Thermoelectric effect is the most efficient way to convert electric energy directly from the temperature gradient. Thermoelectric effect-based power generation, cooling and heating devices are solid-stated, environmen...Thermoelectric effect is the most efficient way to convert electric energy directly from the temperature gradient. Thermoelectric effect-based power generation, cooling and heating devices are solid-stated, environmentally friendly, reliable, long-lived, easily maintainable, and easy to achieve miniaturization and integration. So they have unparalleled advantages in the aerospace, vehicle industry, waste heat recovery, electronic cooling, etc. This paper reviews the progress in thermodynamic analyses and optimizations for single- and multiple-element, single- and multiple-stage, and combined thermoelectric generators, thermoelectric refrigerators and thermoelectric heat pumps, especially in the aspects of non-equilibrium thermodynamics and finite time thermodynamics. It also discusses the developing trends of thermoelectric devices, such as the heat sources of thermoelectric generators, multi-stage thermoelectric devices, combined thermoelectric devices, and heat transfer enhancement of thermoelectric devices.展开更多
The mass entransy and its dissipation extremum principle have opened up a new direction for the mass transfer optimization. Firstly, the emergence and development process of both the mass entransy and its dissipalion ...The mass entransy and its dissipation extremum principle have opened up a new direction for the mass transfer optimization. Firstly, the emergence and development process of both the mass entransy and its dissipalion extremum principle are reviewed. Secondly, the combination of the mass entransy dissipation extremum principle and the finite-time thermodynamics for opti- mizing the mass transfer processes of one-way isothermal mass transfer, two-way isothermal equimolar mass transfer, and iso- thermal throttling and isothermal crystallization are summarized. Thirdly, the combination of the mass entransy dissipation ex- tremum principle and the constructal theory for optimizing the mass transfer processes of disc-to-point and volume-to-point problems are summarized. The scientific features of the mass entransy dissipation extremam principle are emphasized.展开更多
For the terminal guidance problem of missiles intercepting maneuvering targets in the three-dimensional space, the design of guidance laws for non-decoupling three-dimensional engage- ment geometry is studied. Firstly...For the terminal guidance problem of missiles intercepting maneuvering targets in the three-dimensional space, the design of guidance laws for non-decoupling three-dimensional engage- ment geometry is studied. Firstly, by introducing a finite time integral sliding mode manifold, a novel guidance law based on the integral sliding mode control is presented with the target acceler- ation as a known bounded external disturbance. Then, an improved adaptive guidance law based on the integral sliding mode control without the information of the upper bound on the target accel- eration is developed, where the upper bound of the target acceleration is estimated online by a designed adaptive law. The both presented guidance laws can make sure that the elevation angular rate of the line-of-sight and the azimuth angular rate of the line-of-sight converge to zero in finite time. In the end, the results of the guidance performance for the proposed guidance laws are pre- sented by numerical simulations. Although the designed guidance laws are developed for the con- stant speed missiles, the simulation results for the time-varying speed missiles are also shown to further confirm the designed guidance laws.展开更多
In this paper, using finite-time control method, we consider the disturbance analysis of a second-order system with unknown but bounded disturbance. We show that the states of the second-order system will be stabilize...In this paper, using finite-time control method, we consider the disturbance analysis of a second-order system with unknown but bounded disturbance. We show that the states of the second-order system will be stabilized to a region containing the origin. The radius of this region is determined by the control parameters and can be rendered as small as desired. The rigorous stability analysis is also given. Compared with the conventional PD control law, the finite-time control law yields a better disturbance rejection performance. Numerical simulation results show the effectiveness of the method.展开更多
By using finite-time thermodynamics, the optimal performance of a Stirling heat engine with thermal resistance, heat leak and regenerative loss is studied. The fundamental optimal relation is derived and the bounds of...By using finite-time thermodynamics, the optimal performance of a Stirling heat engine with thermal resistance, heat leak and regenerative loss is studied. The fundamental optimal relation is derived and the bounds of power output and efficiency are deduced from it. Then the significance of the relation and bounds are revealed. The results obtained here may provide some new theoretical guides for the optimal design of Stirling heat engines.展开更多
