Research Papers

The Dissipation Function-Based Efficiency for Turbomachinery—Part I: The Efficiency of a Cooled Turbine Row1

[+] Author and Article Information
Chong M. Cha

Turbine Aerodynamics,
Rolls-Royce Corporation,
546 S. Meridian Street,
Indianapolis, IN 46225
e-mail: chong.cha2@rolls-royce.com

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received May 11, 2016; final manuscript received August 29, 2016; published online November 16, 2016. Editor: Kenneth Hall.

J. Turbomach 139(3), 031003 (Nov 16, 2016) (11 pages) Paper No: TURBO-16-1105; doi: 10.1115/1.4034683 History: Received May 11, 2016; Revised August 29, 2016

The effect of coolant addition or “mixing loss” on aerodynamic performance is formulated for the turbine, where mixing takes place between gas streams of different compositions as well as static temperatures. To do this, a second-law efficiency measure is applied to a generalization of the one-dimensional mixing problem between a main gas stream and a single coolant feed, first introduced and studied by Hartsel (1972, “Prediction of Effects of Mass-Transfer Cooling on the Blade-Row Efficiency of Turbine Airfoils,” AIAA Paper No. 1972-11) for the turbine application. Hartsel's 1972 model for mass transfer cooling loss still remains the standard for estimating mixing loss in today's turbines. The present generalization includes losses due to the additional contributions of “compositional mixing” (mixing between unlike compositions of the main and coolant streams) as well as the effect of chemical reaction between the two streams. Scaling of the present dissipation function-based loss model to the mainstream Mach number and relative cooling massflow and static temperature is given. Limitations of the constant specific heats assumptions and the impact of fuel-to-air ratio are also quantified.

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Fig. 1

Motivation of the work. Hartsel's idealized model for coolant mixing with the mainstream [1].

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Fig. 2

One-dimensional control volume analysis of Hartsel's model mixing problem (Fig. 1). The FRM (finite-rate mixing) model imagines a duct with a porous lower wall through which coolant air is added from x = 0 to Lmix. The duct is at constant pressure.

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Fig. 3

Specified massflow rate of the main gas stream with C1 (slope of W) chosen such that Lmix = C, the airfoil chord length

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Fig. 4

Initial conditions for a range in FAR (fuel-to-air ratio) used to specify the main gas stream (FAR > 0) and turbine coolant air (FAR = 0). Subplot (a) shows only a subset of the species considered in this work: O2, CO2, H2O, OH × 10, and CO. In (b), the temperature has been normalized as Θ≡(T−Tref)/(Tad−Tref), where Tad is the LHV adiabatic flame temperature.

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Fig. 5

Compressible FRM solutions for FAR = 0.05 (left column) and FAR = 0.08 (right column). Top row shows species mass fractions for O2, CO2, H2O, OH × 10, and CO. Bottom row shows H/Hg, Θ≡(T−Tref)/(Tad−Tref), h/Hg, and κ/Hg. In each plot, solid lines are for the reacting case, dashed lines nonreacting.

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Fig. 6

Baseline case (FAR = 0.05 or φg=0.75) turbine row efficiencies for all the possible mixed states up to the prescribed final, fully mixed state

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Fig. 7

Scaling of mixing loss with Wc and FAR: φg=0.50, φg=0.75, and φg=1.2. For each φg case, solid lines correspond to the reacting case, dashed lines are nonreacting. Only significant deviation between solid and dashed lines are seen for the φg=1.2 case (black lines). Note, Wc is normalized by Wg instead of Wf, to compare with the Hartsel correlation, Eq. (1).

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Fig. 8

Scaling of mixing loss with (a) coolant to mainstream static temperature ratio and (b) mainstream gas Mach number. Results are for the baseline case (φ=0.75) with ξ0 = 0.1 (thin solid line) and with ξ0 = 0.2 (thick solid line).

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Fig. 9

Enthalpy error (b) due to the neglect of the temperature dependence on cp(T) (a). Solid line is a FAR = 0 case, dashed line is for a FAR = 0.05.



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