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High speed and shock compression behind the bow shock of an aircraft head result in very high temperature, which would subsequently lead to a conductivity plasma flowfield around the vehicle. The plasma gas provides a direct working environment for the application of magnetic field. The magnetohydrodynamic (MHD) flow control, which uses the magnetic field to alter the trajectory of ions or electrons, can improve the aerodynamic characteristics of hypersonic vehicles effectively. It has potential prospects on aerodynamic force control and aerodynamic heating management. Besides, the development of superconducting materials and electromagnetic technology contribute to a great upsurge of MHD flow control research significantly. Although research work has been carried out in the field of MHD flow control at home and abroad, its experimental investigation is still challenging. And for the measurement of pressure and heat flux, there is no systematic conclusion because of the limited test conditions and measurement techniques. The results of different researchers may be different from each other and from the theoretical results and numerical simulations. Thus, the influence on the shock stand-off distance, pressure and heat flux under MHD flow control deserves an in-depth investigation. Besides, the numerical simulations and theoretical methods do also need reliable experimental data for variation. The aim of this review paper is to summarize and discuss the developments on MHD flow control technology based on high temperature real gas effect, including the experimental technique, numerical method, and the influence rules and dynamics mechanism of MHD flow control. Its development trend is also discussed and prospected in the paper.

2021, 53(6): 1515-1531.   doi: 10.6052/0459-1879-21-067
Solving the Reynolds-averaged Navier-Stokes (RANS) equation remains an effective and practical approach in engineering applications, but the uncertainty of Reynolds stress modeling will lead to discrepancies in the prediction accuracy of this approach. With the development of artificial intelligence, the data-driven method of turbulence model combined with machine learning algorithm is more effective than the original RANS model, however, the stability and prediction accuracy of the data-driven method could still be further improved. In the present paper, a fully connected neural network is constructed to predict the eddy viscosity, and this neural network is called as Eddy Viscosity Neural Network (EVNN). Additionally, a tensor-based neural network (TBNN) is also applied to predict the higher-order eddy viscosity relationship between the unclosed quantity and the analytical quantity, and the basis tensors are used to ensure the Galilean invariance. Finally, the closed-loop accuracy of the predicted flow field is realized through multiple modifications. For the method above, the neural network which is combined by EVNN and TBNN, is trained by using the high-fidelity data generated by the large eddy simulation (LES) and the baseline data obtained by the RANS simulation. Compared with the high-fidelity LES results, the results of the modified model exhibit significantly higher accuracy in the posterior velocity field, the mean pressure coefficient, and the mean friction coefficient than the original RANS model. It can be found that the implicit treatment of the linear part of the Reynolds stress can enhance the numerical stability, and the modification of the nonlinear part of the Reynolds stress can better predict the anisotropic characteristics of the flow field. Furthermore, the prediction accuracy is further improved through the multiple modification strategy. Therefore, the combined neural network and multiple modification strategy developed in this paper, have strong potentials in data-driven turbulence modeling and engineering applications in the future.
2021, 53(6): 1532-1542.   doi: 10.6052/0459-1879-21-073
It is a challenging and important issue to establish a nonlinear dynamic model of system by use of limited data. The data-driven sparse identification method is an effective method developed recently to identify the governing equations of the dynamic system from data developed in recent years. In this paper, governing equations for different flows are identified by data-driven sparse identification methods. Partial differential equation functional identification of nonlinear dynamics (PDE-FIND) scheme and least absolute shrinkage and selection operator (LASSO) scheme are used to identify the governing equations of two-dimensional flow past a circular cylinder, liddriven cavity flow, Rayleigh-Bénard convection and three-dimensional turbulent channel flow. An over-complete candidate library is constructed by direct numerical simulation flow field data in the process of identification. Variables in the library are retained up to second order, variable derivatives are retained up to second order, and nonlinear terms are retained up to fourth order. By comparing the results from the two methods, we find both methods show good performance in identifying governing equation with no nonlinear terms, i.e., vorticity transport equation, heat transport equation and continuity equation. PDE-FIND scheme correctly identified the governing equations and Rayleigh number and Reynolds number for the flow field. But LASSO scheme failed to identify the governing equations which contain strong nonlinear terms, i.e., Navier-Stokes equations. This is because grouping effect may occur among the items in the candidate library and only one item in the group is chosen in such case in LASSO scheme. So PDE-FIND scheme is more effective than LASSO scheme in sparse identification of strongly nonlinear partial differential equation. It is also found that selecting data from regions with abundant flow structures can improve the accuracy of data-driven sparse identification results.