以往使用的求取地震波初至时间的射线追踪法具有不同程度的缺陷,因而在实际应用中存在一定的局限性。本文提出一种将局部算法与扫描算法相结合的、用有限差分解程函方程求取地震波初至时间的方法。方法中考虑了散射波、首波及透射波的存...以往使用的求取地震波初至时间的射线追踪法具有不同程度的缺陷,因而在实际应用中存在一定的局限性。本文提出一种将局部算法与扫描算法相结合的、用有限差分解程函方程求取地震波初至时间的方法。方法中考虑了散射波、首波及透射波的存在,因而可以适用于较复杂的速度模型。在求出初至时间后,利用互易性原理,能准确地得到射线路径。理论模型的试算表明,该方法计算精度较高,适宜地震偏移、层析成像以及 Green 函数的计算。展开更多
In order to simultaneously attack a target with impact angle constraint in threedimensional(3-D) space, a novel distributed cooperative guidance law for multiple missiles under directed communication topologies is pro...In order to simultaneously attack a target with impact angle constraint in threedimensional(3-D) space, a novel distributed cooperative guidance law for multiple missiles under directed communication topologies is proposed without radial velocity measurements. First, based on missiles-target 3-D relative motion equations, the multiple missiles cooperative guidance model with impact angle constraint is constructed. Then, in Line-of-Sight(LOS) direction, based on multiagent system cooperative control theory, one guidance law with directed topologies is designed with strict proof, which can guarantee finite time consensus of multiple missiles' impact times. Next, in elevation direction and azimuth direction of LOS, based on homogeneous system stability theory and integral sliding mode control theory, two guidance laws are proposed respectively with strict proof, which can guarantee LOS angles converge to desired values and LOS angular rates converge to zero in finite time. Finally, the effectiveness of the designed cooperative guidance law is demonstrated through simulation results.展开更多
An integrated cooperative guidance framework for multi-missile cooperatively attacking a single stationary target is proposed in this paper by combining both the centralized and decentralized communication topologies....An integrated cooperative guidance framework for multi-missile cooperatively attacking a single stationary target is proposed in this paper by combining both the centralized and decentralized communication topologies. Once missiles are distributed into several groups, missiles within a single group communicate with the centralized leader-follower framework, while the leaders from different groups communicate using the nearest-neighbor topology. To implement the integrated cooperative guidance framework, a group of Finite-Time Cooperative Guidance（FTCG） laws considering the saturation constraint on FOV（FTCG-FOV） are firstly derived within the centralized leader-follower framework to satisfy the communication topology of missiles in a single group.Then, an improved sequential approach is developed to adapt the FTCG-FOV to satisfy the communication topology between groups. The numerical simulations demonstrate the effectiveness and high efficiency of the integrated cooperative guidance framework and the cooperative guidance laws, as well as the superiority of the developed sequential approach.展开更多
This paper proposes a finite-time robust flight controller, targeting for a reentry vehicle with blended aerodynamic surfaces and a reaction control system（RCS）. Firstly, a novel finite-time attitude controller is p...This paper proposes a finite-time robust flight controller, targeting for a reentry vehicle with blended aerodynamic surfaces and a reaction control system（RCS）. Firstly, a novel finite-time attitude controller is pointed out with the introduction of a nonsingular finite-time sliding mode manifold. The attitude tracking errors are mathematically proved to converge to zero within finite time which can be estimated. In order to improve the performance, a second-order finite-time sliding mode controller is further developed to effectively alleviate chattering without any deterioration of robustness and accuracy. Moreover, an optimization control allocation algorithm, using linear programming and a pulse-width pulse-frequency（PWPF） modulator, is designed to allocate torque commands for all the aerodynamic surface deflections and on–off switching-states of RCS thrusters.Simulations are provided for the reentry vehicle considering uncertain parameters and external disturbances for practical purposes, and the results demonstrate the effectiveness and robustness of the attitude control system.展开更多
This paper investigates two finite-time controllers for attitude control of spacecraft based on rotation matrix by an adaptive backstepping method. Rotation matrix can overcome the draw- backs of unwinding which makes...This paper investigates two finite-time controllers for attitude control of spacecraft based on rotation matrix by an adaptive backstepping method. Rotation matrix can overcome the draw- backs of unwinding which makes a spacecraft perform a large-angle maneuver when a small-angle maneuver in the opposite rotational direction is sufficient to achieve the objective, With the use of adaptive control, the first robust finite-time controller is continuous without a chattering phenom- enon. The second robust finite-time controller can compensate external disturbances with unknown bounds. Theoretical analysis shows that both controllers can make a spacecraft following a time-varying reference attitude signal in finite time and guarantee the stability of the overall closed-loop system. Numerical simulations are presented to demonstrate the effectiveness of the proposed control schemes.展开更多
