力学学报

2018, 50(6): 1277-1278.

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Wu Chengkang

As a famous scientist specialized in mechanics and applied mathematics, Professor Kuo Yunghuai had made an outstanding contribution to gas dynamics and its applications in China. Before his tragic death in an air accident during a working trip in 1968, Kuo had been the editor-in-chief of Acta Mechanica Sinica. Under his leadership, the Journal has established and kept up high academic standard, fairness and the truth-seeking spirit.
We give here a very brief description of his illustrious life and publish some original articles by his former students,in fond memory of Professor Kuo Yunghuai on the occasion of his 90th birthday.

2018, 50(6): 1279-1282.

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SHOCK TUNNEL THEORY AND METHODS FOR DUPLICATING HYPERSONIC FLIGHT CONDITIONS

Jiang Zonglin, Li Jinping, Hu Zongmin, Liu Yunfeng, Yu Hongru

This paper reviews the scientific research philosophy and discipline layout of Prof. Yung-huai Kuo in the field of thermo-chemically reacting flows occurring in hypersonic flights, and summarizes the research progress in shock tunnel theories and methods for duplicating hypersonic flight conditions. The work has been achieved from 50 years effort dedicated by the High Temperature Gas Dynamics Research Team founded by Prof. Kuo. Rapid generation and rapid application of high temperature gas are an ideal method for wind tunnel operation, and a shock tunnel is such an experimental facility. The fundamental theory and governing equations for shock tunnel are presented first, and these demonstrate the unique advantages of shock tunnel technology for the ground-based testing of hypersonic vehicles. Then the feasibility, basic equations and key problems in the shock tunnel technology for duplicating required hypersonic flight conditions are discussed. Aiming at solving the key problems, a theory is proposed for the detonation-driven shock tunnel from the technical development of detonation driver and its engineering application/verification. Finally, the tailored condition for the detonation-driven shock tunnel is introduced, and lays the foundation for the operation of shock tunnels with long test time. This condition is one of the most difficult problems encountered in developing high-enthalpy shock tunnels. The problem has been investigated for decades, but not solved perfectly. With the proposed theory and methods, several high-enthalpy tunnels are developed for covering the full flight envelope of hypersonic vehicles and its applications show that the theory proposed here is successful and important for aerodynamic and kinetic study in the hypersonic research field.The Team's research work on the hypersonic ground testing facilities has realized the strategic goal of Prof. Kuo's discipline planning, and a world leading research platform was established for exploring hypersonic thermo-chemically reacting flows.

2018, 50(6): 1283-1291. doi: 10.6052/0459-1879-18-238

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SOME KEY PROBLEMS IN THE STUDY OF AERODYNAMIC CHARACTERISTICS OF NEAR-SPACE HYPERSONIC VEHICLES

Ye Youda, Zhang Hanxin, Jiang Qinxue, Zhang Xianfeng

The advantages of the hypersonic vehicle in maneuverable flight in 30$\sim$70km airspace are that it can carry out long-distance maneuverable gliding flight by coupling the lift generated by the air in the airspace and the centrifugal force of high-speed flight, which has important practical value. Although significant progress has been made in the past decades in the study of hypersonic flows, there are still many challenges in the design and research of hypersonic vehicles for near-space long-range gliding, especially the unclear understanding of the flow mechanism under specific flight conditions. This paper introduces the progress of the author's research team in the development of key aerodynamic problems related to hypersonic vehicles in near space, mainly including: the flow model of hypersonic flight in near space is established, and the relative computational aerodynamics method of the system is developed, a suitable sliding boundary condition is studied for the coupling effect of rarefied gas effect and real gas effect under high altitude and high speed flight conditions, the slippage effect including velocity slip condition, temperature slip condition and pressure slip condition in high-temperature chemically reacting flows are considered. A dynamic optimization method for the aerodynamic shape of the aircraft was proposed, and the aerodynamic shape of the aircraft with high lift-drag ratio, which can be used in engineering, was obtained. The dynamic stability theory of high speed aircraft has been established, and great progress has been made in realizing the dynamic stability of hypersonic vehicles. In the end, some key technical and scientific problems that should be paid more attention to in the design of hypersonic vehicles are discussed, and the possible solutions to these problems are discussed.

