SlideShare ist ein Scribd-Unternehmen logo
1 von 24
Downloaden Sie, um offline zu lesen
A NEW CONTROL MECHANISM FOR TWO-
PHASE EJECTOR IN VAPOR
COMPRESSION CYCLES FOR
AUTOMOTIVE APPLICATIONS USING
ADJUSTABLE MOTIVE NOZZLE INLET
SWIRL
Jingwei Zhu, Stefan Elbel
University of Illinois at Urbana-Champaign
Department of Mechanical Science and Engineering
Air Conditioning and Refrigeration Center (ACRC)
SAE INTERNATIONAL
• Background: opportunities and challenges with ejector
cooling cycles
• Research motivation: optimize ejector cycle performance
under changing working conditions/capacities (common in
automotive applications) by adjusting ejector motive nozzle
• New solution: swirl ejector - utilizing controllable swirl at the
motive inlet of the ejector to adjust mass flow rate and
condenser outlet quality/subcooling (Swirl nozzle/valve has
been recognized as a reliable flow modulation method as
early as 1960s (Mayer, 1967; Wormley, 1969))
• Research approach:
− Swirl nozzle tests with refrigerant (R134a)
− Visualization and modeling of low-quality flow expanded in
the nozzle
• Conclusions
Presentation Outline
Paper 2016-01-0243 Presenter: Jingwei Zhu 2
SAE INTERNATIONAL
Conventional cooling cycle:
• Throttling in the
expansion valve causes
irreversibility
• Cycle efficiency is
impaired
Benefits of Ejector Cooling Cycles
3
𝑷 𝒄𝒐𝒎𝒑,𝒊𝒏 > 𝑷 𝒆𝒗𝒂𝒑
Ejector cooling cycle:
• Irreversibility in the expansion
process is reduced
• Compressor work is saved
• Cooling capacity is increased
• Cycle efficiency is improved
(R134a ~ 5 %; CO2 ~ 20 %)
𝑷 𝒄𝒐𝒎𝒑,𝒊𝒏 ≈ 𝑷 𝒆𝒗𝒂𝒑
Paper 2016-01-0243 Presenter: Jingwei Zhu
SAE INTERNATIONAL
• Different working
conditions/capacities favor
different ejector geometry
• Slightly different geometry
might result in significant
difference in system COP
under the same conditions
• Ejector motive nozzle
throat diameter (nozzle
restrictiveness) is one of
the key points that can
significantly affect COP
Challenges with Ejector Cooling Cycle
4
Test Conditions
R410A ejector air conditioning system COP with
different motive nozzle throat diameters under
three different conditions Hu et al. (2014)
Condition 1 Condition 2 Condition 3
𝑇𝑖𝑛𝑑𝑜𝑜𝑟(dry/wet bulb), ºC 26.7/19.4 26.7/19.4 26.8/19.5
𝑇𝑜𝑢𝑡𝑑𝑜𝑜𝑟(dry/wet bulb), ºC 35.0/19.5 30.6/16.8 27.8/14.9
𝑝 𝑐𝑜𝑛𝑑, MPa 2.4 2.0 1.9
Sumeru et al. (2012); Sarkar (2012);
Elbel and Hrnjak (2008); Elbel (2011);
Paper 2016-01-0243 Presenter: Jingwei Zhu
COP changed by more than 40 %
SAE INTERNATIONAL
Challenges with Ejector Cooling Cycle
5
Less
restrictive
nozzle
Restrictiveness of the motive
nozzle on the two-phase flow
can significantly affect ejector
efficiency and system
performance.
Paper 2016-01-0243 Presenter: Jingwei Zhu
SAE INTERNATIONAL
Challenges with Ejector Cooling Cycle
6
More
restrictive
nozzle
Restrictiveness of the motive
nozzle on the two-phase flow
can significantly affect ejector
efficiency and system
performance.
Paper 2016-01-0243 Presenter: Jingwei Zhu
SAE INTERNATIONAL
How to Adjust Motive Nozzle Geometry
(Restrictiveness on Flow)
7
Eurofighter Typhoon thrust nozzle
http://www.military.com/video/aircraft/engines/eurofighter-thrust-vectoring-
nozzle/2907034546001
Paper 2016-01-0243 Presenter: Jingwei Zhu
SAE INTERNATIONAL
This design is complicated and costly, and more friction losses are
incurred because of the additional surface area and turbulence
introduced.
Previous Approach: Adjustable Needle
8Paper 2016-01-0243 Presenter: Jingwei Zhu
SAE INTERNATIONAL
Utilizing an adjustable swirl at the
motive inlet to control the flow
expanded in the motive nozzle (no
change in geometry; same effect
as changing nozzle throat
diameter)
New Solution: Swirl Ejector
9
Conventional ejector Swirl ejector Swirl ejector cooling cycle
Adjustable Swirl
Paper 2016-01-0243 Presenter: Jingwei Zhu
SAE INTERNATIONAL
Works for both single-phase and two-phase
Hypothesis 1: Share of Tangential Kinetic
Energy in the Available Pressure
Potential Decreases the Mass Flow Rate
10
Nozzle
convergent
part
Paper 2016-01-0243 Presenter: Jingwei Zhu
Axial velocity profile Tangential velocity profile
∆𝑝~
1
2
𝜌 𝑉𝑜𝑢𝑡
2
− 𝑉𝑖𝑛
2
𝑉𝑜𝑢𝑡
2
= 𝑉𝑎𝑥𝑖𝑎𝑙,𝑜𝑢𝑡
2
+ 𝑉𝑡𝑎𝑛𝑔𝑒𝑛𝑡𝑖𝑎𝑙,𝑜𝑢𝑡
2
𝑚~𝜌𝑉𝑎𝑥𝑖𝑎𝑙,𝑜𝑢𝑡 𝐴 𝑜𝑢𝑡
Inlet
Inlet
Outlet
Outlet
SAE INTERNATIONAL
• Two-phase flow during expansion is usually not in equilibrium (Bubble
growth takes time)
• The stronger the swirl is the faster bubbles grow
• Works for two-phase flow
Hypothesis 2: Swirl Boosts Vapor Bubble
Growth
11
No Swirl
With stronger swirl, more relative
motion is created between bubbles
and surrounding liquid in radial
direction
Radial direction
Nozzle
convergent
part
Paper 2016-01-0243 Presenter: Jingwei Zhu
𝒅 𝒎 𝒃𝒖𝒃𝒃𝒍𝒆
𝒅𝒕
𝒉𝒍𝒗 = 𝟒𝝅𝑹 𝒃𝒖𝒃𝒃𝒍𝒆
𝟐
𝒉(𝑻𝒍𝒊𝒒𝒖𝒊𝒅,∞ − 𝑻 𝒔)
𝑵𝒖 𝒔𝒑𝒉𝒆𝒓𝒆 =
𝒉 𝑫 𝒃𝒖𝒃𝒃𝒍𝒆
𝒌
= 𝟐 + 𝟎. 𝟒𝑹𝒆
𝟏
𝟐 + 𝟎. 𝟎𝟔𝑹𝒆
𝟐
𝟑 𝑷𝒓 𝟎.𝟒
𝝁𝒍𝒊𝒒𝒖𝒊𝒅,∞
𝝁𝒍𝒊𝒒𝒖𝒊𝒅,𝒔
𝟏
𝟒
𝑹𝒆~𝑽 𝒓𝒆𝒍𝒂𝒕𝒊𝒗𝒆
SAE INTERNATIONAL
How to Make Nozzle Have More
Restrictiveness on The Two-Phase Flow?
12
Change nozzle geometry
(complicated, costly,
