A Calculation Method for the Acoustic Damping Characteristics of the Mixing Head of a Afterburning Engine Thrust Chamber

Abstract

The present invention provides a calculation method for the acoustic damping characteristics of the mixing head of a afterburning engine thrust chamber, which is used to solve the technical problem that the existing calculation method for the acoustic damping of the mixing head has low accuracy and the analysis results are quite different from the actual situation. First, according to the structural parameters of the gas flow channel of the thrust chamber, the geometric blocks of the gas flow channel are extracted; then the geometric blocks are imported into the acoustic solver to obtain the acoustic solution domains of the respective geometric blocks; after that, based on the boundary impedance equation of the honeycomb and the nozzle impedance equation, as well as the source term equation of the background mean flow, the impedance value and the dissipation source term are calculated; finally, the impedance value and the dissipation source term are respectively applied to their respective calculation domains, and the optimal structure of the afterburning engine thrust chamber can be obtained through calculation.

Description

Technical Field

[0001] The present invention relates to a method for resistance sound attenuation of a hybrid head, and specifically relates to a calculation method for the acoustic damping characteristics of a hybrid head of a staged combustion engine thrust chamber. Background Art

[0002] When a staged combustion cycle liquid rocket engine is operating, usually high-temperature oxygen-rich or fuel-rich gas is introduced into the thrust chamber of the engine. However, if fuel-rich gas is introduced, due to the relatively high pressure of the high-temperature fuel-rich gas, it is easy to cause the working stability of the rocket engine to deteriorate.

[0003] Currently, to solve this problem, the method adopted is to add a fairing grid before the nozzle, which forms a structure similar to an acoustic liner with the gas nozzle. The fairing grid and the gas nozzle are also called the hybrid head. This structure can dissipate the signals of the first-order (1T) and second-order (2T) tangential vibration modes of the combustion chamber to the maximum extent in the fairing cavity through the gas nozzle, thereby maximizing the stability margin of the staged combustion engine thrust chamber and reducing the probability of high-frequency combustion instability in the thrust chamber. This method is an important engineering suppression measure.

[0004] However, in the process of acoustic damping analysis of the hybrid head structure, for simplicity, only the resistance sound attenuation effect of the hybrid head is considered, and the damping caused by local acoustic-vortex dissipation is not considered, thus ignoring the influence of the background mean flow, resulting in a low accuracy of the analysis results, a large difference between the analysis results and the actual situation, and the analysis data having no reference value. Summary of the Invention

[0005] The present invention provides a calculation method for the acoustic damping characteristics of a hybrid head of a staged combustion engine thrust chamber, which is used to solve the technical problem that the existing acoustic damping calculation method of the hybrid head has low accuracy and a large difference between the analysis results and the actual situation.

[0006] The present invention provides a calculation method for the acoustic damping characteristics of a hybrid head of a staged combustion engine thrust chamber, which is characterized by including the following steps:

[0007] S1. According to the structural parameters of the gas flow channel of the hybrid head of the staged combustion engine thrust chamber, extract the geometric blocks of the gas flow channel; the geometric blocks include the fairing grid, nozzle and combustion chamber of the gas flow channel; the structural parameters include the fairing grid aperture, the distance between the central axes of two adjacent holes, the fairing grid height, the nozzle aspect ratio, and the average gas velocity in the combustion chamber;

[0008] S2. Import the geometric blocks described in step S1 into an acoustic solver, and each geometric block automatically becomes an acoustically solvable domain that can be defined separately, and then define the gas parameters in each acoustically solvable domain;

[0009] S3. Based on the rectifying grid boundary impedance equation and the nozzle impedance equation, and combining the gas parameters described in step S2, calculate the rectifying grid boundary impedance value and the nozzle impedance value at any assumed frequency;

[0010] S4. Based on the source term equation of the background mean flow, and combining the average flow velocity of the gas in each geometric block, calculate the dissipation source term of the background mean flow;

[0011] S5. Assign the impedance values obtained in step S3 to the geometric surfaces corresponding to the rectifying grid boundary and the nozzle, and assign the dissipation source terms obtained in step S4 to each acoustic solution domain in step S2; By performing mesh division and solution on each acoustic solution domain, obtain a number of complex frequencies Ω and the corresponding acoustic modes; The real part of the complex frequency Ω represents the natural acoustic frequency under the corresponding acoustic mode, and its imaginary part represents the growth rate of the frequency signal of the corresponding acoustic mode; The acoustic modes include the first-order tangential acoustic mode, the second-order tangential acoustic mode, the first-order longitudinal acoustic mode, and the second-order longitudinal acoustic mode;

