2023 Vol. 44, No. 10

Solid Mechanics
Multi-Scale Prediction of Thermal and Mechanical Properties of C/SiC Braided Composites
ZHANG Yongzheng, LIU Lei, LIU Qi, XU Guangkui
2023, 44(10): 1157-1171. doi: 10.21656/1000-0887.440056
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Abstract:
C/SiC composites have been widely used in aerospace, national defense, and chemical industries due to their excellent mechanical and thermal properties. Accurate knowledge about the mechanical/thermal properties of C/SiC composites is very important for their efficient application in related fields. Based on the representative volume element (RVE) and periodic boundary conditions, a micro/meso single-cell model for C/SiC composites was established in view of the non-uniform and multi-scale characteristics of fiber bundles, such as the volume fraction, the interweaving mode, and the weaving dimension. The finite element software ABAQUS was used to predict the micro-scale thermal and mechanical properties of the fiber bundle, and the fiber bundle properties were introduced into the mesoscopic model to analyze and obtain the macroscopic thermal and mechanical properties of the composite. Based on this multi-scale correlation analysis method, the thermal conductivity and thermal expansion coefficient of fiber bundles and C/SiC composites were further studied at the operating temperatures ranging from 27~1 227 ℃. The study has certain guiding significance for the application of C/SiC composites in engineering.
Study on Energy Absorption Performances of Conical Negative Stiffness Metamaterials
WANG Jingzhe, CHEN Baocai, ZHU Shaowei, CHEN Liming
2023, 44(10): 1172-1179. doi: 10.21656/1000-0887.440055
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Abstract:
Since negative stiffness metamaterials are reusable as energy-absorbing materials, it is necessary to investigate the energy-absorbing performances and reusability of negative stiffness metamaterials. The designed negative stiffness metamaterial was prepared with the 3D printing technology, and the energy absorption performance of the metamaterial in the multi-stable mode and the mono-stable mode was investigated by repeated loading experiments. The effect of the residual stress on the energy absorption performance of the metamaterial was studied with the natural aging method. The results show that, the specific energy absorption of the designed metamaterial first decreases and then stabilizes with the increase of the number of loading times in the case of repeated loading. In both the multi-stable mode and the mono-stable mode, the natural aging method can effectively release the residual stresses in the metamaterial, thus improving its repeated energy absorption performance.
Fixed-Time Asymptotic Stability and Energy Consumption Estimation of Nonlinear Systems
ZHAI Guoqing, CHEN Qiaoyu, TONG Dongbing, ZHOU Wuneng
2023, 44(10): 1180-1186. doi: 10.21656/1000-0887.440041
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Abstract:
The fixed-time asymptotic stability and energy consumption estimation problems of nonlinear systems were discussed. First, a novel dynamic model with nonlinearity and time-varying delays was proposed. Second, to effectively improve the convergence rate of the system, a fixed-time control strategy was adopted. Through construction of the Lyapunov functional and with the inequality analysis method, sufficient conditions for the error system were obtained to achieve the fixed-time asymptotic stability. Moreover, to predict the energy consumption during the operation of the system, the upper bound of the energy consumption for the system was estimated, which is helpful to evaluate the operation time of the system. Finally, a numerical example was given to verify the feasibility and effectiveness of the results.
RBF Neural Network Based Prediction on Blade Surface Pressure Fields in Compressors
YAO Minghui, WANG Xingzhi, WU Qiliang, NIU Yan
2023, 44(10): 1187-1199. doi: 10.21656/1000-0887.440054
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Abstract:
The airflow characteristics of the internal flow path of an aero-engine compressor are complex, and the vortex flow field around the blade is characterized by high pressure, high speed, rotation, and unsteadiness. Therefore, there is an urgent need to calculate and predict the aerodynamic characteristics of the complex flow field around the compressor blade efficiently and accurately. The computational fluid dynamics (CFD) method was used to generate the aerodynamic load distribution on the blade surface under different operating conditions for the study of the complex flow fields around aero-engine blades. The radial based function (RBF) neural network was applied to establish the pressure surface aerodynamic load prediction model, and the neural network modeling method was combined with the flow field calculation. The neural network method can learn and train the CFD-based data set to properly compensate the errors from the CFD, which provides a reference for the effective prediction of the complex flow fields around aero-engine compressor blades.
