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Nonlinear flame response modelling by a parsimonious set of ordinary differential equations 用一组简洁常微分方程建立非线性火焰响应模型
IF 1.6 4区 工程技术 Q3 ENGINEERING, MECHANICAL Pub Date : 2022-03-01 DOI: 10.1177/17568277221094760
Gregor Doehner, M. Haeringer, Camilo F. Silva
In this work we present a parsimonious set of ordinary differential equations (ODEs) that describes with satisfactory precision the linear and non-linear dynamics of a typical laminar premixed flame in time and frequency domain. The proposed model is characterized by two ODEs of second-order that can be interpreted as two coupled mass-spring-damper oscillators with a symmetric, nonlinear damping term. This non-linear term is identified as function of the rate of displacement following x 2 x ˙ . The model requires only four constants to be calibrated. This is achieved by carrying out an optimization procedure on one input and one output broadband signal obtained from high-fidelity numerical simulations (CFD). Note that the Transfer Function (FTF) or describing function (FDF) of the flame under investigation are not known a-priori, and therefore not used in the optimization procedure. Once the model is trained on CFD input and output time series, it is capable of recovering with quantitative accuracy the impulse response of the laminar flame under investigation and, hence, the corresponding frequency response (FTF). If fed with harmonic signals of different frequency and amplitude, the trained model is capable of retrieving with qualitative precision the flame describing function (FDF) of the studied flame. We show that the non-linear term x 2 x ˙ is essential for capturing the gain saturation for high amplitudes of the input signal. All results are validated against CFD data.
在这项工作中,我们提出了一组简约的常微分方程(ODEs),该方程在时域和频域中以令人满意的精度描述了典型层流预混火焰的线性和非线性动力学。所提出的模型具有两个二阶常微分方程的特征,这两个常微分方程可以解释为两个具有对称非线性阻尼项的质量-弹簧-阻尼器耦合振荡器。该非线性项被确定为x 2 x▪之后位移率的函数。该模型只需要校准四个常数。这是通过对从高保真度数值模拟(CFD)获得的一个输入和一个输出宽带信号执行优化程序来实现的。注意,所研究火焰的传递函数(FTF)或描述函数(FDF)不是先验已知的,因此在优化过程中没有使用。一旦该模型在CFD输入和输出时间序列上进行了训练,它就能够定量准确地恢复所研究的层流火焰的脉冲响应,从而恢复相应的频率响应(FTF)。如果输入不同频率和振幅的谐波信号,则训练的模型能够定性精确地检索所研究火焰的火焰描述函数(FDF)。我们证明了非线性项x2 x▪对于捕获输入信号的高振幅的增益饱和是必不可少的。所有结果均根据CFD数据进行了验证。
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引用次数: 2
Iterative solvers for the thermoacoustic nonlinear eigenvalue problem and their convergence properties 热声非线性特征值问题的迭代解及其收敛性
IF 1.6 4区 工程技术 Q3 ENGINEERING, MECHANICAL Pub Date : 2022-03-01 DOI: 10.1177/17568277221084464
G. A. Mensah, Philipp Buschmann, A. Orchini
The spectrum of the thermoacoustic operator is governed by a nonlinear eigenvalue problem. A few different strategies have been proposed by the thermoacoustic community to tackle it and identify the frequencies and growth rates of thermoacoustic eigenmodes. These strategies typically require the use of iterative algorithms, which need an initial guess and are not necessarily guaranteed to converge to an eigenvalue. A quantitative comparison between the convergence properties of these methods has however never been addressed. By using adjoint-based sensitivity, in this study we derive an explicit formula that can be used to quantify the behaviour of an iterative method in the vicinity of an eigenvalue. In particular, we employ Banach’s fixed-point theorem to demonstrate that there exist thermoacoustic eigenvalues that cannot be identified by some of the iterative methods proposed in the literature, in particular fixed-point iterations, regardless of the accuracy of the initial guess provided. We then introduce a family of iterative methods known as Householder’s methods, of which Newton’s method is a special case. The coefficients needed to use these methods are explicitly derived by means of high-order adjoint-based perturbation theory. We demonstrate how these methods are always guaranteed to converge to the closest eigenvalue, provided that the initial guess is accurate enough. We also show numerically how the basin of attraction of the eigenvalues varies with the order of the employed Householder’s method.
