Modeling Method for Acoustic Impedance Calculation of Ablated Surfaces of Carbon-based Composite Materials

Abstract

This invention discloses a modeling method for calculating the acoustic impedance of ablated surfaces of carbon-based composite materials, belonging to the aerospace field. Addressing the shortcomings of existing Fedorov acoustic impedance models for carbon fiber materials, this invention introduces thermal flow resistance and thermal characteristic length into the original impedance model formula, and modifies the dimensionless complex dynamic compressibility coefficient, thus evolving the Fedorov acoustic impedance model from a four-non-acoustic parameter impedance model to a six-non-acoustic parameter impedance model. The impedance model used for modification is the JCAL acoustic impedance model, commonly used in acoustics for predicting the surface acoustic impedance of irregular fiber materials, thereby improving the prediction accuracy of the original impedance model for the surface acoustic impedance of non-uniformly distributed carbon-based fiber materials. Through parameter inversion, the improved impedance model is fitted to the test results of impedance tube experiments to obtain non-acoustic parameter data applicable to ablated carbon-based composite materials, resulting in an improved acoustic impedance model suitable for carbon-based composite materials.

Description

Technical Field

[0001] This invention relates to the aerospace field, and specifically to a modeling method for calculating acoustic impedance on ablated surfaces of carbon-based composite materials. Background Technology

[0002] Future hypersonic vehicles will evolve towards longer ranges, higher speeds, cross-domain capabilities, and greater maneuverability, presenting numerous new challenges to their thermal protection. This necessitates the development of sophisticated thermal environment prediction techniques. The boundary layer flow regime significantly impacts the aerodynamic and thermal environment of hypersonic vehicles. Aerodynamic heating in the turbulent region is far greater than in the laminar region, and peak heat flux often occurs in the flow transition region, reaching up to three times the laminar heat load at hypersonic speeds. Therefore, the thermal load order is: laminar region < turbulent region < transition region. Consequently, boundary layer transition is a crucial issue for predicting the aerodynamic and thermal environment of hypersonic vehicles.

[0003] The transition process during hypersonic flight is often triggered by second-mode instability. The second mode and its higher harmonics are considered to be sound waves that repeatedly expand and compress between relative sound velocity lines within the wall and boundary layer. Acoustic metasurfaces have surface micropores much smaller than the boundary layer thickness and the wavelength of the second-mode perturbation wave. The energy of the perturbation wave can be dissipated through the viscosity within the pores, and the surface microstructure can effectively absorb sound waves (metasurfaces are referred to internationally as ultrasonic absorbing coatings), thus effectively suppressing the second mode and delaying the transition. Carbon / carbon composite materials, due to their excellent oxidation resistance and specific strength, have been used in the thermal protection of hypersonic vehicles. Their naturally occurring pores on the surface hold promise for application in ultrasonic absorbing materials to suppress transition.

[0004] In 2001, Fedorov et al. proposed the acoustic properties of slender apertures and gave a model of the effect of a single aperture on the flow field and sound field: v y ’=A y P’ .in v The normal pulsation velocity of the wall. p For the wall sound field pressure, A yThe admittance is used. Based on this impedance boundary condition, the growth rate of the second mode can be predicted by combining linear stability analysis theory, thus obtaining the approximate location of the second mode instability region and achieving transition prediction. In 2003, Fedorov et al. conducted microstructure modeling research on metal felt materials, approximating the network structure of the internal metal fibers to a certain extent, and using the semi-empirical formula of acoustic impedance proposed by Allard et al. to give an impedance model of metal felt for transition prediction on the surface of metal felt. This impedance model assumes an orthogonal distribution of the microstructure of anisotropic fibers when solving for the shape parameters required by the model, and assumes that the fiber shape is a uniform diameter cylinder, which is significantly different from the internal fiber bundle microstructure of real ablated carbon-based thermal protection materials, thus reducing the prediction accuracy of the model. Therefore, it is currently necessary to further improve the impedance model for cases where the fiber bundle diameter varies non-uniformly along the axial direction and the fiber bundle arrangement is more complex, in order to improve the accuracy of acoustic impedance prediction for real fibrous porous materials, and thus better predict the transition of carbon-based material surfaces. Summary of the Invention

[0005] To address the aforementioned shortcomings in the prior art, this invention provides a modeling method for calculating the acoustic impedance of ablated surfaces of carbon-based composite materials.

