It is well-known that chaotic dynamic systems, e.g., three-body system and turbulent flow, have sensitive dependence on the initial conditions(SDIC). Unfortunately,numerical noises, i.e., truncation error and round-of...It is well-known that chaotic dynamic systems, e.g., three-body system and turbulent flow, have sensitive dependence on the initial conditions(SDIC). Unfortunately,numerical noises, i.e., truncation error and round-off error, always exist in practice. Thus,due to the SDIC, the long-term accurate prediction of chaotic dynamic systems is practically impossible. In this paper, a new strategy for chaotic dynamic systems, i.e., the clean numerical simulation(CNS), is briefly described, and applied to a few Hamiltonian chaotic systems. With negligible numerical noises, the CNS can provide convergent(reliable) chaotic trajectories in a long enough interval of time. This is very important for Hamiltonian systems, and thus should have many applications in various fields. It is found that the traditional numerical methods in double precision cannot give not only reliable trajectories but also reliable Fourier power spectra and autocorrelation functions(ACFs). In addition, even the statistic properties of chaotic systems cannot be correctly obtained by means of traditional numerical algorithms in double precision, as long as these statistics are time-dependent. The CNS results strongly suggest that one had better be very careful on the direct numerical simulation(DNS) results of statistically unsteady turbulent flows, although DNS results often agree well with experimental data when the turbulent flow is in a statistical stationary state.展开更多
In this paper,a three dimension model is built according to real surface cleaner in airport runway rubber mark cleaning vehicle and numerical simulation of this model is carried out using Ansys Fluent software.After c...In this paper,a three dimension model is built according to real surface cleaner in airport runway rubber mark cleaning vehicle and numerical simulation of this model is carried out using Ansys Fluent software.After comparison and analysis of the flow fields between high speed rotating waterjet and static waterjet formerly studied by other researchers,the influences of different standoff distances from nozzle outlet to runway surface and rotation speeds on rubber mark cleaning effect are simulated and analyzed.Results show the optimal operation parameters for the simulated model and quantitative advices are given for design,manufacture and operation of the airport runway rubber mark cleaning vehicle.展开更多
In the commercial utilization of rigid ceramic filters, the performance of pulse cleaning has crucial effects on the long-term stable operation. In order to get a clear insight into the nature of this cleaning process...In the commercial utilization of rigid ceramic filters, the performance of pulse cleaning has crucial effects on the long-term stable operation. In order to get a clear insight into the nature of this cleaning process and provide a solid basis for industrial applications, the flow in ceramic candle filter was investigated. The flow in the pulse-jetspace and inside the ceramic candle is regarded as two- dimensional, unsteady, compressible flow, and numerical simulation is carried out by computational fluid dynamics. The numerical predictions of flow field are in good agreement with the experimental measurements. Effects of the candle diameter, the separation distance between the nozzle and the candle injector and the length of the candle on the flowfield have been numerically analyzed to provide the basis for the optimum design of the pulse cleaning system.展开更多
In this paper,numeric simulations are performed for three dimension models built according to actual surface cleaner in airport runway rubber mark cleaning vehicle using ANSYS FLUENT software on the basis of previous ...In this paper,numeric simulations are performed for three dimension models built according to actual surface cleaner in airport runway rubber mark cleaning vehicle using ANSYS FLUENT software on the basis of previous research finished by the authors.After analyzing the simulated flow fields under different standoff distances between nozzle outlet and runway surface and different discharge pressures at nozzle outlet,the relationships of normal stress and shear stress at striking point to outlet pressure and standoff distance are obtained.Finally,the most appropriate discharge pressure at nozzle outlet for the studied surface cleaner model is found,and this will provide theoretical basis for future rubber mark cleaning process in airports and equipment model selection in subsequent design of airport runway rubber mark cleaning vehicles.展开更多