[0012] S6. Input the natural acoustic frequency corresponding to each acoustic mode into the acoustic solver, and use the methods in steps S3 to S5 to calculate the new rectifying grid boundary impedance value and the nozzle impedance value under each acoustic mode, as well as the calculated acoustic frequencies under all acoustic modes;

[0013] S7. If the errors between the calculated acoustic frequencies and the natural acoustic frequencies under all acoustic modes do not exceed 1%, then proceed to step S8; Otherwise, replace the assumed frequency in step S3 with the calculated acoustic frequency obtained in step S6, and return to step S3;

[0014] S8. Take the calculated acoustic frequency obtained in step S6 as the corresponding acoustic frequency of this acoustic mode, the new rectifying grid boundary impedance value and the nozzle impedance value obtained in step S6 as the impedance values corresponding to this acoustic mode, and the growth rate of the frequency signal obtained in step S5 as the calculated growth rate;

[0015] S9. Judge the calculated growth rate obtained in step S8. If the growth rate is between -20% and -40%, then the calculation ends, and the optimal structure of the afterburning engine thrust chamber is obtained; Otherwise, modify the structural parameters of the gas flow channel in the mixing head of the afterburning engine thrust chamber, return to step S1 and recalculate until the optimal structure of the afterburning engine thrust chamber is obtained.

[0016] Further, in S3, the rectifying grid boundary impedance equation is:

[0017]

[0018] In equation (1), Z is the impedance value of the rectifying grid boundary; θ is the angle between the sound wave propagation direction and the rectifying grid boundary; is the density of the background mean flow, The speed of sound for the background mean flow; k is the wave number, where ω is the angular frequency; d is the distance between the central axes of two adjacent holes of the rectifying grid; i is a complex number and χ is the transfer coefficient.

[0019] Furthermore, in the equation (1), χ = 2R(γ - iδ), where R is the aperture, γ is the first intermediate coefficient, and its calculation formula is as follows:

[0020]

[0021] δ is the second intermediate coefficient, and its calculation formula is as follows:

[0022]

[0023] where I and K are the Bessel functions of the first and second kind respectively, and the subscript 1 represents the first-order tangential; k c is the corresponding wave number, where, k c = ω / u c , ω is the angular frequency, u c is the average velocity of the background flow; R is the aperture; e is the natural constant; cosh is the hyperbolic cosine function; sinh is the hyperbolic sine function; π is the circumference ratio.

[0024] Furthermore, in S3, the nozzle impedance equation is:

[0025]

[0026] In the equation (2), Z inj is the impedance value of the nozzle; is the density of the background mean flow, is the speed of sound of the background mean flow; e is the natural constant; i is a complex number, and π is the circumference ratio; ω is the angular frequency; ν is the kinematic viscosity; Pr is the Prandtl number; is the average specific heat ratio of the gas.

[0027] Furthermore, the complex speed of sound and the complex density ρ v in the nozzle are respectively:

[0028]

[0029] ρ ν ≡ k v Z inj / ω

[0030] In the formula, ω is the angular frequency; kν is the wave number of the quasi-plane wave, Z inj is the impedance value of the nozzle; the complex speed of sound and the complex density ρ in the nozzlev That is, they are respectively in Equation (2) and

[0031] Furthermore, in S3, the Matlab transcendental equation solver is used for calculation.

[0032] Furthermore, in S4, the source term equation of the background mean flow is as follows:

[0033]

[0034] where the right side of the equation is the source term considering the background flow; in Equation (3), is the density of the mean background flow, is the sound speed of the mean background flow; Ω is the complex frequency, is the pulsating pressure variable; is the gradient operator; i is a complex number and is the average flow velocity of the gas in the acoustic calculation domain to be obtained;

[0035] The acoustic boundary conditions required for solving Equation (3) need to satisfy the following form:

[0036]

[0037] where Z is the boundary impedance value of the straightening grid, and n is the unit normal vector; is the gradient operator;

[0038] The solution of Equation (4) needs to satisfy:

[0039]

[0040] where, is the pulsating pressure variable, is the pulsating velocity variable; i is a complex number and e is the natural constant; Ω is the complex frequency; t is an arbitrary time. is the average pressure of the current environment, is the average flow velocity of the gas in the acoustic calculation domain to be obtained.