additional losses)
Decrease the share of
axial kinetic energy in
available pressure
potential energy;
increase vapor
generation before the
flow reaches the throat;
no change in geometry
Our solution
(simple, inexpensive,
effective)
Paper 2016-01-0243 Presenter: Jingwei Zhu
SAE INTERNATIONAL
• Experimental investigation of the influence of motive
inlet swirl on the flow expanded in the motive nozzle
with commonly used refrigerant R134a
• Visualization of the swirling flow expanded in the
nozzle
• Explanation and modeling of the influence of motive
inlet swirl on the flow expanded in the motive nozzle
(ongoing)
• Evaluation of the nozzle efficiency with swirl control and
comparison with other control methods; system tests
with adjustable swirl ejector under different working
conditions in the future
Research Approach
13Paper 2016-01-0243 Presenter: Jingwei Zhu
SAE INTERNATIONAL
Swirl Nozzle
14
Nozzle inlet diameter (mm) 15.0
Nozzle throat diameter (mm) 1.0
Nozzle outlet diameter (mm) 1.7
Nozzle convergent part length (mm) 9.9
Nozzle divergent part length (mm) 40.0
Tangential inlet inner diameter (mm) 2.0
Swirl decay distance (mm) 138.0
Axial inlet
Sleeve (resin)
Nozzle (resin)
Tee (brass)
Tangential inlet
Convergent-divergent nozzle
(resin)
3D printed
prototype
Swirl nozzle geometry
Paper 2016-01-0243 Presenter: Jingwei Zhu
A
A
Section A-A
SAE INTERNATIONAL
• Pumped-refrigerant-loop for
adjustment of nozzle test
conditions
• Pressures and temperatures at
the axial and tangential inlets
are measured; pressure at the
nozzle outlet is measured
• Total mass flow rate and axial
inlet mass flow rate are
measured by Coriolis flow
meters
• Ratio of tangential inlet mass
flow rate to total mass flow rate
is adjusted by two valves
Experimental Facility for Investigation of
Swirl Influence on Nozzle Restrictiveness
15
𝑆𝑤𝑖𝑟𝑙 𝑠𝑡𝑟𝑒𝑛𝑔𝑡ℎ =
𝑚 𝑡𝑎𝑛𝑔𝑒𝑛𝑡𝑖𝑎𝑙
𝑚 𝑡𝑜𝑡𝑎𝑙
Paper 2016-01-0243 Presenter: Jingwei Zhu
SAE INTERNATIONAL
• Working fluid: R134a
• Different nozzle inlet pressures are achieved by adjusting the heating
water temperature and pump speed
• Nozzle outlet pressure can be adjusted by a valve installed in the
downstream of the nozzle
• Flow at the nozzle inlet is subcooled by around 0.5 ºC. No observable
bubbles at the nozzle inlet (guaranteed by observing through the sight
glass installed at the nozzle inlet).
Testing Conditions
16Paper 2016-01-0243 Presenter: Jingwei Zhu
𝑷𝒊𝒏 (kPa) 𝑷 𝒐𝒖𝒕 (kPa) 𝑻𝒊𝒏 (ºC) 𝒎𝒕𝒐𝒕𝒂𝒍 (g/s) Vortex strength (-)
760~1059 407~909 29~41 6~20 0~1
Test Matrix
SAE INTERNATIONAL
Effect of Outlet Pressure on Nozzle Mass
Flow Rate at Constant Inlet Pressure
17
4
6
8
10
12
14
16
18
20
400 500 600 700 800 900 1000
Totalmassflowrate(g/s)
Outlet pressure (kPa)
Inlet subcooling = 0.5 ºC
Theoretically
calculated
incompressible
single phase
liquid mass flow
rate
Choked at low outlet pressure
(decrease in outlet pressure does not increase mass
flow rate)
Observations:
• Flow is choked at low outlet
pressure
• Inlet swirl reduces total mass
flow rate under the same inlet
and outlet conditions (larger
restrictiveness)
Nozzle Inlet: 925 kPa 36 ºC
𝑷𝒊𝒏 = 𝟗𝟐𝟓 𝒌𝑷𝒂
No swirl
With max
swirl
Paper 2016-01-0243 Presenter: Jingwei Zhu
SAE INTERNATIONAL
Preliminary Visualization Results
18
4
6
8
10
12
14
16
18
20
400 600 800 1000
Totalmassflowrate(g/s)
Outlet pressure (kPa)
Inlet 925 kPa 36 ºC no swirl
Inlet 925 kPa 36 ºC pure liquid
Clear flow in the convergent
part of the nozzle
Clear
Choked flow (very low outlet
pressure): becomes bubbly
immediately after the throat
Outlet pressure close to inlet
pressure: flow is still clear
after the throat
BubblyChoked flow
Outlet pressure
close to inlet
pressure
Paper 2016-01-0243 Presenter: Jingwei Zhu
SAE INTERNATIONAL
Choked Mass Flow Rate with Different
Inlet Swirl Strengths at Constant Inlet
Pressure
19
10
12
14
16
18
20
22
0 0.2 0.4 0.6 0.8 1
Totalmassflowrate(g/s)
Tangential mass flow rate/total mass flow rate
Inlet 826 kPa 32 ºC
Inlet 925 kPa 36 ºC
Inlet 1034 kPa 40 ºC
Inlet subcooling = 0.5 ºC
Nozzle
restrictiveness on the
flow is changed by
swirl; the stronger
the swirl is, the larger
the restrictiveness is.
Mass flow rate can be
reduced by 35 % with
swirl under the same
inlet and outlet
conditions (large
control range).
Paper 2016-01-0243 Presenter: Jingwei Zhu
SAE INTERNATIONAL
Nozzle Inlet Pressure Can Vary in A Wide
Range with Different Inlet Swirl Strengths
at Constant Total Mass Flow Rate
(Choked)
20
750
800
850
900
950
1000
1050
1100
0.2 0.4 0.6 0.8 1
InletPressure(kPa)
Tangential mass flow rate/total mass flow rate
Total mass flow rate=15 g/s
Total mass flow rate=14 g/s
Total mass flow rate=13 g/s
Inlet subcooling = 0.5 ºC
Nozzle restrictiveness
on the flow is changed
by swirl; the stronger
the swirl is, the larger
the restrictiveness is.
Mass flow rate ratio
(swirl strength): 0.2 to
0.5
Inlet pressure: 780 kPa
to 1050 kPa (large
control range) for total
mass flow rate = 15 g/s
Paper 2016-01-0243 Presenter: Jingwei Zhu
