Pub Date : 2023-01-01DOI: 10.21656/1000-0887.440066
YUAN Xiaoyu, FENG Xiaoli, ZHANG Yun
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.
{"title":"An Iterative Regularization Method for Solving Backward Problems With 2 Perturbation Data","authors":"YUAN Xiaoyu, FENG Xiaoli, ZHANG Yun","doi":"10.21656/1000-0887.440066","DOIUrl":"https://doi.org/10.21656/1000-0887.440066","url":null,"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.","PeriodicalId":8341,"journal":{"name":"Applied Mathematics and Mechanics","volume":"180 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":"135505364","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: 10.21656/1000-0887.440056
ZHANG Yongzheng, LIU Lei, LIU Qi, XU Guangkui
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.
{"title":"Multi-Scale Prediction of Thermal and Mechanical Properties of C/SiC Braided Composites","authors":"ZHANG Yongzheng, LIU Lei, LIU Qi, XU Guangkui","doi":"10.21656/1000-0887.440056","DOIUrl":"https://doi.org/10.21656/1000-0887.440056","url":null,"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.","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":"135505366","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: 10.21656/1000-0887.440110
XIE Mingyun, PU Tianhao, LIU Hong, WU Shengqi
The liquid jet breakup and atomization interacting with a strong swirling crossflow is of significance in designing advanced aeroengines. The Eulerian-Lagrangian method was utilized to simulate the jet breakup and atomization processes. The volume of fluid (VOF) method was employed to track the gas-liquid interface topology evolution during the jet breakup, while the Lagrangian particle tracing (LPT) method was used to track the discrete droplets and obtain the information on far-field liquid dispersion. The crossflow was designed with different swirl numbers, ranging from 0 to 2.5. Momentum ratio q between the liquid jet and the air flow was set to 10, and the gas Weber number was 39. Under these conditions, both the column and shear breakups were observed. The results indicate that, the development of axial waves induced by the Kevin-Helmholtz (KH) instability was the main cause for column breakup. During the surface breakup, ligaments and small liquid jet branches were stripped from the liquid jet surface, primarily driven by azimuthal shear waves. The strong swirling airflow enhances the jet column breakup process, leading to a lower radial height for the breakup location and a shorter breakup time. However, as the swirl number increases, the radial height of the onset of breakup would increase, which suggests the swirl flow would delay the surface breakup of liquid jets. With the increase of the swirl number, the velocity component in the flow direction decreases, and the jet trajectory in the radial direction increases significantly. The deflection angle of the jet shows a linear relationship with the position of the flow direction, with larger air swirl numbers resulting in a steeper slope. Furthermore, as the swirl number increases, the Sauter mean diameter (SMD) of the entire spray field would decrease, and the liquid dispersion would increase.
{"title":"Breakup and Atomization Characteristics of Liquid Jets in Strong Swirling Crossflow Based on the VOF-LPT Method","authors":"XIE Mingyun, PU Tianhao, LIU Hong, WU Shengqi","doi":"10.21656/1000-0887.440110","DOIUrl":"https://doi.org/10.21656/1000-0887.440110","url":null,"abstract":"The liquid jet breakup and atomization interacting with a strong swirling crossflow is of significance in designing advanced aeroengines. The Eulerian-Lagrangian method was utilized to simulate the jet breakup and atomization processes. The volume of fluid (VOF) method was employed to track the gas-liquid interface topology evolution during the jet breakup, while the Lagrangian particle tracing (LPT) method was used to track the discrete droplets and obtain the information on far-field liquid dispersion. The crossflow was designed with different swirl numbers, ranging from 0 to 2.5. Momentum ratio q between the liquid jet and the air flow was set to 10, and the gas Weber number was 39. Under these conditions, both the column and shear breakups were observed. The results indicate that, the development of axial waves induced by the Kevin-Helmholtz (KH) instability was the main cause for column breakup. During the surface breakup, ligaments and small liquid jet branches were stripped from the liquid jet surface, primarily driven by azimuthal shear waves. The strong swirling airflow enhances the jet column breakup process, leading to a lower radial height for the breakup location and a shorter breakup time. However, as the swirl number