2018, 50(6): 1292-1310. doi: 10.6052/0459-1879-18-247

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HYPERVELOCITY ISSUES OF EARTH IMPACT BY ASTEROIDS

Liu Sen, Dang Leining, Zhao Junyao, Bai Zhiyong, Huang Jie, Li Yi, Shi Yilei

Asteroid impact on the Earth is one of the potential threats to human beings. There are a series of complex physical, chemical and mechanical phenomena in the process of asteroids entry to the earth's atmosphere and impacting the earth's surface, such as ablation, disintegration, airburst, fireballs, impact craters, ejecta debris, earthquakes, and tsunamis. In this paper, scientific issues on hypervelocity aerodynamics and hypervelocity impact dynamics behind these phenomena are summarized and discussed. The hypervelocity aerodynamic issues include: aerodynamic forces and trajectory during ultra-high velocity ($V =12 ~ 20$ km/s) entry, aerodynamic heating and ablation mechanism of asteroids, heat transfer and thermal response of asteroid structure, high-temperature gas effects, physical characteristics of asteroid entry process. The hypervelocity impact dynamics include: cratering and ejecta debris of land impact, ocean impact and tsunamis, earthquake effects caused by impact. Because the entry and impact process of asteroid and man-made hypervelocity flight vehicles are quite different in velocity, material and structure, the existing research methods are insufficient in both ground test and numerical calculation. Finally, based on trajectory equations, mass loss equation, criterion of fragmentation and model of fragmentation, a model for analysis and evaluation of asteroid entry and impact effect is established, and the Chelyabinsk and Tunguska events are analyzed and reconstructed, together with the overpressure and thermal radiation damage caused by fireballs.

2018, 50(6): 1311-1327. doi: 10.6052/0459-1879-18-313

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AN IMPROVED EXPERIMENT FOR ELECTROMAGNETIC WAVE TRANSMISSION IN SHOCK TUBE

Xiong Zhuang, Zhang Yongyong, Wang Su, Li Jinping, Chen Hong, Fan Bingcheng, Cui Jiping

In the study of the transmission mechanism of electromagnetic wave in plasma in $\varPhi $800 mm high temperature and low density shock tube in the Institute of Mechanics, CAS, under conditions of low density and strong shock, the experimental time at region 2 behind shock is significantly reduced due to the non-equilibrium processes such as gas dissociation and ionization. At the same time, the boundary layer effect leads to both the attenuation of the shock wave and the acceleration of the contact surface towards the shock front. Therefore, the experimental time at region 2 will be further reduced. These two effects lead to the reduction of the experimental observation time and the non-equilibrium state of test gas at region 2, resulting in the instability of data observation and the difficulty of data analysis. A mixture of argon and air is used to replace the pure air as the experimental test gas in $\varPhi $800 mm shock tube. Since argon does not dissociate and is difficult to ionize, the compression ratio of shock is significantly reduced, thereby the test time and the gas length at region 2 are largely increased. The electron densities behind shock were measured with both the Langmuir electrostatic probe and the microwave transmission attenuation method. Meanwhile, the test times at region 2 were measured with the Langmuir probe. The results show that the electron densities in the mixtures of argon and air are in the same order of 10$^{13 }$cm$^{ - 3}$ as in the pure air. Under the same electron density and collision frequency conditions, the test times and the gas lengths at region 2 in two mixtures of 90%Ar+10%Air and 95%Ar+5%Air are about 5-10 times than those in the pure air. The test times at region 2 are about 300$\sim$800 $\mu $s, and the gas lengths at region 2 are about 1-1.5 meter. In electromagnetic wave transmission experiments in $\varPhi $800 mm shock tube by using the argon and air mixture as the test gas, the results are more consistent with the theoretical prediction than those in the pure air.

2018, 50(6): 1328-1366. doi: 10.6052/0459-1879-18-284

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EXPERIMENTAL STUDY ON PROCESS AND MECHANISMS OF WAVE DRAG REDUCTION DURING PULSED LASER INTERACTING WITH NORMAL SHOCK

