Method and system for measuring flow resistivity of porous material

Abstract

The invention relates to a porous material flow resistivity measuring method and system.The method comprises the steps that when the rear surface of a to-be-measured sample is tightly attached to the rigid wall of an impedance tube, the first acoustic impedance rate of the front surface of the to-be-measured sample is obtained through measurement; when the distance between the rear surface of the to-be-measured sample and the rigid wall of the impedance tube is L, measuring to obtain a second acoustic impedance rate of the front surface of the to-be-measured sample; deriving the characteristic acoustic impedance of the to-be-tested sample according to the first acoustic impedance rate, and deriving the rear surface acoustic impedance rate of the to-be-tested sample according to the second acoustic impedance rate; based on the first acoustic impedance rate, the second acoustic impedance rate, the characteristic acoustic impedance of the to-be-detected sample and the rear surface acoustic impedance rate of the to-be-detected sample, the wave number of sound propagating in the to-be-detected sample is solved; and calculating the flow resistance rate of the to-be-detected sample according to the wave number of the sound propagating in the to-be-detected sample and the characteristic acoustic impedance of the to-be-detected sample. The method for measuring the flow resistivity of the porous material can remarkably reduce the measurement cost and the measurement complexity.

Description

Technical Field

[0001] The present invention relates to the technical field of porous material resistivity, and in particular to a porous material resistivity measurement method and system. Background Art

[0002] Flow resistivity is a key parameter for measuring the acoustic performance of porous materials and has been widely used in acoustic property research. As an input variable in acoustic models (such as the Johnson-Champoux-Allard model), it can be used to accurately predict the sound absorption coefficient and acoustic impedance of a material at different frequencies, providing a theoretical basis for acoustic design in fields such as architectural acoustics, automotive sound insulation, and aerospace.

[0003] With the advancement of materials science, research into the relationship between the structural characteristics, porosity, and distribution of porous materials and their acoustic performance has deepened. Accurately measuring flow resistivity is not only a fundamental tool for evaluating a material's sound absorption and insulation properties, but also a crucial basis for optimizing its microstructure, enhancing its broadband sound absorption capacity, and ensuring consistent product quality. In practical engineering applications, flow resistivity measurements can help engineers select appropriate materials and improve sound insulation and vibration control.

[0004] Currently, resistivity measurement methods primarily include direct current (DC), alternating current (AC), comparative, and acoustic methods. Acoustic methods can be further categorized into measuring steady-state resistivity and dynamic resistivity. Dynamic resistivity reflects a material's response to fluid flow at varying frequencies, tending toward steady-state resistivity at low frequencies. While theoretically effective, these methods have significant limitations in practical applications.

[0005] Traditional measurement methods rely on specialized equipment that is complex, expensive, and bulky. This not only carries high procurement and maintenance costs, but also involves complex operational procedures and requires a high level of technical expertise. Furthermore, the measurement process is susceptible to interference from external factors such as fluid properties (such as viscosity and density) and ambient temperature and humidity, resulting in inaccurate and inreproducible results, impacting the reliability of material performance assessment and technology optimization. Summary of the Invention

[0006] To this end, the technical problem to be solved by the present invention is to overcome the problem that the resistivity measurement method of porous materials in the prior art needs to rely on complex special equipment, and overcome the problem that the resistivity measurement process is easily disturbed by the fluid properties and environment, resulting in inaccurate measurement results.

[0007] To solve the above technical problems, the present invention provides a method for measuring the flow resistivity of porous materials, comprising:

[0008] When the rear surface of the sample to be tested is pressed against the rigid wall of the impedance tube, the first acoustic impedance of the front surface of the sample to be tested is measured;

[0009] When the rear surface of the sample to be tested is at a distance L from the rigid wall of the impedance tube, the second acoustic impedance of the front surface of the sample to be tested is measured;

[0010] Derived the characteristic acoustic impedance of the sample to be tested according to the first acoustic impedance ratio, and deduced the rear surface acoustic impedance ratio of the sample to be tested according to the second acoustic impedance ratio;

