Modeling method of acoustic impedance calculation model for ablated surface of carbon-based composite material

Abstract

The invention discloses a modeling method of an acoustic impedance calculation model for an ablated surface of a carbon-based composite material, and belongs to the field of aerospace. Aiming at the defects of a modeling method of an existing Fedorov acoustic impedance model on a carbon-based fiber material, heat flow resistance and heat characteristic length are introduced on the basis of a formula of an original impedance model, and a dimensionless complex dynamic compressibility coefficient is modified, so that the Fedorov acoustic impedance model is developed from a four-non-acoustic-parameter impedance model to a six-non-acoustic-parameter impedance model. An impedance model used for correction is a JCAL acoustic impedance model, the impedance model is often used in the acoustics field to predict the surface acoustic impedance of the irregular fiber material, and then the prediction precision of the original impedance model on the surface acoustic impedance of the non-uniformly distributed carbon-based fiber material is improved. And fitting the improved impedance model into a test result of an impedance tube experiment through parameter inversion to obtain non-acoustic parameter data suitable for the ablated carbon-based composite material, and obtaining an improved acoustic impedance model suitable for the carbon-based composite material.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of aerospace, and particularly relates to a sound impedance calculation model modeling method for a carbon-based composite material ablation surface. BACKGROUND

[0002] Future hypersonic vehicles develop towards long-range, high-speed, cross-domain and high maneuverability, and the thermal protection of the vehicles will face many new challenges. In response to this, the development of fine thermal environment prediction is proposed. The boundary layer flow state has a significant impact on the aerodynamic thermal environment of hypersonic vehicles. The aerodynamic heating in the turbulent flow region is much larger than that in the laminar flow region, and the heat flux peak often appears in the flow transition region, which can reach three times the laminar thermal load at hypersonic speed, i.e., for thermal load: laminar flow region < turbulent flow region < transition region. Therefore, for the prediction of the aerodynamic thermal environment of the boundary layer of a hypersonic vehicle, the transition of the boundary layer is a very critical problem.

[0003] The transition process during hypersonic flight is often triggered by the second mode instability. The second mode and its high-order harmonics are considered to be acoustic waves that repeatedly expand and compress between the relative speed lines in the wall and the boundary layer. The surface micro-pores of the acoustic metasurface are much smaller than the thickness of the boundary layer and the wavelength of the second mode disturbance wave, and the energy of the disturbance wave can be dissipated by the viscosity in the hole. The surface microstructure can better absorb sound waves (foreigners call the metasurface a super-sound absorbing coating), thereby effectively suppressing the second mode and achieving the effect of delaying transition. Carbon / carbon composites have been applied to the thermal protection of hypersonic vehicles due to their good oxidation resistance and specific strength, and the natural pores on their surface are expected to be applied to super-sound absorbing materials to suppress transition.

[0004] In 2001, Fedorov et al. proposed the acoustic characteristics of a slender hole, and gave a model of the effect of a single hole on the flow field and the sound field: v y ’=A y P’ where v is the wall normal fluctuating velocity, p is the wall sound field pressure, A yThe second mode growth rate is predicted based on the impedance boundary condition in combination with the linear stability analysis theory to obtain the approximate position of the second mode instability region, thereby achieving transition prediction. In 2003, Fedorov et al. conducted microstructure modeling research on metal felt materials, approximated the network structure of metal fibers inside the metal felt, and used the acoustic impedance semi-empirical formula proposed by Allard et al. to give an impedance model of the metal felt for transition prediction on the surface of the metal felt. The impedance model assumes that the anisotropic fiber microstructure distribution is orthogonal when solving the shape parameters required by the model, and assumes that the fiber shape is a uniform diameter cylinder, which is quite different from the internal fiber bundle microstructure of the actual ablated carbon-based thermal protection material, thereby reducing the prediction accuracy of the model. Therefore, it is necessary to further improve the impedance model for the non-uniform change of the fiber bundle diameter along the axial direction and the more complex arrangement of the fiber bundle to improve the prediction accuracy of the acoustic impedance of the real fiber porous material and better predict the transition on the surface of the carbon-based material. SUMMARY In view of the above problems in the prior art, the present application provides a modeling method for calculating the acoustic impedance of the ablation surface of a carbon-based composite material.

