Derivation of a Revised Tsiolkovsky Rocket Equation That Predicts Combustion Oscillations

Our study identifies a subtle deviation from Newton’s third law in the derivation of the ideal rocket equation, also known as the Tsiolkovsky Rocket Equation (TRE). TRE can be derived using a 1D elastic collision model of the momentum exchange between the differential propellant mass element (dm) and the rocket final mass (m1), in which dm initially travels forward to collide with m1 and rebounds to exit through the exhaust nozzle with a velocity that is known as the effective exhaust velocity ve. We observe that such a model does not explain how dm was able to acquire its initial forward velocity without the support of a reactive mass traveling in the opposite direction. We show instead that the initial kinetic energy of dm is generated from dm itself by a process of self-combustion and expansion. In our ideal rocket with a single particle dm confined inside a hollow tube with one closed end, we show that the process of self-combustion and expansion of dm will result in a pair of differential particles each with a mass dm/2, and each traveling away from one another along the tube axis, from the center of combustion. These two identical particles represent the active and reactive sub-components of dm, co-generated in compliance with Newton’s third law of equal action and reaction. Building on this model, we derive a linear momentum ODE of the system, the solution of which yields what we call the Revised Tsiolkovsky Rocket Equation (RTRE). We show that RTRE has a mathematical form that is similar to TRE, with the exception of the effective exhaust velocity (ve) term. The ve term in TRE is replaced in RTRE by the average of two distinct exhaust velocities that we refer to as fast-jet, vx1, and slow-jet, vx2. These two velocities correspond, respectively, to the velocities of the detonation pressure wave that is vectored directly towards the exhaust nozzle, and the retonation wave that is initially vectored in the direction of rocket propagation, but subsequently becomes reflected from the thrust surface of the combustion chamber to exit through the exhaust nozzle with a time lag behind the detonation wave. The detonation-retonation phenomenon is supported by experimental evidence in the published literature. Finally, we use a convolution model to simulate the composite exhaust pressure wave, highlighting the frequency spectrum of the pressure perturbations that are generated by the mutual interference between the fast-jet and slow-jet components. Our analysis offers insights into the origin of combustion oscillations in rocket engines, with possible extensions beyond rocket engineering into other fields of combustion engineering.

Emission characteristics and combustion instabilities in an oxy-fuel swirl-stabilized combustor

This paper presents an experimental study on the emission characteristics and combustion instabilities of oxy-fuel combustions in a swirl-stabilized combustor. Different oxygen concentrations (Xoxy=25%～45%, where Xoxy is oxygen concentra- tion by volume), equivalence ratios (φ=0.75～1.15) and combustion powers (CP=1.08～2.02 kW) were investigated in the oxy-fuel (CH4/CO2/O2) combustions, and reference cases (Xoxy=25%～35%, CH4/N2/O2 flames) were covered. The results show that the oxygen concentration in the oxidant stream significantly affects the combustion delay in the oxy-fuel flames, and the equivalence ratio has a slight effect, whereas the combustion power shows no impact. The temperature levels of the oxy-fuel flames inside the combustion chamber are much higher (up to 38.7%) than those of the reference cases. Carbon monoxide was vastly produced when Xoxy>35% or φ>0.95 in the oxy-fuel flames, while no nitric oxide was found in the exhaust gases because no N2 participates in the combustion process. The combustion instability of the oxy-fuel combustion is very different from those of the reference cases with similar oxygen content. Oxy-fuel combustions excite strong oscillations in all cases studied Xoxy=25%～45%. However, no pressure fluctuations were detected in the reference cases when Xoxy>28.6% accomplished by heavily sooting flames which were not found in the oxy-fuel combustions. Spectrum analysis shows that the frequency of dynamic pressure oscillations exhibits randomness in the range of 50～250 Hz, therefore resulting in a very small resultant amplitude. Temporal oscillations are very strong with amplitudes larger than 200 Pa, even short time fast Fourier transform (FFT) analysis (0.08 s) shows that the pressure amplitude can be larger than 40 Pa.

Study on Instable Combustion of Solid Rocket Motor with Finocyl Grain

The instable combustion or oscillation combustion which occurs in three high capacity solid rocket motors using high energy composite propellant with finocyl grain is studied. The reasons of the acoustic combustion instability are also discussed. Three engineering methods that can eliminate combustion instability are proposed and discussed. The study shows that the combustion instability mainly depends on the propellant grain shape and nozzle structure. Some measures to reduce the acoustic energy and mass generation rate of combustion gas can be adopted. The test results indicate that the modified rocket motors can significantly eliminate the instable combustion and improve the motor internal ballistic performance.

