Low-frequency Instability Research Articles

Suprathermal corrections on galactic cosmic rays driven magnetohydrodynamic waves and gravitational instability in astrophysical plasmas

The interaction of two populations of highly energetic cosmic rays (CRs) and suprathermal kappa gas in the astrophysical systems manifests exciting features of low-frequency magnetohydrodynamic (MHD) waves and instabilities. Contrary to the previous works on waves and instability analysis in Maxwellian gas, this paper investigates the effects of suprathermal corrections on the CR driven MHD waves and gravitational (Jeans) instability using the kappa distribution function. The equation of state for a kappa gas, including spectral κ− index, is considered in the CR-plasma interactions using the hydrodynamic fluid–fluid approach. The modified dispersion properties of fast, slow, and pure Alfvén waves and Jeans instability have been discussed in a suprathermal gas in astrophysical environments. The suprathermal corrections enhance the phase speed of the fast mode of MHD waves which is found to be greater in the suprathermal gas (κ>3/2) and smaller in the Maxwellian gas (κ→∞). In the absence of CR diffusion, the Jeans instability criterion is modified due to the simultaneous presence of CR pressure and suprathermal corrections. However, in the presence of CR diffusion, only suprathermal corrections modify the Jeans instability criterion. The suprathermal gases with higher degrees of freedom require large values of the Jeans wavenumber to produce gravitational instability and make the system more unstable. The suprathermal corrections along with modified thermal speed stabilize the growth rate of Jean instability, supporting the gravitational collapse of non-thermal gas in astrophysical systems.

Verification of electromagnetic simulation capabilities in global gyrokinetic particle-in-cell code GTS

Recently, the numerical scheme presented by Mishchenko et al. [Phys. Plasmas 21, 052113 (2014); 21, 092110 (2014)] enabled explicit gyrokinetic simulations of low-frequency electromagnetic instabilities in tokamaks at experimentally relevant values of plasma β. This scheme resolved the long-standing cancellation problem that previously hindered gyrokinetic particle-in-cell code simulations of magnetohydrodynamic phenomena with inherently small parallel electric fields. Moreover, the scheme did not employ approximations that eliminate critical tearing-type instabilities. Here, we report on the implementation of this numerical scheme in the global gyrokinetic particle-in-cell code GTS. This implementation allows for a more complete and accurate picture of interaction between small scale turbulence and MHD modes in tokamaks. Additionally, we present a comprehensive set of verification simulations of numerous electromagnetic instabilities relevant to present-day tokamaks. These simulations encompass the kinetic ballooning mode, the internal kink mode, the tearing mode, the micro-tearing mode, and the toroidal Alfven eigenmode destabilized by energetic ions, which are all instrumental in understanding tokamak physics. We will also showcase the preliminary nonlinear simulations of kinetic ballooning instabilities and (2,1) island formation due to tearing mode instability. These simulations validate the accuracy of the scheme implementation and pave the way for studying how these instabilities affect plasma confinement and performance.

Diversity and transition of periodic motion of a periodically excited soft-impacting machinery

Dynamics of a periodically excited vibro-impact system with soft impacts is investigated. Essential features of period-one multi-impact motion group and correlated transition characteristics in low-frequency range are discussed in detail by the way of two-parameter bifurcation space providing qualitative domains for different periodic motions. The main focus is given to the effect of sensitive parameters including constraint stiffness k 0, clearance threshold b, and damping parameter ζ on the system response. The low-frequency characteristics in the finite-dimensional parameter space are particularly explored. It is found that the increase of k 0 induces multi-type bifurcation of period-one double-impact symmetrical motion, which induces a rich variety of periodic motions, and period-one multi-impact motion group orbit primarily exist in the small-clearance b and low-frequency ω zone. Based on the evolution irreversibility of adjacent period-one multi-impact orbit, the mechanism of singularies appearing in pairs and two different transition zones (hysteresis and liguliform zones) is studied, the result of which provides a theoretical reference value for the common low-frequency vibration instability phenomenon in the field of mechanical engineering. For small-damping coefficient ζ, period-one multi-impact motion has a large quantity, and the main bridge for the transition of adjacent period-one multi-impact motion is liguliform zone, which embraces period-one multi-impact asymmetrical motion and period-n multi-impact subharmonic motion and a certain chaotic zone. For large-damping coefficient ζ, the amount of period-one multi-impact motion group is reduced, and the main bridge for the transition of adjacent period-one multi-impact motion is hysteresis zone, where adjacent period-one multi-impact orbits can coexist according to initial conditions. As designing and renovating impact mechanical equipment, the reasonable matching law of dynamic parameters can be determined through two-parameter bifurcation space, which is conducive to making the system work in stable periodic motion and obtaining larger instantaneous impact velocity.