increases, the radial height of the onset of breakup would increase, which suggests the swirl flow would delay the surface breakup of liquid jets. With the increase of the swirl number, the velocity component in the flow direction decreases, and the jet trajectory in the radial direction increases significantly. The deflection angle of the jet shows a linear relationship with the position of the flow direction, with larger air swirl numbers resulting in a steeper slope. Furthermore, as the swirl number increases, the Sauter mean diameter (SMD) of the entire spray field would decrease, and the liquid dispersion would increase.","PeriodicalId":8341,"journal":{"name":"Applied Mathematics and Mechanics","volume":"14 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":"135838476","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: 10.21656/1000-0887.440017
LU Shuang, LI Dongbo, CHEN Jingbo, XI Bo
Based on the Hamiltonian variational principle, the 2D field equations and boundary conditions for flexoelectricity were derived, and the corresponding governing equations were obtained through substitution of the constitutive relation and geometric equations into the field equation. The in-plane tensile deformation, thickness-stretch deformation, symmetric thickness-shear deformation, and their coupled flexoelectric polarization of flexoelectric nanoplates caused by inhomogeneous temperature changes, were studied. The displacement fields and electric potential fields were solved with the double Fourier series method. The results demonstrate that, all fields are sensitive to the temperature load, which raises the prospect of controlling the mechanical and electrical behaviors of flexoelectric nanoplates by means of the temperature field. The effects of the thermal field and mechanical field on the displacement field were compared and examined. The work extends the Mindlin-Medick plate structure analysis theory in view of the flexoelectric and temperature effects, and provides a reference for the structural design of micro- and nano-scale devices.
{"title":"The Mindlin-Medick Plate Theory and Its Application Under Flexoelectricity and Temperature Effects","authors":"LU Shuang, LI Dongbo, CHEN Jingbo, XI Bo","doi":"10.21656/1000-0887.440017","DOIUrl":"https://doi.org/10.21656/1000-0887.440017","url":null,"abstract":"Based on the Hamiltonian variational principle, the 2D field equations and boundary conditions for flexoelectricity were derived, and the corresponding governing equations were obtained through substitution of the constitutive relation and geometric equations into the field equation. The in-plane tensile deformation, thickness-stretch deformation, symmetric thickness-shear deformation, and their coupled flexoelectric polarization of flexoelectric nanoplates caused by inhomogeneous temperature changes, were studied. The displacement fields and electric potential fields were solved with the double Fourier series method. The results demonstrate that, all fields are sensitive to the temperature load, which raises the prospect of controlling the mechanical and electrical behaviors of flexoelectric nanoplates by means of the temperature field. The effects of the thermal field and mechanical field on the displacement field were compared and examined. The work extends the Mindlin-Medick plate structure analysis theory in view of the flexoelectric and temperature effects, and provides a reference for the structural design of micro- and nano-scale devices.","PeriodicalId":8341,"journal":{"name":"Applied Mathematics and Mechanics","volume":"171 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":"135838483","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: 10.21656/1000-0887.440047
TANG Hao, LIU Yunlong, FENG Jituan, JU Xinyang, ZHANG Aman
An underwater explosion out-of-phase bubbles dynamics model was developed based on the Eulerian finite-element method, with the calculation results compared to the unified bubble theory and the out-of-phase explosion experiment to validate the calculation model. Compared with the case of a single bubble in the free field, it is found that the work done by the shock wave of the out-of-phase explosion on the bubble is the cause for the increase of the total energy of the bubble. The closer the absolute value of the phase difference is to π, the smaller the distance parameter is, and the less the total energy loss of the bubble is. The later bubble can cause the first bubble to collapse in advance. The jet direction of the bubble is influenced by the phase difference. When the phase difference is zero, jets are directed toward each other, but for other phase differences, the backward jets occur.
