力学学报

DIRECT NUMERICAL SIMULATION OF HYPERSONIC SHOCK WAVE AND TURBULENT BOUNDARY LAYER INTERACTIONS

Tong Fulin, Li Xin, Yu Changping, Li Xinliang

The peak of local thermal load might be severe due to the interactions of hypersonic shock wave and turbulent boundary layer. It has significant effect on the aerodynamic performance and flight safety of vehicle. Most previous studies on the interaction in hypersonic condition were based on the Reynolds-averaged methods, the corresponding direct numerical simulation is relatively scarce. The direct numerical analysis of hypersonic shock wave and turbulent boundary layer interaction are helpful to the understanding of the relevant mechanisms and the improvement of existing turbulent modes and sub-grid stress models. Numerical analysis of hypersonic shock wave and turbulent boundary layer interactions in a 34° compression ramp are carried out by means of direct numerical simulation for a free-stream Mach number

M ∞ = 6.0

. Based on the Reynolds stress anisotropy tensor, the evolution of turbulent boundary layer along the compression ramp is analyzed. The compressibility effects on turbulent kinetic energy and its transport mechanism are studied through item by item analysis of transport equation. Using dynamic mode decomposition method, the characteristic of unsteadiness in the interaction region is investigated. It is found that along the flow developing downstream, the turbulent state in the near wall region is gradually turned into two-component turbulence from two-component axisymmetric state. The turbulence in outer region approaches the isotropic state from axisymmetric expansion. The results exhibit that there exist significant compressibility effects in the interaction region. The pressure-dilation correlation in turbulent kinetic energy budgets is enhanced significantly. However, it has little effect on the dilatational dissipation. The low-frequency oscillation in hypersonic compression ramp is characterized by the breathing motion of separation bubble. According to the spatial structure of low frequency dynamic modes, the unsteadiness is strongly associated with the separated shear layer.

2018, 50(2): 197-208. doi: 10.6052/0459-1879-17-239

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EXPERIMENTAL INVESTIGATIONS OF EFFECTS OF FOREBODY VORTEX GENERATORS ON THE OSCILLATORY FLOW OF AN AXISYMMETRIC HYPERSONIC INLET

Gao Wenzhi, Li Zhufei, Zeng Yishan, Yang Jiming

Shock oscillations are common flow phenomena encountered in the unstarting processes of hypersonic inlets. They can significantly reduce the airflow capturing and compression efficiency and generate severe unsteady aerodynamic loads. These are highly detrimental to the fight safety of hypersonic vehicles. Aiming at the control of shock oscillation flows, the effects of vortex generators on the oscillatory flows of an axisymmetric hypersonic inlet are studied experimentally. Both started flows and oscillatory flows are investigated with synchronized high speed schlieren imaging and transient surface pressure measurement, as no vortex generators, 0.5 mm and 1 mm thick vortex generators fixed on the inlet forebody. According to the experimental results, minor effects are exerted on the main flowfield and wall pressure of the started flows for vortex generators within 1 mm thickness. However, the vortex generators can substantially reduce the scale of external separations, shorten the oscillatory period and increase the time- averaged pressure magnitude of the oscillatory flows. The effects of vortex generators enhance with the increase of their thickness, and the oscillatory period is shortened from 4 ms for no vortex generator cases to 3.13 ms for 1 mm thick vortex generator cases. In addition, the 0.5 mm thick vortex generators can generally reduce the oscillatory amplitude of surface pressure of the inlet duct, of which decreasing percentage can reach 23%. According to the analysis of the schlieren images and the surface pressure signals, effects of the vortex generators are exerted through streamwise vortexes in the wake flows, including the disturbances of streamwise vortexes exerted on the downstream boundary layers and the interactions between streamwise vortexes and separation regions.

2018, 50(2): 209-220. doi: 10.6052/0459-1879-17-259

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AEROELASTIC STABILITY ANALYSIS OF HEATED FLEXIBLE PANEL IN SHOCK-DOMINATED FLOWS

Ye Liuqing, Ye Zhengyin

In order to analyze the aeroelastic stability of heated flexible panel in shock-dominated flows, a systematic theoretical analysis model is established, and then test its correctness by the numerical simulation method. First of all, based on Hamilton principle and Von-Karman large deflection plate theory, the coupled partial differential governing equations are established with thermal effect based on quasi-steady thermal stress theory. Local first-order piston theory is employed in the region before and after shock waves. The Galerkin discrete method is employed to truncate the partial differential equations into a set of ordinary differential equations. The nonlinear flutter equation is linearized in the equilibrium position based on Lyapunov indirect method,and then Routh-Hurwits criterion is employed to analyze stability of the linear system. Finally, aeroelastic stability of the nonlinear flutter system is obtained. In order to verify the correctness of theoretical results, the nonlinear flutter equations are solved by the fourth-order Runge-Kutta numerical integration method to obtain time history of panel response. The results show that stability of the panel is reduced in the presence of the oblique shock. In other words, the heated panel becomes aeroelastically unstable at relatively small flight aerodynamic pressure. And the LCO amplitude and frequency are observed to increase with shock strength; the stability boundaries of heated flexible panel in shock-dominated flows are distinct from that in regular supersonic flows; only if the non-dimensional dynamic pressure upstream of the shock impingement location and the non-dimensional dynamic pressure downstream of the shock impingement location of the panel satisfy critical condition of flutter stability, will the heated panel be aeroelastically stable.

