Results NASA flow impedance tube case

The present solver is validated with experimental data from NASA Langley Grazing fbw impedance tube. It is used for evaluation of liner in control fbw and acoustic environment. The test section is described in [7] and it has been used intensively for validation of acoustic liner model in frequency domain as well as in time domain [3]. The grid size is 60×11, and cases for Mach number of 0.3 at frequencies of 500 and 3000 Hz and for Mach number of 0.5 at frequeny of 2500 Hz are reported here. The mean flow is a very important factor in the accurate representation of the experimental set-up. As reported by Ozyoruk & al. [5] and Ju & al. [14], the refraction effect is taken into account and improved results are obtained. Thus, two mean flows are considered in this study: uniform flow and sheared flow characterized by a fully developed laminar channel flow as follow:

The impedances used for the calculation are (0.41,-1.56), (1.224,-1.145) and (0.69 ,-0.24) for 500, 2500 and 3000 Hz, respectively.

The results of the computation with uniform flow and shear flow and fre­quency f = 500 Hz confirm the importance in the mean fbw in the propa­gation of acoustic wave in rectangular lined duct. The SPL along the duct is

shown in Figure 1. The improvement is very clear in Figure 2 showing the phase distribution.

The next case considered is the same as the previous one but the frequency is increaesed to 3000 Hz. For this case, the number of points per wavelenght is about 11 for the downstream wave. The acoustic field is computed with the uniform and the shear flow. Very good agreement is obtained with the mean shear flow (Figure 3). The comparison between experimental and computa­tional phase (Figure 4) confirms that the present method predicts correctly the propagation and absorption of noise in a rectangular lined duct.

The last case corresponds to M=0.5 and f=2500 Hz. Again, the SPL com­puted with the shear mean flow is in good agreement (Figure 5). Small dif­ference around the trailing edge of the liner is present. The discrepancy is probably due to the small number of point per wavelength. The downstream wave is well resolved with about 15 PPW but the reflected wave (upstream) is represented with only 5 PPW.

The agreements between computational and experimental results are excel­lent when the mean fbw is treated as sheared fbw. For each case, the CPU time is extremely low, as only 1 min is required on Linux PC Pentium 4 (1.7GHz) with 6000 iterations. Due to the low CPU time, the code may be used for op­timization or for the eduction of liner properties. In [16], the author presents an example of eduction of the liner where the present solver is coupled with a commercial optimizer Pointer ([18]).