We present characterizations of the dynamic turbulence in the lower stratosphere measured by a new balloon-based system designed for detecting finer scale dynamic turbulence. The balloon-based system included a consta...We present characterizations of the dynamic turbulence in the lower stratosphere measured by a new balloon-based system designed for detecting finer scale dynamic turbulence. The balloon-based system included a constant temperature anemometer(CTA) operating at a sampling rate of 2 k Hz at an ascent speed of 5 m s^(-1)(corresponding to a vertical resolution of 2.5 mm), an industrial personal computer, batteries, sensors for ambient temperature and humidity, an A/D converter, and others. The system was successfully launched to 24 km altitude over Bayannur City, Inner Mongolia Province. Results show the spatial intermittence of the turbulence layers, with clear boundaries between turbulent and nonturbulent regions. This is the first time that the dynamic turbulence spectrum down to the viscous sub-range has been obtained throughout the lower stratosphere over China. With that, the energy dissipation rates of dynamic turbulence could be calculated with high precision. The profile of the dissipation rates varied from 7.37 × 10^(-7) to 4.23 W kg^(-1) and increased with altitude in the stratosphere.展开更多
The influence of core sand properties on flow dynamics was investigated synchronously with various core sands, transparent core-box and high-speed camera. To confirm whether the core shooting process has significant t...The influence of core sand properties on flow dynamics was investigated synchronously with various core sands, transparent core-box and high-speed camera. To confirm whether the core shooting process has significant turbulence, the flow pattern of sand particles in the shooting head and core box was reproduced with colored core sands. By incorporating the kinetic theory of granular flow(KTGF), kinetic-frictional constitutive correlation and turbulence model, a two-fluid model(TFM) was established to study the flow dynamics of the core shooting process. Two-fluid model(TFM) simulations were then performed and a areasonable agreement was achieved between the simulation and experimental results. Based on the experimental and simulation results, the effects of turbulence, sand density, sand diameter and binder ratio were analyzed in terms of filling process, sand volume fraction(αs) and sand velocity(Vs).展开更多
Traffic-related pollutants adversely affect air quality, especially in regions near major roadways. The vehicleinduced turbulence(VIT) is a significant factor that controls the initial dilution, dispersion, and ultima...Traffic-related pollutants adversely affect air quality, especially in regions near major roadways. The vehicleinduced turbulence(VIT) is a significant factor that controls the initial dilution, dispersion, and ultimately the chemical and physical fate of pollutants by altering the conditions in the microenvironment. This study used a computational fluid dynamics(CFD) software FLUENT to model the vehicle-induced turbulence(VIT) generated on roadways, with a focus on impact of vehicle-vehicle interactions, traffic density and vehicle composition on turbulent kinetic energy(TKE). We show, for the first time, that the overall TKE from multiple vehicles traveling in series can be estimated by superimposing the TKE of each vehicle, without considering the distance between them while the distance is greater than one vehicle length. This finding is particularly significant since it enables a new approach to VIT simulations where the overall TKE is calculated as a function of number of vehicles. We found that the interactions between vehicles traveling next to each other in adjacent lanes are insignificant,regardless the directions of the traffic flow. Consequently, simulations of different traffic scenarios can be substantially simplified by treating two-way traffic as one-way traffic, with less than 5% difference in the overall volume-averaged TKE. We also developed equations that allow the estimation of the overall volume-averaged TKE as a function of the number and the type of vehicles.展开更多
The recent progress on non-local Lagrangian and quasi-Lagrangian structures in turbulence is reviewed.The quasi-Lagrangian structures, e.g., vortex surfaces in viscous flow, gas-liquid interfaces in multi-phase flow, ...The recent progress on non-local Lagrangian and quasi-Lagrangian structures in turbulence is reviewed.The quasi-Lagrangian structures, e.g., vortex surfaces in viscous flow, gas-liquid interfaces in multi-phase flow, and flame fronts in premixed combustion, can show essential Lagrangian following properties, but they are able to have topological changes in the temporal evolution. In addition,they can represent or influence the turbulent flow field. The challenges for the investigation of the non-local structures include their identification, characterization, and evolution.The improving understanding of the quasi-Lagrangian structures is expected to be helpful to elucidate crucial dynamics and develop structure-based predictive models in turbulence.展开更多
