The hypersonic inlet throat Mach number (Math) and back pressure of precooler are two parameters that denote the design or operating state of the wide-range precooled combined-cycle engines. To investigate the effects of Math and back pressure on the flow and heat transfer through the diffuser-precooler, a model with a precooler mounted downstream of the diffuser was designed, and numerical simulation was carried out by solving the Reynolds-averaged Navier-Stokes equations. Numerical results indicate that the Math and back pressure have significant effects on the flow and heat transfer in the diffuser and precooler. By contrast, the impact of Math on the total pressure recovery of the precooler is the most significant. When Math is 3.0, the precooler total pressure recovery decreases by 90% compared to that of Math = 0.58. Increasing back pressure can remarkably improve the total pressure recovery and enhances the heat transfer for the precooler. When Math is 1.5, the total pressure recovery rises by 103.3% as the back pressure ratio varies from 1.0 to 70.0.

Prediction of the hypersonic inlet unsteady flowfield is crucial for preventing inlet unstart. By combining an autoencoder (AE) for dimensionality reduction with radial basis function (RBF) methods and long short-term memory (LSTM) networks, models for predicting the hypersonic inlet unsteady flowfield were constructed. This study compared the interpolation and extrapolation performance of these models, including several AE-RBF variants with different RBF types and shape parameters, as well as the AE-LSTM model. The results show that within the sample space, the cubic RBF method can accurately predict the unsteady flowfield, but it fails rapidly outside the sample space. The Gaussian RBF yields relatively stable prediction errors with negligible influence from the shape parameter, achieving an extrapolation prediction error of 5.7% at 70 ms after backpressure was applied. The extrapolation error of the multiquadric RBF increases with time, and a larger shape parameter leads to a greater error. Although the extrapolation error of the AE-LSTM method also rises slowly with time, it remains as low as approximately 2.01% at 70 ms post-backpressure. This study reveals that the Gaussian AE-RBF method and the AE-LSTM method have good potential for predicting the unsteady flowfield of the hypersonic inlet.

This study focuses on the demand for rapid prediction of the flow field of aero-engine inlet free jet tests and explores the application of radial basis function interpolation (RBF) and backpropagation neural network (BPNN) methods. The proper orthogonal decomposition (POD) method was used for model order reduction of the full-order flow field results from numerical simulations. Two rapid prediction methods, namely POD-RBF and POD-BPNN, were constructed by utilizing radial basis function interpolation and a backpropagation neural network. These methods successfully achieved rapid prediction of the test flow field under different Mach numbers and angles of attack. To verify the accuracy of the numerical simulation and rapid prediction methods, a free jet test of the jet inlet was conducted under the same conditions. The test results show good agreement with both the CFD calculation results and the rapid prediction results. The research results show that the ninth-order mode can accurately reconstruct the flow field structure with a reconstruction error of 1.83%. Both methods can quickly and accurately predict the flow field under different conditions, and the prediction results are in good agreement with the numerical simulation results. Generally speaking, the prediction error of the POD-BPNN method is smaller than that of the POD-RBF method.

It is crucial to rapidly predict the flowfield for real-time control of a scramjet inlet. Proper orthogonal decomposition (POD) and autoencoder (AE) are combined with radial basis function (RBF) interpolation to develop two methods, namely, POD-RBF and AE-RBF. To further explore the nonlinear effects of the dimensionality reduction method, we modify the AE’s rectified linear unit activation function to a linear function, creating a linear AE-RBF method. These three methods are used to predict hypersonic, inward-turning inlet flowfields under different incoming Mach numbers and angles of attack. By comparing the performance of the AE-RBF, linear AE-RBF, and POD-RBF methods, we find that the three reduced-order models can effectively predict the inlet flowfields; however, the AE-RBF demonstrates an obvious superiority over the POD-RBF and linear AE-RBF method. After changing the AE’s nonlinear activation function to a linear type, the error distributions of the linear AE-RBF and POD-RBF are nearly identical. The research reveals that this superiority of AE-RBF is attributed to its nonlinear dimensionality reduction capability.