Wang Diankai, Wen Ming, Wang Weidong, Qing Zexu

Nanosecond pulsed laser has the prominent advantage of high peak power density, so it is easy to break down air to form plasma. It has an important application value in reducing supersonic wave drag. To deeply reveal the mechanisms of wave drag reduction by nanosecond pulsed laser, in this paper, the basic physical phenomenon of the interaction of pulsed laser plasma with a normal shock is studied by experiments. A high resolved schlieren system is developed to reveal the complex wave structures. Time resolution of the schlieren system reaches up to 30 ns, with a space resolution up to 1 mm. A high speed PIV system is applied to measure the velocity and vorticity of the flow field quantificationally. Time resolution of the PIV system reaches up to 500 ns. Features of the spherical shock wave and high temperature area with low density induced by laser plasma are revealed. The flow features and evolution process of the laser plasma impacted by shock wave are revealed. Simulated results are adopted to prove the basic reason of super sonic wave drag reduced by pulsed laser plasma. Research results show that: the initial Mach number of the shock wave induced by laser plasma increases with the laser energy increasing, and the shape is gradually developed from the droplet shape to the spherical shape. The propagation velocity decreases with time and is close to the sound velocity after 50 $\mu$s. The high temperature with low density region is approximate to sphere at first, and then begins to destabilize from the downstream of the laser incident direction. A sharp spike structure is then formed. Under the impact of the normal shock, the high temperature and low density region evolves into an upper and lower symmetric double vortex ring structure, and the size increases with the laser energy. The entrainment and contra-flow of the vortex can remodel the shape of the shock wave of the nose, which is an important way of flow field remodel. It causes a notable reducing of the surface pressure of the aircraft. It is the key mechanism that causes the wave drag reduction of supersonic vehicle.

2018, 50(6): 1337-1345. doi: 10.6052/0459-1879-18-104

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THE CRUCIAL TECHNIQUE INVESTIGATION OF WIND-TUNNEL DROP-MODEL TESTING FOR THE SUPERSONIC INTERNAL WEAPONS

Song Wei, Lu Wei, Jiang Zenghui, Bai Peng

A wind tunnel drop-model testing technique is applied to study the dynamic separational process for the internal weapon from the open weapon cabin ejection for the separation safety problem of supersonic internal weapon ejection delivery, The light model similar design method is used in the wind tunnel drop-model testing which all movement is strictly comparable in addition to lack of vertical acceleration and the lack of the vertical acceleration can cause displacement deviation real displacement. in the end we use a simple formula method to compensation the lacking vertical displacement. the experiment gives the law of separation trajectory and attitude for the different initial ejection separation condition, the test Mach number is $Ma= 1.5$. The results show that the initial separation angle velocity has a great influence on the motion trajectory and the attitude angle for the internal weapon. When the initial separation angle speed is $\omega _{z0}^s = 0^\circ/{\rm s}$, the internal missile firstly moves down to the disturbed flow field far from the cariier the separation,then it gradually moves towards to the carrier direction and collides the carried vehicle. The experimental results of high speed wind tunnel are unsafe,but the result is optimistic after the formula is corrected. This shows that the unsafe separation of missiles obtained by the high speed wind tunnel test may not necessarily occur for the aircraft and the results that obtained by the high speed wind tunnel test are conservative. When the initial separation angle speed is $\omega _{z0}^s = 15^\circ/{\rm s}$, $\omega _{z0}^s = 30^\circ/{\rm s}$, the movement trend of the embedded missile is almost the same and there is no approaching the carrier aircraft. The embedded missile which has a certain initial delivery angle is conducive to the safe separation of internal weapons.

2018, 50(6): 1346-1355. doi: 10.6052/0459-1879-18-180

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STUDY ON EVOLUTION CHARACTERISTICS OF ISOTROPIC TURBULENCE PASSING THROUGH A NORMAL SHOCK WAVE

Hong Zheng, Ye Zhengyin

Shock-turbulence interaction is a kind of important fundamental problem in aerodynamics. Based on solver Helios which applies cell-centered finite difference method (CCFDM), using fifth-order weighted compact nonlinear scheme (WCNS), we conducted direct numerical simulation (DNS) of the situation where isotropic turbulence passes through a normal shock wave. Turbulence statistics are calculated for analysis. We found after shock, density is a little lower than its non-turbulent value, so do temperature and pressure, on the contrary, longitudinal velocity is a little higher than its non-turbulent value. The commonality is that they all show an overshoot immediately behind the shock, after that they gradually approach towards their non-turbulent values along with downstream distance. Longitudinal Reynolds stress suffers a sudden decrease and increases rapidly followed by decaying. This evolution characteristics is captured in linear interaction analysis (LIA) and a transfer of energy from acoustical to vertical modes behind the shock is thought to be accounted for it according to this analysis. Different from longitudinal Reynolds stress, Transverse Reynolds stress suffers a sudden increase then decay monotonically. Anisotropy of Reynolds stress is apparent after shock, and it gradually increases as downstream distance increases. Turbulent kinetic energy suddenly increases and then evolves non-monotonically. Taylor microscale and Kolmogorov scales apparently decrease after shock, indicating the decrease of turbulent length scales, which leads to a requirement of higher resolution of mesh in this zone to solve the flow field. After shock, the root-mean-squares of density, temperature and pressure fluctuations are enhanced, and intensities of density and pressure decrease while intensity of temperature increases.

