Sarah Alison-Youel Research & Development Ebara International - Cryodynamics Sparks, NV USA. AIChE Spring Meeting Tampa, FL April 2009

Transcription

1 Sarah Alison-Youel Research & Development Ebara International - Cryodynamics Sparks, NV USA AIChE Spring Meeting Tampa, FL April 2009

2 Sarah Alison-Youel received a Bachelor of Science degree in Mechanical Engineering with a minor in Mathematics from the University of Nevada, Reno in 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

3 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

4 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

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6 Actual cryogenic reaction turbine test data was used in the analysis Design and cryogenic atmosphere present a special testing circumstance Closed loop test stand

7 Cryogenic temperatures Design includes vibration and speed monitoring equipment Integrated generator and hydraulics: Efficiency measurements include both hydraulic and generator efficiency

8 Desired Data Instrumentation Raw Data Units Reduced Data Units Flow Rate Venturi Flow Meter Inches of H 2 0 m 3 /s or m 3 /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 Vessel Inlet & Outlet Temperature 1000 Ω RTD Probe o C o F 1000 Ω RTD Probe o C o F Generator Output Power Analyzer kw, Hz, V, A kw, Hz, V, A Drive Output Power Analyzer kw, Hz, V, A kw, Hz, V, A

9 Assumptions General Performance Equation Available Hydraulic Power Shaft Power Efficiency

10 Constant Geometry Fixed: Radius Cross-sectional area Angles Incompressible Fluid Constant Density

11 H 2 N 2 g N Developed in 2008 Most general and complete relationship for turbine performance Includes recirculation in g term

12 No-Load = ln H = 2 + N 2 + gn H = ( + /l 2 + g/l) 2 H = d 2 No-Load Relationship [Finley, 2008] General Performance Equation Relationship between head and flow under the no-load condition

13 Head, H [m] Turbine Performance 1000 No-Load RPM 3110 RPM 4000 RPM No-Load SF 2400 SF SF 4000 SF Flow, [m 3 /s]

14 P hy b ) 2 N 2 gn 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

15 Goal: develop the most general equation for shaft power that follows: Conservation of Energy Conservation of Momentum Affinity Law Relationships

16 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

17 General Taylor Polynomial Method v f n, N ) C m N m, n0 DM rot R m, n C m N n r m, n0 C 1 m, n 2m, n m N n DM rot m, n0 C m, n m N n P shaft N m, n0 C m, n m N n

18 Affinity Law Relationships For two distinct operating points, a & b: x N N b a b a x y N N H H b a b a b a 3 x xy H H P P b b a a b a

19 Affinity Law Relationships Continued P P a b H H a b a b xy 3 x P shaft N m, n0 C m, n m N n 3 x P shaft b m, n0 C m, n X mn1 m1 a N n1 a m n

20 P shaft Final Equation kn ln ) Combined unknown constants C 1,0 and C 0,1 into one unknown constant, k Applied known no-load relationship =ln Resulting equation is the most general equation for shaft power that incorporates: Affinity law relationships Conservation of Energy Conservation of momentum

21 Head, H [m] Power Output, P shaft [kw] Turbine Performance No-Load SF 2400 SF 3110 SF 4000 SF 2400 Power SF 3110 Power SF 4000 Power SF Flow, [m 3 /s]

22 Apply developed equations for available hydraulic and shaft power: b kn ln ) 2 ) 2 N gn

23 Head, H [m] Efficiency, [%] Turbine Performance No-Load SF 2400 SF 3110 SF 4000 SF Eff SF 3110 Eff SF 4000 Eff SF Flow, [m 3 /s]

24 Take first derivative of efficiency, with respect to flow, N BEP BEP l[ 1 1 ]

25 BEP Constant gl 2 l BEP constant signifies an important relationship between the BEP and recirculation flow: 0 l Desired Performanc e 0 l Undesired Performanc e

26 Head, H [m] Efficiency, [%] Turbine Performance Flow, [m 3 /s] No-Load SF 2400 SF 3110 SF 2400 BEP 3110 BEP 2400 Eff SF 3110 Eff SF 2400 Max Eff 3110 Max Eff

27 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

28 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 Article ID Cengel, Y.A., Boles, M. A. Thermodynamics: An Engineering Approach (4 th Ed.). McGraw Hill, Courant, R., Fritz, J. Introduction to Calculus and Analysis. Springer, Finley, C.D. Comparing predicted and tested performance of cryogenic reaction turbines under locked-rotor condition. 12 th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery (ISROMAC). Honolulu, Hawaii, February 17-22, ISROMAC Kimmel, H. E. Speed Controlled Turbines for power recovery in cryogenic and chemical processing. World Pumps, June Lobanoff, V.S., Ross, R.R. Centrifugal Pumps, Design and Application. Gulf Publishing, 1992.