热声算子的谱由一个非线性特征值问题控制。热声界提出了一些不同的策略来解决这一问题,并确定热声本征模的频率和增长率。这些策略通常需要使用迭代算法,迭代算法需要初始猜测,并且不一定保证收敛到特征值。然而,这些方法的收敛特性之间的定量比较从未被提及。通过使用基于伴随的灵敏度,在本研究中,我们导出了一个显式公式,该公式可用于量化迭代方法在特征值附近的行为。特别地,我们使用Banach的不动点定理来证明存在无法通过文献中提出的一些迭代方法来识别的热声特征值,特别是不动点迭代,无论所提供的初始猜测的准确性如何。然后,我们介绍了一系列迭代方法,称为Householder方法,牛顿方法是其中的一个特例。使用这些方法所需的系数是通过基于高阶伴随的微扰理论明确推导的。我们演示了如何始终保证这些方法收敛到最接近的特征值,前提是初始猜测足够准确。我们还从数值上展示了特征值的吸引域如何随着所采用的Householder方法的阶数而变化。
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引用次数: 1
Study on cyclic variation rate of fuel flow in the nozzle during fuel injection 喷油过程中喷管内燃油流量循环变化率的研究
IF 1.6 4区 工程技术 Q3 ENGINEERING, MECHANICAL Pub Date : 2021-09-01 DOI: 10.1177/17568277211055979
W. Hua, Zhang Xin-yu, Jiang Yu-long, Zhao Ling-yao
The fuel flow pattern in the fuel injection nozzle of diesel engine is a complex and changeable phenomenon, which is easily affected by various factors, bringing the differences of flow patterns between multiple injection cycles. To solve the above problem, a visual experimental platform of fuel injection nozzle was built, in which the 100 injection cycles of diesel engine on the same working condition were photographed via shadowgraphy to study the difference in fuel flow pattern in the nozzle by ensemble average processing method. The cyclic variation rate K of fuel flow pattern is defined. Results demonstrate that the fuel flow pattern tends to be the same in multiple fuel injection cycles, but there is a strong randomness at the starting of injection and after ending of injection; the K can be reduced by decreasing the injection pressure and the inclination angle of orifice, so that the fuel flow pattern in the nozzle tends to be consistent.
柴油机喷油嘴内的燃油流型是一种复杂多变的现象,容易受到各种因素的影响,从而导致多个喷油周期之间的流型差异。为了解决上述问题,建立了一个喷油嘴可视化实验平台,在该平台上,通过阴影摄影法拍摄了柴油机在相同工况下的100个喷油循环,用集成平均处理方法研究了喷油嘴内燃料流动模式的差异。定义了燃料流动模式的循环变化率K。结果表明,在多个燃料喷射循环中,燃料流动模式趋于相同,但在喷射开始和结束后具有较强的随机性;K可以通过降低喷射压力和孔口倾角来降低,从而使喷嘴中的燃料流动模式趋于一致。
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引用次数: 0
Autoignition flame transfer matrix: Analytical model versus large eddy simulations 自燃火焰传递矩阵:解析模型与大涡模拟
IF 1.6 4区 工程技术 Q3 ENGINEERING, MECHANICAL Pub Date : 2021-09-01 DOI: 10.1177/17568277221086261
F. Gant, A. Cuquel, M. Bothien
Modern gas turbines need to fulfil increasingly stringent emission targets on the one hand and exhibit outstanding operational and fuel flexibility on the other. Ansaldo Energia GT26 and GT36 gas turbine models address these requirements by employing a combustion system in which two lean premixed combustors are arranged in series. Due to the high inlet temperatures from the first stage, the second combustor stage predominantly relies on autoignition for flame stabilization. In this paper, the response of autoignition flames to temperature, pressure and velocity excitations is investigated. The gas turbine combustor geometry is represented by a backward-facing step. Based on the conservation equations an analytical model is derived by solving the linearized Rankine-Hugoniot conditions. This is a commonly used analytical approach to describe the relation of thermodynamic quantities up- and downstream of a propagation stabilized flame. In particular, the linearized Rankine-Hugoniot jump conditions are derived taking into account the presence of a moving discontinuity as well as upstream entropy inhomogeneities. The unsteady heat release rate of the flame is modelled as a linear superposition of flame transfer functions, accounting for velocity, pressure, and entropy disturbances, respectively. This results in a 3 × 3 flame transfer matrix relating both primitive acoustic variables and the temperature fluctuations across the flame. The obtained analytical expression is compared to large eddy simulations with excellent agreement. A discussion about the contribution of the single terms to the modelling effort is provided, with a focus on autoignition flames.
