To solve the first-order differential equation derived from the problem of a free-falling object and the problem arising from Newton’s law of cooling, the study compares the numerical solutions obtained from Picard’...To solve the first-order differential equation derived from the problem of a free-falling object and the problem arising from Newton’s law of cooling, the study compares the numerical solutions obtained from Picard’s and Taylor’s series methods. We have carried out a descriptive analysis using the MATLAB software. Picard’s and Taylor’s techniques for deriving numerical solutions are both strong mathematical instruments that behave similarly. All first-order differential equations in standard form that have a constant function on the right-hand side share this similarity. As a result, we can conclude that Taylor’s approach is simpler to use, more effective, and more accurate. We will contrast Rung Kutta and Taylor’s methods in more detail in the following section.展开更多
The wall wettability of microchannels plays an important role in the gas-liquid mass transfer dynamics under Taylor flow.In this study,we regulated the contact angle of the wall surface through surface chemical grafti...The wall wettability of microchannels plays an important role in the gas-liquid mass transfer dynamics under Taylor flow.In this study,we regulated the contact angle of the wall surface through surface chemical grafting polymerization under controlled experimental conditions.The dynamic changes of CO_(2)bubbles flowing along the microchannel were captured by a high-speed video camera mounted on a stereo microscope,whilst a unit cell model was employed to theoretically investigate the gas-liquid mass transfer dynamics.We quantitatively characterized the effects of wall wettability,specifically the contact angle,on the formation mechanism of gas bubbles and mass transfer process experimentally.The results revealed that the gas bubble velocity,the overall volumetric liquid phase mass transfer coefficients(kLa),and the specific interfacial area(a)all increased with the increase of the contact angle.Conversely,gas bubble length and leakage flow decreased.Furthermore,we proposed a new modified model to predict the gas-liquid two-phase mass transfer performance,based on van Baten’s and Yao’s models.Our proposed model was observed to agree reasonably well with experimental observations.展开更多
TDOA(Time Difference of Arrival)测距方式是UWB(Ultra Wide Band)室内定位的常用方法,针对其不可避免的随机误差以及目标改变运动状态定位不准确的问题,文中提出了一种Chan-Taylor-IMMKF(Interacting Multiple Model Kalman Filter)...TDOA(Time Difference of Arrival)测距方式是UWB(Ultra Wide Band)室内定位的常用方法,针对其不可避免的随机误差以及目标改变运动状态定位不准确的问题,文中提出了一种Chan-Taylor-IMMKF(Interacting Multiple Model Kalman Filter)定位算法。该算法由Chan-Taylor加权算法与加入自适应算法IMM卡尔曼滤波算法组成,通过Chan-Taylor加权算法初次取得目标估计坐标,将该坐标值作为自适应算法IMM的卡尔曼滤波器的测量值,对目标坐标进行多次滤波处理,最终加权得到目标的最终估计坐标。实验将该算法与未滤波的Chan-Taylor加权算法、使用传统的卡尔曼滤波算法进行对比,结果显示该算法有效减小了系统的随机误差,并克服了传统卡尔曼滤波器在目标忽然改变运动状态时不能及时跟踪从而产生较大误差的问题,将误差标准差均值控制在15 cm之内。展开更多
The hydrodynamic study of the liquid film around Taylor bubbles in slug flow has great significance for understanding parallel flow and interaction between Taylor bubbles.The prediction models for liquid film thicknes...The hydrodynamic study of the liquid film around Taylor bubbles in slug flow has great significance for understanding parallel flow and interaction between Taylor bubbles.The prediction models for liquid film thickness mainly focus on stagnant flow,and some of them remain inaccurate performance.However,in the industrial process,the slug flow essentially is co-current flow.Therefore,in this paper,the liquid film thickness is studied by theoretical analysis and experimental methods under two conditions of stagnant and co-current flow.Firstly,under the condition of stagnant flow,the present work is based on Batchelor's theory,and modifies Batchelor's liquid film thickness model,which effectively improves its prediction accuracy.Under the condition of co-current flow,the prediction model of average liquid film thickness in slug flow is established by force and motion analysis.Taylor bubble length is introduced into the model as an important parameter.Dynamic experiments were carried out in the pipe with an inner diameter of 20 mm.The liquid film thickness,Taylor bubble velocity and length were measured by distributed ultrasonic sensor and intrusive cross-correlation conductivity sensor.Comparing the predicted value of the model with the measured results,the relative error is controlled within 10%.展开更多
Rayleigh–Taylor(RT) instability of gravity-driven viscoelastic self-rewetting film flowing under an inclined substrate uniformly heated or cooled is considered. The surface tension of self-rewetting film is considere...Rayleigh–Taylor(RT) instability of gravity-driven viscoelastic self-rewetting film flowing under an inclined substrate uniformly heated or cooled is considered. The surface tension of self-rewetting film is considered as a quadratic function of temperature. The long wave hypothesis is used to derive a nonlinear free surface evolution equation of the thin viscoelastic film. Linear stability analysis shows that for a prescribed the viscoelastic coefficient, substrate cooling products instability,while substrate heating remains stability. Furthermore, we analyze the influence of viscoelastic coefficient on RT instability. Results show that the viscoelastic coefficient reinforces the RT instability whether the substrate is heated or cooled.Moreover, we use the line method to numerically simulate the nonlinear evolution equation and systematically examine the space-time variation of the film free surface. The numerical results illustrate that increasing the viscoelastic coefficient can enhance the disturbance amplitude and wave frequency. This means that the viscoelastic coefficient makes the system unstable, which is consistent with result of the linear stability analysis. In addition, the oscillation tends to accumulate downstream of the inclined substrate when the evolution time is long enough. Finally, the variation of film thickness with related parameters for different viscoelastic coefficients is investigated.展开更多
The persistence and symmetry of cyclones around the poles of Jupiter are unknown.In the present investigation,inspired by cyclones at the South Pole of the Earth,we propose a mechanism that provides an explanation for...The persistence and symmetry of cyclones around the poles of Jupiter are unknown.In the present investigation,inspired by cyclones at the South Pole of the Earth,we propose a mechanism that provides an explanation for this problem.The negative temperature gradient with respect to latitude may play an important role here.This temperature gradient is induced by solar radiation because of the small axial inclination of Jupiter.Our numerical simulations suggest that cyclones in the polar regions of Jupiter may be modulated or controlled by the radially directional Rayleigh–Taylor instability,driven by centrifugal force and the negative temperature gradient along the latitude.展开更多
文摘To solve the first-order differential equation derived from the problem of a free-falling object and the problem arising from Newton’s law of cooling, the study compares the numerical solutions obtained from Picard’s and Taylor’s series methods. We have carried out a descriptive analysis using the MATLAB software. Picard’s and Taylor’s techniques for deriving numerical solutions are both strong mathematical instruments that behave similarly. All first-order differential equations in standard form that have a constant function on the right-hand side share this similarity. As a result, we can conclude that Taylor’s approach is simpler to use, more effective, and more accurate. We will contrast Rung Kutta and Taylor’s methods in more detail in the following section.
