Analysis of Vortex Tube Applications in Hydrogen Liquefaction
Marshall Crenshaw
Washington State UniversityPullman, WANovember 14, 2017
• >80% of global energy comes from fossil fuels.1
• Since 1976, global temperatures warmer than long-term average.2
• 11 of the top 12 hottest years are from 2003-2016.3
Why is Renewable Energy Necessary?
1 International Energy Agency Technical Report. Key World Energy Statistics. 2016 2 https://climate.nasa.gov/scientific-consensus/3 https://www.ncdc.noaa.gov/sotc/global/201613
• 9th most abundant element in earth’s crust
• Photo-biological bacteria produce hydrogen
H2 Production
http://www.fsec.ucf.edu/en/consumer/hydrogen/basics/images/HydrogenProductionPaths.gif
• Lowest volumetric density
• Containers are pressurized or cryogenic to increase density
Difficulties of H2
https://energy.gov/eere/fuelcells/hydrogen-storage
• Double density when liquefying over pressurizing
Liquid vs Pressurized H2
0
10
20
30
40
50
60
70
80
0 25 50 75 100 125 150 175 200
Den
sity
(kg/
m³)
Pressure of Compressed Hydrogen (MPa)
Pressurized Hydrogen
Liquid Hydrogen
Pressurized Tank @ 70 MPa
Pressurized Tank @ 35 MPa
• Inexpensive cooling device
• 1 high pressure stream 2 low pressure streams
• Transfers cold stream energy hot outer stream
• No moving parts
Diagram of Vortex Tube (VT)
• Low-cost cycle for hydrogen liquefaction
• Low-efficiency method for liquefaction
• Increase cycle efficiency by adding component
Pre-cooled Linde-Hampson Cycle
• Additional compressor and heat exchanger
• Cycle efficiency: Adding compressor > Adding throttle
• 3rd HX reduces O-P ratio of hydrogen
• What is O-P ratio?