A Review of Recent Developments in Hybrid Rocket Propulsion and Its Applications

This paper extensively reviews hybrid rocket propulsion-related activities from combustion engine designs to launch tests. Starting with a brief review of rocket propulsion development history, a comparison among the three bi-propellant rocket propulsion approaches, and hybrid rocket engine design guidelines, a very thorough review related to hybrid rocket propulsion and its applications is presented in this paper. In addition to propellant choice, engine design also affects the hybrid rocket performance and, therefore, a variety of engine designs, considering, e.g., fuel geometry, swirl injection, ignition designs, and some innovative flow-channel designs are also explored. Furthermore, many fundamental studies on increasing hybrid rocket engine performances, such as regression rate enhancement, mixing enhancement, and combustion optimization, are also reviewed. Many problems that will be encountered for practical applications are also reviewed and discussed, including the O/F ratio shift, low-frequency instability, and scale-up methods. For hybrid rocket engine applications in the future, advanced capabilities and lightweight design of the hybrid rocket engine, such as throttling capability, thrust vectoring control concept, insulation materials, 3D-printing manufacturing technologies, and flight demonstrations, are also included. Finally, some active hybrid rocket research teams and their plans for flight activities are briefly introduced.

Detection of a low-frequency ion instability in a magnetic nozzle

Abstract A low-frequency ion instability, with frequency f I between the ion gyrofrequency and the lower hybrid frequency f c , i < f I ≪ f LH , is detected in an argon plasma expanding in a magnetic nozzle for magnetic fields between 240 < B z , max < 700 G. The frequency of the instability exhibits a linear dependence with magnetic field strength, and the wave amplitude has a radial maximum that would match the location of a conical density structure, i.e. high-density cones. For all of the magnetic field cases analysed, the high-frequency spectra showed upper and lower sidebands centred around the driving frequency and at a separation equal to the instability frequency, 27.12 MHz ± f I kHz. Measurements of the perpendicular wavenumber would satisfy, for certain magnetic field strengths, the dispersion relation of both an electrostatic ion cyclotron wave (ICW) and of an ion acoustic wave. It is hypothesised that the observed low-frequency wave could be an acoustic-like instability propagating perpendicular to the magnetic field, which develops as an ICW at some magnetic field strengths. From the data collected, it is suggested that the high-frequency sidebands may be caused by modulation of the low-frequency wave.

Effect of the combustion chamber length in combustion instability of low-toxic hypergolic thruster

In this study, the effect of combustion chamber length on the hypergolic combustion instability of hydrogen peroxide-based propellants was investigated. Twenty-four hot-firing tests were conducted using a combination of 95 wt.% hydrogen peroxide and amine-based fuel with a drop test ignition delay of 5.65 ms and an adjustable length hypergolic thruster. When the chamber length was changed from 80 mm to 120 mm, the root mean square (RMS) combustion instability decreased drastically from 24 % to 9 %. The measured high-frequency instability was considerably consistent with the longitudinal resonance mode of each combustion chamber geometry. Low-frequency instability, that is, the rate of popping, occurred predominantly in all hot-firing tests. Within the 245–418 Hz range, its frequency increased as the chamber length decreased or the chamber pressure increased. The high-speed camera image of the exhaust plume coincided with the period of low-frequency instability, which was confirmed by the periodic popping of the propellant. Combustion instability was analyzed in depth by performing power spectral density (PSD), wavelet synchro squeezed transform (WSST), dynamic mode decomposition (DMD), and image intensity analyses using the chamber pressure and exhaust plume images. DMD decomposed the plume behavior into one expansion mode and three plume decay modes, and it also matched the low-frequency instability of the chamber pressure with an error of less than 5 %.

