Transactions of Nanjing University of Aeronautics & Astronautics
Volume 31,Issue 1,2014 Table of Contents
2014, 31(1):1-15.
Abstract:
A lattice Boltzmann flux solver (LBFS) is presented for simulation of fluid flows. Like the conventional computational fluid dynamics (CFD) solvers, the new solver also applies the finite volume method to discretize the governing differential equations, but the numerical flux at the cell interface is not evaluated by the smooth function approximation or Riemann solvers. Instead, it is evaluated from local solution of lattice Boltzmann equation (LBE) at cell interface. Two versions of LBFS are presented in this paper. One is to locally apply one dimensional compressible lattice Boltzmann (LB) model along the normal direction to the cell interface for simulation of compressible inviscid flows with shock waves. The other is to locally apply multi dimensional LB model at cell interface for simulation of incompressible viscous and inviscid flows. The present solver removes the drawbacks of conventional lattice Boltzmann method (LBM) such as limitation to uniform mesh, tie-up of mesh spacing and time interval, limitation to viscous flows. Numerical examples show that the present solver can be well applied to simulate fluid flows with non-uniform mesh and curved boundary.
A lattice Boltzmann flux solver (LBFS) is presented for simulation of fluid flows. Like the conventional computational fluid dynamics (CFD) solvers, the new solver also applies the finite volume method to discretize the governing differential equations, but the numerical flux at the cell interface is not evaluated by the smooth function approximation or Riemann solvers. Instead, it is evaluated from local solution of lattice Boltzmann equation (LBE) at cell interface. Two versions of LBFS are presented in this paper. One is to locally apply one dimensional compressible lattice Boltzmann (LB) model along the normal direction to the cell interface for simulation of compressible inviscid flows with shock waves. The other is to locally apply multi dimensional LB model at cell interface for simulation of incompressible viscous and inviscid flows. The present solver removes the drawbacks of conventional lattice Boltzmann method (LBM) such as limitation to uniform mesh, tie-up of mesh spacing and time interval, limitation to viscous flows. Numerical examples show that the present solver can be well applied to simulate fluid flows with non-uniform mesh and curved boundary.
2014, 31(1):16-25.
Abstract:
Experimental investigation is conducted to investigate the flow and heat transfer performances of jet impingement cooling inside a semi-confined smooth channel. Effects of jet Reynolds number (varied from 10 000 to 45 000), orifice-to-target spacing (zn=1d—4d) and jet-to-jet pitches (xn=3d—5d, yn=3d—5d) on the convective heat transfer coefficient and discharge coefficient are revealed. For a single-row jets normal impingement, the impingement heat transfer is enhanced with the increase of impingement Reynolds number or the decrease of spanwise jet-to-jet pitch. The highest local heat transfer is achieved when zn/d is 2. For the double-row jets normal impingement, the laterally-averaged Nusselt number distributions in the vicinity of the first row jets impinging stagnation do not fit well with the single-row case. The highest local heat transfer is obtained when zn/d is 1. A smaller jet-to-jet pitch generally results in a lower discharge coefficient. The discharge coefficient in the double-row case is decreased relative to the single-row case at the same impingement Reynolds number.
Experimental investigation is conducted to investigate the flow and heat transfer performances of jet impingement cooling inside a semi-confined smooth channel. Effects of jet Reynolds number (varied from 10 000 to 45 000), orifice-to-target spacing (zn=1d—4d) and jet-to-jet pitches (xn=3d—5d, yn=3d—5d) on the convective heat transfer coefficient and discharge coefficient are revealed. For a single-row jets normal impingement, the impingement heat transfer is enhanced with the increase of impingement Reynolds number or the decrease of spanwise jet-to-jet pitch. The highest local heat transfer is achieved when zn/d is 2. For the double-row jets normal impingement, the laterally-averaged Nusselt number distributions in the vicinity of the first row jets impinging stagnation do not fit well with the single-row case. The highest local heat transfer is obtained when zn/d is 1. A smaller jet-to-jet pitch generally results in a lower discharge coefficient. The discharge coefficient in the double-row case is decreased relative to the single-row case at the same impingement Reynolds number.
2014, 31(1):26-31.