The flow field of pulsing air separation is normally in an unsteady turbulence state.With the application of the basic principles of multiphase turbulent flows,we established the dynamical computational model,which sh...The flow field of pulsing air separation is normally in an unsteady turbulence state.With the application of the basic principles of multiphase turbulent flows,we established the dynamical computational model,which shows a remarkable variation of the unstable pulsing air flow field.CFD(computational fluid dynamics) was used to conduct the numerical simulation of the actual geometric model of the classifier.The inside velocity of the flowing fields was analyzed later.The simulation results indicate that the designed structure of the active pulsing air classifier provided a favorable environment for the separation of the particles with different physical characters by density.We shot the movement behaviors of the typical tracer grains in the active pulsing flow field using a high speed dynamic camera.The displacement and velocity curves of the particles in the continuous impulse periods were then analyzed.The experimental results indicate that the effective separation by density of the particles with the same settling velocity and different ranges of the density and particle size can be achieved in the active pulsing airflow field.The experimental results provide an agreement with the simulation results.展开更多
Separation process undertaken in packed columns often displays anisotropic turbulent mass diffusion. The anisotropic turbulent mass diffusion can be characterized rigorously by using the Reynolds mass flux(RMF) model....Separation process undertaken in packed columns often displays anisotropic turbulent mass diffusion. The anisotropic turbulent mass diffusion can be characterized rigorously by using the Reynolds mass flux(RMF) model.With the RMF model, the concentration and temperature as well as the velocity distributions can be simulated numerically. The modeled Reynolds mass flux equation is adopted to close the turbulent mass transfer equation,while the modeled Reynolds heat flux and Reynolds stress equations are used to close the turbulent heat and momentum transfer equations, so that the Boussinesq postulate and the isotropic assumption are abandoned. To validate the presented RMF model, simulation is carried out for CO2 absorption into aqueous Na OH solutions in a packed column(0.1 m id, packed with 12.7 mm Berl saddles up to a height of 6.55 m). The simulated results are compared with the experimental data and satisfactory agreement is found both in concentration and temperature distributions. The sequel Part II extends the model application to the simulation of an unsteady state adsorption process in a packed column.展开更多
In this paper the modern electron optical equipment is used to translate the clear image of speed moving bubbles in bubbling liquid on a sieve tray into the digital information stored in computer, and the computer aid...In this paper the modern electron optical equipment is used to translate the clear image of speed moving bubbles in bubbling liquid on a sieve tray into the digital information stored in computer, and the computer aided image processing technique is utilized to measure the bubble size distributions and interfacial areas under various operating conditions. And the dynamic behavior of bubbles in turbulent liquid is analyzed theoretically; the mechanism of bubble deformation and breakage is explored on the basis of Kolmogoroff′s isotropic turbulence hypothesis; the mathematical model for predicting the gas liquid interfacial area is proposed. The comparison between the simulated results and the experimental data shows that the model is higher in accuracy, simple in form and convenient in use.展开更多
For engineering applications of water dilution controlling system,the fluid dynamics of a mixed flow was studied with computational fluid dynamics(CFD) simulations and self-designed experimental set-up.In order to exa...For engineering applications of water dilution controlling system,the fluid dynamics of a mixed flow was studied with computational fluid dynamics(CFD) simulations and self-designed experimental set-up.In order to examine the predictability of CFD model for the headbox in industrial scale,two pulp suspensions before mixing were treated as homogeneous flows separately.Standard k-ε turbulence models with the mass diffusion in turbulent flows-species transport approach were applied in the simulations.A numerical simulation of this headbox model was analyzed with semi-implicit method for pressure linked equations scheme with pressure–velocity coupling.Results show that the model can predict hydrodynamic characteristics of headbox with injecting dilution water in a central diffusion tube,and the distribution of water content at the outlet of the slice lip is ideally normal at different speeds.展开更多