Analytical Characterization of Low-Frequency Instabilities in a Simple Duct System

Analytical Characterization of Low-Frequency Instabilities in a Simple Duct System

Experimental study on the hypersonic double incident shock wave/boundary layer interaction regulated by plasma actuation array

In the inlet passage of a hypersonic vehicle, multi-channel shock waves inevitably interact with the boundary layer, producing complex multi-channel shock wave/boundary layer interactions (SWBLIs). The flow separation caused by these interactions significantly decreases the intake efficiency and may prevent the intake from starting. The typical interaction mode of multi-channel interactions is through double incident SWBLIs. Therefore, it is necessary to study the characteristics of double incident SWBLIs and identify relevant flow control techniques. In this paper, the characteristics of hypersonic double incident SWBLIs are first examined, and then the results of an experimental study on regulation using a plasma actuation array are reported. We find that plasma actuation can positively regulate the hypersonic double incident SWBLI, and the optimal control effect reduces the area of the separation bubble by 38.62%. The main regulation mechanism involves suppressing the low-frequency instability of SWBLIs through a high-frequency shock effect. The regional scale of the separation bubble can be controlled by regulating the shock wave oscillation range. Correlative results provide technical and method support for the application of plasma actuation in hypersonic double incident SWBLI regulation and present a new idea for the selection of flow control methods for advanced intake systems.

Gyro-kinetic simulations of trapped electron collision effects on low-frequency drift-wave instabilities in tokamak plasmas

Low-frequency drift-wave instabilities play a crucial role in the radial transport of present-day tokamaks, and trapped electron collisions can significantly influence these instabilities. In this paper, the effects of trapped electron collisions on these instabilities are investigated based on linear gyro-kinetic simulations. The basic numerical techniques including dispersion relation integral method and orthogonal basis function expansion are presented in detail with necessary benchmark work. The results demonstrate that in medium gradients, the increase of trapped electron proportions promotes the growth rate and radial heat transport largely for quasi-linear trapped electron modes (TEMs) and ion temperature gradient (ITG) modes. Moreover, trapped electron collisions have strong stabilizing effects, especially for TEMs driven by electron temperature gradients. Two distinctive branches, namely Mode #1 and #2, are investigated in steep gradients. Both behave in a varied instability nature during different ranges of the normalized wave vector k^θ . Mode #1 mainly induces radial heat transport during k^θ<0.5 and is significantly suppressed by the collisions. Mode #2 mainly induces radial heat transport during 0.4<k^θ<0.8 , and is largely enhanced by the collisions. When the collisionality is large enough, Mode #2 has stronger transport capacity than the other. Mode #2 at the medium wave vector, known as dissipative TEM, may provide the mechanism of the edge coherent mode observed in EAST H-mode plasmas, wherein collisionality plays an important role in the mode excitation.

Low-frequency whistler waves driven by energetic electrons in plasmas of solely electron cyclotron wave heating

Whistler waves are a type of low-frequency electromagnetic wave common in nature, which is usually associated with energetic electron phenomena. This study presents experimental observations of low-frequency whistler wave instabilities driven by energetic electrons through wave–particle interactions on EXL-50. The energetic electrons are generated by electron cyclotron waves (ECWs) through stochastic heating [Wang et al., J. Plasma Phys. 89, 905890603 (2023)] and do not match the characteristics of the runaway electrons [Shi et al., Nucl. Fusion 62, 086047 (2022)]. In the steady-state plasma of the Energy iNNovation XuanLong-50 (EXL-50), whistler waves within the 30–120 MHz frequency range were observed during electron cyclotron resonance heating. These waves displayed multiple frequency bands, and the frequencies of waves were directly proportional to the Alfvén velocity. Furthermore, it was interesting to find that superposition of lower hybrid wave into ECW resulted in the suppression of these whistler waves. The experimental results may indicate that the whistler waves are driven by energetic electrons (excluding runaway electrons). These discoveries carry significant implications for several areas of research, including the investigation of wave–particle interactions, the development of radio frequency wave current drivers, their potential impact on the electron dynamics in future fusion devices, and even the presence of unusually low-frequency whistler waves in Earth's radiation belts.

