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Research Papers

Loss Generation in Transonic Turbine Blading

[+] Author and Article Information
Penghao Duan

Osney Thermo-Fluids Laboratory,
University of Oxford,
Oxford OX1 3PJ, UK
e-mail: penghao.duan@eng.ox.ac.uk

Choon S. Tan

Department of Aeronautics and Astronautics,
Massachusetts Institute of Technology,
77 Massachusetts Avenue,
Cambridge, MA 02139
e-mail: choon@mit.edu

Andrew Scribner

Gas Turbine Engineering,
Siemens Energy Inc.,
Charlotte, NC 28273
e-mail: andrew.scribner@siemens.com

Anthony Malandra

Siemens Energy, Inc.,
11842 Corporate Boulevard,
Orlando, FL 32817
e-mail: anthony.malandra@siemens.com

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received September 9, 2017; final manuscript received December 5, 2017; published online February 6, 2018. Editor: Kenneth Hall.

J. Turbomach 140(4), 041006 (Feb 06, 2018) (12 pages) Paper No: TURBO-17-1155; doi: 10.1115/1.4038689 History: Received September 09, 2017; Revised December 05, 2017

The measured loss characteristic in a high-speed cascade tunnel of two turbine blades of different designs showed distinctly different trends with exit Mach number ranging from 0.8 to 1.4. Assessments using steady Reynolds-averaged Navier--Stokes equations (RANS) computation of the flow in the two turbine blades, complemented with control volume analyses and loss modeling, elucidate why the measured loss characteristic looks the way it is. The loss model categorizes the total loss in terms of boundary layer loss, trailing edge (TE) loss, and shock loss; it yields results in good agreement with the experimental data as well as steady RANS computed results. Thus, RANS is an adequate tool for determining the loss variations with exit isentropic Mach number and the loss model serves as an effective tool to interpret both the computational and the experimental data. The measured loss plateau in blade 1 for exit Mach number of 1–1.4 is due to a balance between a decrease of blade surface boundary layer loss and an increase in the attendant shock loss with Mach number; this plateau is absent in blade 2 due to a greater rate in shock loss increase than the corresponding decrease in boundary layer loss. For exit Mach number from 0.85 to 1, the higher loss associated with shock system in blade 1 is due to the larger divergent angle downstream of the throat than that in blade 2. However, when exit Mach number is between 1.00 and 1.30, blade 2 has higher shock loss. For exit Mach number above an approximate value of 1.4, the shock loss for the two blades is similar as the flow downstream of the throat is completely supersonic. In the transonic to supersonic flow regime, the turbine design can be tailored to yield a shock pattern the loss of which can be mitigated in near equal amount of that from the boundary layer with increasing exit Mach number, hence yielding a loss plateau in transonic-supersonic regime.

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References

Denton, J.-D. , 1993, “Loss Mechanisms in Turbomachines,” ASME J. Turbomach., 115(4), pp. 621–656. [CrossRef]
Mee, D. , Baines, N. , Oldfield, M. , and Dickens, T. , 1992, “An Examination of the Contributions to Loss on a Transonic Turbine Blade in Cascade,” ASME J. Turbomach., 114(1), pp. 155–162. [CrossRef]
Oldfeld, M. , Mee, D. , and Baines, N. , 1992, “Detailed Boundary Layer Measurements on a Transonic Turbine Cascade,” ASME J. Turbomach., 114(1), pp. 163–172. [CrossRef]
Sooriyakumaran, C. , 2014, “Experimental Study of Profile Losses in Three Transonic Turbine Cascades,” Master's thesis, Carleton University, Ottawa, ON, Canada. https://curve.carleton.ca/system/files/etd/bcdefee0-26e0-4f24-aa62-93184aa0d4f8/etd_pdf/2b649c6a0ed666ef3a744ed1f123ce34/sooriyakumaran-experimentalstudyofprofilelossesinthreetransonic.pdf
Schlichting, H. , Gersten, K. , Krause, E. , and Oertel, H. , 1955, Boundary-Layer Theory, Vol. 7, McGraw-Hill, New York.
Greitzer, E.-M. , Tan, C.-S. , and Graf, M.-B. , 2004, Internal Flow: Concepts and Applications, Cambridge University Press, New York. [CrossRef]
Corriveau, D. , and Sjolander, S.-A. , 2004, “Experimental and Numerical Investigation on the Performance of a Family of Three HP Transonic Turbine Blades,” ASME Paper No. GT2004-53087.
Corriveau, D. , and Sjolander, S.-A. , 2002, “Impact of Flow Quality in Transonic Cascade Wind Tunnels: Measurements in an HP Turbine Cascade,” International Council of the Aeronautical Sciences Congress (ICAS), Toronto, ON, Canada, Sept. 8–13, pp. 8–13. http://www.icas.org/ICAS_ARCHIVE/ICAS2002/ABSTRACTS/5114.HTM
Sieverding, C. , Stanislas, M. , and Snoeck, J. , 1980, “The Base Pressure Problem in Transonic Turbine Cascades,” ASME J. Eng. Power, 102(3), pp. 711–718. [CrossRef]
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Figures

