Theoretical and Experimental Studies of Acoustic Reflection of Bubbly Liquid in Multilayer Media

Abstract

Bubbly liquids are widely present in the natural environment and industrial fields, such as seawater near the ocean bottom, the multiphase flow in petroleum reservoirs, and the blood with bubbles resulting in decompression sickness. Therefore, accurate measurement of the gas content is of great significance for hydroacoustic physics, oil and gas resources exploration, and disease prevention and diagnosis. Trace bubbles in liquids can lead to considerable changes in the acoustic properties of gas–liquid two-phase media. Acoustic measurements can therefore be applied for trace bubble detection. This study derived the reflection coefficient of acoustic waves propagating in a sandwich layering model with liquid, bubbly liquid, and liquid. The influences of gas contents on the reflection coefficient at the layer interface were analyzed based on theoretical calculations. It was revealed that the magnitude of the reflection coefficient and the frequency interval between its valleys have a quantitative correlation with the gas contents. Thus, a novel means to detect the contents of trace bubbles was proposed by evaluating the reflection coefficients. The reflection features of a thin layer with bubbly liquid were then studied through experiments. It was validated by acoustical measurements and theories that the reflection coefficient is considerably sensitive to the change of gas contents as long as the gas content is tiny. With the increasing gas content, the maximum value of the reflection coefficient increases; meanwhile, the frequency intervals between the valleys become smaller. However, when the gas content is extensive enough, e.g., greater than 1%, the effect of the change of gas content on the reflection coefficient becomes inapparent. In that case, it is not easy to measure the gas content by the acoustic reflection signals with satisfying precision. This proposed method has potential applications for the detection of trace gas bubble content in several scenarios, e.g., decompression illness prevention and diagnosis.

1. Introduction

There are several places where bubbly liquids exist in nature and industrial settings, including near-bottom and subsurface media in the ocean, mixed oil-gas-water media in petroleum reservoirs, and even within the human body, such as bubble-containing blood when divers experience decompression sickness [1,2,3,4]. Trace bubbles in liquids can lead to dramatic changes in the propagation characteristics of acoustic waves, and thus acoustic methods have the applicable potential for bubble detection, especially when the gas content is relatively tiny [5,6]. When using acoustic methods to detect the bubbles of decompression sickness, human tissues can also be approximated as a stratified medium if the acoustic wavelength is small enough. Therefore, the bubbly liquids mentioned above can be reduced to a stratified medium model to be processed and discussed.

The propagation of acoustic waves in complex, layered media has been widely investigated for many years, and layered media containing bubbly liquid have also attracted much attention [7,8,9]. Research on the reflection and transmission of acoustic waves in these complex media is of great significance. Accurate measurements of their gas content can be applied for hydroacoustic physics, hydrocarbon resources exploration, and the fast diagnosis of decompression sickness [1,2,3].

To study the propagation of sound waves in multilayer media containing bubbly liquid, we first must understand the acoustical properties of gas–liquid media. Mallock [10] proposed that the speed of sound in bubbly liquid is equal to that of a homogeneous medium with the same density and elastic properties. Zabolotskaya et al. [11,12] considered the nonlinear effect of bubbles and calculated the scattering of acoustic waves by bubbles. Hsieh [13] further derived a theoretical model of sound propagation in bubbly liquid and obtained a formula for the speed of sound that is only affected by the gas content. Feldman et al. [14] established a linearized model of plane waves through gas–liquid mixtures. They investigated the compressibility of individual bubbles under the influence of pressure pulses and explored the impact of different kinetic effects on the speed. Caflisch et al. [15,16] constructed an effective model for the propagation of acoustic waves in bubbly liquid and derived an effective sound speed equation. Prosperetti et al. [17,18] rigorously deduced a nonlinear acoustic wave propagation model in gas–liquid media, which used the asymptotic method to derive an approximate analytical solution for the sound speed under nonlinear oscillations. In recent years, Wilson [19] compared different theoretical models in the low-frequency range. Wang et al. [20,21] performed simulations for linear and nonlinear propagation models of acoustic waves in bubbly liquids and obtained the sound speed curves and attenuation coefficient curves under different parameters. Vanhille et al. [22,23,24] numerically simulated the propagation of acoustic waves in bubbly liquids and analyzed their nonlinear characteristics. Cavaro et al. [25,26] experimentally analyzed the acoustical characterization of microbubble clouds.