SAE INTERNATIONAL
• Nozzle inlet swirl can change nozzle restrictiveness on the two-phase
flow. The stronger the swirl is, the larger the restrictiveness is.
• The control range of inlet pressure and mass flow rate is large enough
for real applications. Mass flow rate can be reduced by 35 % with swirl
under the same nozzle inlet and outlet conditions.
• Next step: Compare the efficiency of swirl ejector with other control
methods to see if it reduces the frictional losses for the same range of
flow control.
• Goal: By adjusting the restrictiveness of motive nozzle on the flow
expanded through it, ejector cycle performance can be optimized for
different working conditions/capacities and the improvements could be
more than 40 %.
Summary and Conclusions
21Paper 2016-01-0243 Presenter: Jingwei Zhu
SAE INTERNATIONAL
Thank you for your attention!
Any questions?
22
• Presenter: Jingwei Zhu
• Email: jzhu50@illinois.edu
• Acknowledgments: The authors would like to
thank the member companies of the Air
Conditioning and Refrigeration Center at the
University of Illinois at Urbana-Champaign for
their generous support.
Paper 2016-01-0243 Presenter: Jingwei Zhu
SAE INTERNATIONAL
Reference
23
1. Gay, N. H., “Refrigerating System,” U.S. Patent 1,836,318, 1931.
2. Disawas, S. and Wongwises, S., “Experimental investigation on the performance of the refrigeration cycle
using a two-phase ejector as an expansion device,” International Journal of Refrigeration, 27(6): 587-594,
2004.
3. Lawrence, N., and Elbel, S., “Experimental and Numerical Study on the Performance of R410A Liquid
Recirculation Cycles with and without Ejectors," 15th International Refrigeration and Air Conditioning
Conference at Purdue, West Lafayette, IN, USA, Paper 2187, 2014.
4. Ozaki, Y., Takeuchi, H., and Hirata, T., “Regeneration of expansion energy by ejector in CO2 cycle,” 6th IIR
Gustav Lorentzen Conference on Natural Working Fluid, Glasgow, UK, 11-20, 2004.
5. Banasiak, K., Hafner, A., and Andresen, T., “Experimental and numerical investigation of the influence of the
two-phase ejector geometry on the performance of the R744 heat pump,” International Journal of
Refrigeration, 35(6): 1617-1625, 2012.
6. Elbel, S. and Hrnjak, P., “Experimental validation of a prototype ejector designed to reduce
throttling losses encountered in transcritical R744 system operation,” International Journal of
Refrigeration, 31(3): 411-422, 2008.
7. Elbel, S., “Historical and present developments of ejector refrigeration systems with emphasis on
transcritical carbon dioxide air-conditioning applications,” International Journal of Refrigeration,
34(7): 1545-1561, 2011.
8. Harrell, G. S., and Kornhauser, A. A., “Performance tests of a two-phase ejector,” American Society of
Mechanical Engineers, New York, NY, United States, 1995.
9. Lawrence, N. and Elbel S., “Experimental investigation of a two-phase ejector cycle suitable for use with
low-pressure refrigerants R134a and R1234yf,” International Journal of Refrigeration, 38: 310-322, 2014.
Paper 2016-01-0243 Presenter: Jingwei Zhu
SAE INTERNATIONAL
Reference
24
10. Sumeru, K., Nasution, H., and Ani, F. N., “A review on two-phase ejector as an expansion device in
vapor compression refrigeration cycle,” Renewable and Sustainable Energy Reviews, 16(7): 4927-
4937, 2012.
11. Sarkar, J., “Ejector enhanced vapor compression refrigeration and heat pump systems - A review,”
Renewable and Sustainable Energy Reviews, 16(9): 6647-6659, 2012.
12. Hu, J., Shi, J., Liang, Y., Yang, Z., and Chen, J., “Numerical and experimental investigation on
nozzle parameters for R410A ejector air conditioning system,” International Journal of Refrigeration,
40: 338-346, 2014.
13. Henry, R. E., and Fauske, H. K., “The two-phase critical flow of one-component mixtures in nozzles,
orifices, and short tubes,” Journal of Heat Transfer, 93(2): 179-187, 1971.
14. Schrock, V. E., Starkman, E. S., and Brown, R. A., “Flashing flow of initially subcooled water in
convergent–divergent nozzles,” Journal of Heat Transfer, 99(2): 263-268, 1977.
15. Plesset, M. S., and Zwick, S. A., “The growth of vapor bubbles in superheated liquids,” Journal of Applied
Physics, 25(4): 493-500, 1954.
16. Florschuetz, L. W., Henry, C. L., and Khan, A. R., “Growth rates of free vapor bubbles in liquids at uniform
superheats under normal and zero gravity conditions,” International Journal of Heat and Mass Transfer, 12(11):
1465-1489, 1969.
17. Ruckenstein, E., and Davis, E. J., “The effects of bubble translation on vapor bubble growth in a
superheated liquid,” International Journal of Heat and Mass Transfer, 14(7): 939-952, 1971.
18. Mayer, E. A., “Large-signal vortex valve analysis,” Advances in Fluidics, 233-249, 1967.
19. Wormley, D. N., “An analytical model for the incompressible flow in short vortex chambers,”
Journal of Basic Engineering, 91(2): 264-272, 1969.
Paper 2016-01-0243 Presenter: Jingwei Zhu