2021, 53(6): 1543-1551.   doi: 10.6052/0459-1879-21-052
The numerical computation of vortex-induced vibration of three circular cylinders in a tandem arrangement with two degrees of freedom has been carried out. The effects of Reynolds number, natural frequency ratio and reduced velocity on the dynamic response and spectral characteristics of three tandem cylinders were analyzed. The results indicate that the Reynolds number and natural frequency ratio have little influence on the amplitude and fluid force coefficient of the upstream cylinder. The frequency locked region of the midstream cylinder increases with the increasing of Reynolds number. The dynamic response of the midstream cylinder is greatly affected by the wake of the upstream cylinder, whereas the effect of natural frequency ratio is small. Meanwhile, when the reduced velocity is small, Reynolds number and natural frequency ratio have great influence on the fluid force coefficient. In addition, the amplitude and the fluid force coefficient of the downstream cylinder are greatly affected by Reynolds number and natural frequency ratio. Reynolds number, natural frequency ratio and reduced velocity have great influence on the main peak amplitude, spectrum component and fluctuation of fluid force coefficients PSD curve. The fluctuation of the PSD curve becomes intense, giving rise to the movement trajectory of cylinder from "8" shape to irregular shape. As natural frequency ratio increases to 2.0, the P$+$S mode is found in the wake of the upstream cylinder, which leads to the occurrence of asymmetric motion, and the equality of main peaks of the PSD curve of the lift and drag coefficients. Finally, the variation of average power value of excitation load with reduced velocity is similar to that of corresponding structural dynamic response. In the same reduced velocity range, the strength of structural vibration response is directly proportional to the average power value of displacement. When analyzing the power spectral density of lift coefficient in different intervals, the vibration frequency ratio has more influence on the structural vibration response.
2021, 53(6): 1552-1568.   doi: 10.6052/0459-1879-21-036
When the computational fluid dynamics discrete element method (CFD-DEM) is used for solid-liquid two-phase coupling analysis, the selection of particle calculation time step directly affects the accuracy and efficiency of the coupling calculation. For this reason, each target particle is selected as the research object, and interpolation function is introduced to calculate the motion displacement of the time step, and a variable spatial search grid is constructed. An improved particle collision search algorithm (modified discrete element method, MDEM) was proposed by selecting possible collision particles to build a search list and using reverse search Method to judge collision particles. The algorithm in particle group and fluid coupling calculation, the particle counting the initial time step selection particle collision time without limit, realization of automatic adjustment and correction by large step, calculated by the real-time update of fluid particles and fluid coupling conditions, time step, the granular computing time step selection, as a result of low computational efficiency, selection is too large too small to solve the problem of false negatives, particle collision of particles and fluid coupling numerical simulation provides a effective calculation method. Through the numerical simulation of two particles and multiple particles, the relative errors of the collision forces, collision positions and times between particles obtained are all less than 2% compared with the theoretical calculation results. Compared with the traditional DEM collision search algorithm, the three calculation time steps selected do not affect the calculation accuracy, and the calculation efficiency is higher. Through the coupling numerical simulation of multiple particles and fluid, using the traditional CFD-DEM method, the precise solution can be obtained only when the particle calculation time step is 10$^{-6}$ s or smaller, while the precise solution can be obtained by using the proposed method to take 10$^{-4}$ s, which avoids the problem of missed decision caused by particle collision with the increase of time step, and the calculation time is reduced by 16.7%.
2021, 53(6): 1569-1585.   doi: 10.6052/0459-1879-21-002
Recently, the flux reconstruction (FR) method has attracted more and more attentions for its simplicity and generality. However, it is still computationally expensive and time consuming when simulating the complex flow problems by FR method. There is a huge demand for developing appropriate efficient implicit solvers and parallel computing techniques for FR. This paper proposes an implicit high-order flux reconstruction solver on GPU platform based on the block Jacobi iteration method. As it is inefficient to solve the large global linear system resulting from spatial and implicit temporal discretization of FR directly. A block Jacobi approach is used to change the characteristics of the lift-hand matrix of the global linear system and this avoids the dependence of neighboring elements. Therefore, only the diagonal blocks of global matrix need to be stored and calculated. Then, the problem of solving the huge global linear system is transformed into solving a series of local linear equations simultaneously. Finally, these small local linear equations would be solved by the LU decomposition method in parallel on GPU platforms. Two typical cases, including subsonic flows over a bump and a NACA0012 airfoil, were simulated and compared with the multi-grid explicit Runge-Kutta scheme. The numerical results demonstrated that the present implicit method can reduce the iterations significantly. Meanwhile, the implicit solver has shown at least 10x speedup over the multi-grid Runge-Kutta scheme in all cases.
2021, 53(6): 1586-1598.   doi: 10.6052/0459-1879-20-404
The metal droplet deposition manufacturing technology adopts a point-by-point stacking method, which provide an unsupported manufacturing method for oblique column deposition with high flexibility. In this paper, a lattice Boltzmann model is established for simulating the continuous deposition process of the oblique column, and the horizontal displacement of the droplet on the solidification surface is studied. According to the charging and discharging process of surface energy, the deposition process is divided into four stages: falling, rapid expansion, slow expansion, and rebound. The forces on the deposited droplet are analyzed by the trend of surface energy, the gravitational potential energy, the kinetic energy, and the viscous dissipation. The internal flow of droplet is sliding in the expansion stage and rolling in the rebound stage. The internal flow of the droplet shows sliding state in the expansion stage and rolling state in the rebound stage. The acceleration of the deviation mainly occurs in the expansion stage, while the deviation distance occurs in the rebound stage. Combined with the forces in the expansion stage, it is concluded that the main driving forces of displacement are gravity and capillary force. With the increase of the droplet axial distance, the acceleration in expansion stage is shortened, and the peak of velocity is increased, so that the horizontal deviation is first increased and then decreased. This staged feature stems from the competitive relationship between the acceleration period and the maximum speed in the deviate motion. Under different deposition heights and solid-liquid wettability, the deviation distance maintains the same trend. Under a certain axial distance, the deviate distance decreases with the increasing solid-liquid wettability, or the increasing deposition height. The evolution tendency of the horizontal deviation distance is fitted, and the scanning step is optimized to realize the uniform deposition of the inclined column whose inclination angle is consistent with the theoretical result.
