CN114636169B - Flame stabilizer perforation parameter determination method and device and radial flame stabilizer - Google Patents

Flame stabilizer perforation parameter determination method and device and radial flame stabilizer Download PDF

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CN114636169B
CN114636169B CN202210157808.5A CN202210157808A CN114636169B CN 114636169 B CN114636169 B CN 114636169B CN 202210157808 A CN202210157808 A CN 202210157808A CN 114636169 B CN114636169 B CN 114636169B
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radial
flame stabilizer
radial flame
afterburner
acoustic
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CN114636169A (en
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王晓宇
沈梓涵
孙晓峰
张光宇
杜林�
孙大坤
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Beihang University
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F23—COMBUSTION APPARATUS; COMBUSTION PROCESSES
    • F23R—GENERATING COMBUSTION PRODUCTS OF HIGH PRESSURE OR HIGH VELOCITY, e.g. GAS-TURBINE COMBUSTION CHAMBERS
    • F23R3/00—Continuous combustion chambers using liquid or gaseous fuel
    • F23R3/02—Continuous combustion chambers using liquid or gaseous fuel characterised by the air-flow or gas-flow configuration
    • F23R3/16—Continuous combustion chambers using liquid or gaseous fuel characterised by the air-flow or gas-flow configuration with devices inside the flame tube or the combustion chamber to influence the air or gas flow
    • F23R3/18—Flame stabilising means, e.g. flame holders for after-burners of jet-propulsion plants

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Abstract

The disclosure provides a method and a device for determining perforation parameters of a flame stabilizer and a radial flame stabilizer. The method comprises the following steps: acquiring an acoustic response function of the radial flame stabilizer component to the circumferential modal wave; acquiring a thermoacoustic stability model of the afterburner based on the acoustic response function; presetting a plurality of groups of optimization parameters for any radial flame stabilizer, and respectively substituting the groups of optimization parameters into the thermoacoustic stability model; solving oscillation frequencies corresponding to circumferential modes in the thermoacoustic stability model, and judging whether the radial flame stabilizer component can control thermoacoustic instability of the afterburner or not according to solving results corresponding to each group of optimization parameters; when the imaginary part of the obtained oscillation frequency is less than zero, the radial flame stabilizer component can control the thermoacoustic instability of the afterburner; and obtaining perforation parameters of the flame stabilizer according to the optimization parameters corresponding to the flame stabilizer capable of controlling the thermoacoustic instability of the afterburner.

Description

Flame stabilizer perforation parameter determination method and device and radial flame stabilizer
Technical Field
The disclosure relates to the technical field of aircraft engines, in particular to a method and a device for determining perforation parameters of a flame stabilizer and a radial flame stabilizer.
Background
Combustion instability problems are widely present in various combustion power systems, and when instability problems occur, the coupling of unsteady heat release and the system sound field can generate large pressure pulsations of one or more frequencies, forming thermoacoustic oscillations. When combustion occurs in the form of a flame, the unsteady heat release at the flame is in phase with the acoustic waves or less than ninety degrees in phase, which converts the thermal energy into acoustic energy. When the acoustic dissipation of the system is smaller than the energy addition of the thermoacoustic energy, the acoustic energy is accumulated continuously, so that the pressure pulsation amplitude is increased continuously until the thermoacoustic oscillation reaches saturation under a nonlinear mechanism. Thus, in the case of power plants, thermoacoustic oscillations can cause oscillations in their output power or thrust, in severe cases also ablating the combustion chamber, eventually leading to system failure.
Disclosure of Invention
In view of the problems in the prior art, embodiments of the present disclosure provide a method and an apparatus for determining perforation parameters of a flame stabilizer, and a flame stabilizer, so as to effectively suppress the thermoacoustic oscillation that may occur in an afterburner.
In one aspect, some embodiments of the present disclosure provide a method of determining a flame holder perforation parameter, the method of determining a flame holder perforation parameter being applicable to a radial flame holder in an afterburner; the inner wall of the afterburner is provided with a radial flame stabilizer assembly, the radial flame stabilizer assembly comprises a plurality of radial flame stabilizers with the same structure, the radial flame stabilizers are uniformly arranged along the circumferential direction of the inner wall of the afterburner, and each radial flame stabilizer is provided with a plurality of through holes. The method for determining the perforation parameter of the flame stabilizer comprises S10-S50.
S10, establishing an acoustic response function of the radial flame stabilizer assembly to the circumferential modal wave, and obtaining the acoustic response function of the radial flame stabilizer assembly to the circumferential modal wave.
And S20, acquiring a thermoacoustic stability model of the afterburner based on the acoustic response function.
And S30, presetting a plurality of groups of optimizing parameters for any radial flame stabilizer, and substituting the plurality of groups of optimizing parameters into the thermoacoustic stability model respectively.
S40, solving oscillation frequencies corresponding to the circumferential modes in the thermoacoustic stability model, and judging whether the radial flame stabilizer component can control thermoacoustic instability of the afterburner or not according to solving results corresponding to each group of optimization parameters; and when the imaginary part of the oscillation frequency obtained by solving is less than zero, the radial flame stabilizer component can control the thermoacoustic instability of the afterburner.
S50, obtaining perforation parameters of the flame stabilizer according to the optimization parameters corresponding to the flame stabilizer capable of controlling the thermoacoustic instability of the afterburner.
In the flame stabilizer perforation parameter determination method provided by some embodiments of the present disclosure, in a case where a perforation design is performed on a radially distributed surface of a radial flame stabilizer, a preset optimization parameter is applied to a thermoacoustic stability model of an afterburner, the thermoacoustic stability model obtained based on an acoustic response function is solved to obtain an oscillation frequency corresponding to a circumferential mode corresponding to each set of optimization parameter, and if an imaginary part of the oscillation frequency corresponding to the circumferential mode is smaller than zero, a radial flame stabilizer component can control thermoacoustic instability of the afterburner. And then, by acquiring perforation parameters corresponding to the optimization parameters, such as the perforation rate and the perforation radius, the perforation parameters of the radial flame stabilizer can be determined. The perforation parameters determined by the method for determining the perforation parameters of the flame stabilizer are applied to the radial flame stabilizer, and the perforation can provide additional dissipation and phase change effects for the circumferential pipeline mode, so that the final oscillation frequency and growth rate of the whole thermoacoustic system corresponding to the circumferential mode oscillation are influenced, and the thermoacoustic instability of the afterburner is controlled.
In another aspect, a flame holder penetration parameter determination apparatus is provided, adapted for use with a radial flame holder in an afterburner; the inner wall of afterburner is provided with radial flame holder subassembly, and radial flame holder subassembly includes the same radial flame holder of a plurality of structures, and a plurality of radial flame holders evenly arrange along afterburner's inner wall's circumference, and every radial flame holder has a plurality of perforation. The flame holder penetration parameter determining apparatus includes:
an acquisition module configured to: acquiring an acoustic response function of the radial flame stabilizer component to the circumferential modal wave and a thermoacoustic stability model of the afterburner;
the preset module is connected with the acquisition module and is configured to: presetting a plurality of groups of optimizing parameters for any radial flame stabilizer; wherein, a plurality of groups of optimizing parameters are used for substituting into the thermoacoustic stability model;
the judgment module connected with the acquisition module and the presetting module is configured to: solving oscillation frequencies corresponding to circumferential modes in the thermoacoustic stability model, and judging whether the radial flame stabilizer component can control thermoacoustic instability of the afterburner or not according to solving results corresponding to each group of optimization parameters; when the imaginary part of the obtained oscillation frequency is less than zero, the radial flame stabilizer component can control the thermoacoustic instability of the afterburner;
a puncturing parameter determination module connected with the determination module and configured to: and obtaining perforation parameters of the flame stabilizer according to the optimization parameters corresponding to the flame stabilizer capable of controlling the thermoacoustic instability of the afterburner.