Weitere ähnliche Inhalte

Was ist angesagt?

Ijmer 46055056
Ijmer 46055056Ijmer 46055056
Ijmer 46055056
IJMER
 

Was ist angesagt? (20)

Study and Analysis of Vortex Tube
Study and Analysis of Vortex TubeStudy and Analysis of Vortex Tube
Study and Analysis of Vortex Tube
 
Pressure Safety Valve Sizing - API 520/521/526
Pressure Safety Valve Sizing - API 520/521/526Pressure Safety Valve Sizing - API 520/521/526
Pressure Safety Valve Sizing - API 520/521/526
 
One day gas lift system course
One day gas lift system course One day gas lift system course
One day gas lift system course
 
Production optimization using gas lift technique
Production optimization using gas lift techniqueProduction optimization using gas lift technique
Production optimization using gas lift technique
 
Api 2000 5th vs 6th final
Api 2000 5th vs 6th finalApi 2000 5th vs 6th final
Api 2000 5th vs 6th final
 
Cavitation
CavitationCavitation
Cavitation
 
Non mechanical valves
Non mechanical valvesNon mechanical valves
Non mechanical valves
 
Analysis of cross flow induced vibration in an inline and staggered configura...
Analysis of cross flow induced vibration in an inline and staggered configura...Analysis of cross flow induced vibration in an inline and staggered configura...
Analysis of cross flow induced vibration in an inline and staggered configura...
 
Bladeless Compression System - ICOPE presentation Part 2
Bladeless Compression System - ICOPE presentation Part 2Bladeless Compression System - ICOPE presentation Part 2
Bladeless Compression System - ICOPE presentation Part 2
 
Bladeless Compression System - ICOPE presentation Part 1
Bladeless Compression System - ICOPE presentation Part 1Bladeless Compression System - ICOPE presentation Part 1
Bladeless Compression System - ICOPE presentation Part 1
 
Cold Gun Aircoolant System
Cold Gun Aircoolant SystemCold Gun Aircoolant System
Cold Gun Aircoolant System
 
Flooding of a distillation column
Flooding of a distillation columnFlooding of a distillation column
Flooding of a distillation column
 
Cavitation 101 - v.16
Cavitation 101 - v.16Cavitation 101 - v.16
Cavitation 101 - v.16
 
HAZARDS-Pneumatic Test(1)
HAZARDS-Pneumatic Test(1)HAZARDS-Pneumatic Test(1)
HAZARDS-Pneumatic Test(1)
 
Piping Hydrostatic Test / Hydrotesting
Piping Hydrostatic Test / HydrotestingPiping Hydrostatic Test / Hydrotesting
Piping Hydrostatic Test / Hydrotesting
 
Hydro test pump
Hydro test pumpHydro test pump
Hydro test pump
 
Ijmer 46055056
Ijmer 46055056Ijmer 46055056
Ijmer 46055056
 
Pneumatics – Choose the Best Valve for Optimum Performance
Pneumatics – Choose the Best Valve for Optimum PerformancePneumatics – Choose the Best Valve for Optimum Performance
Pneumatics – Choose the Best Valve for Optimum Performance
 
CFD modeling of hydrodynamic characteristics of a two phase gas–liquid stirre...
CFD modeling of hydrodynamic characteristics of a two phase gas–liquid stirre...CFD modeling of hydrodynamic characteristics of a two phase gas–liquid stirre...
CFD modeling of hydrodynamic characteristics of a two phase gas–liquid stirre...
 
Distillation column: Foundations, Applications and Scientific Progress
Distillation column: Foundations, Applications and Scientific ProgressDistillation column: Foundations, Applications and Scientific Progress
Distillation column: Foundations, Applications and Scientific Progress
 

Andere mochten auch

Viewed csc journals manuscript gas turbine co propulsion power plant for mari...
Viewed csc journals manuscript gas turbine co propulsion power plant for mari...Viewed csc journals manuscript gas turbine co propulsion power plant for mari...
Viewed csc journals manuscript gas turbine co propulsion power plant for mari...
Oladokun Sulaiman Olanrewaju
 
Advances in ic engines
Advances in ic enginesAdvances in ic engines
Advances in ic engines
Sankar Ram
 

Andere mochten auch (20)

AIAA-2007-05-18
AIAA-2007-05-18AIAA-2007-05-18
AIAA-2007-05-18
 
Viewed csc journals manuscript gas turbine co propulsion power plant for mari...
Viewed csc journals manuscript gas turbine co propulsion power plant for mari...Viewed csc journals manuscript gas turbine co propulsion power plant for mari...
Viewed csc journals manuscript gas turbine co propulsion power plant for mari...
 
5s System
5s System5s System
5s System
 
Toyota 5 s system
Toyota 5 s systemToyota 5 s system
Toyota 5 s system
 
Engine company operations
Engine company operationsEngine company operations
Engine company operations
 
Starting With Toyota 5s
Starting With Toyota 5sStarting With Toyota 5s
Starting With Toyota 5s
 
MODERN DEVELOPMENT IN SUCTION PROCESS OF IC ENGINES
 MODERN DEVELOPMENT IN SUCTION PROCESS OF IC ENGINES MODERN DEVELOPMENT IN SUCTION PROCESS OF IC ENGINES
MODERN DEVELOPMENT IN SUCTION PROCESS OF IC ENGINES
 
Advanced Ic engines unit 4
Advanced Ic engines unit 4Advanced Ic engines unit 4
Advanced Ic engines unit 4
 
Divergent, Emergent & Convergent Thinking
Divergent, Emergent & Convergent ThinkingDivergent, Emergent & Convergent Thinking
Divergent, Emergent & Convergent Thinking
 
Working cycle and airflow
Working cycle and airflowWorking cycle and airflow
Working cycle and airflow
 
Fuel injection system in c.i engines
Fuel injection system in c.i enginesFuel injection system in c.i engines
Fuel injection system in c.i engines
 
Conducting Kaizen Events
Conducting Kaizen EventsConducting Kaizen Events
Conducting Kaizen Events
 
Advances in ic engines
Advances in ic enginesAdvances in ic engines
Advances in ic engines
 
