The motion of an elliptical rigid particle in a lid-driven cavity flow was numerically simulated using the immersed boundary lattice Boltzmann method(IB-LBM).The effects of the particle's initial orientation angle...The motion of an elliptical rigid particle in a lid-driven cavity flow was numerically simulated using the immersed boundary lattice Boltzmann method(IB-LBM).The effects of the particle's initial orientation angle,initial position,aspect ratio,and size on the motion characteristics were investigated.The computational results indicate that the particle's motion undergoes two distinct stages:a starting stage that involves moving from the release position to a limit cycle,and a periodic stage that involves moving on the limit cycle.The initial orientation of the particle has a minimal impact on both stages of motion.In contrast,the time it takes for the particle to reach the limit cycle may vary depending on the release position.Furthermore,particles with a larger aspect ratio exhibit a greater maximum velocity magnitude;an increase in particle size causes the particle trajectory to contract more toward the center of the cavity,decreasing the centrifugal force experienced by the particle.展开更多
Supersonic flows past two-dimensional cavities with/without control are investigated by the direct numerical simulation （DNS）. For an uncontrolled cavity, as the thickness of the boundary layer declines, transition ...Supersonic flows past two-dimensional cavities with/without control are investigated by the direct numerical simulation （DNS）. For an uncontrolled cavity, as the thickness of the boundary layer declines, transition of the dominant mode from the steady mode to the Rossiter Ⅱ mode and then to the Rossiter III mode is observed due to the change of vortex-corner interactions. Meanwhile, a low frequency mode appears. However, the wake mode observed in a subsonic cavity flow is absent in the current simulation. The oscillation frequencies obtained from a global dynamic mode decomposition （DMD） approach are consistent with the local power spectral density （PSD） analysis. The dominant mode transition is clearly shown by the dynamic modes obtained from the DMD. A passive control technique of substituting the cavity trailing edge with a quarter-circle is studied. As the effective cavity length increases, the dominant mode transition from the Rossiter Ⅱ mode to the Rossiter Ⅲ mode occurs. With the control, the pressure oscillations are reduced significantly. The interaction of the shear layer and the recirculation zone is greatly weakened, combined with weaker shear layer instability, responsible for the suppression of pressure oscillations. Moreover, active control using steady subsonic mass injection upstream of a cavity leading edge can stabilize the flow.展开更多
Self-sustained oscillation and the sound radiation of flow over an open cavity is of great importance in nature and industry.Influences of filled porous media in the cavity are investigated numerically by using a latt...Self-sustained oscillation and the sound radiation of flow over an open cavity is of great importance in nature and industry.Influences of filled porous media in the cavity are investigated numerically by using a lattice Boltzmann method in two-dimensional space.It is shown that the outcomes of the porous patch depend on the location of the patch and the original flow mode,namely shear layer(SL)and wake mode(WM).For SL flow,the porous patch either damps the vortical flow or suppresses the generation of the secondary vortex sheet on the wall.The later effect destabilizes the SL.Consequently,the radiated sound is reduced as the patch is on the trailing edge,and increased with porous patch on the floor,respectively.For flow in WM,a transition from WM to SL mode is found when the porous patch is set either on the floor or behind the leading wall.In the cases,the recirculating flow on large scale is blocked significantly due to the porous patch,therefore,the WM flow is not sustained.On the other hand,the porous patch on the trailing edge slightly weakens the sound due to dissipation.The study shows that assembling of porous media in the flow field decreases the radiated sound level only if it is done carefully.展开更多
The reduced-order model （ROM） for the two-dimensional supersonic cavity flow based on proper orthogonal decomposition （POD） and Galerkin projection is investigated. Presently, popular ROMs in cavity flows are base...The reduced-order model （ROM） for the two-dimensional supersonic cavity flow based on proper orthogonal decomposition （POD） and Galerkin projection is investigated. Presently, popular ROMs in cavity flows are based on an isentropic assumption, valid only for flows at low or moderate Mach numbers. A new ROM is constructed involving primitive variables of the fully compressible Navier-Stokes （N-S） equations, which is suitable for flows at high Mach numbers. Compared with the direct numerical simulation （DNS） results, the proposed model predicts flow dynamics （e.g., dominant frequency and amplitude） accurately for supersonic cavity flows, and is robust. The comparison between the present transient flow fields and those of the DNS shows that the proposed ROM can capture self-sustained oscillations of a shear layer. In addition, the present model reduction method can be easily extended to other supersonic flows.展开更多
