Research Papers

Engine-Scalable Rotor Casing Convective Heat Flux Evaluation Using Inverse Heat Transfer Methods

[+] Author and Article Information
David Gonzalez Cuadrado

School of Mechanical Engineering,
Purdue University,
500 Allison Road,
West Lafayette, IN 47906
e-mails: david.gonzalez.cuadrado@gmail.com;

Francisco Lozano

School of Mechanical Engineering,
Purdue University,
500 Allison Road,
West Lafayette, IN 47906
e-mail: flozanov@purdue.edu

Valeria Andreoli

School of Mechanical Engineering,
Purdue University,
500 Allison Road,
West Lafayette, IN 47906
e-mail: vale.andreoli@gmail.com

Guillermo Paniagua

School of Mechanical Engineering,
Purdue University,
500 Allison Road,
West Lafayette, IN 47906
e-mail: gpaniagua@me.com

Manuscript received June 23, 2018; final manuscript received June 27, 2018; published online September 14, 2018. Editor: Jerzy T. Sawicki.

J. Eng. Gas Turbines Power 141(1), 011012 (Sep 14, 2018) (10 pages) Paper No: GTP-18-1323; doi: 10.1115/1.4040713 History: Received June 23, 2018; Revised June 27, 2018

In this paper, we propose a two-step methodology to evaluate the convective heat flux along the rotor casing using an engine-scalable approach based on discrete Green's functions . The first step consists in the use of an inverse heat transfer technique to retrieve the heat flux distribution on the shroud inner wall by measuring the temperature of the outside wall; the second step is the calculation of the convective heat flux at engine conditions, using the experimental heat flux and the Green functions engine-scalable technique. Inverse methodologies allow the determination of boundary conditions; in this case, the inner casing surface heat flux, based on measurements from outside of the system, which prevents aerothermal distortion caused by routing the instrumentation into the test article. The heat flux, retrieved from the inverse heat transfer methodology, is related to the rotor tip gap. Therefore, for a given geometry and tip gap, the pressure and temperature can also be retrieved. In this work, the digital filter method is applied in order to take advantage of the response of the temperature to heat flux pulses. The discrete Green's function approach employs a matrix to relate an arbitrary temperature distribution to a series of pulses of heat flux. In this procedure, the terms of the Green's function matrix are evaluated with the output of the inverse heat transfer method. Given that key dimensionless numbers are conserved, the Green's functions matrix can be extrapolated to engine-like conditions. A validation of the methodology is performed by imposing different arbitrary heat flux distributions, to finally demonstrate the scalability of the Green's function method to engine conditions. A detailed uncertainty analysis of the two-step routine is included based on the value of the pulse of heat flux, the temperature measurement uncertainty, the thermal properties of the material, and the physical properties of the rotor casing.

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Fig. 1

Schematic of the inverse heat transfer procedure applied in a plate

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Fig. 2

Computational domain with details of solid and fluid domain

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Fig. 3

Numerical domain used in Numeca for the computation of the conjugate heat transfer in the casing of the turbine blade

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Fig. 4

(a) Transient evolution of the heat flux applied in the conjugate heat transfer simulation in two different points of thedomain and (b) spatial distribution of heat flux at t = 4.5 s in the overtip region in the conjugate heat transfer calculation

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Fig. 5

Temperature distribution in the outer wall of the casing at t = 3 s and t = 5 s for the baseline case of casing thickness (Fo = 200) and tip clearance (1% of the blade span)

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Fig. 6

(a) Comparison between the transient evolution of imposed heat flux and the retrieved heat flux, (b) spatial distribution of the imposed heat flux at t = 1 s in the simulation, and (c) spatial distribution of the retrieved heat flux at t = 1 s in the simulation

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Fig. 7

(a) Imposed heat flux extracted from the conjugate heat transfer simulation with a clearance of 0.25% the blade span, (b) retrieved heat flux from the inverse method in the case of 0.25% of the blade span, (c) imposed heat flux extracted from the conjugate heat transfer simulation with a clearance of 0.55% the blade span, and (d) retrieved heat flux from the inverse method in the case of 0.55% of the blade span

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Fig. 8

T fluctuation damping through Al (dashed lines) and Cu (solid lines) for different thicknesses and frequencies

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Fig. 9

Inner and outer T versus time signals for a frequency of 1 kHz: (a) Al, Fo = 200 and (b) Al, Fo = 20

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Fig. 10

Averaged heat flux evolution at different upstream pressure conditions

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Fig. 11

Pressure prediction based on the inverse heat transfer procedure

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Fig. 12

Mach distribution comparison between the engine simulation and the scaled wind tunnel simulation

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Fig. 13

Convective heat flux in an isothermal CFD and adiabatic wall temperature at engine and facility conditions

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Fig. 14

Green function matrix at experiments conditions

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Fig. 15

Error in predicted temperature at wind tunnel (top) and engine condition (bottom)



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