Transactions of Nanjing University of Aeronautics & Astronautics
Volume 38,Issue 2,2021 Table of Contents
2021, 38(2):193-205.
DOI: 10.16356/j.1005-1120.2021.02.001
Abstract:
A robust anti-swing control method based on the error transformation function is proposed， and the problem is handled for the unmanned helicopter slung-load system （HSLS） deviating from the equilibrium state due to the disturbances in the lifting process. First， the nonlinear model of unmanned HSLS is established. Second， the errors of swing angles are constructed by using the two ideal swing angle values and the actual swing angle values for the unmanned HSLS under flat flight， and the error transformation functions are investigated to guarantee that the errors of swing angles satisfy the prescribed performance. Third， the nonlinear disturbance observers are introduced to estimate the bounded disturbances， and the robust controllers of the unmanned HSLS， the velocity and the attitude subsystems are designed based on the prescribed performance method， the output of disturbance observer and the sliding mode backstepping strategy， respectively. Fourth， the Lyapunov function is developed to prove the stability of the closed-loop system. Finally， the simulation studies are shown to demonstrate the effectiveness of the control strategy.
A robust anti-swing control method based on the error transformation function is proposed， and the problem is handled for the unmanned helicopter slung-load system （HSLS） deviating from the equilibrium state due to the disturbances in the lifting process. First， the nonlinear model of unmanned HSLS is established. Second， the errors of swing angles are constructed by using the two ideal swing angle values and the actual swing angle values for the unmanned HSLS under flat flight， and the error transformation functions are investigated to guarantee that the errors of swing angles satisfy the prescribed performance. Third， the nonlinear disturbance observers are introduced to estimate the bounded disturbances， and the robust controllers of the unmanned HSLS， the velocity and the attitude subsystems are designed based on the prescribed performance method， the output of disturbance observer and the sliding mode backstepping strategy， respectively. Fourth， the Lyapunov function is developed to prove the stability of the closed-loop system. Finally， the simulation studies are shown to demonstrate the effectiveness of the control strategy.
2021, 38(2):206-215.
DOI: 10.16356/j.1005-1120.2021.02.002
Abstract:
The flapping-wing air vehicle （FWAV） is a kind of bio-inspired robot whose wings can flap up and down like bird and insect wings. A vision-based obstacle avoidance method for FWAVs is proposed in this paper. First， the Farneback algorithm is used to calculate the optical flow field of the first-view video frames taken by the on-board image transmission camera. Based on the optical flow information， a fuzzy obstacle avoidance controller is then designed to generate the FWAV steering commands. Experimental results show that the proposed obstacle avoidance method can accurately identify obstacles and achieve obstacle avoidance for FWAVs.
The flapping-wing air vehicle （FWAV） is a kind of bio-inspired robot whose wings can flap up and down like bird and insect wings. A vision-based obstacle avoidance method for FWAVs is proposed in this paper. First， the Farneback algorithm is used to calculate the optical flow field of the first-view video frames taken by the on-board image transmission camera. Based on the optical flow information， a fuzzy obstacle avoidance controller is then designed to generate the FWAV steering commands. Experimental results show that the proposed obstacle avoidance method can accurately identify obstacles and achieve obstacle avoidance for FWAVs.
2021, 38(2):216-224.
DOI: 10.16356/j.1005-1120.2021.02.003
Abstract:
Autonomous aerial refueling （AAR） has demonstrated significant benefits to aviation by extending the aircraft range and endurance. It is of significance to assess system safety for autonomous aerial refueling. In this paper， the reachability analysis method is adopted to assess system safety. Due to system uncertainties， the aerial refueling system can be considered as a stochastic system. Thus， probabilistic reachability is considered. Since there is a close relationship between reachability probability and collision probability， the collision probability of the AAR system is analyzed by using reachability analysis techniques. Then， the collision probability is accessed by using the Monte-Carlo experiment method. Finally， simulations demonstrate the effectiveness of the proposed safety assessment method.