Prevention and control measures of spontaneous combustion of coal and gas accumulation in a goaf require an accurate description of its gas flow state.However,the commonly used fluid dynamics in porous media is not su...Prevention and control measures of spontaneous combustion of coal and gas accumulation in a goaf require an accurate description of its gas flow state.However,the commonly used fluid dynamics in porous media is not suitable for the new-born goaf with fracture cavity combination,multi-scale,and large blocks.In this study,we propose a cavity flow algorithm to accurately describe the gas flow state in the new-born goaf.The genetic algorithm(GA)is used to randomly generate the binary matrix of a goaf caving shape.The difference between the gas flow state calculated by the lattice Boltzmann method(LBM)and the measured data at the boundary or internal measuring points of the real goaf is taken as the GA fitness value,and the real goaf caving shape and the gas flow state are quickly addressed by GA.The experimental model of new-born goaf is established,and the laser Doppler anemometry(LDA)experiment is carried out.The results show that the Jaccard similarity coefficient between the reconstructed caving shape and the real caving shape is 0.7473,the mean square error between the calculated wind speed and the LDA-measured value is 0.0244,and the R2 coefficient is 0.8986,which verify the feasibility of the algorithm.展开更多
To date,there are very few studies on the transition beyond second Hopf bifurcation in a lid-driven square cavity,due to the difficulties in theoretical analysis and numerical simulations.In this paper,we study the ch...To date,there are very few studies on the transition beyond second Hopf bifurcation in a lid-driven square cavity,due to the difficulties in theoretical analysis and numerical simulations.In this paper,we study the characteristics of the third Hopf bifurcation in a driven square cavity by applying a consistent fourth-order compact finite difference scheme rectently developed by us.We numerically identify the critical Reynolds number of the third Hopf bifurcation located in the interval of(13944.7021,13946.5333)by the method of bisection.Through Fourier analysis,it is discovered that the flow becomes chaotic with a characteristic of period-doubling bifurcation when the Reynolds number is beyond the third bifurcation critical interval.Nonlinear time series analysis further ascertains the flow chaotic behaviors via the phase diagram,Kolmogorov entropy and maximal Lyapunov exponent.The phase diagram changes interestingly from a closed curve with self-intersection to an unclosed curve and the attractor eventually becomes strange when the flow becomes chaotic.展开更多
A streamline upwind/Petrov-Galerkin （SUPG） finite element method based on a penalty function is pro- posed for steady incompressible Navier-Stokes equations. The SUPG stabilization technique is employed for the for-...A streamline upwind/Petrov-Galerkin （SUPG） finite element method based on a penalty function is pro- posed for steady incompressible Navier-Stokes equations. The SUPG stabilization technique is employed for the for- mulation of momentum equations. Using the penalty function method, the continuity equation is simplified and the pres- sure of the momentum equations is eliminated. The lid-driven cavity flow problem is solved using the present model. It is shown that steady flow simulations are computable up to Re = 27500, and the present results agree well with previous solutions. Tabulated results for the properties of the primary vortex are also provided for benchmarking purposes.展开更多
The presence of a cavity changes the mean and fluctuating pressure distributions. Similarities are observed between a cylindrical cavity and a rectangular cavity for a compressible flow.The type of cavity flow field d...The presence of a cavity changes the mean and fluctuating pressure distributions. Similarities are observed between a cylindrical cavity and a rectangular cavity for a compressible flow.The type of cavity flow field depends on the diameter-to-depth ratio and the length-to-depth ratio.The feedback loop is responsible for the generation of discrete acoustic tones. In this study, the selfsustained oscillation for a compressible cylindrical cavity flow was investigated experimentally. For open-type cavities, the power spectra show that the strength of resonance depends on the diameterto-depth ratio（4.43–43.0） and the incoming boundary layer thickness-to-depth ratio（0.72–7.0）. The effective streamwise length is used as the characteristic length to estimate the Strouhal number. At higher modes, there is a large deviation from Rossiter＇s formula for rectangular cavities. The gradient-based searching method was used to evaluate the values of the empirical parameters. Less phase lag and a lower convection velocity are observed.展开更多
Based on finite volume method, subsonic and transonic flow in 3-D cavity of different length-to-depth ratios are numerically investigated by using Navier-Stokes equations with k-ε SST two-equation turbulence model an...Based on finite volume method, subsonic and transonic flow in 3-D cavity of different length-to-depth ratios are numerically investigated by using Navier-Stokes equations with k-ε SST two-equation turbulence model and coupled implicit algorithm. The cavity streamline patterns and the static pressure coefficient distributions on the cavity floor are shown, and the flow characteristics of the cavity and the floor pressure coefficient distributions are analyzed. Numerical results demon- strate that the flow characteristics of the cavity at subsonic and transonic speeds are different from that of supersonic ones; length-to-depth ratio is the main factor that affects the flow characteristics of the cavity at subsonic and transonic number has a neglectable effect on the cavity floor pressure distributions. speeds and causes changes of the cavity flow type; Mach cavity flow fields at subsonic and transonic speeds and the展开更多
