(K)

Pressure

(MPa)

Density

(mol∙L-1)

Critical Point 32.938 1.2858 15.538

Triple Point 13.8033 0.007041 38.185

7 9

1 7

142 2

9

, exp

exp

i i i i i

i i

d t d t pr

i i

i i

d t

i i i i i

i

N N

N D


4. Equations of State: 14-term Hydrogen EOS

22

• Consistent between para, normal, and orthohydrogen

• Range: 0-2000 MPa, 13-1000 K

• Uncertainties▪ 0.1% in density from triple point to 250 K up to 40 MPa

▪ 0.04% in density from 250-450 K up to 300 MPa.

▪ 1% in density from 450-1000 K

▪ 1% in heat capacities

▪ 0.5% in speed of sound

▪ 0.1% in saturation properties for parahydrogen

▪ 0.2% in saturation properties for normal hydrogen


5. Mixtures: World’s 1st <77 K PVT-x measurements

23

Rubotherm Isosorp 2000 magnetic suspension microbalance modified for cryogenics.

Conducted first ever liquid He-H2, He-Ne, H2-Ne PVT-x measurements.


5. Mixtures: Residual mixing for He-H2, He-Ne, and H2-Ne

24

• Two new mixture EOS developed

for He-H2, Ne-H2. Currently in NIST

review. Ne-He still preliminary.


In Review: The Science of Cold Hydrogen

• Hydrogen is the simplest molecule in the universe – that makes property calculations at cryogenic temps hard, not easy because of quantum effects.

• Property packages for most fluids and mixtures are now available, though many are preliminary and considerable work remains.

• The unique properties of cryogenic hydrogen, specifically the existance of nuclear spin-isomers (ortho & para) and the large deBroglie wavelength present new opportunities for technology development.

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Quantum Mechanics and the Cool Science of Hydrogen · 2017-05-11 · Quantum Mechanics and the Cool...

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