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Research Papers: Gas Turbines: Turbomachinery

Design Methodology for Supersonic Radial Vanes Operating in Nonideal Flow Conditions

[+] Author and Article Information
Nitish Anand

Propulsion & Power,
Aerospace Engineering Faculty,
Delft University of Technology,
Kluyverweg 1,
Delft 2629 HS, The Netherlands
e-mail: N.Anand@tudelft.nl

Salvatore Vitale

Propulsion & Power,
Aerospace Engineering Faculty,
Delft University of Technology,
Kluyverweg 1,
Delft 2629 HS, The Netherlands
e-mail: S.Vitale@tudelft.nl

Matteo Pini

Propulsion & Power,
Aerospace Engineering Faculty,
Delft University of Technology,
Kluyverweg 1,
Delft 2629 HS, The Netherlands
e-mail: M.Pini@tudelft.nl

Gustavo J. Otero

Energy Technology,
Mechanical Engineering Faculty,
Delft University of Technology,
Leeghwaterstraat 39,
Delft 2628 CB, The Netherlands
e-mail: G.J.OteroRodriguez@tudelft.nl

Rene Pecnik

Energy Technology,
Mechanical Engineering Faculty,
Delft University of Technology,
Leeghwaterstraat 39,
Delft 2628 CB, The Netherlands
e-mail: R.Pecnik@tudelft.nl

1Corresponding author.

Contributed by the Turbomachinery Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received August 21, 2017; final manuscript received April 17, 2018; published online November 14, 2018. Assoc. Editor: David Sánchez.

J. Eng. Gas Turbines Power 141(2), 022601 (Nov 14, 2018) (9 pages) Paper No: GTP-17-1470; doi: 10.1115/1.4040182 History: Received August 21, 2017; Revised April 17, 2018

The stator vanes of high-temperature organic Rankine cycle (ORC) radial-inflow turbines (RIT) operate under severe expansion ratios and the associated fluid-dynamic losses account for nearly two-thirds of the total losses generated within the blading passages. The efficiency of the machine can strongly benefit from specialized high-fidelity design methods able to provide shapes attenuating shock wave formation, consequently reducing entropy generation across the shock-wave and mitigating shock-wave boundary layer interaction. Shape optimization is certainly a viable option to deal with supersonic ORC stator design, but it is computationally expensive. In this work, a robust method to approach the problem at reduced computational cost is documented. The method consists of a procedure encompassing the method of characteristics (MoC), extended to nonideal fluid flow, for profiling the diverging part of the nozzle. The subsonic section and semibladed suction side are retrieved using a simple conformal geometrical transformation. The method is applied to design a supersonic ORC stator working with Toluene vapor, for which two blade shapes were already available. The comparison of fluid-dynamic performance clearly indicates that the MoC-Based method is able to provide the best results with the lowest computational effort, and is therefore suitable to be used in a systematic manner for drawing general design guidelines.

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Figures

Grahic Jump Location
Fig. 1

Method of characteristics implemented to design the diverging section of the supersonic nozzle. The lines with positive slope represent positive characteristics and those with negative slope are negative characteristics.

Grahic Jump Location
Fig. 2

Comparison of nozzle shape for air and Toluene (using MoC)

Grahic Jump Location
Fig. 3

Steps illustrating the design of supersonic radial stator. The axial nozzle from MoC is transformed to the radial inlet design and rotated by the pitch angle (i.e., 360/n).

Grahic Jump Location
Fig. 4

Geometrical construction of the supersonic radial stator vane. The gray vanes are the copy of the black vane rotated by the pitch angle on the either sides.

Grahic Jump Location
Fig. 5

Stator vane geometries: (a) baseline, (b) shape-optimized, and (c) MoC-based

Grahic Jump Location
Fig. 6

Geometry [left] and mesh [right] of the baseline stator. The shaded area in the geometry represents one flow passage in the stator. The flow passage downstream of the throat is representative of the area for which the solution has been reported in this work. aa′; bb′, and cc′ are the cross sections across which the pressure ratios are reported.

Grahic Jump Location
Fig. 7

Variation of solution with grid size

Grahic Jump Location
Fig. 8

CFD results of the baseline stator: (a) Mach number contour and (b) pressure gradient contour

Grahic Jump Location
Fig. 9

CFD results of the Shape-optimized stator: (a) Mach number contour and (b) pressure gradient contour

Grahic Jump Location
Fig. 10

CFD results of the MoC-Based stator: (a) Mach number contour and (b) pressure gradient contour

Grahic Jump Location
Fig. 11

Instantaneous stator exit property distribution. θθ = 0 and 1 represent stator outlets at two adjacent vane trailing edges. Dashed lines represent target values: (a) Mach number and (b) flow angle.

Grahic Jump Location
Fig. 12

Instantaneous property variation on the suction side wall, downstream of the throat. LdssLdss = 0 represents the throat and LdssLdss = 1 represents stator trailing edge, where ΔLdss = distance between points na1 and na3 in Fig. 4: (a) wall angle and (b) static pressure.

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