Hydraulic machinery mainly includes turbine and pump, which is closely related to national economy and people's livelihood involving aerospace industry, marine engineering, hydropower engineering, petroleum industry,...Hydraulic machinery mainly includes turbine and pump, which is closely related to national economy and people's livelihood involving aerospace industry, marine engineering, hydropower engineering, petroleum industry, chemical industry, mining industry, biomedical engineering, environmental engineering, agricultural water-soil engineering, etc.. The internal flow of hydraulic machinery is extremely complex, and its characteristics can be summarized as high Reynolds number, multi-scales, inhomogeneous and vortex-dominant unsteady turbulence which interact with the rotating dynamic boundary(rotor blade). Based on the analysis of the internal flow characteristics of hydraulic machinery, the author and his research team successively proposed a rotation correction model, a curvature corrected filter-based model, a scalable detached eddy simulation method, and a non-linear hybrid RANS/LES turbulence model to capture unsteady flow structures and then predict hydraulic performance and dynamic characteristics more accurately. According to the analysis on the internal flow, the corresponding flow control measures were put forward. It was verified by experiments that these methods could significantly improve the hydraulic performance, anti-cavitation performance and dynamic characteristics(pressure pulsation and vibration) of hydraulic machinery in a certain range of operating conditions. In addition, the mechanism how flow control measures influence internal flow was analyzed in depth, aiming at finding a feasible and effective way to improve hydraulic performance, anti-cavitation performance and dynamic characteristics of hydraulic machinery.展开更多
The closure problem of turbulence is still a challenging issue in turbulence modeling. In this work, a stability condition is used to close turbulence. Specifically, we regard single-phase flow as a mixture of turbule...The closure problem of turbulence is still a challenging issue in turbulence modeling. In this work, a stability condition is used to close turbulence. Specifically, we regard single-phase flow as a mixture of turbulent and non-turbulent fluids, separating the structure of turbulence. Subsequently, according to the picture of the turbulent eddy cascade, the energy contained in turbulent flow is decomposed into different parts and then quantified. A turbulence stability condition, similar to the principle of the energy-minimization multi-scale (EMMS) model for gas-solid systems, is formulated to close the dynamic constraint equa- tions of turbulence, allowing the inhomogeneous structural parameters of turbulence to be optimized. We name this model as the "EMMS-based turbulence model", and use it to construct the corresponding turbulent viscosity coefficient. To validate the EMMS-based turbulence model, it is used to simulate two classical benchmark problems, lid-driven cavity flow and turbulent flow with forced convection in an empty room, The numerical results show that the EMMS-hased turbulence model improves the accuracy of turbulence modeling due to it considers the principle of compromise in competition between viscosity and inertia.展开更多
The hydrodynamics of suspension of solids in liquids are critical to the design and performance of stirred tanks as mixing systems. Modelling a multiphase stirred tank at a high solids concentration is complex owing t...The hydrodynamics of suspension of solids in liquids are critical to the design and performance of stirred tanks as mixing systems. Modelling a multiphase stirred tank at a high solids concentration is complex owing to particle-particle and particle-wall interactions which are generally neglected at low concentra- tions. Most models do not consider such interactions and deviate significantly from experimental data. Furthermore, drag force, turbulence and turbulent dispersion play a crucial role and need to be precisely known in predicting local hydrodynamics. Therefore, critical factors such as the modelling approach, drag, dispersion, coefficient of restitution and turbulence are examined and discussed exhaustively in this paper. The Euler-Euler approach with kinetic theory of granular flow, Syamlal-O'Brien drag model and Reynolds stress turbulence model provide realistic predictions for such systems. The contribution of the turbulent dispersion force in improving the prediction is marginal but cannot be neglected at low solids volume fractions. Inferences drawn from the study and the finalised models will be instrumen- tal in accurately simulating the solids suspension in stirred tanks for a wide range of conditions. These models can be used in simulations to obtain precise results needed for an in-depth understanding of hydrodynamics in stirred tanks.展开更多
