CN112487574A - Combustion stability margin evaluation method - Google Patents

Combustion stability margin evaluation method Download PDF

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CN112487574A
CN112487574A CN202011332465.9A CN202011332465A CN112487574A CN 112487574 A CN112487574 A CN 112487574A CN 202011332465 A CN202011332465 A CN 202011332465A CN 112487574 A CN112487574 A CN 112487574A
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杨尚荣
杨宝娥
陈宏玉
陈鹏飞
刘占一
李舒欣
周晨初
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Xian Aerospace Propulsion Institute
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Abstract

The invention provides a combustion stability margin evaluation method, which solves the problem that the existing method can not accurately acquire the inherent modal frequency and the non-stability judgment criterion when a system works stably, and comprises the following steps: collecting a pressure pulsation time sequence of a combustion chamber; calculating a pressure time series power spectrum; obtaining the peak frequency of the power spectrum through parameter identification; performing band-pass filtering with the peak frequency as the center; calculating an autocorrelation function of the filtered pressure time series; obtaining an envelope of an autocorrelation function through Hilbert transform; fitting an envelope curve by using an exponential function to obtain an attenuation coefficient; evaluating stability of the combustion process in the combustion chamber based on the damping coefficient. The method can evaluate the combustion stability margin in the combustion chamber in the combustion noise stage, and has guidance for evaluating the working reliability of the engine and evaluating the effectiveness of an improved scheme.