2018, 50(6): 1356-1367. doi: 10.6052/0459-1879-18-129

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NUMERICAL INVERSITAGION OF MODE EXCHANGE IN HYPERSONIC BOUNDARY LAYERS

Gao Jun, Li Jia

In hypersonic boundary layer, the first mode and the second mode are the main unstable modes which related to the boundary layer transition. In addition to these unstable modes, there is also a type of stable mode. At the leading edge, the phase speed of this stable mode is close to the phase speed of fast acoustic, so it is called fast mode. In the process of receptivity, it plays an important role of exciting unstable modes in boundary layer. Leading edge receptivity theory explains the mechanism of exciting the first mode. For hypersonic boundary layer, the similar solution is used as the basic flow, and the behavior of fast mode and slow mode are researched using linear stability theory and direct numerical simulation. The results indicate the location of the mode exchange is related to mach number. According to the results of linear stability theory, the critical frequency is defined. If the frequency of the disturbance is larger than the critical frequency, the first mode and the second mode are in the same branch; while the frequency of the disturbance is smaller than the critical frequency, the first mode and conjugate mode of the second mode are in the same branch. With the help of adjoint equations of linear stability equations, numerical results are analyzed. Numerical results indicate that when the fast and slow modes go though the region of second mode, they will evolve into the second mode. It can be explained by the propagation of the mode in the nonparallel flow.

2018, 50(6): 1368-1378. doi: 10.6052/0459-1879-18-260

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PRELIMINARY EXPERIMENTAL STUDY ON THE LIQUID METAL FILM FLOW RELATED WITH FUSION NUCLEAR

Ni Mingjiu, Yang Juancheng, Ren Dongwei, Liu Baiqi, Qi Tianyu, Hu Jiansheng, Li Jiangang

Liquid lithium film flow is a superior choice for the plasma facing components in magnetic confinement fusion due to its advantages of removing impurities, protecting the solid surface directly against the plasma. However, it is a great challenge to overcome the magnetohydrodynamic effect on film flow and to realize the uniform spreading of film flow on a solid plate under the influence of an intense magnetic field in the nuclear fusion plant. In the present paper, based on the liquid GaInSn loop and the liquid lithium loop, we carry out experiments of liquid metal film flowing on the inclined electric conductive plate with the applied transverse magnetic field. The visualization method is adopted to observe the surface structures of film flow under different experimental conditions. By comparing the experimental results of liquid GaInSn and liquid lithium, we find that the characteristics of surface waves of liquid metal are the same as that of normal liquid without a magnetic field, namely the surface waves become chaotic with the increase of Reynolds number, while the characteristics change greatly under the influence of transverse magnetic field. The surface waves of liquid GaInSn film flow become quasi two-dimensional and parallel to the magnetic lines, while the liquid lithium film flow is nearly stagnated at a fixed position, indicating the existence of a strong magnetohydrodynamic resistance. Moreover, the stagnation point moves far away from the film generator at a larger Reynolds number. Finally, by analyzing the force loaded on the film, we make a detailed explanation of the phenomenon that the magnetohydrodynamic effect is much stronger on the liquid lithium flow than on the liquid GaInSn flow.