In yet another aspect, a computer readable storage medium is provided having computer program instructions stored therein which, when executed by a processor of a user equipment, cause the user equipment to perform the flame holder penetration parameter determination method of any of the embodiments described above.
In a further aspect, there is provided a radial flame holder provided with a plurality of perforations, the perforation parameter of the plurality of perforations being determined by the flame holder perforation parameter determination method of any of the embodiments described above.
In yet another aspect, an engine is provided that includes the radial flame holder of the above embodiments.
In yet another aspect, an aircraft is provided, comprising the radial flame holder of the above embodiment, or the engine of the above embodiment.
Drawings
The accompanying drawings, which are included to provide a further understanding of the disclosure and are incorporated in and constitute a part of this specification, illustrate exemplary embodiments of the disclosure and together with the description serve to explain the principles of the disclosure.
FIG. 1 is a schematic structural diagram of a circumferential corrugated plate cooling screen of an afterburner;
FIG. 2 is a blade row model schematic view of a radial flame holder, according to some embodiments;
FIG. 3 is a graphical illustration of the optimization of a perforation parameter as an optimization parameter in a flame holder perforation parameter determination method according to some embodiments;
FIG. 4 is a graphical illustration of the results of optimizing the acoustic impedance of a radial flame holder as an optimization parameter in a flame holder penetration parameter determination method according to some embodiments.
Detailed Description
The present disclosure will be described in further detail with reference to the drawings and embodiments. It is to be understood that the specific embodiments described herein are merely illustrative of the relevant matter and not restrictive of the disclosure. It should be further noted that, for the convenience of description, only the portions relevant to the present disclosure are shown in the drawings.
It should be noted that the embodiments and features of the embodiments in the present disclosure may be combined with each other without conflict. To avoid repetition, corresponding features and advantages of the apparatus and the method of determining flame holder penetration parameters may be referenced to one another.
It should be noted that, the step numbers in the text are only for convenience of explanation of the specific embodiments, and do not serve to limit the execution sequence of the steps.
The method for determining the perforation parameter of the flame holder provided by some embodiments of the present disclosure can be executed by a relevant processor, and the processor is taken as an example of an execution subject in the following description. The execution subject can be adjusted according to a specific case, such as a server, an electronic device, a computer, and the like.
The present disclosure will be described in detail below with reference to the accompanying drawings in conjunction with embodiments.
As discussed in the background, combustion instability problems are widely present in various combustion power systems. In an aero gas turbine engine with an afterburner, the combustion instability phenomenon often occurs due to the fact that the flow structure inside the afterburner is complex and the combustion energy density is high. In general, the afterburner body flow boundary is a circular tube with an annular or undulating heat shield with cooling holes disposed inside the outer wall of the tube. In the related art, this heat shield and the outer rigid wall form a structure with a non-locally reactive acoustic liner with a back cavity that creates a boundary condition of impedance at the outer boundary of the combustion chamber. By designing the heat shield, and particularly the heat shield cooling hole openings, suitable acoustic dissipation can be introduced to suppress most of the low frequency combustion instability phenomena.
Under the geometric constraints of the duct, the acoustic field oscillating inside the afterburner chamber appears in the form of a duct mode wave. When the position of the steady flame is fixed, thermoacoustic oscillation pressure pulsation corresponding to different frequencies may occur corresponding to the circumferential and radial modal numbers of different pipeline modal waves. The corresponding pure radial mode with zero circumferential mode number has lower acoustic mode cut-off frequency, and the acoustic energy is mainly transmitted along the radial direction, so that the acoustic mode can fully act with the dissipation structure of the heat shield to form enough damping to inhibit thermoacoustic oscillation. However, for the rotational mode with the number of circumferential modes different from zero, the cut-off frequency is relatively higher, and the sound energy transmission direction has obvious circumferential components, and a glancing incidence condition exists relative to the heat shield.
Illustratively, as shown in fig. 1, fig. 1 is a schematic structural diagram of a circumferential corrugated plate cooling screen 1 of an afterburner, and through reasonable design of the layout of cooling holes on the corrugated plate cooling screen 1 and the shape of corrugations, suitable sound dissipation and acoustic boundary conditions can be provided, and occurrence of a thermo-acoustic instability phenomenon in the afterburner can be inhibited. The technical scheme is equivalent to inhibiting thermoacoustic oscillation by adopting dissipation boundaries distributed along the circumferential direction, and the dissipation effect on the circumferential rotation mode is poor.
Thus, even with the presence of a heat shield or cooling shield 1 dissipation mechanism, combustion instabilities at higher frequencies than conventional purely radial mode thermoacoustic oscillations may still be formed in the afterburner. Once large-amplitude pressure pulsation is generated after the combustion instability of the afterburner, a series of consequences can be caused, such as failure of air film cooling and ablation of a component structure; combustion instability leads to oscillation of the thrust curve; the flame-connecting effect among different flame zones is influenced, so that flame-connecting failure is caused, the thrust of the engine does not reach the standard, and the like. Besides affecting the normal use of the engine, the engine can be directly disabled seriously, and safety accidents are caused.
Therefore, the circumferentially distributed sound dissipation structure formed by the heat shield and the cooling holes on the surface of the heat shield has a good sound dissipation effect on pure radial mode and axial mode, and the problem of thermoacoustic oscillation of the radial mode can be effectively inhibited in practical application. However, with the progress of the ignition mode and the combustion organization form of the afterburner, the distance between the igniter and the flame stable combustion position is relatively shortened, so that the response time of flame to disturbance is gradually reduced, the thermoacoustic frequency is gradually increased, and the system starts to generate a mode vibration mode in the circumferential direction. For the rotating pipeline mode with circumferential sound propagation components and non-zero circumferential mode number, due to the addition of the circumferential components, the sound wave vector and the surface of the heat shield are in an obvious grazing incidence relation, so that only the sound energy near the outer wall of the pipeline can be effectively dissipated, and the high-frequency thermoacoustic oscillation corresponding to the circumferential pipeline sound mode is difficult to suppress.
In addition, the conventional noise reduction structure represented by an acoustic liner cannot withstand a high-temperature environment in an afterburner, is difficult to be directly popularized to the afterburner, and cannot effectively suppress a rotational mode wave by using the acoustic liner structure or the helmholtz resonator structure.
The inventors have found through research that in addition to the heat shield, another possible arrangement of the sound dissipative surface within the afterburner is the flame holder responsible for the combustion of the tissue. And as the turbine outlet temperature increases, the flame stabilizer also needs to be designed with a certain cooling. In order to facilitate the introduction of the cooling air flow while simultaneously taking into account the compactness of the structure, the flame holders of the engine may be arranged radially. Based on this, some embodiments of the present disclosure provide a method and an apparatus for determining perforation parameters of a flame holder, and a flame holder, in which through an acoustic optimization design of perforations on a surface of a radial flame holder, a radially distributed sound dissipation surface can be directly provided in an afterburner, and the surface can directly act on a circumferentially propagating sound wave, so that a problem of possible thermoacoustic oscillation of a circumferentially rotating pipe mode can be effectively suppressed.
Some embodiments of the present disclosure provide a flame holder perforation parameter determination method suitable for a radial flame holder in an afterburner; the inner wall of the afterburner is provided with a radial flame stabilizer assembly, the radial flame stabilizer assembly comprises a plurality of radial flame stabilizers with the same structure, the radial flame stabilizers are uniformly arranged along the circumferential direction of the inner wall of the afterburner, and each radial flame stabilizer is provided with a plurality of through holes. The method for determining the perforation parameter of the flame stabilizer comprises S10-S50.
S10, establishing an acoustic response function of the radial flame stabilizer assembly to the circumferential modal wave, and obtaining the acoustic response function of the radial flame stabilizer assembly to the circumferential modal wave.
And S20, acquiring a thermoacoustic stability model of the afterburner based on the acoustic response function.