Description

Combustion stability margin evaluation method
Technical Field
The invention belongs to the field of aerospace propulsion systems, and particularly relates to a combustion stability margin evaluation method.
Background
During the rocket engine development stage, external impulse disturbances are typically introduced to evaluate the combustion stability of the engine. If the disturbance triggers combustion instability, the system is in a bistable area, and the stability margin of the system is insufficient. If the oscillation amplitude generated by disturbance gradually attenuates along with time, the distance from the system to a bifurcation point (theoretically, the attenuation coefficient of the system at the bifurcation point is zero) can be judged by calculating the attenuation coefficient, namely the stability margin of the system. However, the introduction of external impulse disturbances requires additional excitation devices to evaluate system stability, and there is a risk of triggering instability and thus damaging the engine, so it is desirable to develop a method for quantifying system stability margins without external excitation devices.
Methods available in the literature, such as Lieuwen, T, Online custom Stability establishment Association Dynamic Pressure Data, ASME J.Eng.Gas Turbines Power,2005,127(3):478-482.Lieuwen calculates the system attenuation coefficient Using the autocorrelation function of the Pressure time series of the stationary working phase based on the nonlinear coupled oscillator model; such as Stadlmain, N.V., Hummel, T.and Sattermain, T.Thermoacoustic damping rate determination from statistical noise using basic dynamics, ASME Turbo Expo 2017: Turboscientific Technical reference and Expo (50848), V04AT04A 04A025. Stadlmain is based on the Lieuwen method and simultaneously adopts the Bayesian statistical recognition method, the attenuation coefficients of a plurality of acoustic modes can be recognized simultaneously; for example, Yi, T, Gutmark, E.J., one prediction of the on set of communication infrastructures based on the calculation of damping rates, J.Sound Vis., 2008,310 (1-5): 442-.
Among the above methods, the Lieuwen method requires band-pass filtering at the center frequency to eliminate the interaction between different acoustic modes. Since the noise stage pressure time sequence is a broadband oscillation around the acoustic mode of the combustion chamber, the judgment of the central frequency has great arbitrariness, which can have great influence on the calculation result. The method has two problems that firstly, when system parameters change (such as mixing ratio), the resonance frequency changes; secondly, in practical applications, it is desirable to determine the stability margin of the system during the stable combustion (combustion noise) stage, and the resonant frequency of the system after the oscillatory combustion is generated cannot be known "precisely" at this time.
Theoretically, when the damping coefficient of the system is zero, the system is indicated to generate combustion instability, namely, the threshold value of the damping coefficient is zero. In practical application, combustion instability of the combustion chamber occurs when the damping coefficient does not reach zero, so that the threshold value of the damping coefficient needs to be corrected according to the existing experimental result.
Disclosure of Invention
The invention aims to solve the problem that the existing method cannot accurately acquire the inherent modal frequency and the non-stability judgment criterion when a system works stably, and provides a combustion stability margin evaluation method.
In order to realize the purpose, the technical scheme of the invention is as follows:
a combustion stability margin evaluation method, comprising the steps of:
step one, acquiring a pressure pulsation time sequence of a combustion chamber;
acquiring a combustion chamber or a pressure pulsation time sequence before combustion chamber injection through a dynamic pressure sensor
Figure BDA0002796211220000021
Step two, calculating a pressure time series power spectrum;
calculating power spectrum of pressure time series by using periodogram method, i.e. for pressure pulsation time series
Figure BDA0002796211220000022
Performing discrete Fourier transform, and dividing the square of the modulus by the number of data points to obtain a pressure time series power spectrum
Figure BDA0002796211220000023
Step three, acquiring the peak frequency of the pressure time series power spectrum through parameter identification;
fitting a pressure time series power spectrum using the following equation
Figure BDA0002796211220000024
The fitting adopts a nonlinear least square method to obtain the peak frequency omegai；
Figure BDA0002796211220000025
Figure BDA0002796211220000031
Wherein S ispp(ω；ωi,Γ,νi) Is a theoretical pressure time series power spectrum; omega is angular frequency, gamma is intensity of noise, omega isiIs the peak frequency, viIs the attenuation coefficient;
step four, using peak frequency omegaiPerforming band-pass filtering for the center;
determining a filter bandwidth omegaHAt peak frequency ωiBand-pass filtering is carried out for the center, and the pressure time sequence after filtering is recorded as pt；
Step five, calculating an autocorrelation function rho of the filtered pressure time sequenceτ；
Autocorrelation function ρτThe following calculation is carried out,
Figure BDA0002796211220000032
where E is the mathematical expectation calculation, pt+τIs ptTime series with a delay of τ, μ is ptThe average or mathematical expectation of (a) of (b),
Figure BDA0002796211220000033
is ptThe variance of (a);
step six, obtaining an envelope curve H of an autocorrelation function through Hilbert transformationt；
