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## 2021 Vol. 53, No. 10

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2021, 53(10): 2613-2615. doi: 10.6052/0459-1879-21-501
Fluid flows can be theoretically described by the Navier−Stokes equations. However, due to the nonlinear convection term, analytical solutions of the equations can only be obtained for a few cases. For complex engineering flow problems at high Reynolds numbers, it is difficult to calculate the flow field efficiently and accurately by numerical simulation, and it is difficult to obtain rich details by experiment or field measurement. With the rapid development of artificial intelligence technology, data-driven technologies such as deep learning can make use of flexible network structures and efficient optimization algorithms to obtain strong approximating ability for high-dimensional and nonlinear problems, bringing opportunities for the development of computational methods for fluid mechanics. Different from traditional data-driven deep learning modeling methods for image classification and natural language processing, the flow fields predicted by deep learning models should obey physical laws of fluids, such as the Navier−Stokes equations and typical energy spectrum. Recently, physics-enhanced deep learning methods have developed rapidly and are gradually becoming a new research paradigm of fluid mechanics: the method of selecting network input features or designing network architecture according to the laws of fluid physics is called the physics-inspired deep learning method, and the method of explicitly integrating the laws of fluid physics into the network loss function or network architecture is called the physics-informed deep learning method. The research content covers the fields of reduced order modelling of fluid mechanics and solution of flow governing equations.
2021, 53(10): 2616-2629. doi: 10.6052/0459-1879-21-373
Smart particles in the present study refer to the particles in fluid that can actively adjust their motions based on the changing environment, and they are usually used to describe micro-swimmers such as microorganisms, plankton, or micro-robots. Due to the complex dynamics of particles and the flow environment, exploring the swimming strategy of smart particles is challenging but of great practical significance. Recently, reinforcement learning has been adopted for exploring the swimming strategies of smart particles, and certain progress was made. Here, we discuss the application of reinforcement learning in the study of smart particles, and introduce the recent progresses in the swimming strategy of plankton, including the swimming particle model for marine plankton, and the framework of reinforcement learning. The vertical migration is vital to the survival and reproduction of plankton. Biological study suggested that some plankton can perceive information from local fluid environment, but whether this information can be used for accelerating vertical migration still remains unknown. In this context, researchers investigated the influence of gravitational settling and particle shape on the vertical swimming strategy of plankton. Swimmers with slender shape can navigate upward more efficiently, and gravitational settling results in significant changes in smart swimming strategies. Furthermore, successive studies were carried out to investigate the effect of local fluid signals, and to discuss the possibility of navigation in the global frame of reference with only local signals. When swimmers only access to local signals, they cannot learn any effective upward swimming strategy unless the rotational symmetry of the dynamics is broken. Moreover, it was also found that reinforcement learning can make use of the underlying physical mechanism of local signals, and obtain efficient swimming strategies for vertical migration in two-dimensional time-independent flows and three-dimensional turbulent flow. Because the mechanism behind these strategies is essential and robust, these strategies is expected to be effective in more complex and realistic flow environments.
2021, 53(10): 2630-2639. doi: 10.6052/0459-1879-21-402
Computational fluid dynamics (CFD) is an important tool for turbulence research, and Reynolds-averaged Navier−Stokes (RANS) has been widely applied in many applications such as aerospace engineering. The predictive accuracy of RANS is usually significantly impacted by turbulence models, while models used in practical RANS simulations are sometimes not accurate enough. Recently, data driven turbulence modelling has gained its popularity, and different machine learning methods have been introduced to develop turbulence models with enhanced accuracy. In the present study, we review recent developments in data-driven turbulence modelling with the gene-expression-programming (GEP) method. We start with a brief introduction of the GEP method applied to turbulence modelling. The topics discussed in this paper include basic concepts of the GEP algorithm, training frameworks for explicit algebraic stress models and turbulent heat flux models, testing methods for data-driven models, and setup of cost functions. Thereafter, the applications of the GEP method in different areas, e.g. wake mixing for gas turbines, natural convection between two vertical plates, and jet in cross flow, have been discussed in details. Based on the given results, the trained GEP models are able to improve the predictive accuracy for different key parameters, including the kinetic wake loss and the turbulent heat flux in these cases. Furthermore, as the model equations are explicitly given by the GEP method, the trained models, either the explicit algebraic stress models or the turbulent heat flux models, can be further analyzed. Moreover, models trained with the CFD-driven methods have been applied in practical RANS calculations of different cases, and the results are shown to be accurate and robust in a posteriori tests. The GEP method has also been applied in sub-grid scale stress modelling in large-eddy simulations and also boundary layer transition, in which the method has demonstrated a great potential in different turbulence modelling areas.