Kaizen – Forms & Checklists
Kaizen – Forms & ChecklistsKaizen – Forms & Checklists
Kaizen – Forms & Checklists
 
Numerical Investigation of the Perfomance of Convergent Divergent Nozzle
Numerical Investigation of the Perfomance of Convergent Divergent NozzleNumerical Investigation of the Perfomance of Convergent Divergent Nozzle
Numerical Investigation of the Perfomance of Convergent Divergent Nozzle
 
Magneto hydro dynamic power generation (mhd power generation)
Magneto hydro dynamic power generation (mhd power generation)Magneto hydro dynamic power generation (mhd power generation)
Magneto hydro dynamic power generation (mhd power generation)
 
Kaizen Ppt
Kaizen PptKaizen Ppt
Kaizen Ppt
 
Fuel Injection and Ignition
Fuel Injection and IgnitionFuel Injection and Ignition
Fuel Injection and Ignition
 
I.C.ENGINE PPT
I.C.ENGINE PPTI.C.ENGINE PPT
I.C.ENGINE PPT
 
presentation on Introducing components of ic engine (automobile engine), Powe...
presentation on Introducing components of ic engine (automobile engine), Powe...presentation on Introducing components of ic engine (automobile engine), Powe...
presentation on Introducing components of ic engine (automobile engine), Powe...
 

Ähnlich wie presentation_swirl nozzle

Hooman_Rezaei_asme_paper1
Hooman_Rezaei_asme_paper1Hooman_Rezaei_asme_paper1
Hooman_Rezaei_asme_paper1
rezaeiho
 
conference paper
conference paperconference paper
conference paper
Rob Rosier
 

Ähnlich wie presentation_swirl nozzle (20)

Gas lift design
Gas lift designGas lift design
Gas lift design
 
Gas Lift Design: Comparative Study of Continuous and Intermittent Gas Lift (C...
Gas Lift Design: Comparative Study of Continuous and Intermittent Gas Lift (C...Gas Lift Design: Comparative Study of Continuous and Intermittent Gas Lift (C...
Gas Lift Design: Comparative Study of Continuous and Intermittent Gas Lift (C...
 
Effect of Geometric Configuration on Performance of Uniflow Cyclone
Effect of Geometric Configuration on Performance of Uniflow CycloneEffect of Geometric Configuration on Performance of Uniflow Cyclone
Effect of Geometric Configuration on Performance of Uniflow Cyclone
 
Review Paper on Experimental Analysis of Vortex Tube
Review Paper on Experimental Analysis of Vortex TubeReview Paper on Experimental Analysis of Vortex Tube
Review Paper on Experimental Analysis of Vortex Tube
 
IRJET-Helical Screw-Tape Influence on Swirl Flow Profile in a Diffuser.
IRJET-Helical Screw-Tape Influence on Swirl Flow Profile in a Diffuser.IRJET-Helical Screw-Tape Influence on Swirl Flow Profile in a Diffuser.
IRJET-Helical Screw-Tape Influence on Swirl Flow Profile in a Diffuser.
 
COMPUTATIONAL ANALYSIS OF FLUID FLOW THROUGH ROTATING VANELESS DIFFUSER
COMPUTATIONAL ANALYSIS OF FLUID FLOW THROUGH ROTATING VANELESS DIFFUSERCOMPUTATIONAL ANALYSIS OF FLUID FLOW THROUGH ROTATING VANELESS DIFFUSER
COMPUTATIONAL ANALYSIS OF FLUID FLOW THROUGH ROTATING VANELESS DIFFUSER
 
IRJET- Numerical Analysis of Butterfly Valve for Industrial Application
IRJET- Numerical Analysis of Butterfly Valve for Industrial ApplicationIRJET- Numerical Analysis of Butterfly Valve for Industrial Application
IRJET- Numerical Analysis of Butterfly Valve for Industrial Application
 
Comparison of Pressure Drop Characteristics of Swing Plate and Dual Plate Che...
Comparison of Pressure Drop Characteristics of Swing Plate and Dual Plate Che...Comparison of Pressure Drop Characteristics of Swing Plate and Dual Plate Che...
Comparison of Pressure Drop Characteristics of Swing Plate and Dual Plate Che...
 
Ijri te-03-010 cfd analysis on ejector cooling system with variable throat ge...
Ijri te-03-010 cfd analysis on ejector cooling system with variable throat ge...Ijri te-03-010 cfd analysis on ejector cooling system with variable throat ge...
Ijri te-03-010 cfd analysis on ejector cooling system with variable throat ge...
 
IRJET- A Review of Design and Analysis of Retainerless Dual Plate Check Valve...
IRJET- A Review of Design and Analysis of Retainerless Dual Plate Check Valve...IRJET- A Review of Design and Analysis of Retainerless Dual Plate Check Valve...
IRJET- A Review of Design and Analysis of Retainerless Dual Plate Check Valve...
 
IRJET- A Literature Review on Investigation of Design Parameter of Cyclone Se...
IRJET- A Literature Review on Investigation of Design Parameter of Cyclone Se...IRJET- A Literature Review on Investigation of Design Parameter of Cyclone Se...
IRJET- A Literature Review on Investigation of Design Parameter of Cyclone Se...
 
Hooman_Rezaei_asme_paper1
Hooman_Rezaei_asme_paper1Hooman_Rezaei_asme_paper1
Hooman_Rezaei_asme_paper1
 
M.E Thesis Presentation
M.E Thesis PresentationM.E Thesis Presentation
M.E Thesis Presentation
 
Ejector Expansion Refrigeration Systems
Ejector Expansion Refrigeration SystemsEjector Expansion Refrigeration Systems
Ejector Expansion Refrigeration Systems
 
anaesthesia machine-140810030802-pptx.pptx
anaesthesia machine-140810030802-pptx.pptxanaesthesia machine-140810030802-pptx.pptx
anaesthesia machine-140810030802-pptx.pptx
 
conference paper
conference paperconference paper
conference paper
 
Valve type-modi-11
Valve type-modi-11Valve type-modi-11
Valve type-modi-11
 
Valve type-modi-11
Valve type-modi-11Valve type-modi-11
Valve type-modi-11
 
Study of Performance & Cavitation Characterization of Mixed Flow Centrifugal ...
Study of Performance & Cavitation Characterization of Mixed Flow Centrifugal ...Study of Performance & Cavitation Characterization of Mixed Flow Centrifugal ...
Study of Performance & Cavitation Characterization of Mixed Flow Centrifugal ...
 
