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A Chebyshev Spectral Method for the Unsteady Maxwell Oblique Stationary Point Flow on an Axially Cosine Oscillating Cylinder 轴向余弦振荡圆柱体上非定常Maxwell斜驻点流动的Chebyshev谱法
Q4 Mathematics Pub Date : 2023-01-01 DOI: 10.21656/1000-0887.430361
BAI Yu, TANG Qiaoli, ZHANG Yan
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.
研究了麦克斯韦流体冲击轴向余弦振荡圆柱体时的斜驻点流动。首先,根据斜驻点流动特性,利用圆柱坐标系下得到的二阶压力微分方程对压力进行修正;在此基础上,建立了振荡圆柱上非定常麦克斯韦流体的边界层模型。通过合理的相似变换对模型进行转换,利用切比雪夫谱法得到数值解。结果表明,靠近圆柱体表面的流体随圆柱体周期性运动。圆柱体曲率越大,流体颗粒在同一时间处于同一位置的速度越高。相反,非定常参数和流体的记忆特性阻碍了流体更靠近汽缸壁。
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引用次数: 0
Quasi-Static Pressure Characteristics of Explosion Venting Vessel Under Confined Explosion 密闭爆炸下爆炸通风容器的准静压特性
Q4 Mathematics Pub Date : 2023-01-01 DOI: 10.21656/1000-0887.430359
XIE Jiang, PAN Hanyuan, LI Xuan, WANG Lixuan, JIANG Yilun, FENG Zhenyu
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.
为了研究爆炸通风容器内部的准静压特性,利用AUTODYN软件建立了3种圆柱形爆炸通风容器的数值模型,包括一端开口的爆炸通风容器、带弹射通风盖的爆炸通风容器和带剪切钉住通风盖的爆炸通风容器。基于伯努利方程,建立了一个理论简化模型来模拟开式爆炸通风容器内的准静压。建立了基于能量守恒方程的理论简化模型,模拟了不同装药重量下带通气盖容器内的准静压。最后讨论了在切断和不切断两种情况下,剪切销对爆炸通风容器压力的影响。建立了前人文献中的数值模型。理论拟静压计算结果与文献实验结果吻合较好,验证了理论计算方法的可靠性。结果表明:开式爆炸通风容器内压衰减迅速,准静态阶段持续时间短;基于伯努利方程的理论简化模型能较好地预测爆炸放空容器内压衰减到大气压力的时间。冲击波在带通气罩的容器内沿轴向往复传播。基于能量守恒方程的理论模型能较好地预测压力衰减过程中的准静压。在非截止剪切销的情况下,容器内准静压表现出明显的平台效应。与不带剪切销的情况相比,带剪切销的容器内压在切断直径为18mm的剪切销后,其衰减方式基本相同,排气盖提前0.25 ms到达开口。本工作主要为防爆容器的结构设计提供理论依据和应用参考。
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引用次数: 0
Surface Acoustic Wave Characterization of Equivalent Young's Moduli for Patterned Films 图像化薄膜等效杨氏模量的表面声波表征
Q4 Mathematics Pub Date : 2023-01-01 DOI: 10.21656/1000-0887.430050
Chen Long, Xiao Xia, Zhang Li, QI Haiyang
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引用次数: 0
Distributed Formation Maneuver Control of Networked Euler-Lagrange Systems 网络欧拉-拉格朗日系统的分布式编队机动控制
Q4 Mathematics Pub Date : 2023-01-01 DOI: 10.21656/1000-0887.430130
Yang Jikang, Yu Jinwei, Yang Weihua
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引用次数: 0
Research on Partial Slip Contact Behavior With Temperature Effects 温度影响下的局部滑移接触行为研究
Q4 Mathematics Pub Date : 2023-01-01 DOI: 10.21656/1000-0887.430334
Yang Yang, Wang Kaimo, Shen Huoming, Wang Yuxing
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引用次数: 0
A Semi-Analytical Model and Seepage Characteristics of Multi-Wing Fracture Off-Center Wells 多翼裂缝离心井半解析模型及渗流特征
Q4 Mathematics Pub Date : 2023-01-01 DOI: 10.21656/1000-0887.430395
JI Anzhao
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.
针对多翼裂缝离心井的实际情况,建立了多翼裂缝离心井的数学模型。基于Laplace变换和压降叠加原理,得到了多翼裂缝离心井井底压力在Laplace空间中的半解析解。采用非均匀流法对半解析解进行离散化。结合Stehfest数值反演,得到了实际空间井底压力和产量分布的数值解。利用sapir试井分析软件建立储层数值试井模型,并进行数值离散计算。将数值结果与半解析模型的计算结果进行了比较,验证了半解析模型的正确性。结果表明:多翼裂缝离心井井底压力变化可划分为8个主要渗流阶段;最后,讨论了无因次导流系数、裂缝不对称系数和离中心距离对井底压力变化和产量分布特征的影响。
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引用次数: 0
Lump Solutions, Interaction Solutions and Breather Solutions of Generalized (3+1)-Dimensional KdV Equations 广义(3+1)维KdV方程的整体解、相互作用解和呼吸解
Q4 Mathematics Pub Date : 2023-01-01 DOI: 10.21656/1000-0887.430353
YU Minghui, WANG Yunhu
Based on the bilinear form of the generalized (3+1)-dimensional KdV equation, the lump solution, the interaction solution and the breather solution of the equation were obtained. The obtained lump solutions were proved to be rationally localized in all directions of the space, then the "fusion" and "fission" phenomena were observed during the interaction between the lump soliton wave and the one-stripe soliton. Finally, the breather solution of the equation was obtained.