2018, 50(6): 1379-1386. doi: 10.6052/0459-1879-18-367

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DIRECT NUMERICAL SIMULATION OF MHD FLOW IN CONDUCTING SQUARE DUCTS WITH INCLINED FRINGING MAGNETIC FIELD

Mao Jie, Wang Yanli, Wang Hao

An essential issue in the application of liquid metal blanks in thermal nuclear fusion reactors is the additional magnetohydrodynamic (MHD) pressure drop caused by the interaction of the liquid metal flow with a strong magnetic field. The additional MHD pressure drop is much higher than hydrodynamic pressure drop. Argonne liquid metal experiment (ALEX) group in Argonne National Laboratory of American studied the MHD effect of Liquid Metal flow in ducts and pipes subjected to a fringing magnetic field by experiments. The experiments were introduced as one of the benchmark cases to test numerical codes for liquid metal blankets. As the liquid metal blankets would be subjected to the magnetic field with different directions, liquid metal flow in a square duct subjected to an inclined fringing magnetic field has been numerically studied in this paper. The model is based on one of the ALEX's experiments. With constant Hartmann number, Reynolds number and wall conductance ratio, the effects of the angle between the magnetic field and the side wall on the velocity, the electric current, and the pressure distribution have been investigated using three-dimensional direct numerical simulation method. The results show that the distribution of the velocity, the electric current and the pressure on the cross section rotates with the increase of the inclination angle of the magnetic field. In the uniform part of the inclined magnetic field, the velocity jets located at the junction corners of the Hartmann layer and the side layer which are parallel to the external magnetic field. The pressure gradient in the part of the uniform magnetic field increases firstly and decreases with the increase of the inclination angle of the magnetic field. In the decreasing part of the inclined magnetic field, the high-speed velocity jet is transferred to another pair of corners due to the three-dimensional MHD effect along the streamwise direction. The three-dimensional MHD pressure drop at the cross-section of the duct increases with the increase of the inclination angle of the magnetic field. Furthermore, the maximum value of the velocity jets decreases, the second flow increases and the laminar-turbulent transition of the duct flow occurs.

2018, 50(6): 1387-1395. doi: 10.6052/0459-1879-18-276

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FLOW CONTROL OVER A CIRCULAR CYLINDER USING PLASMA ACTUATORS

Zhang Xin, Huang Yong, Li Huaxing

In order to develop a novel technology of Moving Surface Boundary Layer Control (MSBLC) and promote efficiency of flow control technology, flow control over a circular cylinder using two Dielectric Barrier Discharge (DBD) symmetrical plasma actuators was investigated by PIV technology, force measurements and hot wire. The circular cylinder which had a diameter of 50 mm and a spanwise length of 480 mm was placed on the support sting. Here, two symmetrical DBD plasma actuators were mounted at the top and bottom of the circular cylinder respectively. The testing model which was made of aluminum was adopted as the covered electrode and was wrapped by the KAPTON film. The exposed electrodes were copper foil tape which was 2 mm wide and 0.02 mm in thickness. Firstly, time-resolved PIV results in still air indicated that a pair of the starting vortexes which were rotating in the opposite direction was induced as the symmetrical plasma actuator was just started to work. The starting vortexes rolled up and moved away from the wall with time. Then, a bi-directional wall jet on both sides of the exposed electrode was formed by the symmetrical plasma actuator. Due to Coanda Effect, the induced jet moved along the surface of circular cylinder. Secondly, the force and hot wire measurement results under incoming flow suggested that vortex shedding from the circular cylinder can be suppressed significantly by the symmetrical plasma actuators and the drag coefficient was decreased by 21.8％ at the wind speed of 10 m/s. Besides, it can be found that a steady vortex can be formed on the surface of cylinder thanks to the interaction effect between the incoming flow and the induced flow filed by plasma actuator. The induced vortex can transfer high momentum from main flow to the near-wall fluid by rotating and moving, enabling the boundary layer to withstand the adverse pressure gradient and prevent the separation around the circular cylinder and acting as the virtual MSBLC. Compared to the traditional MSBLC, the novel technology of MSBLC which is based on plasma actuator without sophisticated and cumbersome devices cannot bring extra drag and has vast application prospect.

2018, 50(6): 1396-1405. doi: 10.6052/0459-1879-18-279

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HEAD-ON COLLISION BETWEEN TWO HYDROELASTIC SOLITARY WAVES WITH PLOTNIKOV--TOLAND'S PLATE MODEL

Bhatti M. M., Lu Dongqiang

Head-on collision between two hydroelastic solitary waves propagating at the surface of an incompressible and ideal fluid covered by a thin ice sheet is analytically studied by means of a singular perturbation method. The ice sheet is represented by the Plotnikov--Toland model with the help of the special Cosserat theory of hyperelastic shells and the Kirchhoff--Love plate theory. The shallow water assumption is taken for the fluid motion with the Boussinesq approximation. The resulting governing equations along with the boundary conditions are solved asymptotically with the aid of the Poincaré--Lighthill--Kuo method, and the solutions up to the third order are explicitly presented. It is observed that solitary waves after collision do not change their shapes and amplitudes. The wave profile is symmetric before collision, and it becomes, after collision, unsymmetric and titled backward in the direction of wave propagation. The wave profile significantly reduces due to greater impacts of elastic plate and surface tension. The graphical comparison between linear and nonlinear elastic plate models is also shown as a special case of our study.