Establishing the accurate relationship between fractional calculus and fractals is an important research content of fractional calculus theory. In the present paper, we investigate the relationship between fractional calculus and fractal functions, based only on fractal dimension considerations. Fractal dimension of the Riemann–Liouville fractional integral of continuous functions seems no more than fractal dimension of functions themselves. Meanwhile fractal dimension of the Riemann–Liouville fractional differential of continuous functions seems no less than fractal dimension of functions themselves when they exist. After further discussion, fractal dimension of the Riemann–Liouville fractional integral is at least linearly decreasing and fractal dimension of the Riemann–Liouville fractional differential is at most linearly increasing for the Hölder continuous functions. Investigation about other fractional calculus, such as the Weyl-Marchaud fractional derivative and the Weyl fractional integral has also been given elementary. This work is helpful to reveal the mechanism of fractional calculus on continuous functions. At the same time, it provides some theoretical basis for the rationality of the definition of fractional calculus. This is also helpful to reveal and explain the internal relationship between fractional calculus and fractals from the perspective of geometry.

It is crucial to consider the fluid–thermal–structural interaction (FTSI) in designing the scramjet inlet for sustained hypersonic flight. To understand the aerothermal and aeroelastic responses of the planar hypersonic inlets under different flight Mach numbers and aspect ratios, a three-dimensional FTSI framework was developed and validated. After that, the FTSI characteristics under different flight Mach numbers and aspect ratios were investigated. The result reveals that the most obvious horizontal displacement happens at the cowl lip leading edge, whereas the maximum vertical displacement takes place at the compression-ramp leading edge. The FTSI improves the capture area and generates an additional compression angle due to the different thermal expansions between the windward and leeward panels. The thermal expansion in the spanwise direction causes the cowl lip to hump into an arc, and the maximum height happens at the midplane. The effects of FTSI on the inlet flowfield, the mass flow rate, and the total pressure ratio under different flight Mach numbers and aspect ratios were obtained. Overall, the FTSI can improve the contraction ratio, the actual mass flow rate, and the pressure ratio while causing the total pressure ratio to decrease by up to 14.64%.

Relaminarization is a reverse transition from turbulent state to laminar or laminar-like state as the turbulent boundary layer is accelerated, which cause the boundary layer easy to separate under the adverse pressure gradient. To investigate the mechanism of relaminarization flow control with air injection, large eddy simulations were performed for a turbulent flow over a convex curved wall at Mach number 3.0 under different blowing ratios. The results show that the acceleration has markedly reduced the turbulent characteristics including the number of large-scale turbulent structures and the turbulence kinetic energy values in the boundary layer for the baseline case. As the air injection is excited, the relaminarization is effectively suppressed. Meanwhile, the simulation reveals that the blowing ratio plays an important role in controlling the turbulence. The air injection with higher blowing ratio is more effective in suppressing the relaminarization under the condition that the jet-to-cross flow momentum flux ratio and static pressure of injected air are kept unchanged.

快速获得温度场和压力场载荷环境是航空发动机涡轮寿命预测的关键.在本征正交分解的基础上,分别采用响应面法、径向基函数、Kriging方法和BP神经网络,构建了E3涡轮三维流场拓扑结构的多种快速预测方法,为载荷环境实时预测提供了途径.结果表明,本征正交分解能成功地实现E3涡轮三维旋转流场的降阶,基于响应面法、径向基函数、Kriging方法和BP神经网络能精确预测涡轮流场预测结构,但在预测精度、速度等方面存在差异.在样本空间范围内点预测上,10阶模型下四种方法预测出的压力场和温度场误差均小于1％,流量、效率预测误差低于0.4％;在样本空间范围以外点的预测上,径向基函数和Kriging方法的表现不稳定.涡轮壁面流场相关性分析表明,压力场预测精度与转速、进口压力高度相关;温度场与转速、进口压力的相关性弱于压力场.