The full-space transient electromagnetic response of water-filled goaves in coal mines were numerically modeled. Traditional numerical modeling methods cannot be used to simulate the underground full-space transient e...The full-space transient electromagnetic response of water-filled goaves in coal mines were numerically modeled. Traditional numerical modeling methods cannot be used to simulate the underground full-space transient electromagnetic field. We used multiple transmitting loops instead of the traditional single transmitting loop to load the transmitting loop into Cartesian grids. We improved the method for calculating the z-component of the magnetic field based on the characteristics of full space. Then, we established the full- space 3D geoelectrical model using geological data for coalmines. In addition, the transient electromagnetic responses of water-filled goaves of variable shape at different locations were simulated by using the finite-difference time-domain （FDTD） method. Moreover, we evaluated the apparent resistivity results. The numerical modeling results suggested that the resistivity differences between the coal seam and its roof and floor greatly affect the distribution of apparent resistivity, resulting in nearly circular contours with the roadway head at the center. The actual distribution of apparent resistivity for different geoelectrical models of water in goaves was consistent with the models. However, when the goal water was located in one side, a false low-resistivity anomaly would appear on the other side owing to the full-space effect but the response was much weaker. Finally, the modeling results were subsequently confirmed by drilling, suggesting that the proposed method was effective.展开更多
Security monitoring system of coal mines is indispensable to ensure the safe and efficient production of colliery. Due to the special and narrow underground field of the coal mine, the electromagnetic interference can...Security monitoring system of coal mines is indispensable to ensure the safe and efficient production of colliery. Due to the special and narrow underground field of the coal mine, the electromagnetic interference can cause a series of misstatements and false positives on the monitoring system, which will severely hamper the safe production of coal industry. In this paper, first, the frequency characteristics of the interference source on the power line are extracted when equipment runs normally. Then the finite difference time domain method is introduced to analyze the effects of the electromagnetic interference parameters on the security monitoring signal line. And the interference voltage of the two terminal sides on the single line is taken as evaluating indexes. Finally, the electromagnetic interference parameters are optimized by orthogonal experimental design based on the MATLAB simulation on the normal operation of equipment.展开更多
To intercept maneuvering targets at desired impact angles, a three-dimensional terminal guidance problem is investigated in this study. Because of a short terminal guidance time, a finitetime impact angle control guid...To intercept maneuvering targets at desired impact angles, a three-dimensional terminal guidance problem is investigated in this study. Because of a short terminal guidance time, a finitetime impact angle control guidance law is developed using the fast nonsingular terminal sliding mode control theory. However, the guidance law requires the upper bound of lumped uncertainty including target acceleration, which may not be accurately obtained. Therefore, by adopting a novel reaching law, an adaptive sliding mode guidance law is provided to release the drawback. At the same time, this method can accelerate the convergence rate and weaken the chattering phenomenon to a certain extent. In addition, another novel adaptive guidance law is also derived; this ensures systems asymptotic and finite-time stability without the knowledge of perturbations bounds.Numerical simulations have demonstrated that all the three guidance laws have effective performances and outperform the traditional terminal guidance laws.展开更多
Using Finite-Time Lyapunov Exponents (FTLE) method, Lagrangian coherent structures (LCSs) in a fully developed flat-plate turbulent boundary layer are successfully identified from a two-dimensional (2D) velocity field...Using Finite-Time Lyapunov Exponents (FTLE) method, Lagrangian coherent structures (LCSs) in a fully developed flat-plate turbulent boundary layer are successfully identified from a two-dimensional (2D) velocity field obtained by time-resolved 2D PIV measurement. The typical LCSs in the turbulent boundary layer are hairpin-like structures, which are characterized as legs of quasi-streamwise vor- tices extending deep into the near wall region with an inclination angle θ to the wall, and heads of the transverse vortex tube located in the outer region. Statistical analysis on the characteristic shape of typical LCS reveals that the probability density distribution of θ accords well with t-distribution in the near wall region, but presents a bimodal distribution with two peaks in the outer region, corresponding to the hairpin head and the hairpin neck, respectively. Spatial correlation analysis of FTLE field is im- plemented to get the ensemble-averaged inclination angle θ R of typical LCS. θ R first increases and then decreases along the wall-normal direction, similar to that of the mean value of θ. Moreover, the most probable value of θ saturates at y+=100 with the maximum value of about 24°, suggesting that the most likely position where hairpins transit from the neck to the head is located around y+=100. The ensem- ble-averaged convection velocity Uc of typical LCS is finally calculated from temporal-spatial correla- tion analysis of FTLE field. It is found that the wall-normal profile of the convection velocity Uc(y) ac- cords well with the local mean velocity profile U(y) beyond the buffer layer, evidencing that the down- stream convection of hairpins determines the transportation properties of the turbulent boundary layer in the log-region and beyond.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.11305266&51576207)the National Basic Research Program of China("973"Project)(Grant No.2012CB720405)