Obtaining an envelope curve H of an autocorrelation function by means of a Hilbert transformtThe calculation is as follows:
Figure BDA0002796211220000034
wherein t is the sampling time of the pressure pulsation time sequence, and tau is the delay time of the autocorrelation function;
seventhly, fitting an envelope curve by using an exponential function to obtain an attenuation coefficient;
using exponential functions
Figure BDA0002796211220000035
Fitting envelope curve HtObtaining the attenuation coefficient vi；
And step eight, comparing the distance between the attenuation coefficient and a threshold value, and evaluating the stability of the combustion process in the combustion chamber.
Further, in step five, the variance
Figure BDA0002796211220000036
Calculated by the following formula
Figure BDA0002796211220000037
Wherein n is the pressure time series length.
Further, in step eight, the threshold is 0.016.
Compared with the prior art, the technical scheme of the invention has the following advantages:
the invention provides a combustion stability margin evaluation method of a combustion chamber, which utilizes a system identification method to identify peak frequency from a pressure time series frequency domain power spectrum as the center frequency of band-pass filtering, reduces the arbitrariness of selecting the center frequency in band-pass filtering calculation, and can more accurately calculate the attenuation coefficient of the inherent modal frequency of the system; meanwhile, the invention establishes a conversion method of the attenuation coefficient and the empirical formula, obtains the attenuation coefficient threshold value when instability occurs, determines the stability judgment criterion, and improves the engineering applicability and reliability of the combustion stability margin evaluation method.
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FIG. 1 is a diagram illustrating an oscillation curve of an autocorrelation function in an embodiment of a method of the present invention.
Detailed Description
The invention is described in further detail below with reference to the figures and specific embodiments.
Because the prior art does not have a quantitative method for determining the center frequency of the band-pass filter, the invention provides a method for quantitatively determining the center frequency, namely a combustion stability margin evaluation method. The method comprises the following steps: collecting a pressure pulsation time sequence of a combustion chamber; calculating a pressure time series power spectrum; obtaining the peak frequency of the power spectrum through parameter identification; performing band-pass filtering with the peak frequency as the center; calculating an autocorrelation function of the filtered pressure time series; obtaining an envelope of an autocorrelation function through Hilbert transform; fitting an envelope curve by using an exponential function to obtain an attenuation coefficient; evaluating stability of the combustion process in the combustion chamber based on the damping coefficient.
The principle of the method of the invention is as follows: an oscillating system (combustion chamber) excited by a random broadband signal (white noise) can be described by the following equation,
Figure BDA0002796211220000041
wherein p isiAmplitude of i-th order modal pressure oscillations, ωiIs the ith order modal peak frequency, viSolving the power spectral density S of the pressure oscillation amplitude of the above formula for the ith order modal attenuation coefficient and xi (t) as a noise excitation termpp(ω), to obtain the following formula,
Figure BDA0002796211220000051
where ω is an angular frequency, Γ is the intensity of the noise ξ (t), and the pressure time series obtained in the experiment satisfies expression (1), and the frequency domain power spectrum form thereof satisfies expression (2), so that the peak frequency can be obtained by fitting the above expression.
The combustion stability margin evaluation method provided by the invention specifically comprises the following steps:
step one, acquiring a pressure pulsation time sequence of a combustion chamber;
monitoring the combustion chamber or the pressure pulse time sequence before the combustion chamber injection by means of a dynamic pressure sensor
Figure BDA0002796211220000052
And storing the measurement result;
step two, calculating a pressure time series power spectrum;
calculating power spectrum of pressure time series by using classical periodogram method, i.e. for pressure pulsation time series
Figure BDA0002796211220000058
Performing Discrete Fourier Transform (DFT), and dividing the square of a modulus (amplitude function) by the number of data points to obtain a pressure time series power spectrum
Figure BDA0002796211220000053
In addition, the autocorrelation method or other parametric and nonparametric model spectrum estimation methods can also be adopted to calculate the pressure time series power spectrum
Figure BDA0002796211220000054
Step three, obtaining the peak frequency omega of the pressure time series power spectrum through parameter identificationi；
Fitting a pressure time series power spectrum using the following equation
Figure BDA0002796211220000055
The fitting adopts a nonlinear least square method, specifically, a group of undetermined parameters (omega) is searchedi,Γ,νi) The following residual sum of squares is minimized, and the calculation can be performed by using algorithms such as Gauss-Newton, Levenberg-Marquardt and the like;
Figure BDA0002796211220000056
Figure BDA0002796211220000057
wherein S ispp(ω；ωi,Γ,νi) Is a theoretical pressure time series power spectrum; omega is angular frequency, gamma is intensity of noise, omega isiIs the peak frequency, viIs the attenuation coefficient;
step four, performing band-pass filtering by taking the peak frequency as a center;