Turbulent dynamical systems involve dynamics with both a large dimensional phase space and a large number of positive Lyapunov exponents. Such systems are ubiqui- tous in applications in contemporary science and engin...Turbulent dynamical systems involve dynamics with both a large dimensional phase space and a large number of positive Lyapunov exponents. Such systems are ubiqui- tous in applications in contemporary science and engineering where the statistical ensemble prediction and the real time filtering/state estimation are needed despite the underlying complexity of the system. Statistically exactly solvable test models have a crucial role to provide firm mathematical underpinning or new algorithms for vastly more complex scien- tific phenomena. Here, a class of statistically exactly solvable non-Gaussian test models is introduced, where a generalized Feynman-Ka~ formulation reduces the exact behavior of conditional statistical moments to the solution to inhomogeneous Fokker-Planck equations modified by linear lower order coupling and source terms. This procedure is applied to a test model with hidden instabilities and is combined with information theory to address two important issues in the contemporary statistical prediction of turbulent dynamical systems: the coarse-grained ensemble prediction in a perfect model and the improving long range forecasting in imperfect models. The models discussed here should be use- ful for many other applications and algorithms for the real time prediction and the state estimation.展开更多
The orientation of suspended fibers in the turbulent contraction is strongly related to the contraction ratio,which in some cases may be detrimental to the actual production.Here for a certain contraction ratio,the co...The orientation of suspended fibers in the turbulent contraction is strongly related to the contraction ratio,which in some cases may be detrimental to the actual production.Here for a certain contraction ratio,the contraction geometry shape is optimized to obtain the desired fiber orientation.In view of the nonlinearity and the complexity of the turbulent flow equations,the parameterized shape curve,the dynamic mesh and a quasi-static assumption are used to model the contraction with the variable boundary and to search the optimal solution.Furthermore the Reynolds stress model and the fiber orientation distribution function are solved for various wall shapes.The fiber orientation alignment at the outlet is taken as the optimization objective.Finally the effect of the wall shape on the flow mechanism is discussed in detail.展开更多
基金supported by the Strategic Priority Research Program of the Chinese Academy of Sciences(Grant No.XDA17010102)。
文摘We present characterizations of the dynamic turbulence in the lower stratosphere measured by a new balloon-based system designed for detecting finer scale dynamic turbulence. The balloon-based system included a constant temperature anemometer(CTA) operating at a sampling rate of 2 k Hz at an ascent speed of 5 m s^(-1)(corresponding to a vertical resolution of 2.5 mm), an industrial personal computer, batteries, sensors for ambient temperature and humidity, an A/D converter, and others. The system was successfully launched to 24 km altitude over Bayannur City, Inner Mongolia Province. Results show the spatial intermittence of the turbulence layers, with clear boundaries between turbulent and nonturbulent regions. This is the first time that the dynamic turbulence spectrum down to the viscous sub-range has been obtained throughout the lower stratosphere over China. With that, the energy dissipation rates of dynamic turbulence could be calculated with high precision. The profile of the dissipation rates varied from 7.37 × 10^(-7) to 4.23 W kg^(-1) and increased with altitude in the stratosphere.
基金supported by the National Science Foundation of China(Grant Number 51575304)the National Science and Technology Major Project of the Ministry of Science and Technology of China(Grant Number 2012ZX04012011)
文摘The influence of core sand properties on flow dynamics was investigated synchronously with various core sands, transparent core-box and high-speed camera. To confirm whether the core shooting process has significant turbulence, the flow pattern of sand particles in the shooting head and core box was reproduced with colored core sands. By incorporating the kinetic theory of granular flow(KTGF), kinetic-frictional constitutive correlation and turbulence model, a two-fluid model(TFM) was established to study the flow dynamics of the core shooting process. Two-fluid model(TFM) simulations were then performed and a areasonable agreement was achieved between the simulation and experimental results. Based on the experimental and simulation results, the effects of turbulence, sand density, sand diameter and binder ratio were analyzed in terms of filling process, sand volume fraction(αs) and sand velocity(Vs).