Observation of low-frequency oscillation in argon helicon discharge

We present here a kind of low-frequency oscillation in argon helicon discharge with a half helical antenna.This time-dependent instability shows a global quasi-periodic oscillation of plasma density and electron temperature,with a typical frequency of a few tens of Hz which increases with external magnetic field as well as radiofrequency(RF)power.The relative oscillation amplitude decreases with magnetic field and RF power,but the rising time and pulse width do not change significantly under different discharge conditions.The oscillation can only be observed in some specific conditions of low magnetic fields and low RF power when the gas flows in from one end of the discharge area and out from another end.This global instability is suggested to be attributed to the pressure instability of neutral depletion,which is the result of compound action of gas depletion by heating expansion and gas replenishment from upstream.There are two kinds of oscillations,large and small amplitude oscillations,occurring in different discharge modes.This study could be a good verification of and complement to earlier experiments.This kind of spontaneous pulse phenomenon is also helpful in realizing a pulsing plasma source without a pulsed power supply.

Excitation of extremely low-frequency chorus emissions: The role of background plasma density

Low-frequency chorus emissions have recently attracted much attention due to the suggestion that they may play important roles in the dynamics of the Van Allen Belts.However, the mechanism(s) generating these low-frequency chorus emissions have not been well understood..In this letter, we report an interesting case in which background plasma density lowered the lower cutoff frequency of chorus emissions from above 0.1 f_(ce)(typical ordinary chorus) to 0.02 f_(ce)(extremely low-frequency chorus).Those extremely low-frequency chorus waves were observed in a rather dense plasma, where the number density N_e was found to be several times larger than has been associated with observations of ordinary chorus waves.For suprathermal electrons whose free energy is supplied by anisotropic temperatures, linear growth rates(calculated using in-situ plasma parameters measured by the Van Allen Probes) show that whistler mode instability can occur at frequencies below 0.1 f_(ce) when the background plasma density N_e increases.Especially when N_e reaches 90 cm–3 or more, the lowest unstable frequency can extend to 0.02 f_(ce) or even less, which is consistent with satellite observations.Therefore, our results demonstrate that a dense background plasma could play an essential role in the excitation of extremely lowfrequency chorus waves by controlling the wave growth rates.

A numerical study of accelerated moderate or intense low-oxygen dilution(MILD)combustion stability for methane in a lab-scale furnace by off-stoichiometric combustion technology

Moderate or intense lowoxygen dilution(MILD)combustion has become a promising lowNOX emission technology,while the delayed mixing of reactants and slower oxidation rate could potentially cause ignition instability in some scenarios.This paper proposes a new idea for enhancing the ignition stability for methane MILD combustion by combining with offstoichiometric combustion(OSC),and its performances have been numerically assessed through a comparison against the original MILD combustion burner.The results reveal although nonpremixed pattern has the lowest NO emission,it suffers from a larger liftoff distance,thus less ignition stability.Contrarily,both partiallypremixed and fully premixed patterns exhibit excellent ignition stability.Among the considered OSC conditions,the pattern of Inner ultrarich and Outer lean produces the lowest NO emission while maintains a high ignition stability.Furthermore,the enhancement of the combustion stability by implementing OSC to the original MILD combustion burner is shown by comparing the operational range of furnace wall temperature(Tf),CO and NO emissions,as well as the evolution of chemical flame.The comparison reveals that OSC can extend the lowest operational Tf from 900 K to 800 K.More importantly,OSC can significantly improve the ignition stability in the whole range of Tf as compared to the original MILD combustion burner.

Study on the influences of interaction behaviors between multiple combustion-gas jets on expansion characteristics of Taylor cavities