2018, 50(2): 221-232. doi: 10.6052/0459-1879-17-242

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THE STUDY OF FLOW PAST MULTIPLE CYLINDERS AT HIGH REYNOLDS NUMBERS

Li Congzhou, Zhang Xinshu, Hu Xiaofeng, Li Wei, You Yunxiang

Flow past circular cylinders and square cylinders at high Reynolds numbers are simulated by improved delayed detached-eddy simulation (IDDES), including a circular cylinder, a square cylinder, two tandem circular cylinders and two tandem square cylinders. The mean drag coefficient, the RMS values of lift coefficient and the Strouhal number are computed for various Reynolds numbers, which show a good agreement with previous experimental and numerical simulation data. It is found that the effect of Reynolds number on the global quantities for square cylinders is not much in this range of Reynolds numbers, which is different for circular cylinders. There is no drag crisis phenomenon for flow past a square cylinder at

2.0 × 103 < Re < 1.0 × 107

. The Strouhal number is Reynolds-independent for

Re > 2.0 × 103

, and the Reynolds-independent is also observed for the mean drag coefficient and the RMS lift coefficient. Simulation for two tandem circular cylinders is performed at Reynolds numbers of

2.2 × 104

and

3.0 × 106

for five different spacing

L

to diameter

D

ratios:

L / D = 2.0

, 2.5, 3.0, 3.5 and 4.0. At the critical spacing (

L c / D)

there is found a distinct step-like jump of mean drag coefficient and RMS lift coefficient of the subcritical Reynolds number of

2.2 × 104

, and the mean drag coefficient of the downstream circular cylinder is negative for

L / D < L c / D

. However, the mean drag coefficient and the RMS lift coefficient are seen to be slightly affected by spacing for

Re = 3.0 × 106

, and the mean drag coefficient of the downstream circular cylinder is always positive. Flow past two tandem square cylinders is considered at Reynolds numbers of

1.6 × 104

and

Re = 1.0 × 106

. The abrupt change in mean drag coefficient and RMS lift coefficient at the critical spacing is clearly seen on both upstream and downstream square cylinders for both Reynolds numbers. When

L / D < L c / D

, the mean drag coefficient of the downstream cylinder is negative for both Reynolds numbers.

2018, 50(2): 233-243. doi: 10.6052/0459-1879-17-346

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NUMERICAL STUDY OF STAGGERED ANGLE ON THE VORTEX-INDUCED VIBRATION OF TWO CYLINDERS

Duan Songchang, Zhao Xizeng, Ye Zhouteng, Wang Kaipeng

The vortex-induced vibration of two cylinders with the effect of the stagger angle is studied numerically. A finite difference model based on an in-house code named CIP (constraint interpolation profile) is utilized. The model is built on a Cartesian coordinate system, with the Navier-Stokes equation solved by a third-order accuracy CIP method. The fluid-structure interaction is modelled by an immersed boundary method. Based on the CIP model, two-dimensional flow past two equal-sized circular cylinders placed at Reynolds number (

Re = 100

) with different stagger angle (

α = 0 ° ~ 9 0 °

with a 15 #x00B0; interval) is investigated. Main attention has been paid to the lift coefficient, drag coefficient, displacement response, vortex-shedding frequency and wake pattern of both cylinders. The results show that the drag coefficient and lift coefficient of both cylinders increase monotonically as the stagger angle increases when reduced velocity

U r = 2.0 ~ 3.0

. For reduced velocity

U r = 5.0 ~ 8.0

, with the increase of stagger angle, the drag coefficient of both cylinders changes slightly and the lift coefficient of both cylinders presents a “convex-like” trend and reaches maximum value at

α = 1 5 ° ~ 3 0 °

. In the case of reduced velocity

U r = 10.0 ~ 13.0

, with the increase of stagger angle, the drag coefficient of both cylinders also displays little change and the lift coefficients of both cylinders show a “concave-like” trend and reach minimum value at

α = 3 0 ° ~ 4 5 °

. However, there is no obvious correspondence between the transverse oscillation amplitude and lift coefficient of cylinder as

U r = 10.0 ~ 13.0

. Finally, the wake pattern of both cylinders is analyzed to explain above phenomenon. Above all, the present result could be helpful to the structure design of ocean engineering.