基金financial support from Environment Canada and the Government of Ontario (72021622) for a scholarship to YK
文摘Traffic-related pollutants adversely affect air quality, especially in regions near major roadways. The vehicleinduced turbulence(VIT) is a significant factor that controls the initial dilution, dispersion, and ultimately the chemical and physical fate of pollutants by altering the conditions in the microenvironment. This study used a computational fluid dynamics(CFD) software FLUENT to model the vehicle-induced turbulence(VIT) generated on roadways, with a focus on impact of vehicle-vehicle interactions, traffic density and vehicle composition on turbulent kinetic energy(TKE). We show, for the first time, that the overall TKE from multiple vehicles traveling in series can be estimated by superimposing the TKE of each vehicle, without considering the distance between them while the distance is greater than one vehicle length. This finding is particularly significant since it enables a new approach to VIT simulations where the overall TKE is calculated as a function of number of vehicles. We found that the interactions between vehicles traveling next to each other in adjacent lanes are insignificant,regardless the directions of the traffic flow. Consequently, simulations of different traffic scenarios can be substantially simplified by treating two-way traffic as one-way traffic, with less than 5% difference in the overall volume-averaged TKE. We also developed equations that allow the estimation of the overall volume-averaged TKE as a function of the number and the type of vehicles.
基金supported in part by the National Natural Science Foundation of China (Grants 11342011, 11472015, and 11522215)the Thousand Young Talents Program of China
文摘The recent progress on non-local Lagrangian and quasi-Lagrangian structures in turbulence is reviewed.The quasi-Lagrangian structures, e.g., vortex surfaces in viscous flow, gas-liquid interfaces in multi-phase flow, and flame fronts in premixed combustion, can show essential Lagrangian following properties, but they are able to have topological changes in the temporal evolution. In addition,they can represent or influence the turbulent flow field. The challenges for the investigation of the non-local structures include their identification, characterization, and evolution.The improving understanding of the quasi-Lagrangian structures is expected to be helpful to elucidate crucial dynamics and develop structure-based predictive models in turbulence.
基金the financial support provided by the National Natural Science Foundation of China (No.51074156)the Natural Science Foundation of China for InnovativeResearch Group (No. 50921002)+1 种基金the Natural Science Foundation of Jiangsu Province of China (No. BK2010002)the Fundamental Research Funds for the Central Universities (No. 2010ZDP01A06)
文摘The flow field of pulsing air separation is normally in an unsteady turbulence state.With the application of the basic principles of multiphase turbulent flows,we established the dynamical computational model,which shows a remarkable variation of the unstable pulsing air flow field.CFD(computational fluid dynamics) was used to conduct the numerical simulation of the actual geometric model of the classifier.The inside velocity of the flowing fields was analyzed later.The simulation results indicate that the designed structure of the active pulsing air classifier provided a favorable environment for the separation of the particles with different physical characters by density.We shot the movement behaviors of the typical tracer grains in the active pulsing flow field using a high speed dynamic camera.The displacement and velocity curves of the particles in the continuous impulse periods were then analyzed.The experimental results indicate that the effective separation by density of the particles with the same settling velocity and different ranges of the density and particle size can be achieved in the active pulsing airflow field.The experimental results provide an agreement with the simulation results.
基金Supported by the National Natural Science Foundation of China(21376163)
文摘Separation process undertaken in packed columns often displays anisotropic turbulent mass diffusion. The anisotropic turbulent mass diffusion can be characterized rigorously by using the Reynolds mass flux(RMF) model.With the RMF model, the concentration and temperature as well as the velocity distributions can be simulated numerically. The modeled Reynolds mass flux equation is adopted to close the turbulent mass transfer equation,while the modeled Reynolds heat flux and Reynolds stress equations are used to close the turbulent heat and momentum transfer equations, so that the Boussinesq postulate and the isotropic assumption are abandoned. To validate the presented RMF model, simulation is carried out for CO2 absorption into aqueous Na OH solutions in a packed column(0.1 m id, packed with 12.7 mm Berl saddles up to a height of 6.55 m). The simulated results are compared with the experimental data and satisfactory agreement is found both in concentration and temperature distributions. The sequel Part II extends the model application to the simulation of an unsteady state adsorption process in a packed column.