And S30, presetting a plurality of groups of optimizing parameters for any radial flame stabilizer, and substituting the plurality of groups of optimizing parameters into the thermoacoustic stability model respectively.
S40, solving oscillation frequencies corresponding to the circumferential modes in the thermoacoustic stability model, and judging whether the radial flame stabilizer component can control thermoacoustic instability of the afterburner or not according to solving results corresponding to each group of optimization parameters; and when the imaginary part of the oscillation frequency obtained by solving is less than zero, the radial flame stabilizer component can control the thermoacoustic instability of the afterburner.
S50, obtaining perforation parameters of the flame stabilizer according to the optimization parameters corresponding to the flame stabilizer capable of controlling the thermoacoustic instability of the afterburner.
In the flame stabilizer perforation parameter determination method provided by some embodiments of the present disclosure, in a case where a perforation design is performed on a radially distributed surface of a radial flame stabilizer, a preset optimization parameter is applied to a thermoacoustic stability model of an afterburner, the thermoacoustic stability model obtained based on an acoustic response function is solved to obtain an oscillation frequency corresponding to a circumferential mode corresponding to each set of optimization parameter, and if an imaginary part of the oscillation frequency corresponding to the circumferential mode is smaller than zero, a radial flame stabilizer component can control thermoacoustic instability of the afterburner. And then, the perforation parameters of the radial flame stabilizer can be determined by acquiring the perforation parameters corresponding to the optimization parameters, such as the perforation rate and the perforation radius. The perforation parameter determined by the perforation parameter determination method of the flame stabilizer is applied to the radial flame stabilizer, and the perforation can provide additional dissipation and phase change effects for the circumferential pipeline mode, so that the final oscillation frequency and growth rate of the circumferential mode oscillation corresponding to the whole thermoacoustic system are influenced, and the thermoacoustic instability of the afterburner is controlled. For the circumferential pipeline modal wave, the wave vector, namely the propagation direction of the wave front, has an obvious circumferential component, so that the influence of the acoustic soft wall surface formed by the traditional circumferentially distributed outer wall surface cooling screen structure on the circumferential modal wave is limited, and the acoustic soft wall surface can only directly act on the acoustic energy near the wall surface. For radially distributed acoustically soft walls provided by the radial flame holder assembly, particularly at acoustic frequencies near cut-off, the wave vector of the circumferential modal wave is nearly normal to the normal incidence perforated surface, thereby nearly enabling the full spatial acoustic energy to interact with the perforated surface of the radial flame holder assembly surface; meanwhile, the radial flame stabilizer which determines the perforation parameters by applying the method for determining the perforation parameters of the flame stabilizer can obviously dissipate the sound energy of the circumferential modal waves in combination with the sound dissipation brought by the sound vortex energy conversion generated by the shedding of the wake vortexes of the radial flame stabilizer, so that the heat acoustic oscillation caused by the circumferential modal waves can be effectively controlled.
Optionally, the perforation parameter may be used as a preset optimizing parameter. The perforation parameters may be perforation rate and perforation radius. Perforation ratio alpha H In practical application, the flow loss caused by perforation to the main flow cannot be too large in consideration of efficiency, and it is more suitable to preset the value and tour in the range of 0-0.2 or 0-0.1. If too small, the perforation radius R can cause clogging, and if too large, the nature of the local acoustic response can be lost. The perforation radius R can therefore be preset in the order of millimetres, for example between 0.5mm and 10mm.
In addition, the acoustic impedance of the radial flame holder assembly can be used as an optimization parameter, and the acoustic impedance can be functionally related to the perforation parameter through a Kooi impedance model. The process of deriving the perforation parameters (perforation rate and perforation radius) from the acoustic impedance of the radial flame stabilizer assembly according to the Kooi impedance model can be referred to in the prior art and will not be described herein.
In some embodiments, prior to step S10, the method of determining flame holder penetration parameters further comprises: s1, establishing an acoustic response function of the radial flame stabilizer component to the circumferential modal wave.
The process of establishing the acoustic response function of the radial flame stabilizer to the circumferential mode wave using the perforation parameter as the predetermined optimization parameter and the acoustic impedance of the radial flame stabilizer assembly as the optimization parameter will be described in detail below.
The radial flame stabilizer structure in the afterburner can be simplified into a blade row form which is shown in fig. 2 and is distributed in a circular tube in a circumferential periodic mode, and when the sound wave frequency is not too high (below 1000 Hz), the influence of the thickness of the blade row on sound propagation can be ignored. Recording the radius of the outer wall of the afterburner pipeline as R d The boundary radius of the hollow range at the tip of the radial flame stabilizer, namely the center of the pipeline is R h . Assuming that the average main flow in the pipeline is an axial uniform main flow, the flow can be in a pressure and isentropic manner, the flow Mach number is M, and the average density is rho 0 Average sound velocity of c 0 Under the online assumption, the idea of an equivalent distribution source is applied without considering the main flow viscosity, and a dipole sound source on the surface of the radial flame stabilizer assembly, namely a secondary scattering sound field generated by an unsteady load under the incident disturbance of sound waves, can be expressed as a first relation by using a generalized Lighthill formula:
Figure GDA0003898607680000071
in the first relation, the first and second relations are different,
Figure GDA0003898607680000072
a secondary scattered acoustic field generated by unsteady loading of the radial flame holder surfaces;
Figure GDA0003898607680000073
three-dimensional coordinates of the observation point;
t is the time of the observation point;
g is a Green function in the rigid-wall pipeline under the uniform axial average main flow condition;
t is the integration time of a Green function method, and is an intermediate variable;
tau is the source point time and is an intermediate variable;
s (tau) is a source point integral surface corresponding to a Green function method;
y i the coordinate of the source point coordinate system is taken as an intermediate variable;
ΔP s an unsteady load distribution for the radial flame holder assembly surface;
Figure GDA0003898607680000081
and integrating the surface element for the source point corresponding to the Green function method.
Ignoring the relatively minor monopole and quadrupole source terms, the response of the radial flame holder assembly to sound wave incidence can be fully described by the equation above,
Figure GDA0003898607680000082
which is an expression for the secondary diffuse sound field produced by the radial flame holder assembly. Substituting a Green function of the rigid-wall pipeline into the first relational expression and adopting e -iωt The radial flame stabilizer produces a secondary diffuse sound field that satisfies a second relationship:
Figure GDA0003898607680000083
in the second relation, the first relation is that,
Figure GDA0003898607680000084
omega is oscillation frequency or incident disturbance frequency;
v is the number of radial flame stabilizers in the radial flame stabilizer assembly;
q is a circumferential modal series summation index, q =8230, q is-3, -2, 1,0,1,2,3, \8230, and q is an intermediate variable;
n is the number of the radial modes of the pipeline in the calculation process;
m is the number of the circumferential modes of the pipeline in the calculation process, and m = m in -qV；
m in The number of circumferential modes of incident sound waves;
φ m (k mn r) is a pipeline radial characteristic function;
r is a radial coordinate/direction axis of the observation point cylindrical coordinate system and is a middle variable;
k mn the characteristic value of the pipeline is taken as the characteristic value,
Figure GDA0003898607680000085
k 0 the number of waves is the number of corresponding waves,
Figure GDA0003898607680000086
c 0 is the average sound velocity of the average main flow in the pipeline;
m is the axial flow Mach number of the average main flow in the pipeline;
beta is a Prandtl-Glauert coefficient,
Figure GDA0003898607680000087
Figure GDA0003898607680000089
a circumferential coordinate/direction axis of the observation point cylindrical coordinate system is taken as an intermediate variable;
z is an axial coordinate/direction axis of the observation point cylindrical coordinate system and is an intermediate variable;
r' is a radial coordinate/direction axis of a source point column coordinate system and is a middle variable;
Figure GDA0003898607680000088
a circumferential coordinate/direction axis of a source point cylindrical coordinate system is taken as an intermediate variable;
z' is the axial coordinate/direction axis of the source point cylindrical coordinate system and is an intermediate variable;
h (x) is a Heaviside function,
Figure GDA0003898607680000091
α 1 the axial wave number of the sound wave transmitted after the pipeline modal sound wave/transmitted downstream is obtained;
α 2 as pipe modal soundThe axial wave number of the acoustic wave propagating forward/upstream;
the axial wave number of the corresponding pipeline modal sound wave meets a third relation:
Figure GDA0003898607680000092
the acoustic soft boundary of the perforated surface of the radial flame stabilizer is described by adopting an acoustic admittance model, so that the volume flow Q in a single small hole on the surface of any radial flame stabilizer and the pressure difference between the two sides, namely the local unsteady load distribution delta P s Can be represented by the acoustic admittance K R Expressed as a fourth relation:
Figure GDA0003898607680000093
in the fourth relation, ρ 0 Is the average density of the average main flow in the pipeline;
q is the volume flow in a single perforation of the surface of the radial flame stabilizer.