{"title":"Eulerian Finite-Element Numerical Simulation Investigation on the Dynamic Characteristics of Out-of-Phase Bubbles in Underwater Explosions","authors":"TANG Hao, LIU Yunlong, FENG Jituan, JU Xinyang, ZHANG Aman","doi":"10.21656/1000-0887.440047","DOIUrl":"https://doi.org/10.21656/1000-0887.440047","url":null,"abstract":"An underwater explosion out-of-phase bubbles dynamics model was developed based on the Eulerian finite-element method, with the calculation results compared to the unified bubble theory and the out-of-phase explosion experiment to validate the calculation model. Compared with the case of a single bubble in the free field, it is found that the work done by the shock wave of the out-of-phase explosion on the bubble is the cause for the increase of the total energy of the bubble. The closer the absolute value of the phase difference is to π, the smaller the distance parameter is, and the less the total energy loss of the bubble is. The later bubble can cause the first bubble to collapse in advance. The jet direction of the bubble is influenced by the phase difference. When the phase difference is zero, jets are directed toward each other, but for other phase differences, the backward jets occur.","PeriodicalId":8341,"journal":{"name":"Applied Mathematics and Mechanics","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":"135838490","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: 10.21656/1000-0887.430370
WANG Bin, ZHOU Yanping, BIE Qunyi
The energy conservation of 4D incompressible Navier-Stokes equations was studied. In the case of a singular set with a dimension number less than 4 for the Leray-Hopf weak solution (suitable weak solution), the begin{document}$L^qleft([0, T] ; L^pleft(mathbb{R}^4right)right)$end{document} condition in the 4D space was obtained based on Wu's partial regularity results about the 4D incompressible Navier-Stokes equations, to ensure the energy conservation.
The energy conservation of 4D incompressible Navier-Stokes equations was studied. In the case of a singular set with a dimension number less than 4 for the Leray-Hopf weak solution (suitable weak solution), the begin{document}$L^qleft([0, T] ; L^pleft(mathbb{R}^4right)right)$end{document} condition in the 4D space was obtained based on Wu's partial regularity results about the 4D incompressible Navier-Stokes equations, to ensure the energy conservation.
{"title":"Energy Conservation of the 4 D Incompressible Navier-Stokes Equations","authors":"WANG Bin, ZHOU Yanping, BIE Qunyi","doi":"10.21656/1000-0887.430370","DOIUrl":"https://doi.org/10.21656/1000-0887.430370","url":null,"abstract":"The energy conservation of 4D incompressible Navier-Stokes equations was studied. In the case of a singular set with a dimension number less than 4 for the Leray-Hopf weak solution (suitable weak solution), the <inline-formula><tex-math id=\"M2\">begin{document}$L^qleft([0, T] ; L^pleft(mathbb{R}^4right)right)$end{document}</tex-math></inline-formula> condition in the 4D space was obtained based on Wu's partial regularity results about the 4D incompressible Navier-Stokes equations, to ensure the energy conservation.","PeriodicalId":8341,"journal":{"name":"Applied Mathematics and Mechanics","volume":"82 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":"135838747","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: 10.21656/1000-0887.440103
XIAO Yexin, JIN Tai
Aimed at the phenomenon of flame flashback and low-frequency combustion oscillation in the scramjet combustor with equal straight cross sections, 3D simulations were conducted, with the hybrid RANS/LES method (delayed detached-eddy simulation, DDES) for turbulence modeling and the partially stirred reactor (PaSR) for turbulence-reaction interactions. The obtained entire combustion oscillation period is consistent with the low-frequency combustion oscillation phenomenon observed in the experiment. The low-frequency combustion oscillation period can be divided into 3 stages: the cavity-holding flame, the flame flashback, and the flame blowout. By analysis of the reacting flow field in different stages of the low-frequency combustion oscillation cycle, the possible formation mechanism of low-frequency combustion oscillations was summarized. The results show that, there is no choking in the combustion chamber during the whole low-frequency combustion oscillation period. The pressure rise induced by shock interaction and the heat released by combustion are the key factors for the formation of low-frequency combustion oscillations in the combustion chamber.