Dynamic Stabilization of a Centralized Weak Grid-Tied VSC System Considering PV Generator Dynamics

This paper addresses the instabilities and dynamic interactions in a centralized vector-controlled voltage-source converter interfacing a single-stage utility-scale photovoltaic (PV) generator to a high-impedance grid system. The dynamic resistance of the PV generator is considered, and effective active stabilization methods to guarantee the entire system's stability are proposed. Further, a complete state-space linearized model is developed, and different operating conditions alongside the maximum-power operation (MPO) are considered, such as fixed-voltage operation (FVO) and fixed-current operation (FCO). It is found that with the change of the PV generator operation from the FVO or MPO to the FCO region under the weak grid and nominal dc-link capacitance conditions, the dominant eigenmodes are relocated to the open-right-half-plane of the S-plane. This eventually induces inevitable high- and low-frequency oscillation instabilities. Further, it is found that medium-frequency oscillation instability is induced in the FVO region under a weak grid and reduced dc-link capacitance conditions. Active compensators are proposed to reduce the interaction dynamics and stabilize the entire system by reshaping the converter transfer functions; hence, the Nyquist stability criterion is maintained. Finally, detailed nonlinear time-domain simulation results are provided, showing the effectiveness of the proposed method in preserving the system's stability under a wide range of operation conditions.

Periodic repolarization dynamics: Different methods for quantifying low-frequency oscillations of repolarization

BackgroundPeriodic repolarization dynamics (PRD) is an electrocardiographic biomarker that quantifies low-frequency (LF) instabilities of repolarization. PRD is a strong predictor of mortality in patients with ischaemic and non-ischaemic cardiomyopathy. Until recently, two methods for calculating PRD have been proposed. The wavelet analysis has been widely tested and quantifies PRD in deg2 units by application of continuous wavelet transformation (PRDwavelet). The phase rectified signal averaging method (PRDPRSA) is an algebraic method, which quantifies PRD in deg. units. The correlation, as well as a conversion formula between the two methods remain unknown. MethodThe first step for quantifying PRD is to calculate the beat-to-beat change in the direction of repolarization, called dT°. PRD is subsequently quantified by means of either wavelet or PRSA-analysis. We simulated 1.000.000 dT°-signals. For each simulated signal we calculated PRD using the wavelet and PRSA-method. We calculated the ratio between PRDwavelet and PRDPRSA for different values of dT° and RR-intervals and applied this ratio in a real-ECG validation cohort of 455 patients after myocardial infarction (MI). We finally calculated the correlation coefficient between real and calculated PRDwavelet. PRDwavelet was dichotomized at the established cut-off value of ≥5.75 deg2. ResultsThe ratio between PRDwavelet and PRDPRSA increased with increasing heart-rate and mean dT°-values (p < 0.001 for both). The correlation coefficient between PRDwavelet and PRDPRSA in the validation cohort was 0.908 (95% CI 0.891–0.923), which significantly (p < 0.001) improved to 0.945 (95% CI 0.935–0.955) after applying the formula considering the ratio between PRDwavelet and PRDPRSA obtained from the simulation cohort. The calculated PRDwavelet correctly classified 98% of the patients as low-risk and 87% of the patients as high-risk and correctly identified 97% of high-risk patients, who died within the follow-up period. ConclusionThis is the first analytical investigation of the different methods used to calculate PRD using simulated and clinical data. In this article we propose a novel algorithm for converting PRDPRSA to the widely validated PRDwavelet, which could unify the calculation methods and cut-offs for PRD.

Reactive Flow Dynamics of Low-Frequency Instability in a Scramjet Combustor

This study numerically investigated the combustion instability and characteristics of a laboratory-scale gaseous hydrogen-fueled scramjet combustor. For this purpose, a numerical simulation with an improved detached eddy simulation and a detailed hydrogen/oxygen reaction mechanism was performed. The numerical framework used high-resolution schemes with high-order accuracy to ensure high resolution and fidelity. A total of five fuel injection pressures were considered to characterize the combustion instability as a function of the equivalence ratio. A sampling time of up to 100 ms was considered to sufficiently accumulate several cycles of low-frequency combustion instability dynamics with a period in the order of 100 Hz. Numerical results revealed the repetitive formation/dissipation dynamics of the upstream-traveling shock wave, and it acts as a key factor of combustion instability. The period and derived principal frequency of these upstream-traveling shock waves is several ms. The frequency analysis showed that the instability frequency increased in the low-frequency range as the combustion mode transitioned from the cavity shear-layer to the jet-wake type. This characteristic was derived from the transition in combustion mode at the same equivalence ratio. Therefore, it suggests that the instability frequency shifting is governed by the combustion mode rather than the equivalence ratio. These comprehensive numerical results demonstrated not only the effect of the equivalence ratio but also the important role of the combustion mode on the low-frequency combustion instability.