The purpose of this study is to investigate means of controlling the interior ballistic stability of a bulk-loaded propellant gun（BLPG）.Experiments on the interaction of twin combustion gas jets and liquid medium in a cylindrical stepped-wall combustion chamber are conducted in detail to obtain time series processes of jet expansion,and a numerical simulation under the same working conditions is also conducted to verify the reliability of the numerical method by comparing numerical results and experimental results.From this,numerical simulations on mutual interference and expansion characteristics of multiple combustion gas jets（four,six,and eight jets） in liquid medium are carried out,and the distribution characteristic of pressure,velocity,temperature,and evolutionary processes of Taylor cavities and streamlines of jet flow Held are obtained in detail.The results of numerical simulations show that when different numbers of combustion gas jets expand in liquid medium,there are two different types of vortices in the jet flow field,including corner vortices of liquid phase near the step and backflow vortices of gas phase within Taylor cavities.Because of these two types of vortices,the radial expansion characteristic of the jets is increased,while changing numbers of combustion gas jets can restrain Kelvin-Helmholtz instability to a certain degree in jet expansion processes,which can at last realize the goal of controlling the interior ballistic stability of a BLPG.The optimum method for both suppressing Kelvin-Helmholtz instability and promoting radial expansion of Taylor cavities can be determined by analyzing the change of characteristic parameters in a jet flow field.

斜坡限制域对脱体火焰宏观形状和燃烧振荡影响实验研究

燃烧振荡是贫油预混火焰中广泛存在的非定常过程,是燃烧室设计中必须避免的。其中,脱体火焰对降低氮氧化物排放有优势,但其燃烧振荡往往更加严重。本文在中心分级燃烧器中,通过实验方法研究了斜坡限制域对脱体火焰燃烧振荡的被动控制效果。本文通过单反相机和高速摄像获取了火焰平均结构和瞬态图像,并通过相平均图像和本征正交分解研究了火焰动态演变过程。结果表明,当台阶高度为0 mm时,不同斜坡张角的斜坡限制域均能对燃烧振荡起到非常显著的抑制效果。而在30°斜坡张角的斜坡限制域中,随着台阶高度的增加,抑制效果变差,但振幅相较突扩限制域发生了明显的降低。

稀燃工况下天然气发动机燃烧不稳定性分析

为了研究稀燃工况下天然气发动机燃烧不稳定性的变化规律,在25%负荷、转速为1000 r/min工况下针对6组不同过量空气系数λ进行试验,采用统计分析方法研究了最大爆压、最大爆压对应的曲轴转角、指示平均有效压力(IMEP)的频率分布规律,并分析了各燃烧特征参数之间的关联性。结果表明:随着λ增大,天然气发动机燃烧不稳定性增强;最大爆压、最大爆压对应曲轴转角的频率分布范围逐渐增大,IMEP频率分布范围先减小后增大,循环间差异性均增加;各燃烧特征参数的关系图中,点的分布范围均增大,且存在线性关系,当混合气浓度过稀时线性关系减弱。稀燃工况下天然气发动机产生燃烧不稳定分析,为天然气发动机稀燃稳定性优化和控制提供了理论依据。

液体火箭发动机隔板研究综述

隔板是在液体火箭发动机当中用来抑制不稳定燃烧的一种阻尼装置,国内外多种型号的运载火箭都通过隔板消除了不稳定燃烧,得益于其简单的结构和较好的阻尼效果,隔板将在当下和未来保障推进系统稳定运行。简要介绍了隔板的结构形式,分析了隔板的存在对燃烧室内燃烧过程和声场的影响机理,给出了隔板的结构参数(隔板形式、叶片长度、叶片数量等)对阻尼效果的影响,分析了国内外针对隔板的研究成果。最后,基于当前的研究现状提出了对隔板未来研究的展望。

基于火焰结构特征提取的振荡燃烧故障快速检测技术

随着先进燃气轮机不断向高负荷、低排放的趋势发展,燃烧室内发生振荡燃烧的概率持续增大,亟需发展新的检测技术,对振荡燃烧故障进行精确、快速检测。本文提出了基于火焰化学发光图像采集、本征正交分解特征提取、连续小波变换时频分析的振荡燃烧快速检测技术,该技术具有同时解析频谱和频谱随时间演变的能力。通过实验验证,对于振荡到稳定、稳定到振荡、一个主频到另一个主频等多种情况,利用火焰图像本征正交分解得到的模态时间系数,均可获得比压力信号更快的检测速度。在本文涉及的工况,检测速度可提升60%以上。

燃气轮机轴向贫燃分级燃烧技术进展

在碳减排背景下,燃气轮机燃烧室需要在出口温度不断提高的同时控制NO_(x)排放、提高功率调节范围和燃料适应性。为了应对以上挑战,燃气轮机厂商正在发展轴向分级燃烧技术。本文介绍了轴向分级燃烧原理,分析了轴向分级参数、交叉射流火焰形态、喷嘴结构和燃料种类对污染物排放和燃烧不稳定性的影响。现有研究表明,降低一级燃烧室当量比、增强二级燃烧室的掺混均匀性能够降低污染物排放;轴向分级燃烧室的热声振荡特性复杂,合理选取分级参数能够抑制振荡。轴向分级燃烧室的减排效益和工况调节能力已经在商业运行中得到验证。基于目前研究现状,展望了轴向分级燃烧技术的关键问题和未来研究方向。

