АЛГОРИТМ ОЦЕНКИ ЗАПАСОВ УСТОЙЧИВОСТИ РАБОЧЕГО ПРОЦЕССА В КАМЕРАХ СГОРАНИЯ И ГАЗОГЕНЕРАТОРАХ ЖИДКОСТНЫХ РАКЕТНЫХ ДВИГАТЕЛЕЙ

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Introduction. All produced combustion chambers and gas generators of liquid rocket engines (LRE) have to be experimentally tested on the stability of the working process with the respect to high-frequency pressure fluctuations in these components in the range of ±10 % of their nominal modes [1]. The main task in evaluating the stability of the work- ing combustion process is to determine, with the smallest number of experiments, the tendency of rocket engine components to maintain the instability of combustion and thus to develop measures to suppress it. Another task solved by the methods of stability evaluation is to deter- mine the effectiveness of various means of stabilizing the working process, such as anti-pulsation partitions and acoustic absorbers [2; 3]. Unfortunately, there are no prin- cipal means of ensuring the sustainability of the working process. Thus, we always need some relative evaluations of the effectiveness of the chosen method of stabilizing the working process in the developed LRE. Using the experimental methods [1-3] of the stability evaluation, it is possible to determine the most critical mode of oscil- lations, susceptible to resonant interaction with the com- bustion process, and to take the necessary measures to suppress it. In addition, the methods of evaluating sta- bility stocks allow us to investigate the effect of changes in the structural elements of engine components and vari- ous parameters of the working process on the stability of combustion [1-3]. At present, the evaluation of the stabil- ity of the working combustion process in LRE is carried out by introducing a pulse of pressure from the external device into the reaction volume of the combustion chamber through the channel in its wall [1; 3-12]. As a source of pressure in these external impulse devices (EID), a necessary amount of explosive (E) - hexogen, isolated from the channel by a metal membrane [1; 3; 12-14] is used. When the explosive charge is exploded, the frag- ments of such a membrane can damage the bronze inner shell of the combustion chamber, deform the blast noz- zles, etc. In this regard, the presence of a membrane in these devices is their disadvantage. The disadvantages of traditional EID can also include a considerable range in the values of the pressure pulses generated by them in the combustion chamber while the amount of the explosive stays the same and the parameters of the atmosphere in the combustion chamber are constant, which is apparently related to the range of the explosive characteristics, such as: its laydown thickness, the thickness of the membrane, etc. To eliminate the disadvantages of EID, it has been proposed to use an explosion of a metallic conductor of electric current (wire) when discharging a capacitor with accumulated energy of several thousand joules [4]. At pre- sent, hexogen is used as an explosive in EID, with a weight of about 0.5 to 3.5 grams in TNT equivalent. The explosion of one gram of TNT is equivalent to the energy released at the time of the wire explosion of approxi- mately 4390 J. To release this energy, it is sufficient to charge a capacitor of 500 MkF with an electrical voltage of 4200 V to evaporate the conductor. The development of an electro-impulse disturbing device. The disturbing device [4] is made with an explosive chamber connected by a channel to the reaction volume of the combustion chamber. In the electro-impulse dis- turbing device (EIDD), instead of the explosive charge, a wire (0.1-0.5 mm) is attached to isolated electrodes. As a substance used to create a pressure pulse, this generator uses the gas filling the blasting chamber, the mass of which depends on the pressure in the combustion chamber and in the EIDD chamber. Thus, for example, the mass of nitrogen, which is used to purge the DD, which fills an explosive chamber with a volume of 8 cm3 at a pressure of 10 MPa, is ~1 g. If you immediately heat this nitrogen to a temperature of several thousand degrees, you can get a gas that is close in parameters to the products of com- bustion of explosives in traditional disturbing impulse device (DID). It is possible to carry out such heating by discharging through a wire of an electric capacitor charged to several thousand volts. First, instantaneous (for several microseconds) evaporation of the wire takes place, and then through the plasma channel formed at the site of the wire, the final discharge of the capacitor