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Wang Piguang, Lu Ranran, Yan Qiushi, Li Shutao, Du Xiuli
Abstract The infinite domain absorption boundary and explosion wave input method are two keys of numerical simulation research on underwater explosion. This paper draws on the seismic wave input method based on the internal substructure and the multiscale analysis method for explosion problems based on the substructure of explosion source and proposes a shock wave input method for underwater explosion based on the substructure of explosion source considering that the underwater explosion load and the seismic load belong to the same fluctuation problem. The method first decomposes the shock wave field in the explosion source region and the free wave field motions were transformed into the equivalent explosive loads, which enables the input of shock waves in the underwater explosion problem. In this paper, a circular substructure of explosion source is used, and a one-dimensional model in AUTODYN software is used to calculate the free shock wave pressure in this region under the action of the underwater explosion. Further, based on the continuous fractional approximation method, a high-precision time-domain artificial boundary condition is proposed to simulate the radiation effects of infinite domain, which can be placed close to the structure and explosive source substructure is proposed. The method proposed in this paper transforms the underwater explosion load through the substructure of explosion source and adopts the high accuracy absorption boundary to greatly reduce the calculation area, which not only ensures the calculation accuracy, but also reduces the number of elements, with high calculation efficiency and practicability. Finally the numerical example is analyzed to verify the accuracy of the model and method of this paper, The pressure time history curves of measuring points during shock wave and bubble pulsation stage under underwater explosion are simulated, and the effect of circular structure on the scattering effect of underwater near-field explosion wave is studied.
, Available online  , doi: 10.6052/0459-1879-22-450
Gong Geng, Hu Weibo, Wu Jianhui, Tu Guohua, Chen Jianqiang
Boundary layer transition can significantly increase the wall friction and heat flow of hypersonic vehicles, which often plays an important role in the design process of hypersonic vehicles. A coupled control method of microgrooves and boundary layer suction was proposed for the control of the hypersonic transition in this paper. The stability of a Ma 4.5 flat-plate boundary layer and the control effects of transition were studied using direct numerical simulation and linear stability theory. The results show that there exist both of the unstable first and second mode without the coupled control, between which the two-dimensional second mode is the most unstable one. Sole microgrooves lead to a significant reduction in the second-mode growth rate and a weak excitation of the first-mode. In contrast, the "microgrooves-suction" method not only enhances the suppression effects of the second-mode wave but also weakens the excitation degree of the first-mode. For the microgrooves located upstream of the synchronization point, the growth of the disturbance wave can still be suppressed in the control region but may be promoted in the downstream; while the "microgrooves-suction" method can effectively avoid the disturbance growth. In addition, with the increase of suction intensity, the unstable region of the second-mode shrinks obviously and the frequency becomes higher; while the first-mode only change slightly. Due to the enhancement of "microgroove absorption" and "acoustic wave scattering" effects caused by the suction, the “microgrooves-suction” coupled method reduces the thickness of boundary layer and enhances the expansion and compression waves system respectively, which achieves an inhibition effect of 12.63% and 28.02% for the growth rate of the first and second mode, respectively. The results show that the "microgrooves-suction" coupled method has the advantages of wide frequency application and flexible location, and also states the achievement of multi-mode control effects in a certain degree.