基金the financial supports from National Natural Science Foundation of China(21978250,22208278)Natural Science Foundation of Shandong Province(ZR2020KB013,ZR2020QE211,2019KJC012).
文摘The wall wettability of microchannels plays an important role in the gas-liquid mass transfer dynamics under Taylor flow.In this study,we regulated the contact angle of the wall surface through surface chemical grafting polymerization under controlled experimental conditions.The dynamic changes of CO_(2)bubbles flowing along the microchannel were captured by a high-speed video camera mounted on a stereo microscope,whilst a unit cell model was employed to theoretically investigate the gas-liquid mass transfer dynamics.We quantitatively characterized the effects of wall wettability,specifically the contact angle,on the formation mechanism of gas bubbles and mass transfer process experimentally.The results revealed that the gas bubble velocity,the overall volumetric liquid phase mass transfer coefficients(kLa),and the specific interfacial area(a)all increased with the increase of the contact angle.Conversely,gas bubble length and leakage flow decreased.Furthermore,we proposed a new modified model to predict the gas-liquid two-phase mass transfer performance,based on van Baten’s and Yao’s models.Our proposed model was observed to agree reasonably well with experimental observations.
基金supported by National Natural Science Foundation of China(42074142,51527805)。
文摘The hydrodynamic study of the liquid film around Taylor bubbles in slug flow has great significance for understanding parallel flow and interaction between Taylor bubbles.The prediction models for liquid film thickness mainly focus on stagnant flow,and some of them remain inaccurate performance.However,in the industrial process,the slug flow essentially is co-current flow.Therefore,in this paper,the liquid film thickness is studied by theoretical analysis and experimental methods under two conditions of stagnant and co-current flow.Firstly,under the condition of stagnant flow,the present work is based on Batchelor's theory,and modifies Batchelor's liquid film thickness model,which effectively improves its prediction accuracy.Under the condition of co-current flow,the prediction model of average liquid film thickness in slug flow is established by force and motion analysis.Taylor bubble length is introduced into the model as an important parameter.Dynamic experiments were carried out in the pipe with an inner diameter of 20 mm.The liquid film thickness,Taylor bubble velocity and length were measured by distributed ultrasonic sensor and intrusive cross-correlation conductivity sensor.Comparing the predicted value of the model with the measured results,the relative error is controlled within 10%.
基金Project supported by the National Natural Science Foundation of China(Grant No.12262026)the Natural Science Foundation of Inner Mongolia Autonomous Region of China(Grant No.2021 MS01007)the Inner Mongolia Grassland Talent,China(Grant No.12000-12102013)。
文摘Rayleigh–Taylor(RT) instability of gravity-driven viscoelastic self-rewetting film flowing under an inclined substrate uniformly heated or cooled is considered. The surface tension of self-rewetting film is considered as a quadratic function of temperature. The long wave hypothesis is used to derive a nonlinear free surface evolution equation of the thin viscoelastic film. Linear stability analysis shows that for a prescribed the viscoelastic coefficient, substrate cooling products instability,while substrate heating remains stability. Furthermore, we analyze the influence of viscoelastic coefficient on RT instability. Results show that the viscoelastic coefficient reinforces the RT instability whether the substrate is heated or cooled.Moreover, we use the line method to numerically simulate the nonlinear evolution equation and systematically examine the space-time variation of the film free surface. The numerical results illustrate that increasing the viscoelastic coefficient can enhance the disturbance amplitude and wave frequency. This means that the viscoelastic coefficient makes the system unstable, which is consistent with result of the linear stability analysis. In addition, the oscillation tends to accumulate downstream of the inclined substrate when the evolution time is long enough. Finally, the variation of film thickness with related parameters for different viscoelastic coefficients is investigated.
基金supported by the National Nature Science Foundation of China(Grant No.NSFC41974204).
文摘The persistence and symmetry of cyclones around the poles of Jupiter are unknown.In the present investigation,inspired by cyclones at the South Pole of the Earth,we propose a mechanism that provides an explanation for this problem.The negative temperature gradient with respect to latitude may play an important role here.This temperature gradient is induced by solar radiation because of the small axial inclination of Jupiter.Our numerical simulations suggest that cyclones in the polar regions of Jupiter may be modulated or controlled by the radially directional Rayleigh–Taylor instability,driven by centrifugal force and the negative temperature gradient along the latitude.