[0005] To achieve the above-mentioned purposes, the technical scheme adopted by the present application is as follows: A modeling method for calculating the acoustic impedance of the ablation surface of a carbon-based composite material, comprising the following steps: S1, establishing a six non-acoustic parameter impedance model: by introducing a heat flow resistance and a thermal characteristic length to modify the dimensionless complex dynamic compression coefficient term of the original four non-acoustic parameter impedance model, a six non-acoustic parameter impedance model is obtained; S2, simplifying the six non-acoustic parameters into three pore distribution parameters based on a semi-empirical formula: porosity, average pore size, and pore size standard deviation; S3, obtaining the pore size relative volume distribution through computer tomography or mercury intrusion experiment, fitting the lognormal distribution function of the pore size distribution to determine the porosity, average pore size, and standard deviation; S4, substituting the pore parameters into the six non-acoustic parameter impedance model, calculating the acoustic impedance in combination with the wind tunnel incoming flow conditions, and verifying the model accuracy through experiments; S5, optimizing the non-acoustic parameters through parameter inversion to adapt to the ablation surface microstructure of different carbon-based composite materials.

[0006] Further, the modified six non-acoustic parameter impedance model in S1 is represented as:

[0007]

[0008]

[0009]

[0010] where the superscript * denotes a dimensional physical quantity, the superscript w denotes a wall physical quantity, the superscript e denotes an outer boundary layer parameter, and i is the imaginary unit. A y is the normal admittance, Λ is the propagation constant, and Z0 is the characteristic impedance, are the dimensionless complex dynamic density and the dimensionless complex dynamic compressibility, respectively, where , = p e ,P e are the density and pressure at the outer boundary layer, respectively. is the porosity tortuosity, r P is the shape factor, is the viscous flow resistance, is the porosity, is the thermal flow resistance, is the thermal characteristic length, h is the dimensionless thickness, and the boundary layer scale l * dimensionless, i.e. h = h * / l * where l * (L * is the reference length). Me is the outer boundary layer Mach number. T * w and p * w are the temperature and density at the wall. μ * w is the dynamic viscosity coefficient corresponding to the wall temperature, Pr is the Prandtl number, and γ is the specific heat ratio. λ1 and λ1 ’ are parameters defined for the purpose of simplifying the equation, g(x) and g ’ (x) are functions defined for the purpose of adapting the equation form, g(λ1) and g ’ (λ1 ’ ) are the results of the corresponding parameters being brought into the g function.

[0011] Further, the S2 specifically comprises the following steps: S21, converting the non-acoustic parameters using a semi-empirical formula, expressed as:

[0012] wherein,​​φ porosity, average pore diameter of the pore distribution, pore diameter standard deviation of the pore distribution S22, simplify the six-parameter model to three pore distribution parameters of porosity, average pore diameter and pore diameter standard deviation through parameter inversion.

[0013] Further, the S3 specifically comprises the following steps: S31, obtain the relative volume distribution of the pore diameter by using the computer tomography technology or the mercury intrusion experiment, and measure and analyze the sample porosity and the relative volume distribution histogram of the pore diameter multiple times; S32, convert the relative volume distribution into a lognormal distribution function, and obtain the mean value and the standard deviation of the sample distribution function.

[0014] Further, the specific mode of the S4 is: S41, solve the flow field parameters behind the shock wave by using the Taylor-Maclaurin equation based on the high-enthalpy shock tunnel inflow conditions; S42, substitute the pore parameters and the flow field parameters into the six non-acoustic parameter impedance model to calculate the frequency domain acoustic impedance; S43, compare the ultrasonic wave impedance experimental results, if the error is less than the set threshold value, then enter S5, if the error is greater than or equal to the set threshold value, then return to S3 to recalculate the pore distribution parameters.