文摘In this paper the modern electron optical equipment is used to translate the clear image of speed moving bubbles in bubbling liquid on a sieve tray into the digital information stored in computer, and the computer aided image processing technique is utilized to measure the bubble size distributions and interfacial areas under various operating conditions. And the dynamic behavior of bubbles in turbulent liquid is analyzed theoretically; the mechanism of bubble deformation and breakage is explored on the basis of Kolmogoroff′s isotropic turbulence hypothesis; the mathematical model for predicting the gas liquid interfacial area is proposed. The comparison between the simulated results and the experimental data shows that the model is higher in accuracy, simple in form and convenient in use.
基金Supported by the Science&Technology Plan Projects of Guangzhou City(15020079,Study on Quality Intelligent Control of Modern Paper Machine and Energy-saving Technology with Equipment)Guangdong Provincial Science&Technology Plan Projects(2015B020241001,Research and Application of Biomass Pretreatment and Ethanol Production Technology)
文摘For engineering applications of water dilution controlling system,the fluid dynamics of a mixed flow was studied with computational fluid dynamics(CFD) simulations and self-designed experimental set-up.In order to examine the predictability of CFD model for the headbox in industrial scale,two pulp suspensions before mixing were treated as homogeneous flows separately.Standard k-ε turbulence models with the mass diffusion in turbulent flows-species transport approach were applied in the simulations.A numerical simulation of this headbox model was analyzed with semi-implicit method for pressure linked equations scheme with pressure–velocity coupling.Results show that the model can predict hydrodynamic characteristics of headbox with injecting dilution water in a central diffusion tube,and the distribution of water content at the outlet of the slice lip is ideally normal at different speeds.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.51379120,51179100)
文摘Hydraulic machinery mainly includes turbine and pump, which is closely related to national economy and people's livelihood involving aerospace industry, marine engineering, hydropower engineering, petroleum industry, chemical industry, mining industry, biomedical engineering, environmental engineering, agricultural water-soil engineering, etc.. The internal flow of hydraulic machinery is extremely complex, and its characteristics can be summarized as high Reynolds number, multi-scales, inhomogeneous and vortex-dominant unsteady turbulence which interact with the rotating dynamic boundary(rotor blade). Based on the analysis of the internal flow characteristics of hydraulic machinery, the author and his research team successively proposed a rotation correction model, a curvature corrected filter-based model, a scalable detached eddy simulation method, and a non-linear hybrid RANS/LES turbulence model to capture unsteady flow structures and then predict hydraulic performance and dynamic characteristics more accurately. According to the analysis on the internal flow, the corresponding flow control measures were put forward. It was verified by experiments that these methods could significantly improve the hydraulic performance, anti-cavitation performance and dynamic characteristics(pressure pulsation and vibration) of hydraulic machinery in a certain range of operating conditions. In addition, the mechanism how flow control measures influence internal flow was analyzed in depth, aiming at finding a feasible and effective way to improve hydraulic performance, anti-cavitation performance and dynamic characteristics of hydraulic machinery.