2018, 50(2): 244-253. doi: 10.6052/0459-1879-17-345

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INFLUENCE OF EXPANDED CAVITY ON MIXING PERFORMANCE OF SQUARE-WAVE MICRO-MIXER

Liu Zhaomiao, Wang Wenkai, Pang Yan

Micro-mixer has great application potentials in many fields such as material synthesis, pharmaceutical preparation and biochemical detection due to its advantages of saving reagents, higher mixing index and easy integration. In order to further improve the mixing performance, to ensure the safety of the mixing process and the accuracy of the biochemical reaction results, a new square wave micro-mixer with extended cavity was designed. Under the premise of considering the mixing index and pressure drop, the effects of the width of slit, the length of slit, and the height of extended cavity on the mixing performance of micro-mixer were analyzed by experiment and simulation. The optimal structural parameters were achieved under different Reynolds number (

Re = 20

). Compared with the square-wave micro-mixer, the mixing strength of the square-wave micro-mixer with the extended cavity is higher when

Re

. Moreover, the gap of mixing index between two square-wave micro-mixer reaches maximum, up to 12%, at

Re < 10

. Under the same Reynolds number, the pressure drop of the square-wave micro-mixer with the extended cavity is lower than that of the square-wave micro-mixer. Meanwhile, the analysis for the internal flow field of the square-wave micro-mixer with the extended cavity was carried out. It is found that the eddy current is introduced on the basis of the laminar flow state of the fluid because of the existence of the extended cavity structure, which means the change of the flow state of the fluid in the channel and the enhancement of convection effect, thus the mixing performance is further improved.

2018, 50(2): 254-262. doi: 10.6052/0459-1879-17-291

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EXPERIMENTAL INVESTIGATION ON THE MOTION FEATURE OF INCLINED WATER-ENTRY OF A SEMI-CLOSED CYLINDER

Lu Zhonglei, Sun Tiezhi, Wei Yingjie, Wang Cong

The objective of this present study is to address the cavitating flowing characteristics and kinetic features in inclined water-entry created by a semi-closed cylinder. For this purpose, based on the high speed camera technology, an experimental study of the inclined water-entry of a semi-closed cylinder are investigated. According to the results of the experiment, the special fluctuation flow pattern form of the semi-closed cylinder cavitation is found around the body and the typical kinetic motion law is gained by analyzing the cavity image data. A further insight into the influence of the initial impact velocity and attitude on the movement characteristics such as water trajectory and cavity shape is discussed. The obtained results show that the cavitation flow pattern form of fluctuation cavitation appears two cavity deep closure successively. The cavity evolution of water entry alerts the hydrodynamic distribution, and then influences the movement pattern of the semi-closed cylinder and trajectory characteristics. The internal flow of the cylinder is relatively independent of the flow filed. Interestingly, a periodic flow occurs at the open end. We also found that the surface pressure on the lower wall of the model is larger, which is related to the stability of the water entry. With the increase of water velocity, the characteristics of cavitation fluctuation are obvious, the closing time is delayed and the lateral displacement caused by asymmetric deepening is reduced, but the deflection angle is independent of the inlet velocity. As the initial attitude inclination decreases, the degree of cavitation fluctuation decreases, the closing time is delayed, both the deflection angular velocity and the lateral displacement are increasing subsequently.

2018, 50(2): 263-273. doi: 10.6052/0459-1879-17-191

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DRAG CHARACTERISTICS OF A DRAG-REDUCING SURFACTANT SOLUTION FLOWING OVER A SUDDEN-EXPANSION PIPE

Cai Shupeng, Wang Zhineng, Duan Chuanwei, Li Dan

The minor loss characteristics of a drag-reducing surfactant solution flowing over a circular sudden-expanded pipe have been investigated experimentally with an expansion ratio of 1:1.52. The surfactant used is cetyltrimethyl ammonium bromide (CTAB) with concentrations of 1×10^{- 4} and 2×10^-4 by weight. The maximum drag reduction rate for both solutions is achieved 70% in the fully developed flow in straight pipes. But at lower inlet Reynolds numbers than the critical one, the expansion loss coefficient is only 10%~20% below that for water, while at inlet Reynolds numbers much higher than the critical one, it is found to be much greater than that for water and to approach 1.5 times one for water at the Reynolds number at which the friction factor reaches that for water. Furthermore, a much longer distance is required for the micelle solution flowing across the sudden-expanded step, than 7.8 times the diameter (45 times the step height) of expansion-downstream pipe for water in order to reform a fully developed flow in the downstream. And as inlet flow for the solution of concentration 2 ×10^-4 loses its drag-reducing efficiency, approximately 158 times diameter (920 times the step height) of the expansion downstream pipe is necessary for reforming the fully developed drag-reducing flow in the downstream. From the present rheological measuring results for the surfactant solutions, the drag and its development behaviour of the sudden expansion pipe can be considered to be closely related to the time characteristics in forming and relaxing of the netlike micelle structure induced by shearing.