The fractional volumetric lattice Boltzmann method with much better stability was used to simulate two-chmensional cavity flows. Because the effective viscosity was reduced by the fraction factor, it is very effective...The fractional volumetric lattice Boltzmann method with much better stability was used to simulate two-chmensional cavity flows. Because the effective viscosity was reduced by the fraction factor, it is very effective for simulating high Reynolds number flows. Simulations were carried out on a uniform grids system. The stream lines and the velocity profiles obtained from the simulations agree well with the standard lattice Boltzmann method simulations. Comparisons of detailed flow patterns with other studies via location of vortex centers are also satisfactory.展开更多
The generalized lattice Boltzmann equation(GLBE),with the addition of the standard Smagorinsky subgrid-stress(SGS) model,has been proved that it is more suitable for simulating high Reynolds number turbulent flows whe...The generalized lattice Boltzmann equation(GLBE),with the addition of the standard Smagorinsky subgrid-stress(SGS) model,has been proved that it is more suitable for simulating high Reynolds number turbulent flows when compared with the lattice BGK Boltzmann equation(LBGK).However,the computing efficiency of lattice Boltzmann method(LBM) is too low to make it for practical applications,unless using a massive parallel computing clusters facility.In this study,the massive parallel computing power from an inexpensive graphic processor unit(GPU) and a typical personal computer has been developed for improving the computing efficiency,more than 100 times.This developed three-dimensional(3-D) GLBE-SGS model,with the D3Q19 scheme for simplifying collision and streaming courses,has been successfully used to study 3-D rectangular cavity flows with Reynolds number up to 10000.展开更多
By coupling the non-equilibrium extrapolation scheme for boundary condition with the multi-relaxation-time lattice Boltzmann method, this paper finds that the stability of the multi-relaxation-time model can be improv...By coupling the non-equilibrium extrapolation scheme for boundary condition with the multi-relaxation-time lattice Boltzmann method, this paper finds that the stability of the multi-relaxation-time model can be improved greatly, especially on simulating high Reynolds number （Re） flow. As a discovery, the super-stability analysed by Lallemand and Luo is verified and the complex structure of the cavity flow is also exhibited in our numerical simulation when Re is high enough. To the best knowledge of the authors, the maximum of Re which has been investigated by direct numerical simulation is only around 50 000 in the literature; however, this paper can readily extend the maximum to 1000 000 with the above combination.展开更多
In recent years, the Lattice Boltzmann Method (LBM) has developed into an alternative and promising numerical scheme for simulating fluid flows and modeling physics in fluids. In order to propose LBM for high Reynolds...In recent years, the Lattice Boltzmann Method (LBM) has developed into an alternative and promising numerical scheme for simulating fluid flows and modeling physics in fluids. In order to propose LBM for high Reynolds number fluid flow applications, a subgrid turbulence model for LBM was introduced based on standard Smagorinsky subgrid model and Lattice Bhatnagar-Gross-Krook (LBGK) model. The subgrid LBGK model was subsequently used to simulate the two-dimensional driven cavity flow at high Reynolds numbers. The simulation results including distribution of stream lines, dimensionless velocities distribution, values of stream function, as well as location of vertex center, were compared with benchmark solutions, with satisfactory agreements.展开更多
Flow induced oscillation in a cavity and its suppression by means of acoustic excitation were studied both experimentally and numerically. In the experiment it was found that with the leading edge pure tone excitation...Flow induced oscillation in a cavity and its suppression by means of acoustic excitation were studied both experimentally and numerically. In the experiment it was found that with the leading edge pure tone excitation at some frequencies and intensities. the flow-induced oscillation in the cavity could be greatly suppressed. Cavity flows both with and without acoustic excitation were studied by solving the 2-D time-dependent Reynolds averaged Navier Stokes equations using explicit predictor-corrector difference algorithm of MacCormack. Effects of turbulence were simulated via Cebeci-Smith turbulence mode with relaxation modification. The computational and experimental results are compared. and good agreement is obtained.展开更多