2021, 53(10): 2640-2655. doi: 10.6052/0459-1879-21-391
The interactions between the particles and the walls often have significant effects on the particle flows. In order to study the mechanism of the interactions between the particles and the walls, the discrete element method (DEM) simulations of the particle flow in the rotating drum are carried out. Based on the statistical analysis of the simulation results, the characteristics of the near-wall particle motion are shown. The results indicate that the particle translational and rotational velocity approximately satisfy the normal distribution when the friction coefficient is small. However, due to the wall effects, the axial rotational velocity deviates from the normal distribution when the friction coefficient increasing. The kinetic theory of granular flow should consider the correction of the velocity normal distribution and also the anisotropic of the velocity fluctuation when deriving the wall boundary conditions. An artificial neural network (ANN) is used to construct a function model between dimensionless particle rotational temperature and particle slip velocity and particle translational temperature, and then the influence of particle rotation can be incorporated in the conventional boundary conditions within the two-flow model. Through comprehensive DEM simulation and result analysis could provide basic data and closure models for the theoretical construction and semi-empirical correction of the wall boundary conditions.
2021, 53(10): 2656-2666. doi: 10.6052/0459-1879-21-313
Subgrid-scale (SGS) stress modelling can be of particular importance in large-eddy simulation (LES) of turbulent flows. Traditional SGS stress models usually suffer from the drawbacks of large relative errors, excessive dissipations, etc. With the rapid progress in computer technology, machine learning methods such as artificial neural network (ANN) have gradually become a new research paradigm for SGS stress modeling. In the present paper, an ANN is employed to establish the SGS stress model for incompressible turbulent channel flow with particular attention devoted to the effect of filter width and Reynolds number. To this end, the filtered direct numerical simulation (fDNS) flow field and filter width are used as the inputs and the SGS stress at the corresponding filter width as the outputs. After training based on the data at different filter widths and different Reynolds numbers, the SGS stress predicted by ANN model is in acceptable agreement with the direct numerical simulation (DNS) data. Furthermore, excellent performance can also be found in non-modeling quantities of ANN such as SGS dissipation. The correlation coefficients between the ANN-based quantities and those calculated using DNS data are all above 0.9, indicating obvious improvements of the present ANN model over the gradient model and Smagorinsky model. In the a posteriori test, the ANN model can give better predictions on the streamwise mean velocity as compared with a variety of traditional LES models including the gradient model, Smagorinsky model and implicit LES. For the prediction of root-mean-square (RMS) fluctuating velocity, the ANN-based model is generally superior to the other three models except for some specific wall-normal locations. However, the RMS fluctuating velocities predicted by ANN-based model deviate from the fDNS results with the increase of grid size. It is suggested that ANN should have great potential for development of SGS stress models with high accuracy.
2021, 53(10): 2667-2681. doi: 10.6052/0459-1879-21-356
Automatic mesh generation and adaptation are bottleneck problems restricting computational fluid dynamics (CFD). Grid quality, efficiency, flexibility, automation level, and robustness are several key issues in grid generation. Mesh size control is significant in unstructured mesh generation which directly impacts the mesh quality, efficiency, and solution accuracy. Controlling mesh size by the background grid method requires mesh size defined on a background mesh by solving differential equations and interpolating from background mesh to specific location, which is very tedious and time-consuming in traditional unstructured grid generation. In this paper, two novel mesh size control methods are proposed in terms of efficiency and automation level. Firstly, radial basis function (RBF) interpolation was developed to control mesh size. In order to improve the efficiency of RBF interpolation, the greedy algorithm was applied to reduce the list of reference nodes. Meanwhile, an artificial neural network (ANN) is used to control the mesh size, relative wall distance, and relative mesh size are introduced as input and output parameters for the ANN. Training models are established and samples (2D cylinder and airfoil grids) are generated by commercial software. The relationship is established between wall distance and mesh size by machine learning. Several meshes are generated with the aforementioned three methods, the results demonstrate that the RBF method and the ANN method are 5-10 times more efficient than the background mesh method, which contributes to efficiency improvement of the grid generation process. Finally, the ANN method is extended to mesh size control of anisotropic hybrid grids, which also obtained meshes of good quality.