Abstract:
Flapping characteristics of the self-excited flapping motion of submerged vertical turbulent jet in narrow channels are studied theoretically and experimentally. It is found that the water depth is a most important parameter to the critical jet exit velocity and the jet flapping frequency. The results indicate that the critical jet exit velocity increases with water depth and the jet flapping frequency is inversely proportional to the water depth. Meanwhile, experimental result also shows that the surface disturbance wave changes the frequency of flapping motion, i.e. the flapping frequency locks-in the disturbing frequency when the disturbing frequency is near and less than the natural flapping frequency.
Flapping characteristics of the self-excited flapping motion of submerged vertical turbulent jet in narrow channels are studied theoretically and experimentally. It is found that the water depth is a most important parameter to the critical jet exit velocity and the jet flapping frequency. The results indicate that the critical jet exit velocity increases with water depth and the jet flapping frequency is inversely proportional to the water depth. Meanwhile, experimental result also shows that the surface disturbance wave changes the frequency of flapping motion, i.e. the flapping frequency locks-in the disturbing frequency when the disturbing frequency is near and less than the natural flapping frequency.
2014, 31(1):32-38.
Abstract:
The critical lengths of an oscillator based on double-walled carbon nanotubes (DWCNTs) are studied by energy minimization and molecular dynamics simulation. Van der Waals (vdW) potential energy in DWCNTs is shown to be changed periodically with the lattice matching of the inner and outer tubes by using atomistic models with energy minimization method. If the coincidence length between the inner and outer tubes is long enough, the restoring force cannot drive the DWCNT to slide over the vdW potential barrier to assure the DWCNT acts as an oscillator. The critical coincidence lengths of the oscillators are predicted by a very simple equation and then confirmed with energy minimization method for both the zigzag/zigzag system and the armchair/armchair system. The critical length of the armchair/armchair system is much larger than that of the zigzag/zigzag system. The vdW potential energy fluctuation of the armchair/armchair system is weaker than that of the zigzag/zigzag system. So it is easier to slide over the barrier for the armchair/armchair system. The critical lengths of zigzag/zigzag DWCNT-based oscillator are found increasing along with temperature, by molecular dynamics simulations.
The critical lengths of an oscillator based on double-walled carbon nanotubes (DWCNTs) are studied by energy minimization and molecular dynamics simulation. Van der Waals (vdW) potential energy in DWCNTs is shown to be changed periodically with the lattice matching of the inner and outer tubes by using atomistic models with energy minimization method. If the coincidence length between the inner and outer tubes is long enough, the restoring force cannot drive the DWCNT to slide over the vdW potential barrier to assure the DWCNT acts as an oscillator. The critical coincidence lengths of the oscillators are predicted by a very simple equation and then confirmed with energy minimization method for both the zigzag/zigzag system and the armchair/armchair system. The critical length of the armchair/armchair system is much larger than that of the zigzag/zigzag system. The vdW potential energy fluctuation of the armchair/armchair system is weaker than that of the zigzag/zigzag system. So it is easier to slide over the barrier for the armchair/armchair system. The critical lengths of zigzag/zigzag DWCNT-based oscillator are found increasing along with temperature, by molecular dynamics simulations.
2014, 31(1):39-48.
Abstract:
A time-varying modal parameter identification method combined with Bayesian information criterion (BIC) and grey correlation analysis (GCA) is presented for a kind of thermo-elastic structures with sparse natural frequencies and subject to an unsteady temperature field. To demonstrate the method, the thermo-elastic structure to beidentified is taken as a simply-supported beam with an axially movable boundary and subject to both random excitation and an unsteady temperature field, and the dynamic outputs of the beam are first simulated as the measured data for the identification. Then, an improved time-varying autoregressive (TVAR) model is generated from the simulated input and output of the system. The time-varying coefficients of the TVAR model are expanded as a finite set of time basis functions that facilitate the time-varying coefficients to be time-invariant. According to the BIC for preliminarily determining the scope of the order number, the grey system theory is introduced to determine the order of TVAR and the dimension of the basis functions simultaneously via the absolute grey correlation degree (AGCD). Finally, the time-varying instantaneous frequencies of the system are estimated by using the recursive least squares method. The identified results are capable of tracking the slow time-varying natural frequencies with high accuracy no matter for noise-free or noisy estimation.