And (3) carrying out area averaging on the volume flow in a single perforation, then:
under the condition that the perforation parameter is taken as the preset optimizing parameter, the physically allowed actual normal penetration speed corresponding to the acoustic soft wall surface of the radial flame stabilizer assembly meets a fifth relational expression:
Figure GDA0003898607680000094
in the fifth relation, α H The open porosity of the perforations;
r is the radius of the perforation.
Under the condition that the acoustic impedance of the radial flame stabilizer is taken as an optimization parameter, the physically allowed actual normal penetration speed corresponding to the acoustic soft wall surface of the radial flame stabilizer assembly meets a tenth relational expression:
Figure GDA0003898607680000095
in the tenth relationship, Z is the acoustic impedance of the radial flame holder.
Note the first incident sound wave p i1 And a second incident sound wave p i2 The normal acoustic particle velocity generated on the surface of the radial flame stabilizer component is v d Scattered acoustic field formed by unsteady loads
Figure GDA0003898607680000096
Corresponding to a normal acoustic particle velocity of
Figure GDA0003898607680000097
The velocity boundary condition satisfied at the acoustically soft boundary of the radial flame holder assembly surface is a sixth relationship:
Figure GDA0003898607680000098
wherein v is d As can be found from the known incident sound wave,
Figure GDA0003898607680000099
and unsteady load distribution Δ P s The linear relation is formed between the two groups of the material,
Figure GDA0003898607680000101
then, the scattering sound field expression is combined with the circumferential momentum equation to obtain an analytic expression, and the analytic expression is equal to delta P s Are directly related.
Figure GDA0003898607680000102
Satisfies the seventh relation:
Figure GDA0003898607680000103
wherein alpha is 3 ＝ω/(Mc 0 )；
U is the axial flow velocity of the average main flow in the pipe.
Thus, the velocity boundary is conditioned to be unknown Δ P s The integral equation of (1). The local acoustic admittance value of the blade is set to be infinite at the hollow position of the center of the pipeline so as to approach the condition of a free interface in the fluid. And (3) applying a finite radial expansion method to process the convergence and singularity of infinite series, namely expanding the pipeline radial characteristic function by using a finite circumferential infinite order Bessel function to obtain an eighth relational expression:
Figure GDA0003898607680000104
in the eighth relational expression, BB is a finite radial modal expansion coefficient;
Figure GDA0003898607680000105
is a peripheral infinite Bessel function.
Under the condition that the perforation parameters are used as preset optimizing parameters, the fifth relational expression and the seventh relational expression are substituted into the sixth relational expression to obtain an integral equation; alternatively, in the case where the acoustic impedance of the radial flame holder assembly is used as the optimization parameter, the integral equation is obtained by substituting the tenth relation and the seventh relation into the sixth relation. And solving an integral equation by adopting a point matching method to obtain the distribution of the unsteady load on the surface of the radial flame stabilizer component under the incident condition of the sound waves.
Substituting the obtained distribution of the unsteady loads of the surface of the radial flame stabilizer component into a second relational expression to obtain a secondary scattered sound field generated by the unsteady loads of the surface of the radial flame stabilizer component
Figure GDA0003898607680000106
The incident sound field is a superposition of a plurality of orthogonal pipe acoustic modes, wherein the spatial distribution of each mode satisfies a ninth relation:
Figure GDA0003898607680000107
in the ninth relational expression, the first and second expression,
Figure GDA0003898607680000108
is an incident sound field;
A mn is the modal amplitude coefficient under the incident sound wave coaxial mode.
Superposing the secondary scattering sound field with the incident sound field to obtain a transmission sound field
Figure GDA0003898607680000109
The reflected sound field is equal to the distribution of the scattered sound waves with the same modal axial propagation direction, namely
Figure GDA00038986076800001010
Here, if the incident sound wave is a backward (downstream) sound wave, the forward sound field reflected by the radial flame holder to the front of the radial flame holder position corresponds to a reflected sound wave, and the backward sound field transmitted through the radial flame holder position corresponds to a transmitted sound wave. The opposite is true if the incident sound wave is a forward (upstream) sound wave.
Therefore, the acoustic response function of the radial flame stabilizer component to the circumferential modal wave is obtained, and the response function is established on a full three-dimensional model and directly comprises three-dimensional effects such as radial interaction, pipeline geometry and the like.
Then, based on the acoustic response function, a thermoacoustic stability model of the afterburner can be obtained.
A mode of combining the acoustic response function directly with the thermoacoustic stability model is to rewrite the acoustic response function of the radial flame stabilizer assembly into a transfer unit form, namely to directly reflect the relation between the amplitude coefficients of an incident mode wave and an emergent mode wave in a matrix form. The scattering relation among the acoustic modes expressed in the form of a linear equation set of a radial flame stabilizer assembly unit (a unit corresponds to one component unit in a transfer unit method, and refers to a unit of a cascade whole body consisting of a circle of radial flame stabilizer blades uniformly arranged in the circumferential direction) can be obtained by combining the acoustic response function with the continuous sound pressure condition of the upstream surface, the continuous sound pressure condition of the downstream surface and the continuous axial sound particle velocity condition of the radial flame stabilizer, and a coefficient matrix in the scattering relation is not changed along with the position of the radial flame stabilizer unit. The obtained coefficient matrix and the coefficient matrixes of other units, such as units of a circumferential cooling screen, a rigid-wall pipeline and the like, are combined together according to the position relationship, and then a flame surface model is combined, and appropriate boundary conditions are given to the inlet and the outlet of the afterburner, so that a larger linear equation system for finally describing the acoustic properties of the whole thermoacoustic system can be obtained. By solving the characteristic value problem of the oscillation frequency of the system, the final complex oscillation frequency of different modes can be obtained.
In the case that the acoustic response function of the radial flame stabilizer assembly to the circumferential modal wave is obtained, the above specific derivation process of obtaining the thermoacoustic stability model of the afterburner according to the acoustic response function may refer to the prior art, and the details of the disclosure are not repeated herein.
In short, at the end of the establishment of the thermoacoustic stability model, a closed linear equation system with the acoustic wave modal amplitude as a coefficient is finally established by the boundary condition, and can be written as
X(ω)P＝0
Where X (ω) is a coefficient matrix containing the parameter ω (i.e., the oscillation frequency or the incident disturbance frequency), and a portion (sub-matrix) of the matrix is the previously obtained acoustic response function of the radial flame holder assembly to the circumferential modal wave. And P is a vector formed by modal amplitude coefficients of all the acoustic modes to be determined. In order for the equation to have a non-trivial solution, the determinant of the coefficient matrix of the linear equation must be equal to zero, i.e.
det|X(ω)|＝0
Solving the equation (namely solving the characteristic value problem) about the complex unknown number omega with the determinant being in a zero form can obtain the final oscillation frequency, and judging whether the thermoacoustics of the afterburner is stable or not and the stability degree according to the size of the imaginary part of the oscillation frequency.