[0041] Furthermore, in S2 and S6, the acoustic solver is the Comsol acoustic solver.

[0042] Compared with the prior art, the beneficial effects of the present invention are:

[0043] 1. The calculation method for the acoustic damping characteristics of the mixing head of a staged combustion engine thrust chamber. First, according to the structural parameters of the thrust chamber gas flow channel, the geometric segmentation of the gas flow channel is extracted; then the geometric segmentation is imported into the acoustic solver to obtain the acoustic solution domain of each geometric segmentation; after that, based on the boundary impedance equation of the honeycomb and the nozzle impedance equation, as well as the source term equation of the background mean flow, the impedance value and the dissipation source term are calculated; finally, the impedance value and the dissipation source term are respectively applied to their respective calculation domains, and the optimal structure of the staged combustion engine thrust chamber can be obtained through calculation. The results calculated by this method have high accuracy and are consistent with the structure of the staged combustion engine thrust chamber, and can be used to evaluate the acoustic damping characteristics of the thrust chamber of a staged combustion cycle liquid rocket engine. Based on the principle of maximum damping, the acoustic damping characteristics including the honeycomb, nozzle, and acoustic baffle structures can be optimized.

[0044] 2. The calculation method for the acoustic damping characteristics of the mixing head of a staged combustion engine thrust chamber according to the present invention can, on this basis, construct a more accurate stability analysis model of the staged combustion engine thrust chamber by introducing a combustion response function. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 is a flowchart of an embodiment of the present invention;

[0046] Figure 2 is a three-dimensional view of the mixing head structure of the staged combustion engine thrust chamber in an embodiment of the present invention;

[0047] Figure 3 is a sectional view of the mixing head structure of the staged combustion engine thrust chamber in an embodiment of the present invention; <<

[0048] Figure 4 is a schematic diagram of the honeycomb structure of the staged combustion engine thrust chamber in an embodiment of the present invention;

[0049] Figure 5 is Figure 4 a top view of;

[0050] Figure 6 is the structure diagram calculated in an embodiment of the present invention;

[0051] Figure 7 is the optimized structure diagram obtained in an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0052] The technical solutions of the present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0053] As Figure 1 shown, the present invention provides a calculation method for the acoustic damping characteristics of the mixing head of a staged combustion engine thrust chamber, which specifically includes the following steps:

[0054] S1. Extract the geometric blocks of the gas flow channel in the mixing head of the afterburning engine thrust chamber according to the structural parameters of the gas flow channel. The geometric blocks include the rectifying grid, nozzle, and combustion chamber of the gas flow channel. The structural parameters include the rectifying grid aperture, the distance between the central axes of adjacent holes, the rectifying grid height, the nozzle aspect ratio, and the average flow velocity of the gas in the combustion chamber.

[0055] S2. Import the geometric blocks described in step S1 into the acoustic solver, and each geometric block automatically becomes an independently definable acoustic solution domain, and then define the gas parameters in each acoustic solution domain. The acoustic solver in this embodiment is the Comsol acoustic solver. The gas parameters generally include the total gas flow rate, gas density, flow area, gas density, sound speed, specific heat at constant pressure, and gas constant, etc.

[0056] S3. Based on the rectifying grid boundary impedance equation and the nozzle impedance equation, combined with the gas parameters described in step S2, use the Matlab transcendental equation solver to calculate the rectifying grid boundary impedance value and the nozzle impedance value at any assumed frequency.

[0057] Combined with Figures 2 to 5 As shown, in this embodiment, the rectifying grid boundary impedance equation adopts the Jing-Sun model proposed by Sun Xiaofeng et al. When the background average flow Mach number is high enough, it is approximately considered that the rectifying grid is infinitely thin, thus ignoring the thickness of the rectifying grid. The specific equation is as follows:

[0058]

[0059] In equation (1), Z is the impedance value of the rectifying grid boundary; θ is the angle between the sound wave propagation direction and the rectifying grid boundary; is the density of the average background flow, is the sound speed of the average background flow; k is the wave number, where ω is the angular frequency; d is the distance between the central axes of adjacent holes of the rectifying grid; i is a complex number and χ is the transfer coefficient.