The acoustic properties of bubbly liquid have been extensively studied for many years. Based on the deep understanding of the acoustic properties in gas–liquid media, the laws of sound propagation in multilayer media containing a bubbly liquid layer have also received much attention [7,8,9]. Ostrovsky [27] and Karpov et al. [28] investigated the differential frequency sound generated by the interaction of two high-frequency harmonics in a bubbly liquid layer based on the strong nonlinearity of bubbles. V’yugin et al. [29] conducted experimental measurements of the scattering intensity of the bubble-containing layer. For the case of oblique incidence, Shagapov and Sarapulova [7] examined the reflection and refraction of acoustic waves at the interface between pure water and bubbly water. Gubaidullin et al. [8,9,30] calculated the reflection coefficient of the bubble inhomogeneously distributed liquid layer under a nonlinear model and the reflection coefficient curves of the bubble-containing layer under various bubble distributions.

Although the previous research on acoustic reflection of the bubbly liquid has obtained meaningful results, the correlation between the reflection coefficient and gas content needs to be further studied. There have been few relevant experimental data until now. In this present study, theoretical analyses and experimental measurements of the reflection coefficient of bubbly liquids related to the gas content were carried out, and a novel method to detect the trace gas content by measuring the reflection coefficient was proposed. Both the calculated results and the measured ones showed that this proposed method is effective for detecting trace gas content.

2. Theory

2.1. The Sound Speed of Bubbly Liquids

The medium under consideration is a liquid containing gas bubbles that are supposed to be uniformly dispersed [17]. The bubbles should be sufficiently small compared to the sound wavelength so that the medium can be considered homogeneous and isotropic. Its physical parameters can be replaced by the average equivalent parameters. The equivalent density is:

$$\rho =\frac{{\rho }_1+\beta {\rho }_2}{1+\beta }$$

(1)

The average thermal conductivity coefficient is:

$$\kappa =\frac{{\kappa }_1+{\kappa }_2\beta }{1+\beta }$$

(2)

The average specific heat capacity is:

$$C=\frac{{\rho }_1{C}_1+\beta {\rho }_2{C}_2}{{\rho }_1+\beta {\rho }_2}$$

(3)

The subscripts 1 and 2 represent the parameter values of liquid and gas, respectively. β is the volume ratio of gas and liquid, and since the volume content of the gas is considered to be very small, β is approximately equal to the gas content rate, which is the volume ratio of gas and the mixed medium. ρ is the density of the media. And κ is the thermal conductivity coefficient. C is the specific heat capacity.

Without considering the medium viscosity and the surface tension, the propagation equation of small-amplitude acoustic disturbances in bubbly liquid is similar to that in pure fluids. Hsieh et al. [13] derived the sound velocity in a mixed medium from the acoustic wave equation in an equivalent pure fluid.

Similar to the derivation in a pure fluid, three basic equations are listed based on the conservation of momentum, mass, and energy:

$$\frac{\partial \rho }{\partial t}+\rho \nabla ·v+v·\nabla \rho =0$$

(4)

$$\frac{\partial v}{\partial t}+(v·\nabla )v=-\frac{1}{\rho }\nabla P$$

(5)

$$\rho C\frac{\partial T}{\partial t}=\kappa \Delta T+P(\nabla ·v)$$

(6)

The average equivalent parameters of the medium are substituted into the above basic equation. Here, ρ is the equivalent density of medium; v is the velocity and P is the pressure; T denotes the temperature. Under the condition that the gas–liquid volume ratio cannot be too small so that the gas compressibility plays the dominant role in the overall compressibility of the mixture, linearization is carried out [13].

$$\rho ={\rho }_0(1+\sigma )$$

(7)

$${\rho }_1={\rho }_{10}(1+{\sigma }_1)$$

(8)

$${\rho }_2={\rho }_{20}(1+{\sigma }_2)$$

(9)

$$P=P_0(1+p)$$

(10)

$$T=T_0(1+\theta )$$

(11)

Here, the subscript 0 represents the parameter values without acoustic disturbance; σ is the change of density of the mixed medium perturbed by acoustic waves; σ₁ and σ₂ are the changes of density of liquid and gas, respectively, perturbed by acoustic waves; p and θ are the changes of pressure and temperature in the mixed medium by acoustic disturbance.