2018, 50(2): 274-283. doi: 10.6052/0459-1879-17-328

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MESO-MECHANICALLY INFORMED MACROSCOPIC CHARACTERIZATION OF DAMAGE-HEALING-PLASTICITY FOR GRANULAR MATERIALS

Wang Zenghui, Li Xikui

The multiscale characterization of coupled damage-healing and plasticity for granular materials is presented in the frame of second-order computation homogenization. The structure composed of granular materials is modeled as Cosserat continuum at the macroscale. The representation volume element (RVE) possessing the meso-structure of discrete particle assembly is assigned at each of the integration points of the finite element mesh generated in the macroscopic continuum. The incremental non-linear constitutive relation for the discrete particle assembly of RVE is established. The incremental forces and couple moments applied to the peripheral particles on the boundary of the RVE from the medium outside the RVE are expressed in terms of the incremental translational and rotational displacements of peripheral particles of the RVE, the elastic stiffness of the current deformed meso-structural RVE, and the incremental dissipative frictional forces condensed to the peripheral particles of the RVE. Based on the average field theory and the Hill’s lemma, meso-mechanically informed macroscopic incremental nonlinear constitutive relation is derived for the gradient-enhanced Cosserat continuum. The tensorial damage, healing factors, and the tensorial net damage factor combining the effects of both the damage and the healing and the plastic strain to characterize anisotropic damage-healing and plasticity of granular materials are defined in the isothermal thermodynamic framework. In addition, densities of damage and plastic dissipative energies, the density of healing energy are defined so that the damage, the healing and the plastic effects on the failure of granular material are quantitatively comparable. The results of the example problem of strain localization demonstrate validity of the proposed method for characterizing the damage-healing-plasticity occurring in granular materials.

2018, 50(2): 284-296. doi: 10.6052/0459-1879-17-362

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THE CALIBRATION OF MICRODEFECTS INDUCED EQUIVALENT DAMAGE AREA/VOLUME OF BRITTLE MATERIALS BY USING THE M-INTEGRAL

Zhu Wenjie, Lü Junnan, Li Qun

In view of the integrity, reliability and functionality of brittle materials are substantially limited by the existence of microdefects, the calibration of materials’ damage level is of great scientific value and underlying engineering applications. An unified method of evaluating the microdefects induced equivalent damage area/volume is proposed in present study by the aid of M-integral. The damage area/volume induced by underlying multiple microdefects is assumed as equivalent to the area/volume of an individual circular/spherical void while the values of M-integral are equal for the both cases. Firstly, the analytical expression of M-integral is deduced by using the Lagrangian energy density function, the corresponding physical meaning is briefly elucidated. The domain integral method is applied to numerically calculating the M-integral for both two-dimensional (2D) and three-dimensional (3D) cases. Subsequently, the damage calibration process of arbitrary dispersed microdefects is given, the corresponding equivalent damage area for 2D defects and volume for 3D defects are defined. Finally, the elastic 2D plane and 3D body under uniaxial tensile loading condition is simulated, within which a series of different defect configurations are considered, including the singular defect (void, crack and ellipse) and the dual-defects (void-void, crack-crack, void-crack). Corresponding equivalent damage area or volume are calculated, the inherent “interactive effects” and influence factors are elucidated detailedly and quantitatively. Through the proposed damage calibration method in this study, we can estimate the damage level of any microdefects within brittle solids, the calibration process is simple and convenient, which will be beneficial to the damage tolerance design and integrity assessment of engineering structures.

2018, 50(2): 297-306. doi: 10.6052/0459-1879-17-378

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EDGE CRACKING BEHAVIOR OF A COATED HOLLOW CYLINDER DUE TO THERMAL CONVECTION

Peng Zhongfu, Chen Xuejun

Edge cracking is one of major damage modes for coatings subjected to thermal transients. After penetrating across coating thickness, edge cracks usually cause interfacial decohesion and hence result in the detachment of coating from substrate, which leads to the ultimate loss of the protective effect on the substrate. The edge cracking behavior due to thermal convection is studied in this paper for a coated hollow cylinder, where the thermal stress intensity factor is used to characterize the crack driving force. Firstly, by using the Laplace transform technique, closed-form solutions are obtained for the transient temperature as well as thermal stresses. Secondly, the weight function for an edge crack in a coated hollow cylinder is determined by using the three-parameter method proposed by Fett et al. Finally, the thermal stress intensity factor at the edge crack tip is evaluated based on the principle of superposition and the derived weight function. The dependence of the normalized thermal stress intensity factor is examined on the normalized time, edge crack depth, substrate/coating thickness ratio as well as thermal convection severity. It is shown that the peak thermal stress intensity factor occurs neither at the very beginning nor at the thermal steady state of a thermal transient, but at an intermediate instant. The severer thermal convection generates a peak thermal stress intensity factor not only higher in magnitude but also earlier in time. Should other conditions remain invariant, the thermal stress intensity factor is a decreasing function of the edge crack depth; a thicker coating or a thinner substrate may enhance the thermal transient resistance of a coating.