为发展一种兼具乘波体高升阻比和升力体高容积率的气动设计与预测方法,开展了3个方面的研究工作.基于升力体和乘波体融合设计理念,提出了一种大容积率、高升阻比的乘波前体的扩容设计方法.对扩容设计的乘波前体进行了数值模拟,获得了典型设计参数对前体容积率、升阻比等气动性能参数的影响规律.基于本征正交分解理论和径向基函数建立了高超声速乘波前体流场结构和气动性能参数的快速预测模型,并对扩容设计的乘波前体流场开展了快速预测研究.研究表明:相比于未扩容之前,高度为5、10 mm时,容积增加8.00％和15.00％;基于本征正交分解理论的快速预测方法可精确、快速地获得不同几何设计参数下乘波前体的流场,预测误差不高于2.00％.

为研究隔离段自激振荡现象,采用2阶时间和空间精度、非结构网格、剪切应力输运(SST)k-ω湍流模型有限体积法程序对二元进气道在高反压下的非定常特性进行数值模拟,成功捕捉到激波串自激振荡现象,在此基础上利用本征正交分解(POD)和动力学模态分解(DMD)方法对其进行分析.结果表明:该自激振荡是低频主导、多频耦合的复杂振荡现象;基于本征正交分解和动力学模态分解构建的预测模型均能准确快速地预测出非定常流场的演变特性,预测误差小于0.2％,前者耗时为0.22s,后者耗时为0.05s.

我国航空发动机技术与欧美等航空强国尚存在较大差距,培养高质量专业队伍是缩小差距的重要途径.飞机/发动机一体化设计要在飞行器总体性能最优前提下进行飞机和动力系统的匹配设计,兼具基础性和前沿性两大特点,非常适合开展研究型教学模式.为此,该文在国内几大航空院校课程体系调研的基础上,重点阐述了飞机/发动机一体化设计课程研究型教学模式的重要性、必要性和迫切性,并进行了研究型教学模式的初步探索尝试.

The ramjet/scramjet engines require the control-oriented model to predict the inlet flow field in less than a few seconds. However, it is challenging for these kinds of inlets which utilize curved shock waves to compress the air flow. In this paper, a reduced-order model based on the computational fluid dynamics, the proper orthogonal decomposition theory, and the radial basis function interpolation method is developed. After that, the curved shock waves dominated flow fields of a ramjet inlet under different angles of attack and free stream Mach numbers are predicted with this reduced-order model and compared to the full order computational fluid dynamics solutions. The results show that this reduced-order model can successfully predict the curved shock waves, the curved shock wave/boundary layer interactions, and the shock trains caused by a back pressure with high accuracies. The consumed time is only 0.11 s. The performance parameters are also predicted with the relative errors no more than 2%.

The eigentime identity for random walks on the weighted networks is the expected time for a walker going from a node to another node. Eigentime identity can be studied by the sum of reciprocals of all nonzero Laplacian eigenvalues on the weighted networks. In this paper, we study the weighted [Formula: see text]-flower networks with the weight factor [Formula: see text]. We divide the set of the nonzero Laplacian eigenvalues into three subsets according to the obtained characteristic polynomial. Then we obtain the analytic expression of the eigentime identity [Formula: see text] of the weighted [Formula: see text]-flower networks by using the characteristic polynomial of Laplacian and recurrent structure of Markov spectrum. We take [Formula: see text], [Formula: see text] as example, and show that the leading term of the eigentime identity on the weighted [Formula: see text]-flower networks obey superlinearly, linearly with the network size.

More and more attention has focused on consensus problem in the study of complex networks. Many researchers investigated consensus dynamics in a linear dynamical system with additive stochastic disturbances. In this paper, we construct iterated line graphs of multi-subdivision graph by applying multi-subdivided-line graph operation. It has been proven that the network coherence can be characterized by the Laplacian spectrum of network. We study the recursion formula of Laplacian eigenvalues of the graphs. After that, we obtain the scalings of the first-and second-order network coherence.