Formulation and Performance of Multi-Transmitting Formula with Spectral Element Method in 2D Ground Motion Simulations Under Plane-Wave Incidence: SV Wave Problem

ABSTRACT To simulate the ground motions of 2D arbitrary sites subjected to plane SV waves, we put forward a numerical method combining the multi-transmitting formula (MTF) and spectral element method (SEM). The investigation results demonstrate a high simulation accuracy of the presented method. Most importantly, the MTF exhibits a notably superior stability performance in the SEM than in traditional finite-element method (FEM). Without any additional treatment, high-frequency instability does not occur when controlling the Courant number value C and the ratio between the MTF parameter S and C; the upper limit value of this ratio is significantly smaller than that of the SH-wave problem. In addition, a preliminary stability criterion for the MTF in SEM is given based on the homogeneous half-space model. For low-frequency stability, the occurrence time of instability is considerably lagged when no interventions are adopted. Moreover, the low-frequency instability can be readily eliminated by using smaller modification parameter in the SEM compared with the FEM.

Ignition delay and low-frequency coupling in hybrid rocket combustion

Hybrid rocket engines (HREs) require a post chamber to allow additional enthalpy production of unburned mixture, which may be expelled without participating in combustion. Many studies have confirmed that the post chamber is responsible for generating low-frequency instability (LFI). This study performed various tests with increasing post-chamber lengths. The test results show that post-chamber length is an important factor that determines the occurrence of the LFI. While the LFI persists, there is an observed positive coupling between pressure oscillations (p′) and heat release oscillations (q′), which share the same high-frequency band (400–500 Hz). But a phase difference changes periodically over time, it forms pressure beats of approximately 15–20 Hz. Video images (with LFI) show that combustion flows bounce back upstream after impinging on the nozzle wall. The bounced-back flow then collides with the incoming flow and forms a counter flow in the post chamber. In addition, re-ignitions with delays are observed in the counter-flow region, which is discontinuous and periodic. This study revealed that the periodic positive coupling of p′ and q′ is one of the manifestations of thermoacoustic instability. A modified kick oscillator model is used to account for the ignition delay and successfully predicted the pressure beats.

A radiomics model fusing clinical features to predict microsatellite status preoperatively in colorectal cancer liver metastasis

PurposeTo study the combined model of radiomic features and clinical features based on enhanced CT images for noninvasive evaluation of microsatellite instability (MSI) status in colorectal liver metastasis (CRLM) before surgery.MethodsThe study included 104 patients retrospectively and collected CT images of patients. We adjusted the region of interest to increase the number of MSI-H images. Radiomic features were extracted from these CT images. The logistic models of simple clinical features, simple radiomic features, and radiomic features with clinical features were constructed from the original image data and the expanded data, respectively. The six models were evaluated in the validation set. A nomogram was made to conveniently show the probability of the patient having a high MSI (MSI-H).ResultsThe model including radiomic features and clinical features in the expanded data worked best in the validation group.ConclusionA logistic regression prediction model based on enhanced CT images combining clinical features and radiomic features after increasing the number of MSI-H images can effectively identify patients with CRLM with MSI-H and low-frequency microsatellite instability (MSI-L), and provide effective guidance for clinical immunotherapy of CRLM patients with unknown MSI status.

Energetic passing particle-driven instabilities and their impact on discharge evolution in KSTAR

An experimental study is conducted on the onset and evolution characteristics of energetic particle-driven instabilities in Korea Superconducting Tokamak Advanced Research (KSTAR) with dominant tangential neutral beam injection (NBI). A scan of NBI beam energy shows the evanescence of the sawtooth crash and the concomitant onset of the strong passing particle-driven low-frequency fishbone instability. A quantitative analysis shows that the safety factor (q)-profile in the core region is clamped by a balance between the depletion of energetic passing particles by the fishbone instability and their external replenishment. Two synchronized chirping modes with distinct toroidal mode numbers (n = 1 and n = 5) supersede the fishbone instability after a self-organized q-profile is attained. An analysis shows that the n = 1 mode is likely to be a high-frequency beta-induced Alfvén eigenmode fishbone branch, while the n = 5 mode is an energetic particle mode (EPM). A dynamic system analysis of the synchronized EPM (S-EPM) shows that a stable S-EPM cycle can exist when the coupling between the two modes involved is insignificant. The potential impact of such EPMs on the establishment of a burning plasma scenario with a flat core q-profile is briefly discussed.