2021, 53(10): 2682-2691. doi: 10.6052/0459-1879-21-334
Wall immersed in fluid will form highly complex wake flow with specific features. Therefore, the extraction and analysis of flow feature has important research value. However, in the case of high Reynolds number, the wake flow field are complex, so it is difficult to identify and extract the flow features by traditional mathematical and statistical method. In this paper, a new flow field feature extraction and analysis method based on deep learning of wake time history data is proposed, and the shape recognition based on local time history is realized; At the same time, accuracy of different time history parameter is analyzed, and the optimal physical parameters suitable for target recognition are obtained. Research results on the flow field data of cylinder and square cylinder show that the model based on convolution neural network proposed in this paper has good training convergence and high prediction accuracy, and model using transverse velocity time history has highest accuracy. At the same time, it is proved that method proposed in this paper is a new high-precision method for target recognition immersed in fluid.
2021, 53(10): 2692-2702. doi: 10.6052/0459-1879-21-332
Gappy POD is a method of data reconstruction based on the proper orthogonal decomposition (POD). We study the applicability of gappy POD to the reconstruction of fluid turbulence configurations and focus mainly on two factors. The first factor is the complexity of the data, which mostly depends on the number of POD modes with non-zero eigenvalues. The second factor is the area and the geometry of the gap. By taking these factors into account, we reformulate the gappy POD reconstruction and derive a formula to compute the reconstruction error. Rotating turbulence data is used as a case study of gappy POD reconstruction, where the reconstruction error can be separated into two parts. The first contribution to the reconstruction error is from the truncation error during the POD expansion and it is amplified by the smallest eigenvalue of the matrix, which consists of POD modes at known indexes. This error mainly depends on the flow complexity, e.g. for flow of moderate complexity, this error decreases with the increase in number of POD modes employed during the reconstruction process. For flow of large complexity, a small POD truncation error can be detrimental and contribute signification to the reconstruction error. Therefore, all POD modes should be considered when utilizing Gappy POD reconstruction to eliminate the truncation error, especially for the turbulent flow field. The second part of the reconstruction error appears when the matrix composed of POD modes at the known points is not of full column rank. This part of error depends on the area and the geometry of the gap. The gap area determines the amount of the lost information. For the same gap area, the gap geometry determines the correlation of the lost information. Gappy POD reconstruction works well when both the amount and the correlation of the lost information are small.
2021, 53(10): 2703-2711. doi: 10.6052/0459-1879-21-464
The macroscopic mechanical behaviours of granular materials are affected by not just material properties such as particle composition but also state parameters of granular assembly, like porosity and coordination number, etc. Meanwhile, granular materials are of complex loading path- and loading history-dependent features. Establishing a constitutive model incorporating multiple internal variables and their inherent relations for granular materials is an important scientific challenge. Different from the traditional phenomenological constitutive model based on the framework of yield surface, flow rule and hardening function, this study establishes a directed graph-based data-driven constitutive model with the average porosity, fabric tensor and equivalent elastic stiffness tensor being considered as internal variables, which are critical to the constitutive behaviour of granular materials from the perspectives of the particulate mechanics. The constitutive models containing different internal variables and having different predictive capabilities are represented by different directed graphs with various internal variables linking networks. The recurrent neural network is trained to represent the source-target mapping relationships of the information flows between internal variables. The process of establishing constitutive models is simplified as a sequence of forming graph edges with the goal of finding the optimal combination of internal variables. Therefore, the modelling of the constitutive model can be formulated as a Markov decision process and implemented by the deep reinforcement learning algorithm. Specifically, the well-known AlphaGo Zero algorithm is used to automatically discover the optimal data-driven constitutive modelling path for granular materials. Our numerical examples show that this modeling framework can produce constitutive models with higher prediction accuracy. Furthermore, this study provides a new research paradigm by integrating different theoretical models from the point of data and leveraging the algorithms in artificial intelligence to develop a superior model. The same idea can be extended to seek new insights for similar scientific problems.