, Available online  , doi: 10.6052/0459-1879-22-530
Zhang Weipeng, Ren Jianxin, Guo Hang, Wang Zibin, Hu Jian
The evolutions of propeller wake can be impacted by interaction between the propeller and rudder which results in turbulence enhancement in the propeller wake. The turbulence in the propeller wake worsens vibrations and noise on vessels. The intensive research aimed on the wake evolution in the propeller-rudder interaction brings sights on the control of propeller wake and relief of vibrations and noises. Hence, the rudders with different chord and profile are employed to investigate the impact of rudder geometry on the evolutions of propeller wake. Large Eddy simulation method is used to simulate the turbulence in the flow field. The propeller vortices obtained with different rudder chords and profiles are compared in present study. The impact of trapezoidal rudder on the propeller wake evolution are studied based on the research aimed on the impact of rudder chords and profiles on the propeller wake. The distributions of turbulence kinetic energy in the interaction between the trapezoidal rudder and propeller are also researched in present study. Results show that both of rudder chord and rudder profile can impact the evolutions of propeller wake. Larger chord and thicker profile of the rudder enhance the span-wise displacement of propeller tip vortices. Thinner profile leads to more intense displacement of propeller hub vortex. The vortex trajectory and pressure fluctuations on the rudder surface indicate that trapezoidal rudder enhances the span-wise displacement occurring in anti-direction of rudder tapering. This enhancement takes asymmetry to the propeller wake around the rudder and in the downstream. The turbulences in the propeller wake can be related to the collisions between the propeller vortices and rudder, between the propeller vortices and rudder trail vortex, between the propeller tip vortices and hub vortex. The more intense span-wise displacement of propeller wake induced by trapezoidal rudder brings earlier enhancement on turbulence in the propeller wake.
, Available online  , doi: 10.6052/0459-1879-22-552
Qu Yipeng, Sun Xiuting, Xu Jian
It is observed that the necks of birds generally have the characteristics of rigid-flexible coupling and variable stiffness, which can cause large head deformation with the body movement when the bird moves as walking or flighting. In the fields such as robotics and aerospace, structures with the characteristics of large deformation, variable stiffness and rigid-flexible coupling are generally required to achieve relevant functions. Inspired by the structure of the bird neck, this paper proposes a kind of rigid-flexible coupling structure imitating the chicken neck which clarifies its bionic mechanism, and establishes the mechanical model for flexible large deformations. Firstly, it discovers that bionic structure must have the characteristics of high-degree of freedom and rigid-flexible coupling based on the biological anatomical structure of the chicken neck. A bionic single standard unit is constructed according to the characteristics of the chicken neck skeleton and a model of spring connection between nodes is constructed according to the connection mode of muscles, thus a bionic rigid-flexible coupling structure is established by combining these two elements. Then, this paper describes the distribution and function of the elastic elements between nodes by defining the connectivity matrix, with which the force balance equation of any standard rigid section under any movement is obtained. Finally, several representative working conditions are selected for simulation, which verifies the accuracy of the established theoretical modeling method by the comparation with finite element analysis, and the nonlinear variable stiffness characteristics of the structure are displayed; The relations between deformations under four typical plane bending conditions and corresponding muscles force generation are obtained. The analysis on the bionic rigid-flexible coupling structure clearly shows the characteristics of bionic mechanism of chicken neck, which gives the theoretical calculation model for large deformations, representing the nonlinear stiffness characteristics. It also explains the deformation mechanism of the chicken neck.
, Available online  , doi: 10.6052/0459-1879-22-553
Lu Dechun, Gao Yixin, Wang Guosheng, Song Zhiqiang, Du Xiuli
The peridynamic (PD) method has been widely used to study the cracking and failure of reinforced concrete structures. The control equations and material parameters of the traditional PD method are determined based on the energy equation of homogeneous materials. When dealing with the interaction between different materials, the mechanical behavior of their interfaces cannot be reasonably reflected in the traditional PD method. In order to solve this problem, the interaction model of material points in the interface region of the PD method is proposed by analyzing the bond-slip mechanism of the interface of reinforced concrete. Then the bond-based PD method considering the interface bond of reinforced concrete is developed based on the proposed interaction model. Based on the energy density equivalent principle of the bond-based PD and continuum mechanics, the method to determine the interface micro elastic parameters of the PD is proposed. According to the stress distribution law of concrete between steel ribs, the equivalent relationship between the point radius of interface material and the radius of restricted wedge is obtained. Based on the slip deformation corresponding to the peak stress of the interfacial bond slip curve, a method for determining the critical tensile constant of the interface is presented. So far, the PD method for the interface in the reinforced concrete has been established. By comparing with the pull-out test of two groups of reinforced concrete members, the developed interface PD method of the reinforced concrete is verified, and numerical tests of reinforced concrete members under different conditions are carried out. The results show that the developed PD can reasonably reflect the influence of rebar diameter, anchorage length, concrete strength and rib spacing on the bond behavior of reinforced concrete interface, which well reflects the rationality and superiority of the proposed method, which reflects the rationality and superiority of the proposed method.
