Research Papers: Gas Turbines: Turbomachinery

Preliminary Design Method for Dense-Gas Supersonic Axial Turbine Stages

[+] Author and Article Information
Elio A. Bufi

Laboratoire DynFluid Arts et Metiers ParisTech,
Paris FR-75013, France;
DMMM Politecnico di Bari,
Bari IT-70126, Italy
e-mail: Elio-Antonio.BUFI@ensam.eu

Paola Cinnella

Laboratoire DynFluid Arts et Metiers ParisTech,
Paris FR-75013, France
e-mail: paola.cinnella@ensam.eu

1Corresponding author.

Contributed by the Turbomachinery Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received October 7, 2017; final manuscript received March 25, 2018; published online August 6, 2018. Assoc. Editor: David Sánchez.

J. Eng. Gas Turbines Power 140(11), 112605 (Aug 06, 2018) (11 pages) Paper No: GTP-17-1546; doi: 10.1115/1.4039837 History: Received October 07, 2017; Revised March 25, 2018

A fast preliminary design methodology for supersonic organic Rankine cycle (ORC) stator and rotor axial turbine blades with low degree of reaction is presented. First, the stator and rotor blade mean-line profiles are designed by using the two-dimensional (2D) method of characteristics (MOC), extended to gases governed by general equations of state (EOS). We focus more specifically on working fluids with medium to high molecular complexity, operating at thermodynamic conditions such that the fundamental derivative of gas dynamics Γ is lower than one in a significant portion of the flow field. For rotor blades, MOC is combined with a free-vortex method to achieve a smooth deflection of the supersonic incoming flow. A numerical approach is developed for solving the unique incidence problem in the case of gases governed by general EOS. Both stator and rotor blade geometries designed according to the inviscid MOC model are subsequently corrected to account for the development of viscous boundary layers by solving the compressible integral boundary layer equations extended to dense gases. The resulting blade designs are assessed by means of computational fluid dynamics (CFD) simulations based on a high-order finite volume solver equipped with advanced thermodynamic and transport-property models. Properly accounting for dense gas and viscous effects at an early design stage is found to improve the expected performance of ORC turbine rows significantly and delivers valuable baseline profiles for any further optimization.

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Fig. 1

Typical characteristic line patterns and nozzle divergent shape design

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Fig. 2

Sketch of the geometrical postprocessing used for the design of the axial ORC nozzle vane profile

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Fig. 3

Sketch of the system of characteristic lines in a rotor vane [21]

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Fig. 4

Schematic description of the rotor blade design

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Fig. 10

Mach number contour plot for DGMOC nozzle vane without (a) and with (b) boundary layer correction

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Fig. 11

Pressure distribution along the vane axis for DMOG designs with and without boundary layer correction, and comparison with the target inviscid distribution

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Fig. 6

Characteristic line patterns and expansion fan lines for a supersonic rotor (a); definition of the control volume upstream and downstream of the bow-shock (b)

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Fig. 7

Unique incidence solution: inlet flow angle, βi,1, as a function of the inlet Mach number M1 for the R245fa fluid. Dense gas conditions: pr0=1.05, Tr0=1.05; dilute gas: pr0=0.01, Tr0=1.15. The solution is calculated for a blade with r/s=0.05 (with r being the leading edge radius and s the cascade pitch) and a stagger angle βs=π/3.

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Fig. 8

Comparison between inviscid and viscous nozzle vane shapes with view enlargement of the exit section. The operating conditions are specified in Table 4.

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Fig. 9

Comparison between inviscid and viscous impulse rotor blade shapes. The operating conditions are those of Table5 with βin=βout=60 deg.

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Fig. 5

Blade designs for R245fa at various operating conditions (see Table 2). Dashed lines represent designs obtained under the perfect gas model.

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Fig. 12

Mach number contour (a) and entropy deviation (b) for DGMOC blades (no boundary layer correction)

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Fig. 13

Mach number contour plot (a) and entropy deviation (b) for RODEC rotors with boundary layer correction

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Fig. 14

Wall pressure distribution on the rotor blade for the viscous simulation with boundary layer correction and comparison with the target design distribution



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