[0015] Further, the S5 specifically comprises the following steps: S51, use the impedance tube experimental data to invert the flow resistance, the characteristic length, the thermal flow resistance and the thermal characteristic length; S52, adjust the pore distribution parameters in a small range according to the ablation degree and the pore diameter distribution results, thereby adjusting the inversion results and updating the acoustic impedance prediction results.

[0016] The present application has the following beneficial effects: (1) Compared with the existing Fedorov acoustic impedance model, the calculation accuracy is improved when calculating the acoustic impedance of the fiber material; (2) Compared with the original acoustic impedance model, the thermal flow resistance and the thermal characteristic length are approximately processed by using the uniform diameter cylindrical pore, the present model gives a complete six non-acoustic parameters, and the prediction accuracy at low frequency is better; (3) The present model only needs the relative volume distribution of the pore diameter, does not need to make an approximate assumption on the fiber distribution, and improves the prediction accuracy of the impedance under the complex pore distribution inside the fiber material. BRIEF DESCRIPTION OF DRAWINGS

[0017] Figure 1 is the flow chart of the method for predicting the surface acoustic impedance of the carbon-based composite material disclosed by the present application; Figure 2 is a pore size relative volume distribution histogram obtained from mercury intrusion experiment applied to the carbon / carbon material referenced in the present application; Figure 3 is a logarithmic probability density distribution result converted from the pore size relative volume distribution histogram; Figure 4 is a comparison between the prediction result of the improved impedance model for the carbon / carbon material under the high-enthalpy shock tunnel incoming flow condition and the ultrasonic impedance experimental test result; Figure 5 is a comparison between the prediction result of the original impedance model for the carbon / carbon material under the high-enthalpy shock tunnel incoming flow condition and the ultrasonic impedance experimental test result. DETAILED DESCRIPTION

[0018] The specific embodiments of the present application are described below to facilitate the understanding of the present application for those skilled in the art, but it should be clear that the present application is not limited to the scope of the specific embodiments, and for those skilled in the art, it is obvious that various changes are within the spirit and scope of the present application defined and determined by the appended claims, and all the inventions utilizing the concept of the present application are within the scope of protection.

[0019] A sound impedance calculation model modeling method for the ablation surface of carbon-based composite material, as shown in Figure 1 , comprising the following steps: S1, establishing a six non-acoustic parameter impedance model, by introducing heat flow resistance and thermal characteristic length to modify the established six non-acoustic parameter impedance model, improving the dimensionless complex dynamic compression coefficient; The impedance model for stability analysis of high-speed boundary layer random microstructure surface is: (1) (2) (3) In the formula, the symbol * is a dimensioned physical quantity, the symbol w is a wall physical quantity, the symbol e is a boundary layer outer edge parameter, and i is an imaginary unit.A y is a normal admittance, Λ is a propagation constant, Z0 is a characteristic impedance, are dimensionless complex dynamic density and dimensionless complex dynamic compression coefficient, respectively, wherein , = ( p e ,P e are density and pressure at the outer edge of the boundary layer, respectively. is the tortuosity of the porous medium, r P is a shape factor, is the viscous flow resistance, is the porosity, h is the dimensionless thickness, using the boundary layer scale l * dimensionless, i.e. h = h * / l * where l * = (L * is the reference length). Me is the Mach number at the outer edge of the boundary layer. T * w and p * w is the temperature and density at the wall. μ * w is the dynamic viscosity coefficient corresponding to the wall temperature, Pr is the Prandtl number, and γ is the specific heat ratio. λ1 and λ2 are parameters defined for the simplification of the equation, and g(x) is a function defined to adapt the form of the equation. g(λ1) and g(λ2) are the results of corresponding parameters brought into the g function.