A time-varying modal parameter identification method combined with Bayesian information criterion (BIC) and grey correlation analysis (GCA) is presented for a kind of thermo-elastic structures with sparse natural frequencies and subject to an unsteady temperature field. To demonstrate the method, the thermo-elastic structure to beidentified is taken as a simply-supported beam with an axially movable boundary and subject to both random excitation and an unsteady temperature field, and the dynamic outputs of the beam are first simulated as the measured data for the identification. Then, an improved time-varying autoregressive (TVAR) model is generated from the simulated input and output of the system. The time-varying coefficients of the TVAR model are expanded as a finite set of time basis functions that facilitate the time-varying coefficients to be time-invariant. According to the BIC for preliminarily determining the scope of the order number, the grey system theory is introduced to determine the order of TVAR and the dimension of the basis functions simultaneously via the absolute grey correlation degree (AGCD). Finally, the time-varying instantaneous frequencies of the system are estimated by using the recursive least squares method. The identified results are capable of tracking the slow time-varying natural frequencies with high accuracy no matter for noise-free or noisy estimation.
2014, 31(1):49-55.
Abstract:
The primary resonance of a single-degree-of-freedom (SDOF) system subjected to aharmonic excitation is mitigated by the method of optimal time-delay feedback control. The stable regions of the time delays and feedback gains are obtained from the stable conditions of eigenvalue equation. Attenuation ratio is applied for evaluating the performance of the vibration control by taking a proportion of peak amplitude of primary resonance for the suspension system with or without controllers. Taking the attenuation ratio as the objective function and the stable regions of the time delays and feedback gains as constrains, the optimal feedback gains are determined by using minimum optimal method. Finally, simulation examples are also presented.
The primary resonance of a single-degree-of-freedom (SDOF) system subjected to aharmonic excitation is mitigated by the method of optimal time-delay feedback control. The stable regions of the time delays and feedback gains are obtained from the stable conditions of eigenvalue equation. Attenuation ratio is applied for evaluating the performance of the vibration control by taking a proportion of peak amplitude of primary resonance for the suspension system with or without controllers. Taking the attenuation ratio as the objective function and the stable regions of the time delays and feedback gains as constrains, the optimal feedback gains are determined by using minimum optimal method. Finally, simulation examples are also presented.
2014, 31(1):56-62.
Abstract:
A new approach to modifying the stiffness and mass matrices of finite element models is presented to improve the calculation precision. By measuring the mode frequencies and shapes of both of the original and the new structures with changed stiffness and mass, the stiffness and mass matrices of the finite element model can be updated through matrices calculation and solving algebra equations. Taking a multi-freedom model as an example, the relation between the number of the modes and the correction precision of stiffness and mass matrix elements is researched. The facility and precision of the method are totally confirmed especially when the modeling error is known limited to a definite local range. The feasibility of the approach is proven by an effective engineering application to the model updating of a wing piece used in flutter test.
A new approach to modifying the stiffness and mass matrices of finite element models is presented to improve the calculation precision. By measuring the mode frequencies and shapes of both of the original and the new structures with changed stiffness and mass, the stiffness and mass matrices of the finite element model can be updated through matrices calculation and solving algebra equations. Taking a multi-freedom model as an example, the relation between the number of the modes and the correction precision of stiffness and mass matrix elements is researched. The facility and precision of the method are totally confirmed especially when the modeling error is known limited to a definite local range. The feasibility of the approach is proven by an effective engineering application to the model updating of a wing piece used in flutter test.
2014, 31(1):63-69.
Abstract:
The dynamical and physical behavior of a complex system can be more accurately described by using the fractional model. With the successful use of fractional calculus in many areas of science and engineering, it is necessary to extend the classical theories and methods of analytical mechanics to the fractional dynamic system. Birkhoffian mechanics is a natural generalization of Hamiltonian mechanics, and its core is the Pfaff-Birkhoff principle and Birkhoff′s equations. The study on the Birkhoffian mechanics is an important developmental direction of modern analytical mechanics. Here, the fractional Pfaff-Birkhoff variational problem is presented and studied. The definitions of fractional derivatives, the formulae for integration by parts and some other preliminaries are firstly given. Secondly, the fractional Pfaff-Birkhoff principle and the fractional Birkhoff′s equations in terms of Riesz-Riemann-Liouville fractional derivatives and Riesz-Caputo fractional derivatives are presented respectively. Finally, an example is given to illustrate the application of the results.