{"title":"Numerical Analysis of Flame Flashback and Instability in Cavity-Stabilized Supersonic Combustion","authors":"XIAO Yexin, JIN Tai","doi":"10.21656/1000-0887.440103","DOIUrl":"https://doi.org/10.21656/1000-0887.440103","url":null,"abstract":"Aimed at the phenomenon of flame flashback and low-frequency combustion oscillation in the scramjet combustor with equal straight cross sections, 3D simulations were conducted, with the hybrid RANS/LES method (delayed detached-eddy simulation, DDES) for turbulence modeling and the partially stirred reactor (PaSR) for turbulence-reaction interactions. The obtained entire combustion oscillation period is consistent with the low-frequency combustion oscillation phenomenon observed in the experiment. The low-frequency combustion oscillation period can be divided into 3 stages: the cavity-holding flame, the flame flashback, and the flame blowout. By analysis of the reacting flow field in different stages of the low-frequency combustion oscillation cycle, the possible formation mechanism of low-frequency combustion oscillations was summarized. The results show that, there is no choking in the combustion chamber during the whole low-frequency combustion oscillation period. The pressure rise induced by shock interaction and the heat released by combustion are the key factors for the formation of low-frequency combustion oscillations in the combustion chamber.","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":"135838752","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: 10.21656/1000-0887.440068
ZHANG Weijie, WANG Jinhua, HU Guangya, LI Deli, WANG Ziqi, HUANG Zuohua
The LES of partially premixed turbulent flame MRB in TU Darmstadt was conducted based on the flamelet-tabulated combustion model FGM, and effects of premixed and partially premixed tabulations on the modelling results were studied. The results show that, different methods of tabulation exhibit limited influences on the predictions of the flame structure, velocity, and major species, but using a partially premixed tabulation largely improves the reliability of modelling intermediate minor species CO and H2. The underlying reason lies in a better inclusion of the fuel-air mixing effects through the partially premixed tabulation, which is built based on laminar counter-flow flames. Adding extra transport equations for the intermediate species improves the predictions of intermediate species, especially given a premixed tabulation adopted; meanwhile, the stretch effects in this turbulent flame are ignorable. The results are significant to guide the high-fidelity simulation of partially premixed turbulent flames based on the flamelet-tabulated combustion model.
{"title":"Modelling Intermediate Species in Partially Premixed Turbulent Combustion Based on the LES-FGM Method","authors":"ZHANG Weijie, WANG Jinhua, HU Guangya, LI Deli, WANG Ziqi, HUANG Zuohua","doi":"10.21656/1000-0887.440068","DOIUrl":"https://doi.org/10.21656/1000-0887.440068","url":null,"abstract":"The LES of partially premixed turbulent flame MRB in TU Darmstadt was conducted based on the flamelet-tabulated combustion model FGM, and effects of premixed and partially premixed tabulations on the modelling results were studied. The results show that, different methods of tabulation exhibit limited influences on the predictions of the flame structure, velocity, and major species, but using a partially premixed tabulation largely improves the reliability of modelling intermediate minor species CO and H<sub>2</sub>. The underlying reason lies in a better inclusion of the fuel-air mixing effects through the partially premixed tabulation, which is built based on laminar counter-flow flames. Adding extra transport equations for the intermediate species improves the predictions of intermediate species, especially given a premixed tabulation adopted; meanwhile, the stretch effects in this turbulent flame are ignorable. The results are significant to guide the high-fidelity simulation of partially premixed turbulent flames based on the flamelet-tabulated combustion model.","PeriodicalId":8341,"journal":{"name":"Applied Mathematics and Mechanics","volume":"68 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":"135839221","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: 10.21656/1000-0887.420211
Li Chuangdi, Liao Yuxiang, Yang Xuefeng, Ge Xinguang
{"title":"Analytical solution of wind-induced response of six-parameter practical viscoelastic damping energy dissipation structure based on Davenport wind speed spectrum","authors":"Li Chuangdi, Liao Yuxiang, Yang Xuefeng, Ge Xinguang","doi":"10.21656/1000-0887.420211","DOIUrl":"https://doi.org/10.21656/1000-0887.420211","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":"67807857","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：