2018, 50(6): 1406-1417. doi: 10.6052/0459-1879-18-287

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APPLICATION OF SINGULAR PERTURBATION IN THE ANALYSIS OF LAMINAR PREMIXED FLAMES

Chen Zheng

Singular perturbation is widely used to obtain the approximate solutions for mechanical problems. A typical problem is the boundary layer in fluid mechanics. Yung-Huai Kuo has developed the singular perturbation theory for the boundary layer over a plate. Similar to the boundary layer in fluid mechanics, the laminar premixed flame in combustion can also be analyzed by the singular perturbation method, which is usually called as the large-activation-energy asymptotics. The laminar premixed flame structure consists of the preheat zone, reaction zone, and equilibrium zone. Under the limit of the large activation energy, the chemical reaction rate is very sensitive to the temperature and thereby chemical reaction only occurs in the very thin reaction zone. The ratio between the reaction zone thickness and the preheat zone thickness is a small parameter, based on which the asymptotic analysis can be conducted for a laminar premixed flame. This paper reviews the application and progress of the large-activation-energy asymptotic analysis in the one-dimensional planar premixed flame and spherically propagating flame. First, the structure of the premixed flame and its different characteristic length scales are introduced. The length scale separation due to large activation energy is analyzed. The detailed derivation of the large-activation-energy asymptotic analysis of a planar premixed flame is presented. The analytical solutions for the preheat zone, reaction zone, and equilibrium zone are first sepratedly obtained and then matched aound the interfaces among these three zones. The effects of radiation heat loss on premixed planar flames are discussed. Then, the application of the large-activation-energy asymptotic analysis to the ignition and spherically propagating flame is introduced. It is pointed out that in order to accurately predict the critical ignition conditions, the theory should be able to describe both the ignition kernel development and the spherical flame propagation afterwards. The ignition and flame propagation theory considering chain reactions is discussed, and the trend of theoretical research on flame instability is described. Moreover, the effects of radiation heat loss on spherical flame propagation are discussed. Finally, the future research directions are prospected based on the current research progress, which includes multi-step chemistry, low-temperature cool flame, complicated flow and radiation reabsorption.

2018, 50(6): 1418-1435. doi: 10.6052/0459-1879-18-243

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THERMAL INSTABILITY OF VISCOELASTIC FLUIDS IN POROUS MEDIA

Kang Jianhong, Tan Wenchang

Based on the modified Darcy model, the status and progress in research of thermal instability of viscoelastic fluids in porous media are reviewed. By using the method of linear stability analysis, the effects of the geometry of porous media (i.e. horizontal porous layer, porous cylinder and porous cavity), thermal boundary conditions (i.e. bottom heated with constant temperature, bottom heated with constant heat flux, bottom with Newtonian heating and open top), flow model of viscoelastic fluids (i.e. modified Darcy-Jeffrey, Darcy-Brinkman-Oldroyd and Darcy-Brinkman- Maxwell models), local thermal non-equilibrium and rotation on the critical Rayleigh number of thermal instability of viscoelastic fluids can be calculated. By using the method of weakly non-linear analysis, the bifurcation from the basic state and the analytical solution of Nusselt number at the neighborhood of critical point can be obtained. By the numerical simulation method, the evolution of flow pattern as well as the variations of Nusselt number at high Rayleigh number can be revealed. It has been found that (1) the elasticity of viscoelastic fluids can destabilize the oscillatory convection; (2) the rotation effect and local thermal non-equilibrium effect can suppress the thermal instability of viscoelastic fluids; (3) at the neighborhood of critical point, the bifurcation from the basic state for stationary convection is supercritical, while the bifurcation for the oscillatory can be supercritical or subcritical, mainly depending on the values of viscoelastic parameters, Prandtl number and Darcy number; (4) with the increasing Rayleigh number, the flow pattern of thermal convection evolve from one-cell pattern into multi-cell roll pattern, and finally a chaotic pattern.