occurs, with the release of all the energy stored in the capacitor. The plasma temperature in this case, according to different sources, can reach from several tens of thousands to one million degrees. The gas is also heated by adiabatic com- pression with a shock wave. The metal particles formed after the evaporation of the wire and the condensation of the vapor have a value of several nanometers and, there- fore, do not damage the inner shell of the combustion chamber. The scheme of the installation with the EIDD is shown in fig. 1. The design of the experimental sample of a single- charged electro-impulse disturbing device [4] is shown in fig. 2. EIDD contains the case 1 with the nipple 2 attached to it, through which a pressure pulse is introduced into the combustion chamber. In the case 1, a cavity 3 is formed in which an electrical node 4 is mounted, which is an axi- symmetric body made of a dielectric with electrodes 5 firmly fixed therein. The electrodes are retained in the insulator by means of thread bushes 6. The insulator itself is fixed in the case 1 by means of a closing sleeve 7 and a coupling nut 8. Between the end face of the insulator 4 and the end surface of the cavity 3, an explosive chamber 9 is formed into which the ends of the electrodes 5 protrude. A detonating wire 10 is soldered to the ends of the elec- trodes 5. In the case 1 the hole 11 with the welded fitting pipe 12 is made for blowing the explosion chamber with nitrogen. The results of preliminary studies confirm the sufficiency of the energy of the shock wave in calculating the stocks of stability of the working process in the com- bustion chambers of LRE in relation to high-frequency (HF) pressure fluctuations. The algorithm for estimating stability reserves of working process as the result of the spectral proces- sing of pressure pulsations in LRE aggregates during bench tests. The dynamics of a quasilinear system with given initial conditions and external influences is de- scribed by a system of equations for preserving the mate- rial balance, and after their linearization, the harmonic oscillator equation is obtained [2; 5-11]. Often, Laplace transforms over time variable t are applied to the equa- tions of free oscillations in perturbations, or the change of variables x = x = e∫δdt is introduced. As a result, we obtain a nonlinear characteristic equation of the dynamical system, which has order one unity less than the initial one. In general, it can be represented as: (δ + p)n-1δ + b1(δ + p)n-2 + … + + bn-2(δ + p) + bn-1δ + bn = 0, (1) here р - differentation operator, p = d . dt The characteristic equation (1) has n roots that form the fundamental system of solutions of the free oscillation equations after the reverse transition to the variable x. The case of forced oscillations of a linear dynamical system is investigated by the influence of an impulse signal on the system. Then variables mean output values, and external influences make input. The impulse response function of the system w describes the change in the output volume from the rest state to the new state and is characterized by a change in time t and the moment of application of the pulse δ1. The condition of physical feasibility can be formulated as w(t, δ1) = 0, t < Ø1. (2) Fig. 1. The scheme of the proposed concept of EIDD (electro-impulse disturbing device): 1 - combustion chamber of a liquid rocket engine; 2 - electro-impulse disturbing device; 3 - electrodes; 4 - exploding electric cord (wire); 5 - electrical insulator Рис. 1. Схематическое изображение предлагаемой концепции ЭИВУ: 1 - камера сгорания ЖРД; 2 - ЭИВУ; 3 - электроды; 4 - взрывающийся электрический провод (проволочка); 5 - электроизолятор Fig. 2. The design of the pressure pulse generator (electro-impulse disturbing device): 1, 2 - the case with a nipple; 3 - the volume for introduction of nitrogen; 4 - insulator; 5 - electrodes; 6 - thread bushings; 7 - closing sleeve; 8 - coupling nut; 9 - blasting chamber; 10 - wire; 11, 12 - the channel and the nitrogen supply connection Рис. 2. Конструкция генератора импульсов давления (ЭИВУ): 1, 2 - корпус с ниппелем; 3 - объем для ввода азота; 4 - изолятор; 5 - электроды; 6 - резьбовые втулки; 7 - втулка нажимная; 8 - гайка накидная; 9 - взрывная камера; 10 - проволочка; 11, 12 - канал и штуцер подачи азота The transfer function W (s, t) is a function of the com- plex variable s and real t, related to the impulse response of the equation a sm + a sm-1 +¼+ a W (s) = 0 0 m . sn + b1sn-1 +¼+ bn (7) ¥ W (s, t ) = ò w(t, t - τ)e-sτdτ, 0 where τ = t - δ1. (3) The transfer function of a nonstationary