[0060] In equation (1), χ = 2R(γ - iδ), R is the aperture, γ is the first intermediate coefficient, and its calculation formula is as follows:

[0061]

[0062] δ is the second intermediate coefficient, and its calculation formula is as follows:

[0063]

[0064] Among them, I and K are the Bessel functions of the first and second kinds respectively, and the subscript 1 represents the first-order tangential; k c is the corresponding wave number, where, k c = ω / uc , where ω is the angular frequency and u c is the average velocity of the background flow; R is the aperture; e is the natural constant; cosh is the hyperbolic cosine function; sinh is the hyperbolic sine function; π is the pi.

[0065] There are two dissipation mechanisms in the nozzle, viscous dissipation during the perturbation propagation process and acoustic-vortex conversion. When St is much greater than 1, viscous dissipation dominates, and vice versa. In this embodiment, the nozzle impedance equation is as follows:

[0066]

[0067] In Equation (2), Z inj is the impedance value of the nozzle; is the density of the average background flow, is the sound speed of the average background flow; e is the natural constant; i is a complex number, and π is the pi; ω is the angular frequency; ν is the kinematic viscosity; Pr is the Prandtl number; is the average specific heat ratio of the gas.

[0068] The complex sound speed and complex density in the nozzle are respectively:

[0069]

[0070] ρ ν ≡ k v Z inj / ω

[0071] In the formula, ω is the angular frequency; k ν is the wave number of the quasi-plane wave, and Z inj is the impedance value of the nozzle.

[0072] When considering the nozzle impedance, the nozzle impedance is defined by using the complex sound speed and complex density to replace the actual sound speed and density, that is, using the complex sound speed and complex density ρ v in the formula (2) to replace and

[0073] Among them, the calculation formula for the wave number kν of the quasi-plane wave in the nozzle is:

[0074]

[0075] Among them, ω is the angular frequency; is the sound speed of the average background flow; e is the natural constant; i is a complex number, and π is the pi; R is the aperture of the nozzle, ν is the kinematic viscosity; is the average specific heat ratio of the gas, and Pr is the Prandtl number.

[0076] S4. Based on the source term equation of the background mean flow and combining with the average flow velocity of the gas in each geometric block, the dissipation source term of the background mean flow is calculated.

[0077] Specifically, the source term equation of the background mean flow adopted in this step is:

[0078]

[0079] Among them, the right side of the equation is the source term considering the background flow (the source term can also be in other forms); in Equation (3), is the density of the mean background flow, is the sound speed of the mean background flow; Ω is the complex frequency, is the pulsating pressure variable; is the gradient operator; i is a complex number and is the average flow velocity of the gas in the acoustic calculation domain to be obtained.

[0080] The acoustic boundary conditions required for solving Equation (3) need to satisfy the following form:

[0081]

[0082] Among them, Z is the boundary impedance value of the fairing grid. For a solid wall, the impedance Z→∞. For the case where the thrust chamber throat reaches the sound speed, it can be approximately treated as an acoustic rigid boundary; n is the unit normal vector; is the gradient operator.

[0083] The solution of Equation (4) needs to satisfy:

[0084]

[0085] Among them, is the pulsating pressure variable, is the pulsating velocity variable; i is a complex number and e is the natural constant; Ω is the complex frequency; t is an arbitrary time. is the average pressure of the current environment, is the average flow velocity of the gas in the acoustic calculation domain to be obtained. The real part real(Ω)=ω of the complex frequency Ω is the final oscillation frequency (generally close to the natural modal frequency of the thrust chamber); the imaginary part Imag(Ω)=α represents the growth rate of the oscillation frequency signal. A positive value means the signal will be amplified and thus unstable, and vice versa. Under linear conditions, Imag(Ω) can be used to approximately describe the stability or structural damping characteristics of the thrust chamber under the action of different response source terms.

[0086] S5. Assign the impedance values obtained in step S3 to the geometric surfaces corresponding to the rectifying grid boundary and the nozzle, and assign the dissipation source terms obtained in step S4 to each acoustic solution domain in step S2. By performing mesh generation and solution for each acoustic solution domain, a number of complex numbers and corresponding acoustic modes are obtained. The real part of the complex number represents the natural acoustic frequency in this acoustic mode, and its imaginary part represents the growth rate of the frequency signal of this acoustic mode; the acoustic modes include the first-order tangential acoustic mode, the second-order tangential acoustic mode, the first-order longitudinal acoustic mode, and the second-order longitudinal acoustic mode.