Pre-cooled L-H cycle with VT
• Equilibrium O-P ratio depends on temperature of hydrogen
• Normal hydrogen 3:1 O-P ratio
• Liquid hydrogen all parahydrogen
• Catalyst added to HXs to maintain equilibrium O-P ratio
• Why is equilibrium hydrogen important?
Orthohydrogen & Parahydrogen
https://3c1703fe8d.site.internapcdn.net/newman/gfx/news/hires/2011/1-nuclearmagne.jpg
• 50% of normal hydrogen boils away in 200 hours
Importance of Ortho-Para Equilibrium
Gursu, S. et al. An Optimization Study of Liquid Hydrogen Boil-Off Losses,Int. J. Hydrogen Energy., v. 17, p. 227, 1992.
Statistical Thermodynamic Properties of H2
https://3c1703fe8d.site.internapcdn.net/newman/gfx/news/hires/2011/1-nuclearmagne.jpg
Stat Thermo
https://hydrogen.wsu.edu/2015/06/22/why-equilibrium-hydrogen-doesnt-exist/
REFPROP
0
2.5
5
7.5
0 100 200 300
Idea
l-gas
ent
halp
y [M
J/kg
]
Temperature [K]
Ortho [REFPROP]
Para [REFPROP]
REFPROP with Corrected Orthohydrogen vs. Stat Thermo
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0.25
0.5
0.75
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5
7.5
0 100 200 300
Con
vers
ion
enth
alpy
[MJ/
kg]
Idea
l-gas
ent
halp
y [M
J/kg
]
Temperature [K]
Corrected Ortho
Para [REFPROP]
Stat Thermo
MATLAB
https://hydrogen.wsu.edu/2015/06/22/why-equilibrium-hydrogen-doesnt-exist/
r2 = 0.999996
Equilibrium Ofrac
0
0.25
0.5
0.75
1
0 50 100 150 200 250 300
Equi
libriu
m O
rthoh
ydro
gen
Frac
tion
Temperature (K)
Piece-Wise Equilibrium H2 Function
Coefficients of equilibrium MATLAB function
a1 1.935x10-4 b1 -2.044 c1 1.111x10-7
a2 -5.832x10-3 b2 -2.724x10-2 c2 -2.243x10-6
a3 3.448x10-2 b3 0.75 c3 -1.886x10-5
