Acoustic reconstruction of the velocity field in a furnace using a characteristic flow model
Experimental configuration considered in this paper with eight acoustic transceiver units installed around the stationary wall on a cross-section of a lab-scale furnace. The width along x was 982 mm and the depth along y was 937 mm. The distances of units 1, 2, 5 and 6 from the x axis were 236 mm; and of units 3, 4, 7, and 8 from the y axis were 259 mm.
A schematic rotation curved surface by Eq. (4), wherein R = 0.28 m, (x 0, y 0) = (0, 0) m, σ = 0.1 m, V A = 15 s/m, and V 0 = 0.5 s/m.
Simulated deflecting velocity fields and reconstructions by the two models. The magnitude of the velocity vectors has a scale as the width of a grid, shown as in the vector field, equivalent to 4.2 m/s, and it is the same with the following acoustic measurement results. (a), (b) and (c) are benchmark velocity fields; (d), (e), (f) and (g), (h), (i) are reconstructions from models 1 and 2, respectively; (j), (k), (l) and (m), (n), (o) show relative reconstruction errors by models 1 and 2, respectively.
(Color online) Experimental setup for the acoustic and traditional measurements (unit: mm): 1—Orifices in the wall for installation of acoustic transceivers as shown in Fig. 1; 2—Regions in corners of the furnace for setting of burner nozzles; 3—Enlarged schematic of the burner mounting segment; 4—Burner nozzles, Nos. 1, 4, 6, 8, 9, 10, 12, and 14, from the top, represent secondary air burners, Nos. 2 and 3 denote third air burner nozzles, and Nos. 5, 7, 11, and 13 are for primary air.
Illustrative acoustic signals at the start and the end of projection shown in Fig. 1: (a) primitive acoustic signals; (b) denoised signals with wavelet method.
Results from traditional methods: (a) strip display of the flow field; (b) measurement by anemometer (maximal velocity: 4.9 m/s). The strip display is a quasi-plan view for a restrained shooting bearing; the display is the same for both working conditions.
(a) to (e) are velocity fields from five individual acoustic measurements with only primary air cast, reconstructed by model 1; (f) is the same flow field as that in (e), reconstructed by model 2; and (g) shows the distribution of RSTD from acoustic measurements displayed in (a) to (e).
Results from traditional methods: (a) strip display of the flow field; (b) anemometer measurement (maximal velocity: 8.7 m/s).
(a) to (e) are five individual acoustic measurement results under condition 2, reconstructed by model 1; (f) is the same flow field as (e), but reconstructed by model 2; and (g) is the distribution of RSTD from acoustic measurements shown in (a) to (e).
Schematic of the distribution of the basis functions in the vector field, with n = 3×3 and λ = 6, and .
Comparison of models on acoustic measurement of velocity fields in furnaces.
Characteristic parameters of the simulated flow fields and the reconstructions.
Configuration of the experimental setup.
Parameters obtained by acoustic measurements shown in Fig. 7.
Parameters obtained by acoustic measurements shown in Fig. 9.
Comparison between flight time differences (unit: s) of two individual acoustic measurements under two operating conditions.
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