Autonomous aerial refueling （AAR） has demonstrated significant benefits to aviation by extending the aircraft range and endurance. It is of significance to assess system safety for autonomous aerial refueling. In this paper， the reachability analysis method is adopted to assess system safety. Due to system uncertainties， the aerial refueling system can be considered as a stochastic system. Thus， probabilistic reachability is considered. Since there is a close relationship between reachability probability and collision probability， the collision probability of the AAR system is analyzed by using reachability analysis techniques. Then， the collision probability is accessed by using the Monte-Carlo experiment method. Finally， simulations demonstrate the effectiveness of the proposed safety assessment method.
2021, 38(2):225-236.
DOI: 10.16356/j.1005-1120.2021.02.004
Abstract:
Single gimbal control moment gyroscope （SGCMG） with high precision and fast response is an important attitude control system for high precision docking， rapid maneuvering navigation and guidance system in the aerospace field. In this paper， considering the influence of multi-source disturbance， a data-based feedback relearning （FR） algorithm is designed for the robust control of SGCMG gimbal servo system. Based on adaptive dynamic programming and least-square principle， the FR algorithm is used to obtain the servo control strategy by collecting the online operation data of SGCMG system. This is a model-free learning strategy in which no prior knowledge of the SGCMG model is required. Then， combining the reinforcement learning mechanism， the servo control strategy is interacted with system dynamic of SGCMG. The adaptive evaluation and improvement of servo control strategy against the multi-source disturbance are realized. Meanwhile， a data redistribution method based on experience replay is designed to reduce data correlation to improve algorithm stability and data utilization efficiency. Finally， by comparing with other methods on the simulation model of SGCMG， the effectiveness of the proposed servo control strategy is verified.
Single gimbal control moment gyroscope （SGCMG） with high precision and fast response is an important attitude control system for high precision docking， rapid maneuvering navigation and guidance system in the aerospace field. In this paper， considering the influence of multi-source disturbance， a data-based feedback relearning （FR） algorithm is designed for the robust control of SGCMG gimbal servo system. Based on adaptive dynamic programming and least-square principle， the FR algorithm is used to obtain the servo control strategy by collecting the online operation data of SGCMG system. This is a model-free learning strategy in which no prior knowledge of the SGCMG model is required. Then， combining the reinforcement learning mechanism， the servo control strategy is interacted with system dynamic of SGCMG. The adaptive evaluation and improvement of servo control strategy against the multi-source disturbance are realized. Meanwhile， a data redistribution method based on experience replay is designed to reduce data correlation to improve algorithm stability and data utilization efficiency. Finally， by comparing with other methods on the simulation model of SGCMG， the effectiveness of the proposed servo control strategy is verified.
2021, 38(2):237-248.
DOI: 10.16356/j.1005-1120.2021.02.005
Abstract:
This paper investigates the optimal control problem of spacecraft reorientation subject to attitude forbidden constraints， angular velocity saturation and actuator saturation simultaneously. A second-order cone programming （SOCP） technology is developed to solve the strong nonlinear and non-convex control problem in real time. Specifically， the nonlinear attitude kinematic and dynamic are transformed and relaxed to a standard affine system， and linearization and L1 penalty technique are adopted to convexify non-convex inequality constraints. With the proposed quadratic performance index of angular velocity， the optimal control solution is obtained with high accuracy using the successive SOCP algorithm. Finally， the effectiveness of the algorithm is validated by numerical simulation.
This paper investigates the optimal control problem of spacecraft reorientation subject to attitude forbidden constraints， angular velocity saturation and actuator saturation simultaneously. A second-order cone programming （SOCP） technology is developed to solve the strong nonlinear and non-convex control problem in real time. Specifically， the nonlinear attitude kinematic and dynamic are transformed and relaxed to a standard affine system， and linearization and L1 penalty technique are adopted to convexify non-convex inequality constraints. With the proposed quadratic performance index of angular velocity， the optimal control solution is obtained with high accuracy using the successive SOCP algorithm. Finally， the effectiveness of the algorithm is validated by numerical simulation.
2021, 38(2):249-258.