2021, 53(10): 2712-2723. doi: 10.6052/0459-1879-21-312
The identification of structural internal defects is an important research content of structural health monitoring. At present, the structural safety inspection based on non-destructive testing mainly focuses on qualitative analysis, so it is difficult to identify the scale of defects quantitatively. In this paper, an inversion model is proposed by combing the scaled boundary finite element methods (SBFEM) and deep learning. The identification of crack-like defects can be performed in structures based on the feedback signal of Lamb wave propagation. By randomly generating defect information, i.e. position and size, the SBFEM can be used to simulate the signal propagation process of Lamb wave in structures with defects. The SBFEM only needs to discretize the structure boundary, which can minimize the re-meshing process and greatly improve the computational efficiency. When Lamb wave propagates in a cracked structure, the feedback signal of the observation point can reflect crack information. Based on this characteristic, enough training data reflecting the characteristics of the problem can be provided for the deep learning model. The proposed defect inversion model avoids the iterative process of minimizing the objective function of the traditional inverse problems, and greatly reduces the computational cost on the premise of ensuring accuracy. Numerical examples of plates with single and multiple cracks are analyzed. The results show that the defect identification model can accurately quantify the defects in the structure. It also has a good identification effect for shallow cracks. The model also shows robustness to the noisy signal model.
2021, 53(10): 2724-2735. doi: 10.6052/0459-1879-21-360
Bubbles in an electric field have a significant effect on enhancing heat transfer. The study of the dynamic characteristics of bubbles in an electric field is important for enhancing the efficiency of heat exchangers and improving energy efficiency. In order to obtain the dynamics of bubbles under an applied electric field, a visualization experiment was designed and built. A 50 kV high voltage direct current power supply was used to construct a uniform electric field and a high-definition camera was used to capture the experimental images. The electric field strength, bubble volume and dielectric constant of the solution were introduced as variables to investigate their effects on the dynamic properties of the bubbles. The rise of the bubble in a vertical and horizontal uniform electric field was observed and the variation of the bubble deformation and rise velocity for different variables was analyzed. The bubble aspect ratio L/D was used to represent the degree of bubble stretching and deformation, and the individual bubble rising process was captured in separate time periods to show the shape change process. The results show that the bubble elongates in the direction of the electric field, and the larger the electric field strength, the more obvious the deformation is; in the vertical electric field, the elongation of the bubble causes the rising speed to increase, while in the horizontal electric field, the rising speed decreases. As the size of the bubble increases, the buoyancy force on the bubble increases and the rate of rising bubbles increases. As the dielectric constant of the solution increases, the electric field force on the bubble increases significantly and the bubble deformation becomes more pronounced.
2021, 53(10): 2736-2744. doi: 10.6052/0459-1879-21-352
Impact of spheres on liquid surfaces is a universal phenomenon in nature and industrial processes. However, the relevant researches mainly focused on the impact of millimeter or larger spheres on the horizontal liquid surface. Further studies on the dynamic characteristics of submillimeter sphere impact process and the influence of curved interface on impact behavior is necessary. Herein, we presented the observation on the impact of submillimeter spheres on the curved surface of droplet by using high-speed microphotography technology. Owing to the existence of curved liquid surface, the impact phenomenon is different from those after impact horizontal liquid surface. The azimuthal angle of TPCL (three phase contact line) pinned point is positive linear correlation with the impact angle during wetting process, while the non-axisymmetric cavity is first formed on the higher side of TPCL pinned point and the curvature radius is larger. The evolution of the dominant forces and the energy conversion mechanism during the impact process were revealed. The influence of impact velocity and angle α on impact behavior were analyzed, and the impact pattern diagram was provided. The results show that the form drag dominates the motion of the sphere at the slamming stage, while the kinetic energy loss of the sphere is positive correlation with spheres velocity. The surface tension dominates the process at the cavity development stage, and the kinetic energy of the sphere is transformed into the surface energy that maintains the cavity. The cavity length of oscillation mode increases with the increase of Weber number We, and the cavity development velocity is basically consistent. According to the dimensional analysis and experimental results, the relationship between critical Weber number Wecr and α is $We_{cr}^{1/2}$ = α/40 by fitting.