文摘Thermoelectric effect is the most efficient way to convert electric energy directly from the temperature gradient. Thermoelectric effect-based power generation, cooling and heating devices are solid-stated, environmentally friendly, reliable, long-lived, easily maintainable, and easy to achieve miniaturization and integration. So they have unparalleled advantages in the aerospace, vehicle industry, waste heat recovery, electronic cooling, etc. This paper reviews the progress in thermodynamic analyses and optimizations for single- and multiple-element, single- and multiple-stage, and combined thermoelectric generators, thermoelectric refrigerators and thermoelectric heat pumps, especially in the aspects of non-equilibrium thermodynamics and finite time thermodynamics. It also discusses the developing trends of thermoelectric devices, such as the heat sources of thermoelectric generators, multi-stage thermoelectric devices, combined thermoelectric devices, and heat transfer enhancement of thermoelectric devices.
基金supported by the National Natural Science Foundation China(Grant Nos.51176203 and 10905093)
文摘The mass entransy and its dissipation extremum principle have opened up a new direction for the mass transfer optimization. Firstly, the emergence and development process of both the mass entransy and its dissipalion extremum principle are reviewed. Secondly, the combination of the mass entransy dissipation extremum principle and the finite-time thermodynamics for opti- mizing the mass transfer processes of one-way isothermal mass transfer, two-way isothermal equimolar mass transfer, and iso- thermal throttling and isothermal crystallization are summarized. Thirdly, the combination of the mass entransy dissipation ex- tremum principle and the constructal theory for optimizing the mass transfer processes of disc-to-point and volume-to-point problems are summarized. The scientific features of the mass entransy dissipation extremam principle are emphasized.
基金financial support provided by the National Natural Science Foundation of China(Nos.61174037 and 61021002)the Aeronautical Science Foundation of China(No.20140177002)
文摘For the terminal guidance problem of missiles intercepting maneuvering targets in the three-dimensional space, the design of guidance laws for non-decoupling three-dimensional engage- ment geometry is studied. Firstly, by introducing a finite time integral sliding mode manifold, a novel guidance law based on the integral sliding mode control is presented with the target acceler- ation as a known bounded external disturbance. Then, an improved adaptive guidance law based on the integral sliding mode control without the information of the upper bound on the target accel- eration is developed, where the upper bound of the target acceleration is estimated online by a designed adaptive law. The both presented guidance laws can make sure that the elevation angular rate of the line-of-sight and the azimuth angular rate of the line-of-sight converge to zero in finite time. In the end, the results of the guidance performance for the proposed guidance laws are pre- sented by numerical simulations. Although the designed guidance laws are developed for the con- stant speed missiles, the simulation results for the time-varying speed missiles are also shown to further confirm the designed guidance laws.
基金supported by National Natural Science Foundation of China (No.60504007)the PhD Programs Foundation of Ministry of Educationof China (No.20070286040)the Scientific Research Foundation of Graduate School of Southeast University
文摘In this paper, using finite-time control method, we consider the disturbance analysis of a second-order system with unknown but bounded disturbance. We show that the states of the second-order system will be stabilized to a region containing the origin. The radius of this region is determined by the control parameters and can be rendered as small as desired. The rigorous stability analysis is also given. Compared with the conventional PD control law, the finite-time control law yields a better disturbance rejection performance. Numerical simulation results show the effectiveness of the method.
文摘By using finite-time thermodynamics, the optimal performance of a Stirling heat engine with thermal resistance, heat leak and regenerative loss is studied. The fundamental optimal relation is derived and the bounds of power output and efficiency are deduced from it. Then the significance of the relation and bounds are revealed. The results obtained here may provide some new theoretical guides for the optimal design of Stirling heat engines.