现代燃气轮机一方面需要满足日益严格的排放目标,另一方面要表现出出色的操作和燃料灵活性。安萨尔多能源GT26和GT36燃气轮机模型通过采用两个精益预混燃烧器串联布置的燃烧系统来解决这些要求。由于第一级的进口温度很高,第二级主要依靠自燃来稳定火焰。本文研究了自燃火焰对温度、压力和速度的响应。燃气轮机燃烧室的几何形状由一个面向后的台阶表示。在守恒方程的基础上,通过求解线性化的Rankine-Hugoniot条件,导出了一个解析模型。这是一种常用的分析方法,用于描述传播稳定火焰的上下热力学量的关系。特别是,考虑到移动不连续和上游熵不均匀性的存在,推导了线性化的Rankine-Hugoniot跳变条件。火焰的非定常热释放率被建模为火焰传递函数的线性叠加,分别考虑了速度、压力和熵扰动。这就产生了一个3 × 3的火焰传递矩阵,它与原始声学变量和火焰上的温度波动有关。将得到的解析表达式与大涡模拟结果进行了比较,结果吻合良好。讨论了单项对建模工作的贡献,重点是自燃火焰。
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引用次数: 2
Development of a wall jet model dedicated to 1D combustion modelling for CI engines 开发了一种专门用于内燃机一维燃烧建模的壁面射流模型
IF 1.6 4区 工程技术 Q3 ENGINEERING, MECHANICAL Pub Date : 2021-09-01 DOI: 10.1177/17568277211059073
A. Osorio, X. Tauzia, A. Maiboom
Diesel engines are becoming smaller as technology advances, which means that the fuel spray (or jet) interacts with the cylinder walls before combustion starts. Most fuel injection 1D models (especially for diesel fuel) do not consider this interaction. Therefore, a wall-jet sub-model was created on an Eulerian 1D diesel spray model. It was calibrated using data from the literature and validated with experimental data from a fuel spray impacting a plate in a constant volume combustion chamber. Results show that the spray moving along the wall has a higher mixing rate but less penetration as an equivalent free jet, therefore they show a similar volume. Spray-wall interaction creates a stagnation zone right before the impact with the wall, and friction of the jet with the wall is relatively low. All these phenomena are well captured by the wall-jet sub-model.
随着技术的进步,柴油发动机变得越来越小,这意味着燃料喷雾(或喷射)在燃烧开始前与气缸壁相互作用。大多数燃料喷射1D模型(尤其是柴油燃料)没有考虑这种相互作用。因此,在欧拉一维柴油喷雾模型上建立了壁面射流子模型。它使用文献中的数据进行了校准,并使用恒定体积燃烧室中燃料喷雾冲击板的实验数据进行了验证。结果表明,作为等效自由射流,沿壁移动的喷雾具有较高的混合速率,但穿透较小,因此它们显示出相似的体积。喷雾-壁的相互作用在与壁碰撞之前产生了一个停滞区,并且射流与壁的摩擦相对较低。壁面射流子模型很好地捕捉到了所有这些现象。
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引用次数: 0
Thermal explosion characteristics of a combustible gas containing fuel droplets 含有燃料液滴的可燃气体的热爆炸特性
IF 1.6 4区 工程技术 Q3 ENGINEERING, MECHANICAL Pub Date : 2021-09-01 DOI: 10.1177/17568277211057360
S. El-Sayed
This paper investigated the critical ignition conditions of combustible gas containing liquid fuel droplets. The analysis is done based on the criteria of the thermal explosion theory. It includes analytical and numerical solutions of modeling equations of fuel droplets heating and evaporation by convection and radiation from the surrounding reactive hot gas. The exothermic reaction is usually modeled as a single-step reaction obeying an Arrhenius temperature dependence. The thermal conductivity of the fuel droplet is dependent on temperature. The analytical solution produced relations between the main critical characteristic parameters in all planes of the solution. The results obtained from investigating the effect of the characteristic parameters on the explosion behavior of gas and fuel droplets and the thermal radiation proved that both of them are significant. The study proved that the criticality definitions of the thermal explosion of a single-phase system can be used effectively and efficiently to determine the critical conditions of a multi-phase system. Finally, the application of the numerical solutions of the modeling equations was used to analyze the explosion characteristics of a diesel fuel spray system.