[0087] S6. Input the natural acoustic frequency corresponding to each acoustic mode into the acoustic solver, and use the method of steps S3 to S5 to calculate the new rectifying grid boundary impedance value and nozzle impedance value under each acoustic mode, as well as the calculated acoustic frequencies under all acoustic modes. The acoustic solver in this embodiment is the Comsol acoustic solver.

[0088] S7. If the errors between the calculated acoustic frequencies and the natural acoustic frequencies under all acoustic modes do not exceed 1%, then proceed to step S8; otherwise, replace the assumed frequency in step S3 with the calculated acoustic frequency obtained in step S6, and return to step S3.

[0089] S8. Use the calculated acoustic frequency obtained in step S6 as the corresponding acoustic frequency of this acoustic mode, the new rectifying grid boundary impedance value and nozzle impedance value obtained in step S6 as the impedance values corresponding to this acoustic mode, and the growth rate of the frequency signal obtained in step S5 as the calculated growth rate.

[0090] S9. Judge the calculated growth rate obtained in step S8. If the growth rate is between -20% and -40%, the calculation ends, and the optimal structure of the thrust chamber of the staged combustion engine is obtained (as shown in Figure 6 and Figure 7 ); otherwise, modify the structural parameters of the gas flow channel of the mixing head of the thrust chamber of the staged combustion engine, return to step S1 for recalculation until the optimal structure of the thrust chamber of the staged combustion engine is obtained.

[0091] This method is used to evaluate the acoustic damping characteristics of the thrust chamber of a staged combustion cycle liquid rocket engine, and based on the principle of maximum damping, it can optimize the acoustic damping including structures such as the rectifying grid, nozzle, and acoustic baffle.

Claims

1. A calculation method for the acoustic damping characteristics of the mixing head of a afterburning engine thrust chamber, characterized in that It includes the following steps: S1. Extract the geometric blocks of the gas flow channel according to the structural parameters of the gas flow channel in the mixing head of the afterburning engine thrust chamber; the geometric blocks include the flow rectifying grid, nozzle and combustion chamber of the gas flow channel; the structural parameters include the aperture of the flow rectifying grid, the distance between the central axes of two adjacent holes, the height of the flow rectifying grid, the length-diameter ratio of the nozzle, and the average flow velocity of the gas in the combustion chamber; S2. Import the geometric blocks described in step S1 into the acoustic solver, and each geometric block automatically becomes an acoustically solvable domain that can be defined separately, and then define the gas parameters in each acoustically solvable domain; S3. Based on the boundary impedance equation of the flow rectifying grid and the nozzle impedance equation, combined with the gas parameters described in step S2, calculate the boundary impedance value of the flow rectifying grid and the nozzle impedance value at any assumed frequency; S4. Based on the source term equation of the background mean flow, combined with the average flow velocity of the gas in each geometric block, calculate the dissipation source term of the background mean flow; S5. Assign the impedance values obtained in step S3 to the geometric surfaces corresponding to the flow rectifying grid boundary and the nozzle, and assign the dissipation source terms obtained in step S4 to each acoustically solvable domain in step S2. By performing mesh generation and solution on each acoustically solvable domain, several complex frequencies Ω and corresponding acoustic modes are obtained; the real part of the complex frequency Ω represents the natural acoustic frequency in the corresponding acoustic mode, and its imaginary part represents the growth rate of the frequency signal of the corresponding acoustic mode; the acoustic modes include the first-order tangential acoustic mode, the second-order tangential acoustic mode, the first-order longitudinal acoustic mode, and the second-order longitudinal acoustic mode; S6. Input the natural acoustic frequency corresponding to each acoustic mode into the acoustic solver, and use the methods in steps S3 to S5 to calculate the new boundary impedance value of the flow rectifying grid and the nozzle impedance value in each acoustic mode, as well as the calculated acoustic frequencies in all acoustic modes; S7. If the errors between the calculated acoustic frequencies and the natural acoustic frequencies in all acoustic modes do not exceed 1%, go to step S8; Otherwise, replace the assumed frequency in step S3 with the calculated acoustic frequency obtained in step S6, and return to step S3; S8. Take the calculated acoustic frequency obtained in step S6 as the corresponding acoustic frequency of this acoustic mode, the new boundary impedance value of the flow rectifying grid and the nozzle impedance value obtained in step S6 as the impedance values corresponding to this acoustic mode, and the growth rate of the frequency signal obtained in step S5 as the calculated growth rate; S9. Judge the calculated growth rate obtained in step S8. If the growth rate is between -20% and -40%, the calculation ends, and the optimal structure of the afterburning engine thrust chamber is obtained; otherwise, modify the structural parameters of the gas flow channel in the mixing head of the afterburning engine thrust chamber, and return to step S1 until the optimal structure of the afterburning engine thrust chamber is obtained.