Ijri te-03-011 performance testing of vortex tubes with variable parameters
Ijri te-03-011 performance testing of vortex tubes with variable parametersIjri te-03-011 performance testing of vortex tubes with variable parameters
Ijri te-03-011 performance testing of vortex tubes with variable parameters
 

presentation_swirl nozzle

  • 1. A NEW CONTROL MECHANISM FOR TWO- PHASE EJECTOR IN VAPOR COMPRESSION CYCLES FOR AUTOMOTIVE APPLICATIONS USING ADJUSTABLE MOTIVE NOZZLE INLET SWIRL Jingwei Zhu, Stefan Elbel University of Illinois at Urbana-Champaign Department of Mechanical Science and Engineering Air Conditioning and Refrigeration Center (ACRC)
  • 2. SAE INTERNATIONAL • Background: opportunities and challenges with ejector cooling cycles • Research motivation: optimize ejector cycle performance under changing working conditions/capacities (common in automotive applications) by adjusting ejector motive nozzle • New solution: swirl ejector - utilizing controllable swirl at the motive inlet of the ejector to adjust mass flow rate and condenser outlet quality/subcooling (Swirl nozzle/valve has been recognized as a reliable flow modulation method as early as 1960s (Mayer, 1967; Wormley, 1969)) • Research approach: − Swirl nozzle tests with refrigerant (R134a) − Visualization and modeling of low-quality flow expanded in the nozzle • Conclusions Presentation Outline Paper 2016-01-0243 Presenter: Jingwei Zhu 2
  • 3. SAE INTERNATIONAL Conventional cooling cycle: • Throttling in the expansion valve causes irreversibility • Cycle efficiency is impaired Benefits of Ejector Cooling Cycles 3 𝑷 𝒄𝒐𝒎𝒑,𝒊𝒏 > 𝑷 𝒆𝒗𝒂𝒑 Ejector cooling cycle: • Irreversibility in the expansion process is reduced • Compressor work is saved • Cooling capacity is increased • Cycle efficiency is improved (R134a ~ 5 %; CO2 ~ 20 %) 𝑷 𝒄𝒐𝒎𝒑,𝒊𝒏 ≈ 𝑷 𝒆𝒗𝒂𝒑 Paper 2016-01-0243 Presenter: Jingwei Zhu
  • 4. SAE INTERNATIONAL • Different working conditions/capacities favor different ejector geometry • Slightly different geometry might result in significant difference in system COP under the same conditions • Ejector motive nozzle throat diameter (nozzle restrictiveness) is one of the key points that can significantly affect COP Challenges with Ejector Cooling Cycle 4 Test Conditions R410A ejector air conditioning system COP with different motive nozzle throat diameters under three different conditions Hu et al. (2014) Condition 1 Condition 2 Condition 3 𝑇𝑖𝑛𝑑𝑜𝑜𝑟(dry/wet bulb), ºC 26.7/19.4 26.7/19.4 26.8/19.5 𝑇𝑜𝑢𝑡𝑑𝑜𝑜𝑟(dry/wet bulb), ºC 35.0/19.5 30.6/16.8 27.8/14.9 𝑝 𝑐𝑜𝑛𝑑, MPa 2.4 2.0 1.9 Sumeru et al. (2012); Sarkar (2012); Elbel and Hrnjak (2008); Elbel (2011); Paper 2016-01-0243 Presenter: Jingwei Zhu COP changed by more than 40 %
  • 5. SAE INTERNATIONAL Challenges with Ejector Cooling Cycle 5 Less restrictive nozzle Restrictiveness of the motive nozzle on the two-phase flow can significantly affect ejector efficiency and system performance. Paper 2016-01-0243 Presenter: Jingwei Zhu
  • 6. SAE INTERNATIONAL Challenges with Ejector Cooling Cycle 6 More restrictive nozzle Restrictiveness of the motive nozzle on the two-phase flow can significantly affect ejector efficiency and system performance. Paper 2016-01-0243 Presenter: Jingwei Zhu
  • 7. SAE INTERNATIONAL How to Adjust Motive Nozzle Geometry (Restrictiveness on Flow) 7 Eurofighter Typhoon thrust nozzle http://www.military.com/video/aircraft/engines/eurofighter-thrust-vectoring- nozzle/2907034546001 Paper 2016-01-0243 Presenter: Jingwei Zhu
  • 8. SAE INTERNATIONAL This design is complicated and costly, and more friction losses are incurred because of the additional surface area and turbulence introduced. Previous Approach: Adjustable Needle 8Paper 2016-01-0243 Presenter: Jingwei Zhu
  • 9. SAE INTERNATIONAL Utilizing an adjustable swirl at the motive inlet to control the flow expanded in the motive nozzle (no change in geometry; same effect as changing nozzle throat diameter) New Solution: Swirl Ejector 9 Conventional ejector Swirl ejector Swirl ejector cooling cycle Adjustable Swirl Paper 2016-01-0243 Presenter: Jingwei Zhu
  • 10. SAE INTERNATIONAL Works for both single-phase and two-phase Hypothesis 1: Share of Tangential Kinetic Energy in the Available Pressure Potential Decreases the Mass Flow Rate 10 Nozzle convergent part Paper 2016-01-0243 Presenter: Jingwei Zhu Axial velocity profile Tangential velocity profile ∆𝑝~ 1 2 𝜌 𝑉𝑜𝑢𝑡 2 − 𝑉𝑖𝑛 2 𝑉𝑜𝑢𝑡 2 = 𝑉𝑎𝑥𝑖𝑎𝑙,𝑜𝑢𝑡 2 + 𝑉𝑡𝑎𝑛𝑔𝑒𝑛𝑡𝑖𝑎𝑙,𝑜𝑢𝑡 2 𝑚~𝜌𝑉𝑎𝑥𝑖𝑎𝑙,𝑜𝑢𝑡 𝐴 𝑜𝑢𝑡 Inlet Inlet Outlet Outlet
  • 11. SAE INTERNATIONAL • Two-phase flow during expansion is usually not in equilibrium (Bubble growth takes time) • The stronger the swirl is the faster bubbles grow • Works for two-phase flow Hypothesis 2: Swirl Boosts Vapor Bubble Growth 11 No Swirl With stronger swirl, more relative motion is created between bubbles and surrounding liquid in radial direction Radial direction Nozzle convergent part Paper 2016-01-0243 Presenter: Jingwei Zhu 𝒅 𝒎 𝒃𝒖𝒃𝒃𝒍𝒆 𝒅𝒕 𝒉𝒍𝒗 = 𝟒𝝅𝑹 𝒃𝒖𝒃𝒃𝒍𝒆 𝟐 𝒉(𝑻𝒍𝒊𝒒𝒖𝒊𝒅,∞ − 𝑻 𝒔) 𝑵𝒖 𝒔𝒑𝒉𝒆𝒓𝒆 = 𝒉 𝑫 𝒃𝒖𝒃𝒃𝒍𝒆 𝒌 = 𝟐 + 𝟎. 𝟒𝑹𝒆 𝟏 𝟐 + 𝟎. 𝟎𝟔𝑹𝒆 𝟐 𝟑 𝑷𝒓 𝟎.𝟒 𝝁𝒍𝒊𝒒𝒖𝒊𝒅,∞ 𝝁𝒍𝒊𝒒𝒖𝒊𝒅,𝒔 𝟏 𝟒 𝑹𝒆~𝑽 𝒓𝒆𝒍𝒂𝒕𝒊𝒗𝒆