2021, 53(6): 1599-1608.   doi: 10.6052/0459-1879-21-022
2021, 53(6): 1609-1621.   doi: 10.6052/0459-1879-21-091
In recent years, artificial neural networks (ANNs), especially deep neural networks (DNNs), have become a promising new approach in the field of numerical computation due to their high computational efficiency on heterogeneous platforms and their ability to fit high-dimensional complex systems. In the process of numerically solving the partial differential equations, the large-scale linear equations are usually the most time-consuming problems; therefore, utilizing the neural network methods to solve linear equations has become a promising new idea. However, the direct prediction of deep neural networks still has obvious shortcomings in numerical accuracy, which becomes one of the bottlenecks for its application in the field of numerical computation. To break this limitation, a solving algorithm combining Residual network architecture and correction iteration method is proposed in this paper. In this paper, a deep neural network-based method for solving linear equations is proposed to accelerate the solving process of partial differential equations on heterogeneous platforms. Specifically, Residual network resolves the problems of network degradation and gradient vanishing of deep network models, reducing the loss of the network to 1/5000 of the classical network model; the correction iteration method iteratively reduce the error of the prediction solution based on the same network model, and the residual of the prediction solution has been decreased to 10−5 times of that before the iteration. To verify the effectiveness and universality of the proposed method, we combined the method with the finite difference method to solve the heat conduction equation and the Burger’s equation. Numerical results demonstrate that the algorithm has more than 10 times the acceleration effect for equations of size larger than 1000, and the numerical error is lower than the discrete error of the second-order difference scheme.
2021, 53(7): 1912-1921.   doi: 10.6052/0459-1879-21-040
Since organisms can accomplish specific tasks through various motion forms, bionic design methods have been received extensive attention from scholars. Inspired by the fact that earthworms have excellent mobility and adaptability in a variety of environments, earthworm-like robots have been proposed and applied in search and rescue, medical treatment and other fields. However, existing earthworm-like robots generally realize rectilinear motion through axial deformation of its body segments, which cannot be applied to realize the erecting function of snake organisms. In order to solve the problem that existing earthworm-like robot cannot erect, a bio-inspired flexible joint with nonlinear multi-stable property is proposed. Based on the proposed bio-inspired flexible joint, a multi-segment bio-inspired erecting structure is built to realize the erecting function of inchworms, snakes and other organisms. First, the model of the bio-inspired erecting joint is proposed. The potential energy of multi-segment bio-inspired erecting structure is obtained, and the dynamic model of the multi-segment bio-inspired erecting structure is established. Then, based on the potential energy and extremum principle, the structural design criteria is proposed to realize required erecting configuration. The effectiveness of structural design criteria is verified and the condition to trigger required configuration is studied by using the dynamic model. Finally, according to different design requirement for the number of erecting segments, corresponding bio-inspired erecting structure is designed. The results show that the design criteria of structural parameters can make the multi-segment bio-inspired erecting structure reach the required erecting configuration and maintain stable at the required erecting configuration. Besides, based on the basin of attraction of different stable configurations, the configuration triggering criteria of the bio-inspired erecting structure is studied, and the configuration triggering criteria composed of the excitation variables and configuration variables is revealed, which provide a theoretical basis for configuration switching of the bio-inspired erecting structure. The bio-inspired erecting structure proposed in this paper provide guidelines for function expansion of the earthworm-like robot. It is also a further improvement of the bionic design theory.
2021, 53(7): 2023-2036.   doi: 10.6052/0459-1879-21-176
Phase equilibrium calculations of complex fluids in shale gas reservoirs require the establishment of advanced numerical models that consider capillary effects, and the design of fast and reliable algorithms to handle the various components in the reservoir fluids in practical working conditions. In this study, we develop a thermodynamically consistent VT-type pore-scale flash calculation scheme based on realistic equations of state suitable for oil/gas reservoirs, e.g. the Peng-Robinson equation of state. The effect of capillarity has been incorporated in the scheme for a more accurate description of the thermodynamic properties of shale gas, and the diffuse interface model is applied to establish a dynamic evolution scheme in the phase equilibrium process, and a convex splitting method is used to model the evolution of compositional moles and volume. In order to accelerate the iterative flash calculations for realistic reservoir fluids containing a large number of components, a self-adaptive deep learning algorithm is developed in this paper with a novel structure to achieve wider applicability to various components in different fluids. The input and output features of the neural network are selected as the key thermodynamic features on the basis of thermodynamic analysis, and the network hyper-parameters have been carefully tuned to achieve a better performance on both accuracy and efficiency. Advanced deep learning technics resolving overfitting problems have been applied in our algorithm. The trained model significantly accelerates the conventional flash calculation based on iterative methods, while a good prediction accuracy has been preserved. Phase stability test and phase splitting calculations are automatically incorporated in our prediction, and we can significantly capture the effect of capillarity on phase equilibrium behaviors. Such a fast, accurate and reliable shale gas phase equilibrium calculation scheme using deep learning algorithms can provide an initial phase distribution field with physical meanings for subsequent multiphase flow simulations, while the number of phases can be also determined. The thermodynamic information and analysis can also be used as a thermodynamic basis for a multiphase numerical model with built-in physical conservation.