, Available online  , doi: 10.6052/0459-1879-22-470
Wu Xueyan, Li Yu, Xie Yanyan, Li Fei, Chen Sheng
The Energy-Minimization Multi-Scale (EMMS) theory has been introduced into the multiphase particle-in-cell (MP-PIC) method to establish the heterogeneous EMMS solid stress model to account for the effect of non-uniform solid distribution. However, the calculation process is very complex and also very time consuming for this heterogeneous solid stress model. The expression of the heterogeneous EMMS solid stress can be obtained by manual fitting method. However, the fitting variable describes heterogeneous solid distribution as well as the fitting function describe the shape of solid stress are required for manually fitting. Since the heterogeneous solid stress function is highly nonlinear in nature, the fitting precision is not high enough for the manually fitting model. And there is an obvious deviation between the fitting correlation and the original EMMS solid stress, because it is hard to find out an appropriate parameter to characterize the heterogeneous solid concentration distribution as well as to find out an appropriate fitting function. In order to solve the above problems, an artificial neutral network (ANN) based machine learning method was proposed to avoid the characterization of the local distribution of solid volume fraction. Subsequently an ANN solid stress model which accounts for the detailed distribution of particle concentration was proposed to improve the fitting accuracy. Firstly, a two-marker based ANN solid stress model was established based on local particle concentration and particle non-uniform distribution index. Further, particle concentrations in the current cell and its neighboring cells were arrayed to represent the particle concentration distribution, thus to establish the ANN solid stress model based on particle concentration distribution. Then, the two models are compared with the EMMS solid stress model, and the effects of grid resolution and coarse-graining ratio on the model are also tested. The simulation results predicted with ANN model agreed well with that of the EMMS solid stress model, and the dependence of simulation results on grid resolution and coarse-graining ratio was also reduced.
, Available online  , doi: 10.6052/0459-1879-22-511
Longlong Li, Huijun Fang, Tengze Ge, Yuewu Liu, Feng Wang, Danlu Liu, Jiuge Ding, Yueyu Yu
Carbon Capture and Storage (CCS) could help a lot to achieve carbon peaking and carbon neutrality goals and is an effective way to deal with the Greenhouse effect. Among the geologic sequestration formations, the cavities resulting from deep underground coal gasification (UCG) becomes a hot topic in the research area of geologic CO2 sequestration. However, compared with conventional sequestration methods, the related work is still in the theoretical exploration stage and lack of trial tests. To promote the development of UCG cavity sequestration, we have done the work as follows. First, we introduce the research progress of UCG and post UCG cavity sequestration, and divide the development of the latter one into three stages including the early stage of conception, stage of quantitative assessment and feasibility analysis, and stage of mechanism analysis. Currently, it is still in a stage of theory exploration. Second, we compare the UCG cavity sequestration with the conventional sequestration options in detail from the perspective of injectivity, sealing capacity, economy, storage capacity, and trapping mechanism. The results show that the UCG cavity sequestration holds an excellent injectivity, has a similar sealing capacity to the unmined coal seams but more complex, is capable to reduce transport cost a lot, has a great potential in storage capacity, and has complex trapping mechanisms, owing to the additional effects of cavity morphology, wall properties, and interactions between supercritical CO2 and in-situ fluid on the injection and storage processes. Third, we point out the key scientific and engineering issues, and basic future development trends of the UCG cavity sequestration. Based on the above work, we suggest that the government introduces some policies to encourage and support the development of UCG and post cavity sequestration which could enrich the CCS family and promote the clean and low-carbon utilization of coal resources.