system is con- sidered similarly to the concept of a stationary system. Let the external pulse δ(t - u) act on the input of the non- stationary linear system, which is further amplified by the The transfer function is meaningful only in the region of the complex variable s, where for its real part Re(s) the inequality takes place Rе(s) > c0 and at the same time the conditions are observed ¥ ò w(t, t - τ) e-sτdτ < ¥ if с ≥ с0. (4) coefficient esu (modulated complex gain), then the response of the system can be written as exp su*w(t - u). Applying the superposition principle, we have: t ò exp(su)δ(t - u)du = exp st; -¥ t ¥ 0 In the theory of stationary linear systems, the transfer ò exp(su)w(t - u)du = exp stò exp(sτ)w(τ)dτ. -¥ 0 function is treated as the Laplace transform of the function w(τ), which is the response of the system to a unit The transfer function W(s) for Re(s) > c0 is the ratio pulse at time t = 0: ¥ ¥ -sτ -sτ of x(t)/y(t) in the process caused by the “action” y(t) = exp(st), see formula (6). The transfer function of a nonstationary system for a fixed time is defined as the W (s) = ò w(a, a - τ)e dτ = ò w(τ)e dτ. (5) Laplace transform with respect to the argument τ of the 0 0 function describing the output quantity that is a response The transfer function of a linear stationary system is the Laplace transform from the function w(τ), which shows its response at time t = a to the impulse applied earlier: a - τ. For the characteristic equation in the form of to a unit pulse with a delay of τ. In a nonstationary proc- ess, the difference is the dependence of the transfer func- tion on the time t as a parameter. The transfer function of a stationary system is analytically expressed in terms of the coefficients of the oscillation equation (6). For a nondnx + dn-1x dm y stationary system, therefore, the transfer function can not dtn b1 dtn-1 + ... + bnx = a0 dtm + ... + am y (6) be expressed, and it is calculated only approximately [1]. There are few approaches for determining the transfer such a transfer function has the following form: functions of dynamical systems. The methods most widely used in acoustic problems are based on the con- nection between the transfer function and the impulse response function, in particular the method expressing the impulse response function through the roots of the gener- alized characteristic equation [10; 15]. In this case, an approximate expression of the transfer function is ob- tained in the form of a fractional-rational function with clearly expressed poles. Another method of calculating the transfer function is to expand the impulse response function into a formal power series. The coefficients of the Taylor series are analytic functions. Both methods are applied under the condition that the oscillation equation is given in the interval (-∞, T). The response of acoustic dynamic systems to external influences differs from the exciting force. One of the characteristics is the moment of application of the impact, which can be remote to minus infinity or finite. In this case, time start is t = 0. The reaction of the system can be determined in the following cases: - if the impulse response function of the system w(t, u) is known and the external action y(t), which causes a definite reaction, this reaction can be calculated using the convolution integral; - if the external action can be transformed according to Laplace, the dependence describing the output quantity can be described using the transfer function of the system; - if the transfer function and the “left” Laplace trans- form of the input action are known [15]. Also, the system response is calculated using the equation of oscillations and frequency characteristics. The latter method is applied if the frequency characteristics of the system are known. Then, when calculating the response to an external action, it is appropriate to use Fourier transforms [10]. The frequency characteristics of non-stationary sys- tems are functions of two variables: frequency and time. The complex frequency response is equal to the ratio of the output value of the system or the dynamic link to the external action, if the response of the system satisfies the condition ¥ The transfer function of a linear dynamic system or a complex frequency response, as well as a transient response, fully reflect the response of the system to external influences. Let a harmonic signal be applied to the input of the linear link х = А(х) sin ωt, where А(х) is the amplitude; ω is an angular frequency of this influence. At the output of the link at the end of the transient process, harmonic