2021, 53(10): 2745-2751. doi: 10.6052/0459-1879-21-351
Moving bed technology of dense granular flow has been widely applied in industrial processes. A practical simulation method and detailed studies on the characteristics of granular flow in moving bed are of great significance for its design and operation. In this paper, an improved μ(I) rheology model for dense granular flow in moving beds is presented. Specifically, the relationship among local particle volume fraction, local granular pressure and granular flow density, is proposed, based on which the governing equations by treating the dense granular flow as a compressible pseudo-fluid are established. The particle-wall shear slip boundary condition, together with the regularisation method in the calculation of pseudo-fluid viscosity and granular pressure are presented as well. Firstly, the proposed model is validated and the rheological parameters involved in μ(I) model are determined by the experimental results of velocity distributions for 3 kinds of typical granular materials, namely, glass beads, corundum beads, and coarse sand in a silo. Detailed results regarding the particle velocity, solid volume fraction, velocity shear rate and inertial number of the 3 different granular flow in the silo are obtained. The two typical different flow modes, i.e. the funnel flow for coarse sand and the mass flow for glass beads in silos, are well predicted. Secondly, the granular flow of glass beads passing through a moving bed with an inbuilt pipe is studied as well. Reasonable results including particle velocity, solid volume fraction and granular pressure around the pipe are revealed and analyzed. The typical solid volume fraction of the studied cases ranges from 0.510 ~ 0.461, and the inertial numbers in most region of the beds are less than 0.1. The simulated results show that the proposed model is feasible for dense granular flow in moving beds and the calculation amount is significantly reduced compared with that of the multi-phase simulation method.
2021, 53(10): 2752-2761. doi: 10.6052/0459-1879-21-320
Flow-induced oscillation (FIO) of underwater aperture-cavities is one of prominent noise sources of underwater vehicles. In order to explore the effective control method and suppression characteristics of FIO of underwater aperture-cavity, experiments of FIO characteristics and its control of underwater aperture-cavities were carried out in the circulating water tunnel. The experimental model of underwater aperture-cavity was designed based on the surface aperture structure of underwater vehicles, and the FIO control device, leading-edge flow splitter (LFS), was proposed based on the principle of incoming boundary layer diversion. The FIO characteristics of underwater aperture-cavities and the effects of LFS on FIO at different freestream velocities were discussed from the two aspects of the frequency spectrum characteristics and the spatial distribution characteristics of the intracavity pressure fluctuations, while the intracavity pressure fluctuations were measured by the streamwise and spanwise installed dynamic pressure transducers at the bottom of the cavity. The investigation results show that the form of FIO of underwater aperture-cavities is dominated by the self-sustained oscillation of the shear layer, which occurs at a relatively low freestream velocity, such as 2.4 m/s, and has an intensive reinforcement with the increase of the freestream velocity. It was proved that the LFS has a good suppression effect on the FIO of aperture-cavities in water, and the suppression effect is significantly enhanced with the increase of the freestream velocity. Specifically, the maximum suppression of the peak and total level of the intracavity pressure fluctuations spectrum reaches 25.3 dB and 15.6 dB, respectively. Besides, the LFS has a low frequency shift effect on the FIO of aperture-cavities, which is beneficial for avoiding the occurrence of flow-induced cavity resonance. Finally, the spatial distribution characteristics of pressure fluctuations indicate that the suppression mechanism of the FIO of underwater aperture cavities by the LFS mainly lies in destroying the periodic modulation effect of the intracavity flow field.
2021, 53(10): 2762-2775. doi: 10.6052/0459-1879-21-143
Most of the existing researches on deformation reconstruction of flexible structures with finite deformation are only based on the geometric relationship between curvature and strain, which ignores the longitudinal deformation and the coupling effect of the longitudinal deformation and the bending deformation. In order to construct a more accurate deformation reconstruction method which can be extended with the help of existing mechanical tools, this paper takes the plane beam as the object, partially inherits inverse finite element method developed by Tessler A, and regards the deformation reconstruction problem of plane beam as a kind of numerical optimization problem. Firstly, by introducing the absolute nodal coordinate formulation (ANCF) into the description of mapping relationship between strain and displacement, an inverse gradient reduced ANCF plane beam element is derived. Secondly, the inverse ANCF element is modified to simplify the degree of freedom of nodes and ensure the C2 continuity at nodes by introducing the penalty function, which not only ensures the problem is well-posed, but also improves the accuracy of the final result. Finally, based on the inverse ANCF element, the Newton method is used to develop two types of algorithms for deformation reconstruction under different working conditions, one is the element-by-element algorithm and the other is the multi-element algorithm. The numerical simulation results show that the reconstruction relative error of this method is less than 1% under the condition of large deformation, and it still maintains high accuracy under the condition of few measuring points. The convergence and computational efficiency of the method are verified by numerical simulation example.