A lattice Boltzmann model combined with curvilinear coordinate is proposed for lid-driven cavity three-dimensional (3D) flows. For particle velocity distribution, the particle collision process is performed in physica...A lattice Boltzmann model combined with curvilinear coordinate is proposed for lid-driven cavity three-dimensional (3D) flows. For particle velocity distribution, the particle collision process is performed in physical domain, and the particle streaming process is carried out in the corresponding computational domain, which is transferred from the physical domain using interpolation method. For the interpolation calculation, a second-order upwind interpolation method is adopted on internal lattice nodes in flow fields while a second-order central interpolation algorithm is employed at neighbor-boundary lattice nodes. Then the above-mentioned model and algorithms are used to numerically simulate the 3D flows in the lid-driven cavity at Reynolds numbers of 100, 400 and 1000 on non-uniform meshes. Various vortices on the x-y, y-z and x-z symmetrical planes are successfully predicted, and their changes in position with the Reynolds number increasing are obtained. The velocity profiles of u component along the vertical centerline and w component along the horizontal centerline are both in good agreement with the data in literature and the calculated results on uniform meshes. Besides, the velocity vector distributions on various cross sections in lid-driven cavity predicted on non-uniform meshes are compared with those simulated on uniform meshes and those in the literature. All the comparisons and validations show that the 3D lattice Boltzmann model and all the numerical algorithms on non-uniform meshes are accurate and reliable to predict effectively flow fields.展开更多
An experimental study of cavity oscillating flow carried out on subsonic wall jet facilities in an anechoic room is summarized. The jet exit Mach number range is from 0.2 to 0.8. The effects of the flow Mach number (...An experimental study of cavity oscillating flow carried out on subsonic wall jet facilities in an anechoic room is summarized. The jet exit Mach number range is from 0.2 to 0.8. The effects of the flow Mach number ( Ma ) and the cavity depth ( D ) on the oscillation are studied. It is found that for L/D =4, (shallow cavity), the oscillation is mainly due to the self exciting of the free shear layer above the cavity opening, for L/D =2, the acoustic resonance is responsible for the oscillation. Preliminary tests are performed to study the suppression effect of the leading edge tone excitation on cavity flow, and considerable reduction of oscillation has been achieved when Ma ≤0.6.展开更多
This paper investigates the chaotic lid-driven square cavity flows at extreme Reynolds numbers.Several observations have been made from this study.Firstly,at extreme Reynolds numbers two principles add at the genesis ...This paper investigates the chaotic lid-driven square cavity flows at extreme Reynolds numbers.Several observations have been made from this study.Firstly,at extreme Reynolds numbers two principles add at the genesis of tiny,loose counterclockwise-or clockwise-rotating eddies.One concerns the arousing of them owing to the influence of the clockwise-or counterclockwise currents nearby;the other,the arousing of counterclockwise-rotating eddies near attached to the moving(lid)top wall which moves from left to right.Secondly,unexpectedly,the kinetic energy soon reaches the qualitative temporal limit’s pace,fluctuating briskly,randomly inside the total kinetic energy range,fluctuations which concentrate on two distinct fragments:one on its upper side,the upper fragment,the other on its lower side,the lower fragment,switching briskly,randomly from each other;and further on many small fragments arousing randomly within both,switching briskly,randomly from one another.As the Reynolds number Re→∞,both distance and then close,and the kinetic energy fluctuates shorter and shorter at the upper fragment and longer and longer at the lower fragment,displaying tall high spikes which enlarge and then disappear.As the time t→∞(at the Reynolds number Re fixed)they recur from time to time with roughly the same amplitude.For the most part,at the upper fragment the leading eddy rotates clockwise,and at the lower fragment,in stark contrast,it rotates counterclockwise.At Re=109 the leading eddy-at its qualitative temporal limit’s pace—appears to rotate solely counterclockwise.展开更多
With the aid of numerical method, both flow field and its accompanied loss mechanism within the rotating cavity are investigated in detail in the 1^(st) part of the two parts paper. For ease of comparison, rotating ca...With the aid of numerical method, both flow field and its accompanied loss mechanism within the rotating cavity are investigated in detail in the 1^(st) part of the two parts paper. For ease of comparison, rotating cavity is further classified as the rotor-stator cavity case and the rotor-rotor cavity case. Results indicate that flow within both kinds of the cavity act as the inviscid flow except that the flow near walls, neighboring the lower G region and in the vicinity of the rotating orifices. In the regions except such inviscid-flow-dominate domains, the theoretical core rotation factor can be safely used to predict the swirl ratio within the cavity. When detailed flow pattern is considered, Ekman-type flow exists near periphery of the surface's boundary layer where viscous effect is non-negligible. However, due to the complex profile of the simulated cavity case, vortices structure is varied within the cavity. By comparison, swirl ratio can be used to predict the