文摘以往使用的求取地震波初至时间的射线追踪法具有不同程度的缺陷,因而在实际应用中存在一定的局限性。本文提出一种将局部算法与扫描算法相结合的、用有限差分解程函方程求取地震波初至时间的方法。方法中考虑了散射波、首波及透射波的存在,因而可以适用于较复杂的速度模型。在求出初至时间后,利用互易性原理,能准确地得到射线路径。理论模型的试算表明,该方法计算精度较高,适宜地震偏移、层析成像以及 Green 函数的计算。
基金supported by the National Natural Science Foundation of China(Nos.61603114,61673135)
文摘In order to simultaneously attack a target with impact angle constraint in threedimensional(3-D) space, a novel distributed cooperative guidance law for multiple missiles under directed communication topologies is proposed without radial velocity measurements. First, based on missiles-target 3-D relative motion equations, the multiple missiles cooperative guidance model with impact angle constraint is constructed. Then, in Line-of-Sight(LOS) direction, based on multiagent system cooperative control theory, one guidance law with directed topologies is designed with strict proof, which can guarantee finite time consensus of multiple missiles' impact times. Next, in elevation direction and azimuth direction of LOS, based on homogeneous system stability theory and integral sliding mode control theory, two guidance laws are proposed respectively with strict proof, which can guarantee LOS angles converge to desired values and LOS angular rates converge to zero in finite time. Finally, the effectiveness of the designed cooperative guidance law is demonstrated through simulation results.
基金supported by the National Natural Science Foundation of China(No.11532002)
文摘An integrated cooperative guidance framework for multi-missile cooperatively attacking a single stationary target is proposed in this paper by combining both the centralized and decentralized communication topologies. Once missiles are distributed into several groups, missiles within a single group communicate with the centralized leader-follower framework, while the leaders from different groups communicate using the nearest-neighbor topology. To implement the integrated cooperative guidance framework, a group of Finite-Time Cooperative Guidance（FTCG） laws considering the saturation constraint on FOV（FTCG-FOV） are firstly derived within the centralized leader-follower framework to satisfy the communication topology of missiles in a single group.Then, an improved sequential approach is developed to adapt the FTCG-FOV to satisfy the communication topology between groups. The numerical simulations demonstrate the effectiveness and high efficiency of the integrated cooperative guidance framework and the cooperative guidance laws, as well as the superiority of the developed sequential approach.
基金co-supported by the National Basic Research Program of China(No.2012CB720000)the National Natural Science Foundation of China(No.61104153)the Research Fund for the Doctoral Program of Higher Education of China(No.20091101110025)
文摘This paper proposes a finite-time robust flight controller, targeting for a reentry vehicle with blended aerodynamic surfaces and a reaction control system（RCS）. Firstly, a novel finite-time attitude controller is pointed out with the introduction of a nonsingular finite-time sliding mode manifold. The attitude tracking errors are mathematically proved to converge to zero within finite time which can be estimated. In order to improve the performance, a second-order finite-time sliding mode controller is further developed to effectively alleviate chattering without any deterioration of robustness and accuracy. Moreover, an optimization control allocation algorithm, using linear programming and a pulse-width pulse-frequency（PWPF） modulator, is designed to allocate torque commands for all the aerodynamic surface deflections and on–off switching-states of RCS thrusters.Simulations are provided for the reentry vehicle considering uncertain parameters and external disturbances for practical purposes, and the results demonstrate the effectiveness and robustness of the attitude control system.
基金the financial support provided by the National Natural Science Foundation of China (No. 61174037)the National Basic Research Program of China (973) (No. 2012CB821205, CAST20120602)the National High Technology Research and Development Program of China (863) (No. 2012AA120602)
文摘This paper investigates two finite-time controllers for attitude control of spacecraft based on rotation matrix by an adaptive backstepping method. Rotation matrix can overcome the draw- backs of unwinding which makes a spacecraft perform a large-angle maneuver when a small-angle maneuver in the opposite rotational direction is sufficient to achieve the objective, With the use of adaptive control, the first robust finite-time controller is continuous without a chattering phenom- enon. The second robust finite-time controller can compensate external disturbances with unknown bounds. Theoretical analysis shows that both controllers can make a spacecraft following a time-varying reference attitude signal in finite time and guarantee the stability of the overall closed-loop system. Numerical simulations are presented to demonstrate the effectiveness of the proposed control schemes.
