Pub Date : 2023-01-01DOI: 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.
{"title":"Quasi-Static Pressure Characteristics of Explosion Venting Vessel Under Confined Explosion","authors":"XIE Jiang, PAN Hanyuan, LI Xuan, WANG Lixuan, JIANG Yilun, FENG Zhenyu","doi":"10.21656/1000-0887.430359","DOIUrl":"https://doi.org/10.21656/1000-0887.430359","url":null,"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.","PeriodicalId":8341,"journal":{"name":"应用数学和力学","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135505374","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.21656/1000-0887.440077
QIN Wenjin, HAN Tianxiang, ZHANG Zhendong, SUN Yuedong
Fuel spray wall impingement is a common phenomenon in small high-pressure direct injection diesel engines. Fuel spray wall impingement influences the in-cylinder combustion process, and significantly impacts the engine’s dynamics, fuel economy, and emissions. To better understand the combustion characteristics of fuel spray wall impingement, the numerical simulation was applied to calculate the process and explore this process. The results show that, during the 2-stage combustion process of spray wall impingement, the impingement promotes the radial development radius and the vortex height of the spray, enhances oil-gas mixing near the wall, and forms favorable conditions for low-temperature ignition near the wall. Low-temperature combustion reactions start in the near-wall region, where the mixture is relatively dilute, and then develop into the dense mixed gas area in the center of the impinging spray. As low-temperature oxidation combustion continues to release heat, the maximum temperature in the center of the impinging spray will gradually increase, and a large amount of CH2O will accumulate. Meanwhile, the impinging spray can cause the formation of a more concentrated mixture in the center of the impinging spray, and low-temperature combustion would release less heat, resulting in the incomplete combustion of some carbon, and increasing the amount of soot generated. Additionally, as high-temperature combustion proceeds, the temperature will continue rising, and the impinging spray will draw more oxygen, generating a large amount of NOx through oxidation reactions.
{"title":"Numerical Simulation Study of Spray Wall Impingement Combustion","authors":"QIN Wenjin, HAN Tianxiang, ZHANG Zhendong, SUN Yuedong","doi":"10.21656/1000-0887.440077","DOIUrl":"https://doi.org/10.21656/1000-0887.440077","url":null,"abstract":"Fuel spray wall impingement is a common phenomenon in small high-pressure direct injection diesel engines. Fuel spray wall impingement influences the in-cylinder combustion process, and significantly impacts the engine’s dynamics, fuel economy, and emissions. To better understand the combustion characteristics of fuel spray wall impingement, the numerical simulation was applied to calculate the process and explore this process. The results show that, during the 2-stage combustion process of spray wall impingement, the impingement promotes the radial development radius and the vortex height of the spray, enhances oil-gas mixing near the wall, and forms favorable conditions for low-temperature ignition near the wall. Low-temperature combustion reactions start in the near-wall region, where the mixture is relatively dilute, and then develop into the dense mixed gas area in the center of the impinging spray. As low-temperature oxidation combustion continues to release heat, the maximum temperature in the center of the impinging spray will gradually increase, and a large amount of CH<sub>2</sub>O will accumulate. Meanwhile, the impinging spray can cause the formation of a more concentrated mixture in the center of the impinging spray, and low-temperature combustion would release less heat, resulting in the incomplete combustion of some carbon, and increasing the amount of soot generated. Additionally, as high-temperature combustion proceeds, the temperature will continue rising, and the impinging spray will draw more oxygen, generating a large amount of NO<sub>x</sub> through oxidation reactions.","PeriodicalId":8341,"journal":{"name":"应用数学和力学","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135838495","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.21656/1000-0887.430130
Yang Jikang, Yu Jinwei, Yang Weihua
{"title":"Distributed Formation Maneuver Control of Networked Euler-Lagrange Systems","authors":"Yang Jikang, Yu Jinwei, Yang Weihua","doi":"10.21656/1000-0887.430130","DOIUrl":"https://doi.org/10.21656/1000-0887.430130","url":null,"abstract":"","PeriodicalId":8341,"journal":{"name":"Applied Mathematics and Mechanics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67811900","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.21656/1000-0887.430334
Yang Yang, Wang Kaimo, Shen Huoming, Wang Yuxing
{"title":"Research on Partial Slip Contact Behavior With Temperature Effects","authors":"Yang Yang, Wang Kaimo, Shen Huoming, Wang Yuxing","doi":"10.21656/1000-0887.430334","DOIUrl":"https://doi.org/10.21656/1000-0887.430334","url":null,"abstract":"","PeriodicalId":8341,"journal":{"name":"Applied Mathematics and Mechanics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67814560","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 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.
{"title":"A Semi-Analytical Model and Seepage Characteristics of Multi-Wing Fracture Off-Center Wells","authors":"JI Anzhao","doi":"10.21656/1000-0887.430395","DOIUrl":"https://doi.org/10.21656/1000-0887.430395","url":null,"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.","PeriodicalId":8341,"journal":{"name":"Applied Mathematics and Mechanics","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135505381","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 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.
{"title":"Lump Solutions, Interaction Solutions and Breather Solutions of Generalized (3+1)-Dimensional KdV Equations","authors":"YU Minghui, WANG Yunhu","doi":"10.21656/1000-0887.430353","DOIUrl":"https://doi.org/10.21656/1000-0887.430353","url":null,"abstract":"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.","PeriodicalId":8341,"journal":{"name":"Applied Mathematics and Mechanics","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135800479","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 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.
{"title":"Low-Order Predictions of Spatial Distributions of Conserved Scalars in Swirl Combustors Based on the Gaussian Plume Function","authors":"WU Ziheng, ZHANG Chi, ZHANG Shihong, WANG Bosen","doi":"10.21656/1000-0887.440119","DOIUrl":"https://doi.org/10.21656/1000-0887.440119","url":null,"abstract":"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.","PeriodicalId":8341,"journal":{"name":"Applied Mathematics and Mechanics","volume":"127 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135838738","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 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.
{"title":"Analytical Solutions of Steady Flow Toward a Partially Penetrating Well in a Rectangular Leaky-Confined Aquifer","authors":"SUN Qianlin, TAN Weijia, XU Beiyi, WANG Xudong","doi":"10.21656/1000-0887.430398","DOIUrl":"https://doi.org/10.21656/1000-0887.430398","url":null,"abstract":"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.","PeriodicalId":8341,"journal":{"name":"Applied Mathematics and Mechanics","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135838755","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.21656/1000-0887.430152
LI Dianzhe, Liu Lu, Ji Shunying
{"title":"A Discrete Element Method for Irregular Granular Materials Based on Multi-Dilated Polyhedron Elements","authors":"LI Dianzhe, Liu Lu, Ji Shunying","doi":"10.21656/1000-0887.430152","DOIUrl":"https://doi.org/10.21656/1000-0887.430152","url":null,"abstract":"","PeriodicalId":8341,"journal":{"name":"Applied Mathematics and Mechanics","volume":"231 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67811598","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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