DOI: 10.16356/j.1005-1120.2021.02.006
Abstract:
An adaptive backstepping multi-sliding mode approximation variable structure control scheme is proposed for a class of uncertain nonlinear systems. An actuator model with compound nonlinear characteristics is established based on the model decomposition method. The unmodeled dynamic term of the radial basis function neural network approximation system is presented. The Nussbaum gain design technique is utilized to overcome the problem that the control gain is unknown. The adaptive law estimation is used to estimate the upper boundary of neural network approximation and uncertain interference. The adaptive approximate variable structure control effectively weakens the control signal chattering while enhancing the robustness of the controller.Based on the Lyapunov stability theory， the stability of the entire control system is proved. The main advantage of the designed controller is that the compound nonlinear characteristics are considered and solved. Finally， simulation results are given to show the validity of the control scheme.
An adaptive backstepping multi-sliding mode approximation variable structure control scheme is proposed for a class of uncertain nonlinear systems. An actuator model with compound nonlinear characteristics is established based on the model decomposition method. The unmodeled dynamic term of the radial basis function neural network approximation system is presented. The Nussbaum gain design technique is utilized to overcome the problem that the control gain is unknown. The adaptive law estimation is used to estimate the upper boundary of neural network approximation and uncertain interference. The adaptive approximate variable structure control effectively weakens the control signal chattering while enhancing the robustness of the controller.Based on the Lyapunov stability theory， the stability of the entire control system is proved. The main advantage of the designed controller is that the compound nonlinear characteristics are considered and solved. Finally， simulation results are given to show the validity of the control scheme.
2021, 38(2):259-270.
DOI: 10.16356/j.1005-1120.2021.02.007
Abstract:
A robust control strategy using the second-order integral sliding mode control （SOISMC） based on the variable speed grey wolf optimization （VGWO） is proposed. The aim is to maximize the wind power extraction of wind turbine. Firstly， according to the uncertainty model of wind turbine， a SOISMC torque controller with fast convergence speed， strong robustness and effective chattering reduction is designed， which ensures that the torque controller can effectively track the reference speed. Secondly， given the strong local search ability of the grey wolf optimization （GWO） and the fast convergence speed and strong global search ability of the particle swarm optimization （PSO）， the speed component of PSO is introduced into GWO， and VGWO with fast convergence speed， high solution accuracy and strong global search ability is used to optimize the parameters of wind turbine torque controller. Finally， the simulation is implemented based on Simulink/SimPowerSystem. The results demonstrate the effectiveness of the proposed strategy under both external disturbance and model uncertainty.
A robust control strategy using the second-order integral sliding mode control （SOISMC） based on the variable speed grey wolf optimization （VGWO） is proposed. The aim is to maximize the wind power extraction of wind turbine. Firstly， according to the uncertainty model of wind turbine， a SOISMC torque controller with fast convergence speed， strong robustness and effective chattering reduction is designed， which ensures that the torque controller can effectively track the reference speed. Secondly， given the strong local search ability of the grey wolf optimization （GWO） and the fast convergence speed and strong global search ability of the particle swarm optimization （PSO）， the speed component of PSO is introduced into GWO， and VGWO with fast convergence speed， high solution accuracy and strong global search ability is used to optimize the parameters of wind turbine torque controller. Finally， the simulation is implemented based on Simulink/SimPowerSystem. The results demonstrate the effectiveness of the proposed strategy under both external disturbance and model uncertainty.
2021, 38(2):271-287.
DOI: 10.16356/j.1005-1120.2021.02.008
Abstract:
The determination of the dynamic load is one of the indispensable technologies for structure design and health monitoring for aerospace vehicles. However， it is a significant challenge to measure the external excitation directly. By contrast， the technique of dynamic load identification based on the dynamic model and the response information is a feasible access to obtain the dynamic load indirectly. Furthermore， there are multi-source uncertainties which cannot be neglected for complex systems in the load identification process， especially for aerospace vehicles. In this paper， recent developments in the dynamic load identification field for aerospace vehicles considering multi-source uncertainties are reviewed， including the deterministic dynamic load identification and uncertain dynamic load identification. The inversion methods with different principles of concentrated and distributed loads， and the quantification and propagation analysis for multi-source uncertainties are discussed. Eventually， several possibilities remaining to be explored are illustrated in brief.