c4 6.514x10-4
c5 -3.499x10-3
Ofrac =
a1T2 + a2T + a3 T ≤ 24.82Kb1eb2T + b3 T ≤ 51.51K
�i=1
4
ciTi + c5 T > 51.51K
Approximate Equilibrium O-P Function
0
0.25
0.5
0.75
1
0 50 100 150 200 250 300Equi
libriu
m O
rthoh
ydro
gen
Frac
tion
Temperature (K)
Stat ThermoMATLAB
r2 = 0.99986
Liquefaction Components & Cycle Assumptions
• Bath pressure is atmospheric (101.3 kPa) and temperature is 77 K
• LN2 Bath is catalyzed: Ofrac = ~0.5
• Heat extracted:
�̇�𝑄𝐵𝐵𝐵𝐵𝐵𝐵𝐵 = �̇�𝑚𝐻𝐻2 ℎ𝐵𝐵𝐵𝐵𝐵𝐵𝐵,𝑖𝑖𝑖𝑖 − ℎ𝐵𝐵𝐵𝐵𝐵𝐵𝐵,𝑜𝑜𝑜𝑜𝐵𝐵 + Δℎ𝐵𝐵𝐵𝐵𝐵𝐵𝐵,𝑐𝑐𝑜𝑜𝑖𝑖𝑐𝑐
• Added work to hydrogen liquefaction:
�̇�𝑊𝐵𝐵𝐵𝐵𝐵𝐵𝐵 =�̇�𝑄𝐵𝐵𝐵𝐵𝐵𝐵𝐵 �
𝐿𝐿𝐿𝐿2𝑖𝑖𝑖𝑖𝑖𝑖𝐵𝐵𝑖𝑖𝐿𝐿𝐿𝐿2𝐹𝐹𝐹𝐹𝐹𝐹
�̇�𝑚𝐿𝐿𝐻𝐻2 � Δ𝐻𝐻𝑐𝑐𝐵𝐵𝑣𝑣,𝑁𝑁2
LN2 Bath
𝐿𝐿𝐿𝐿2 𝐵𝐵𝐵𝐵𝐵𝐵ℎ
• Energy balance equation:
�𝑖𝑖=1
𝑖𝑖
∆ℎ𝑖𝑖 + ∆ℎ𝑐𝑐𝑜𝑜𝑖𝑖𝑐𝑐,𝑖𝑖 = 0
• Minimum temperature approach solves for outlet temperatures
• Hot stream T limit: 𝑇𝑇𝐻𝐻𝑜𝑜𝐵𝐵,𝑜𝑜𝑜𝑜𝐵𝐵,𝑖𝑖𝑖𝑖𝑙𝑙𝑖𝑖𝐵𝐵 = Δ𝑇𝑇𝑙𝑙𝑖𝑖𝑖𝑖 + 𝑇𝑇𝐶𝐶𝑜𝑜𝑖𝑖𝑖𝑖𝑖𝑖𝐶𝐶𝐵𝐵,𝑖𝑖𝑖𝑖
• Cold streams T limit: 𝑇𝑇𝐶𝐶𝑜𝑜𝑖𝑖𝑖𝑖,𝑜𝑜𝑜𝑜𝐵𝐵,𝑖𝑖𝑖𝑖𝑙𝑙𝑖𝑖𝐵𝐵 = 𝑇𝑇𝐻𝐻𝑜𝑜𝐵𝐵,𝑖𝑖𝑖𝑖 − Δ𝑇𝑇𝑙𝑙𝑖𝑖𝑖𝑖
Counter-flow Heat Exchanger
𝐻𝐻𝐻𝐻3
Cold
Nitrogen𝐻𝐻𝐻𝐻2
Hot𝐻𝐻𝐻𝐻4
• Staging compressors decreases their work
• 4 stages is optimal for compressors
Staged Compression with Intercooling
• Pressure Ratio per stage: 𝑃𝑃𝑃𝑃𝐶𝐶𝐵𝐵𝐵𝐵𝑠𝑠𝑖𝑖 =𝑛𝑛
�𝑃𝑃𝑜𝑜𝑜𝑜𝑜𝑜𝑃𝑃𝑖𝑖𝑛𝑛
• Enthalpy of compressor: ℎ2 = 𝐵𝑠𝑠−𝐵1𝜂𝜂𝐶𝐶
+ ℎ1
• Work of compressor: 𝐿𝐿𝑐𝑐 = ∑𝑖𝑖=1𝑖𝑖 �̇�𝑚𝐶𝐶 ℎ2,𝑖𝑖 − ℎ1,𝑖𝑖
• Heat extracted: �̇�𝑄𝐶𝐶 = 𝐿𝐿𝑐𝑐 + ∑𝑖𝑖=1𝑖𝑖 ℎ𝑖𝑖 − ℎ𝑖𝑖−1
• Enthalpy of expander: ℎ2 = 𝜂𝜂𝐸𝐸 ℎ1 − ℎ𝐶𝐶 + ℎ1
Compressor/Expander Component
𝐶𝐶
𝐿𝐿𝐶𝐶
�̇�𝑄𝐶𝐶
𝐿𝐿𝐸𝐸
𝐸𝐸
• Throttle is ideally isenthalpic: ℎ𝑖𝑖𝑖𝑖 = ℎ𝑜𝑜𝑜𝑜𝐵𝐵• Quality of LH2: solved with enthalpy & pressure
• Heat of O-P conversion in tank:�̇�𝑄𝑇𝑇𝐵𝐵𝑖𝑖𝑇𝑇,𝑐𝑐𝑜𝑜𝑖𝑖𝑐𝑐 = �̇�𝑚𝑇𝑇𝐵𝐵𝑖𝑖𝑇𝑇,𝑖𝑖𝑖𝑖∆ℎ𝑐𝑐𝑜𝑜𝑖𝑖𝑐𝑐