基金supported by the National Key Scientific Instrument and Equipment Development Project(No.2011YQ03013307)the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education InstitutionsKey Laboratory of Coal Resources Exploration and Comprehensive Utilization,Ministry of Land and Resources
文摘The full-space transient electromagnetic response of water-filled goaves in coal mines were numerically modeled. Traditional numerical modeling methods cannot be used to simulate the underground full-space transient electromagnetic field. We used multiple transmitting loops instead of the traditional single transmitting loop to load the transmitting loop into Cartesian grids. We improved the method for calculating the z-component of the magnetic field based on the characteristics of full space. Then, we established the full- space 3D geoelectrical model using geological data for coalmines. In addition, the transient electromagnetic responses of water-filled goaves of variable shape at different locations were simulated by using the finite-difference time-domain （FDTD） method. Moreover, we evaluated the apparent resistivity results. The numerical modeling results suggested that the resistivity differences between the coal seam and its roof and floor greatly affect the distribution of apparent resistivity, resulting in nearly circular contours with the roadway head at the center. The actual distribution of apparent resistivity for different geoelectrical models of water in goaves was consistent with the models. However, when the goal water was located in one side, a false low-resistivity anomaly would appear on the other side owing to the full-space effect but the response was much weaker. Finally, the modeling results were subsequently confirmed by drilling, suggesting that the proposed method was effective.
文摘Security monitoring system of coal mines is indispensable to ensure the safe and efficient production of colliery. Due to the special and narrow underground field of the coal mine, the electromagnetic interference can cause a series of misstatements and false positives on the monitoring system, which will severely hamper the safe production of coal industry. In this paper, first, the frequency characteristics of the interference source on the power line are extracted when equipment runs normally. Then the finite difference time domain method is introduced to analyze the effects of the electromagnetic interference parameters on the security monitoring signal line. And the interference voltage of the two terminal sides on the single line is taken as evaluating indexes. Finally, the electromagnetic interference parameters are optimized by orthogonal experimental design based on the MATLAB simulation on the normal operation of equipment.
基金co-supported by the National Natural Science Foundation of China (No. 61333003)the China Aerospace Science and Technology Innovation Foundation (No. JZ20160008)
文摘To intercept maneuvering targets at desired impact angles, a three-dimensional terminal guidance problem is investigated in this study. Because of a short terminal guidance time, a finitetime impact angle control guidance law is developed using the fast nonsingular terminal sliding mode control theory. However, the guidance law requires the upper bound of lumped uncertainty including target acceleration, which may not be accurately obtained. Therefore, by adopting a novel reaching law, an adaptive sliding mode guidance law is provided to release the drawback. At the same time, this method can accelerate the convergence rate and weaken the chattering phenomenon to a certain extent. In addition, another novel adaptive guidance law is also derived; this ensures systems asymptotic and finite-time stability without the knowledge of perturbations bounds.Numerical simulations have demonstrated that all the three guidance laws have effective performances and outperform the traditional terminal guidance laws.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 10425207 and 10832001)
文摘Using Finite-Time Lyapunov Exponents (FTLE) method, Lagrangian coherent structures (LCSs) in a fully developed flat-plate turbulent boundary layer are successfully identified from a two-dimensional (2D) velocity field obtained by time-resolved 2D PIV measurement. The typical LCSs in the turbulent boundary layer are hairpin-like structures, which are characterized as legs of quasi-streamwise vor- tices extending deep into the near wall region with an inclination angle θ to the wall, and heads of the transverse vortex tube located in the outer region. Statistical analysis on the characteristic shape of typical LCS reveals that the probability density distribution of θ accords well with t-distribution in the near wall region, but presents a bimodal distribution with two peaks in the outer region, corresponding to the hairpin head and the hairpin neck, respectively. Spatial correlation analysis of FTLE field is im- plemented to get the ensemble-averaged inclination angle θ R of typical LCS. θ R first increases and then decreases along the wall-normal direction, similar to that of the mean value of θ. Moreover, the most probable value of θ saturates at y+=100 with the maximum value of about 24°, suggesting that the most likely position where hairpins transit from the neck to the head is located around y+=100. The ensem- ble-averaged convection velocity Uc of typical LCS is finally calculated from temporal-spatial correla- tion analysis of FTLE field. It is found that the wall-normal profile of the convection velocity Uc(y) ac- cords well with the local mean velocity profile U(y) beyond the buffer layer, evidencing that the down- stream convection of hairpins determines the transportation properties of the turbulent boundary layer in the log-region and beyond.
