Sarah Alison-Youel Research & Development

Ebara International - Cryodynamics

Sparks, NV USA

AIChE Spring Meeting

Tampa, FL

April 2009

Sarah Alison-Youel received a Bachelor of Science degree in Mechanical Engineering with a minor in Mathematics from the University of Nevada, Reno in 2006. Since joining Ebara in 2007 she has been working with prototype engineering, taking a project from concept through to final testing. Currently Sarah is the Project Engineer for the first two-phase Tandem Expander, two of which will be installed in a Polish Oil and Gas LNG plant in Poland.

salison-youel@ebaraintl.com

Lobanoff et al Affinity Law

Relationships for Turbines

Alison-Youel Partial model

of turbine performance

Finley No-Load and Locked-Rotor

Characteristics

This Paper Complete Turbine

Performance Modeling

Particulars of Cryogenic Testing Assumptions General Performance Equation

• No-load • Turbine Performance Model

Available Hydraulic Power Shaft Power

• General Taylor Polynomial • Affinity Law Relationships

Power Curves & Efficiency Best Efficiency

• BEP Constant Conclusions

New Shaft Power

Equation

Actual cryogenic reaction turbine

test data was used in the analysis

Design and cryogenic atmosphere

present a special testing

circumstance

Closed loop test stand

Cryogenic temperatures

Design includes vibration and speed

monitoring equipment

Integrated generator and hydraulics: • Efficiency measurements include both hydraulic

and generator efficiency

Desired Data Instrumentation Raw Data Units Reduced Data Units

Flow Rate Venturi Flow Meter Inches of H20 m3/s or

m3/hr

Turbine Differential

Pressure

Differential Pressure

Transmitter

PSI Bar

Vessel Inlet & Outlet

Pressure

Pressure Transmitter

(Bordon Tube)

PSIG Barg

Speed Eddy Probe and Target Voltage Pulse RPS or

RPM

Turbine Inlet & Outlet

Temperature

1000 Ω RTD Probe oC oF

Vessel Inlet & Outlet

Temperature

1000 Ω RTD Probe oC oF

Generator Output Power Analyzer kW, Hz, V, A kW, Hz, V, A

Drive Output Power Analyzer kW, Hz, V, A kW, Hz, V, A

Assumptions General Performance Equation

Available Hydraulic Power Shaft Power

Efficiency

Constant Geometry • Fixed:

Radius

Cross-sectional area

Angles

Incompressible Fluid • Constant Density

Developed in 2008

Most general and complete relationship for

turbine performance

Includes recirculation in g term

QNNQH g 22

No-Load

Q = lN

H = Q2 + N2 + gQN

H = ( + /l2 + g/l)Q2

H = dQ2

No-Load Relationship [Finley, 2008]

General Performance

Equation

Relationship between

head and flow under

the no-load condition

Turbine Performance

0

200

400

600

800

1000

0.000 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500

Hea

d, H

[m

]

Flow, Q [m3/s]

No-Load

2400 RPM

3110 RPM

4000 RPM

No-Load SF

2400 SF

3110 SF

4000 SF

Available hydraulic power for

turbomachinery is proportional to the

volume flow rate and the head [Lobanoff et al, 1992]

b is a unit conversion constant which

includes fluid density and gravity

)QNNQbQPhy g 22

Goal: develop the most general equation

for shaft power that follows: • Conservation of Energy

• Conservation of Momentum

• Affinity Law Relationships

Basics: • Shaft power is rotational speed * shaft torque

• Conservation of momentum for rotating

machinery:

shaft torque = D rotational momentum

• D rotational momentum is a function of the

change in velocity

General Taylor Polynomial

Method

) n

nm

mNCQNQfv

0,

,

D

nm

nm

nm

nm

rot NQCrNQCRQMnmnm

0,

2

,

1 ,,

D0,

,

nm

nm

nmrot NQCQM

0,

,

nm

nm

nmshaft NQCNQP

Affinity Law Relationships

For two distinct operating points, a & b:

xN

N

Q

Q

b

a

b

a

2

2

2

2

2

xyN

N

Q

Q

H

H

b

a

b

a

b

a

3xxyQH

QH

P

P

bb

aa

b

a

Affinity Law Relationships

Continued

0,

,

nm

nm

nmshaft NQCNQP3xxy

QH

QH

P

P

bb

aa

b

a

0,

111

,

3xnm

n

a

m

a

nm

nmshaft NQXCPb

m n

0 1

1 0

Final Equation

Combined unknown constants C1,0 and C0,1 into one unknown constant, k

Applied known no-load relationship Q=lN

Resulting equation is the most general equation for shaft power that incorporates: • Affinity law relationships

• Conservation of Energy

• Conservation of momentum

)NQkNQPshaft l

Turbine Performance

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0

200

400

600

800

1000

1200

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Po

we

r O

utp

ut,

Psh

aft [k

W]

He

ad, H

[m

]

Flow, Q [m3/s]

No-Load SF

2400 SF

3110 SF

4000 SF

2400 Power SF

3110 Power SF

4000 Power SF

Apply developed equations for available

hydraulic and shaft power:

) )QNNQb

NQkN

g

l

22

Turbine Performance

0

50

100

150

200

250

300

350

400

0

200

400

600

800

1000

1200

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Effi

cie

ncy

, [

%]

He

ad, H

[m

]

Flow, Q [m3/s]

No-Load SF

2400 SF

3110 SF

4000 SF

2400 Eff SF

3110 Eff SF

4000 Eff SF

]11[ l BEPBEP NQ

Take first derivative of efficiency, with

respect to flow, Q

Undesired ePerformanc

Desired ePerformanc

BEP Constant

2l

gl

l

0

l

0

BEP constant signifies an important relationship

between the BEP and recirculation flow:

Turbine Performance

88.51 88.19

0

50

100

150

200

250

300

0

100

200

300

400

500

600

700

800

900

0 0.1 0.2 0.3 0.4 0.5 0.6

Effi

cie

ncy

, [

%]

He

ad, H

[m

]

Flow, Q [m3/s]

No-Load SF 2400 SF 3110 SF 2400 BEP 3110 BEP

2400 Eff SF 3110 Eff SF 2400 Max Eff 3110 Max Eff

Complete set of general equations for

turbine performance that incorporate the

affinity laws and the conservation of

energy and momentum principles

More accurate model for performance and

efficiency

Discovered the BEP constant provides

important insight

Improve future turbine design

Alison-Youel, S.D. "Observation and analysis of affinity law deviations through tested performance of liquefied gas reaction turbines." International Journal of Rotating Machinery (IJRM), Vol. 2008. Article ID 737285.

Cengel, Y.A., Boles, M. A. Thermodynamics: An Engineering Approach (4th

Ed.). McGraw Hill, 2002. Courant, R., Fritz, J. Introduction to Calculus and Analysis. Springer, 2000. Finley, C.D. “Comparing predicted and tested performance of cryogenic

reaction turbines under locked-rotor condition.” 12th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery (ISROMAC). Honolulu, Hawaii, February 17-22, 2008. ISROMAC12-2008-20252.

Kimmel, H. E. “Speed Controlled Turbines for power recovery in cryogenic

and chemical processing.” World Pumps, June 1997. Lobanoff, V.S., Ross, R.R. Centrifugal Pumps, Design and Application. Gulf

Publishing, 1992.