2018, 50(2): 307-314. doi: 10.6052/0459-1879-17-412

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STUDY ON DISPERSION BEHAVIOR AND BAND GAP IN GRANULAR MATERIALS BASED ON A MICROMORPHIC MODEL

Xiu Chenxi, Chu Xihua

The design of metamaterials is paid more attention to control the behaviors of the wave propagation based on response characteristics of shock and wave in granular materials, and it requires in-depth understanding of the propagation mechanism and control mechanism of waves for granular materials. The dispersion behavior and frequency band gap of granular materials are closely related to the heterogeneity. Generally, the dispersion behavior and frequency band gap are based on the elastic theory framework to establish a generalized continuum model including the microstructural continuum or the high order gradient continuum. This study proposes a micromorphic continuum model based on micromechanics for granular materials. In this model, the translation and the rotation of particles are taken into consideration, and the relative motion between particles is decomposed into two parts: the macroscopic mean motion and the microscopic actual motion. Based on this decomposition, a complete pattern of deformation is obtained. The macroscopic deformation energy is defined by a summation of the microscopic deformation energy at each contact. As a result, the micromorphic constitutive relation can be derived, and the corresponding constitutive modulus can be derived by microscopic parameters in terms of contact stiffness parameters and microscopic geometric parameters. The proposed model investigates the propagation of waves in an elastic granular medium, give dispersion curves for different waves such as longitudinal, transverse and rotational waves and predict the frequency band gap. It proves that the proposed model has the ability to describe dispersion behaviors and predict the frequency band gap in granular materials.

2018, 50(2): 315-328. doi: 10.6052/0459-1879-17-420

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A ZERO-ENERGY MODE CONTROL METHOD OF NON-ORDINARY STATE-BASED PERIDYNAMICS

Li Pan, Hao Zhiming, Zhen Wenqiang

Non-ordinary state-based peridynamics suffers from zero-energy mode due to nodal integration. Instabilities of displacement, stress and strain fields are induced and they will affect the computational precision or even ruin the results. Thus, the zero-energy mode needs to be suppressed. However, so far there are no effective zero-energy mode control methods. To address this issue, this work proposes a general and high efficient control method. The specific form of the elastic coefficient tensor corresponding to the nonuniform part of deformation is proposed according to linearized bond-based peridynamic theory in which the difference of micromodulus of different bonds is considered. The force state incorporated by nonuniform deformation is derived through minimum potential principle. The stabilized force state is arrived at by adding the nonuniform force state to the peridynamic force state. The linearlized bond-based peridynamics based stabilized correspondence material model is established and applied to the simulation of the elastic properties and damage process of the plate with a circular hole and the three point bend specimen. The numerical results indicate that the proposed model is effective for controlling zero-energy mode in non-ordinary state-based peridynamics. In comparison with existing zero-energy mode control methods, it has definite physical meaning and the complicated process of adjusting parameters is avoided. Hence, the computational efficiency is evidently improved.

2018, 50(2): 329-338. doi: 10.6052/0459-1879-17-386

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STUDY OF THERMAL CONDUCTION PROBLEM USING COUPLED PERIDYNAMICS AND FINITE ELEMENT METHOD

Liu Shuo, Fang Guodong, Wang Bing, Fu Maoqing, Liang Jun

To accurately model discontinuous problems with cracks is one important topic in computational mechanics. It is very difficult to solve discontinuous problems using continuum mechanics methods based on partial differential equations. However, peridynamics (PD), a non-local theory based on integral equations, has great advantages in solving these problems. In this paper, a new method is proposed to solve heat conduction problems with cracks using coupled PD and finite element method (FEM). This method has both the advantage of the computational efficiency of FEM and the advantage of PD in solving discontinuous problems. The computational domain can be partitioned into two regions, PD region and FEM region. The region containing the crack is modeled by PD, and the other region is modeled by FEM. Application of the coupling scheme proposed in this paper is simple and convenient, since there is no need to introduce an overlapping region between PD region and FEM region. As for the coupling approach, the PD particle is connected non-locally to all particles (PD particles and finite element nodes) within its horizon, whereas the finite element node interacts with other nodes in the finite element manner. The heat conduction matrices of FEM and the matrices of the interaction between PD particles are combined to be a global heat conduction matrix. The Guyan reduction method is used to further reduce the computational cost. The temperature fields of a one-dimensional bar and a two-dimensional plate obtained by the coupling approach are compared with classical solutions. Results show that the proposed coupling method is accurate and efficient. The coupling scheme can be extended to solve crack propagation problems with the thermo-mechanical load.

2018, 50(2): 339-348. doi: 10.6052/0459-1879-17-332

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ONE-DIMENSIONAL TIME-DOMAIN METHOD FOR FREE FIELD IN LAYERED SATURATED POROELASTIC MEDIA BY PLANE WAVE OBLIQUE INCIDENCE

Li Weihua, Xia Peilin, Zhang Kui, Zhao Chenggang

The input of free field under oblique incidence of seismic waves is one of the urgent problems to be solved in the seismic analysis of large structures. Because of the complexity of the problem, there are few studies on the free field of layered saturated poroelastic media at present. In this paper, a 1-D time-domain finite element method is proposed to simulate the plane wave motion in layered saturated poroelastic media overlaid on bedrock subjected to the oblique incidence plane wave. The method is on the basis of Biot dynamic theory for saturated poroelastic media. Firstly, the spatially 2-D problem is transformed into a 1-D time-domain problem along the vertical direction according to Snell’s law. 1-D finite element equations for poroelastic media are established by discretization principle and finite element. Then an exact artificial boundary condition for elastic media is used to model the wave absorption and input effects of the truncated bedrock half space. The global finite element equations for the system of layered saturated poroelastic media overlaid on bedrock are developed according to the drained or undrained boundary conditions between the poroelastic medium and the bedrock. By solving the 1D equations, the displacements of nodes in any vertical line can be obtained combining the method of central differences and Average acceleration of Newmark, and the wave motions in layered poroelastic medium system are finally determined based on the characteristic of traveling wave. The method is verified and by comparing with the frequency-domain transfer matrix method with fast Fourier transform in analyzing two engineering site.