magnitude of loss. Due to the relatively evident rotating effects of the rotor-rotor cavity, swirl ratio even increases to 1.4 in the current model, which means that flow is moving faster than the surrounding disc. Further investigation finds that this kind of highly rotating flow is accompanied with serious undesirable pressure loss. Parenthetically, unlike its counterpart, swirl ratio above 1.0 doesn't happen when fluid passes through the rotor-stator cavity. So it is suggested that rotor-rotor flow cavity with the superimposed inward throughflow should be avoided in the engine design or certain measurements should be provided when such structure design is unavoidable. Simulation done in the current paper is meaningful since these dimensional parameters are typical in the design of state-of-art. Relatively lower range of Re_φ and C_w is not considered in the current two parts paper.展开更多
Combining the detached eddy simulation(DES)method and Ffowcs Williams-Hawkings(FW-H)equation,the effect of bogie cavity end wall inclination on the flow field and aerodynamic noise in the bogie region is numerically s...Combining the detached eddy simulation(DES)method and Ffowcs Williams-Hawkings(FW-H)equation,the effect of bogie cavity end wall inclination on the flow field and aerodynamic noise in the bogie region is numerically studied.First,the simulation is conducted based on a simplified cavity-bogie model,including five cases with different inclination angles of the front and rear walls of the cavity.By comparing and analyzing the flow field and acoustic results of the five cases,the influence of the regularity and mechanism of the bogie cavity end wall inclination on the flow field and the aerodynamic noise of the bogie region are revealed.Then,the noise reduction strategy determined by the results of the simplified cavity-bogie model is applied to a three-car marshaling train model to verify its effectiveness when applied to the real train.The results reveal that the forward inclination of the cavity front wall enlarges the influence area of shear vortex structures formed at the leading edge of the cavity and intensifies the interaction between the vortex structures and the front wheelset,frontmotor,and front gearbox,resulting in the increase of the aerodynamic noise generated by the bogie itself.The backward inclination of the cavity rear wall is conducive to guiding the vortex structures flow out of the cavity and weakening the interaction between the shear vortex structures and the cavity rear wall,leading to the reduction of the aerodynamic noise generated by the bogie cavity.Inclining the rear end wall of the foremost bogie cavity of the head car is a feasible aerodynamic noise reduction measure for high-speed trains.展开更多
Experimental and computational analysis has been carried out by many researchers on supersonic cavity flow,but detailed analysis based on Rossiter’s model still requires some insight.In the current study an open rect...Experimental and computational analysis has been carried out by many researchers on supersonic cavity flow,but detailed analysis based on Rossiter’s model still requires some insight.In the current study an open rectangular cavity with a length to depth ratio of 2(L/D=2)and Mach number at the inlet as 1.71,was considered as a baseline configuration for experimental analysis.Statistical techniques such as power spectral density(PSD),correlation,and overall sound pressure level(OASPL)were carried out on the unsteady pressure data,to analyze the aero-acoustic flow physics.High-speed schlieren images were processed to obtain spatially coherent modes by proper orthogonal decomposition(POD).The analysis was extended for different dimensions of subcavities on the aft,floor,and front wall.This detailed analysis of these configurations with different dimensions and combinations revealed the various flow features and mode frequencies in supersonic cavity.As the front wall subcavity act as a passive control device,reducing the overall sound pressure level inside the cavity whereas,the aft wall subcavity acts as a passive resonator with distinct harmonic fluidresonant modes,a similar phenomenon was observed for floor subcavity at different locations.A novel method was employed to analyze Rossiter’s model and its applicability in estimating experimental modes was verified,as it accurately predicted the dominant frequencies with a maximum of 2.74% uncertainty among all the configurations.展开更多
文摘The motion of an elliptical rigid particle in a lid-driven cavity flow was numerically simulated using the immersed boundary lattice Boltzmann method(IB-LBM).The effects of the particle's initial orientation angle,initial position,aspect ratio,and size on the motion characteristics were investigated.The computational results indicate that the particle's motion undergoes two distinct stages:a starting stage that involves moving from the release position to a limit cycle,and a periodic stage that involves moving on the limit cycle.The initial orientation of the particle has a minimal impact on both stages of motion.In contrast,the time it takes for the particle to reach the limit cycle may vary depending on the release position.Furthermore,particles with a larger aspect ratio exhibit a greater maximum velocity magnitude;an increase in particle size causes the particle trajectory to contract more toward the center of the cavity,decreasing the centrifugal force experienced by the particle.