, Available online  , doi: 10.6052/0459-1879-22-538
In recent years, a family of methods based on integral correction have been developed to address the increasing requirements of accuracy and efficiency of orbit computation in aerospace engineering. These methods are fast and accurate via integral correction in a large domain, but limited by scarceness of computing resources in serial computing environment. The serial computing is essentially a waste of the advantage of the integral correction type methods which can support parallel computing. In addition, the appropriate calculation parameters of these methods are usually difficult to determine. That makes it difficult to to choose a proper large step size to ensure both accuracy and efficiency. For the above issues, a parallel accelerated local variation iteration method (PA-LVIM) is presented in this paper based on the local variation iteration method (LVIM) which is a classical method based on integral correction. By exploiting parallel computing, the amount of computational burden in the LVIM is distributed to multiple computing nodes so as to accelerate the computing speed. In addition, the calculation parameters of the PA-LVIM are optimized by a novel polishing mesh refinement method, which divides the integration stepsize according to the second derivatives of the dynamic system states. Three classical orbit propagation problems are solved to verify the validity of the proposed PA-LVIM. Simulation results show that the PA-LVIM is dramatically accelerated, and its computational efficiency is further improved in combination with the polishing mesh refinement method, which increases the efficiency of current methods by more than 5 times.
, Available online  
Jet interaction is an effective approach for hypersonic flight controls with higher agility and improved maneuverability. Previous researches are mainly focused on the mechanisms of jet interaction effects in continuous region, classical flowfield structures of jet interaction based on different models have been proposed theoretically, on the other hand, scarce experimental data on characterizations of jet interaction in rarefied region exist. Therefore, the objective of this work aims to experimentally investigate the effects of jet pressure and hypersonic rarefied flow condition on the characterizations of transverse jet interaction based on a flat plate model, whereas hypersonic rarefied flows are generated in a JFX detonation shock tunnel. Evolution and typical structure of transverse jet interaction in hypersonic rarefied flow are recorded using high-speed schlieren imaging approach, and variations of spatial positions of different shock waves are analyzed using imaging process technique. Compared to the flowfield without the presence of jet flow, the interaction between jet flow and hypersonic rarefied flow makes the flowfield much more complex. Oblique shock could instantaneously penetrate through the flowfield of jet interaction due to the pressure fluctuation of jet flow caused by the incoming flow. With increasing the jet pressure, the affecting region of the barrel shock gradually becomes broader. The spatial position of the oblique shock wave in the upstream of the triple point barely changes with an increase in the jet pressure, while in the downstream of the triple point, the bow shock moves upstream with increasing pressure. The spatial position of the barrel shock would not overlap with the other two when the jet pressure is low. The pressure reduction of the incoming hypersonic rarefied flow can broaden the affecting region of the barrel shock and thus move the bow shock upstream as well, but it has little influence on the spatial position of the oblique shock wave.