• Return stream flow:�̇�𝑚𝑇𝑇𝐵𝐵𝑖𝑖𝑇𝑇,𝑜𝑜𝑜𝑜𝐵𝐵 = �̇�𝑚𝑇𝑇𝐵𝐵𝑖𝑖𝑇𝑇,𝑖𝑖𝑖𝑖 � X𝐻𝐻2 +
�̇�𝑄𝑇𝑇𝐵𝐵𝑖𝑖𝑇𝑇,𝑐𝑐𝑜𝑜𝑖𝑖𝑐𝑐 + �̇�𝑄𝑇𝑇𝐵𝐵𝑖𝑖𝑇𝑇,𝐵𝑖𝑖𝐵𝐵𝐵𝐵 𝑖𝑖𝑖𝑖𝐵𝐵𝑇𝑇
ℎ𝐿𝐿𝐻𝐻,𝐻𝐻2
Throttle & Tank
𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿 𝐻𝐻2 𝑇𝑇𝐵𝐵𝑇𝑇𝑇𝑇
𝐽𝐽𝑇𝑇
• Specific exergy: 𝐻𝐻1 = ℎ0 − ℎ1 − 𝑇𝑇0 𝑠𝑠0 − 𝑠𝑠1
• Exergy destruction: ∆𝐻𝐻𝐷𝐷𝑖𝑖𝐶𝐶𝐵𝐵= � �̇�𝑚𝑖𝑖𝑖𝑖𝐻𝐻𝑖𝑖𝑖𝑖 −� �̇�𝑚𝑜𝑜𝑜𝑜𝐵𝐵𝐻𝐻𝑜𝑜𝑜𝑜𝐵𝐵 −𝑊𝑊
• Limits are set to the exergy destruction of throttle (lower) and expander (higher)
Effectiveness of a VT
• Exergy destruction of devices:∆𝐻𝐻𝑉𝑉𝑇𝑇= �̇�𝑚𝑉𝑉𝑇𝑇,𝑖𝑖𝑖𝑖𝐻𝐻𝑉𝑉𝑇𝑇,𝑖𝑖𝑖𝑖 − �̇�𝑚𝑉𝑉𝑇𝑇,𝑐𝑐𝑜𝑜𝑖𝑖𝑖𝑖𝐻𝐻𝑉𝑉𝑇𝑇,𝑐𝑐𝑜𝑜𝑖𝑖𝑖𝑖 − �̇�𝑚𝑉𝑉𝑇𝑇,𝐵𝑜𝑜𝐵𝐵𝐻𝐻𝑉𝑉𝑇𝑇,𝐵𝑜𝑜𝐵𝐵
∆𝐻𝐻𝐽𝐽𝑇𝑇= �̇�𝑚𝑉𝑉𝑇𝑇,𝑐𝑐𝑜𝑜𝑖𝑖𝑖𝑖 𝐻𝐻𝑉𝑉𝑇𝑇,𝑖𝑖𝑖𝑖 − 𝐻𝐻𝐽𝐽𝑇𝑇,𝑐𝑐𝑜𝑜𝑖𝑖𝑖𝑖 + �̇�𝑚𝑉𝑉𝑇𝑇,𝐵𝑜𝑜𝐵𝐵 𝐻𝐻𝑉𝑉𝑇𝑇,𝑖𝑖𝑖𝑖 − 𝐻𝐻𝐽𝐽𝑇𝑇,𝐵𝑜𝑜𝐵𝐵
∆𝐻𝐻𝐸𝐸𝐸𝐸𝑣𝑣
= �̇�𝑚𝑉𝑉𝑇𝑇,𝑐𝑐𝑜𝑜𝑖𝑖𝑖𝑖 𝐻𝐻𝑉𝑉𝑇𝑇,𝑖𝑖𝑖𝑖 − 𝐻𝐻𝐸𝐸𝐸𝐸𝑣𝑣,𝑐𝑐𝑜𝑜𝑖𝑖𝑖𝑖 − 𝑊𝑊𝐸𝐸𝐸𝐸𝑣𝑣,𝑐𝑐𝑜𝑜𝑖𝑖𝑖𝑖 + �̇�𝑚𝑉𝑉𝑇𝑇,𝐵𝑜𝑜𝐵𝐵 𝐻𝐻𝑉𝑉𝑇𝑇,𝑖𝑖𝑖𝑖 − 𝐻𝐻𝐸𝐸𝐸𝐸𝑣𝑣,𝐵𝑜𝑜𝐵𝐵 − 𝑊𝑊𝐸𝐸𝐸𝐸𝑣𝑣,𝐵𝑜𝑜𝐵𝐵
• Exergy destruction using effectiveness• ∆𝐻𝐻𝑉𝑉𝑇𝑇= ∆𝐻𝐻𝐸𝐸𝐸𝐸𝑣𝑣 + 1 − 𝜀𝜀𝑉𝑉𝑇𝑇 ∆𝐻𝐻𝐽𝐽𝑇𝑇 − ∆𝐻𝐻𝐸𝐸𝐸𝐸𝑣𝑣
Effectiveness of a VT cont.
• Cold fraction: 𝑉𝑉𝑇𝑇𝑐𝑐𝑐𝑐 = �̇�𝑙𝑉𝑉𝑉𝑉,𝑐𝑐𝑜𝑜𝑐𝑐𝑐𝑐�̇�𝑙𝑉𝑉𝑉𝑉,𝑖𝑖𝑛𝑛
• Pressure Ratio: 𝑉𝑉𝑇𝑇𝑃𝑃𝑃𝑃 = 𝑃𝑃𝑖𝑖𝑛𝑛𝑃𝑃𝑉𝑉𝑉𝑉,𝑐𝑐𝑜𝑜𝑐𝑐𝑐𝑐
• Hot outlet Pressure: 𝑃𝑃𝑉𝑉𝑇𝑇,𝐵𝑜𝑜𝐵𝐵 = ⁄1 3 𝑃𝑃𝑉𝑉𝑇𝑇,𝑖𝑖𝑖𝑖 + ⁄2 3 𝑃𝑃𝑉𝑉𝑇𝑇,𝑐𝑐𝑜𝑜𝑖𝑖𝑖𝑖
• Outlet temperatures are solved with effectiveness
Variables of the VT
Cycle Parameters
Previous Cycle Parameters
Cycle Analysis & Results
• Liquid hydrogen yield: 𝜑𝜑 = �̇�𝑙𝑓𝑓
�̇�𝑙
• Ratio of nitrogen to compressed hydrogen flow: 𝜓𝜓 =�̇�𝑙𝑁𝑁2�̇�𝑙
• Liquid yield maximum: 𝜑𝜑𝑙𝑙𝐵𝐵𝐸𝐸 = 𝐵9−𝐵4𝐵9−𝐵7
• Relating 𝜓𝜓 to 𝜑𝜑𝑙𝑙𝐵𝐵𝐸𝐸: 𝜓𝜓 = 𝐵1−𝐵2𝐵11−𝐵10
+ 𝜑𝜑𝑙𝑙𝐵𝐵𝐸𝐸𝐵7−𝐵1𝐵11−𝐵10
State-Point Analysis of Ideal Cycle
Peschka W. Liquid hydrogen: fuel of the future. Springer Science & Business Media; 2012 Dec 6.