[0011] Calculating the wave number of sound propagating inside the sample to be tested based on the first acoustic impedance ratio, the second acoustic impedance ratio, the characteristic acoustic impedance of the sample to be tested, and the acoustic impedance ratio of the rear surface of the sample to be tested;

[0012] Calculate the flow resistivity of the sample to be tested based on the wave number of sound propagating inside the sample to be tested and the characteristic acoustic impedance of the sample to be tested;

[0013] The rear surface of the sample to be tested is the surface where the rigid wall of the impedance tube is located, and the front surface of the sample to be tested is the surface where the speaker of the impedance tube is located.

[0014] In one embodiment of the present invention, when the distance between the rear surface of the sample to be tested and the rigid wall of the impedance tube is L, the position of the rigid wall of the impedance tube is taken as the zero coordinate. Then, when the coordinates are x = -L-2l to x = -L, the second acoustic impedance formula of the front surface of the sample to be tested is:

[0015]

[0016] Among them, Z s2 is the second acoustic impedance of the front surface of the sample to be tested, Z m is the characteristic impedance of the sample to be tested, k m is the wave number of the sound when it propagates inside the sample to be tested, 2l is the thickness of the sample to be tested, j is the imaginary unit, Z L2 When L≠0, the surface acoustic impedance of the rear surface of the sample to be tested at x=-L~x=0 satisfies:

[0017]

[0018] Among them, Z L3 is the surface acoustic impedance of the rigid wall of the impedance tube at coordinate x = 0 and Z L3 →∞; k0 is the wave number of sound when it propagates in air; Z0 is the characteristic impedance of air and Z0=ρ0c0, ρ0 is the air density, and c0 is the speed of sound propagation in air.

[0019] In one embodiment of the present invention, the method for deriving the rear surface acoustic impedance of the sample to be tested according to the second acoustic impedance comprises: L3 →∞, then formula (2) can be simplified to:

[0020] Z L2=-jρ0c0cot(k0L) (3).

[0021] In one embodiment of the present invention, when the rear surface of the sample to be tested is placed against the rigid wall of the impedance tube, when the coordinates are x = -L - 2l = -2l to x = -L = 0, the first acoustic impedance formula of the front surface of the sample to be tested is:

[0022]

[0023] Among them, Z s1 is the first acoustic impedance of the front surface of the sample to be tested, Z L1 It is the surface acoustic impedance of the rear surface of the sample to be tested when L=0, that is, the coordinate x=-L=0.

[0024] In one embodiment of the present invention, since the rear surface of the sample to be tested is in close contact with the rigid wall of the impedance tube when L=0, Z L1 =Z L3 →∞, then simplify formula (4) to:

[0025] Z m =jZ s1 tan(2k m l) (5).

[0026] In one embodiment of the present invention, the method for solving the wave number of sound propagating inside the sample to be tested based on the first acoustic impedance ratio, the second acoustic impedance ratio, the characteristic acoustic impedance of the sample to be tested, and the acoustic impedance ratio of the back surface of the sample to be tested includes:

[0027] Combine formula (1), formula (3), formula (4), and formula (5) to solve the wave number k when the sound propagates inside the sample to be tested. m :

[0028]

[0029] In one embodiment of the present invention, the flow resistivity of the sample to be tested is calculated based on the wave number of sound propagating inside the sample to be tested and the characteristic acoustic impedance of the sample to be tested, and the formula is:

[0030]

[0031] Where σ is the resistivity of the porous material of the sample to be tested, ω=2πf is the circular frequency of the sound, f is the frequency of the sound, and Imag represents the Z m k m The imaginary part of .