[0006] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows:

[0007] A modeling method for calculating the acoustic impedance of ablated surfaces of carbon-based composite materials includes the following steps:

[0008] S1. Establishing a six-non-acoustic parameter impedance model: By introducing thermal flow resistance and thermal characteristic length to correct the dimensionless complex dynamic compressibility coefficient term of the original four-non-acoustic parameter impedance model, a six-non-acoustic parameter impedance model is obtained. The corrected six-non-acoustic parameter impedance model is expressed as follows:

[0009]

[0010] In the formula, the annotation is... For physical quantities of the wall surface, label These are the boundary layer outer edge parameters. The imaginary unit, For the sake of the guide, Let be the propagation constant. Characteristic impedance, These are the dimensionless complex dynamic density and the dimensionless complex dynamic compressibility, respectively. , = , ， These represent the density and pressure at the outer edge of the boundary layer, respectively. For the tortuosity of porous media, For shape factor, For viscous flow resistance, Porosity For thermal flow resistance, The thermal characteristic length; For dimensionless thickness, the boundary layer scale is adopted. Dimensionless, i.e. ,in , For reference length; The Mach number at the outer edge of the boundary layer. Let be the dimensionless temperature at the wall surface. Density at the wall surface γ is the dynamic viscosity coefficient corresponding to the wall temperature, Pr is the Prandtl number, and γ is the specific heat ratio. and These are parameters defined to simplify the equations. and It is a function defined to fit the form of the equation. and The corresponding parameters are substituted into The result of the function;

[0011] S2. Based on semi-empirical formulas, the six non-acoustic parameters are simplified into three pore distribution parameters: porosity, average pore size, and pore size standard deviation.

[0012] S3. Obtain the relative volume distribution of pore size through computed tomography or mercury intrusion experiments, and fit a log-normal distribution function to determine porosity, average pore size and standard deviation;

[0013] S4. Substitute the pore parameters into the six non-acoustic parameter impedance model, calculate the acoustic impedance in combination with the wind tunnel flow conditions, and verify the accuracy of the model through experiments.

[0014] Furthermore, step S2 specifically includes the following steps:

[0015] S21. The non-acoustic parameters are transformed using a semi-empirical formula, expressed as:

[0016]

[0017] In the formula, φ For porosity, The average pore size of the pore distribution, Pore ​​size standard deviation of pore distribution

[0018] S22. The six-parameter model is simplified to three pore distribution parameters—porosity, average pore size, and pore size standard deviation—through parameter inversion.

[0019] Furthermore, step S3 specifically includes the following steps:

[0020] S31. Using computed tomography or mercury intrusion experiments, obtain the relative volume distribution of pore size, and repeatedly measure and analyze the histogram of the relative volume distribution of porosity and pore size of the sample.

[0021] S32. Convert the relative volume distribution to a log-normal distribution function to obtain the mean and standard deviation of the sample distribution function.

[0022] Furthermore, the specific method of S4 is as follows:

[0023] S41. Based on the inflow conditions of the high-enthalpy shock tunnel, the flow field parameters after the shock wave are solved by the Taylor-Mack equation.

[0024] S42. Substitute the pore parameters and flow field parameters into the six non-acoustic parameter impedance model to calculate the frequency domain acoustic impedance.

[0025] S43. Compare the ultrasonic impedance test results. If the error is less than the set threshold, proceed to S5. If the error is greater than or equal to the set threshold, return to S3 to recalculate the hole distribution parameters.

[0026] Furthermore, the specific method for solving the flow field parameters after the shock wave using the Taylor-Marker equation in S41 is as follows:

[0027]

[0028] At the shock wave:

[0029]

[0030] At the conical surface: ;

[0031] The airflow deflection angle and shock wave angle satisfy the following:

[0032]

[0033] In the formula, The velocity is perpendicular to the generatrix of the cone. The velocity is in the direction of the generatrix of the cone. The angle between the local location and the axis of cone symmetry. The velocity after the shock wave, The maximum velocity after the shock wave. δ is the shock wave angle, and δ is the airflow deflection angle. Specific heat ratio, This is the shock angle.