determining a filter bandwidth omegaHAt peak frequency ωiBand-pass filtering is carried out for the center, and the pressure time sequence after filtering is recorded as pt；
The band-pass filtering algorithm is mature, taking a Butterworth filter as an example, the general flow is as follows: firstly, designing a corresponding analog filter according to parameter requirements, and then converting the analog filter into a filter by an impulse response invariant method or a bilinear transformation methodDigital filter, filtered pressure time series denoted pt；
Step five, calculating an autocorrelation function of the filtered pressure time sequence;
autocorrelation function ρτThe following calculation is carried out,
Figure BDA0002796211220000061
where E is the mathematical expectation calculation, pt+τIs ptTime series with a delay of τ, μ is ptThe average or mathematical expectation of (a) of (b),
Figure BDA0002796211220000062
is ptVariance, variance of
Figure BDA0002796211220000063
Calculated by the following formula
Figure BDA0002796211220000064
Wherein n is the pressure time series length;
step six, obtaining an envelope curve H of an autocorrelation function through Hilbert transformationt；
Obtaining an envelope curve H of an autocorrelation function by means of a Hilbert transformtThe calculation is as follows:
Figure BDA0002796211220000065
wherein t is the sampling time of the pressure pulsation time sequence, and tau is the delay time of the autocorrelation function;
seventhly, fitting an envelope curve by using an exponential function to obtain an attenuation coefficient;
using exponential functions
Figure BDA0002796211220000066
FittingEnvelope curve HtObtaining the attenuation coefficient vi；
In this step, the linear expression y- ω is equivalently usediνit + b fitting curve lnHtA linear least square method is adopted to find a group of undetermined parameters (v)iB) minimizing the sum of squares of the following residuals, the linear least squares method being an existing mature algorithm;
Figure BDA0002796211220000071
and 8) comparing the distance between the attenuation coefficient and a threshold value, and evaluating the stability of the combustion process in the combustion chamber.
The farther the damping coefficient is from the threshold value, the more stable the combustion state in the combustion chamber is, and correspondingly, the closer the damping coefficient is to the threshold value, the more unstable the combustion state in the combustion chamber is.
The document M.L.Dranovsky, V. (Ed.) Yang, F. (Ed.) Culick, and D. (Ed.) Talley.Combustion instruments in Liquid pockets Engineers: Testing and Development Practices in Russia.AIAA Progress in dynamics and Aeronautics, Volume 221,2007 defines a rate of pulse pressure decay δ T which, when obtained by a number of tests, is within a range of δ T0.1. 0.1 … 0.3.3, the combustion chamber can operate stably. By calculation, the attenuation coefficient viV is related to the attenuation rate delta Tiδ T/2 pi, so the attenuation coefficient threshold can be determined to be 0.016. The farther the damping coefficient is from the threshold value, the more stable the combustion state in the combustion chamber is. Accordingly, the closer the damping coefficient is to the threshold value, the more unstable the combustion state in the combustion chamber.
The process of the present invention is described in further detail below by way of example.
Monitoring combustion chamber or combustion chamber pre-injection pressure pulsation time sequence by dynamic pressure sensor
Figure BDA0002796211220000072
In the example, the sampling frequency is 12.8kHz, the sampling time length is 5s, and the measurement result is stored;
to pressure pulsationTime series
Figure BDA0002796211220000073
Performing Discrete Fourier Transform (DFT), dividing the square of the modulus (amplitude function) by the number n of data points, and calculating the power spectrum of the pressure time series
Figure BDA0002796211220000074
Obtaining a power spectrum by fitting
Figure BDA0002796211220000075
Peak frequency ω ofiIn the present example, the parameter identification calculation is performed by using a nonlinear least square method, in the present example, the peak frequency ωiIs 2900 Hz;
determining a filter bandwidth omegaHAt peak frequency ωiBand-pass filtering is carried out for the center, and the pressure time sequence after filtering is recorded as ptThe filter bandwidth is 10% -20% of the peak frequency, in this example filter bandwidth omegaHIs the peak frequency omega i20% of (i.e., 580 Hz);
calculating an autocorrelation function ρ of the filtered pressure time seriesτThe calculation formula is shown as step five, the autocorrelation curve has a calculation length of 3-10 oscillation cycles for the next effective identification of the envelope curve (as shown in fig. 1, the calculation result of the autocorrelation function in step five is an oscillation curve, but the length of the autocorrelation function is controlled by the delay time tau, the delay time tau is given in advance, for the following effective identification, the length of the autocorrelation function is controlled by giving a suitable value of the delay time tau so as to contain 3-10 oscillation cycles), and the autocorrelation function rho is calculated in the exampleτAbout 8 oscillation cycles;
calculating the envelope of the autocorrelation function by Hilbert transform, wherein the calculation formula is shown as step six, and an exponential function is utilized
Figure BDA0002796211220000081
Fitting envelope curve HtObtaining the attenuation coefficient viThe attenuation ratio v obtained in this exampleiIs 0.11, largeWhen the damping coefficient threshold value is 0.016, the combustion state in the combustion chamber is stable.