[0032] To solve the above technical problems, the present invention provides a porous material resistivity measurement system, comprising:

[0033] The first measurement module is used to measure the first acoustic impedance of the front surface of the sample to be tested when the rear surface of the sample to be tested is pressed against the rigid wall of the impedance tube;

[0034] The second measuring module is used to measure the second acoustic impedance of the front surface of the sample to be tested when the distance L between the rear surface of the sample to be tested and the rigid wall of the impedance tube is L;

[0035] Derivation module: used to derive the characteristic acoustic impedance of the sample to be tested according to the first acoustic impedance ratio, and to derive the rear surface acoustic impedance ratio of the sample to be tested according to the second acoustic impedance ratio;

[0036] Solving module: used to solve the wave number of sound propagating inside the sample to be tested based on the first acoustic impedance ratio, the second acoustic impedance ratio, the characteristic acoustic impedance of the sample to be tested, and the acoustic impedance ratio of the back surface of the sample to be tested;

[0037] Calculate the flow resistivity of the sample to be tested based on the wave number of sound propagating inside the sample to be tested and the characteristic acoustic impedance of the sample to be tested;

[0038] The rear surface of the sample to be tested is the surface where the rigid wall of the impedance tube is located, and the front surface of the sample to be tested is the surface where the speaker of the impedance tube is located.

[0039] To solve the above technical problems, the present invention provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and runnable on the processor. When the processor executes the computer program, the steps of the above-mentioned method for measuring the flow resistivity of porous materials are implemented.

[0040] To solve the above technical problems, the present invention provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the steps of the above-mentioned method for measuring the flow resistivity of porous materials are implemented.

[0041] To solve the above technical problem, the present invention provides a computer program product, including a computer program, characterized in that when the computer program is executed by a processor, the steps of the above porous material resistivity measurement method are implemented.

[0042] The above technical solution of the present invention has the following advantages over the prior art:

[0043] The porous material resistivity measurement method constructed by the present invention can significantly reduce the measurement cost while being able to accurately measure the porous material resistivity.

[0044] The measurement process of the present invention is simple and easy. It only requires placing the sample to be measured in the impedance tube and performing two measurements respectively. This avoids cumbersome experimental equipment and complicated operation steps, greatly reduces the difficulty of operation, and enables ordinary technicians to easily complete the flow resistivity measurement, thereby improving the convenience and popularity of the operation.

[0045] The present invention can accurately calculate the wave number and flow resistivity of the sample to be measured, which not only effectively improves the accuracy and stability of the measurement, but also improves the repeatability of the results and ensures the reliability of the experimental data. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to make the contents of the present invention more clearly understood, the present invention is further described in detail below based on specific embodiments of the present invention in conjunction with the accompanying drawings.

[0047] Figure 1 is a flow chart of the method of the present invention;

[0048] Figure 2 This is a simplified cross-sectional diagram of an impedance tube according to an embodiment of the present invention;

[0049] Figure 3 1 is a schematic diagram of the first acoustic impedance ratio of the front surface measured when the rear surface of the sample to be tested is placed against the rigid wall of the impedance tube in an embodiment of the present invention;

[0050] Figure 4 1 is a schematic diagram of a second acoustic impedance ratio of the front surface of the sample to be tested measured when the distance between the rear surface of the sample to be tested and the rigid wall of the impedance tube is 2 cm in an embodiment of the present invention;

[0051] Figure 5 Schematic diagram of characteristic impedance of a sample to be tested in an embodiment of the present invention;

[0052] Figure 6 Schematic diagram of the acoustic wave number inside the sample to be tested in an embodiment of the present invention;

[0053] Figure 7 Schematic diagram of the imaginary part of the product of the characteristic impedance of the sample to be measured and the internal acoustic wave number in an embodiment of the present invention. DETAILED DESCRIPTION

[0054] The present invention will be further described below with reference to the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it. However, the embodiments are not intended to limit the present invention.