2021, 53(8): 1-12.   doi: 10.6052/0459-1879-21-229
The shock tunnel ground test is vitally important to the research of the high-enthalpy aerodynamic characteristics of hypersonic vehicles, and the high-precision aerodynamic measurement is the key technology. When a force measurement test is conducted in an impulse shock tunnel, the flow field is established instantly after the starting process of shock tunnel, at this time, the great impact loads are acting on the force measurement system. The force measurement system is excited under the action of instantaneous impact, and the inertial vibration signal of the system cannot be rapidly attenuated during the short test time. The output signal of the balance will contain the interference due to the inertial vibration, which leads to a bottleneck in the further improvement of the accuracy of the transient force test. In order to improve the force measurement accuracy in the short-duration shock tunnel, the development of high-precision dynamic calibration technology is the key method to improve the performance of balance affected by inertial interference. Therefore, in this paper, Recurrent Neural Network is used to train and intelligently process the balance dynamic calibration data, aiming to eliminate the vibration interference signals in the output dynamic signals. The error analysis of the current method is carried out, and the reliability of the current method is verified. The method is applied to the data processing of force test obtained in shock tunnel, and the effect of inertial vibration on the output signal of the balance is effectively reduced. According to the sample verification analysis of the intelligent model, the relative error of each component load is relatively small, where the case of high-frequency axial force component is about 1%. In the verification of wind tunnel force test data, the good results are also obtained, which are compared with those processed by the Convolutional Neural Network model.
2021, 53(8): 1-9.   doi: 10.6052/0459-1879-21-168
Phononic crystals represent a special kind of artificial periodic composite materials. The peculiar band-gap characteristics provide potential applications in the vibration reduction, wave filtering, sound insulation and acoustic functional devices. However, how to accurately manipulate acoustic and elastic waves is a major challenge for designing phononic crystals. The conventional design method is based on matching the specific application requirements by analyzing and adjusting the geometrical and material parameters of the phononic crystal structures. This method has a low efficiency and can hardly achieve the optimal performance. An artificial neural networks inverse design method for muti-layered phononic crystals based on the Softmax logistic regression and the multi-task learing is proposed in this study. In the proposed method, the Softmax logistic regression is used to choose the material type and the multi-task learing is used to determine the material distribution for each area of the multi-layered structure, so the phononic crystal reverse design problem is transformed into the classification problem of multi-component materials for the unit cell by the proposed method. First, a large number of the samples for the topological structures are randomly generated. Second, the band-gap structures of the samples are obtained by parallel finite element calculation. After that, the relationship between the topological structures and the band-gaps are established by the neural networks. Finally, the trained neural network is ultimately employed to design a phononic crystal structure with the targeted band-gaps, that is, the targeted band gap is used as the input of the neural network, and the trained neural network will output the corresponding cell topology of the phononic crystal unit cell directly. The example shows that the proposed method can obtain one-dimensional (1D) phononic crystals with the targeted band-gaps for the specified application requirements quickly and efficiently. This method provides a new way for the inverse design of phononic crystals.
2021, 53(7): 1807-1813.   doi: 10.6052/0459-1879-21-142
The flow field behind a rotating cylinder with Reynolds number Re = 20000 ~ 90000 and relative speed ɑ = 0 ~ 0.72 was measured experimentally, and the velocity distribution and turbulence distribution at different sections behind the rotating cylinder were analyzed. The flow around a rotating cylinder is numerically simulated by LES method, and the characteristics of the flow field around a rotating cylinder are analyzed. Finally, the theoretical model is used to analyze the flow field variation and came to the following conclusions: When the cylinder rotates counterclockwise, with the increase of the relative speed at the same Reynolds number, the position of the velocity mutation below the wake region of the rotating cylinder moves up with the increase of the relative speed, while the position of the velocity mutation above remains unchanged. With the increase of Reynolds number, the position of velocity mutation below the wake region of the rotating cylinder moves down to a small extent. Through numerical simulation, it is found that the position of the lower vortex behind the cylinder moves up obviously after the cylinder rotates, and the amplitude is large. The lower free shear layer has obvious upward movement, while the upper free shear layer has little change in position. Finally, through theoretical analysis, it is found that the upward movement of the lower vortex on the rear side of the rotating cylinder has a significant effect on the lift force of the rotating cylinder. Under the condition of high Reynolds number and low relative speed, the change of the lower vortex position on the rear side of the rotating cylinder has an important effect on the lift force of the rotating cylinder and the change of the free shear layer in the wake region.