Fluid Mechanics
Semi-Analytical Model and Seepage Characteristics of Multi-Wing Fracture Off-Center Wells
JI Anzhao
2023, 44(10): 1200-1212. doi: 10.21656/1000-0887.430395
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Abstract:
In view of the actual situation of multi-wing fracture off-center wells, the mathematical model for the wells was established. Based on the Laplace transform and the pressure drop superposition principle, the semi-analytical solution of the bottom hole pressure in the multi-wing fracture off-center well in the Laplace space, was obtained. The semi-analytical solution was discretized with the non-uniform flow method. Combined with Stehfest numerical inversion, the numerical solution of the real space bottom hole pressure and the production distribution were obtained. The numerical well test model for the reservoir was established with the SAPHIR well test analysis software, and the numerical discrete calculation was carried out. The numerical results were compared with the calculation results of the semi-analytical model, which verifies the correctness of the semi-analytical model. The results show that, the bottom hole pressure variation of the multi-wing fracture off-center well can be divided into 8 main flow stages. Finally, the effects of the dimensionless conductivity, the fracture asymmetry factor and the off-center distance on the bottom hole pressure variation and production distribution characteristics, were discussed.
Electroosmotic Micro Thrusters of Phan-Thien-Tanner (PTT) Fluid at High Zeta Potential
ZHENG Jiaxuan, LIANG Yundi, JIAN Yongjun
2023, 44(10): 1213-1225. doi: 10.21656/1000-0887.430346
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Abstract:
Electroosmotic micro thrusters filled with Phan-Thien-Tanner (PTT) viscoelastic fluid between 2 parallel plates were investigated at high wall zeta potential. The nonlinear Poisson-Boltzmann equation was solved without the Debye-Hückel linear approximation, to obtain the analytical electric potential at the high zeta potential. The numerical velocity of the micro thruster was given under the Navier slip condition in solution of the Cauchy momentum equation satisfied by the PTT fluid. Performances of the micro thrusters, including the specific impulse, the thrust, the efficiency, and the thrust-to-power ratio, were obtained through numerical integration. Finally, effects of the viscoelastic parameters, the wall zeta potential, the slip coefficient, and the double electric layer thickness on the velocity distributions and propeller performances, were discussed. The results show that, compared with the Newtonian fluid, the PTT fluid as a propellant is conducive to the improvement of propeller performances. For example, the fluid velocity increases with the viscoelastic parameters, resulting in an increasing trend of propeller performances. The present thruster delivers a thrust about 0~250 μN with a specific impulse of 800~1 000 ms, achieving an efficiency of 6%~12% and a thrust-power ratio of 0~20 mN/W.
A Chebyshev Spectral Method for the Unsteady Maxwell Oblique Stationary Point Flow on an Axially Cosine Oscillating Cylinder
BAI Yu, TANG Qiaoli, ZHANG Yan
2023, 44(10): 1226-1235. doi: 10.21656/1000-0887.430361
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Abstract:
The oblique stationary point flow of the Maxwell fluid impacting an axially cosine oscillating cylinder was studied. Firstly, based on the oblique stationary point flow characteristics, the pressure was corrected with the 2nd-order ordinary differential equation of pressure obtained in the cylindrical coordinate system. Later, the boundary layer model for the unsteady Maxwell fluid on an oscillating cylinder was established. The model was converted through the reasonable similarity transform, and the numerical solutions were obtained with the Chebyshev spectral method. The results show that, the fluid near the surface of the cylinder moves periodically with the cylinder. The larger the curvature of the cylinder is, the higher the velocity of the fluid particle will be in the same position at the same time. In contrast, the unsteady state parameter and the memory properties of the fluid hinder the flow closer to the cylinder wall.