The dynamical and physical behavior of a complex system can be more accurately described by using the fractional model. With the successful use of fractional calculus in many areas of science and engineering, it is necessary to extend the classical theories and methods of analytical mechanics to the fractional dynamic system. Birkhoffian mechanics is a natural generalization of Hamiltonian mechanics, and its core is the Pfaff-Birkhoff principle and Birkhoff′s equations. The study on the Birkhoffian mechanics is an important developmental direction of modern analytical mechanics. Here, the fractional Pfaff-Birkhoff variational problem is presented and studied. The definitions of fractional derivatives, the formulae for integration by parts and some other preliminaries are firstly given. Secondly, the fractional Pfaff-Birkhoff principle and the fractional Birkhoff′s equations in terms of Riesz-Riemann-Liouville fractional derivatives and Riesz-Caputo fractional derivatives are presented respectively. Finally, an example is given to illustrate the application of the results.
2014, 31(1):70-77.
Abstract:
In an active magnetic bearing (AMB) system, the catcher bearings (CBs) are indispensable to protect the rotor and stator in case the magnetic bearings fail or overload. A new CB structure composed of two ball bearings is introduced. Detailed simulation models containing contact model between rotor and inner race, double decker catcher bearing(DDCB) model as well as single-decker catcher bearing (SDCB) model are established using multi body dynamics simulation software MSC.ADAMS. Then, using those established models, the rotor orbits and the contact forces between rotor and inner race are simulated respectively after rotor drop on DDCBs and SDCBs. The simulation result shows that the rotor vibration range using DDCBs is significantly smaller than that using SDCBs; the maximum contact forces drop about 15%—27% compared with the contact forces using SDCBs. Finally, the test bench for the rotor drop experiments is built and the rotor drop experiments for different types of CBs are carried out. Labview data acquisition system is utilized to collect the displacement of rotor and the rotating frequencies of both inner race and intermediate races after rotor drop. The experimental results are comparatively analyzed, and the conclusion that DDCB can help to reduce vibration amplitude and collision force is obtained. The studies can provide certain theoretical and experimental references for the application of DDCBs in AMB system.
In an active magnetic bearing (AMB) system, the catcher bearings (CBs) are indispensable to protect the rotor and stator in case the magnetic bearings fail or overload. A new CB structure composed of two ball bearings is introduced. Detailed simulation models containing contact model between rotor and inner race, double decker catcher bearing(DDCB) model as well as single-decker catcher bearing (SDCB) model are established using multi body dynamics simulation software MSC.ADAMS. Then, using those established models, the rotor orbits and the contact forces between rotor and inner race are simulated respectively after rotor drop on DDCBs and SDCBs. The simulation result shows that the rotor vibration range using DDCBs is significantly smaller than that using SDCBs; the maximum contact forces drop about 15%—27% compared with the contact forces using SDCBs. Finally, the test bench for the rotor drop experiments is built and the rotor drop experiments for different types of CBs are carried out. Labview data acquisition system is utilized to collect the displacement of rotor and the rotating frequencies of both inner race and intermediate races after rotor drop. The experimental results are comparatively analyzed, and the conclusion that DDCB can help to reduce vibration amplitude and collision force is obtained. The studies can provide certain theoretical and experimental references for the application of DDCBs in AMB system.
2014, 31(1):78-84.
Abstract:
Drag reducing and increasing mechanism on riblet surface has been studied through computational fluid dynamics (CFD). Drag reduction is achieved through the optimization of riblet geometry which would affect flow structure inside riblet grooves. Force and flow structure on riblet surface are analyzed and compared with those of smooth surface based on thek-εturbulence model. Drag reducing and increasing mechanism is proved to be related to microvortexes induced inside riblets which lead to Reynolds shear stress reduction significantly and is considered to be the dominant factor resulting in wall friction reduction. Simulation results also show that the pressure drag generating from the deviation of static pressure on the front and rear ends of riblets occurs and grows exponentially with Mach number, which can cause drag increasing. Furthermore, near-wall vortical structures, Reynolds shear stress and static pressure on riblet surfaces are also analyzed in detail.