2021, 53(7): 1973-1984.   doi: 10.6052/0459-1879-21-153
Time-dependent transient heat conduction problems are widely encountered in aerospace, civil engineering, metallurgical engineering, etc., and for such problems, accurate and fast numerical approaches have always attracted attention in the past decades. To achieve this goal, this paper proposes an unconditionally stable single-step time integration method for general transient heat conduction systems. In the proposed method, the temperature vector and its time derivative are formulated independently by the Langrage interpolation function, and then the relation between the temperature vector and its time derivative is defined with the weighted residual method. Theoretical analysis, including convergence rate and amplification factor, illustrates that the proposed method is strictly second-order accurate for the temperature vector and its time derivative, and it has the strong algorithmic dissipation (L-dissipation), meaning that it can quickly filter out the unwanted numerical oscillations in the high-frequency range. At present, most existing time integration methods, such as the Crank-Nicolson method and the Galerkin method, are unconditionally stable for linear transient heat conduction systems, but they are conditionally stable for nonlinear ones. To this end, this work improved the stability analysis theory for nonlinear transient heat conduction systems proposed by Hughes and used the improved stability analysis theory to design the free parameters of the proposed method. Because of this reason, the proposed method is unconditionally stable for both linear and nonlinear transient heat conduction problems. Due to the desirable algorithmic stability, the proposed method can still provide accurate and stable predictions for nonlinear transient heat conduction problems where the excellent Crank-Nicolson method fails. Some linear and nonlinear transient heat conduction problems are solved in this paper, and the results of these problems show that compared to the currently popular time integration methods, such as the Crank-Nicolson method and the backward difference formula, the proposed method enjoys noticeable advantages in accuracy, dissipation and stability.
2021, 53(7): 1859-1869.   doi: 10.6052/0459-1879-21-140
As an important component transporting resources such as oil and mineral ores mixture from the seabed to the surface in ocean engineering, vortex-induced vibration (VIV) of flexible risers can be encountered when the risers are subjected to the external environmental conditions. As VIV can lead to structural fatigue for the riser system, which threatens to the facility safety during deepsea resource exploitation, it is of great significance to investigate VIV mechanism and dynamics. Therefore, VIV dynamics of a flexible fluid-conveying riser undergoing external shear current is studied based on the combination of the Euler-Bernoulli beam theory and the semi-empirical hydrodynamic model. The finite element method and Newmark-β method are adopted to discretize and solve the governing equation. The model is firstly validated by comparing with the experimental data in order to examine the accuracy of the present model. Subsequently, cross-flow (CF) VIV response of the fluid-conveying riser is mainly examined and analyzed while various internal flow velocity and fluid density are considered and changed. The results show that when the flexible riser is subjected to both internal flow and shear current, there appears multi-frequency response for CF VIV. And the CF vibrating frequency and the CF root mean square (RMS) displacement are evidently influenced by the internal flow velocity and fluid density. With the increase of the internal flow velocity and fluid density, the CF vibrating frequency decreases while the RMS displacement shows an increasing trend in CF direction. Furthermore, in addition to the variation of the CF vibrating frequency and RMS displacement, the change of internal flow densities can cause notable mode and frequency transitions.
2021, 53(7): 1814-1822.   doi: 10.6052/0459-1879-21-171

High speed and shock compression behind the bow shock of an aircraft head result in very high temperature, which would subsequently lead to a conductivity plasma flowfield around the vehicle. The plasma gas provides a direct working environment for the application of magnetic field. The magnetohydrodynamic (MHD) flow control, which uses the magnetic field to alter the trajectory of ions or electrons, can improve the aerodynamic characteristics of hypersonic vehicles effectively. It has potential prospects on aerodynamic force control and aerodynamic heating management. Besides, the development of superconducting materials and electromagnetic technology contribute to a great upsurge of MHD flow control research significantly. Although research work has been carried out in the field of MHD flow control at home and abroad, its experimental investigation is still challenging. And for the measurement of pressure and heat flux, there is no systematic conclusion because of the limited test conditions and measurement techniques. The results of different researchers may be different from each other and from the theoretical results and numerical simulations. Thus, the influence on the shock stand-off distance, pressure and heat flux under MHD flow control deserves an in-depth investigation. Besides, the numerical simulations and theoretical methods do also need reliable experimental data for variation. The aim of this review paper is to summarize and discuss the developments on MHD flow control technology based on high temperature real gas effect, including the experimental technique, numerical method, and the influence rules and dynamics mechanism of MHD flow control. Its development trend is also discussed and prospected in the paper.

2021, 53(6): 1515-1531.   doi: 10.6052/0459-1879-21-067
Graphene and other two-dimensional (2D) materials possess various excellent properties and hold great promises for next generation of electronic devices and other applications. The mechanical properties are of fundamental importance in the research and application of 2D materials. Despite the fact that 2D materials have been extensively investigated in the past two decades, efforts on the mechanical properties are strikingly lacking and vastly needed. Atomic force microscopy (AFM) is one of the most widely used tools for the mechanical characterizations of low-dimensional materials. Particularly, the AFM-based nano-indentation technique has been extensively employed to explore the mechanical properties of 2D materials. In this review, we first introduce the basic backgrounds of 2D materials and atomic force microscopy. The mechanism and theoretical background of AFM-based nano-indentation are then demonstrated. In the second part, we review the research work by employing nano-indentation on studying the in-plane mechanical properties of 2D materials. The measurement errors of AFM-based nano-indentation and their origins are also discussed. Nano-indentation is perfectly suitable for the in-plane/intralayer mechanical measurement but also greatly limited in probing the out-of-plane/interlayer elasticity, due to the extreme anisotropy of 2D materials. Therefore, in the third part, we introduce an unconventional AFM-based technique - Angstrom-indentation which allows for sub-nm deformation on 2D materials. With such a shallow indentation depth comparable to the interlayer spacing of 2D materials, Angstrom-indentation is capable of measuring and tuning the interlayer van der Waals interactions in 2D materials. The interlayer elasticities of graphene and graphene oxide measured by Angstrom-indentation are discussed as examples in the third part. In the final part, we give a quick overview of a new type of 2D material - van der Waals heterostructure and its novel mechanical properties. We also discuss the potential application of Å-indentation in the investigation of the mechanical properties of van der Waals heterostructures.