The determination of the dynamic load is one of the indispensable technologies for structure design and health monitoring for aerospace vehicles. However， it is a significant challenge to measure the external excitation directly. By contrast， the technique of dynamic load identification based on the dynamic model and the response information is a feasible access to obtain the dynamic load indirectly. Furthermore， there are multi-source uncertainties which cannot be neglected for complex systems in the load identification process， especially for aerospace vehicles. In this paper， recent developments in the dynamic load identification field for aerospace vehicles considering multi-source uncertainties are reviewed， including the deterministic dynamic load identification and uncertain dynamic load identification. The inversion methods with different principles of concentrated and distributed loads， and the quantification and propagation analysis for multi-source uncertainties are discussed. Eventually， several possibilities remaining to be explored are illustrated in brief.
2021, 38(2):288-297.
DOI: 10.16356/j.1005-1120.2021.02.009
Abstract:
To ensure flight safety， the complex network method is used to study the influence and invulnerability of air traffic cyber physical system （CPS） nodes. According to the rules of air traffic management， the logical coupling relationship between routes and sectors is analyzed， an air traffic CPS network model is constructed， and the indicators of node influence and invulnerability are established. The K-shell algorithm is improved to identify node influence， and the invulnerability is analyzed under random and selective attacks. Taking Airspace in Eastern China as an example， its influential nodes are sorted by degree， namely， K-shell， the improved K-shell （IKS） and betweenness centrality. The invulnerability of air traffic CPS under different attacks is analyzed. Results show that IKS can effectively identify the influential nodes in the air traffic CPS network， and IKS and betweenness centrality are the two key indicators that affect the invulnerability of air traffic CPS.
To ensure flight safety， the complex network method is used to study the influence and invulnerability of air traffic cyber physical system （CPS） nodes. According to the rules of air traffic management， the logical coupling relationship between routes and sectors is analyzed， an air traffic CPS network model is constructed， and the indicators of node influence and invulnerability are established. The K-shell algorithm is improved to identify node influence， and the invulnerability is analyzed under random and selective attacks. Taking Airspace in Eastern China as an example， its influential nodes are sorted by degree， namely， K-shell， the improved K-shell （IKS） and betweenness centrality. The invulnerability of air traffic CPS under different attacks is analyzed. Results show that IKS can effectively identify the influential nodes in the air traffic CPS network， and IKS and betweenness centrality are the two key indicators that affect the invulnerability of air traffic CPS.
2021, 38(2):298-305.
DOI: 10.16356/j.1005-1120.2021.02.010
Abstract:
With the rapid growth of the number and flight time of unmanned aerial vehicles （UAVs）， safety accidents caused by UAVs flight risk is increasing gradually. Safe air route planning is an effective means to reduce the operational risk of UAVs at the strategic level. The optimal air route planning model based on ground risk assessment is presented by considering the safety cost of UAV air route. Through the rasterization of the ground surface under the air route， the safety factor of each grid is defined with the probability of fatality on the ground per flight hour as the quantitative index. The air route safety cost function is constructed based on the safety factor of each grid. Then， the total cost function considering both air route safety and flight distance is established. The expected function of the ant colony algorithm is rebuilt and used as the algorithm to plan the air routes. The effectiveness of the new air route planning model is verified through the logistical distribution scenario on urban airspace. The results indicate that the new air route planning model considering safety factor can greatly improve the overall safety of air route under small increase of the total flight time.