[0020] On the basis of the original impedance model, a thermal flow resistance σ' and a thermal characteristic length r p ' are introduced to represent the influence of the thermal conductivity of the pore structure of the porous medium on sound propagation, thereby modifying the original impedance model. The improved six non-acoustic parameter impedance model is: (4) (5) (6) S2, the six non-acoustic parameters are simplified to three pore distribution parameters based on semi-empirical formulas: porosity, average pore diameter, and pore diameter standard deviation; The following semi-empirical formula is introduced: (7) The above six non-acoustic parameter impedance model can be converted into a three-parameter model, and the three parameters are porosity φ , average pore diameter of pore distribution , and pore diameter standard deviation of pore distribution .

[0021] S3, the relative volume distribution of pore diameter is obtained by computer tomography or mercury intrusion experiment, and a lognormal distribution function is fitted to determine the porosity, average pore diameter, and standard deviation; The relative volume of pore diameter is obtained by computer tomography or mercury intrusion experiment (ΔV / V total) distribution, multiple measurements and analysis of representative sample porosity and pore size relative volume distribution histogram, the results of the present application are shown in Figure 2 . The relative volume distribution is converted into a lognormal distribution function, and the mean and standard deviation of the sample distribution function are obtained, and the converted results are shown in Figure 2 . Figure 3 .

[0022] The calculated porosity is 0.15, the average pore size is 4.37 μm, and the standard deviation is 0.1.

[0023] S4, substitute the pore parameters into the six non-acoustic parameter impedance model, combine the wind tunnel inflow conditions to calculate the acoustic impedance, and verify the model accuracy through experiments; The experimental data of supersonic impedance measurement under the high-enthalpy shock wave wind tunnel inflow condition are used as verification.

[0024] The high-enthalpy shock wave wind tunnel inflow condition is shown in Table 1. Different flow conditions are marked with different colors, and the marking description is shown in Table 1. The experimental model of this experiment is a 7° half-cone angle sharp cone.

[0025] Table 1 Inflow condition

[0026] S5, optimize the non-acoustic parameters by parameter inversion, and adapt the ablation surface microstructure of different carbon-based composite materials.

[0027] The parameters such as Reynolds number, Mach number, static pressure, static temperature and density after the conical shock wave are obtained by Taylor-MacLaurin equation, which are used for impedance model calculation; the non-acoustic parameters of step three and the parameters after the conical shock wave (i.e. the boundary layer outer edge physical parameters mentioned in S1) are substituted into the calculation formula of the new impedance model, and the calculation results are obtained. The improved impedance model is verified, and the comparison of the improved impedance model calculation results and the experimental results, and the comparison of the original impedance model calculation results and the experimental results are shown in Figure 4 and Figure 5 . The prediction accuracy of the improved impedance model under high Reynolds number is better than that of the original impedance model, and the prediction accuracy is improved by 6% at Re m =9.80×10 6 , around 300 kHz frequency.

[0028] (8) (9) (10) Formula (8) is the complete form of Taylor-MacLaurin equation (conical shock wave angle equation), wherein V r is perpendicular to the conical generatrix direction, V θis the conical generatrix direction, and θ is the angle between the local position and the conical symmetry axis. Equation (9) is the boundary equation of the Taylor-Maccoll equation, where V is the velocity after the shock wave, and θ shock is the shock wave angle, and δ is the gas flow deflection angle. The solution to the conical shock wave angle equation starts by advancing from the shock wave surface to the conical surface, the relationship between the gas flow deflection angle and the shock wave angle satisfies the oblique shock wave equation (10), and when the iteration converges, the gas flow deflection angle is equal to the half conical angle, and V θ = 0 at the conical surface. γ is the specific heat ratio.

[0029] The present application is described with reference to flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to embodiments of the present application. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, as well as combinations of flows and / or blocks in the flowcharts 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, a special-purpose computer, an embedded processor, or other programmable data processing apparatus to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing apparatus generate a means for implementing the functions specified in the flow Figure 1 one or more flows and / or blocks in the flowcharts and / or block diagrams. Figure 1 one or more flows and / or blocks in the flowcharts and / or block diagrams.