The linearized equations are the following:

$$\frac{\partial v}{\partial t}=-\frac{P_0}{{\rho }_0}\nabla p$$

(12)

$$\frac{\partial \sigma }{\partial t}=-\nabla ·v$$

(13)

$$p={\sigma }_2+\theta$$

(14)

The actual specific heat ratio of air and water is substituted after ignoring the influence of a small amount, and the simplified acoustic wave equation is obtained below

$$\frac{{\partial }^{2}p}{\partial t^2}-\frac{P_0\delta }{{\rho }_0}\Delta p=0$$

(15)

where δ is the parameter introduced for simplification, the specific expression is as follows,

$$\delta =\frac{({\rho }_1+{\rho }_2\beta ){\rho }_{20}}{\beta {\rho }_2{\rho }_0}$$

(16)

Then, from Equation (15), the equivalent sound velocity in the bubbly liquid can be obtained as:

$$c=\sqrt{\frac{P_0\delta }{{\rho }_0}}=\frac{1}{{\rho }_0}\sqrt{\frac{P_0({\rho }_1+{\rho }_2\beta ){\rho }_{20}}{\beta {\rho }_2}}\cong \frac{1}{{\rho }_0}\sqrt{\frac{P_0({\rho }_1+{\rho }_2\beta )}{\beta }}$$

(17)

c is the sound velocity in the bubbly liquid, ρ₀ is the initial density of the mixed medium without acoustic disturbance, P₀ is the initial pressure, and ρ₂₀ is the initial densities of the gas. The approximation of the sound velocity is obtained by approximating ρ₂ and ρ₂₀ being small amplitudes.

In addition, it is also possible to derive the speed of sound directly from the defining equation by substituting the equivalent density and equivalent pressure of the medium into the equations,

$$\frac{1}{c^2}=\frac{d\rho }{dp}=-(\frac{M_1+M_2}{V_1+V_2})\frac{1}{V_1+V_2}\frac{d}{dp}(V_1+V_2)$$

(18)

$$\frac{1}{c^2}=\frac{\rho }{{\rho }_2+\beta {\rho }_2}(\frac{{\rho }_2}{{\rho }_1}\frac{1}{c_1^2}+\frac{\beta }{c_2^2})$$

(19)

where c₁ and c₂ are the velocities of sound in liquid and gas respectively; M₁ and M₂ are the mass of liquid and gas, respectively; V₁ and V₂ are the volume of liquid and gas, respectively. If $\frac{{\rho }_2}{{\rho }_1}<<\beta$ is assumed, a good approximation to Equation (19) is:

$$c^2\cong \frac{{\rho }_2(1+\beta )}{\rho \beta }{c}_2^2$$

(20)

Under the same approximate conditions, the sound velocity equations derived from the two methods are equal. The statement shows that the physical characteristics of the gas and liquid and the gas content are the factors that influence the sound velocity under this theoretical model. If the type of material in the bubbly liquid is identified, the corresponding sound velocity of the mixed medium is non-dispersive and is only connected to the gas content of the medium.

2.2. Acoustic Reflection of Bubbly Liquid in Multilayer Media

Sound waves are incident on the boundary surface of the two media, due to the difference in acoustic impedance, sound waves are reflected and transmitted. The boundary conditions of acoustic pressure continuity and normal velocity continuity are satisfied on the boundary surface. The equations are as follows [7]:

$$p_{in}+p_{rn}=p_{i(n+1)}+p_{r(n+1)}$$

(21)

$$v_{in}+v_{rn}=v_{i(n+1)}+v_{r(n+1)}$$

(22)

Based on the boundary conditions and the acoustic properties of the liquid containing bubbles, the reflection coefficient of the acoustic wave in the multilayer medium containing the bubbly liquid layer can be calculated. The reflection coefficient R of the vertical incidence on the infinite interface of pure liquid and bubbly liquid is:

$$R=\frac{Z_2-Z_1}{Z_2+Z_1}=\frac{\sqrt{\frac{{\rho }_2{(1+\beta )}^2}{({\rho }_1+\beta {\rho }_2)\beta }}({\rho }_1+\beta {\rho }_2)c_2-(1+\beta ){\rho }_1{c}_1}{\sqrt{\frac{{\rho }_2{(1+\beta )}^2}{({\rho }_1+\beta {\rho }_2)\beta }}({\rho }_1+\beta {\rho }_2)c_2+(1+\beta ){\rho }_1{c}_1}$$