本文研究了含有液体燃料液滴的可燃气体的临界点火条件。分析是根据热爆炸理论的准则进行的。它包括通过周围反应性热气的对流和辐射加热和蒸发燃料液滴的建模方程的分析和数值解。放热反应通常被建模为服从阿伦尼斯温度依赖性的单步反应。燃料液滴的热导率取决于温度。分析解在解的所有平面上产生了主要临界特征参数之间的关系。研究了特征参数对气滴和燃料液滴爆炸行为以及热辐射的影响,结果表明,这两个参数都是显著的。研究证明,单相系统热爆炸的临界定义可以有效地确定多相系统的临界条件。最后,应用模型方程的数值解对柴油喷雾系统的爆炸特性进行了分析。
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引用次数: 0
Forecasting thermoacoustic instabilities in liquid propellant rocket engines using multimodal Bayesian deep learning 基于多模态贝叶斯深度学习的液体火箭发动机热声不稳定性预测
IF 1.6 4区 工程技术 Q3 ENGINEERING, MECHANICAL Pub Date : 2021-07-01 DOI: 10.1177/17568277221139974
Ushnish Sengupta, Gunther Waxenegger-Wilfing, J. Hardi, M. Juniper
We present a method that combines multiple sensory modalities in a rocket thrust chamber to predict impending thermoacoustic instabilities with uncertainties. This is accomplished by training an autoregressive Bayesian neural network model that forecasts the future amplitude of the dynamic pressure time series, using multiple sensor measurements (injector pressure/ temperature measurements, static chamber pressure, high-frequency dynamic pressure measurements, high-frequency OH* chemiluminescence measurements) and future flow rate control signals as input. The method is validated using experimental data from a representative cryogenic research thrust chamber. The Bayesian nature of our algorithms allows us to work with a dataset whose size is restricted by the expense of each experimental run, without making overconfident extrapolations. We find that the networks are able to accurately forecast the evolution of the pressure amplitude and anticipate instability events on unseen experimental runs 500 milliseconds in advance. We compare the predictive accuracy of multiple models using different combinations of sensor inputs. We find that the high-frequency dynamic pressure signal is particularly informative. We also use the technique of integrated gradients to interpret the influence of different sensor inputs on the model prediction. The negative log-likelihood of data points in the test dataset indicates that prediction uncertainties are well-characterized by our model and simulating a sensor failure event results in a dramatic increase in the epistemic component of the uncertainty, as would be expected when a Bayesian method encounters unfamiliar, out-of-distribution inputs.