2021, 53(4): 929-943.   doi: 10.6052/0459-1879-20-354
This paper experimentally and numerically investigates the fluid-structure interaction between a spark-induced bubble and a floating structure. The boundary integral method is adopted to simulate the bubble dynamic behaviors and the auxiliary function method is used to improve the computational accuracy of the nonlinear fluid-structure interaction. The double-node method is employed to maintain the computational stability of the gas-liquid-solid interaction line. Besides, we use the underwater electric discharge technique to generate bubbles and the high-speed photography to record the bubble dynamics and the structural responses. Firstly, we compare the numerical result with the experimental data and favorable agreement is achieved which validates this numerical model. Through parametric study with respect to the dimensionless distance $\gamma _{s}$ from the initial bubble center to the floating structure (the reference length is the maximum bubble radius), we then find that (1) as $\gamma_{s}$ increases from 0.2 to 2, five types of jetting pattern such as necking together with annular jet ($0.2\leqslant \gamma_{s} \leqslant 0.3)$, contacting jet ($0.4\leqslant \gamma_{s} \leqslant 0.6)$, non-contacting jet ($0.7\leqslant \gamma_{s} \leqslant 1)$, collision of a jet directed towards the floating body and a counter-jet ($1.1\leqslant \gamma_{s} \leqslant 1.3)$ and individual counter-jet ($1.4\leqslant \gamma_{s} \leqslant 2)$ can be formed; (2) it is also found that the velocity of the jet directed towards the structure first increases, then decreases and finally increases again as $\gamma_{s}$ increases; additionally, it may be in the order of $\sim$1000m/s when $\gamma _{s}$ varies from 0.7 to 0.9; as $\gamma_{s}$ increases, the counter-jet velocity increases; (3) under the conditions of the presented experiments, the bubble migrates towards the floating structure when $\gamma_{s} <\mbox{1.5}$ due to the stronger Bjerknes attraction of the floating structure than the Bjerknes repellence of the free surface on the bubble during the collapsing phase. When $\gamma_{s} \geqslant \mbox{1.5}$, however, the free surface has stronger effects on the migratory behavior of the bubble than the floating structure which causes the bubble to migrate away from the free surface at the collapse stage.
2021, 53(4): 944-961.   doi: 10.6052/0459-1879-20-357
Bubble directional transportation using the superhydrophobic surfaces of different specific geometry in the water has broad application prospects in the fields of mineral flotation and biological incubation. The surface orientation of the planar straight superhydrophobic surfaces is a crucial parameter for the related engineering structures. However, it is still unclear that the effect of surface orientation on the bubble slipping along the inclined surface. The high-speed shadowgraphy is used to study the movement characteristics of the slipping bubble ($D_{eq}=2.4$ mm, $Re=500$ $\sim$ 700, $We=7$ $\sim$ 13) on the superhydrophobic linear trajectory with the width of 2 mm under different surface orientations ($-90^\circ\leqslant \beta \leqslant 90^\circ$) and inclination angles ($45^\circ\leqslant \alpha \leqslant 75^\circ$). The slipping velocity of the bubble ($u)$ on the trajectory is approximately stable, and the shape like semi-bullet with multi-ridges. The slipping bubble can be divided into two shape types: the stable and the unstable according to the fluctuation level of the gas-liquid interface. Stable bubble only appear when the inclination angle is small and the azimuth angle is large ($45^\circ\leqslant \alpha <70^\circ$, $| \beta | \geqslant 45^\circ$). As $\alpha$ changes, two kinds of $u$-$\beta$ relations can be found: When $\alpha \leqslant 65^\circ$, the slipping velocity is approximately a unimodal distribution about $\beta =0^\circ$ (the maximum sliding velocity at $\beta =0^\circ$); When $\alpha \geqslant 70^\circ$, the azimuth angle has no significant influence on $u$. The maximum sliding velocity can be upto 0.66 m/s ($\beta =0^\circ$, $\alpha =70^\circ$), which is much higher than that of the free-rising bubble of the similar size ($\sim$0.25 m/s), mainly as a combined effect of the wall-wettability and the inertial force. Surface orientation ($\beta$) and trajectory inclination angle ($\alpha$) affect the slipping velocity and the stability of the gas-liquid interface by changing the driving force, as a buoyance component, of the bubble along the trajectory direction and the bubble frontal area.