(23)

Z₁ and Z₂ are the acoustic impedance of pure liquid and bubbly liquid, respectively. The constants employed in the calculation are ρ₁ = 1000 kg/m³, c₁ = 1540 m/s, ρ₂ = 1.29 kg/m³, and c₂ = 340 m/s. Figure 1 shows the reflection coefficient as a function of gas content when the plane acoustic wave is incident vertically to the interface of water–bubbly water. It can be seen that the reflection coefficient tends to increase rapidly in the range of gas content from 0.05% to 1%, with a difference of about 0.35 between the maximum and minimum values. While the variation of the reflection coefficient is no longer severe after the gas content is greater than 2%. It is concluded that the change of reflection coefficient is very sensitive when the gas content is small. However, as the gas content further increases, the curve of reflection coefficient gradually flattens out and the change with the rise of gas content is no longer noticeable.

Human tissue containing bubbles can be approximated as a stratified medium containing bubbly liquid. The reflection and transmission of sound waves become very complex due to the sound propagation properties of gas–liquid mixed media. Considering the physical model shown in Figure 2, the three layers of media are water-bubbly water–water and bubbly liquid layer thickness d is 0.004 m. In this model (see Figure 2), Z₁ and Z₂ are the acoustic impedance of pure liquid and bubbly liquid, respectively, and the reflection coefficient R for vertical incidence is derived as:

$$R=\frac{Z_2^2-Z_1^2}{Z_2^2+Z_1^2-2j{Z}_1{Z}_2\cot (\frac{2\pi fd}{c_2})}$$

(24)

f is the frequency of the incident acoustic wave. Then, the reflection coefficient is obtained by substituting Equations (17)–(24):

$$R=\frac{(({\rho }_1^2{c}_1^2-{\rho }_2^2{c}_2^2)\beta -c_2^2{\rho }_1{\rho }_2)(1+\beta )}{2\sqrt{\frac{{\rho }_2{(1+\beta )}^2}{({\rho }_1+\beta {\rho }_2)\beta }}\beta c_1{c}_{2}j{\rho }_1({\rho }_1+\beta {\rho }_2)\cot (\frac{2\pi fd}{\sqrt{\frac{{\rho }_2{(1+\beta )}^2}{({\rho }_1+\beta {\rho }_2)\beta }}{c}_2})-(({\rho }_1^2{c}_1^2+{\rho }_2^2{c}_2^2)\beta +c_2^2{\rho }_1{\rho }_2)(1+\beta )}$$

(25)

Figure 3 shows the three reflection coefficient curves for the gas content being 0.05%, 0.25%, and 0.5%. It can be seen from Figure 3 that the changes of reflection coefficients are all periodic and undulating. There are a series of resonance peaks and valleys in the frequency range. At the valley frequencies, the incident acoustic energy is almost completely transmitted, while the reflection coefficient tends to zero. The magnitudes of the reflection coefficients at different gas content are different. In the reflection coefficient curve for a given gas-content value, the frequency interval Δf between two adjacent valleys is constant, and $\Delta f\propto c/d$. The value of Δf is proportional to the sound velocity of the mixed medium and inversely proportional to the thickness of the bubbly liquid layer. Therefore, in the case where d is known, the sound velocity of the mixed medium can be developed by measuring the value of Δf.

Based on the above frequency response curve of the reflection coefficient, the change in valley frequency interval with gas content can be calculated. Figure 4 depicts the relationship between gas concentration and the maximum reflection coefficient and frequency interval. The figure shows that when the gas concentration increases, the Δf drops. The value of Δf ranges from 67 kHz to 15 kHz in the range of 0.05–1% of the gas concentration. Additionally, the variation in Δf for various gas contents is clear. When the gas content is small, Δf is especially sensitive to the change of the gas content, and the 0.01% increase of the gas content can lead to the Δf about 5 kHz change. Therefore, by measuring the frequency response curve of the reflection coefficient, the value of the valley frequency spacing Δf can be obtained, and the gas content of the intermediate bubbly liquid layer can be further deduced.