oscillations of the same frequency are represented by the dependence y = A(y) sin (ωt + φ), where A(y) is the amplitude of the steady state oscilla- tions; φ is the phase shift between input and output oscil- lations. For a fixed amplitude of the input oscillations, the amplitude and phase of the steady-state oscillations at the output of the link are a function of the frequency of these oscillations. The analytical dependences A(ω) and φ(ω) are called the amplitude and phase functions. Amplitude and phase frequency characteristics are often combined into one: amplitude-phase frequency response (APFF). In this case, APFF is constructed in the complex plane, where the abscissa axis is the axis for the real part Re [W] of the transfer function of the link, and the ordinate axis for its imaginary part Im [W]. The frequency response can be presented in exponential form. Let at the input of the linear link be a signal of the form x = A(x)exp(iωt), and at the output the amplitude of the oscillations changes from it and the harmonic receives a phase shift y = A(y)exp(iωt + φ). In general terms C(ω, t) = │A(ω, t)│eiφ(ω, t), (10) where │A(ω, t)│is the amplitude frequency response; φ(ω, t) = argF(ω, t) is a phase frequency response. The steady-state reaction of the stationary system to the considered action is also harmonic and with the same frequency. The amplitude and phase of the oscillations change. In this case, the ratio of the amplitude of the out- put quantity to the amplitude of the input action is equal to the value of the amplitude-frequency response (AFR) at the value of the argument, which coincides with ò w (t, t - τ) dτ < ¥. 0 (8) the frequency of the action of ω. Thus, the phase shift between the output signal and the external action is equal If the process is considered in a finite time interval, then the oscillation equation must be defined on an infi- nite interval adjoining to the left. To determine the com- plex frequency response, it is sufficient to calculate the transfer function and make a substitution: s = iω. The task of determining the frequency characteristics of nonto the value of the phase frequency characteristic of the dynamic link at a value of ω. If the oscillation equation is known, then the expression of the frequency character- istics through its coefficients is realized on the basis of formula (1) in the following form: a0iωm +¼+ am stationary systems differs from stationary by doubling C(ω) = (iω)n + b (iω)n-1 +¼+ b . (11) of independent variables, for example, when showing 1 n characteristics graphically, which is associated with the construction of each curve for a certain time. The experimental determination of frequency characteristics. The frequency characteristics of the system are defined as the characteristics of the transfer function section for the values of the argument s = iω. The complex frequency function [2; 5; etc.] is the section C (ω, t) of the transfer function W (iω, t): C(ω, t) = W(iω, t). (9) In the case when the free oscillations of the system are undamped under some initial conditions, the frequency characteristics lose the physical meaning considered above, but the relation in the form of formula (11) with the coefficients of the oscillation equation remains valid. The experimental determination of the frequency characteristics is based on the equality of the complex frequency response to the ratio x(t)/y(t) under the external action y(t) = exp(iωt) and the fulfillment of the condition (11). To do this, it is necessary that the time interval during which the process is analyzed is limited to the left and that the response to the harmonic effect of the link is also limited in an infinite time interval. In gas-dynamic experiments, as a rule, the first condition is satisfied. Sup- pose that condition (11) is also satisfied. Also, a necessary condition for the experiment is multiple repeatability of results in the absence of external influences, except for one specially organized harmonic effect of a given frequency from the frequency interval determined by the sensitivity of the system to harmonic effects. Let t be the time counted from the beginning of the process studied, and [0, T] is the time interval at which the particular experiment (process) takes place. The initial conditions for this process should be able to vary widely. Then, in order to obtain the frequency characteristics of the system or link, it is sufficient to record changes in the output quantity in the interval [0, T] in processes caused by the effects y′i(t) = aicos ωit; y″i(t) = aisin ωit, i = 1, 2, …, m, for arbitrarily