Global Journal of Researches in Engineering, I: Numerical Methods, Volume 23 Issue 1

Figure 2: The incident and reflected signals of a monolayer porous medium constructed in frequency via expression (5) and in time via Eq. (6) The simulated incident and reflected signals of a single-layer porous medium are shown in Fig. 2, and were obtained by expression (5) in the frequency domain and equation (6) in the time domain. The characteristic parameters of the porous medium are as follows: L = 3.0 cm, ϕ = 0.85, α ∞ = 1.2, Λ = 300 μ m, Λ '/ Λ = 3, ξ = 10, and ξ / ξ ' = 2. These signals were generated using the Gauss function in Matlab with center frequencies of 50 kHz and 120 kHz. In the time domain, two successive reflections on the first and second interface can be clearly observed, as shown in black color below in Figure 2. III. S imulation S tudy To investigate the influence of physical parameters, such as porosity, tortuosity, viscous and thermal characteristic lengths, and newly introduced shape factors on the reflected waves, a parameter analysis was performed. Specifically, each parameter was varied while holding the others constant, and the impact on the first and second reflected waves in the time domain, as indicated by equation (6), was observed. By systematically varying each parameter and analyzing its effect on the reflected waves, we can better understand the individual contributions of these physical factors to the overall acoustic behavior of the porous material. a) Effect of Porosity on the Reflected Signal Figure 3 shows the impact of varying the porosity ( ϕ ) on the amplitude of the first and second reflected waves through a rigid porous medium, while keeping the other parameters fixed at α ∞ = 1.2, Λ = 300 μ m, Λ '/ Λ = 3, ξ = 10, and ξ / ξ ' = 2. The porosity ϕ varies from +20% to -20% of its initial value ( ϕ = 0.85). Table 1 presents the variation ratio of the reflection coefficient compared to a ±20% variation of each parameter. According to Table 1, a significant influence of porosity on the reflected signal is observed at frequencies of 50 kHz and 120 kHz. When the porosity increases by +20%, the modulus of the first and second reflected signals decrease by -66.84% and -65.06%, respectively. Conversely, when the porosity decreases by -20%, the amplitude of the 1st and 2nd reflected signals increases by +80.26% and +71.32% respectively. Moreover, the sensitivity of the porosity ϕ increases with frequency, as also shown in Table 1. Global Journal of Researches in Engineering Volume XxXIII Issue I Version I 36 Year 2023 © 2023 Global Journals ( ) I Investigating the Effects of Physical Parameters on First and Second Reflected Waves in Air-Saturated Porous Media under Low-Frequency Ultrasound Excitation