Wherein the real part of the oscillation frequency represents a circumferential modeThe time frequency of the state thermoacoustic oscillation, and the imaginary part represents the growth rate of the thermoacoustic oscillation; at e -iωt If the positive and imaginary parts are obtained, the amplitude of thermoacoustic oscillation continuously increases along with the time, and the radial flame stabilizer cannot control the thermoacoustic instability of the afterburner corresponding to the instability of the thermoacoustic mode, which belongs to the condition that needs to be avoided as much as possible; if the negative imaginary part is obtained, the amplitude value of the thermoacoustic oscillation is continuously reduced along with the increase of time, namely the thermoacoustic oscillation is effectively controlled, and the radial flame stabilizer can control the thermoacoustic instability of the afterburner and belongs to the stable combustion state.
The magnitude of the growth rate (i.e., the absolute value of the imaginary part of the oscillation frequency) may also characterize the suppression of thermoacoustic oscillations corresponding to the circumferential mode. That is, the larger the absolute value of the negative imaginary part of the oscillation frequency is, the better the control effect of the thermo-acoustic instability phenomenon is.
Therefore, under the condition that other geometric conditions of the afterburner are not changed, multiple groups of preset optimization parameters can be respectively applied to the obtained thermoacoustic stability models, and the value of the imaginary part of the oscillation frequency is obtained through solving. And respectively evaluating the control effect of the thermo-acoustic instability phenomenon corresponding to each group of optimization parameters according to the value of the imaginary part of the oscillation frequency corresponding to each group of optimization parameters, namely optimizing the perforation parameters or the acoustic impedance of the radial flame stabilizer component, selecting the preset parameters with better thermo-acoustic instability control effect, and obtaining the perforation parameters of the flame stabilizer according to the preset parameters.
In one example, afterburner duct outer wall radius R d =0.5m, afterburner pipe inner wall radius R h And =0.0m, the pipe is a circular pipe, and the perforations in each radial flame holder are uniformly distributed on the surface of the whole radial flame holder, that is, the perforation rate and the perforation radius at each position are the same. The preset perforation radius is R =10mm, and the perforation rate is alpha H And (3) taking a plurality of preset values in the range of 0-0.2, applying different perforation radius and perforation rate combinations to the thermoacoustic stability model, and solving the oscillation frequency. Here, the porosity is represented by H Traversing optimization is carried out within the range of 0-0.2, and the obtained growth rateThe imaginary part of (c) as a function of the puncture rate is shown in fig. 3. It can be seen that the corresponding predetermined perforation radius is R =10mm, at the perforation rate α H At 0.01, there are perforation parameters for which the thermoacoustic stability is optimal, i.e. R =10mm, α H ＝0.01。
Similarly, the perforation radius R can be preset to be 3mm, 5mm, 7mm and the like, and the perforation ratio alpha can be respectively set H Traversing optimization is carried out within the range of 0-0.2, the change of the imaginary part of the growth rate along with the perforation rate is obtained, finally, the optimal perforation radius and perforation rate combination is selected according to the numerical value of the growth rate, and the perforation parameter is used as the design parameter of the radial flame stabilizer of the practical engine.
In another example, afterburner duct outer wall radius R d =0.5m, afterburner pipe inner wall radius R h =0.0m, the duct is a circular tube, and the perforations in each radial flame holder are uniformly distributed on the surface of the entire radial flame holder, that is, the impedance of the surface of the radial flame holder is uniformly distributed. Taking the acoustic impedance of the radial flame stabilizer assembly as a preset parameter, and adjusting the dimensionless acoustic impedance value z nor Go through traversal optimization (z) nor ＝Z/ρ 0 c 0 ) The obtained results are shown in FIG. 4. But since perforated radial flame holders generally do not provide negative impedance, optimization occurs in the first quadrant, thereby determining the value of the dimensionless acoustic impedance of the target radial flame holder assembly as z nor =0.6+0.0i. And substituting the acoustic impedance model of the perforated plate developed by Kooi, and reversely deducing the perforation parameter corresponding to the optimized dimensionless acoustic impedance value as alpha H ＝0.027＝2.7％，R＝1mm。
The perforation parameters obtained by optimizing the method for determining the perforation parameters of the flame stabilizer provided by some embodiments of the present disclosure are used as the design parameters of the perforation on the surface of the radial flame stabilizer, and through reasonable perforation design, the circumferential modal sound wave incidence can be properly dissipated or a phase change effect can be generated, so that the thermoacoustic response of the whole afterburner system can be changed, and finally the appearance of destabilized circumferential modal thermoacoustic oscillation is suppressed. The thermoacoustic feedback oscillation is inhibited through the pure acoustic effect, and the radial flame stabilizer structure can provide a more effective sound dissipation mechanism for circumferential modal wave incidence relatively speaking by combining a radially distributed sound dissipation surface provided after the radial flame stabilizer is perforated and a sound-vortex energy conversion mechanism of the blade structure under the average main flow condition. In the thermoacoustic system, even if the acoustic dissipation of a single part is only slightly increased, the final oscillation frequency growth rate can be obviously changed, so that the perforation parameters obtained by the flame stabilizer perforation parameter determination method disclosed by the disclosure are applied to a radial flame stabilizer, and the high-frequency thermoacoustic instability phenomenon of the circumferential mode can be effectively inhibited.
Some embodiments of the present disclosure also provide a flame holder penetration parameter determination apparatus adapted for use with a radial flame holder in an afterburner; the inner wall of afterburner is provided with radial flame holder subassembly, and radial flame holder subassembly includes the same radial flame holder of a plurality of structures, and a plurality of radial flame holders evenly arrange along afterburner's inner wall's circumference, and every radial flame holder has a plurality of perforation. The flame holder penetration parameter determining apparatus includes:
an acquisition module configured to: acquiring an acoustic response function of the radial flame stabilizer component to the circumferential modal wave and a thermoacoustic stability model of the afterburner;
the presetting module is connected with the obtaining module and is configured to: presetting a plurality of groups of optimizing parameters for any radial flame stabilizer; wherein, a plurality of groups of optimizing parameters are used for substituting into the thermoacoustic stability model;
the judgment module is connected with the acquisition module and the preset module and is configured to: solving the oscillation frequency corresponding to the circumferential mode in the thermoacoustic stability model, and judging whether the radial flame stabilizer component can control the thermoacoustic instability of the afterburner or not according to the solving result corresponding to each group of optimizing parameters; when the imaginary part of the obtained oscillation frequency is less than zero, the radial flame stabilizer component can control the thermoacoustic instability of the afterburner;
a puncturing parameter determination module connected with the determination module and configured to: and obtaining perforation parameters of the flame stabilizer according to the optimization parameters corresponding to the flame stabilizer capable of controlling the thermoacoustic instability of the afterburner.
Embodiments of the present disclosure also provide a flame holder penetration parameter determination apparatus that includes a processor and a memory. Wherein the memory has stored therein computer program instructions adapted to be executed by the processor. When the computer program instructions are executed by the processor, the processor performs the flame holder penetration parameter determination method provided by any of the embodiments described above.
It should be noted that, when the flame holder penetration parameter determining apparatus provided in the foregoing embodiment is used to determine a flame holder penetration parameter, the division of the above functional modules is merely used as an example, and in practical applications, the above function distribution may be performed by different functional modules according to needs, that is, the internal structure or program of the apparatus may be divided into different functional modules to perform all or part of the above described functions. In addition, the device provided by the above embodiment and the embodiment of the method for determining the perforation parameter of the flame stabilizer belong to the same concept, and the specific implementation process thereof is described in the embodiment of the method for determining the perforation parameter of the flame stabilizer, and is not described herein again.