Drag reducing and increasing mechanism on riblet surface has been studied through computational fluid dynamics (CFD). Drag reduction is achieved through the optimization of riblet geometry which would affect flow structure inside riblet grooves. Force and flow structure on riblet surface are analyzed and compared with those of smooth surface based on thek-εturbulence model. Drag reducing and increasing mechanism is proved to be related to microvortexes induced inside riblets which lead to Reynolds shear stress reduction significantly and is considered to be the dominant factor resulting in wall friction reduction. Simulation results also show that the pressure drag generating from the deviation of static pressure on the front and rear ends of riblets occurs and grows exponentially with Mach number, which can cause drag increasing. Furthermore, near-wall vortical structures, Reynolds shear stress and static pressure on riblet surfaces are also analyzed in detail.
2014, 31(1):85-90.
Abstract:
The tracking of orientation and angular velocity is a primary attitude control task for an on-orbit spacecraft. The problem for a rigid spacecraft tracking a desired angular velocity profile is addressed using an adaptive feedback control. An angular velocity feedback tracking algorithm is firstly developed based on the precisely known attitude dynamics of the spacecraft, and the global tracking of the control algorithm is proved based on the Lyapunov analysis. An adaptation mechanism is then designed to deal with the dynamic uncertainties of the spacecraft. Such an adaptation mechanism enables the controller to track any desired angular velocity trajectories evenin the presence of uncertain inertia parameters, although it does not guarantee the inertia tensor being precisely identified. To verify the effectiveness of the proposed adaptive control policy, computer simulations on dynamic equations of a spacecraft are conducted and their results are discussed.
The tracking of orientation and angular velocity is a primary attitude control task for an on-orbit spacecraft. The problem for a rigid spacecraft tracking a desired angular velocity profile is addressed using an adaptive feedback control. An angular velocity feedback tracking algorithm is firstly developed based on the precisely known attitude dynamics of the spacecraft, and the global tracking of the control algorithm is proved based on the Lyapunov analysis. An adaptation mechanism is then designed to deal with the dynamic uncertainties of the spacecraft. Such an adaptation mechanism enables the controller to track any desired angular velocity trajectories evenin the presence of uncertain inertia parameters, although it does not guarantee the inertia tensor being precisely identified. To verify the effectiveness of the proposed adaptive control policy, computer simulations on dynamic equations of a spacecraft are conducted and their results are discussed.
12 Compensation Algorithm Based on Estimation State for Transmission Delay in Cooperative Localization
2014, 31(1):91-98.
Abstract:
In order to maximize the utilization of the observati on information in the cooperative localization, a compensation algorithm based on the estimation state is presented for transmission delay. Under the framework of the Kalman filter, two different processes of state estimating with and without transmission delay are investigated and contrasted. The expression of difference quantity caused by transmission delay is derived. It is used to compensate the present estimation state instead of the observed information compensation. According to the characteristics of state transition matrix, an equivalent expression of which successively impacts on the covariance factor in delay time is obtained. The simulation results show that the present estimated state is effectively corrected by transmission information and the relevance among agents is accurately updated. As a result, a higher positioning accuracy is achieved. Meanwhile, the consumption of recording and multiplication of the state transition matrix is saved.
In order to maximize the utilization of the observati on information in the cooperative localization, a compensation algorithm based on the estimation state is presented for transmission delay. Under the framework of the Kalman filter, two different processes of state estimating with and without transmission delay are investigated and contrasted. The expression of difference quantity caused by transmission delay is derived. It is used to compensate the present estimation state instead of the observed information compensation. According to the characteristics of state transition matrix, an equivalent expression of which successively impacts on the covariance factor in delay time is obtained. The simulation results show that the present estimated state is effectively corrected by transmission information and the relevance among agents is accurately updated. As a result, a higher positioning accuracy is achieved. Meanwhile, the consumption of recording and multiplication of the state transition matrix is saved.
