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Research Papers: Gas Turbines: Turbomachinery

Budgets of Disturbances Energy for Nozzle Flows at Subsonic and Choked Regimes

[+] Author and Article Information
Maxime Huet

The French Aerospace Lab,
ONERA,
Châtillon F-92322, France
e-mail: maxime.huet@onera.fr

Contributed by the Turbomachinery Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received August 2, 2017; final manuscript received August 29, 2017; published online July 5, 2018. Assoc. Editor: Riccardo Da Soghe.

J. Eng. Gas Turbines Power 140(11), 112602 (Jul 05, 2018) (9 pages) Paper No: GTP-17-1427; doi: 10.1115/1.4038473 History: Received August 02, 2017; Revised August 29, 2017

The noise generated by the passage of acoustic and entropy perturbations through subsonic and choked nozzle flows is investigated numerically using an energetic approach. Low-order models are used to reproduce the experimental results of the hot acoustic test rig (HAT) of Deutsches Zentrum für Luft- und Raumfahrt (DLR), and energy budgets are performed to characterize the reflection, transmission, and dissipation of the fluctuations. Because acoustic and entropy perturbations are present in the flow in the general case, classical acoustic energy budgets cannot be used and the disturbances energy budgets proposed by Myers (1991, “Transport of Energy by Disturbances in Arbitrary Steady Flows,” J. Fluid Mech., 226, pp. 383–400.) are used instead. Numerical results are in very good agreement with the experiments in terms of acoustic transmission and reflection coefficients. The normal shock present in the diffuser for choked regimes is shown to attenuate the scattered acoustic fluctuations, either by pure dissipation effect or by converting a part of the acoustic energy into entropy fluctuations.

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Figures

Grahic Jump Location
Fig. 1

Integration domain

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Fig. 2

Sketch of the hot acoustic test rig. Pthr: pressure at nozzle throat, PS1/2: static pressure, TT: total temperature, TC: fast thermocouple probes [18]

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Fig. 3

Experimental and simulated scattering coefficients as a function of the temperature (subsonic case). Experiments: 20 °C, 100 °C, 200 °C, 400 °C. Marcan: 20 °C, 100 °C, 200 °C, 400 °C. Sunday: 20 °C, 100 °C, 200 °C, 400 °C. See color figure online.

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Fig. 4

Experimental and simulated scattering coefficients as a function of the temperature (choked case). Experiments: 20 °C, 100 °C, 200 °C, 400 °C. Marcan: 20 °C, 100 °C, 200 °C, 400 °C. Sunday: 20 °C, 100 °C, 200 °C, 400 °C.

Grahic Jump Location
Fig. 5

Reflection coefficients as a function of the temperature with nondimensionalized frequency. (a) subsonic case and (b) choked case. Experiments: 20 °C, 100 °C, 200 °C, 400 °C. Marcan: 20 °C, 100 °C, 200 °C, 400 °C. See color figure online.

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Fig. 6

Time evolution of the different terms of Eq. (10) for nozzle case T400_M07 with harmonic entropy forcing at 3000 Hz (period τ). — dE/dt, ■−(W1+W2+D).

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Fig. 7

Comparison between numerical and analytical mean disturbances energy budgets for nozzle case T400_M07. Analytical: W¯1/|W¯f|, W¯2/|W¯f|, — D¯/|W¯f|. Simulation: W¯1/|W¯f|, W¯2/|W¯f|, D¯/|W¯f|. See color figure online.

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Fig. 8

Comparison between numerical and analytical mean disturbances energy budgets for nozzle case T400_M10. Analytical: W¯1/|W¯f|, W¯2/|W¯f|, — D¯/|W¯f|. Simulation: W¯1/|W¯f|, W¯2/|W¯f|. See color figure online.

Grahic Jump Location
Fig. 9

Analytical evaluation of the contribution of the different terms to the energy balance for nozzle case T400_M07. W¯1−/|W¯f|, W¯1−,s/|W¯f|, W¯2+/|W¯f|, W¯2s/|W¯f|, W¯2+,s/|W¯f|, D¯/|W¯f|. See color figure online.

Grahic Jump Location
Fig. 10

Analytical evaluation of the contribution of the different terms to the energy balance for nozzle case T400_M10. W¯1−/|W¯f|, W¯1−,s/|W¯f|, W¯2+/|W¯f|, W¯2s/|W¯f|, W¯2+,s/|W¯f|, W¯2−,s/|W¯f|, D¯/|W¯f|. See color figure online.

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Fig. 11

Power spectral densities of the acoustic and entropy fluctuations generated by the flame inside the combustion chamber. p1 rms+/Δf, — s1 rms/Δf. See color figure online.

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Fig. 12

Analytical mean disturbances energy budget for a real combustion noise source. W¯1/|W¯f|, W¯2/|W¯f|, — D¯/|W¯f|. See color figure online.

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Fig. 13

Analytical evaluation of the contribution of the different terms to the energy balance for a real combustion noise source. W¯1+/|W¯f|, W¯1−/|W¯f|, —× W¯1s/|W¯f|, W¯1+,s/|W¯f|, W¯1−,s/|W¯f|, W¯2+/|W¯f|, W¯2s/|W¯f|, W¯2+,s/|W¯f|, D¯/|W¯f|. See color figure online.

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