With the rapid growth of the number and flight time of unmanned aerial vehicles （UAVs）， safety accidents caused by UAVs flight risk is increasing gradually. Safe air route planning is an effective means to reduce the operational risk of UAVs at the strategic level. The optimal air route planning model based on ground risk assessment is presented by considering the safety cost of UAV air route. Through the rasterization of the ground surface under the air route， the safety factor of each grid is defined with the probability of fatality on the ground per flight hour as the quantitative index. The air route safety cost function is constructed based on the safety factor of each grid. Then， the total cost function considering both air route safety and flight distance is established. The expected function of the ant colony algorithm is rebuilt and used as the algorithm to plan the air routes. The effectiveness of the new air route planning model is verified through the logistical distribution scenario on urban airspace. The results indicate that the new air route planning model considering safety factor can greatly improve the overall safety of air route under small increase of the total flight time.
2021, 38(2):306-315.
DOI: 10.16356/j.1005-1120.2021.02.011
Abstract:
A method for formation flight trajectory optimization was established. This method aims at minimizing fuel consumption of a two-aircraft formation flight， without changing the original trajectory of the leader. Candidate flight pairs were selected from all international flights arriving at or departing from China in one day according to the requirement of the proposed method. Aircraft performance database Base of Aircraft Data （BADA）was employed in the trajectory computation. By assuming different fuel-saving percentages for the following aircraft， pre-flight plan trajectories of formation flight were optimized. The fuel consumption optimization effect under the influence of different trajectory optimization parameters was also analyzed. The results showed that the higher the fuel savings percentage， the longer the flight distance of formation flight， but the smaller the number of formation combinations that can be realized， which is limited by the aircraft performance. The following aircraft flying along the approximate actual flight trajectory can be benefited as well， and the optimal fuel-saving efficiency is related to the expected fuel-saving efficiency of formation flight.
A method for formation flight trajectory optimization was established. This method aims at minimizing fuel consumption of a two-aircraft formation flight， without changing the original trajectory of the leader. Candidate flight pairs were selected from all international flights arriving at or departing from China in one day according to the requirement of the proposed method. Aircraft performance database Base of Aircraft Data （BADA）was employed in the trajectory computation. By assuming different fuel-saving percentages for the following aircraft， pre-flight plan trajectories of formation flight were optimized. The fuel consumption optimization effect under the influence of different trajectory optimization parameters was also analyzed. The results showed that the higher the fuel savings percentage， the longer the flight distance of formation flight， but the smaller the number of formation combinations that can be realized， which is limited by the aircraft performance. The following aircraft flying along the approximate actual flight trajectory can be benefited as well， and the optimal fuel-saving efficiency is related to the expected fuel-saving efficiency of formation flight.
2021, 38(2):316-324.
DOI: 10.16356/j.1005-1120.2021.02.012
Abstract:
The prediction process often runs with small samples and under-sufficient information. To target this problem， we propose a performance comparison study that combines prediction and optimization algorithms based on experimental data analysis. Through a large number of prediction and optimization experiments， the accuracy and stability of the prediction method and the correction ability of the optimization method are studied. First， five traditional single-item prediction methods are used to process small samples with under-sufficient information， and the standard deviation method is used to assign weights on the five methods for combined forecasting. The accuracy of the prediction results is ranked. The mean and variance of the rankings reflect the accuracy and stability of the prediction method. Second， the error elimination prediction optimization method is proposed. To make， the prediction results are corrected by error elimination optimization method （EEOM）， Markov optimization and two-layer optimization separately to obtain more accurate prediction results. The degree improvement and decline are used to reflect the correction ability of the optimization method. The results show that the accuracy and stability of combined prediction are the best in the prediction methods， and the correction ability of error elimination optimization is the best in the optimization methods. The combination of the two methods can well solve the problem of prediction with small samples and under-sufficient information. Finally， the accuracy of the combination of the combined prediction and the error elimination optimization is verified by predicting the number of unsafe events in civil aviation in a certain year.