According to Lorenz, chaotic dynamic systems have sensitive dependence on initial conditions（SDIC）, i.e., the butterfly-effect： a tiny difference on initial conditions might lead to huge difference of computer-gene...According to Lorenz, chaotic dynamic systems have sensitive dependence on initial conditions（SDIC）, i.e., the butterfly-effect： a tiny difference on initial conditions might lead to huge difference of computer-generated simulations after a long time. Thus, computer-generated chaotic results given by traditional algorithms in double precision are a kind of mixture of ＂true＂（convergent） solution and numerical noises at the same level. Today, this defect can be overcome by means of the ＂clean numerical simulation＂（CNS） with negligible numerical noises in a long enough interval of time. The CNS is based on the Taylor series method at high enough order and data in the multiple precision with large enough number of digits, plus a convergence check using an additional simulation with even smaller numerical noises. In theory, convergent（reliable） chaotic solutions can be obtained in an arbitrary long（but finite） interval of time by means of the CNS. The CNS can reduce numerical noises to such a level even much smaller than micro-level uncertainty of physical quantities that propagation of these physical micro-level uncertainties can be precisely investigated. In this paper, we briefly introduce the basic ideas of the CNS, and its applications in long-term reliable simulations of Lorenz equation, three-body problem and Rayleigh-Bénard turbulent flows. Using the CNS, it is found that a chaotic three-body system with symmetry might disrupt without any external disturbance, say, its symmetry-breaking and system-disruption are ＂self-excited＂, i.e., out-of-nothing. In addition, by means of the CNS, we can provide a rigorous theoretical evidence that the micro-level thermal fluctuation is the origin of macroscopic randomness of turbulent flows. Naturally, much more precise than traditional algorithms in double precision, the CNS can provide us a new way to more accurately investigate chaotic dynamic systems.展开更多
The background numerical noise#0 is determined by the maximum of truncation error and round-off error.For a chaotic system,the numerical error#(t)grows exponentially,say,#(t)=#0exp(kt),where k>0 is the so-called no...The background numerical noise#0 is determined by the maximum of truncation error and round-off error.For a chaotic system,the numerical error#(t)grows exponentially,say,#(t)=#0exp(kt),where k>0 is the so-called noise-growing exponent.This is the reason why one can not gain a convergent simulation of chaotic systems in a long enough interval of time by means of traditional algorithms in double precision,since the background numerical noise#0 might stop decreasing because of the use of double precision.This restriction can be overcome by means of the clean numerical simulation(CNS),which can decrease the background numerical noise#0 to any required tiny level.A lot of successful applications show the novelty and validity of the CNS.In this paper,we further propose some strategies to greatly increase the computational efficiency of the CNS algorithms for chaotic dynamical systems.It is highly suggested to keep a balance between truncation error and round-off error and besides to progressively enlarge the background numerical noise#0,since the exponentially increasing numerical noise#(t)is much larger than it.Some examples are given to illustrate the validity of our strategies for the CNS.展开更多
基金Project supported by the National Natural Science Foundation of China(No.91752104)
文摘It is well-known that chaotic dynamic systems, e.g., three-body system and turbulent flow, have sensitive dependence on the initial conditions(SDIC). Unfortunately,numerical noises, i.e., truncation error and round-off error, always exist in practice. Thus,due to the SDIC, the long-term accurate prediction of chaotic dynamic systems is practically impossible. In this paper, a new strategy for chaotic dynamic systems, i.e., the clean numerical simulation(CNS), is briefly described, and applied to a few Hamiltonian chaotic systems. With negligible numerical noises, the CNS can provide convergent(reliable) chaotic trajectories in a long enough interval of time. This is very important for Hamiltonian systems, and thus should have many applications in various fields. It is found that the traditional numerical methods in double precision cannot give not only reliable trajectories but also reliable Fourier power spectra and autocorrelation functions(ACFs). In addition, even the statistic properties of chaotic systems cannot be correctly obtained by means of traditional numerical algorithms in double precision, as long as these statistics are time-dependent. The CNS results strongly suggest that one had better be very careful on the direct numerical simulation(DNS) results of statistically unsteady turbulent flows, although DNS results often agree well with experimental data when the turbulent flow is in a statistical stationary state.
文摘In this paper,a three dimension model is built according to real surface cleaner in airport runway rubber mark cleaning vehicle and numerical simulation of this model is carried out using Ansys Fluent software.After comparison and analysis of the flow fields between high speed rotating waterjet and static waterjet formerly studied by other researchers,the influences of different standoff distances from nozzle outlet to runway surface and rotation speeds on rubber mark cleaning effect are simulated and analyzed.Results show the optimal operation parameters for the simulated model and quantitative advices are given for design,manufacture and operation of the airport runway rubber mark cleaning vehicle.