, Available online  
Yu Jiarui, Yue Baozeng, Li Xiaoyu
With long mission cycles and complicated space missions, modern spacecraft usually need to carry a lot of liquid propellant. Large-amplitude sloshing of liquid propellant in storage tanks will seriously affect the attitude stability and control accuracy of the spacecraft, which is an important problem for the modeling of the spacecraft coupled dynamics system and the accurate control of orbit and attitude. In this paper, a new computational fluid dynamics method for the numerical simulation of large-amplitude liquid sloshing is proposed. The modeling and spatial discretization of the whole gas and liquid mixed fluid system in the tank are carried out by using isogeometric analysis. The pressure-modified fractional step method is used for the time discretization of the governing equations. By decoupling the pressure and velocity variables, the implicit equations are transformed into the explicit equations to improve the computational efficiency. For the common liquid sloshing problem, a simple and efficient mass correction method is proposed to eliminate the liquid mass error caused by the evolution of level set function. Based on the numerical method of isogeometric analysis for liquid sloshing, the coupled dynamics system of liquid-filled spacecraft with solar panels is modeled and the motion of the coupled spacecraft is simulated. The liquid sloshing momentum equation is transformed and introduced into the spacecraft dynamics equations. The numerically stable rigid-liquid coupled equations of spacecraft affected by liquid sloshing is established. The modeling of solar panels is based on the Kirchhoff-Love plate theory and the vibration of solar panels is solved by modal analysis. By comparing the numerical simulation results with the analytical results, the correctness of the proposed method is proved. Besides, the motion of rigid-liquid-flexible coupled spacecraft is simulated. It is found that liquid sloshing has a significant effect on the amplitude and frequency of spacecraft attitude change and structural vibration.
, Available online  , doi: 10.6052/0459-1879-22-539
Gao Tianyu, Yu Yongliang, Bao Lin
During the long history of evolution, carangiform swimmers have mastered an exquisite capacity to efficiently cruise in water by undulatory locomotion. Under the dynamic balance of the fluid forces, the carangiform swimmers show excellent ability to swim forward at a high speed and its performance is far superior to traditional artificial underwater vehicles. Hence, it is of great significance to discover the scaling law of hydrodynamic forces and cruising speeds for the self-propulsion of fish, and to develop formulas for the quick estimation of the forces and forward swimming velocity. Based on the open-source OpenFOAM platform, the simulation algorithm is implemented by utilizing the flexible body self-propulsion dynamics. The forward self-propulsion motions of the NACA0012 airfoil undulating in the carangiform mode are numerically simulated. Be inspired by our earlier study on thrust scaling law for the tethered models, the pressure forces and friction forces acting on the self-propelled fish-like body are analyzed. The results indicate that the pressure force coefficients, as well as the friction drag coefficients, obey the same form of scaling law in all cases under the condition of Reynolds number between 500 and 5$ \times $104, and then the quantitative prediction formulas of the forces are obtained according to the numerical results. Furthermore, the scaling law of the forward self-propulsion velocity can be derived from the equilibrium condition between pressure force and friction force, which makes it accessible to explicitly predict the cruising speed with the undulatory motion parameters of the fish body. Also, the influence of the thickness to chord ratio of fish body on the scaling laws for the hydrodynamic forces and propulsion velocity is discussed under conditions of Re = 500 and Re = 50000, the frequency f = 0.5 Hz ~ 2 Hz and the undulatory amplitude A = 0.05L ~ 0.1L. The effect of different fish body shapes on the energy-utilization ratio is considered, it can be found that slenderer fish body tends to achieve optimal energy-utilization ratio as the Reynolds number increases.
, Available online  , doi: 10.6052/0459-1879-22-567
The effective permeability of rock fractures is a fundamental parameter for describing unsaturated flow and multi-phase flow in fractured media, and the fracture aperture is an important factor affecting this parameter. In this paper, to investigate the effect of aperture on the flow structures of water-oil multiphase flow and on the effective permeability, we develope a visualization experimental system, and perform multiphase flow experiments in fracture models replicated from real rock fractures with three different apertures. Visualization experimental results show that the flow of non-wetting phase in the fracture can be categorized as unstable bubble flow at the low flow-ratio conditions and stable channel flow for high flow-ratios. As fracture aperture increases, the flow channel of non-wetting phase becomes less branching and wider, and the effective permeabilities of the two phases both increase, during which the flow structures become stable. The visualization results also reveal the competing mechanism of fluid-fluid alternately occupying the fracture space in the slug flow structure. When the non-wetting phase fluid channel changes from continuous to discontinuous, the pressure difference between the inlet and the outlet of the fracture increases significantly; conversely, when the channel changes from discontinuous to continuous, the pressure difference decreases significantly. Finally, based on the fractal theory and the statistical model for permeability, the effective permeability model proposed for multiphase flow in rock fractures with variable apertures, and the correctness and reliability of the model is evaluated by the measured effective permeability data.