For human tissues, the relevant parameters can be substituted into a three-layer medium model containing a bubbly liquid layer for approximate calculation. The calculated reflection coefficient curve with frequency is shown in Figure 5. The model parameters employed are ρ₁ = 1090 kg/m³, c₁ = 1590 m/s, ρ₃ = 1200 kg/m³, c₃ = 3400 m/s, d = 0.004 m, ${\rho }_2^l=1050 {\mathrm{kg}/\mathrm{m}}^3$, $c_2^l=1570 \mathrm{m}/\mathrm{s}$, ${\rho }_2^g=1.29 {\mathrm{kg}/\mathrm{m}}^3$, and $c_2^g=340 \mathrm{m}/\mathrm{s}$. The subscripts 1, 2, and 3 represent the parameter values of the first, second and third layers respectively. The superscripts g and l represent the parameter values of gas and liquid, and d is the thickness of the second layer medium. Compared with the reflection curve of water containing gas bubbles shown in Figure 3, the change of the acoustic impedance of the medium also makes the value taken at the valley of the curve increase, and the valleys are not as prominent as in Figure 3. Nevertheless, the curves in Figure 3 and Figure 5 show the same patterns of changes, i.e., the valley frequency spacing varies with the change of gas content in the intermediate bubbly liquid layer. Therefore, the magnitude of the gas content in the intermediate blood layer can be evaluated by the valley interval on the reflection curve. This method has potential applications in human body bubble detection.

To compare with the subsequent experimental results, acrylic plates are added on both sides of the bubbly liquid layer. The thickness of the acrylic plate is 3 mm. The specific distribution of the model is pure liquid- acrylic plate-bubbly liquid- acrylic plate-pure liquid. The parameters of the plating layer are ρ = 1300 kg/m³ and c = 3000 m/s. Additionally, the density and the sound velocity of water are also substituted into the calculation. Assuming that the middle layer is a pure liquid case, the calculated acoustic reflection coefficient frequency response curve is shown in Figure 6, the three curves are the results of small changes in the sound speed and the thickness of the middle layer of the liquid. The results in the figure show that the influence of the two on the curve is almost the same when the adjustment of both the sound speed and the thickness of the middle layer is about 2.5%. Furthermore, the two both have an influence on the magnitude of the valley frequency on the reflection curve, and the valley position at near 200 kHz is shifted by 4 kHz. The influence on the valley frequency interval is smaller, and the frequency spacing decreases by 2 kHz with the increase of the layer’s thickness or the decrease of the sound speed. Hence, it is relatively stable to determine the gas content by the valley interval on the reflection curve.

3. Experiment

To verify the above calculation results, an experimental measurement study relating to the vertical reflection coefficient of acoustic waves was carried out, and the experimental setup is shown in Figure 7. A tank of 90 × 55 × 40 cm is filled with water that has been rested for more than 24 h and degassed. Two acrylic plates of 0.3 × 50 × 40 cm are placed in the middle of the tank with a spacing of 4 cm. The bubbles are generated by electrolytic water. Copper and graphite electrodes connected to the DC power are placed at the bottom of the tank, in the middle of two acrylic plates, thus forming a bubbly liquid layer of 4 cm thickness [29]. The sound waves are generated and received vertically by a cylindrical transducer placed 35 cm in front of the bubble layer. The transducer is connected to both a signal generator and an oscilloscope. The signal generator emits a pulse-modulated sinusoidal signal for excitation with a central frequency of 175 kHz, and the echo signal received by the transducer is sent to a digital oscilloscope for storage and display.

First, the reflection signal of vertical incidence at the water-steel plate interface was measured, and the spectrum of the reflection signal was obtained to analyze the emission–reception spectrum of the detection transducer. And the reflection signal at the water–steel plate interface was used as the reference signal for calculating the relative reflection coefficient in subsequent experiments. The reflection coefficient in the case of pure water was obtained by comparing the FFT-transformed signal with the spectrum of the reference signal, and the results are shown in Figure 8. The results show that the theoretical reflection coefficients match well with the experimental measurements. The frequency spacing of the valleys is around 19 kHz, which is a reasonable verification of the reliability of the experiment. However, it should be noted that, due to the limitation of the transducer bandwidth, the results are reliable only near the center frequency of the transducer. The experimental measurements far from the center frequency have a low signal-to-noise ratio, and the difference with the theoretical calculation results increases.