基于广义(3+1)维KdV方程的双线性形式,得到了该方程的整体解、相互作用解和呼吸解。证明了所得到的块状孤子解在空间各方向上的合理局域性,并在块状孤子波与单条纹孤子相互作用过程中观察到“聚变”和“裂变”现象。最后,得到了方程的呼吸解。
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引用次数: 0
Low-Order Predictions of Spatial Distributions of Conserved Scalars in Swirl Combustors Based on the Gaussian Plume Function 基于高斯羽流函数的涡流燃烧室守恒标量空间分布的低阶预测
Q4 Mathematics Pub Date : 2023-01-01 DOI: 10.21656/1000-0887.440119
WU Ziheng, ZHANG Chi, ZHANG Shihong, WANG Bosen
The mixture fraction is a conserved scalar characterizing the fuel-air mixing. As a key reference scalar for turbulent combustion modelling, its spatial distribution is usually obtained through 3D numerical simulation, which are, however, time-consuming and costly for combustors with complex geometries. To overcome such low efficiency in the iterative designing process, a low-order model was developed based on the Gaussian plume function to compute the mixture fraction field in the swirl combustor to accelerate the evaluation of the fuel-air mixing strategy and the parameterized design process. Compared with the conventional formulation, the derived new Gaussian plume function includes the effects of convection and corrections due to swirl flows. A mirror image reflection model was further developed to simulate the wall-plume interactions, together with the relevant corrections to ensure mass conservation. This newly derived Gaussian plume model was applied to the low-older prediction of the mixture fraction field in a methane swirl combustor. Based on the database generated through 3D numerical simulations, the model parameters were optimized with the least square method first. The prediction accuracy under broad working conditions was demonstrated. This study not only provides a novel approach for quick predictions of mixture fractions in swirl combustors, but also sets an instance for further development and application of the Gaussian plume model.
混合分数是表征燃料-空气混合的守恒标量。作为湍流燃烧建模的关键参考标量,其空间分布通常是通过三维数值模拟获得的,但对于形状复杂的燃烧器来说,三维数值模拟耗时且成本高。为了克服迭代设计过程中效率低的问题,建立了基于高斯羽流函数的低阶模型来计算旋流燃烧室的混合分数场,以加快燃料-空气混合策略的评估和参数化设计过程。与传统公式相比,导出的新高斯羽流函数考虑了对流的影响和涡流的修正。进一步建立了镜像反射模型来模拟壁柱相互作用,并进行了相应的修正以确保质量守恒。将新导出的高斯羽流模型应用于甲烷旋流燃烧室混合馏分场的低年龄预测。基于三维数值模拟生成的数据库,首先采用最小二乘法对模型参数进行优化。验证了在广泛工况下的预测精度。该研究不仅为旋涡燃烧室混合馏分的快速预测提供了一种新方法,而且为高斯羽流模型的进一步发展和应用提供了实例。
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引用次数: 0
Analytical Solutions of Steady Flow Toward a Partially Penetrating Well in a Rectangular Leaky-Confined Aquifer 矩形限漏含水层部分穿透井稳定渗流的解析解
Q4 Mathematics Pub Date : 2023-01-01 DOI: 10.21656/1000-0887.430398
SUN Qianlin, TAN Weijia, XU Beiyi, WANG Xudong
For the complicated problem of groundwater flow to a partially penetrating well in a rectangular confined aquifer, a mathematical model describing the groundwater flow to a partially penetrating well pumped at a constant rate in a rectangular leaky-confined aquifer, was established. The analytical solutions of the 3D steady flow in the Cartesian coordinate system under different boundary conditions, were derived through the finite Fourier transform and the inverse transform. After the verification of the analytical solution of drawdown, the number of calculation items satisfying the calculation accuracy requirement was given, based on the analysis of the calculation accuracy of the analytical solution and the characteristics of the groundwater flow to a partially penetrating well. Moreover, the effects of orthotropy, well integrity and well location on the drawdown and seepage fields, were discussed. The engineering examples demonstrate the applicability of the proposed analytical method.
摘要针对矩形承压含水层部分渗透井的复杂渗流问题,建立了矩形承压含水层部分渗透井匀速抽水渗流数学模型。通过有限傅里叶变换和反变换,得到了不同边界条件下直角坐标系下三维定常流动的解析解。在对落差解析解的计算精度进行分析的基础上,结合部分穿透井的地下水流动特点,对落差解析解进行了验证,给出了满足计算精度要求的计算项数。此外,还讨论了正交异性、井完整性和井位对降渗场的影响。工程实例验证了该分析方法的适用性。
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引用次数: 0
A Discrete Element Method for Irregular Granular Materials Based on Multi-Dilated Polyhedron Elements 基于多重膨胀多面体单元的不规则颗粒材料离散元方法
Q4 Mathematics Pub Date : 2023-01-01 DOI: 10.21656/1000-0887.430152
LI Dianzhe, Liu Lu, Ji Shunying
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引用次数: 0
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