2018, 50(6): 1436-1457. doi: 10.6052/0459-1879-18-309

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NUMERICAL ANALYSIS OF THREE-DIMENSIONAL ELECTRO-CONVECTION OF DIELECTRIC LIQUIDS IN A CUBICAL CAVITY

Wu Jian, Zhang Mengqi, Tian Fang-Bao

A full three-dimensional numerical study on the electro-convection of dielectric liquids contained in a cubical cavity is reported. All boundaries are solid walls. The four lateral sides are electrically insulating and the top and bottom walls are planar electrodes. The flow motion is driven by the volumetric Coulomb force exerting on the free charge carriers introduced by a strong unipolar injection from the bottom electrode. The charge injection takes place due to the electro-chemical reaction at the interface between liquid and electrode. The unsteady Navier-Stokes equations and a reduced set of Maxwell's equations in the limit of electroquasistatics are solved using an efficient finite volume method with 2$^{\rm nd}$ order accuracy in space and time. Considering the strong convection-dominating nature of the charge conservation equation, a total variation diminishing scheme is specially used to solve this equation in order to obtain physically-bounded and accurate solution. It is found that the flow is characterized by a subcritical bifurcation in the finite amplitude regime. A linear stability criterion and a nonlinear one, which correspond respectively to the onset and stop of the flow motion, are numerically determined. Since the nonlinear criterion is smaller than the linear one, there exists a hysteresis loop. Compared to the free convection in the infinitely large domain case, the constraint imposed by the lateral walls dramatically changes the flow structure and increases the two criteria. In addition, the spatial features of charge density distribution and velocity field are discussed in details. A central region free of charges is observed. This void region is formed due to the competition between the fluid velocity and the drift velocity, and it is closely related to the subcritical bifurcation feature of the flow. In addition, computations are also performed with a case with smaller domain sizes, and the results show that the linear bifurcation of the flow is supercritical. Once the system losses its linear stability, a steady convection state without charge void region is reached. The present results extend previous research on the two-dimensional electro-convection in confined cavities, and they provide reference for the three-dimensional theoretical analysis of the linear and weakly nonlinear stability.

2018, 50(6): 1458-1469. doi: 10.6052/0459-1879-18-301

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HIGH-ORDER DDG/FV HYBRID METHOD FOR VISCOUS FLOW SIMULATION ON UNSTRUCTURED/HYBRID GRIDS

Shao Shuai, Li Ming, Wang Nianhua, Zhang Laiping

In recent years, the discontinuous Galerkin method (DGM) has become one of the most popular high-order methods on unstructured/hybrid grids due to its excellent features: high accuracy, compact stencils and high parallelizability. At the same time, DGM is recognized as computationally intensive with respect to both computational costs and storage requirements. When it simulates the flow over 3D realistic complex configuration with large-scale grid, the huge memory requirements and high computational costs of DG method are usually unbearable. Recently, based on the idea of `hybrid reconstruction', a class of DG/FV hybrid schemes has been proposed and developed, which can successfully reduce the expensive computational costs and memory requirements. In this work, we introduce the efficient viscous term discretization method DDG into DG/FV method, and get a new hybrid scheme named as DDG/FV in order to further improve the efficiency of DG/FV scheme for simulating viscous flow problems. A variety of typical 2D laminar cases are tested, including Couette flow, laminar flow over a flat plate, steady flow over a cylinder, unsteady flow over a cylinder, and laminar flow over a NACA0012 airfoil. According to these cases, we select proper coefficients for DDG formulation, verify the order of accuracy and computational efficiency of DDG/FV for the simulation of steady and unsteady viscous flow, and compare the simulation results and computational efficiency with the widely used BR2-DG scheme. The numerical results demonstrate that the new DDG/FV hybrid scheme can achieve the designed order of accuracy. It can achieve the same accuracy as BR2-DG scheme with efficiency increased by more than 2 times for steady problems with implicit time scheme and by 1.6 times for unsteady problems with explicit time scheme in solving Navier-Stokes equations on unstructured/hybrid grids. And in some cases, the DDG/FV scheme has stronger robustness than the BR2-DG scheme. Because of the improvement of efficiency and robustness, the DDG/FV hybrid scheme shows good potential in future applications.

2018, 50(6): 1470-1482. doi: 10.6052/0459-1879-18-199

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