2021, 53(4): 962-972.   doi: 10.6052/0459-1879-20-405
Water-air two-phase flow can be found in many practical engineering projects in various fields. To simulate water-air two-phase flow with high accuracy has always been a challenging problem and a highlight in the realm of computational fluid dynamics. Based on the assumption that both water and air can be considered as incompressible fluid, for free surface flow in open water areas, the WENO-THINC/WLIC model for water-air two-phase flow is therefore established. In the developed model, the fifth-order accurate weighted essentially non-oscillation (WENO) scheme is used to solve the Navier-Stokes equation for fluid flows, and the improved multi-dimensional tangent of hyperbola for interface capturing scheme with weighted line interface calculation method (THINC/WLIC) is adopted to track the interface. The fractional step method is applied to discretize and solve the governing equations, the pressure projection method is adopted to compute the pressure field, and the third-order accurate total variation diminishing (TVD) Runge-Kutta (RK) method is used to discretize the temporal terms. In order to verify the model, it is applied to simulate two benchmarks of interface evolution subjected to an external velocity field, Zalesak's disk and shearing vortex, the linear sloshing, and the dam-breaking flow problem. Through comparison of the simulated results with the analytical or experimental ones, adaptability and accuracy of the water-air two-phase model are discussed. The analysis indicates that the simulation outputs are in good accordance with theoretical or experimental results, which means the model is capable to simulate incompressible water-air two-phase flows. With the further improved WENO schemes and THINC schemes, more precise prediction results for water-air two phase flow problems can be achieved with the proposed combined WENO-THINC model.
2021, 53(4): 973-985.   doi: 10.6052/0459-1879-20-430
The study of wave propagation in granular materials is of great significance in metamaterial manufacturing. The boundary design of wave-conducting metamaterials needs to consider the reflection and absorption of stress waves. First, the wave propagation behavior in a one-dimensional particle chain has been studied. According to the difference in the maximum kinetic energy that the particles can obtain at different positions from the boundary, the definition of the boundary area is given. Then the stress wave propagation behaviors of multiple sets of two-dimensional particle samples under impact load are analyzed. The influences of different boundary shapes and particle arrangement on the propagation behavior of stress waves in the pro-border zone have been considered. The results show that the arrangement of particles in the pro-border zone mainly affects the relative position and local porosity of particles near the boundary. The stress wave reflected by the boundary propagates directly in the pro-border zone in the shape of the boundary line. The more complicated the boundary situation (high local porosity, random arrangement of particles), the more accurate the conclusion. The wave velocity mainly determines the shape of the wave-front outside the pro-border zone i.e. in the material center area. The convergence effect of the arc boundary on the wave reflection and the dispersion effect caused by the arrangement of the particles in the pro-border zone are two competing factors, which together determine the reflection process of the wave in the pro-border zone. Finally, the changes of the force chain network in the pro-border zone before and after reflection are analyzed. The distribution of kinetic energy intuitively reflects the phenomenon of reflection hysteresis. The process of particle contact and rebound in the boundary area corresponds to the storage and release of energy. This research will provide reference for the handling of boundary problems in metamaterial design.
Tight oil reservoirs have achieved certain oil increase effect by supplementing formation energy with water-injection huff and puff. However, formation pressure and production decrease rapidly after multiple rounds of water injection. In order to improve the oil enhancement effect of tight oil reservoirs, changing the development method quickly became hotspot research. This paper analysis the stress field distribution near the tip of type I fracture considered the complex fracture morphology of tight oil reservoirs based on Irwin theory and elastic mechanics. A multi-fracture cross-fracture propagation model is established based on seepage mechanics, fractured tight reservoir characteristics and dynamic fracture seepage characteristics. The fracture propagation length is obtained based on the fracture propagation mechanism and the energy conservation principle. It is proposed to turn water-injection huff and puff into unstable pulse water injection according to the principle of reverse imbibition in tight oil reservoirs. Comparative analysis of two energy supplementary generation methods, water-injection huff and puff and pulse water injection, predicting cumulative oil production, pressure and remaining oil distribution in 10 years. The results show that the net internal pressure of the fracture increases with the increase of water injection, and the stress field intensity factor also increases. When the stress field intensity factor reaches the fracture toughness, it will expand at the fracture tip. The expanded and extended natural fractures communicate with each other, presenting irregular and complex fracture networks. Reverse imbibition mainly occurs in the complex fracture networks. Pulse water injection has a high cumulative oil production, a wide area of water injection and strong reverse imbibition. The findings of this study can help for better understanding of the transformation of water-injection huff and puff into pulsed water injection from horizontal wells in fractured tight oil reservoirs. It can give full play to the effects of reverse imbibition and linear displacement. This research provides guidance for it can achieve the purpose of effective oil displacement of the dynamic fracture network.
The fractional-order Bingham model of magnetorheological fluid damper has simple structure and can better describe the hysteretic characteristics of the system. The vibration control of a nonlinear vehicle suspension system with magnetorheological fluid damper under harmonic excitation is studied, where the single-degree-of-freedom 1/4 vehicle suspension system with fractional-order Bingham model of magnetorheological fluid damper is considered. The primary resonance response of suspension system with fractional-order Bingham model under sky-hook damping semi-active control is analyzed, and the approximate analytical solution is obtained by means of averaging method. The amplitude-frequency response equation of the steady-state solution of the suspension system is obtained, and the stability condition of the suspension system is also obtained according to Lyapunov's stability theory. By comparing the amplitude-frequency response curves of the numerical solution and approximate analytical solution, the accuracy of the approximate analytical solution has been verified. The influence of semi-active control on the ride comfort of the vehicle is illustrated by the root mean square values of acceleration of the sprung mass in the vertical direction, it is found that the semi-active control strategy of sky-hook damping can not improve the ride comfort of vehicle in low frequency excitation region of road. Therefore, a combined control strategy of passive control and semi-active control is proposed, and the influence of semi-active control parameter on the vibration control effect is analyzed. The results show that the combined control strategy can not only improve the ride comfort of the vehicle, but also effectively suppress the primary resonance vibration amplitude of suspension system.