2018, 50(2): 349-361. doi: 10.6052/0459-1879-17-393

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BEHAVIORS OF MODIFIED CHUA’S OSCILLATOR TWO TIME SCALES UNDER TWO EXCITATOINS WITH FREQUENCY RATIO AT 1:2

Xia Yu, Bi Qinsheng, Luo Chao, Zhang Xiaofang

The complicated behaviors as well as the bifurcation mechanism of the dynamical systems with different time scales have become one of the hot subjects at home and abroad, since they often behave in bursting attractors characterized by the combinations between large-amplitude oscillations and small-amplitude oscillations. Since the slow-fast analysis was employed to investigate the mechanism of the special forms of movements, a lot of results related to the bursting oscillations in autonomous systems with two scales in time domain have been obtained. Recently, based on the transformed phase portraits, different types of bursting oscillations as well as the mechanism in the vector fields with single periodic excitation have been presented. However, few works has been published related to the systems with multiple periodic excitations, the dynamics of which still remains an open problem. The main purpose of the manuscript is to explore effect of the multiple scales in such systems. As a example, based on a relatively simple four-dimensional Chua’s circuit, by introducing two periodically changed electric sources, when the two exciting frequencies are strictly resonant, both of which are far less than the natural frequency of the system, a dynamical model with scales under two periodic excitations is established. Note that the combination of the two exciting terms can be transformed as a function of a periodic term with single frequency, which can be regarded as a slow-varying parameter. The equilibrium branches as well as the associated bifurcations with the variation of the slow-varying parameter can be derived by employing the characteristics analysis of the equilibrium points. It is found that the distribution of the equilibrium branches as well as the bifurcation details may changed with the variation the amplitudes of the excitations, which may influence the attractors of the whole dynamical system. Three typical cases corresponding to the different situations of the equilibrium branches are considered, in which different forms of bursting oscillations are observed. Based on the transformed phase portraits, the bifurcation mechanism of the bursting oscillations has been presented. It is found that the trajectory may move almost strictly along one of the stable equilibrium branches, while jumping to another stable equilibrium branch may occur at the fold bifurcation points, the transient process of which leads to the large-amplitude oscillations corresponding to spiking states. Furthermore, it is pointed out that when more fold bifurcation points involve the behaviors of the system, more complicated bursting oscillations may appear.

2018, 50(2): 362-372. doi: 10.6052/0459-1879-18-017

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ANALYSIS OF THE CORED STRANDED WIRE ROPE ON THE NONLINEAR BENDING DYNAMIC CHARACTERISTICS

Guo Jiawen, Wei Cheng, Tan Chunlin, Zhao Yang

When modeling the slender structures such as cable and tether with large flexibility, the complex twirling geometry in practical situation is usually ignored and the cable is simplified as a general beam with homogeneous material. In doing so, the result of dynamic simulation diverges from the physical significance. Therefore, this paper provides an equivalent dynamic method for the typical nonlinear helix wire strand considering the inner line contact under the static and large scale dynamic conditions. The variable bending stiffness affected by the contact friction and bending curvature is obtained through the equivalent constitutive law, by which the massive computation resulting from fine modeling method is able to be avoided. Based on the absolute nodal coordinate formulation, a series of the generalized coordinates have been selected to establish the dynamic differential equations. To verify the equivalent method, a fine strand model based on the finite segment element has been provided to test the accuracy according to the practical strand configuration. Furtherer, the distribution of the variable bending stiffness in practical strand under certain load is obtained through the quasi-static analysis. Compared with traditional ANCF model, the dynamic simulation of the one-tip-fixed equivalent beam under gravity coincides with the fact that the stiffness decreases as well as the flexibility increases in twirling strand. At last, the conversion among each kind of the energy component has been researched. The equivalent model of the twirling strand with large deformation can be used to improve the efficiency of the motion prediction in cable dynamic systems. Besides, the results provide the evidence for wire rope design.