基于预训练模型的中心分级燃烧室燃烧振荡 预报方法

为促进实现燃气轮机燃烧室中的燃烧振荡预报,提出一种结合预训练和迁移学习的研究思路。在预训练阶段,开展短火焰筒和长火焰筒下两类火焰图像的对比学习以完成编码器的自监督预训练。在迁移阶段,除了对特征编码构建线性分类器的直接迁移,本文还提出将工况参数作为先验条件的贝叶斯迁移学习。结果表明,在两种迁移学习方式下预训练模型相比传统监督学习模型具有4.6%左右的性能提升。同时基于贝叶斯推断的迁移学习相比直接迁移鲁棒性更好。通过主成分分析和分层聚类,验证预训练模型能够提取火焰图像更为通用的热声特征。

模型燃烧室中值班火焰的燃烧不稳定性分析

针对模型燃烧室中值班火焰的燃烧不稳定性问题,实验测量燃烧室内多点动态压力和火焰图像,利用快速傅里叶分析、本征正交分解(POD)等方法进行分析。结果表明:随着当量比增大,值班火焰的稳定性发生2次分岔现象,相应的不稳定模态分别对应系统的3阶、2阶本征纵向声学模态,均发生极限环振荡。POD结果表明:涡声频率锁定,发生在燃烧室纵向声学模态频率处,燃烧室内发生声-涡-火焰耦合的不稳定过程。而伴随着当量比提高,一方面,大尺度旋涡脱落改变火焰面积引发强烈放热振荡,声能产生增大;另一方面,两分支火焰张角不断增大,火焰位置主要波动方向与主要声学波动沿同一轴线。两方面作用下热声耦合更加容易,热释放脉动与压力脉动耦合的相位角减小,进而发生模态转换。

Theoretical model of azimuthal combustion instability subject to non-trivial boundary conditions

The problem of evaluating the sensitivity of non-trivial boundary conditions to the onset of azimuthal combustion instability is a longstanding challenge in the development process of modern gas turbines.The difficulty lies in how to describe three-dimensional in-and outlet boundary conditions in an artificial computational domain.To date,the existing analytical models have still failed to quantitatively explain why the features of the azimuthal combustion instability of a combustor in laboratory environment are quite different from that in a real gas turbine,making the stability control devices developed in laboratory generally lose the effectiveness in practical applications.To overcome this limitation,we provide a novel theoretical framework to directly include the effect of non-trivial boundary conditions on the azimuthal combustion instability.A key step is to take the non-trivial boundary conditions as equivalent distributed sources so as to uniformly describe the physical characteristics of the inner surface in an annular enclosure along with different in-and outlet configurations.Meanwhile,a dispersion relation equation is established by the application of three-dimensional Green's function approach and generalized impedance concept.Results show that the effects of the generalized modal reflection coefficients on azimuthal unstable modes are extremely prominent,and even prompt the transition from stable to unstable mode,thus reasonably explaining why the thermoacoustic instability phenomena in a real gas turbine are difficult to observe in an isolated combustion chamber.Overall,this work provides an effective tool for analysis of the azimuthal combustion instability including various complicated boundary conditions.

Sliding behaviors of the trapezoidal roof rock block under a lateral dynamic disturbance

The surrounding rock of underground space is always affected by external dynamic disturbance from the side position,such as blasting vibration from a stope at the same level or seismic waves from adjacent strata.A series of laboratory tests,numerical simulations and theoretical analyses were carried out in this study to disclose the sliding mechanism of roof rock blocks under lateral disturbance.Firstly,the experiments on trapezoidal key block under various clamping loads and disturbance were conducted,followed by numerical simulations using the fast Lagrangian analysis of continua(FLAC3D).Then,based on the conventional wave propagation model and the classical shear-slip constitutive model,a theoretical model was proposed to capture the relative displacement between blocks and the sliding displacement of the key block.The results indicate that the sliding displacement of the key block increased linearly with the disturbance energy and decreased exponentially with the clamping load when the key block was disturbed to slide(without instability).Meanwhile,when the key block was disturbed to fall,two types of instability process may appear as immediate type or delayed type.In addition,the propagation of stress waves in the block system exhibited obvious low-velocity and lowfrequency characteristics,resulting in the friction reduction effect appearing at the contact interface,which is the essential reason for the sliding of rock blocks.The results can be applied to practical underground engineering and provide valuable guidance for the early detection and prevention of rockfalling disasters.