  • 12. SAE INTERNATIONAL How to Make Nozzle Have More Restrictiveness on The Two-Phase Flow? 12 Change nozzle geometry (complicated, costly, additional losses) Decrease the share of axial kinetic energy in available pressure potential energy; increase vapor generation before the flow reaches the throat; no change in geometry Our solution (simple, inexpensive, effective) Paper 2016-01-0243 Presenter: Jingwei Zhu
  • 13. SAE INTERNATIONAL • Experimental investigation of the influence of motive inlet swirl on the flow expanded in the motive nozzle with commonly used refrigerant R134a • Visualization of the swirling flow expanded in the nozzle • Explanation and modeling of the influence of motive inlet swirl on the flow expanded in the motive nozzle (ongoing) • Evaluation of the nozzle efficiency with swirl control and comparison with other control methods; system tests with adjustable swirl ejector under different working conditions in the future Research Approach 13Paper 2016-01-0243 Presenter: Jingwei Zhu
  • 14. SAE INTERNATIONAL Swirl Nozzle 14 Nozzle inlet diameter (mm) 15.0 Nozzle throat diameter (mm) 1.0 Nozzle outlet diameter (mm) 1.7 Nozzle convergent part length (mm) 9.9 Nozzle divergent part length (mm) 40.0 Tangential inlet inner diameter (mm) 2.0 Swirl decay distance (mm) 138.0 Axial inlet Sleeve (resin) Nozzle (resin) Tee (brass) Tangential inlet Convergent-divergent nozzle (resin) 3D printed prototype Swirl nozzle geometry Paper 2016-01-0243 Presenter: Jingwei Zhu A A Section A-A
  • 15. SAE INTERNATIONAL • Pumped-refrigerant-loop for adjustment of nozzle test conditions • Pressures and temperatures at the axial and tangential inlets are measured; pressure at the nozzle outlet is measured • Total mass flow rate and axial inlet mass flow rate are measured by Coriolis flow meters • Ratio of tangential inlet mass flow rate to total mass flow rate is adjusted by two valves Experimental Facility for Investigation of Swirl Influence on Nozzle Restrictiveness 15 𝑆𝑤𝑖𝑟𝑙 𝑠𝑡𝑟𝑒𝑛𝑔𝑡ℎ = 𝑚 𝑡𝑎𝑛𝑔𝑒𝑛𝑡𝑖𝑎𝑙 𝑚 𝑡𝑜𝑡𝑎𝑙 Paper 2016-01-0243 Presenter: Jingwei Zhu
  • 16. SAE INTERNATIONAL • Working fluid: R134a • Different nozzle inlet pressures are achieved by adjusting the heating water temperature and pump speed • Nozzle outlet pressure can be adjusted by a valve installed in the downstream of the nozzle • Flow at the nozzle inlet is subcooled by around 0.5 ºC. No observable bubbles at the nozzle inlet (guaranteed by observing through the sight glass installed at the nozzle inlet). Testing Conditions 16Paper 2016-01-0243 Presenter: Jingwei Zhu 𝑷𝒊𝒏 (kPa) 𝑷 𝒐𝒖𝒕 (kPa) 𝑻𝒊𝒏 (ºC) 𝒎𝒕𝒐𝒕𝒂𝒍 (g/s) Vortex strength (-) 760~1059 407~909 29~41 6~20 0~1 Test Matrix
  • 17. SAE INTERNATIONAL Effect of Outlet Pressure on Nozzle Mass Flow Rate at Constant Inlet Pressure 17 4 6 8 10 12 14 16 18 20 400 500 600 700 800 900 1000 Totalmassflowrate(g/s) Outlet pressure (kPa) Inlet subcooling = 0.5 ºC Theoretically calculated incompressible single phase liquid mass flow rate Choked at low outlet pressure (decrease in outlet pressure does not increase mass flow rate) Observations: • Flow is choked at low outlet pressure • Inlet swirl reduces total mass flow rate under the same inlet and outlet conditions (larger restrictiveness) Nozzle Inlet: 925 kPa 36 ºC 𝑷𝒊𝒏 = 𝟗𝟐𝟓 𝒌𝑷𝒂 No swirl With max swirl Paper 2016-01-0243 Presenter: Jingwei Zhu
  • 18. SAE INTERNATIONAL Preliminary Visualization Results 18 4 6 8 10 12 14 16 18 20 400 600 800 1000 Totalmassflowrate(g/s) Outlet pressure (kPa) Inlet 925 kPa 36 ºC no swirl Inlet 925 kPa 36 ºC pure liquid Clear flow in the convergent part of the nozzle Clear Choked flow (very low outlet pressure): becomes bubbly immediately after the throat Outlet pressure close to inlet pressure: flow is still clear after the throat BubblyChoked flow Outlet pressure close to inlet pressure Paper 2016-01-0243 Presenter: Jingwei Zhu
  • 19. SAE INTERNATIONAL Choked Mass Flow Rate with Different Inlet Swirl Strengths at Constant Inlet Pressure 19 10 12 14 16 18 20 22 0 0.2 0.4 0.6 0.8 1 Totalmassflowrate(g/s) Tangential mass flow rate/total mass flow rate Inlet 826 kPa 32 ºC Inlet 925 kPa 36 ºC Inlet 1034 kPa 40 ºC Inlet subcooling = 0.5 ºC Nozzle restrictiveness on the flow is changed by swirl; the stronger the swirl is, the larger the restrictiveness is. Mass flow rate can be reduced by 35 % with swirl under the same inlet and outlet conditions (large control range). Paper 2016-01-0243 Presenter: Jingwei Zhu
  • 20. SAE INTERNATIONAL Nozzle Inlet Pressure Can Vary in A Wide Range with Different Inlet Swirl Strengths at Constant Total Mass Flow Rate (Choked) 20 750 800 850 900 950 1000 1050 1100 0.2 0.4 0.6 0.8 1 InletPressure(kPa) Tangential mass flow rate/total mass flow rate Total mass flow rate=15 g/s Total mass flow rate=14 g/s Total mass flow rate=13 g/s Inlet subcooling = 0.5 ºC Nozzle restrictiveness on the flow is changed by swirl; the stronger the swirl is, the larger the restrictiveness is. Mass flow rate ratio (swirl strength): 0.2 to 0.5 Inlet pressure: 780 kPa to 1050 kPa (large control range) for total mass flow rate = 15 g/s Paper 2016-01-0243 Presenter: Jingwei Zhu