2018, 50(2): 373-384. doi: 10.6052/0459-1879-17-297

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STRESS-CONSTRAINED TOPOLOGY OPTIMIZATION BASED ON IMPROVED BI-DIRECTIONAL EVOLUTIONARY OPTIMIZATION METHOD

Wang Xuan, Liu Hongliang, Long Kai, Yang Dixiong, Hu Ping

It is necessary to limit maximum nominal stress for engineering structural design generally, so as to avoid that the failure of fracture or fatigue occurs. Topology optimization approach is a feasible strategy. The conventional bi-evolutionary structural optimization (BESO) method cannot effectively address the topology optimization problem with stress constraint. To overcome this limitation, this paper suggests an improved BESO method for stress-constrained topology optimization, in which the minimum compliance design problem with volume and stress constraints is considered. A global stress measure based on the K-S function is introduced to reduce the computational cost associated with the local stress constraint. Meanwhile, the stress constraint function is added to the objective function by using the Lagrange multiplier method. Moreover, the appropriate value of the Lagrangian multiplier is then determined by a bisection method so that the stress constraint is satisfied. The model of BESO method for solving stress-constrained topology optimization and its sensitivity analysis are detailed. Finally, three typical topology optimization examples are performed to demonstrate the validity of the present method, in which the stress constrained designs are compared with the traditional stiffness based designs to illustrate the merit of considering stress constraint. The optimized results indicate that the improved BESO method, as a robust algorithm with stable iterative history, achieves an ambiguous topology with clearly defined boundaries, and realizes a design that effectively reduces stress concentration effect at the critical stress areas.

2018, 50(2): 385-394. doi: 10.6052/0459-1879-17-286

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A PARTITIONED STRONG COUPLING ALGORITH FOR FLUID-STRUCTURE INTERACTION USING ARBITRARY LAGRANGIAN-EULERIAN FINITE ELEENT FORULATION

He Tao

In this paper a partitioned strong coupling algorith is proposed for the nuerical resolution of different fluid-structure interaction (FSI) probles within the arbitrary Lagrangian-Eulerian finite eleent fraework. The incopressible viscous Navier-Stokes equations are solved by the sei-iplicit characteristic-based split (CBS) schee. Both the generalized rigid-body otion and the geoetrically nonlinear solid are taken into account. The resultant equations governing the structural otions are advanced in tie by the coposite iplicit tie integration schee that allows for a larger tie step size. In particular, the celled-based soothed finite eleent ethod is adopted for the ore accurate solution of the nonlinear elastic solid without coproising the nuerical efficiency. The oving subesh approach in conjunction with the ortho-sei-torsional spring analogy ethod is used to efficiently update the dynaic esh within the fluid doain. A ass source ter (ST) is iplanted into the pressure Poisson equation in the second step of the CBS schee in order to respect the so-called geoetric conservation law. Given the CBS schee, the ST releases the requireent on the differencing schee of the esh velocity. The partitioned iterative solution is easily achieved via the fixed-point ethod with Aitken’s △² accelerator. The proposed ethodology is in possession of both the flexibility of coupling individual fields and the progra odularity. The flutter of an H-profile bridge deck and vortex-induced vibrations of a restrictor flap in a unifor channel flow are nuerically siulated by eans of the developed partitioned strong coupling algorith. The nuerical results are in good agreeent with the available data, and deonstrate the desirably coputational accuracy and nuerical efficiency.

2018, 50(2): 395-404. doi: 10.6052/0459-1879-17-197

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ADAPTIVE FRONT ADVANCING ALGORITHM FOR COMPUTING TWO-DIMENSIONAL STABLE MANIFOLDS

Yuan Guoqiang*, Li Yinghui

The stable and unstable manifolds are important tools for studying the global characteristics of dynamical systems. The curvature of the stable and unstable manifolds of a general system varies significantly over the global range. Different sizes of simplexes should be used to compute global manifolds. However the size of the computational simplex is globally unified in the existing algorithms. To compute global stable manifolds continuously and efficiently and to improve the adaptability of computational grid simplex to the curvature variation of the manifolds. In this paper, an adaptive front advancing algorithm for computing two-dimensional stable manifolds is proposed based on the PDE method. The basic idea of this algorithm is to adaptively adjust the size of the grid simplex according to the change of the curvature of the stable manifold. First, an initial estimate of the stable manifolds is determined in the stable subspace of the system, and the grid simplex of the initial estimate is set to be the initial size. Then, the considered mesh simplexes are generated adaptively according to the geometric characteristics of the stable manifolds. The coordinates of the considered mesh points are updated according to the tangency conditions and the nearest considered mesh points to the equilibrium point is accepted. Finally, update the front of the stable manifold and adaptively generate new considered mesh simplex. Through this iterative process, the manifold grid is adaptively moved forward. In this paper, the Lorentz manifold and the sphere-like manifold are calculated by introducing the simplex size adaptiveness. Compared with the PDE method, the size of the manifold simplex of the adaptive front advancing algorithm can be adjusted adaptively according to the manifold curvature in the global range. Computing the two-dimensional stable manifold with the adaptive front advancing algorithm can realize adaptive advancement of the stable manifold.