Quasi-Static Pressure Characteristics of Explosion Venting Vessel Under Confined Explosion
XIE Jiang, PAN Hanyuan, LI Xuan, WANG Lixuan, JIANG Yilun, FENG Zhenyu
2023, 44(10): 1236-1249. doi: 10.21656/1000-0887.430359
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Abstract:
To study the quasi-static pressure characteristics inside the explosion venting vessels, 3 numerical models for cylindrical explosion venting vessels were established with the AUTODYN software, including a one-end-opening explosion venting vessel, an explosion venting vessel with an ejectable venting cover, and an explosion venting vessel with a shear pinned venting cover. Based on the Bernoulli equation, a theoretical simplified model was established to simulate the quasi-static pressure inside the opening explosion venting vessel. A theoretical simplified model based on the energy conservation equation was established to simulate the quasi-static pressure in the vessel with a venting cover under different charge weights. In the end, the effects of the shear pin on the pressure of the explosion venting vessel were discussed in the cases of cutoff or non-cutoff. The numerical models in previous literatures were established. The theoretical quasi-static pressure results are in good agreement with the experimental results in the literatures, which verifies the reliability of the proposed theoretical calculation method. The results show that, the internal pressure of the open explosion venting vessel decays rapidly, and the quasi-static stage lasts for a short time. The theoretical simplified model based on the Bernoulli equation can better predict the time when the internal pressure in the explosion venting vessel decays to the atmospheric pressure. The shock wave in the vessel with a venting cover propagates reciprocally along the axial direction. The theoretical model based on the energy conservation equation can better predict the quasi-static pressure during the pressure decaying process. In the case of the non-cutoff shear pin, the quasi-static pressure inside the vessel exhibits an obvious platform effect. Compared with the case without a shear pin, the internal pressure in the vessel with a shear pin will decay basically in the same way after the shear pin with a diameter of 18 mm is cut off, and the venting cover will reach the opening in advance by 0.25 ms. This work mainly provides a theoretical basis and applicable reference for the structural design of explosion venting vessels.
Applied Mathematics
On the Liouville Theorems for 3D Stationary Magnetohydrodynamic Equations
TIAN Qin, XIANG Changlin, BIE Qunyi
2023, 44(10): 1250-1259. doi: 10.21656/1000-0887.430375
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Abstract:
The Liouville theorems for 3D stationary magnetohydrodynamic equations were studied. First, a Caccioppoli type inequality was obtained with the energy method, then 3 sufficient conditions for the Liouville theorems were obtained based on the Sobolev embedding theorems, of which 1 sufficient condition indicates that, given a smooth solution to the 3D stationary magnetohydrodynamic equation satisfying( u , b )∈Lp, 3/2 < p < 3, equality u = b 0 will be tenable. This work extends the lower bound of the integrable index in the Lebesgue space from 2 to 3/2 without the finite Dirichlet integral condition, which improves and generalizes some conclusions about the Liouville theorems for stationary magnetohydrodynamic equations.
An Iterative Regularization Method for Solving Backward Problems With 2 Perturbation Data
YUAN Xiaoyu, FENG Xiaoli, ZHANG Yun
2023, 44(10): 1260-1271. doi: 10.21656/1000-0887.440066
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Abstract:
The backward problem of space-fractional diffusion equations with perturbed diffusion coefficients and perturbed final data was considered. The initial data were recovered from the measured data at the final time. Given the severe ill-posedness of this problem, an iterative regularization method was proposed to tackle it. The convergence error estimate between the exact and approximate solutions was obtained under the assumption of an a-priori bound on the exact solution. Finally, several numerical simulations were conducted to verify the effectiveness of this method.
Existence and Uniqueness of the Solutions to High-Dimensional McKean-Vlasov SDEs Under Non-Lipschitz Conditions
MA Li, SUN Fangfang
2023, 44(10): 1272-1290. doi: 10.21656/1000-0887.440010
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Abstract:
The existence and uniqueness of the solutions to high-dimensional McKean-Vlasov stochastic differential equations with discontinuous drift coefficients and corresponding particle systems, were investigated. With the drift coefficient being piecewise Lipschitz continuous about the space variable, through Zvonkin's transformation, the original equation was converted into a new McKean-Vlasov stochastic differential equation with Lipschitz continuous coefficients. Therefore, the new equation has a unique solution. Moreover, the existence and Lipschitz continuity of the inverse function were proven according to the transformation function characteristics. Finally, based on the It's formula and the inverse function characteristics, the existence and uniqueness of the solutions to the McKean-Vlasov stochastic differential equation and the corresponding particle system were obtained.