Some embodiments of the present disclosure also provide a computer-readable storage medium having stored therein computer program instructions that, when executed by a processor of a user device, cause the user device to perform the flame holder penetration parameter determination method of any of the embodiments described above.
Computer-readable storage media provided by any embodiment of the present disclosure include permanent and non-permanent, removable and non-removable media, and information storage may be implemented by any method or technology. The information may be computer readable instructions, data structures, modules of a program, or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static Random Access Memory (SRAM), dynamic Random Access Memory (DRAM), other types of Random Access Memory (RAM), read Only Memory (ROM), electrically Erasable Programmable Read Only Memory (EEPROM), flash memory or other memory technology, compact disc read only memory (CD-ROM), digital Versatile Discs (DVD) or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other non-transmission medium that can be used to store information that can be accessed by a computing device.
Embodiments of the present disclosure also provide an electronic device, including a processor and a memory, where the memory stores computer program instructions adapted to be executed by the processor, and the computer program instructions, when executed by the processor, implement the method for determining a perforation parameter of a flame holder disclosed in any of the above embodiments.
The electronic device provided by any embodiment of the present disclosure may be a mobile phone, a computer, a tablet computer, a server, a network device, or may also be a usb disk, a removable hard disk, a Read Only Memory (ROM), a magnetic disk, or an optical disk.
For example, the electronic device may include: a processor, a memory, an input/output interface, a communication interface, and a bus. Wherein the processor, the memory, the input/output interface and the communication interface are communicatively connected to each other within the device via a bus.
The processor may be implemented by a general-purpose CPU (Central Processing Unit), a microprocessor, an Application Specific Integrated Circuit (ASIC), or one or more Integrated circuits, and is configured to execute a relevant program to implement the technical solutions provided in the embodiments of the present specification.
The Memory may be implemented in the form of a ROM (Read Only Memory), a RAM (Random Access Memory), a static storage device, a dynamic storage device, or the like. The memory may store an operating system and other application programs, and when the technical solution provided by the embodiments of the present specification is implemented by software or firmware, the relevant program codes are stored in the memory and called by the processor to be executed.
The input/output interface is used for connecting the input/output module to realize information input and output. The input/output/modules may be configured in the device as components or may be external to the device to provide corresponding functionality. The input devices may include a keyboard, a mouse, a touch screen, a microphone, various sensors, etc., and the output devices may include a display, a speaker, a vibrator, an indicator light, etc.
The communication interface is used for connecting the communication module so as to realize the communication interaction between the equipment and other equipment. The communication module can realize communication in a wired mode (such as USB, network cable and the like) and also can realize communication in a wireless mode (such as mobile network, WIFI, bluetooth and the like).
A bus includes a path that transfers information between various components of the device, such as the processor, memory, input/output interfaces, and communication interfaces.
It should be noted that although the above-described device only shows a processor, a memory, an input/output interface, a communication interface and a bus, in a specific implementation, the device may also include other components necessary for normal operation. In addition, those skilled in the art will appreciate that the above-described apparatus may also include only the components necessary to implement the embodiments of the present description, and not necessarily all of the described components.
From the above description of the embodiments, it is clear to those skilled in the art that the embodiments of the present disclosure can be implemented by software plus necessary general hardware platform. Based on such understanding, the technical solutions of the embodiments of the present specification or portions contributing to the prior art may be embodied in the form of a software product, which may be stored in a storage medium, such as a ROM/RAM, a magnetic disk, an optical disk, or the like, and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the method for determining the puncturing parameter of the flame stabilizer according to each embodiment or some portions of the embodiments of the present specification.
The method or module for determining the perforation parameter of the flame holder, which is illustrated in the above embodiments, may be implemented by a computer chip or an entity, or by a product having a certain function. A typical implementation device is a computer, which may take the form of a personal computer, laptop computer, cellular telephone, camera phone, smart phone, personal digital assistant, media player, navigation device, email messaging device, game console, tablet computer, wearable device, or a combination of any of these devices.
Some embodiments of the present disclosure also provide a radial flame holder provided with a plurality of perforations, the perforation parameter of the plurality of perforations being determined by the flame holder perforation parameter determination method of any of the embodiments described above.
Some embodiments of the present disclosure also provide an engine including a radial flame holder as described in any of the above embodiments.
Some embodiments of the present disclosure also provide an aircraft comprising: a radial flame holder as in any of the embodiments above, or an engine as in any of the embodiments above.
The beneficial effects that can be achieved by the flame holder perforation parameter determination device, the radial flame holder, the engine or the aircraft provided by some embodiments of the present disclosure are the same as the beneficial effects that can be achieved by the flame holder perforation parameter determination method provided above, and are not described herein again.
In the description herein, reference to the description of the terms "one embodiment/mode," "some embodiments/modes," "example," "specific example," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment/mode or example is included in at least one embodiment/mode or example of the application. In this specification, the schematic representations of the terms used above are not necessarily intended to be the same embodiment/mode or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments/modes or examples. Furthermore, the various embodiments/aspects or examples and features of the various embodiments/aspects or examples described in this specification can be combined and combined by one skilled in the art without conflicting therewith.
Furthermore, the terms "first," "second," and the like are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or to implicitly indicate a number of the indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present disclosure, "a plurality" means at least two, e.g., two, three, etc., unless explicitly specifically limited otherwise. Meanwhile, in the description of the present disclosure, unless otherwise explicitly specified or limited, the terms "connected" and "connected" should be interpreted broadly, e.g., as being fixedly connected, detachably connected, or integrally connected; the connection can be mechanical connection or electrical connection; may be directly connected or indirectly connected through an intermediate. The specific meaning of the above terms in the present disclosure can be understood by those of ordinary skill in the art as appropriate.
It will be understood by those skilled in the art that the foregoing embodiments are merely for clarity of illustration of the disclosure and are not intended to limit the scope of the disclosure. Other variations or modifications may occur to those skilled in the art, based on the foregoing disclosure, and are still within the scope of the present disclosure.

Claims (11)

1. A method of flame holder penetration parameter determination, wherein the method of flame holder penetration parameter determination is adapted for use with a radial flame holder in an afterburner; the inner wall of the afterburner is provided with a radial flame stabilizer assembly, the radial flame stabilizer assembly comprises a plurality of radial flame stabilizers with the same structure, the radial flame stabilizers are uniformly arranged along the circumferential direction of the inner wall of the afterburner, and each radial flame stabilizer is provided with a plurality of through holes; the flame holder penetration parameter determination method comprises:
establishing an acoustic response function of the radial flame stabilizer component to the circumferential modal wave, and acquiring the acoustic response function of the radial flame stabilizer component to the circumferential modal wave;
acquiring a thermoacoustic stability model of the afterburner based on the acoustic response function;
presetting a plurality of groups of optimization parameters for any radial flame stabilizer, and respectively substituting the groups of optimization parameters into the thermoacoustic stability model;
solving the oscillation frequency corresponding to the circumferential mode in the thermoacoustic stability model, and judging whether the radial flame stabilizer component can control the thermoacoustic instability of the afterburner or not according to the solving result corresponding to each group of optimizing parameters; when the imaginary part of the obtained oscillation frequency is less than zero, the radial flame stabilizer component can control the thermoacoustic instability of the afterburner;
and obtaining perforation parameters of the flame stabilizer according to optimization parameters corresponding to the flame stabilizer capable of controlling the thermoacoustic instability of the afterburner.
2. The method of claim 1, wherein the optimization parameters are perforation parameters, each set of optimization parameters includes a perforation rate and a perforation radius, the preset value of the perforation rate ranges from 0 to 0.2, and the preset value of the perforation radius ranges from 0.5mm to 10mm.