Effect of compressibility on industrial DC electric arcs

The paper reports on the behaviour and dynamics of direct current electric arc in an industrial electric arc furnace. Electric arcs are intense energy sources involved in many industrial processes. The behaviour of electric arc is simulated in a 2D axisymmetric geometry. A 40 kA current flows between two electrodes with a gap of 0.25 cm. The flow of current creates a very powerful jet up to km/s. Such speeds pose the question of the importance of compressibility and what is the extent of the effects of compressibility on arc behaviour. To assess the effect of compressibility, two different simulations are performed: an incompressible and a compressible simulation. The first simulation considers a temperature-dependent density based on experimental measurement whereas the latter adopts the ideal gas law to calculate the density variation of the plasma. The incompressible results were previously validated and compared to the well-known results predicted by the literature. The numerical results of the two models are reported and compared in terms of flow, thermal fields, and voltage drop. The results show that compressibility affects several aspects of the arc. As expected, the velocity drops when compressibility is present, however, the voltage drop increase significantly. Additionally, compressibility introduces a repetitive pattern of voltage drop over time which also depicted in the arc dynamics. The pattern is divided into three distinctive dynamics: (1) High-frequency low amplitude instabilities, followed by (2) low low-frequency high amplitude instabilities region, and finally, a relatively (3) stable interval of voltage with a bell-shaped arc.

Performance Comparison of Paraffin/Ethanol Fuel Blends in a Laboratory-Scale Hybrid Rocket Motor

This paper discusses the performance characteristics of a paraffin-based blend of liquid ethanol with paraffin as compared to pure paraffin in a hybrid rocket motor. Since the disclosure of the high regression rates of liquefying fuels as compared to classic fuels such as hydroxyl-terminated polybutadiene (HTPB), many studies using paraffin have been reported in the literature. Although pure paraffin regresses three to four times faster than HTPB, it is not an ideal fuel for launcher applications for the following reasons: it does not provide the optimum mechanical strength, it may suffer from combustion instability, and it offers low combustion efficiency. The proposed blend is biphasic, with drops of liquid ethanol trapped in a paraffin binder; and a nonionic surfactant was employed to emulsify the ethanol into paraffin wax. The results indicated that at a mean prefiring of 0.6 and a of 60, both the P95E05 and P90E10 fuels demonstrated no significant statistical difference compared to pure paraffin in terms of thrust, specific impulse, fuel mass flow rate, characteristic velocity, and combustion efficiency. However, the P95E05 and P90E10 fuels did show damping in the pressure oscillations relative to paraffin, indicating a reduction in the low-frequency combustion instability observed in the ballistic responses of paraffin.

Simulation and analysis of low-frequency instability in hot-fire test of a cryogenic hydrogen-oxygen preburner

Low-frequency chamber pressure oscillation is observed in the hot-fire test of a subscale cryogenic hydrogen-oxygen preburner. A lumped parameter simulation model with bipropellant injector is established by solving differential equations directly. Under the condition of constant inlet pressure, the frequency of oscillation of combustion chamber pressure increases with the decrease of combustion delay, while the variation trend of amplitude of oscillation of chamber pressure is opposite. As the combustion delay decreases to 1.76 ms, the pressure oscillation gradually converges and stabilizes, but its initial oscillation frequency is still about 2.7 Hz lower than that of the test. In addition, the influence of the volume ratio of liquid propellant in the combustion chamber is analyzed. The combustion time delay is set to 1.76 ms, and the frequency and amplitude of the pressure oscillation increase with the increase of the liquid volume ratio. With the liquid volume ratio set at 2.8%, the frequency and amplitude obtained by simulation are in good agreement with the test. In order to reproduce the continuous oscillation of the combustion chamber pressure during the 30 s process in the test, the pre-injection pressure test curve varying with time is used as the inlet condition. The liquid volume ratio and combustion delay are empirically corrected in real time using propellant flow rate and mixture ratio, respectively. The continuous oscillation of the simulated pressure during the 30 s test was obtained, and its frequency value and trend are completely consistent with the test data. It can be inferred that low-frequency unstable combustion related to combustion delay may have occurred in the hot-fire test of the preburner.