[0034] Furthermore, the modeling method also includes:

[0035] S5. Optimize non-acoustic parameters through parameter inversion to adapt to the microstructure of ablation surfaces of different carbon-based composite materials.

[0036] Furthermore, S5 specifically includes the following steps:

[0037] S51. Invert the flow resistance, characteristic length, thermal flow resistance and thermal characteristic length using impedance tube experimental data;

[0038] S52. Adjust the pore distribution parameters within a small range based on the ablation degree and pore diameter distribution results, thereby adjusting the inversion results and updating the acoustic impedance prediction results.

[0039] The present invention has the following beneficial effects:

[0040] (1) Compared with the existing Fedorov acoustic impedance model, the calculation accuracy is improved when calculating the acoustic impedance of fiber materials;

[0041] (2) Compared with the original acoustic impedance model, which uses a cylindrical pore with uniform diameter to approximate the thermal flow resistance and thermal characteristic length, the existing model gives complete six non-acoustic parameters, which improves the prediction accuracy at low frequencies.

[0042] (3) The existing model only requires the relative volume distribution of pore diameter and does not require approximate assumptions about fiber distribution, which improves the accuracy of impedance prediction under complex pore distribution inside fiber materials. Attached Figure Description

[0043] Figure 1 This is a flowchart of the method for predicting the surface acoustic impedance of carbon-based composite materials disclosed in this invention;

[0044] Figure 2 This is a histogram of relative pore size volume distribution obtained from a mercury intrusion experiment applied to carbon / carbon materials, which is referenced in this invention.

[0045] Figure 3 It is the log probability density distribution result transformed from the relative volume distribution histogram of aperture;

[0046] Figure 4 This is a comparison between the predicted results of the improved impedance model of the carbon / carbon material under the inflow conditions of a high-enthalpy shock tunnel and the experimental results of ultrasonic impedance testing.

[0047] Figure 5 This is a comparison between the original impedance model prediction results and the ultrasonic impedance test results of the carbon / carbon material under high enthalpy shock tunnel inflow conditions. Detailed Implementation

[0048] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0049] A modeling method for calculating the acoustic impedance of ablated surfaces of carbon-based composite materials, such as... Figure 1 As shown, it includes the following steps:

[0050] S1. Establish a six-non-acoustic parameter impedance model. Improve the dimensionless complex dynamic compressibility coefficient by introducing thermal flow resistance and thermal characteristic length corrections to the established six-non-acoustic parameter impedance model.

[0051] The impedance model used for surface stability analysis of random microstructures in high-speed boundary layers is as follows:

[0052] (1) (2)

[0053] (3)

[0054] In the formula, the annotation is... For physical quantities of the wall surface, label These are the boundary layer outer edge parameters. The imaginary unit, For the sake of the guide, Let be the propagation constant. Characteristic impedance, These are the dimensionless complex dynamic density and the dimensionless complex dynamic compressibility, respectively. , = , 、 These represent the density and pressure at the outer edge of the boundary layer, respectively. For the tortuosity of porous media, For shape factor, For viscous flow resistance, Porosity; For dimensionless thickness, the boundary layer scale is adopted. Dimensionless, i.e. ,in , For reference length; The Mach number at the outer edge of the boundary layer. Let be the dimensionless temperature at the wall surface. Density at the wall surface This represents the dynamic viscosity coefficient corresponding to the wall temperature. Where γ is the Prandtl number and γ is the specific heat ratio. and These are parameters defined to simplify the equations. It is a function defined to fit the form of the equation. and The corresponding parameters are substituted into The result of the function.

[0055] Introducing thermal flow resistance into the original impedance model and thermal characteristic length This model is used to characterize the effect of thermal conductivity of porous media on sound propagation at high frequencies, thereby correcting the original impedance model. The improved six-non-acoustic parametric impedance model is as follows:

[0056] (4)

[0057] (5)

[0058] (6)

[0059] It is a function defined to fit the form of the equation. The corresponding parameters are substituted into The result of the function.

[0060] S2. Based on semi-empirical formulas, the six non-acoustic parameters are simplified into three pore distribution parameters: porosity, average pore size, and pore size standard deviation.

[0061] Introduce the following semi-empirical formula:

[0062] (7)

[0063] The above six-parameter non-acoustic impedance model can be transformed into one requiring only three parameters: porosity. φ Average pore size of pore distribution Pore ​​size standard deviation of pore distribution .