单喷嘴模型火箭发动机中高频不稳定燃烧的预测

为实现模型火箭发动机中高频不稳定燃烧的早期辨识和提前预测,建立了基于数据驱动的预测框架。该框架基于递归矩阵对燃烧噪声的非线性特征进行提取,并利用深度学习模型对这些特征进行训练和预测。以单喷嘴模型火箭发动机为例,基于热试车试验中的动态压力信号数据,开展了高频不稳定燃烧的预测,可提前约35 ms预测不稳定燃烧的发生。共使用25组动态压力数据,其中包含了不同燃烧室构型的热试车试验数据。对预测框架进行交叉验证后,结果表明模型的预测准确率高于95%,说明了该预测框架的有效性和鲁棒性。

喷嘴布局对钝体非预混火焰响应特性影响的试验研究

航空发动机加力燃烧室由于能量密度大、进口速度大、进口温度高,燃料和空气掺混不均匀等,易发生燃烧不稳定现象。加力燃烧室为多喷嘴结构,喷嘴布局会影响燃烧室内的释热率分布,进而影响火焰响应。以模型加力燃烧室为研究对象,对不同喷嘴数量和喷嘴直径的钝体非预混火焰的释热率响应特性进行研究。利用扬声器对火焰施加声激励,通过双麦克风法测量速度脉动,光电倍增管结合CH*滤光片测量释热率脉动。研究表明,喷嘴布局的改变对燃烧室内的释热率分布会产生显著影响,火焰传递函数(FTF)增益呈现典型的双峰特征。随着喷嘴数量增加,增益峰值先减小后增大,增益峰值对应的频率有向高频移动的趋势,系统时滞并未发生明显变化;随着喷嘴直径增加,FTF增益先减小后增大,系统时滞明显增大。

单喷嘴火箭发动机高频燃烧不稳定的RANS和SBES数值模拟

为了研究不同湍流模型对高频燃烧不稳定的捕捉能力,采用非稳态雷诺时均(Unsteady Reynolds averaged Navier-Stockes,URANS)和应力混合涡模拟(Stress-blended eddy simulation,SBES),开展了单喷嘴模型火箭发动机数值仿真。化学反应与湍流的相互作用采用基于详细化学反应机理(GRI Mech 3.0)的小火焰生成流模型(Flamelet-generated manifolds,FGM)。对比试验数据,验证了模型的准确性;全面对比了URANS和SBES仿真结果;分析了燃烧室的压力波模态特性和流场动态特性。发现两者都能捕捉到高频燃烧不稳定,但URANS对动态特性的捕捉明显不足,压力振荡峰峰值与试验值相比误差高达57.6%。而SBES对包含涡脱落、湍流混合、压力波的传播等动态特性能够实现较好的捕捉,压力振荡峰峰值与试验值误差仅为7.6%。URANS结果表现出高度的对称性,而SBES结果则更加合理。燃烧室和氧管的压力振荡相互耦合,引起推进剂质量流量脉动和燃烧室突扩面周期性涡脱落。涡脱落及其与燃烧室壁面的相互作用增强了脉动释热,是维持燃烧不稳定的关键。

矩形模型火箭发动机横向不稳定燃烧的数值模拟

为研究火箭发动机横向不稳定燃烧特性,采用详细化学反应机理(GRI Mech 3.0)建表的小火焰生成流型,对模型火箭发动机中出现的横向不稳定燃烧进行数值模拟。通过与实验数据对比验证了模型的准确性;采用动态模态分解对压力场进行分析,研究了流场的动态特性;结合瑞利因子定量分析了不稳定燃烧的驱动特性。结果表明,数值模型能够有效捕捉横向不稳定燃烧,其主频与实验值相差不到1%;燃烧室横向压力振荡与喷嘴氧管纵向压力振荡相耦合,引起推进剂质量流量振荡;不稳定燃烧的驱动源主要位于燃烧室两侧,最边缘喷嘴对维持不稳定燃烧的贡献最大;推进剂与燃烧室侧壁面的相互作用极大增强了释热脉动,周期性释热为压力振荡提供能量,形成了不稳定燃烧极限环。