The rolling resistance between particles plays an important role in the stability of the particulate systems. In a conventional discrete element method, the rolling resistance model between particles is usually made of springs, dashpots, and sliders in the rotational direction. The particles rolling kinetic energy is dissipated by the viscous (moment) and friction forces. With this model, the viscous force (moment) is directly related to the rolling velocity. Consequently, the dynamic dissipation capacity of particles close to the static state becomes weaker with the rolling velocity decreasing. It is known that the time required to simulate a particle rolling with a velocity close to zero by using the traditional discrete element method is longer than the experimental results. To solve this problem, the mechanism of rolling resistance caused by material hysteresis is analyzed based on tribological principle, and a new discrete element model of hysteresis rolling resistance (HDEM) is established. A hysteresis spring with velocity-independent kinetic energy dissipation is proposed, and its constitutive law’s formula is derived. To verify the new rolling resistance model, the free-rolling of a single round particle specimen on a flat surface is measured through a physical experiment. The measured data are compared with the results simulated by the new rolling resistance model HDEM and the conventional rolling resistance model. The results show that the results based on HDEM are more consistent with the experimental data, and the particle oscillation frequency is in better agreement with the experimental phenomenon observed.
The propeller wake dynamics is a fundamental but very complicated fluid mechanics problem. Its complexity comes from its sophisticated vortex system, which keeps evolving in high-speed shear layer flow. The mechanism of propeller wake behaviors such as the evolution from stable regime to unstable regime and the flow phenomenon in a complex operating environment have always been difficult and hot topics in the field of fluid mechanics. From the perspective of engineering applications, propeller wakes are directly related to the macroscopic characteristics of marine structures, a better understanding of the dynamic characteristic of the propeller wake under multiple operating conditions helps to improve the propulsion performance related to vibration, noise, and structure problems and has important practical significance for the design and optimization of next-generation propellers with good comprehensive performance. In this paper, the propeller wake dynamics are analyzed numerically using DDES, LES and NTM methods and experimentally based on PIV flow measurements, and the triggering mechanism of the instability of the propeller wake is revealed. Based on the evolution mechanism of the tip vortex in the uniform inflow, an evolution model of the tip vortices is proposed. The proposed model can accurately reproduce the evolution process of propeller tip vortex, predict the instant and position of tip vortex merging, which is of great significance to the prediction and control of propeller flow noise and the design of propellers with excellent performance.
2016, 48(4): 756-766.   doi: 10.6052/0459-1879-16-159

2017, 49(1): 3-21.   doi: 10.6052/0459-1879-16-348

2017, 49(1): 22-30.   doi: 10.6052/0459-1879-16-345

2016, 48(4): 767-783.   doi: 10.6052/0459-1879-16-161

2016, 48(4): 741-753.   doi: 10.6052/0459-1879-16-069

2017, 49(3): 550-564.   doi: 10.6052/0459-1879-17-064

2016, 48(3): 519-535.   doi: 10.6052/0459-1879-15-436

2019, 51(1): 1-13.   doi: 10.6052/0459-1879-18-054

2016, 48(5): 1126-1135.   doi: 10.6052/0459-1879-16-070

2017, 49(3): 507-516.   doi: 10.6052/0459-1879-16-399

2012, 44(2): 269-277.   doi: 10.6052/0459-1879-2012-2-20120210
Abstract PDF(4)
Abstract:
In order to predict the cavitating flow characteristics in cryogenic fluids more exactly, a revised cavitation model considering the thermal effect with modified the evaporation and condensation source terms is established, which is based on Kubota cavitation model. The computations for cavitating flows in liquid nitrogen are conducted around an axisymmetric ogive by employing Kubota cavitation model and the revised cavitation model, respectively. The computational results are compared with the experimental data to evaluate the revised cavitation model. It is found that for the results of the revised cavitation model due to considering the thermal effects, the evaporation becomes smaller and the condensation becomes larger, the cavity length is shorter and the cavity interface becomes more porous compared with the results of original Kubota model. The results of the revised cavitation model are more accordant with the experimental data, and it dictates that the revised cavitation model can describe the process of mass transport more accurately in the cavitation process in cryogenic fluids and it is applicable for computations of cavitating flows in cryogenic fluids flow.
2012, 44(2): 252-258.   doi: 10.6052/0459-1879-2012-2-20120208
Abstract PDF(5)
Abstract:
This study focuses on the velocity-annular-effect (VAE) of compressible oscillatory flow inside parallel plate channel. By analyzing the mechanism of VAE, we conclude that VAE, which inevitably occurs in viscous oscillatory pipe flow, is most visible at the phase when the centerline velocity reaches zero. In order to quantitatively evaluate the VAE, coefficient of velocity annular effect (CVAE) was proposed as an index parameter, based on the slope of velocity profile when the centerline velocity reaches zero. Numerical computations with the index parameter CVAE were conducted to analyze the impacts of dimensionless parameters, i.e., Valensi number Va and maximum Reynolds number Remax, on the VAE of oscillatory flow inside parallel plate channel.

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