, Available online  
Mastering the migration principle of active particles in shear flow is of great significance for particle separation and process intensification. Based on the theory of dissipative particle dynamics, a mathematical model describing the migration of active particles in Poiseuille flow near wall in microchannels is established. The effects of the circular angular velocity, chirality-induced angular velocity, self-propulsion velocity and rotational diffusion coefficient on the lateral migration velocity and forced tumble frequency of Escherichia coli and conventional active particles are investigated. The formation mechanism of the lateral migration of active particles in the shear flow near wall is determined. The results show that the lateral migration velocity of Escherichia coli in the shear flow near wall increases rapidly at first and then stabilizes with the shear rate. The lateral migration velocity of Escherichia coli decreases with the increase of circular angular velocity, and increases with the increase of chirality-induced angular velocity, self-propulsion velocity and rotational diffusion coefficient. The forced tumble frequency of Escherichia coli is less affected by the circular angular velocity, self-propulsion velocity and rotational diffusion coefficient but increases with the increase of the chirality-induced angular velocity. Compared with Escherichia coli, the lateral migration velocity of conventional active particles is significantly reduced, and the forced tumble frequency is significantly slower. Both the lateral migration velocity and the forced tumble frequency of conventional active particles are affected by the self-propulsion velocity and rotational diffusion coefficient in a similar way to that of Escherichia coli. The forward locomotion is the precondition for the formation of lateral migration of active particles, while other kinematic parameters and structural parameters can promote or inhibit the lateral migration of active particles in shear flow near wall to some extent.
, Available online  
Ture mode II crack simulation based on a structured deformation driven nonlocal macro-meso-scale consistent damage model
The fracture problem in which the crack deformation mode under mode II loading is also mode II is called the true mode II fracture problem. It is challenging to accurately and quantitively capture the whole process of true mode II fracture. In this paper, a structured deformation driven nonlocal macro-meso-scale consistent damage model is adopted to simulate the true mode II fracture problem. The nonlocal strain of a material point pair is decomposed into elastic strain and structured strain based on the theory of structured deformation. Then the structured positive elongation quantity of the material point pair can be evaluated by using the Cauchy-Born rule and the structured strain. In the present paper, the structured strain is taken as the deviatoric part of the nonlocal strain. When the structured positive elongation quantity of a material point pair exceeds the critical elongation quantity, mesoscopic damage starts to emerge at the point-pair level. The topologic damage can be obtained by weighted summing of the mesoscopic damage within the influence domain, then it is embedded into the framework of continuum damage mechanics through the energetic degradation function bridging the geometric damage and energetic damage for numerical solution. Further, the Gauss-Lobatto integration scheme is adopted in this paper to evaluate the nonlocal strain of point pairs, which reduces the number of integral points to 4 and thus considerably reduces the computational cost of preprocessing and nonlinear analysis. The reason for adopting the deviatoric strain as structured strain is revealed based on the analysis of the strain field at the crack tip under mode II loading. Numerical results for two typical true mode II fracture problems indicate that the proposed model can not only well capture the crack deformation pattern of true mode II cracks, but also quantitatively characterize the load-deformation curves without mesh size sensitivity. Problems to be further investigated are also discussed.