2021, 53(10): 2776-2789. doi: 10.6052/0459-1879-21-338
The concrete structure is easy to appear cracks under external loading during service, which leads to the reduction of structural stiffness and the decline of bearing capacity. Using accurate calculation method to predict the cracks development of concrete is the basic premise for crack control, and also the important measure to ensure the safety of structure. Continuous damage method (CDM) can describe the propagation process of micro cracks, but cannot represent discrete crack surface and contained disadvantages of grid induced deviation and false stress transfer, mechanics-extended finite element method (XFEM) can describe the propagation process of macro cracks, but cannot reflect the dynamic propagation of micro cracks, the cracks distribution calculated by the two methods are all quite different from the actual situation. The existing CDM-XFEM method can effectively simulate the whole process of concrete micro and macro cracks development, but the concrete plastic strain is ignored when the macro cracks appeared, so the energy conversion between CDM and XFEM is lack of balance. In this paper, the plastic dissipation of energy conversion is considered, the exponential function is selected as the traction separation mode of cohesive crack, based on the principle of energy and stress equivalence, the energy conversion equation between CDM and XFEM is reconstructed, the generalized inverse least square method is used to solve the energy conversion coefficient and determine the critical displacement during energy conversion, the updating algorithm of crack level set and overall calculation procedure are given out. Taking the shear tensile cracking experiment of concrete with double incisions as an example, various calculation methods of concrete crack are compared with the experiment. The results show that the crack distribution and tension-displacement curve calculated by CDM-XFEM method considered concrete plastic dissipation is most close to the experiment, which indicates that CDM-XFEM calculation method considered concrete plastic dissipation can better calculate concrete cracks.
2021, 53(10): 2790-2799. doi: 10.6052/0459-1879-21-272
K0 consolidated clay is widely distributed in nature. It usually has both overconsolidation property and natural structural property, and it is a significant difference for the property of overconsolidation of K0 to the normal consolidation of K0 clay. In order to effectively describe the overconsolidation properties of K0 consolidated clay, three improvements were made on the basis of the natural structure consolidated model for clay, so that the original model can be extended to a constitutive model that consider both the properties of K0 overconsolidation clay and the effects of natural structures for natural clay. (1) The relative stress ratio is introduced into the yield surface equation to describe the yield property, and the initial anisotropic consolidation stress ratio parameter ξ is introduced into the yield surface equation to express the influence of the initial anisotropy on the position of the yield surface in p-q space. (2) Based on the given yield surface equation, the phase transformation stress ratio parameter was derived, and the phase transformation stress ratio was introduced into the unified hardening parameter. The unified hardening parameter can effectively describe both the initial anisotropic shearing behavior and the dilatancy behavior, strain hardening and softening phenomenon for initial anisotropic consolidated clay. (3) The cementation parameter pe, which reflects the structural cementation, is introduced into the yield surface equation and the decay evolution equation of pe with deviatoric plastic strain is given. The dilatancy properties of structural clay can be described by using the cementation parameter. The comparison between the prediction and the test results shows that the proposed K0 consolidation model can effectively describe the stiffness enhancement effect of K0 overconsolidated clay, the Bauschinger effect of clay, the cementation strength loss phenomenon and the strain softening phenomenon of structural clay. The applicability and rationality of the proposed model are proved.
2021, 53(10): 2800-2813. doi: 10.6052/0459-1879-21-265
By using symmetry and conservation laws, we can simplify dynamical problem and even obtain the exact solution of mechanical system, and better understand the dynamical behavior of system. Time scales analysis unifies and extends the continuous and discrete dynamics models to the time scales framework, which not only avoids repeated studies but also reveals the differences and connections between them. Therefore, it is necessary to explore new conservation laws in the framework of time scale through symmetry. Firstly, the Lagrange equations on time scales are established, and two important relations of time scales Lagrange system are derived by using the properties of time scales calculus. Secondly, according to the invariance of differential equation under the one-parameter Lie group of transformations, the definition of Lie symmetry on time scales and its determining equation are established. Thirdly, the Lie symmetry theorem on time scales is established and proved by using the above relations, and the new conservation laws of time scales Lagrange system are obtained. When the time scale is taken to the set of real numbers, the conservation laws degenerate to the famous Hojman conserved quantity. Finally, a two-degree-of-freedom time scales Lagrange system is investigated, and its Hojman conserved quantities are obtained in three different time scales, and the correctness of the theorem we obtained is verified by numerical calculation.