[0055] Example 1

[0056] Reference Figure 1 The present invention relates to a method for measuring the flow resistivity of porous materials, comprising:

[0057] When the rear surface of the sample to be tested is pressed against the rigid wall of the impedance tube (L=0), the first acoustic impedance of the front surface of the sample to be tested is measured;

[0058] When the distance L between the rear surface of the sample to be tested and the rigid wall of the impedance tube is L≠0, the second acoustic impedance of the front surface of the sample to be tested is measured;

[0059] Derived the characteristic acoustic impedance of the sample to be tested according to the first acoustic impedance ratio, and deduced the rear surface acoustic impedance ratio of the sample to be tested according to the second acoustic impedance ratio;

[0060] Calculating the wave number of sound propagating inside the sample to be tested based on the first acoustic impedance ratio, the second acoustic impedance ratio, the characteristic acoustic impedance of the sample to be tested, and the acoustic impedance ratio of the rear surface of the sample to be tested;

[0061] Calculate the flow resistivity of the sample to be tested based on the wave number of sound propagating inside the sample to be tested and the characteristic acoustic impedance of the sample to be tested;

[0062] The rear surface of the sample to be tested is the surface where the rigid wall of the impedance tube is located, and the front surface of the sample to be tested is the surface where the speaker of the impedance tube is located.

[0063] The following is a detailed introduction to this embodiment:

[0064] See also Figure 1 In this embodiment, the flow resistivity of the sample to be tested (i.e., porous material) is measured by combining an impedance tube and theory. First, the front surface acoustic impedance of the sample to be tested is measured twice using an impedance tube. Once, the rear end of the sample to be tested is close to a rigid wall (the rigid wall in this embodiment is the closed end of the impedance tube), and once the distance between the rear end of the sample to be tested and the rigid wall is L. The characteristic acoustic impedance of the sample to be tested and the rear surface acoustic impedance of the sample to be tested are respectively obtained from the results of the two measurements. Finally, the wave number of the sound wave inside the sample to be tested is solved, and the flow resistivity to be tested is obtained.

[0065] The theoretical approach is as follows:

[0066] Press the impedance tube Figure 2 Measure the acoustic impedance of the sample to be tested. Figure 2 In the example, the loudspeaker is used to output plane wave sound waves, and microphones 1 and 2 are used to record the sound pressure signals at the corresponding positions. The distance between X1 and X2 represents the position of the microphones. Specifically, in this embodiment, when the back surface of the sample to be tested is placed close to the rigid wall of the impedance tube for measurement (L=0), the acoustic impedance of the front surface of the sample to be tested can be obtained as Z. s1 In this embodiment, when the distance L (L≠0) between the rear surface of the sample to be tested and the rigid wall of the impedance tube is measured, the acoustic impedance of the front surface of the sample to be tested can be obtained as Z s2 .

[0067] When L≠0, that is, when the distance between the rear surface of the sample to be tested and the rigid wall of the impedance tube is L, the position of the rigid wall of the impedance tube is taken as the 0 coordinate of the x-axis (the impedance tube part is located in the negative direction of the x-axis), and the transmission line acoustic impedance transfer formula is established at the coordinates x=-L-2l~x=-L, that is, the second acoustic impedance formula of the front surface of the sample to be tested is:

[0068]

[0069] Among them, Z s2 is the second acoustic impedance of the front surface of the sample to be tested, Z L2 is the surface acoustic impedance of the sample rear surface at coordinate x = -L when L≠0, Z m is the characteristic impedance of the sample to be tested, k m is the wave number of sound when it propagates inside the sample to be tested, 2l is the thickness of the sample to be tested, and j is the imaginary unit.

[0070] At this time (when L≠0), the transmission line acoustic impedance transfer formula is established at x=-L~x=0 (that is, the surface acoustic impedance at x=-L is calculated), and the surface acoustic impedance formula of the sample to be tested is:

[0071]

[0072] Among them, Z L3 is the surface acoustic impedance of the rigid wall of the impedance tube at coordinate x = 0 and Z L3 →∞; k0 is the wave number of sound when it propagates in air; Z0 is the characteristic impedance of air and Z0=ρ0c0, ρ0 is the air density, and c0 is the speed of sound propagation in air.

[0073] It should be noted that formula (2) is to convert Figure 2 The distance L between the sample to be tested and the rigid wall (i.e. Figure 2 The air medium where -L to 0 is located is taken as the object to be measured.