基金supported by the National Natural Science Foundation of China(No.21106155)Science Foundation of the Chinese Academy of Sciences(No.XDA07080303)China Postdoctoral Science Foundation(No.2012M520385)
文摘The closure problem of turbulence is still a challenging issue in turbulence modeling. In this work, a stability condition is used to close turbulence. Specifically, we regard single-phase flow as a mixture of turbulent and non-turbulent fluids, separating the structure of turbulence. Subsequently, according to the picture of the turbulent eddy cascade, the energy contained in turbulent flow is decomposed into different parts and then quantified. A turbulence stability condition, similar to the principle of the energy-minimization multi-scale (EMMS) model for gas-solid systems, is formulated to close the dynamic constraint equa- tions of turbulence, allowing the inhomogeneous structural parameters of turbulence to be optimized. We name this model as the "EMMS-based turbulence model", and use it to construct the corresponding turbulent viscosity coefficient. To validate the EMMS-based turbulence model, it is used to simulate two classical benchmark problems, lid-driven cavity flow and turbulent flow with forced convection in an empty room, The numerical results show that the EMMS-hased turbulence model improves the accuracy of turbulence modeling due to it considers the principle of compromise in competition between viscosity and inertia.
文摘The hydrodynamics of suspension of solids in liquids are critical to the design and performance of stirred tanks as mixing systems. Modelling a multiphase stirred tank at a high solids concentration is complex owing to particle-particle and particle-wall interactions which are generally neglected at low concentra- tions. Most models do not consider such interactions and deviate significantly from experimental data. Furthermore, drag force, turbulence and turbulent dispersion play a crucial role and need to be precisely known in predicting local hydrodynamics. Therefore, critical factors such as the modelling approach, drag, dispersion, coefficient of restitution and turbulence are examined and discussed exhaustively in this paper. The Euler-Euler approach with kinetic theory of granular flow, Syamlal-O'Brien drag model and Reynolds stress turbulence model provide realistic predictions for such systems. The contribution of the turbulent dispersion force in improving the prediction is marginal but cannot be neglected at low solids volume fractions. Inferences drawn from the study and the finalised models will be instrumen- tal in accurately simulating the solids suspension in stirred tanks for a wide range of conditions. These models can be used in simulations to obtain precise results needed for an in-depth understanding of hydrodynamics in stirred tanks.
基金Project supported by the Office of Naval Research (ONR) Grants (No. ONR DRI N00014-10-1-0554)the DOD-MURI award "Physics Constrained Stochastic-Statistical Models for Extended Range Environmental Prediction"
文摘Turbulent dynamical systems involve dynamics with both a large dimensional phase space and a large number of positive Lyapunov exponents. Such systems are ubiqui- tous in applications in contemporary science and engineering where the statistical ensemble prediction and the real time filtering/state estimation are needed despite the underlying complexity of the system. Statistically exactly solvable test models have a crucial role to provide firm mathematical underpinning or new algorithms for vastly more complex scien- tific phenomena. Here, a class of statistically exactly solvable non-Gaussian test models is introduced, where a generalized Feynman-Ka~ formulation reduces the exact behavior of conditional statistical moments to the solution to inhomogeneous Fokker-Planck equations modified by linear lower order coupling and source terms. This procedure is applied to a test model with hidden instabilities and is combined with information theory to address two important issues in the contemporary statistical prediction of turbulent dynamical systems: the coarse-grained ensemble prediction in a perfect model and the improving long range forecasting in imperfect models. The models discussed here should be use- ful for many other applications and algorithms for the real time prediction and the state estimation.
基金supported by the National Natural Science Foundation of China(Grant No.11302110)the Public Project of Science and Technology Department of Zhejiang Province(Grant No.2015C31152)+1 种基金the Natural Science Foundation of Ningbo(Grant No.2014A610086)“Wang Weiming”Entrepreneurship Supporting Fund
文摘The orientation of suspended fibers in the turbulent contraction is strongly related to the contraction ratio,which in some cases may be detrimental to the actual production.Here for a certain contraction ratio,the contraction geometry shape is optimized to obtain the desired fiber orientation.In view of the nonlinearity and the complexity of the turbulent flow equations,the parameterized shape curve,the dynamic mesh and a quasi-static assumption are used to model the contraction with the variable boundary and to search the optimal solution.Furthermore the Reynolds stress model and the fiber orientation distribution function are solved for various wall shapes.The fiber orientation alignment at the outlet is taken as the optimization objective.Finally the effect of the wall shape on the flow mechanism is discussed in detail.