[0064] S3. Obtain the relative volume distribution of pore size through computed tomography or mercury intrusion experiments, and fit a log-normal distribution function to determine porosity, average pore size and standard deviation;

[0065] The relative volume of the pore size was obtained using computed tomography (CT) or mercury intrusion experiments.

[0066] (ΔV / V) totalThe distribution of porosity and pore size was analyzed through multiple measurements to obtain representative sample volumetric histograms. The results referenced in this invention are shown in [reference needed]. Figure 2 The relative volume distribution is transformed into a log-normal distribution function to obtain the mean and standard deviation of the sample distribution function. Figure 2 See the converted result Figure 3 .

[0067] The calculated porosity is 0.15, and the average pore size is... The value is 4.37 μm, and the standard deviation is 0.1.

[0068] S4. Substitute the pore parameters into the six non-acoustic parameter impedance model, calculate the acoustic impedance in combination with the wind tunnel inflow conditions, and verify the accuracy of the model through experiments.

[0069] The experimental data of ultrasonic impedance measurement conducted under the inflow conditions of a high-enthalpy shock tunnel were used as verification.

[0070] The inflow conditions for the high-enthalpy shock tunnel are shown in Table 1. Different flow conditions are marked with different colors, and the markings are explained in Table 1. The experimental model for this experiment is a 7° semi-cone angle pointed cone.

[0071] Table 1 Incoming Flow Conditions

[0072]

[0073] S5. Optimize non-acoustic parameters through parameter inversion to adapt to the microstructure of ablation surfaces of different carbon-based composite materials.

[0074] The parameters such as unit Reynolds number, Mach number, hydrostatic pressure, hydrostatic temperature, and density after the conical shock wave are obtained using the Taylor-Marker equations and used for impedance model calculations. The non-acoustic parameters from step three and the parameters after the conical shock wave (i.e., the boundary layer outer edge physical parameters with subscript e mentioned in S1) are substituted into the calculation formula of the new impedance model to obtain the results. The effectiveness of the improved impedance model is verified by comparing the calculation results of the improved impedance model with experimental results, and comparing the calculation results of the original impedance model with experimental results. Figure 4 and Figure 5 As shown. The improved impedance model has better prediction accuracy than the original impedance model at high Reynolds numbers. m =9.80×10 6 The prediction accuracy around 300kHz frequency has improved by 6%.

[0075] (8)

[0076] (9)

[0077] (10)

[0078] Equation (8) is the complete form of the Taylor-Marker equation (conical shock angle equation), where V r V is perpendicular to the direction of the generatrix of the cone. θ Let V be the direction of the generatrix of the cone, and θ be the angle between the local position and the cone's axis of symmetry. Equation (9) is the boundary equation of the Taylor-Marker equation, where V is the velocity after the shock wave, and θ is the direction of the generatrix of the cone. shock Let θ be the shock wave angle and δ be the airflow deflection angle. Solving the conical shock wave angle equation begins by progressing from the shock wave surface towards the cone surface. The relationship between the airflow deflection angle and the shock wave angle satisfies the oblique shock wave equation (10). Upon convergence of the iteration, the airflow deflection angle equals half the cone angle, and V0 is at the cone surface. θ =0. γ is the specific heat ratio.

[0079] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0080] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0081] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0082] Specific embodiments have been used to illustrate the principles and implementation methods of this invention. The descriptions of the embodiments above are only for the purpose of helping to understand the method and core ideas of this invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this invention. Therefore, the content of this specification should not be construed as a limitation of this invention.