Claims (3)

1. A combustion stability margin evaluation method, characterized by comprising the steps of:
step one, acquiring a pressure pulsation time sequence of a combustion chamber;
acquiring a combustion chamber or a pressure pulsation time sequence before combustion chamber injection through a dynamic pressure sensor
Figure FDA0002796211210000011
Step two, calculating a pressure time series power spectrum;
calculating power spectrum of pressure time series by using periodogram method, i.e. for pressure pulsation time series
Figure FDA0002796211210000012
Performing discrete Fourier transform, and dividing the square of the modulus by the number of data points to obtain a pressure time series power spectrum
Figure FDA0002796211210000013
Step three, acquiring the peak frequency of the pressure time series power spectrum through parameter identification;
fitting a pressure time series power spectrum using the following equation
Figure FDA0002796211210000014
The fitting adopts a nonlinear least square method to obtain the peak frequency omegai；
Figure FDA0002796211210000015
Figure FDA0002796211210000016
Wherein S ispp(ω；ωi,Γ,νi) Is a theoretical pressure time series power spectrum; omega is angular frequency, gamma is intensity of noise, omega isiIs the peak frequency, viIs the attenuation coefficient;
step four, using peak frequency omegaiPerforming band-pass filtering for the center;
determining a filter bandwidth omegaHAt peak frequency ωiBand-pass filtering is carried out for the center, and the pressure time sequence after filtering is recorded as pt；
Step five, calculating an autocorrelation function rho of the filtered pressure time sequenceτ；
Autocorrelation function ρτThe following calculation is carried out,
Figure FDA0002796211210000017
where E is the mathematical expectation calculation, pt+τIs ptTime series with a delay of τ, μ is ptThe average or mathematical expectation of (a) of (b),
Figure FDA0002796211210000018
is ptThe variance of (a);
step six, obtaining an envelope curve H of an autocorrelation function through Hilbert transformationt；
Obtaining an envelope curve H of an autocorrelation function by means of a Hilbert transformtThe calculation is as follows:
Figure FDA0002796211210000021
wherein t is the sampling time of the pressure pulsation time sequence, and tau is the delay time of the autocorrelation function;
seventhly, fitting an envelope curve by using an exponential function to obtain an attenuation coefficient;
using exponential functions
Figure FDA0002796211210000022
Fitting envelope curve HtObtaining the attenuation coefficient vi；
And step eight, comparing the distance between the attenuation coefficient and a threshold value, and evaluating the stability of the combustion process in the combustion chamber.
2. The combustion stability margin evaluation method according to claim 1, characterized in that: in step five, variance
Figure FDA0002796211210000023
Calculated by the following formula
Figure FDA0002796211210000024
Wherein n is the pressure time series length.
3. The combustion stability margin evaluation method according to claim 1 or 2, characterized in that: in step eight, the threshold is 0.016.
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Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20050247064A1 (en) * 2004-02-06 2005-11-10 Lieuwen Tim C Systems and methods for detection of combustor stability margin
CN106709144A (en) * 2016-11-22 2017-05-24 中国人民解放军装备学院 Autocorrelation theory-based engine instability prediction and assessment method
CN109184913A (en) * 2018-10-08 2019-01-11 南京航空航天大学 The aero-engine aerodynamic stability active composite control method with prediction is estimated based on stability
CN109344510A (en) * 2018-10-08 2019-02-15 南京航空航天大学 A kind of active stability control method based on the estimation of aero-engine stability margin

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20050247064A1 (en) * 2004-02-06 2005-11-10 Lieuwen Tim C Systems and methods for detection of combustor stability margin
CN106709144A (en) * 2016-11-22 2017-05-24 中国人民解放军装备学院 Autocorrelation theory-based engine instability prediction and assessment method
CN109184913A (en) * 2018-10-08 2019-01-11 南京航空航天大学 The aero-engine aerodynamic stability active composite control method with prediction is estimated based on stability
CN109344510A (en) * 2018-10-08 2019-02-15 南京航空航天大学 A kind of active stability control method based on the estimation of aero-engine stability margin

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