After the DC power supply is energized, bubbles are generated from the electrodes at the bottom of the water and move upward until escaping from the water surface. The content of bubbles is related to the voltage and current of energization. Due to the large resistance, the sensitivity of adjusting the current is low when the energizing current is small (<0.04 A), so the bubble content is changed by adjusting the voltage to a small degree. The reflection signal of the bubbly liquid layer was measured after 5 min of energization. The time-domain waveforms of the reflection signal at different energization voltages were obtained, as shown in Figure 9. The difference in the reflection signal at different gas contents can be seen in the figure.

The received time domain signal is processed by FFT and then divided by the reference signal to obtain the reflection coefficient. The reflection coefficient at different voltages in Figure 9 is shown in Figure 10. As can be seen from the figure, the presence of bubbles causes a significant change in the spectrum of the reflected signal. The maximum value of the reflection coefficient decreases as the energizing voltage increases. This is caused by the attenuation of sound waves due to the bubbles, and the more bubbles there are, the more significant the attenuation is. However, the minimum value of the reflection coefficient increases with the increase of the energizing voltage. This is due to the effect of bubble scattering, which prevents the complete transmission of the acoustic wave. Additionally, due to the heterogeneity of bubble dispersion and the influence of noise, the resonance peaks and valleys on the curve become less evident as the bubble content increases.

According to the results of the reflection coefficient curve in Figure 10, the variation of the valley interval of the spectrum with the applied electrolytic voltage can be given. However, due to the effect of bubble scattering, the exact location of the valleys is difficult to identify. And the reflection coefficient changes more rapidly at the half position of the peak, and this position is less affected by the error. Therefore, the half-height width of the peak between the two valleys is used to approximate the spacing of the valleys instead. The specific results are shown in Figure 11. The pentagrams are the experimentally measured data, and the dashed line is the curve obtained from the polynomial fit. The results show that the half-height width of the peak decreases with the increase of the gas content, and the decreasing trend is more dramatic when the voltage is small. It is consistent with the trend of the theoretical calculation results, further verifying the feasibility of detecting the gas content according to the reflection coefficient.

We increased the amplitude of the energizing voltage, resulting in a significant increase in the content of the generated bubbles. The acoustic reflection signal was measured at this time. The reflection coefficient curve is shown in Figure 12, where the results are given for 0 V, 45 V, 50 V, and 55 V of the energizing voltage, respectively. It can be seen from the figure that the bubble content is larger when the energizing voltage is relatively large, and the difference in the reflection coefficient in different cases is very small, indicating that the reflection signal is not sensitive to the change of bubble content at this time. To summarize, the reflection coefficient curve is smooth when the bubble content is large enough. The valley is not apparent, and the dispersion effect is not strong.

According to the principle of electrolyzed water and the law of rising motion of bubbles, the number of gas molecules and the volume of gas produced by electrolysis can be introduced in the period from bubble generation to escape. As a result, the volume content of gas in the mixed medium can be estimated. By adding the threshold current and considering the occurrence of bubble aggregation at the interface, it is possible to roughly estimate the gas concentration of the liquid in this experiment. Therefore, we estimate that it is difficult to detect the magnitude of the gas content from the reflected signal of the bubbly liquid layer when the gas content in the layer is larger than 1%.

4. Conclusions

In this paper, the reflection of acoustic waves in a multilayer medium containing a bubbly liquid was studied by theoretical calculations and experimental measurements. On the premise that the bubble size is much smaller than the wavelength and the bubbles are uniformly distributed, an equivalent sound velocity equation was derived relating only to the gas content in the bubbly liquid. The reflection coefficient of acoustic waves in a multilayer media with a bubbly liquid interlayer was calculated. At the interface between the layers of pure water and bubbly water, the change of the reflection coefficient with gas content was examined. The calculation results showed that with increasing gas content the valley frequency interval of the reflection coefficient decreases, while the amplitude becomes higher without considering attenuation. Thus, a novel method was proposed to detect trace bubbles in gas–liquid mixed media by measuring the reflection coefficient. Finally, the experimental measurements, which mainly consider the acoustic reflection characteristics of the thin layer of bubbly liquid medium, were conducted to verify the theoretical calculation results. Both the calculated results and the measured results showed that the reflection coefficient is sensitive to the change of gas concentration when the gas content is very small. However, when the gas content is greater than 1%, the reflection coefficient is not sensitive to the change of the gas content, and thus it is difficult to measure the gas concentration accurately by acoustic reflection signal in this condition. The proposed method has potential applications in hydroacoustic physics, hydrocarbon resources exploration, and the prevention and diagnosis of decompression sickness.