• O-P conversion happens at LN2 Bath and LH2 tank
• �̇�𝑚𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖 = �̇�𝑄𝑉𝑉𝑇𝑇𝑛𝑛𝑇𝑇𝐵𝑔𝑔−𝐵𝑓𝑓
• �̇�𝑚∗ = �̇�𝑚 + �̇�𝑙𝑏𝑏𝑜𝑜𝑖𝑖𝑐𝑐𝜑𝜑𝑚𝑚𝑇𝑇𝑚𝑚
• 𝜑𝜑∗ = �̇�𝑙𝑓𝑓
�̇�𝑙∗= 𝜑𝜑𝑚𝑚𝑇𝑇𝑚𝑚
1+ ��̇�𝑄𝑉𝑉𝑇𝑇𝑛𝑛𝑇𝑇 �̇�𝑙𝑓𝑓 𝐵8−𝐵7
• 𝜓𝜓∗ =�̇�𝑙𝑁𝑁2�̇�𝑙∗
O-P conversion at LH2 Tank
• Maximum yield of LN2 Bath: 𝜑𝜑𝑁𝑁2,𝑙𝑙𝐵𝐵𝐸𝐸 =�̇�𝑙𝑁𝑁2,𝑓𝑓
�̇�𝑙𝑁𝑁2= 𝐵𝑁𝑁,1−𝐵𝑁𝑁,2
𝐵𝑁𝑁,1−𝐵𝑁𝑁,5
• Work of LN2 Bath: 𝛼𝛼 = 1𝜑𝜑
�̇�𝑊�̇�𝑙 𝑐𝑐𝑜𝑜𝑙𝑙𝑣𝑣
• Work of compressor: �̇�𝑊�̇�𝑙 𝑐𝑐𝑜𝑜𝑙𝑙𝑣𝑣
= 𝑇𝑇𝑖𝑖𝑖𝑖 � 𝑠𝑠𝑖𝑖𝑖𝑖 − 𝑠𝑠𝑜𝑜𝑜𝑜𝐵𝐵 − ℎ𝑖𝑖𝑖𝑖 − ℎ𝑜𝑜𝑜𝑜𝐵𝐵
• 𝛼𝛼𝑁𝑁2 = 1𝜑𝜑𝑁𝑁2,𝑚𝑚𝑇𝑇𝑚𝑚
𝑇𝑇𝑁𝑁,1 � 𝑠𝑠𝑁𝑁,1 − 𝑠𝑠𝑁𝑁,2 − ℎ𝑁𝑁,1 − ℎ𝑁𝑁,2
Work of LN2 Bath
Peschka W. Liquid hydrogen: fuel of the future. Springer Science & Business Media; 2012 Dec 6.
• State-Point work of liquefaction for pre-cooled L-H cycle:
𝛼𝛼𝐻𝐻2 =1𝜑𝜑∗
𝑇𝑇1 � 𝑠𝑠1 − 𝑠𝑠2 − ℎ1 − ℎ2 + 𝛼𝛼𝑁𝑁2 𝜓𝜓∗ +�̇�𝑄𝐵𝐵𝐵𝐵𝐵𝐵𝐵
ℎ12 − ℎ11
• Peak pressure of LN2 Bath: 100 bar (10 MPa)
• Temperature of LN2 Bath: 63.2 K or 77 K
• State-Point work of liquefaction results:- 𝛼𝛼𝐶𝐶,63.2 𝐾𝐾 = 13.65 kWh∙kg-1
- 𝛼𝛼𝐶𝐶,77 𝐾𝐾 = 19.95 kWh∙kg-1
• Peschka value: 𝛼𝛼𝑃𝑃 = 16.27 kWh∙kg-1
State-Point Results
• Work of liquefaction for component-based model:
- 𝛼𝛼𝑐𝑐,63.2 𝐾𝐾 = 14.82 kWh∙kg-1
- 𝛼𝛼𝑐𝑐,77 𝐾𝐾 = 20.83 kWh∙kg-1
• Percentage error between results:
- 63.2 K: 8.57%
- 77 K: 4.41%
• Error caused by heat exchanger and LN2 components
State-Point vs. Component Results
Vortex Tube Simulation
Reduced Work for L-H w/VT Cycle
Cycle Analysis & Results
Simulation of L-H w/VT Cycle
• Simulate higher complexity cycles e.g. pre-cooled Claude
• Vary the LN2 Bath temperature to 63.2 K
• Higher inlet pressure tests for vortex tube
• Continued tests of vortex tube catalyzation
• Test vortex tube as a final liquefaction component
Recommendations
• Simplified Statistical thermodynamic models created
• Variable components created for the pre-cooled L-H cycle
• Component model verified with state-point model
• Effectiveness introduced as a new VT variable
• Required effectiveness provided for combinations of 𝑉𝑉𝑇𝑇𝑐𝑐𝑐𝑐 and 𝑉𝑉𝑇𝑇𝑃𝑃𝑃𝑃 values
Summary