[0030] These computer program instructions can also be stored in a computer-readable memory capable of causing the computer or other programmable data processing apparatus to work in a specific manner, so that the instructions stored in the computer-readable memory produce a manufactured product including instruction means, which implements the functions specified in the flow Figure 1 one or more flows and / or blocks in the flowcharts and / or block diagrams. Figure 1 one or more flows and / or blocks in the flowcharts and / or block diagrams.

[0031] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus, so that a series of operation steps are performed on the computer or other programmable data processing apparatus to produce a computer-implemented process, so that the instructions executed on the computer or other programmable data processing apparatus provide steps for implementing the functions specified in the flow Figure 1 one or more flows and / or blocks in the flowcharts and / or block diagrams. Figure 1 one or more flows and / or blocks in the flowcharts and / or block diagrams.

[0032] The principles and implementation manners of the present application are described in the specific embodiments, and the above embodiment descriptions are only used to help understand the method of the present application and its core idea; at the same time, for those skilled in the art, according to the idea of the present application, the specific implementation manners and application ranges will be changed, and the above description should not be understood as a limitation of the present application.

[0033] Those skilled in the art will appreciate that the embodiments described herein are presented for purposes of illustration and that the inventive principles are not limited to these particular embodiments. Other variations and modifications can be made to the embodiments without departing from the spirit and scope of the inventive principles.

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; 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 modified six non-acoustic parameter impedance model in S1 is expressed as: where * denotes a dimensional physical quantity, w denotes a wall physical quantity, e denotes a boundary layer outer edge parameter, i is the imaginary unit, A y is the normal admittance, Λ is the propagation constant, and Z0 is the characteristic impedance, are the dimensionless complex dynamic density and the dimensionless complex dynamic compressibility, respectively, where , = , ρ e ,P e are the density and pressure at the boundary layer outer edge, respectively; is the porosity tortuosity, r P is the shape factor, is the viscous flow resistance, is the porosity, is the thermal flow resistance, is the thermal characteristic length, h is the dimensionless thickness, and the boundary layer scale is used l * dimensionless, i.e. h=h * / l * where l * = , L * is the reference length; Me is the boundary layer outer edge Mach number, T * w and ρ * w are the temperature and density at the wall, μ * w is the dynamic viscosity coefficient corresponding to the wall temperature, Pr is the Prandtl number, γ is the specific heat ratio, λ1 and λ1 ’ are parameters defined for the simplification of the equation, g(x) and g ’ (x) are functions defined for the adaptation of the equation form, g(λ1) and g ’ (λ1 ’ ) are the results of the corresponding parameters brought into the g function.

3. The method of modeling acoustic impedance calculations for ablated surfaces of carbon-based composites of claim 2, wherein, The S2 specifically comprises the following steps: S21, converting the non-acoustic parameters by using a semi-empirical formula, which is expressed as: wherein φ is the porosity, is the average pore size of the pore size distribution, is the standard deviation of the pore size of the pore size 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.

4. 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 the sample distribution function.

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

6. The method of modeling acoustic impedance calculations for ablated surfaces of carbon-based composites of claim 5, wherein, The specific manner of solving the flow field parameters after the shock wave by using the Taylor-Maccle equation in S41 is: At the shock wave: At the conical surface: ; The airflow deflection angle and the 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, is the maximum velocity after the shock, is the shock angle, δ is the angle of deflection of the flow, is the ratio of specific heat capacities, is the shock angle, is the Mach number.

7. 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.

8. The method of modeling acoustic impedance calculations for ablated surfaces of carbon-based composites of claim 7, 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 the impedance tube experimental data; S52, adjusting the pore distribution parameters in a small range according to the ablation degree and the pore diameter distribution results, thereby adjusting the inversion results and updating the acoustic impedance prediction results.

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