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Research Papers

Quantification of the Impact of Uncertainties in Operating Conditions on the Flame Transfer Function With Nonintrusive Polynomial Chaos Expansion

[+] Author and Article Information
Alexander Avdonin

Technische Universität München,
Fakultät für Maschinenwesen,
Garching b., München 85748, Germany
e-mail: avdonin@tfd.mw.tum.de

Wolfgang Polifke

Technische Universität München,
Fakultät für Maschinenwesen,
Garching b, München 85748, Germany

Manuscript received June 26, 2018; final manuscript received June 28, 2018; published online September 17, 2018. Editor: Jerzy T. Sawicki.

J. Eng. Gas Turbines Power 141(1), 011020 (Sep 17, 2018) (8 pages) Paper No: GTP-18-1364; doi: 10.1115/1.4040745 History: Received June 26, 2018; Revised June 28, 2018

Nonintrusive polynomial chaos expansion (NIPCE) is used to quantify the impact of uncertainties in operating conditions on the flame transfer function (FTF) of a premixed laminar flame. NIPCE requires only a small number of system evaluations, so it can be applied in cases where a Monte Carlo simulation is unfeasible. We consider three uncertain operating parameters: inlet velocity, burner plate temperature, and equivalence ratio. The FTF is identified in terms of the finite impulse response (FIR) from computational fluid dynamics (CFD) simulations with broadband velocity excitation. NIPCE yields uncertainties in the FTF due to the uncertain operating conditions. For the chosen uncertain operating bounds, a second-order expansion is found to be sufficient to represent the resulting uncertainties in the FTF with good accuracy. The effect of each operating parameter on the FTF is studied using Sobol indices, i.e., a variance-based measure of sensitivity, which are computed from the NIPCE. It is observed that in the present case, uncertainties in the FIR as well as in the phase of the FTF are dominated by the equivalence-ratio uncertainty. For frequencies below 150 Hz, the uncertainty in the gain of the FTF is also attributable to the uncertainty in equivalence-ratio, but for higher frequencies, the uncertainties in velocity and temperature dominate. At last, we adopt the polynomial approximation of the output quantity, provided by the NIPCE method, for further uncertainty quantification (UQ) studies with modified input uncertainties.

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Figures

Grahic Jump Location
Fig. 1

Left: Sketch of the experimental test rig. Right: truncated CFD domain. Adapted from Ref. [13].

Grahic Jump Location
Fig. 2

Top: All identified firs used for construction of the NIPCEs (); FIR represented by the mean coefficients and their confidence intervals ±2.58σ for the NIPCE with p = 1 (, ), p = 2 (, ), and p = 3 (, ). Bottom: sobol indices Su (+), ST (), Sϕ (), and STϕ () for the NIPCE with p = 3

Grahic Jump Location
Fig. 3

Probability density function (of FIR coefficients with the mean (—) and confidence intervals ±2.58σ ()

Grahic Jump Location
Fig. 4

Complex-valued frequency response of all identified firs used for construction of the NIPCES (). Mean FFR and its confidence intervals ±2.58σ for the NIPCE with p = 1 (, ), p = 2 (, ), p = 2 (, ) AND p = 3 (, ).

Grahic Jump Location
Fig. 5

Top: frequency response of all identified FIRS used for construction of the NIPCES (); mean FFR and its confidence intervals ±2.58σ for the NIPCE with p = 1 (,), p = 2 (, ), and p = 3 (, ). Bottom: Sobol indices Su (+), ST (), Sϕ (), and STϕ () for the NIPCE with p = 3.

Grahic Jump Location
Fig. 6

Probability density function of frequency response with the mean (—) and confidence intervals ±2.58σ ()

Grahic Jump Location
Fig. 7

Mean FIR with confidence intervals ±2.58σ for reduced input-parameter uncertainties with normal distribution (top) and uniform distribution (bottom) cf. Fig. 2

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