[0074] The method for deriving the rear surface acoustic impedance of the sample to be tested according to the second acoustic impedance includes: L3 →∞ (it approaches infinity because it is a rigid wall), then formula (2) is simplified to formula (3):

[0075] Z L2 =-jρ0c0cot(k0L) (3).

[0076] When L = 0, when the rear surface of the sample to be tested is placed against the rigid wall of the impedance tube, the transmission line acoustic impedance transfer formula is established at the coordinates x = -L-2l = -2l ~ x = -L = 0, that is, the first acoustic impedance formula of the front surface of the sample to be tested is:

[0077]

[0078] Among them, Z s1 is the first acoustic impedance of the front surface of the sample to be tested, Z L1 It is the surface acoustic impedance of the rear surface of the sample to be tested when L=0, that is, the coordinate x=-L=0.

[0079] Since the rear surface of the sample to be tested is close to the rigid wall of the impedance tube when L=0, Z L1 =Z L3 →∞ (because the rear surface of the sample to be tested is close to the rigid wall, it approaches infinity), then formula (4) is simplified to formula (5):

[0080] Z m =jZ s1 tan(2k m l) (5).

[0081] The method for calculating the wave number of sound propagating inside the sample to be tested based on the first acoustic impedance ratio, the second acoustic impedance ratio, the characteristic acoustic impedance of the sample to be tested, and the acoustic impedance ratio of the back surface of the sample to be tested includes:

[0082] Combine formula (1), formula (3), and formula (5) to solve the wave number k when the sound propagates inside the sample to be tested. m :

[0083]

[0084] For porous material samples, the flow resistivity of the sample is calculated based on the wave number of sound propagating inside the sample and the characteristic acoustic impedance of the sample. The formula is:

[0085]

[0086] Where σ is the resistivity of the porous material of the sample to be tested, ω=2πf is the circular frequency of the sound, f is the frequency of the sound, and Imag represents the Z m k m The imaginary part of .

[0087] The experimental analysis is as follows:

[0088] The measured density is 40kg / m 3 The flow resistivity of glass fiber wool. First, use an impedance tube to measure the acoustic impedance of the front surface of the glass fiber wool to be tested twice. The first time, the back surface of the sample is close to the rigid wall at the end of the impedance tube. The second time, the back surface of the sample is 2 cm away from the rigid wall at the end of the impedance tube. The acoustic impedance of the front surface of the sample to be tested is as follows: Figure 3 、 Figure 4 As shown, Figure 3 、 Figure 4Here, real represents the real part of the front surface acoustic impedance, and imag represents the imaginary part of the front surface acoustic impedance.

[0089] Now, according to equations (2) and (4), we can calculate the characteristic impedance of the material and the wave number of the sound wave inside the material. The calculation results are as follows: Figure 5 、 Figure 6 As shown, it is not difficult to find that the characteristic impedance of the material and the wave number of the sound wave inside the material can be correctly calculated by formula (4) and formula (5).

[0090] Now, in this embodiment, the material characteristic impedance is multiplied by the internal acoustic wave number, and the imaginary part is taken and the angular frequency is made close to 0. The calculation result is as follows: Figure 7 As shown, Figure 7 represents Imag(Z m k m ) value with the frequency transformation image, by Figure 7 The curve approaches the frequency of 0 smoothly (as the frequency approaches 0, the circular frequency also approaches 0 ω = 2πf) and takes the opposite number to obtain the flow resistivity of the sample to be tested. In this embodiment, the density is calculated to be 40kg / m 3 The flow resistance of glass fiber wool is 7704.3Pa*s / m 2 .

[0091] It can be seen that the measurement process of the present invention is simple and easy. It only requires placing the sample to be measured in the impedance tube and performing two measurements separately. This avoids cumbersome experimental equipment and complicated operating steps, greatly reduces the difficulty of operation, and enables ordinary technicians to easily complete the flow resistivity measurement, thereby improving the convenience and popularity of the operation.