chosen amplitudes and frequencies from the range [Ω1, ..., Ωn] under the corresponding initial condicharacteristics of systems with periodically changing pa- rameters will depend on the time with the period of varia- tion of the coefficients of the oscillation equation. In this case, the obtained characteristics are extrapolated on the interval of time preceding the moment of establishment of the system reaction, which is equivalent in the experiment to the input of the initial conditions in accordance with the analytical extension of definition. In combustion cham- bers and LRE gas generators, the effects of capacitance and inertia can vary with time and determine the tendency of the system to pulsations with some characteristic frequencies. With an external effect on the dynamic sys- tem and after its removal, the response of the system, the establishment or damping of oscillations, is characterized by its transient response. The steady-state and transient processes are determined by the complex transmission coefficient KT, which can be represented as the ratio of the signal at the output ŝ2 from the system to the sinusoidal signal at its input ŝ1: KT = ŝ2/ ŝ1 = Kпер(ω)e-iφ(ω) = = Re│ KТ (ω)│ + iIm│ KТ (ω)│. (15) Here Re│K (ω)│, Im│K (ω)│ are the real and tions. If the initial conditions for the experiment can be пер пер extended to the interval (-∞, 0), then they are computed. If the processes in the system with the coefficients of the oscillation equation frozen at the time t = 0 are asymptoti- cally stable with respect to the output signal, then the option of additional definition is the assumption of stationa- rity of the system for t < 0, while the coefficients of the oscillation equation are equal to the frozen values. For example, if the external harmonic effect on the investi- gated link has the form aicosωit, then the steady-state re- action is an expression x(t) = aiA(ωi)cos[ωit + Θ(ωi)], (12) where A(ω) and Θ(ω) are the amplitude and phase frequency characteristics of the stationary system used to extend the system. Then from formula (12) it follows that imaginary parts of the transmission coefficient. The absolute value of the transmission coefficient characterizes the reaction of attenuation or amplification of the input sinusoidal signal, and its phase determines the shift. The connection between the shape and duration of the pulse and its spectrum is realized in practice using filters with a narrow bandpass. The signal is represented as the sum of the harmonic components. The filter inte- grates the signal over a time interval T approximately equal to the reciprocal of the bandpass of the filter Δf. If the main process period is greater than T = 1 / Δf, then the signal spectrum at the filter output will be the same as the envelope spectrum of the signal ŝ (t) at the input [10; 12; 15]. Fourier integral for large values of the period T represents the spectrum of the signal S'(ω) in the form ¥ x(0) = aiA(ωi)cos Θ(ωi), (13) i i i i d2k-1x/dt2k-1│t = 0 = (-1)ka ω 2k-1 = A(ω )sin θ(ω ), S'(ω) = ò s(t)e-iωt dt -¥ (16) d2k-1x/dt2k-1│t = 0 = (-1)ka ω 2kA(ω )cos θ(ω ), from here its backward transformation gives i i i i 2π n ¥ 1 ¢ -iwt k = 1, 2, …, . (14) 2 Another option to extend the system is to equate the coefficients of the right-hand side of the oscillation equa- tion with zero. In this case, the frequency characteristics can not be used to obtain the response of the link to the pulse. The frequency characteristics obtained with differ- ent variants of pre-determination will be different. For stationary systems and systems with periodically changing parameters, one can do without calculating the initial conditions, taking them into account by appropriate organization of the experiment. To do this, the frequency characteristics should be removed after the expiration of the practical attenuation of free oscillations. The reaction of the system in this case is of a steady nature, and the output value (or output signal) will vary with a period equal to the external action. The frequency characteristics of stationary systems will not depend on time, and the s(t) = ò S (w)e dw . (17) -¥ A rectangular pulse has an infinitely wide spectrum. It follows from the property of the mutual correspondence of the time function and its spectrum that the bounded spectrum can only be of a function that slowly falls to zero value with the passage of time. It is found out that in the frequency domain, where the normalized frequency is less than ½ (half-period is less than the correlation interval), the spectrum has an approximately constant amplitude, and