我们提出了一种结合火箭推力室中多种传感模态的方法来预测具有不确定性的即将发生的热声不稳定性。这是通过训练一个自回归贝叶斯神经网络模型来实现的,该模型使用多个传感器测量(喷油器压力/温度测量、静态腔室压力、高频动态压力测量、高频OH*化学发光测量)和未来流量控制信号作为输入,预测未来动态压力时间序列的幅度。并利用某典型低温研究推力室的实验数据对该方法进行了验证。我们算法的贝叶斯性质允许我们处理数据集,其大小受到每次实验运行费用的限制,而不会做出过于自信的推断。我们发现,该网络能够准确地预测压力振幅的演变,并提前500毫秒预测未知实验运行中的不稳定事件。我们比较了使用不同传感器输入组合的多个模型的预测精度。我们发现高频动态压力信号的信息量特别大。我们还使用积分梯度技术来解释不同传感器输入对模型预测的影响。测试数据集中数据点的负对数似然表明,我们的模型很好地表征了预测的不确定性,模拟传感器故障事件会导致不确定性的认知成分急剧增加,正如贝叶斯方法遇到不熟悉的、超出分布的输入时所预期的那样。
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引用次数: 2
Low-order modeling of high-altitude relight of jet engine combustors 喷气发动机燃烧室高空点火的低阶建模
IF 1.6 4区 工程技术 Q3 ENGINEERING, MECHANICAL Pub Date : 2021-06-01 DOI: 10.1177/17568277211021322
P. M. de Oliveira, M. Sitte, M. Zedda, A. Giusti, E. Mastorakos
A physics-based, low-order ignition model is used to assess the ignition performance of a kerosene-fueled gas-turbine combustor under high-altitude relight conditions. The ignition model used in this study is based on the motion of virtual flame particles and their extinction according to a Karlovitz number criterion, and a stochastic procedure is used to account for the effects of spray polydispersity on the flame’s extinction behavior. The effects of large droplets arising from poor fuel atomization at sub-idle conditions are then investigated in the context of the model parameters and the combustor’s ignition behavior. For that, a Reynolds-averaged Navier-Stokes simulation of the cold flow in the combustor was performed and used as an input for the ignition model. Ignition was possible with a Sauter mean diameter (SMD) of 50 μm, and was enhanced by increasing the spark volume. Although doubling the spark volume at larger SMDs (75 and 100 μm) resulted in the suppression of short-mode failure events, ignition was not achieved due to a reduction of the effective flammable volume in the combustor. Overall, a lower ignition probability is obtained when using the stochastic procedure for the spray, which is to be expected due to the additional detrimental effects associated with poor spray atomisation and high polydispersity.
采用一种基于物理的低阶点火模型,对高空光照条件下煤油燃气轮机燃烧室的点火性能进行了评估。本文所采用的点火模型是基于虚拟火焰粒子的运动及其熄灭,根据Karlovitz数准则,并采用随机过程来考虑喷雾多分散性对火焰熄灭行为的影响。然后在模型参数和燃烧室点火行为的背景下,研究了亚怠速条件下燃料雾化不良引起的大液滴的影响。为此,对燃烧室中的冷流进行了reynolds -average Navier-Stokes模拟,并将其用作点火模型的输入。当SMD直径为50 μm时,可以实现点火,并通过增加火花体积来增强点火效果。虽然在较大的smd (75 μm和100 μm)上,火花体积增加了一倍,可以抑制短模故障事件,但由于燃烧室中有效可燃体积的减少,无法实现点火。总的来说,当使用随机程序进行喷雾时,可以获得较低的点火概率,这是可以预期的,因为与较差的喷雾雾化和高多分散性相关的额外有害影响。
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引用次数: 7
Numerical prediction of the ignition probability of a lean spray burner 稀薄喷雾燃烧器点火概率的数值预测
IF 1.6 4区 工程技术 Q3 ENGINEERING, MECHANICAL Pub Date : 2021-06-01 DOI: 10.1177/17568277211012536
L. Palanti, A. Andreini, B. Facchini
The optimization of the igniter position is a critical issue in modern aviation gas turbines since it can help to minimize the amount of energy required for ignition and to guarantee a fast relight in case of flameout. From a numerical perspective, several spark discharges should be simulated for each spark position, to account for different realizations due to time-dependent turbulent motions. Unfortunately, standard simulations are impractical to use for this purpose, due to the need of carrying out several unsteady simulations, leading to a huge associated computational effort. This is why low-order models have been developed, providing an affordable estimation of the local ignition probability, by sacrificing the accuracy and the physical consistency of the prediction. In the present work, a previously developed low-order design model has been implemented in ANSYS Fluent 2019R1® and used to investigate the ignition performance of a single-sector, confined spray flame, where data from laser ignition experiments are available. A non-reactive Large Eddy Simulation, which is validated against experimental data, provides the base flow needed to feed the model. If the tuning parameters of the ignition model are well calibrated, it provides quite good results. In the test case here investigated, it is shown that ignition is possible in the outer recirculation zone and very unlikely elsewhere. Later, a discussion about the effect of the most relevant tuning parameters is carried out. It is shown that the model mostly succeed to identify the area of possible ignition, even if the lack of calibration could lead to a poorer agreement with the experimental data.