[0092] Example 2

[0093] This embodiment provides a porous material resistivity measurement system, comprising:

[0094] The first measurement module is used to measure the first acoustic impedance of the front surface of the sample to be tested when the rear surface of the sample to be tested is pressed against the rigid wall of the impedance tube;

[0095] The second measuring module is used to measure the second acoustic impedance of the front surface of the sample to be tested when the distance L between the rear surface of the sample to be tested and the rigid wall of the impedance tube is L;

[0096] Derivation module: used to derive the characteristic acoustic impedance of the sample to be tested according to the first acoustic impedance ratio, and to derive the rear surface acoustic impedance ratio of the sample to be tested according to the second acoustic impedance ratio;

[0097] Solving module: used to solve the wave number of sound propagating inside the sample to be tested based on the first acoustic impedance ratio, the second acoustic impedance ratio, the characteristic acoustic impedance of the sample to be tested, and the acoustic impedance ratio of the back surface of the sample to be tested;

[0098] Calculate the flow resistivity of the sample to be tested based on the wave number of sound propagating inside the sample to be tested and the characteristic acoustic impedance of the sample to be tested;

[0099] The rear surface of the sample to be tested is the surface where the rigid wall of the impedance tube is located, and the front surface of the sample to be tested is the surface where the speaker of the impedance tube is located.

[0100] Example 3

[0101] This embodiment provides a flow resistivity measurement device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of the porous material flow resistivity measurement method described in the first embodiment are implemented.

[0102] Example 4

[0103] This embodiment provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the steps of the method for measuring the flow resistivity of porous materials described in the first embodiment are implemented.

[0104] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code. The scheme in the embodiment of the present application can be implemented in various computer languages, for example, object-oriented programming language Java and literal translation scripting language JavaScript, etc.

[0105] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the steps in the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0106] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0107] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0108] Although the preferred embodiments of the present application have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present application.

[0109] Obviously, the above embodiments are merely examples for clarity of explanation and are not intended to limit the implementation methods. Those skilled in the art will appreciate that other variations or modifications can be made based on the above description. It is not necessary and impossible to enumerate all implementation methods here. Obvious variations or modifications arising therefrom remain within the scope of protection of the present invention.

Claims

1. A method for measuring the flow resistivity of porous materials, characterized by: include: When the rear surface of the sample to be tested is pressed against the rigid wall of the impedance tube, the first acoustic impedance of the front surface of the sample to be tested is measured; When the rear surface of the sample to be tested is at a distance L from the rigid wall of the impedance tube, the second acoustic impedance of the front surface of the sample to be tested is measured; Derived the characteristic acoustic impedance of the sample to be tested according to the first acoustic impedance ratio, and deduced the rear surface acoustic impedance ratio of the sample to be tested according to the second acoustic impedance ratio; Calculating the wave number of sound propagating inside the sample to be tested based on the first acoustic impedance ratio, the second acoustic impedance ratio, the characteristic acoustic impedance of the sample to be tested, and the acoustic impedance ratio of the rear surface of the sample to be tested; Calculate the flow resistivity of the sample to be tested based on the wave number of sound propagating inside the sample to be tested and the characteristic acoustic impedance of the sample to be tested; The rear surface of the sample to be tested is the surface where the rigid wall of the impedance tube is located, and the front surface of the sample to be tested is the surface where the speaker of the impedance tube is located.

2. The method for measuring the flow resistivity of porous materials according to claim 1, wherein: When the distance between the rear surface of the sample to be tested and the rigid wall of the impedance tube is L, and the position of the rigid wall of the impedance tube is taken as the zero coordinate, then when the coordinates are x = -L-2l to x = -L, the second acoustic impedance formula of the front surface of the sample to be tested is: Among them, Z s2 is the second acoustic impedance of the front surface of the sample to be tested, Z m is the characteristic impedance of the sample to be tested, k m is the wave number of the sound when it propagates inside the sample to be tested, 2l is the thickness of the sample to be tested, j is the imaginary unit, Z L2 When L≠0, the surface acoustic impedance of the rear surface of the sample to be tested at x=-L satisfies: Among them, Z L3 is the surface acoustic impedance of the rigid wall of the impedance tube at coordinate x = 0 and Z L3 →∞; k0 is the wave number of sound when it propagates in air; Z0 is the characteristic impedance of air and Z0=ρ0c0, ρ0 is the air density, and c0 is the speed of sound propagation in air.