The prediction process often runs with small samples and under-sufficient information. To target this problem， we propose a performance comparison study that combines prediction and optimization algorithms based on experimental data analysis. Through a large number of prediction and optimization experiments， the accuracy and stability of the prediction method and the correction ability of the optimization method are studied. First， five traditional single-item prediction methods are used to process small samples with under-sufficient information， and the standard deviation method is used to assign weights on the five methods for combined forecasting. The accuracy of the prediction results is ranked. The mean and variance of the rankings reflect the accuracy and stability of the prediction method. Second， the error elimination prediction optimization method is proposed. To make， the prediction results are corrected by error elimination optimization method （EEOM）， Markov optimization and two-layer optimization separately to obtain more accurate prediction results. The degree improvement and decline are used to reflect the correction ability of the optimization method. The results show that the accuracy and stability of combined prediction are the best in the prediction methods， and the correction ability of error elimination optimization is the best in the optimization methods. The combination of the two methods can well solve the problem of prediction with small samples and under-sufficient information. Finally， the accuracy of the combination of the combined prediction and the error elimination optimization is verified by predicting the number of unsafe events in civil aviation in a certain year.
2021, 38(2):325-332.
DOI: 10.16356/j.1005-1120.2021.02.013
Abstract:
Current health monitoring systems often do not concern about the needs of the elderly， leading to inaccurate health status monitoring and delayed treatment for emergency health conditions. Similarly， they do not consider the variable factors affecting each patient， resulting in discrepancies between the measured values and real health status. To solve the problems， we propose a new health monitoring system with physiological parameter measurement， correction， and feedback. The study collects clinical samples of the elderly to formulate regression equations and statistical models for analyzing the relationship between gender， age， measurement time， and physical signs. After multiple adjustments to measurements of physical signs， the correction algorithm compares the data with a standard value. The process significantly reduces the risk of misjudgment while matching users’health status more accurately. The application case of this paper proves the validity of the method for measuring and correcting heart rate results in the elderly and presents a specific correction procedure. Additionally， the correction algorithm provides a scientific basis for eliminating or modifying other influencing factors in future health monitoring studies.
Current health monitoring systems often do not concern about the needs of the elderly， leading to inaccurate health status monitoring and delayed treatment for emergency health conditions. Similarly， they do not consider the variable factors affecting each patient， resulting in discrepancies between the measured values and real health status. To solve the problems， we propose a new health monitoring system with physiological parameter measurement， correction， and feedback. The study collects clinical samples of the elderly to formulate regression equations and statistical models for analyzing the relationship between gender， age， measurement time， and physical signs. After multiple adjustments to measurements of physical signs， the correction algorithm compares the data with a standard value. The process significantly reduces the risk of misjudgment while matching users’health status more accurately. The application case of this paper proves the validity of the method for measuring and correcting heart rate results in the elderly and presents a specific correction procedure. Additionally， the correction algorithm provides a scientific basis for eliminating or modifying other influencing factors in future health monitoring studies.
2021, 38(2):333-343.
DOI: 10.16356/j.1005-1120.2021.02.014
Abstract:
The dynamic responses of suspension system of a vehicle travelling at varying speeds are generally non-stationary random processes， and the non-stationary random analysis has become an important and complex problem in vehicle ride dynamics in the past few years. This paper proposes a new concept， called dynamic frequency domain （DFD）， based on the fact that the human body holds different sensitivities to vibrations at different frequencies， and applies this concept to the dynamic assessment on non-stationary vehicles. The study mainly includes two parts， the first is the input numerical calculation of the front and the rear wheels， and the second is the dynamical response analysis of suspension system subjected to non-stationary random excitations. Precise time integration method is used to obtain the vertical acceleration of suspension barycenter and the pitching angular acceleration， both root mean square （RMS） values of which are illustrated in different accelerating cases. The results show that RMS values of non-stationary random excitations are functions of time and increase as the speed increases at the same time. The DFD of vertical acceleration is finally analyzed using time-frequency analysis technique， and the conclusion is obviously that the DFD has a trend to the low frequency region， which would be significant reference for active suspension design under complex driving conditions.