点火器位置的优化是现代航空燃气轮机中的一个关键问题,因为它可以帮助最大限度地减少点火所需的能量,并保证在熄火的情况下快速重新点火。从数值的角度来看,每个火花位置都应该模拟几个火花放电,以说明由于时间相关的湍流运动而产生的不同实现。不幸的是,由于需要进行几次非稳态模拟,因此标准模拟无法用于此目的,这导致了巨大的相关计算工作量。这就是为什么开发了低阶模型,通过牺牲预测的准确性和物理一致性,提供了对局部点火概率的可负担的估计。在本工作中,先前开发的低阶设计模型已在ANSYS Fluent 2019R1®中实现,并用于研究单个扇形、受限喷雾火焰的点火性能,其中可获得激光点火实验的数据。根据实验数据验证的无反应大涡模拟提供了模型所需的基本流量。如果点火模型的调谐参数得到很好的校准,它将提供相当好的结果。在这里调查的测试案例中,表明在外部再循环区点火是可能的,而在其他地方则不太可能。随后,对最相关的调谐参数的影响进行了讨论。结果表明,即使缺乏校准可能导致与实验数据的一致性较差,该模型也能成功地识别出可能的点火区域。
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引用次数: 2
Experimental investigation on spray characteristics of Jet A-1 and alternative aviation fuels Jet A-1及其替代航空燃料喷雾特性的实验研究
IF 1.6 4区 工程技术 Q3 ENGINEERING, MECHANICAL Pub Date : 2021-06-01 DOI: 10.1177/17568277211010140
Manish Kumar, S. Karmakar, Sonu Kumar, S. Basu
Potential alternative fuels that can mitigate environmental pollution from gas turbine engines (due to steep growth in the aviation sector globally) are getting significant attention. Spray behavior plays a significant role in influencing the combustion performance of such alternative fuels. In the present study, spray characteristics of Kerosene-based fuel (Jet A-1) and alternative aviation fuels such as butyl butyrate, butanol, and their blends with Jet A-1 are investigated using an air-blast atomizer under different atomizing air-to-fuel ratios. Phase Doppler Interferometry has been employed to obtain the droplet size and velocity distribution of various fuels. A high-speed shadowgraphy technique has also been adopted to make a comparison of ligament breakup characteristics and droplet formation of these alternative biofuels with that of Jet A-1. An effort is made to understand how the variation in fuel properties (mainly viscosity) influences atomization. Due to the higher viscosity of butanol, the SMD is higher, and the droplet formation seems to be delayed compared to Jet A-1. In contrast, the lower viscosity of butyl butyrate promotes faster droplet formation. The effects of the blending of these biofuels with Jet A-1 on atomization characteristics are also compared with that of Jet A-1.
潜在的替代燃料可以减轻燃气涡轮发动机对环境的污染(由于全球航空业的急剧增长)正在受到极大的关注。喷雾特性对这类替代燃料的燃烧性能有重要影响。在不同的雾化空气燃料比下,利用空气雾化喷嘴研究了煤油基燃料(Jet A-1)和替代航空燃料(如丁酸丁酯、丁醇)及其与Jet A-1的混合燃料的喷雾特性。采用相位多普勒干涉法测量了不同燃料的液滴大小和速度分布。采用高速阴影成像技术,将这些替代生物燃料的韧带断裂特性和液滴形成与Jet A-1进行比较。努力了解燃料性质(主要是粘度)的变化如何影响雾化。由于丁醇的粘度更高,SMD更高,与Jet A-1相比,液滴的形成似乎延迟了。相反,丁酸丁酯的低粘度促进了更快的液滴形成。将这些生物燃料与Jet A-1混合对雾化特性的影响也与Jet A-1进行了比较。
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引用次数: 13
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International Journal of Spray and Combustion Dynamics
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