3. The method for measuring the flow resistivity of porous materials according to claim 2, wherein: The method for deriving the rear surface acoustic impedance of the sample to be tested according to the second acoustic impedance comprises: L3 →∞, then formula (2) is simplified to: WITH L2 =-jρ0c0cot(k0L) (3)。 4. The method for measuring the flow resistivity of porous materials according to claim 2, wherein: When the rear surface of the sample to be tested is pressed against the rigid wall of the impedance tube, when the coordinates are x=-L-2l=-2l to x=-L=0, the first acoustic impedance formula of the front surface of the sample to be tested is: Among them, Z s1 is the first acoustic impedance of the front surface of the sample to be tested, Z L1 It is the surface acoustic impedance of the rear surface of the sample to be tested when L=0, that is, the coordinate x=-L=0.

5. The method for measuring the flow resistivity of porous materials according to claim 4, wherein: Since the rear surface of the sample to be tested is close to the rigid wall of the impedance tube when L=0, Z L1 =Z L3 →∞, then simplify formula (4) to: <h2 style=";text-align:left;direction:ltr">Z<h2 style=";text-align:left;direction:ltr"> m <h2 style=";text-align:left;direction:ltr"> =jZ<h2 style=";text-align:left;direction:ltr"> s1 <h2 style=";text-align:left;direction:ltr"> tan(2k<h2 style=";text-align:left;direction:ltr"> m <h2 style=";text-align:left;direction:ltr"> l) (5)。 6. The method for measuring the flow resistivity of porous materials according to claim 5, wherein: The method for calculating the wave number of sound propagating inside the sample to be tested based on the first acoustic impedance ratio, the second acoustic impedance ratio, the characteristic acoustic impedance of the sample to be tested, and the rear surface acoustic impedance ratio of the sample to be tested includes: Combine formula (1), formula (3), and formula (5) to solve the wave number k when the sound propagates inside the sample to be tested. m :

7. The method for measuring the flow resistivity of porous materials according to claim 6, wherein: The flow resistivity of the sample to be tested is calculated based on the wave number of sound propagating inside the sample to be tested and the characteristic acoustic impedance of the sample to be tested. The formula is: Where σ is the resistivity of the porous material of the sample to be tested, ω=2πf is the circular frequency of the sound, f is the frequency of the sound, and Imag represents the Z m k m The imaginary part of .

8. A porous material resistivity measurement system, characterized by: include: The first measurement module is used to measure the first acoustic impedance of the front surface of the sample to be tested when the rear surface of the sample to be tested is pressed against the rigid wall of the impedance tube; The second measuring module is used to measure the second acoustic impedance of the front surface of the sample to be tested when the distance L between the rear surface of the sample to be tested and the rigid wall of the impedance tube is L; Derivation module: used to derive the characteristic acoustic impedance of the sample to be tested according to the first acoustic impedance ratio, and to derive the rear surface acoustic impedance ratio of the sample to be tested according to the second acoustic impedance ratio; Solving module: used to solve the wave number of sound propagating inside the sample to be tested based on the first acoustic impedance ratio, the second acoustic impedance ratio, the characteristic acoustic impedance of the sample to be tested, and the acoustic impedance ratio of the back surface of the sample to be tested; Calculate the flow resistivity of the sample to be tested based on the wave number of sound propagating inside the sample to be tested and the characteristic acoustic impedance of the sample to be tested; The rear surface of the sample to be tested is the surface where the rigid wall of the impedance tube is located, and the front surface of the sample to be tested is the surface where the speaker of the impedance tube is located.

9. A flow resistivity measuring device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the steps of the method for measuring the flow resistivity of porous materials according to any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method for measuring the flow resistivity of porous materials according to any one of claims 1 to 7 are implemented.

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