  • 21. SAE INTERNATIONAL • Nozzle inlet swirl can change nozzle restrictiveness on the two-phase flow. The stronger the swirl is, the larger the restrictiveness is. • The control range of inlet pressure and mass flow rate is large enough for real applications. Mass flow rate can be reduced by 35 % with swirl under the same nozzle inlet and outlet conditions. • Next step: Compare the efficiency of swirl ejector with other control methods to see if it reduces the frictional losses for the same range of flow control. • Goal: By adjusting the restrictiveness of motive nozzle on the flow expanded through it, ejector cycle performance can be optimized for different working conditions/capacities and the improvements could be more than 40 %. Summary and Conclusions 21Paper 2016-01-0243 Presenter: Jingwei Zhu
  • 22. SAE INTERNATIONAL Thank you for your attention! Any questions? 22 • Presenter: Jingwei Zhu • Email: jzhu50@illinois.edu • Acknowledgments: The authors would like to thank the member companies of the Air Conditioning and Refrigeration Center at the University of Illinois at Urbana-Champaign for their generous support. Paper 2016-01-0243 Presenter: Jingwei Zhu
  • 23. SAE INTERNATIONAL Reference 23 1. Gay, N. H., “Refrigerating System,” U.S. Patent 1,836,318, 1931. 2. Disawas, S. and Wongwises, S., “Experimental investigation on the performance of the refrigeration cycle using a two-phase ejector as an expansion device,” International Journal of Refrigeration, 27(6): 587-594, 2004. 3. Lawrence, N., and Elbel, S., “Experimental and Numerical Study on the Performance of R410A Liquid Recirculation Cycles with and without Ejectors," 15th International Refrigeration and Air Conditioning Conference at Purdue, West Lafayette, IN, USA, Paper 2187, 2014. 4. Ozaki, Y., Takeuchi, H., and Hirata, T., “Regeneration of expansion energy by ejector in CO2 cycle,” 6th IIR Gustav Lorentzen Conference on Natural Working Fluid, Glasgow, UK, 11-20, 2004. 5. Banasiak, K., Hafner, A., and Andresen, T., “Experimental and numerical investigation of the influence of the two-phase ejector geometry on the performance of the R744 heat pump,” International Journal of Refrigeration, 35(6): 1617-1625, 2012. 6. Elbel, S. and Hrnjak, P., “Experimental validation of a prototype ejector designed to reduce throttling losses encountered in transcritical R744 system operation,” International Journal of Refrigeration, 31(3): 411-422, 2008. 7. Elbel, S., “Historical and present developments of ejector refrigeration systems with emphasis on transcritical carbon dioxide air-conditioning applications,” International Journal of Refrigeration, 34(7): 1545-1561, 2011. 8. Harrell, G. S., and Kornhauser, A. A., “Performance tests of a two-phase ejector,” American Society of Mechanical Engineers, New York, NY, United States, 1995. 9. Lawrence, N. and Elbel S., “Experimental investigation of a two-phase ejector cycle suitable for use with low-pressure refrigerants R134a and R1234yf,” International Journal of Refrigeration, 38: 310-322, 2014. Paper 2016-01-0243 Presenter: Jingwei Zhu
  • 24. SAE INTERNATIONAL Reference 24 10. Sumeru, K., Nasution, H., and Ani, F. N., “A review on two-phase ejector as an expansion device in vapor compression refrigeration cycle,” Renewable and Sustainable Energy Reviews, 16(7): 4927- 4937, 2012. 11. Sarkar, J., “Ejector enhanced vapor compression refrigeration and heat pump systems - A review,” Renewable and Sustainable Energy Reviews, 16(9): 6647-6659, 2012. 12. Hu, J., Shi, J., Liang, Y., Yang, Z., and Chen, J., “Numerical and experimental investigation on nozzle parameters for R410A ejector air conditioning system,” International Journal of Refrigeration, 40: 338-346, 2014. 13. Henry, R. E., and Fauske, H. K., “The two-phase critical flow of one-component mixtures in nozzles, orifices, and short tubes,” Journal of Heat Transfer, 93(2): 179-187, 1971. 14. Schrock, V. E., Starkman, E. S., and Brown, R. A., “Flashing flow of initially subcooled water in convergent–divergent nozzles,” Journal of Heat Transfer, 99(2): 263-268, 1977. 15. Plesset, M. S., and Zwick, S. A., “The growth of vapor bubbles in superheated liquids,” Journal of Applied Physics, 25(4): 493-500, 1954. 16. Florschuetz, L. W., Henry, C. L., and Khan, A. R., “Growth rates of free vapor bubbles in liquids at uniform superheats under normal and zero gravity conditions,” International Journal of Heat and Mass Transfer, 12(11): 1465-1489, 1969. 17. Ruckenstein, E., and Davis, E. J., “The effects of bubble translation on vapor bubble growth in a superheated liquid,” International Journal of Heat and Mass Transfer, 14(7): 939-952, 1971. 18. Mayer, E. A., “Large-signal vortex valve analysis,” Advances in Fluidics, 233-249, 1967. 19. Wormley, D. N., “An analytical model for the incompressible flow in short vortex chambers,” Journal of Basic Engineering, 91(2): 264-272, 1969. Paper 2016-01-0243 Presenter: Jingwei Zhu