基金Supported by the National Natural Science Foundation of China(No.59976023)
文摘In the commercial utilization of rigid ceramic filters, the performance of pulse cleaning has crucial effects on the long-term stable operation. In order to get a clear insight into the nature of this cleaning process and provide a solid basis for industrial applications, the flow in ceramic candle filter was investigated. The flow in the pulse-jetspace and inside the ceramic candle is regarded as two- dimensional, unsteady, compressible flow, and numerical simulation is carried out by computational fluid dynamics. The numerical predictions of flow field are in good agreement with the experimental measurements. Effects of the candle diameter, the separation distance between the nozzle and the candle injector and the length of the candle on the flowfield have been numerically analyzed to provide the basis for the optimum design of the pulse cleaning system.
文摘In this paper,numeric simulations are performed for three dimension models built according to actual surface cleaner in airport runway rubber mark cleaning vehicle using ANSYS FLUENT software on the basis of previous research finished by the authors.After analyzing the simulated flow fields under different standoff distances between nozzle outlet and runway surface and different discharge pressures at nozzle outlet,the relationships of normal stress and shear stress at striking point to outlet pressure and standoff distance are obtained.Finally,the most appropriate discharge pressure at nozzle outlet for the studied surface cleaner model is found,and this will provide theoretical basis for future rubber mark cleaning process in airports and equipment model selection in subsequent design of airport runway rubber mark cleaning vehicles.
基金Project supported by the National Natural Science Foundation of China(Grant No.1432009)
文摘According to Lorenz, chaotic dynamic systems have sensitive dependence on initial conditions（SDIC）, i.e., the butterfly-effect： a tiny difference on initial conditions might lead to huge difference of computer-generated simulations after a long time. Thus, computer-generated chaotic results given by traditional algorithms in double precision are a kind of mixture of ＂true＂（convergent） solution and numerical noises at the same level. Today, this defect can be overcome by means of the ＂clean numerical simulation＂（CNS） with negligible numerical noises in a long enough interval of time. The CNS is based on the Taylor series method at high enough order and data in the multiple precision with large enough number of digits, plus a convergence check using an additional simulation with even smaller numerical noises. In theory, convergent（reliable） chaotic solutions can be obtained in an arbitrary long（but finite） interval of time by means of the CNS. The CNS can reduce numerical noises to such a level even much smaller than micro-level uncertainty of physical quantities that propagation of these physical micro-level uncertainties can be precisely investigated. In this paper, we briefly introduce the basic ideas of the CNS, and its applications in long-term reliable simulations of Lorenz equation, three-body problem and Rayleigh-Bénard turbulent flows. Using the CNS, it is found that a chaotic three-body system with symmetry might disrupt without any external disturbance, say, its symmetry-breaking and system-disruption are ＂self-excited＂, i.e., out-of-nothing. In addition, by means of the CNS, we can provide a rigorous theoretical evidence that the micro-level thermal fluctuation is the origin of macroscopic randomness of turbulent flows. Naturally, much more precise than traditional algorithms in double precision, the CNS can provide us a new way to more accurately investigate chaotic dynamic systems.
基金supported by National Natural Science Foundation of China(No.12272230)Shanghai Pilot Program for Basic Research-Shanghai Jiao Tong University(No.21TQ1400202).
文摘The background numerical noise#0 is determined by the maximum of truncation error and round-off error.For a chaotic system,the numerical error#(t)grows exponentially,say,#(t)=#0exp(kt),where k>0 is the so-called noise-growing exponent.This is the reason why one can not gain a convergent simulation of chaotic systems in a long enough interval of time by means of traditional algorithms in double precision,since the background numerical noise#0 might stop decreasing because of the use of double precision.This restriction can be overcome by means of the clean numerical simulation(CNS),which can decrease the background numerical noise#0 to any required tiny level.A lot of successful applications show the novelty and validity of the CNS.In this paper,we further propose some strategies to greatly increase the computational efficiency of the CNS algorithms for chaotic dynamical systems.It is highly suggested to keep a balance between truncation error and round-off error and besides to progressively enlarge the background numerical noise#0,since the exponentially increasing numerical noise#(t)is much larger than it.Some examples are given to illustrate the validity of our strategies for the CNS.