基金supported by the National Natural Science Foundation of China(Nos.11232011 and11402262)the 111 Project of China(No.B07033)+1 种基金the China Postdoctoral Science Foundation(No.2014M561833)the Fundamental Research Funds for the Central Universities
文摘Supersonic flows past two-dimensional cavities with/without control are investigated by the direct numerical simulation （DNS）. For an uncontrolled cavity, as the thickness of the boundary layer declines, transition of the dominant mode from the steady mode to the Rossiter Ⅱ mode and then to the Rossiter III mode is observed due to the change of vortex-corner interactions. Meanwhile, a low frequency mode appears. However, the wake mode observed in a subsonic cavity flow is absent in the current simulation. The oscillation frequencies obtained from a global dynamic mode decomposition （DMD） approach are consistent with the local power spectral density （PSD） analysis. The dominant mode transition is clearly shown by the dynamic modes obtained from the DMD. A passive control technique of substituting the cavity trailing edge with a quarter-circle is studied. As the effective cavity length increases, the dominant mode transition from the Rossiter Ⅱ mode to the Rossiter Ⅲ mode occurs. With the control, the pressure oscillations are reduced significantly. The interaction of the shear layer and the recirculation zone is greatly weakened, combined with weaker shear layer instability, responsible for the suppression of pressure oscillations. Moreover, active control using steady subsonic mass injection upstream of a cavity leading edge can stabilize the flow.
基金supported by the National Natural Science Foundation of China(Grant No.11872315)the Natural Science Basic Research Program of Shaanxi(Grant No.2019JM-105).
文摘Self-sustained oscillation and the sound radiation of flow over an open cavity is of great importance in nature and industry.Influences of filled porous media in the cavity are investigated numerically by using a lattice Boltzmann method in two-dimensional space.It is shown that the outcomes of the porous patch depend on the location of the patch and the original flow mode,namely shear layer(SL)and wake mode(WM).For SL flow,the porous patch either damps the vortical flow or suppresses the generation of the secondary vortex sheet on the wall.The later effect destabilizes the SL.Consequently,the radiated sound is reduced as the patch is on the trailing edge,and increased with porous patch on the floor,respectively.For flow in WM,a transition from WM to SL mode is found when the porous patch is set either on the floor or behind the leading wall.In the cases,the recirculating flow on large scale is blocked significantly due to the porous patch,therefore,the WM flow is not sustained.On the other hand,the porous patch on the trailing edge slightly weakens the sound due to dissipation.The study shows that assembling of porous media in the flow field decreases the radiated sound level only if it is done carefully.
基金Project supported by the National Natural Science Foundation of China(Nos.11232011,11402262,11572314,and 11621202)
文摘The reduced-order model （ROM） for the two-dimensional supersonic cavity flow based on proper orthogonal decomposition （POD） and Galerkin projection is investigated. Presently, popular ROMs in cavity flows are based on an isentropic assumption, valid only for flows at low or moderate Mach numbers. A new ROM is constructed involving primitive variables of the fully compressible Navier-Stokes （N-S） equations, which is suitable for flows at high Mach numbers. Compared with the direct numerical simulation （DNS） results, the proposed model predicts flow dynamics （e.g., dominant frequency and amplitude） accurately for supersonic cavity flows, and is robust. The comparison between the present transient flow fields and those of the DNS shows that the proposed ROM can capture self-sustained oscillations of a shear layer. In addition, the present model reduction method can be easily extended to other supersonic flows.
