Research Papers: Gas Turbines: Turbomachinery

The Application of Similitude Theory for the Performance Prediction of Radial Turbines Within Small-Scale Low-Temperature Organic Rankine Cycles

[+] Author and Article Information
Martin White

School of Mathematics,
Computer Science and Engineering,
City University London,
Northampton Square,
London EC1V 0HB, UK
e-mail: Martin.White.1@city.ac.uk

Abdulnaser I. Sayma

School of Mathematics,
Computer Science and Engineering,
City University London,
Northampton Square,
London EC1V 0HB, UK
e-mail: A.Sayma@city.ac.uk

1Corresponding author.

Contributed by the Turbomachinery Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received March 18, 2015; final manuscript received June 5, 2015; published online July 7, 2015. Editor: David Wisler.

J. Eng. Gas Turbines Power 137(12), 122605 (Jul 07, 2015) (10 pages) Paper No: GTP-15-1099; doi: 10.1115/1.4030836 History: Received March 18, 2015

For small-scale organic Rankine cycles (ORCs) to be a competitive technology, it is reasonable to assume that the same turbine design will be implemented into a range of different applications. It is therefore critical to be able to predict turbine off-design performance over a range of different operating conditions while utilizing different working fluids. Similitude theory can be used for this purpose, and it has been well validated for ideal gases. However, the same cannot be said for its applications to the organic fluids found within ORCs. This paper considers a candidate subsonic turbine design operating with R245fa and the corresponding turbine performance map. Similitude theory is used to predict the performance of the same turbine operating at different inlet conditions using R245fa, R123, and R1234yf. The similitude predictions are compared to computational fluid dynamics (CFD) results obtained using ansys CFX. The original similitude theory using turbine total inlet conditions was found to only apply within a small range of operating conditions, so a modified similitude theory has been suggested that uses the choked flow conditions instead. This modified similitude theory agrees with the CFD predictions to within 2%, right up until the choked mass flow rate. Further studies considering supersonic turbines are required to establish the applicability of similitude for applications beyond the choked pressure ratio.

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Fig. 1

Deviation in Reynolds number with variations in turbine total inlet conditions for R245fa assuming that the blade Mach number has been conserved (the dots represent the operating conditions considered within this paper)

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Fig. 2

Variation in thermodynamic properties over a range of operating conditions for superheated R245fa between operating point and design point: (a) percentage deviation in density, (b) percentage deviation in speed of sound, (c) percentage deviation in dynamic viscosity, and (d) variation in compressibility factor

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Fig. 3

Results from grid independence study showing the percentage difference in mass flow rate for three meshes, compared to the result obtained for the finest mesh

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Fig. 4

Variation of flow coefficient with head coefficient at 80%, 100%, and 120% of the design blade Mach number for the developed ORC turbine operating with R245fa

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Fig. 5

Variation of isentropic total-to-static efficiency with head coefficient at 80%, 100%, and 120% of the design blade Mach number for the developed ORC turbine operating with R245fa

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Fig. 6

Comparison between the flow coefficient predicted by similitude theory and the flow coefficient found from the CFD results for the R245fa operating points

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Fig. 7

Comparison between the isentropic total-to-static isentropic efficiency predicted by similitude theory and the efficiency found from the CFD results for the R245fa operating points

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Fig. 8

Comparison between the CFD results for R245fa cases 6–8 and the nondimensional performance curves used during the application of similitude theory: (a) case 6, (b) case 7, and (c) case 8

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Fig. 10

Comparison between the isentropic total-to-static isentropic efficiency predicted by the updated similitude theory and the efficiency found from the CFD results for the R245fa operating points

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Fig. 9

Comparison between the flow coefficient predicted by the updated similitude theory and the flow coefficient found from the CFD results for the R245fa operating points

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Fig. 11

Summary of the stator vane performance over a range of flow coefficients. Bottom group of data points refers to the throat, while the top group of data points refers to the stator outlet set at the rotor inlet radius. The dashed lines represent the change from subsonic to supersonic operation.

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Fig. 12

Distribution of Mach number within the turbine stator for case 8, and flow coefficient of 2.92 × 10−4

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Fig. 13

Comparisons between the predictions made for the flow coefficient and isentropic efficiency by similitude theory and CFD for the alternative working fluids: (a) R123 flow coefficient, (b) R123 isentropic efficiency, (c) R1234yf flow coefficient, and (d) R1234yf isentropic efficiency




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