The dynamic responses of suspension system of a vehicle travelling at varying speeds are generally non-stationary random processes， and the non-stationary random analysis has become an important and complex problem in vehicle ride dynamics in the past few years. This paper proposes a new concept， called dynamic frequency domain （DFD）， based on the fact that the human body holds different sensitivities to vibrations at different frequencies， and applies this concept to the dynamic assessment on non-stationary vehicles. The study mainly includes two parts， the first is the input numerical calculation of the front and the rear wheels， and the second is the dynamical response analysis of suspension system subjected to non-stationary random excitations. Precise time integration method is used to obtain the vertical acceleration of suspension barycenter and the pitching angular acceleration， both root mean square （RMS） values of which are illustrated in different accelerating cases. The results show that RMS values of non-stationary random excitations are functions of time and increase as the speed increases at the same time. The DFD of vertical acceleration is finally analyzed using time-frequency analysis technique， and the conclusion is obviously that the DFD has a trend to the low frequency region， which would be significant reference for active suspension design under complex driving conditions.
2021, 38(2):344-352.
DOI: 10.16356/j.1005-1120.2021.02.015
Abstract:
The cascade model was tested using transient liquid crystal temperature measurement technology. The effects of main flow Reynolds number， blowing ratio and tip clearance height on the convective heat transfer coefficient of the turbine outer ring were studied. Two feature lines were marked on the turbine outer ring corresponding to the position of the blade. The conclusions are as follows： The tip clearance leakage flow has a great influence on the convective heat transfer coefficient of the turbine outer ring. When the clearance height and the blowing ratio are kept constant， gradually increasing the main flow Reynolds number will result in an increase in the convective heat transfer coefficient of the turbine outer ring. When the clearance height and the main flow Reynolds number are kept constant and the blowing ratio is gradually increased， the convective heat transfer coefficient of the turbine outer ring is almost constant. The heat transfer coefficient of the turbine outer ring surface is little affected by the blowing ratio； The clearance height has great influence on the heat transfer characteristics of the turbine outer ring. Under the typical working condition in this paper， when the tip clearance height ratio is 1.6%， the convective heat transfer coefficient of the outer surface of the turbine is the highest.
The cascade model was tested using transient liquid crystal temperature measurement technology. The effects of main flow Reynolds number， blowing ratio and tip clearance height on the convective heat transfer coefficient of the turbine outer ring were studied. Two feature lines were marked on the turbine outer ring corresponding to the position of the blade. The conclusions are as follows： The tip clearance leakage flow has a great influence on the convective heat transfer coefficient of the turbine outer ring. When the clearance height and the blowing ratio are kept constant， gradually increasing the main flow Reynolds number will result in an increase in the convective heat transfer coefficient of the turbine outer ring. When the clearance height and the main flow Reynolds number are kept constant and the blowing ratio is gradually increased， the convective heat transfer coefficient of the turbine outer ring is almost constant. The heat transfer coefficient of the turbine outer ring surface is little affected by the blowing ratio； The clearance height has great influence on the heat transfer characteristics of the turbine outer ring. Under the typical working condition in this paper， when the tip clearance height ratio is 1.6%， the convective heat transfer coefficient of the outer surface of the turbine is the highest.
2021, 38(2):353-360.
DOI: 10.16356/j.1005-1120.2021.02.016
Abstract:
Mei symmetry on time scales is investigated for Lagrangian system， Hamiltonian system， and Birkhoffian system. The main results are divided into three sections. In each section， the definition and the criterion of Mei symmetry are first presented. Then the conserved quantity deduced from Mei symmetry is obtained， and perturbation to Mei symmetry and adiabatic invariant are studied. Finally， an example is given to illustrate the methods and results in each section. The conserve quantity achieved here is a special case of adiabatic invariant. And the results obtained in this paper are more general because of the definition and property of time scale.
Mei symmetry on time scales is investigated for Lagrangian system， Hamiltonian system， and Birkhoffian system. The main results are divided into three sections. In each section， the definition and the criterion of Mei symmetry are first presented. Then the conserved quantity deduced from Mei symmetry is obtained， and perturbation to Mei symmetry and adiabatic invariant are studied. Finally， an example is given to illustrate the methods and results in each section. The conserve quantity achieved here is a special case of adiabatic invariant. And the results obtained in this paper are more general because of the definition and property of time scale.
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