with a further increase in frequency, the spectral amplitudes decrease rapidly to zero. It follows that the energy of the process is mainly concentrated in the frequency range from 0 to f = 1/tcp, where tcp is the average pulse duration equal to the ratio of the pulse area to its amplitude. To determine the relations between the real and imaginary parts of the transfer function, we consider the excitation of the system by the step function σ0(t), whose amplitude is zero for t < 0. The spectral density of such a function has the form S'(ω) = 1/iωA. (18) Here ωA = ω + iδ, δ > 0 of positive values t и ωA = ω - iσ for negative ones; δ - any small quantity. The signal at the output of the system can be repre- sented by a transition function or a characteristic of the system [10; 12; 15; 16]: 1 ¥-iδ é ù i(ωt -φ(ω)) The operation for other time points is repeated and the amplitude variation graph in time is constructed. The slope of the graph of A(t) characterizes the damping decrement. According to another technique, the pressure transducers are passed through a logarithmic amplifier and the amplitude levels are fixed, then the attenuation decrement is determined from the envelope of the pres- sure pulsations. Both methods for unfiltered pulsation readings allow us to determine the rate of attenuation of all pressure fluctuations. If it is necessary to determine the characteristics of the oscillations for a particular fre- 2π σ'0(t) = ò -¥-iδ ëKT (ω) / iωûe dω. (19) quency, the pressure transducer should be passed through the filter and then the rate of damping of the oscillations The way of integration can be closed in the upper half- plane for positive values of t and a semicircle in the lower plane for negative t. For a step function, the transmission factor is one. For the real system when ω → ∞, the transfer coefficient KТ (ω)/iω(ω) → 0, and its time derivative also tends to zero [15]: is determined. For filtering, it is desirable to reproduce the signal in the reverse mode, in this case only the last 3, 4 periods of damped oscillations are distorted. The inclined straight line approximating the periodic dependence characterizes the magnitude of the damping decrement. To determine the experimental values of the vibration ¶σ¢ (t) ¥-iδ decrement the following methods can also be applied: 0 = ¶t ò -¥-iδ KT (w)eiwt = 0, t < 0. (20) spectral, correlation, amplitude and instantaneous method [1; 12]. The amplitude method and the method of the Let the transmission coefficient be in the form KТ (ω) = = K1(ω) + iK2(ω), assuming δ → 0 and replacing t by -t in formula (20), we obtain the relation between the real and imaginary parts of the transmission coefficient: ¥ ¥ instantaneous period almost did not get used in practice. In experimental studies of the working process stability in liquid rocket engines [1; 3; 12], spectral and correlation methods were most widely used. The decrement of oscil- lations according to the spectral method is determined from the width of the signal power spectrum, fig. 3. ò K1 (w)cos wtdw = - ò K2 (w)sin wtdw > 0. -¥ -¥ (21) To detail the complex oscillation process in real com- bustion chambers, the spectral width is taken into account If we know the real part, we can calculate the imaginary, and vice versa. Under the assumption that the functions of four- terminal network are rational, in a number of papers [5; 6; 10; etc.] the relations between their real and imaginary parts are obtained, according to which it is easy to calcu- late the impedances or conductivities of the contours under study. There are different methods for calculating the damp- ing decrement [2; 3; 5; 6; 10; 14-16]. One of the methods measures the sweep of oscillations during one cycle and determines the time interval between the onset of the disturbance and the period of oscillation being analyzed. by means of a specific filter Δf of the spectro-analyzer. A three-point method is used in the algorithm [1; 3; 10; 12], and the method takes into account the dependencies of the left and right ascents, background and other inter- ference, relative to the calculated point. At the same time, the pair of points near the maximum is searched, and a pair of those points is chosen, which yields the mini- mum sum of the magnitude of the decrement and its calculated spread. The correlation method is used to cal- culate the decrement from the magnitude of the decay rate of the interrelationship function, an approximate calcula- tion scheme is shown in fig. 4. Fig. 3. The scheme for determining the decrement of oscillations by the spectral method Рис. 3. Схема определения декремента