2018, 50(2): 405-414. doi: 10.6052/0459-1879-17-353

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ANALYTICAL SOLUTION FOR POROUS-FLUID FLOW CHARACTERISTICS WITH STRESS JUMP INTERFACIAL CONDITION

Li Qi, Zhao Yiyuan, Hu Pengfei

The complicated mass and momentum transfer problems in the porous region,especially at the interface between porous and free fluid region were analyzed in an asymmetric and coupled porous-fluid channel. By taking the Brinkman-extended Darcy model in the porous region with the velocity continuity and the shear stress jump interface conditions, the fluid transfer characteristics were solved. The analytical expressions for the fluid flow velocity of each region and friction coefficient in the coupled asymmetric channel were proposed by considering the stress jump interfacial condition. Then the effects of interfacial stress jump coefficient, Darcy number and dimensionless off-center thickness of porous layer on fluid flow velocity and friction coefficient were studied. The results show that under certain conditions changing the interface property can obviously control the velocity profile in each region of the coupled channel. For certain values of Darcy number and porous off-center thickness, increasing the interfacial stress coefficient has a reducing effect on the interfacial velocity but an increasing effect on the fluid friction coefficient, and the effect is more obvious when the interfacial stress coefficient is less than 0, in this case that without considering the effect of the interfacial stress coefficient can cause larger error. When both the interfacial stress coefficient and the porous off-center thickness are smaller negative values, the effect by varying the porous off-center thickness on the interfacial velocity is greater than the effect of altering the interfacial stress coefficient, while when the interfacial stress coefficient and the porous off-center thickness of porous layer are larger positive values, the result is quite the opposite. At a larger Darcy number, both the interfacial stress coefficient and porous off-center thickness have greater influence on the fluid friction coefficient; reducing Darcy number to a certain small value, the influence of interfacial stress coefficient on fluid friction coefficient can be neglected and the fluid friction coefficient is only related to the porous off-center thickness, and much more sensitive to a larger porous off-center thickness.

2018, 50(2): 415-426. doi: 10.6052/0459-1879-17-357

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DEFORMATION AND RUPTURE OF BUBBLE WHEN THE HOLLOW DROPLET IMPACTS ON THE OIL FILM

Zhou Jianhong, Tong Baohong, Wang Wei, Su Jialei

Hollow oil droplets are easily formed by the high velocity air turbulence in the process of oil-gas lubrication. The micro bubble has an important influence on the movement process and oil film formation quality when an oil droplet impacting on the wall. The coupled level set and volume of fluid (CLSVOF) method is adopted to simulate the impact of a hollow droplet on the oil film wall. The dynamic mechanism of bubble rupture is investigated by investigating the deformation and movement of bubbles when the hollow droplets are impacted on the wall of the oil film. And the influence of bubble size, collision velocity and liquid viscosity on the characteristic parameters of bubble deformation in the process of bubble wall collision is also analyzed. The results reveal that the bubbles will deform and break up to form film droplet after the hollow droplets impact the wall of the oil film. The change of pressure and velocity gradient inside and outside the bubble is the main cause of bubble rupture. The bubble size has a great influence on the bubble rupture mode, single-point rupture occurs when the bubble is small, larger bubbles are more likely to cause multiple ruptures. The difference of force between different sizes of bubbles is larger, and there is no obvious correlation between the size of the bubble and the moment of rupture. The velocity of the collision and the viscosity of the liquid have a certain influence on the deformation, rupture and rupture time of the bubble. The larger the collision velocity, the greater the kinetic energy of the oils droplet, and the more likely the bubble deformation and rupture. When the viscosity of the liquid increases, the bubble deformation is promoted at the early stage of the movement of the oil droplet, and the rupture behavior of the bubble can be delayed in the later period of the movement.

2018, 50(2): 427-437. doi: 10.6052/0459-1879-17-405

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A NUMERICAL STUDY ON ENDOCYTOSIS OF NANOPARTICLES

Liu Xinyue, Gong Xiaobo, Huang Huaxiong

Receptor-mediated endocytosis is one of the means for cells to exchange materials with their environments. Vesicles coated with ligands on their surface are often adopted for the drug delivery in cancer therapy through receptor-mediated endocytosis as well. In the present work, we used a 3D mathematical model and energy minimization to study the endocytosis process of spherical drug nanoparticles. The total energy of the system including catch bonds was established. The minimization of the energy functional was carried out numerically. The shape of particle and cell membrane in each wrapping stage was obtained, and the influence of particle size on the minimum energy required for passive endocytosis was analysed. The results show that cell membrane and receptor-ligand bonds deformation energies are the major components of the total deformation energy, and each component changes as the wrapping area is increased. There exists an optimal size of nanoparticles for which the total energy consumption is minimum under given membrane stiffness and receptor-ligand bond strength. We also found that at the final stage of wrapping the endocytosis may not be completed because of the breaking of overstretched receptor-ligand bonds. This study provides a theoretical insight for the design of receptor mediated high efficiency drug delivery system.

2018, 50(2): 438-445. doi: 10.6052/0459-1879-17-411

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A BRIEF INTRODUCTION OF COMPLETED KEY PROGRAM PROJECTS ON MECHANICS IN 2017

Bai Kunchao, Zhan Shige, Wang Jianshan, Cao Dongxing

：The paper briefly introduced the completion and evaluation of 15 NSFC key program projects on mechanics in 2017. The projects list and the evaluation assessments provided by expert committee have been given in detail.

2018, 50(2): 446-451. doi: 10.6052/0459-1879-18-087

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