[0083] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A method for modeling the acoustic impedance calculation model of ablated surfaces of carbon-based composite materials, characterized in that, The method comprises the following steps: S1, establishing a six non-acoustic parameter impedance model: by introducing a thermal flow resistance and a thermal characteristic length to modify a dimensionless complex dynamic pressure coefficient term of an original four non-acoustic parameter impedance model, a six non-acoustic parameter impedance model is obtained, wherein the modified six non-acoustic parameter impedance model is represented as: wherein is the wall surface physical quantity, denoted by is the boundary layer outer edge parameter, is the imaginary unit, is the normal admittance, is the propagation constant, is the characteristic impedance, are the dimensionless complex dynamic density and the dimensionless complex dynamic compressibility, respectively, where , = , 、 are the density and pressure at the boundary layer outer edge, respectively; is the porosity tortuosity, is the shape factor, is the viscous flow resistance, is the porosity, is the thermal flow resistance, is the thermal characteristic length; is the dimensionless thickness, using the boundary layer scale is dimensionless, i.e. wherein , is the reference length; is the boundary layer outer edge Mach number, is the dimensionless wall surface temperature, is the wall surface density, is the dynamic viscosity coefficient corresponding to the wall surface temperature, is the Prandtl number, γ is the specific heat ratio, and are parameters defined for simplifying the equation, and are functions defined for adapting the equation form, and are the results of the corresponding parameters brought into the function; S2, simplifying the six non-acoustic parameters into three pore distribution parameters based on a semi-empirical formula: porosity, average pore diameter and pore diameter standard deviation; S3, obtaining a pore diameter relative volume distribution through a computer tomography or a mercury intrusion experiment, and fitting a lognormal distribution function to determine the porosity, the average pore diameter and the standard deviation; S4, substituting the pore parameters into the six non-acoustic parameter impedance model, combining a wind tunnel inflow condition to calculate the acoustic impedance, and verifying the model accuracy through an experiment.

2. The method of modeling acoustic impedance calculations for ablated surfaces of carbon-based composites of claim 1, wherein, The S2 specifically comprises the following steps: S21, converting the non-acoustic parameters by using a semi-empirical formula, represented as: wherein D50 is the average pore diameter of the pore distribution, D50 is the average pore diameter of the pore distribution, S22, simplifying the six parameter model into the three pore distribution parameters: the porosity, the average pore diameter and the pore diameter standard deviation through parameter inversion.

3. The method of modeling acoustic impedance calculations for ablated surfaces of carbon-based composites of claim 1, wherein, The S3 specifically comprises the following steps: S31, obtaining a pore diameter relative volume distribution by using a computer tomography technology or a mercury intrusion experiment, and measuring and analyzing a sample porosity and a pore diameter relative volume distribution histogram multiple times; S32, converting the relative volume distribution into a lognormal distribution function, and obtaining a mean value and a standard deviation of a sample distribution function.

4. The method of modeling acoustic impedance calculations for ablated surfaces of carbon-based composites of claim 1, wherein, The specific manner of the S4 is: S41, based on a high-enthalpy shock wave wind tunnel inflow condition, solving a flow field parameter after a shock wave by using a Taylor-Maccor equation; S42, substituting the pore parameters and the flow field parameters into the six non-acoustic parameter impedance model to calculate a frequency domain acoustic impedance; S43, comparing an ultrasonic wave impedance experiment result, if an error is less than a set threshold value, entering S5, if the error is greater than or equal to the set threshold value, returning to S3 to recalculate the pore distribution parameters.

5. The method of modeling acoustic impedance calculations for ablated surfaces of carbon-based composites of claim 4, wherein, The specific manner of solving the flow field parameter after the shock wave by using the Taylor-Maccor equation in the S41 is: At the shock wave: At the conical surface: ; A gas flow deflection angle and a shock wave angle satisfy: wherein is the velocity perpendicular to the conical generatrix direction, is the velocity in the conical generatrix direction, is the angle between the local position and the axis of conical symmetry, is the velocity after the shock wave, is the maximum velocity after the shock wave, is the shock angle, and δ is the angle of deflection of the flow, is the ratio of specific heat capacities, is the shock angle.

6. The method of modeling acoustic impedance calculations for ablated surfaces of carbon-based composites of claim 1, wherein, The modeling method further comprises: S5, optimizing the non-acoustic parameters through parameter inversion, and adapting the ablation surface microstructure of different carbon-based composite materials.

7. The method of modeling acoustic impedance calculations for ablated surfaces of carbon-based composites of claim 6, wherein, The S5 specifically comprises the following steps: S51, inverting the flow resistance, the characteristic length, the thermal flow resistance and the thermal characteristic length by using impedance tube experiment data; S52, adjusting the pore distribution parameters in a small range according to an ablation degree and a pore diameter distribution result, thereby adjusting the inversion result, and updating an acoustic impedance prediction result.

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