2021, 53(10): 2814-2822. doi: 10.6052/0459-1879-21-413
As the first-stage equipment of purifying drilling fluid, the screening performance of drilling shaker will directly determine the production efficiency of subsequent solid-control system. Meanwhile, in material screening engineering, the dynamics characteristics of vibrating system with single frequency actuation is difficult to match with the particle size of material, which usually leads to blocking of the screen mesh. Thus, to solve the problem mentioned above, a self-synchronous vibratory system actuated with multiple-frequency and dual-rotor is proposed in the present work. Firstly, motion differential equation of the multi-degree-of-freedom vibration system is obtained according to mathematical model and generalized Lagrange’s equations, and amplitude responses of the oscillating body in stable state are solved by applying complex number method. Then, considering revised small parameters method and Poincare−Lyapunov theory, the precondition and the stability evaluation criterion of implementing multiple-frequency synchronization are systematically revealed. Subsequently, relationship among the synchronous characteristics of rotors and the structural parameters of system is discussed quantitatively by numerical calculation. Moreover, combining with Runge−Kutta algorithm, an electromechanical coupling dynamics simulation model related to the proposed vibration system is established, and the double-frequency synchronization mechanism among the rotors and the oscillating body are analyzed in detail. Finally, an experimental platform is established to test the synchronous motion state and the dynamic characteristics of the system under different working conditions, which further demonstrates correctness of the theoretical investigation and the computation simulation. Research shows that synchronous ability index of the system is infinitely closed to zero with the increase of mounting distance. In this case, the possibility that the high-speed rotor and the low-speed rotor achieve steady synchronous vibration is gradually increased. Furthermore, the synchronous state of the motors is hardly affected with the stiffness coefficients of springs, but the phase difference value will be decreased and locked around a constant value with the change of dip angle and mounting distance of the exciters in a single period. This study not only has important reference value for the invention of vibrating screen in petroleum industry, but also will promote the development of other vibration machines.
2021, 53(10): 2823-2840. doi: 10.6052/0459-1879-21-359
Due to the tumbling motion of the target, the dual-arm space robot to grasp a dynamic target is more challenging compared to a static target. Besides, optimization of the grasping strategy can improve the manipulability of the space robot to operate on the tumbling targets to ensure the success of the grasping mission. In this paper, a method for grasping strategy optimization is proposed based on the manipulability evaluation. When the dual-arm space robot cooperatively grasping a target, the dual-arm end-effectors contact the target simultaneously and a closed kinematics chain is formed. As a result, the formation of the closed-chain constraint complicates the evaluation of the manipulability of the space robot. First, the kinematics and dynamics of a dual-arm space robot manipulating a target are analyzed in this paper. Following this, a cooperative workspace considering the closed-chain constraint is established, and a task compatibility based detumbling manipulability metric is analyzed. The established cooperative workspace contains both the position and the attitude information of the manipulated target in the task space, which can be used for the calculation of dexterity. Then, the optimal grasping points of the end-effectors to grasping a target are determined based on the global dexterity metric, as well as the optimal grasping configuration of the space robot to grasp a tumbling target is found based on the force task compatibility metric considering the field-of-view constraint of the camera and the velocity tracking constraint of the end-effectors to the tumbling motion of the target. Using the manipulability metrics to determine the grasping strategy can make full use of the coordination of both arms to increase the manipulability of the space robot to manipulate dynamic targets, and simulations are conducted using a 7 degree of freedom dual-arm space robot to verify the feasibility and effectiveness of the proposed grasping strategy.