, Available online  
Natural vibration analysis of two-dimensional flexible wing based onnon-uniform beam model
In order to improve the flight performance of the aircraft, morphing technologies are used to change aerodynamic characteristics through smooth and continuous structural deformation. Since this new concept requires changing the structural shape to obtain the best performance, its inherent dynamic characteristics will be affected and even change its aeroelastic performance. In this paper, an equivalent modelling method of the two-dimensional flexible wing with camber morphing is developed. The dynamic model of the flexible wing is established based on the hypothesis of a non-uniform beam model. The analytical solution and natural frequencies are obtained by the method of Frobenius and verified by comparison with the finite element method solution. The errors of the first four natural frequencies are within 1% and the corresponding modes are consistent. The flexible wing is prepared by 3D printing engineering plastic (ABS) and silica gel skin material. The Young's modulus of the 3D printing material and silica gel skin material are respectively measured by dynamic measurement method and tensile test. The vibration response test platform is built to carry out vibration test of the flexible wing. It is found that the fundamental frequency obtained by vibration test is consistent with the theoretical model results, and the error is less than 3% compared with the finite element method. The equivalent modelling method of a two-dimensional flexible wing is established through theoretical analysis and experimental verification. The research results will provide theoretical support for applying the flexible trailing edge structures.
, Available online  
Nonlinear energy sink is a kind of vibration energy absorption device, which plays an important role in vibration suppression of structure. In this paper, the correlation analysis of vibration suppression for a system with combined nonlinear damping nonlinear energy sink is carried out. Firstly, the theoretical model of the system with combined nonlinear damping nonlinear energy sink is described. The motion equations of the system model are derived by using the complex variable average method, and the slow variable equations of the system are obtained. Secondly, the slow variable equations of the system are analyzed by using the multi-scale method. By studying the slow invariant manifold and phase trajectories of the system, the condition basis of the strongly modulated response of the system is described. In addition, the influence law of the external excitation amplitude on the frequency detuning coefficient interval in the presence of the strongly modulated response is revealed by analyzing the system with one-dimensional mapping. Finally, the energy spectrum, time response and Poincare mapping are applied to study the vibration suppression of the system with combined nonlinear damping nonlinear energy sink, the influence law of different damping and stiffness of nonlinear energy sink on its vibration suppression effect is revealed. Meanwhile, it is found that the response of the nonlinear energy sink with combined nonlinear damping is consistent with that of the main structure. In addition, it is verified that the nonlinear energy sink with combined nonlinear damping proposed in this study has good vibration suppression ability.
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The experimental measurement of the flow field of counterflowing wall jet using the particle image velocimetry. The jet velocity ratio to the main flow velocity is 8.89, and the Reynolds number based on the jet pipe is 9127. This paper focuses on the statistical characteristics of turbulence at different streamwise positions in the jet shear layer, including scale characteristics and structural characteristics. Statistical analysis of the fluctuating velocity field at different flow direction positions on the jet centerline shows that: in the range of x/D=30~43, Q1 and Q4 events dominate due to the feedback mechanism. Q3 event is dominant in the region near the stagnation point (x/D=43~50). The spatial scale of the turbulent structure in the jet shear layer is analyzed. The total scale in the interval x/D=0~37 shows an increasing trend downstream, and it is almost unchanged in the interval x/D=37~46. The total scale in the interval x/D=46~51 tends to decrease downstream. In the interval x/D=0~35, the upstream scale of the reference point is similar to the downstream scale. In the interval x/D=35~41, the downstream scale of the reference point is larger than the upstream scale. In the interval x/D=41~51, the downstream scale of the reference point is smaller than the upstream scale. The spectral proper orthogonal decomposition (SPOD) is used to quantitatively analyzes the turbulent structure. It shows that the energy of the mode is concentrated in low frequency. The most energetic mode in the flow field has a frequency of fD/Uj=0.0005 and appears in the recirculation region. The first mode with a frequency equal to fD/Uj=0.0026 indicates that the turbulent structure is generated when the jet is deflected by the interaction with the main flow, and transported along the periphery of the recirculation region. The configurations of high-frequency structures are similar, all located in the jet shear layer, and the higher the frequency, the closer to the jet outlet, the smaller the scale.
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