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Fig. 4

Integration domain for computing accumulated entropy generation. Entropy generated from inlet plane Ain up to a selected axial Aj with P1 and P2 as the periodic boundaries. The inset shows the mesh surrounding the blade profile.

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Fig. 3

Normalized geometries of two blades

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Fig. 2

Experimental results of mixed-out averaged loss at measurement plane

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Fig. 1

Test rig to measure total loss in turbine cascade

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Fig. 8

Comparison of CFD computed base pressure with Sieverding's correlation and Xu's experimental results—the four measures from Xu are from a family of four turbine blades

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Fig. 10

Blade loading plots of three distinct shock patterns for blade 1

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Fig. 9

Three distinct shock patterns with increasing Misen,exit for blade 1. In the velocity divergence plot, the negative values represent the flow under compression. For supersonic flow in turbine nozzle guide vanes passage, the compression processes mainly occur at the shock waves and leading edge. Therefore, the locations of the shock can be determined by regions of negative value in the velocity divergence plot, which are shown as dark strips at the blade suction side and downstream of the TE.

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Fig. 5

Boundary layer loss characteristics of two blades

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Fig. 6

TE loss characteristics of blade 1

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Fig. 7

TE loss characteristics of blade 2

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Fig. 11

Shock system losses accounting of blade 1

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Fig. 12

Shock system losses accounting of blade 2

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Fig. 13

Comparison of total loss computed by two different approaches for blade 1

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Fig. 14

Comparison of total loss computed by two different approaches for blade 2

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Fig. 15

Comparison of CFD results with experimental data for blade 1

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Fig. 16

Comparison of CFD results with experimental data for blade 2

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Fig. 17

Explanation of the prolonged loss plateau in blade 1

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Fig. 18

Comparison of shock patterns when 0.90 ≤ Misen,exit ≤ 1.05

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Fig. 19

Comparison of shock patterns when 1.10 ≤ Misen,exit ≤ 1.30

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Fig. 20

Comparison of shock patterns when Misen,exit equals to 1.67 for blade 1 and 1.55 for blade 2

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Fig. 21

TE loss variation with Misen,exit of two blades

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Fig. 22

Shock loss variation with Misen,exit of two blades

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Fig. 23

Comparison of variation in SSR shock loss and TE shock loss between the two blades

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Fig. 24

Effective flow area distribution of two blades

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Fig. 25

Effective flow area distribution of two blades shown as a nozzle

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Fig. 30

Computation of normal Mach number

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Fig. 28

Example to compute base pressure coefficient for the case of Misen,exit = 0.5—from the blade pressure profile at TE, the base pressure region can be found between the pressure side and the suction side

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Fig. 29

The velocity divergence plot and the Mach number contour plot that serve to identify the presence of shock wave at Misen,exit = 1.67

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Fig. 26

Partitions along blade surface—the blade profile is divided into segments demarcated by normals to the blade surface. Freestream values at each segment are used to evaluate boundary layer loss in Eq. (A1). In the two entropy profiles, the black dots, the points closest to the blade with zero pointwise entropy variations, indicate the approximated locations external to boundary layer.

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Fig. 27

Computed and the constant Cd along blade surface. Here, the value of Cd is shown as the length of the normals perpendicular to the blade surface. The length when Cd = 0.002 is presented in the upper right-hand corner.

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