The multiple subdivision graph of a graph [Formula: see text], denoted by [Formula: see text], is the graph obtained by inserting [Formula: see text] paths of length 2 replacing every edge of [Formula: see text]. When [Formula: see text], [Formula: see text] is the subdivision graph of [Formula: see text]. Let [Formula: see text] be a graph with [Formula: see text] vertices and [Formula: see text] edges, [Formula: see text] be a graph with [Formula: see text] vertices and [Formula: see text] edges. The quasi-corona SG-vertex join [Formula: see text] of [Formula: see text] and [Formula: see text] is the graph obtained from [Formula: see text] and [Formula: see text] copies of [Formula: see text] by joining every vertex of [Formula: see text] to every vertex of [Formula: see text], and multiple SG-vertex join [Formula: see text] is the graph obtained from [Formula: see text] and [Formula: see text] by joining every vertex of [Formula: see text] to every vertex of [Formula: see text]. In this paper, we calculate analytic expression of characteristic polynomial of adjacency matrix of the above two types of joins of graphs for the case of [Formula: see text] being a regular graph. Then we obtain their adjacency spectra for the case of [Formula: see text] and [Formula: see text] being regular graphs.

With the deepening of research on complex networks, many properties of complex networks are gradually studied, for example, the mean first-passage times, the average receive times and the trapping times. In this paper, we further study the average trapping time of the weighted directed treelike network constructed by an iterative way. Firstly, we introduce our model inspired by trade network, each edge [Formula: see text] in undirected network is replaced by two directed edges with weights [Formula: see text] and [Formula: see text]. Then, the trap located at central node, we calculate the weighted directed trapping time (WDTT) and the average weighted directed trapping time (AWDTT). Remarkably, the WDTT has different formulas for even generations and odd generations. Finally, we analyze different cases for weight factors of weighted directed treelike network.

In this paper a family of weighted fractal networks, in which the weights of edges have been assigned to different values with certain scale, are studied. For the case of the weighted fractal networks the definition of modified box dimension is introduced, and a rigorous proof for its existence is given. Then, the modified box dimension depending on the weighted factor and the number of copies is deduced. Assuming that the walker, at each step, starting from its current node, moves uniformly to any of its nearest neighbors. The weighted time for two adjacency nodes is the weight connecting the two nodes. Then the average weighted receiving time (AWRT) is a corresponding definition. The obtained remarkable result displays that in the large network, when the weight factor is larger than the number of copies, the AWRT grows as a power law function of the network order with the exponent, being the reciprocal of modified box dimension. This result shows that the efficiency of the trapping process depends on the modified box dimension: the larger the value of modified box dimension, the more efficient the trapping process is.

In this paper, we consider the Sierpinski carpet fractal networks G(t) constructed by the Sierpinski carpet F. Firstly, the structure properties of G(t), including degree distribution and clustering coefficient, are studied. Then, the weighted average geodesic distances of the Sierpinski carpet fractal F are analyzed by using the integral of geodesic distance in terms of self-similar measure with respect to the weight vector. Further the weighted average geodesic distances of the Sierpinski carpet fractal networks is obtained.

In this paper, we consider the unbiased random walk on the level-3 Sierpinski gasket (SG(3)). Due to the self-similar structure and iterative mechanism of the network, we obtain the exact analytic expression of the average trapping time (ATT) on SG(3). By comparing with the numerical result, we find that the analytical expression is very consistent with the corresponding numerical solution. Further, the obtained results indicate that ATT scales superlinearly with network size.

This paper concerns the weight-dependent random walk on a class of weighted tree-like fractal networks controlled by a positive integer parameter [Formula: see text] [Formula: see text] and the weight factor [Formula: see text] [Formula: see text]. We study the first return time (FRT) of a given hub and the global first-passage time (GFPT) to a given hub on the networks. By the probability generating function method, we derive the analytic expressions of the first and second moments of FRT and GFPT. In order to evaluate the fluctuation of FRT and GFPT, we further calculate the variance and the reduced moments of FRT and GFPT.