2014, 31(1):99-103.
Abstract:
A differential steering system is presented for electric vehicle with motorized wheels and a dynamic model of three freedom car is built. Based on these models, the quantitative expressions of the road feel, sensitivity, and operation stability of the steering are derived. Then, according to the features of multi-constrained optimization of multi-objective function, a multi-island genetic algorithm (MIGA) is designed. Taking the roadfeel and the sensitivity of the steering as optimization objectives and the operation stability of the steering as a constraint, the system parameters are optimized. The simulation results show that the system optimized with MIGA can improve the steering road feel, and guarantee the operation stability and steering sensibility.
A differential steering system is presented for electric vehicle with motorized wheels and a dynamic model of three freedom car is built. Based on these models, the quantitative expressions of the road feel, sensitivity, and operation stability of the steering are derived. Then, according to the features of multi-constrained optimization of multi-objective function, a multi-island genetic algorithm (MIGA) is designed. Taking the roadfeel and the sensitivity of the steering as optimization objectives and the operation stability of the steering as a constraint, the system parameters are optimized. The simulation results show that the system optimized with MIGA can improve the steering road feel, and guarantee the operation stability and steering sensibility.
2014, 31(1):104-110.
Abstract:
The purpose of this study is to investigate the effect of graphite lubricant on the dry grinding performance of Ti-6Al-4V alloy, using graphite-coated, brazed monolayer, cubic boron nitride (cBN) wheels. Brazed monolayer cBN wheels both with and without a coating of polymer-based graphite lubricant are fabricated and subsequently compared for grinding performance based on measurements of grinding temperature, surface microstructure and grinding. In terms of grinding temperature, considerable improvement in dry grinding performance of titanium alloy is achieved using coated brazed monolayer cBN wheels, with 42%—47% reduction in grinding temperature as opposed to uncoated wheels. The grinding force ratio with the coated wheels is observed to remain between 1.45 to 1.85 despite material removal rates reaching up to 1 950 mm3/mm. No tangible change in ground titanium surface microstructure is noted as a result of grinding with the graphite coated wheels as opposed to the uncoated ones.
The purpose of this study is to investigate the effect of graphite lubricant on the dry grinding performance of Ti-6Al-4V alloy, using graphite-coated, brazed monolayer, cubic boron nitride (cBN) wheels. Brazed monolayer cBN wheels both with and without a coating of polymer-based graphite lubricant are fabricated and subsequently compared for grinding performance based on measurements of grinding temperature, surface microstructure and grinding. In terms of grinding temperature, considerable improvement in dry grinding performance of titanium alloy is achieved using coated brazed monolayer cBN wheels, with 42%—47% reduction in grinding temperature as opposed to uncoated wheels. The grinding force ratio with the coated wheels is observed to remain between 1.45 to 1.85 despite material removal rates reaching up to 1 950 mm3/mm. No tangible change in ground titanium surface microstructure is noted as a result of grinding with the graphite coated wheels as opposed to the uncoated ones.
2014, 31(1):111-118.
Abstract:
The principle of electric braking system is analyzed and an anti-skid braking system based on the slip rate control is proposed. The fuzzy-PID controller with parameter self-adjustment feature is designed for the anti-skid braking system. The dynamic model of aircraft ground braking is established in the simulation environment of MATLAB/SIMULINK, and simulation results of dry runway and wet runway are presented. The results show that the fuzzy-PID controller with parameter self-adjustment feature for the electric anti-skid braking system keeps working in the state of stability and the brake efficiencies are increased to 93% on dry runway and 82% on wet runway respectively.
The principle of electric braking system is analyzed and an anti-skid braking system based on the slip rate control is proposed. The fuzzy-PID controller with parameter self-adjustment feature is designed for the anti-skid braking system. The dynamic model of aircraft ground braking is established in the simulation environment of MATLAB/SIMULINK, and simulation results of dry runway and wet runway are presented. The results show that the fuzzy-PID controller with parameter self-adjustment feature for the electric anti-skid braking system keeps working in the state of stability and the brake efficiencies are increased to 93% on dry runway and 82% on wet runway respectively.
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