Research Papers

Unsteady Work Transfer Within a Turbine Blade Row Passage

[+] Author and Article Information
Martin G. Rose

Institute of Aeronautical Propulsion Systems,
Stuttgart University,
Pfaffenwaldring 6,
Stuttgart 70569, Germany
e-mail: rose@ila.uni-stuttgart.de

Martin Marx

Institute of Aeronautical Propulsion Systems,
Stuttgart University,
Pfaffenwaldring 6,
Stuttgart 70569, Germany
e-mail: marx@ila.uni-stuttgart.de

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received December 10, 2012; final manuscript received January 8, 2014; published online February 27, 2014. Assoc. Editor: Ricardo F. Martinez-Botas.

J. Turbomach 136(9), 091001 (Feb 27, 2014) (12 pages) Paper No: TURBO-12-1236; doi: 10.1115/1.4026601 History: Received December 10, 2012; Revised January 08, 2014

There is evidence in the literature of strong static pressure pulsation on the suction and pressure sides of turbine aerofoil rows experiencing unsteady wake interaction from upstream blade rows. This evidence is both computational and experimental. It has been proposed that this unsteady pulsation causes an unsteady work transfer between the wake and free-stream fluid. It has also been proposed that such a work transfer process may cause a reduction in downstream mixing losses and, thus, an improvement in turbine efficiency. While the literature has provided evidence of the existence of such pulsations, there is no clear explanation of why they occur. This paper addresses the above topic from an analytic perspective; a one-dimensional, incompressible, linear solution to the governing differential equation is used to shed light on this behavior. While the model lacks a lot of physical detail, the pulsation effect is captured, and it is shown that the unsteady pressure attenuates the amplitude of the unsteady total pressure through the transfer of work. The significance of reduced frequency is also clearly demonstrated with convection dominated flow at low reduced frequency and unsteady work dominated flow at high reduced frequencies. The model allows the specification of the amplitude and phase of the down stream static pressure perturbation. This variability is shown to have a significant effect on the attenuation of the unsteady total pressure. New insight is provided in to the much studied topic of “clocking” in axial turbines.

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Fig. 1

The flow passage between two turbine aerofoils; inlet, throat, and exit are identified

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Fig. 2

One-dimensional model of the turbine blade passage showing the assumed quadratic variation of flow area, the inlet total pressure, and the exit static pressure versus ωt

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Fig. 3

Results of the unsteady 1D analysis of an LP turbine vane passage flow at a reduced frequency β = 10.4: original case 1. The four diagrams are in space time format; the perturbations are plotted as a function of the normalized length of passage (x/xe) and time (cycles): (a) velocity, (b) static pressure, (c) total pressure, and (d) unsteady work.

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Fig. 4

Particle paths length (x/xe) versus time (s): original case 1. Three paths are shown with particles starting at x = 0 with total pressure perturbation at three different levels: high, zero, and low.

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Fig. 5

Particle path data: local particle values of velocity, static pressure, total pressure, and unsteady work all plotted against length along the passage x/xe: original case 1. Three particle paths are shown, chosen with different inlet total pressure perturbations: high, zero, and low.

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Fig. 6

A comparison of unsteady static pressure on passage walls: analytical result on left and experimental vane 2 surface data on right: Marx et al. [11]. Pressure contours are in pascal, and the analytical result has spot heights. The white dashed diagonal lines are approximate convection lines in each case.

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Fig. 7

Results of the same analysis as Fig. 3 but at a lower reduced frequency (β = 1.04) case 2. Four graphs: (a) velocity perturbation, (b) static pressure perturbation, (c) total pressure perturbation, and (d) unsteady work.

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Fig. 8

Particle path data for case 2 with lower reduced frequency (β = 1.04). (a) Perturbation velocity, (b) perturbation static pressure, (c) perturbation total pressure, and (d) unsteady work.

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Fig. 9

Results for case 3 with a phase adjustment of the exit static pressure field Δφ = π (rad) compared to Fig. 3. Four graphs are shown: (a) unsteady velocity, (b) fluctuating static pressure, (c) unsteady total pressure, and (d) unsteady work.

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Fig. 10

Particle path data for case 3 with phase shift of the static pressure at exit Δφ = π (rad): three particle tracks are shown for particles of high (1050 Pa) total pressure perturbation at inlet, low (–1050 Pa) and zero p′t. (a) Perturbation velocity, (b) perturbation static pressure, (c) perturbation total pressure, and (d) unsteady work.

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Fig. 11

Attenuation of the inlet total pressure distortion in percentage terms at throat and exit planes versus the phase angle φ of the exit static pressure fluctuation




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