2. The calculation method for the acoustic damping characteristics of the mixing head of the afterburning engine thrust chamber according to claim 1, wherein: In S3, the boundary impedance equation of the flow rectifying grid is: In equation (1), Z is the impedance value of the flow rectifying grid boundary; θ is the angle between the sound wave propagation direction and the boundary of the rectifying grid; is the density of the background mean flow, is the sound speed of the background mean flow; k is the wave number, where ω is the angular frequency; d is the distance between the central axes of two adjacent holes of the rectifying grid; i is a complex number and χ is the transfer coefficient.

3. The calculation method for the acoustic damping characteristics of the mixing head of the afterburning engine thrust chamber according to claim 2, wherein: In the said equation (1), χ = 2R(γ - iδ), R is the aperture, and γ is the first intermediate coefficient, and its calculation formula is as follows: δ is the second intermediate coefficient, and its calculation formula is as follows: where I and K are Bessel functions of the first and second kind, respectively, and the subscript 1 denotes the first-order tangential; k c is the corresponding wave number, where k c = ω / u c , ω is the angular frequency, and u c is the mean velocity of the background flow; R is the aperture; e is the natural constant; cosh is the hyperbolic cosine function; sinh is the hyperbolic sine function; and π is the pi constant.

4. The calculation method of the acoustic damping characteristics of the mixing head of the afterburning engine thrust chamber according to claim 3, wherein: In S3, the nozzle impedance equation is: In Equation (2), Z inj is the impedance value of the nozzle; is the density of the background flow, is the speed of sound of the background flow; e is the natural constant; i is a complex number, and π is the pi; ω is the angular frequency; ν is the kinematic viscosity; Pr is the Prandtl number; is the average specific heat ratio of the gas.

5. The calculation method of the acoustic damping characteristics of the mixing head of the afterburning engine thrust chamber according to claim 4, wherein: The complex sonic velocity within the nozzle and the complex density ρ v are respectively: ρ ν ≡k v Z inj / ω In the formula, ω is the angular frequency; k ν is the wave number of the quasi-plane wave, and Z inj is the nozzle impedance value; the complex sound speed and the complex density ρ v in the nozzle are respectively and 6. The calculation method of the acoustic damping characteristics of the mixing head of the afterburning engine thrust chamber according to claim 5, wherein: In S3, Matlab transcendental equation solver is used for calculation.

7. The calculation method of the acoustic damping characteristics of the mixing head of the afterburning engine thrust chamber according to claim 1, wherein: In S4, the source term equation of the background mean flow is: where the right side of the equation is the source term considering the background flow; in Equation (3), is the density of the average background flow, is the sound speed of the average background flow; Ω is the complex frequency, is the pulsating pressure variable; ▽ is the gradient operator; i is a complex number and is the average flow velocity of the gas in the acoustic calculation domain to be obtained. The acoustic boundary conditions required for solving equation (3) need to satisfy the following form: where Z is the boundary impedance value of the flow straightener, n is the unit normal vector; ▽ is the gradient operator; The solution of equation (4) needs to satisfy: Among them, is the pulsating pressure variable, is the pulsating velocity variable; i is a complex number and e is the natural constant; Ω is the complex frequency; t is any time, is the average pressure of the current environment, is the average flow velocity of the gas in the acoustic calculation domain to be obtained.

8. The calculation method of the acoustic damping characteristics of the mixing head of the afterburning engine thrust chamber according to any one of claims 1-7, wherein: In S2 and S6, the acoustic solver is the Comsol acoustic solver.

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