2021, 53(10): 2841-2852. doi: 10.6052/0459-1879-21-436
Detonation combustion is characterized by the high thermodynamic efficiency and fast heat release. Benefitting from these potential advantages, an oblique detonation wave (ODW) is introduced into the combustion chamber and oblique detonation engine (ODE) plays an important role in hypersonic air-breathing propulsion systems. Previous studies mainly focused on the initiation structures, standing features and wave systems of oblique detonation, but the global analysis of ODE propulsive performance is still absent at the macro-level. In this paper, the flow and combustion processes of an ODE are decomposed into four basic modules, named as inlet model, mixing model, combustion mode and nozzle model, respectively. We solve these four basic flow processes using theoretical methods and propose a systematically theoretical approach that can be used to predict the ODE propulsion performance. On the basis of previous ODW initiation structures and waves systems, four different combustion modes, i.e., over-driven ODW, Chapman-Jouguet ODW, over-driven normal detonation wave and oblique shock-induced constant-volume combustion, are chosen to describe the heat release processes of combustible mixture in the ODE combustor. The effects of different combustion modes on fuel specific impulse of the ODE are also analyzed. In addition, the influence mechanisms of inflow parameters, combustor parameters and intake-exhaust parameters on the thrust performance of ODE are also obtained, and the results show that the major factor of fuel specific impulse of an ODE consists mainly of the inflow Mach number and the expansion ratio of engine nozzle. Finally, combined with precious detonation research results, such as the standing features and initiation structures of oblique detonation in a confined space, the preliminary design direction of oblique detonation engine are proposed, which mainly involve some constrained conditions, such as geometrical constraints, inflow velocity limitations and stability ranges of a detonation wave in ODE combustor.
2021, 53(10): 2853-2864. doi: 10.6052/0459-1879-21-206
The initiation, steady propagation and failure mechanism of gaseous detonation wave in periodic inhomogeneous media are very complex, and many physical mechanisms are still unclear, which is an active topic in detonation physics. Numerical simulation of propagation of gaseous detonations in the inhomogeneous medium is studied by using the reactive Euler equations coupled with a two-step chemical reaction model. The inhomogeneity is generated by placing artificial temperature perturbations with different wavelengths and amplitudes. The influence of temperature disturbance with different wavelength and amplitude on the structure of wave front is analyzed. The results show that, the transition of ZND detonation to cellular detonation under artificial temperature disturbance is mainly controlled by two competitive factors: one is the intrinsic instability of detonation wave, the other is the wavelength and amplitude of artificial disturbance, the former is the internal factor, the latter is the external factor. The existence of artificial temperature disturbance delays the evolution of ZND detonation to cellular detonation by suppressing the development of shear wave, and the increase of internal instability can slow down this delay phenomenon. This shows that the artificial temperature disturbance can restrain the development of cell instability in a certain range, but it cannot stop the process. The discontinuity of temperature makes the detonation wave front more distorted, which leads to the existence of a weak triple-wave structure near the shear wave, which is, the artificial disturbance increases the inherent instability of detonation wave and changes the propagation mechanism of detonation wave front. The propagation of detonation and the instability of detonation are restrained by the artificial temperature disturbance with large amplitude. The formation of detonation front cellular structure depends on the artificial temperature disturbance and its own instability.
2021, 53(10): 2865-2879. doi: 10.6052/0459-1879-21-069
Using CO2 to produce shale gas can not only improve shale gas recovery, but also save water resources and carry out geological storage of CO2, which is helpful to achieve carbon neutrality in shale gas production process. The gas migration mechanism in micro-nano pores of organic-rich shale reservoir is different from that of conventional reservoir. CO2 has supercritical properties in the reservoir, which makes the exploitation mechanism complicated and it is impossible to obtain an accurate understanding of the microscopic mechanism of CO2 exploitation of shale gas. Therefore, it is very important to study the adsorption and displacement characteristics of CH4, CO2 and their binary mixtures in micro-nano pores of shale reservoir for accurate evaluation and efficient exploitation of shale gas. In this paper, review on the adsorption properties of CH4, CO2/CH4 binary mixture competitive adsorption and displacement properties in micro-nano pores of shale reservoir were carried out from three aspects: experiment, basic theory and numerical simulation. The key question and research trend on the CO2/CH4 adsorption and displacement characteristics of micro-nano pores in shale reservoir has been discussed. The results show that CH4 is physically adsorbed in shale reservoirs, and the characteristics of organic matter (abundance, maturity and type), pore structure, inorganic mineral composition, temperature and pressure, and water content all have a certain degree of influence on CH4 adsorption capacity of shale. Under the same conditions, CO2 is more easily adsorbed by shale reservoir than CH4. Injecting CO2 into shale reservoir can promote the desorption of CH4 and facilitate the geological storage of CO2. The deployment of the production plan can adopt the injection production method in the form of well pattern. The production plan can be optimized by adjusting the location, number and CO2 injection rate of injection wells.
2021, 53(10): 2880-2890. doi: 10.6052/0459-1879-21-292