колебаний по спектральному методу Fig. 4. The scheme for determining the decrement of oscillations from the magnitude of the decay rate of the interrelationship function Рис. 4. Схема определения декремента колебаний по величине скорости затухания взаимокорреляционной функции The EDD (external disturbing device) and EID (exter- nal impulse device) must provide the following [12]: a) the correspondence of the disturbing amplitude of the most frequently observed natural pressure pulses in combustion chambers or gas generators; b) the spectral composition of the pulse must have such a distribution of energy over the frequencies that would ensure that excitation in the combustion chamber (as an acoustic resonator) of pressure fluctuations of suf- ficient intensity in the required frequency region; c) the possibility of changing the amplitude in the desired range and the stability of the characteristics during a repeated disturbance, as well as providing a series of periodic pulses; d) ensure the introduction of disturbances for a wide range of operating pressures in the chamber or gas gen- erator, as well as in the operation of the gas generator with an oxidizing environment. At the same time, there are some operating restrictions imposed on EID, for example: the minimum possible diameter of the input port for introducing disturbances in order to reduce the effect on the integrity of the com- bustion chamber, as well as the minimum dimensions and resistance to high temperatures, vibrations, etc. The most important is the choice of the place of the disturbance input. The answer to this question can be found from the prediction of the mode and the frequency of the natural oscillations of the path. An important fact is the method of optimal processing of experimental data, which provides sufficient accuracy and reliability of the obtained values of the damping decrement. The criterion for the adequacy of the stability margin for “hard” excita- tion [1-3; 5-14] is provided if the pressure oscillations after the pulse rapidly decay and a certain ratio is estab- lished between the initial peak deviation of the pressure from the mean and total high-frequency signal to the per- turbation input. It is stated [3; 12] that in order to evaluate the stability of the working process to finite disturbances, it is required: - introduce a pressure pulse in the range 15Asv < Am < 25Asv; - determine the relaxation time of the process tr, here Am is the average value of the absolute maximum of the pulse; - Asv is the average rectified value of natural noises pulsations; - tr = t1B + tb is the total relaxation time of the working process; - t1B is the time of action on the working process of the first disturbance wave; - tb is the time of decrease in the amplitude of pressure oscillations by e times. The combustion chamber is supposed to be stable to finite disturbances [3; 10; 12], if the relaxation time is tr < 15 ms. Further, it should be noted that in testing of full-scale motors, it is necessary to evaluate the decrements and the spectra of pressure oscillations, both before the introduc- tion of disturbance and after damping of the oscillations. Decrements of pressure fluctuations and spectra should not differ within the limits of measurement accuracy. A significant difference will mean the instability of the working process. Conclusion. The algorithm is proposed for estimating reserves of stability towards the high high-frequency pressure oscillations in gas-generators and combustion chambers of liquid rocket engines, which means spectral processing of the combustion process reaction to pulsed artificial disturbances. In contrast to pyro cartridges, which are now used to create pulses with different gas pressure amplitudes in combustion chambers, electric pulse disturbing devices have been developed. They reduce the risk of damage to the components of LRE units in full-scale and model tests, and have an obvious pros- pect for widespread use.

Об авторах

В. И. Бирюков

Московский авиационный институт (национальный исследовательский университет)

Российская Федерация, 125993, г. Москва, Волоколамское шоссе, д. 4, А-80, ГСП-3

В. П. Назаров

Сибирский государственный университет науки и технологий имени академика М. Ф. Решетнёва

Email: Nazarov@sibsau.ru
Российская Федерация, 660037, г. Красноярск, просп. им. газ. «Красноярский рабочий», 31

Р. А. Царапкин

Московский авиационный институт (национальный исследовательский университет)

Российская Федерация, 125993, г. Москва, Волоколамское шоссе, д. 4, А-80, ГСП-3

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