3. The flame holder perforation parameter determination method of claim 2, wherein said establishing an acoustic response function of the radial flame holder assembly to a circumferential modal wave comprises:
taking the average main flow in the pipeline of the afterburner as an axial uniform main flow, and enabling the flow to be pressurized and isentropic, under the assumption of linearization, the viscosity of the main flow is not considered, and a secondary scattering sound field generated by the unsteady load on the surface of the radial flame stabilizer component under the incident disturbance of sound waves is expressed as a first relational expression by using a generalized Lighthill formula:
Figure FDA0003898607670000011
in the first relation, the first and second values are,
Figure FDA0003898607670000012
a secondary diffuse acoustic field generated for unsteady load distribution of the radial flame holder assembly surface;
Figure FDA0003898607670000021
three-dimensional coordinates of the observation point;
t is the time of the observation point;
g is a Green function in the rigid-wall pipeline under the uniform axial average main flow condition;
t is the integration time of a Green function method, and is an intermediate variable;
tau is the source point time and is an intermediate variable;
s (tau) is a source point integral surface corresponding to a Green function method;
y i the coordinates of the source point coordinate system are used as intermediate variables;
ΔP s an unsteady load distribution for the radial flame holder assembly surface;
Figure FDA0003898607670000022
integrating bins for source points corresponding to a Green function method;
neglecting the monopole source item and the quadrupole source item, substituting the Green function into a first relational expression, and adopting e -iωt The radial flame holder assembly produces a secondary diffuse acoustic field that satisfies a second relationship:
Figure FDA0003898607670000023
in the second relation, the first relation is that,
Figure FDA0003898607670000024
omega is oscillation frequency or incident disturbance frequency;
v is the number of radial flame holders in the radial flame holder assembly;
q is a circumferential modal series summation index, q =8230, 3, -2, -1,0,1,2,3, 8230, and is an intermediate variable;
n is the number of the radial modes of the pipeline in the calculation process;
m is the number of the circumferential modes of the pipeline in the calculation process, and m = m in -qV；
m in The number of circumferential modes of incident sound waves;
φ m (k mn r) is a pipeline radial characteristic function;
r is a radial coordinate/direction axis of the observation point cylindrical coordinate system and is a middle variable;
k mn the characteristic value of the pipeline is used as the characteristic value,
Figure FDA0003898607670000025
k 0 the wave number is corresponded to the sound wave number,
Figure FDA0003898607670000026
c 0 is the average sound velocity of the average main flow within the pipe;
m is the axial flow Mach number of the average main flow in the pipeline;
beta is a Prandtl-Glauert coefficient,
Figure FDA0003898607670000031
Figure FDA0003898607670000032
a circumferential coordinate/direction axis of the observation point cylindrical coordinate system is taken as an intermediate variable;
z is an axial coordinate/direction axis of the observation point cylindrical coordinate system and is an intermediate variable;
r' is a radial coordinate/direction axis of the source point cylindrical coordinate system and is a middle variable;
Figure FDA0003898607670000033
a circumferential coordinate/direction axis of a source point column coordinate system is taken as a middle variable;
z' is the axial coordinate/direction axis of the source point cylindrical coordinate system and is an intermediate variable;
h (x) is a Heaviside function,
Figure FDA0003898607670000034
α 1 the axial wave number of the sound wave propagating backwards/downwards is the axial wave number of the sound wave propagating backwards/downwards in the pipeline mode;
α 2 the axial wave number of the acoustic wave which is transmitted forwards/upstream in the pipeline mode;
the corresponding axial wave number of the pipeline modal sound wave meets a third relation:
Figure FDA0003898607670000035
the volume flow in a single perforation of any radial flame stabilizer surface and the local unsteady load distribution satisfy a fourth relation:
Figure FDA0003898607670000036
in the fourth relation, ρ 0 Is the average density of the average main flow within the pipe;
q is the volume flow in a single perforation on the surface of the radial flame stabilizer;
and averaging the volume flow in the single perforation, so that the physically allowed actual normal penetration speed corresponding to the acoustic soft wall surface of the radial flame stabilizer assembly meets a fifth relational expression:
Figure FDA0003898607670000037
in the fifth relation, α H The open porosity of the perforations;
r is the radius of the perforation;
note the first incident sound wave p i1 And a second incident acoustic wave p i2 The normal acoustic particle velocity generated on the surface of the radial flame stabilizer component is v d Scattered sound field formed by unsteady loads
Figure FDA0003898607670000038
Corresponding to a normal acoustic particle velocity of
Figure FDA0003898607670000039
The velocity boundary condition satisfied at the acoustic soft boundary of the radial flame holder assembly surface is a sixth relationship:
Figure FDA00038986076700000310
wherein the content of the first and second substances,
Figure FDA00038986076700000311
satisfies the seventh relation:
Figure FDA00038986076700000312
Figure FDA0003898607670000041
wherein alpha is 3 ＝ω/(Mc 0 )；
U is the axial flow velocity of the average main flow in the pipeline;
expanding the pipeline radial characteristic function by using a finite number of circumferential infinite order Bessel functions to obtain an eighth relational expression:
Figure FDA0003898607670000042
in the eighth relational expression, BB is a finite radial modal expansion coefficient;
Figure FDA0003898607670000043
is a peripheral infinite-order Bessel function;
substituting the fifth relational expression and the seventh relational expression into the sixth relational expression to obtain an integral equation, and solving the integral equation by a point matching method to obtain the distribution of the unsteady load on the surface of the radial flame stabilizer component under the condition of sound wave incidence;
substituting the obtained distribution of the unsteady loads of the surface of the radial flame stabilizer component into a second relational expression to obtain a secondary scattered sound field generated by the unsteady loads of the surface of the radial flame stabilizer component
Figure FDA0003898607670000044
The incident sound field is a superposition of a plurality of orthogonal pipe acoustic modes, wherein the spatial distribution of each mode satisfies a ninth relation:
Figure FDA0003898607670000045
in the ninth relational expression, the first and second expression,
Figure FDA0003898607670000046
is an incident sound field;
A mn is a modal amplitude coefficient under the incident sound wave coaxial mode;
superposing the secondary scattering sound field with an incident sound field to obtain a transmission sound field
Figure FDA0003898607670000047
Figure FDA0003898607670000048
The reflected sound field is equal to the distribution of the scattered sound waves with the same modal axial propagation direction, namely
Figure FDA0003898607670000049
4. The flame holder penetration parameter determination method of claim 1, wherein the optimization parameter is an acoustic impedance of the radial flame holder assembly, the acoustic impedance being functionally related to the penetration parameter by a Kooi impedance model.
5. The flame holder perforation parameter determination method of claim 4, wherein said establishing an acoustic response function of the radial flame holder assembly to a circumferential modal wave comprises:
taking the average main flow in the pipeline of the afterburner as an axial uniform main flow, and enabling the flow to be compressible and isentropic, under the assumption of online, not considering the viscosity of the main flow, and expressing a secondary scattering sound field generated by the unsteady load distribution on the surface of the radial flame stabilizer component under the incident disturbance of sound waves as a first relational expression by using a generalized Lighthill formula:
Figure FDA0003898607670000051
in the first relation, the first and second values are,
Figure FDA0003898607670000052
a secondary diffuse acoustic field generated for unsteady load distribution of the radial flame holder assembly surface;
Figure FDA0003898607670000053
three-dimensional coordinates of the observation point;
t is the time of the observation point;
g is a Green function in the rigid-wall pipeline under the uniform axial average main flow condition;
t is the integral time of a Green function method, and is an intermediate variable;
tau is the source point time and is an intermediate variable;
s (tau) is a source point integral surface corresponding to a Green function method;
y i the coordinate of the source point coordinate system is taken as an intermediate variable;
ΔP s unsteady load distribution for the radial flame holder assembly surface;
Figure FDA0003898607670000054
a source point integral surface element corresponding to a Green function method;
ignoring monopole source items and quadrupole source items, substituting the Green function into a first relational expression, and adopting e -iωt The radial flame holder assembly generates a secondary diffuse sound field that satisfies a second relationship:
Figure FDA0003898607670000055
in the second relation, the first relation is that,
Figure FDA0003898607670000056
omega is oscillation frequency or incident disturbance frequency;
v is the number of radial flame holders in the radial flame holder assembly;
q is a circumferential modal series summation index, q =8230, q is-3, -2, 1,0,1,2,3, \8230, and q is an intermediate variable;
n is the number of the radial modes of the pipeline in the calculation process;
m is the circumferential modal number of the pipeline in the calculation process, and m = m in -qV；
m in The number of circumferential modes of incident sound waves;
φ m (k mn r) is a pipeline radial characteristic function;
r is a radial coordinate/direction axis of the observation point cylindrical coordinate system and is a middle variable;
k mn the characteristic value of the pipeline is used as the characteristic value,
Figure FDA0003898607670000061
k 0 the wave number is corresponded to the sound wave number,
Figure FDA0003898607670000062
c 0 is the average sound velocity of the average main flow within the pipe;
m is the axial flow Mach number of the average main flow in the pipeline;
beta is Prandtl-Glauert coefficient,
Figure FDA0003898607670000063
Figure FDA0003898607670000064
a circumferential coordinate/direction axis of the observation point cylindrical coordinate system is taken as an intermediate variable;
z is an axial coordinate/direction axis of the observation point cylindrical coordinate system and is a middle variable;
r' is a radial coordinate/direction axis of a source point column coordinate system and is a middle variable;
Figure FDA0003898607670000065
a circumferential coordinate/direction axis of a source point cylindrical coordinate system is taken as an intermediate variable;
z' is the axial coordinate/direction axis of the source point cylindrical coordinate system and is an intermediate variable;
h (x) is a Heaviside function,
Figure FDA0003898607670000066
α 1 as a pipe modal sound waveAxial wave number of backward/downstream propagating sound waves;
α 2 the axial wave number of the acoustic wave which is transmitted forwards/upstream for the pipeline mode acoustic wave;
the axial wave number of the corresponding pipeline modal sound wave meets a third relation:
Figure FDA0003898607670000067
the volume flow in a single perforation of any radial flame stabilizer surface and the local unsteady load distribution satisfy a fourth relation:
Figure FDA0003898607670000068
in the fourth relation, ρ 0 Is the average density of the average main flow in the pipeline;
q is the volume flow in a single perforation on the surface of the radial flame stabilizer;
and averaging the volume flow in a single perforation, wherein the physically allowed actual normal penetration speed corresponding to the acoustic soft wall surface of the radial flame stabilizer assembly meets the tenth relational expression:
Figure FDA0003898607670000069
in the tenth relationship, Z is the acoustic impedance of the radial flame holder;
record the first radiated sound wave p i1 And a second radiated sound wave p i2 The normal acoustic particle velocity generated on the surface of the radial flame stabilizer component is v d Scattered acoustic field formed by unsteady loads
Figure FDA00038986076700000610
Corresponding to a normal acoustic particle velocity of
Figure FDA00038986076700000611
The velocity boundary condition satisfied at the acoustically soft boundary of the radial flame holder assembly surface is a sixth relationship:
Figure FDA0003898607670000071
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003898607670000072
satisfies the seventh relation:
Figure FDA0003898607670000073
wherein alpha is 3 ＝ω/(Mc 0 )；
U is the axial flow velocity of the average main flow in the pipeline;
expanding the pipeline radial characteristic function by using a finite number of circumferential infinite order Bessel functions to obtain an eighth relational expression:
Figure FDA0003898607670000074
in the eighth relational expression, BB is a finite radial modal expansion coefficient;
Figure FDA0003898607670000075
is a peripheral infinite-order Bessel function;
substituting the tenth relational expression and the seventh relational expression into the sixth relational expression to obtain an integral equation, and solving the integral equation by a point matching method to obtain the distribution of the unsteady load on the surface of the radial flame stabilizer component under the condition of sound wave incidence;
substituting the obtained distribution of the unsteady load of the surface of the radial flame stabilizer component into a second relational expression to obtain the unsteady load of the surface of the radial flame stabilizer componentGenerated secondary scattered acoustic field
Figure FDA0003898607670000076
The incident sound field is a superposition of a plurality of orthogonal pipe acoustic modes, wherein the spatial distribution of each mode satisfies a ninth relation:
Figure FDA0003898607670000077
in the ninth relational expression, the first and second expression,
Figure FDA0003898607670000078
is an incident sound field;
A mn the mode amplitude coefficient is under the incident sound wave coaxial mode;
superposing the secondary scattering sound field with an incident sound field to obtain a transmission sound field
Figure FDA0003898607670000079
Figure FDA00038986076700000710
The reflected sound field is equal to the distribution of the scattered sound waves with the same modal axial propagation direction, namely
Figure FDA00038986076700000711
6. The method for determining the perforation parameters of the flame holder according to claim 3 or 5, wherein the solving the oscillation frequencies corresponding to the circumferential modes in the thermoacoustic stability model and the determining whether the radial flame holder assembly can control the thermoacoustic instability of the afterburner according to the solving results corresponding to each set of optimized parameters comprises:
the real part of the oscillation frequency represents the time frequency of the thermoacoustic oscillation of the circumferential mode, and the imaginary part represents the growth rate of the thermoacoustic oscillation; in thate -iωt Under the time harmonic expression of (a) is,
if the positive imaginary part is obtained, the size of the thermoacoustic oscillation amplitude value is continuously increased along with the time, and the radial flame stabilizer cannot control the thermoacoustic instability of the afterburner corresponding to the condition of the instability of the thermoacoustic mode;
if the negative imaginary part is obtained, the amplitude value of thermoacoustic oscillation continuously decreases along with the increase of time, and the radial flame stabilizer can control the thermoacoustic instability of the afterburner corresponding to the condition of stable combustion.
7. A flame holder penetration parameter determination apparatus adapted for use with a radial flame holder in an afterburner; the inner wall of the afterburner is provided with a radial flame stabilizer assembly, the radial flame stabilizer assembly comprises a plurality of radial flame stabilizers with the same structure, the radial flame stabilizers are uniformly arranged along the circumferential direction of the inner wall of the afterburner, and each radial flame stabilizer is provided with a plurality of through holes; the flame holder penetration parameter determination apparatus includes:
an acquisition module configured to: acquiring an acoustic response function of the radial flame stabilizer component to circumferential modal waves and a thermoacoustic stability model of the afterburner;
the preset module is connected with the acquisition module and is configured to: presetting a plurality of groups of optimizing parameters for any radial flame stabilizer; wherein, the multiple groups of optimizing parameters are used for substituting into the thermoacoustic stability model;
the judgment module is connected with the acquisition module and the preset module and is configured to: solving the oscillation frequency corresponding to the circumferential mode in the thermoacoustic stability model, and judging whether the radial flame stabilizer component can control the thermoacoustic instability of the afterburner or not according to the solving result corresponding to each group of optimizing parameters; when the imaginary part of the obtained oscillation frequency is less than zero, the radial flame stabilizer component can control the thermoacoustic instability of the afterburner;
a puncturing parameter determining module connected with the judging module and configured to: and obtaining perforation parameters of the flame stabilizer according to optimization parameters corresponding to the flame stabilizer capable of controlling the thermoacoustic instability of the afterburner.
8. A computer readable storage medium, having stored therein computer program instructions, which when executed by a processor of a user equipment, cause the user equipment to perform the flame holder perforation parameter determination method of any of claims 1-5.
9. A radial flame holder, characterized in that the radial flame holder is provided with a plurality of perforations, the perforation parameters of which are determined by the flame holder perforation parameter determination method according to any of claims 1 to 6.
10. An engine comprising the radial flame holder of claim 9.
11. An aircraft, characterized in that it comprises: a radial flame holder as claimed in claim 9, or an engine as claimed in claim 10.
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