基金This work was supported by the Natural Science Foundation of China(Nos.51774169 and 51574142)the National Key Research and Development Program of China(No.2017YFC0804401).
文摘Prevention and control measures of spontaneous combustion of coal and gas accumulation in a goaf require an accurate description of its gas flow state.However,the commonly used fluid dynamics in porous media is not suitable for the new-born goaf with fracture cavity combination,multi-scale,and large blocks.In this study,we propose a cavity flow algorithm to accurately describe the gas flow state in the new-born goaf.The genetic algorithm(GA)is used to randomly generate the binary matrix of a goaf caving shape.The difference between the gas flow state calculated by the lattice Boltzmann method(LBM)and the measured data at the boundary or internal measuring points of the real goaf is taken as the GA fitness value,and the real goaf caving shape and the gas flow state are quickly addressed by GA.The experimental model of new-born goaf is established,and the laser Doppler anemometry(LDA)experiment is carried out.The results show that the Jaccard similarity coefficient between the reconstructed caving shape and the real caving shape is 0.7473,the mean square error between the calculated wind speed and the LDA-measured value is 0.0244,and the R2 coefficient is 0.8986,which verify the feasibility of the algorithm.
基金Project supported by the National Natural Science Foundation of China(Grant No.12162001)the Natural Science Foundation of Ningxia(Grant No.2019AAC03129)the Construction Project of First-Class Disciplines in Ningxia Higher Education(Grant No.NXYLXK2017B09)。
文摘To date,there are very few studies on the transition beyond second Hopf bifurcation in a lid-driven square cavity,due to the difficulties in theoretical analysis and numerical simulations.In this paper,we study the characteristics of the third Hopf bifurcation in a driven square cavity by applying a consistent fourth-order compact finite difference scheme rectently developed by us.We numerically identify the critical Reynolds number of the third Hopf bifurcation located in the interval of(13944.7021,13946.5333)by the method of bisection.Through Fourier analysis,it is discovered that the flow becomes chaotic with a characteristic of period-doubling bifurcation when the Reynolds number is beyond the third bifurcation critical interval.Nonlinear time series analysis further ascertains the flow chaotic behaviors via the phase diagram,Kolmogorov entropy and maximal Lyapunov exponent.The phase diagram changes interestingly from a closed curve with self-intersection to an unclosed curve and the attractor eventually becomes strange when the flow becomes chaotic.
基金the National Natural Science Foundation of China (Grants 41372301 and 51349011)the Preeminent Youth Talent Project of Southwest University of Science and Technology (Grant 13zx9109)
文摘A streamline upwind/Petrov-Galerkin （SUPG） finite element method based on a penalty function is pro- posed for steady incompressible Navier-Stokes equations. The SUPG stabilization technique is employed for the for- mulation of momentum equations. Using the penalty function method, the continuity equation is simplified and the pres- sure of the momentum equations is eliminated. The lid-driven cavity flow problem is solved using the present model. It is shown that steady flow simulations are computable up to Re = 27500, and the present results agree well with previous solutions. Tabulated results for the properties of the primary vortex are also provided for benchmarking purposes.
基金support of the Ministry of Science and Technology (No. MOST 103-2923-E-006MY3)
文摘The presence of a cavity changes the mean and fluctuating pressure distributions. Similarities are observed between a cylindrical cavity and a rectangular cavity for a compressible flow.The type of cavity flow field depends on the diameter-to-depth ratio and the length-to-depth ratio.The feedback loop is responsible for the generation of discrete acoustic tones. In this study, the selfsustained oscillation for a compressible cylindrical cavity flow was investigated experimentally. For open-type cavities, the power spectra show that the strength of resonance depends on the diameterto-depth ratio（4.43–43.0） and the incoming boundary layer thickness-to-depth ratio（0.72–7.0）. The effective streamwise length is used as the characteristic length to estimate the Strouhal number. At higher modes, there is a large deviation from Rossiter＇s formula for rectangular cavities. The gradient-based searching method was used to evaluate the values of the empirical parameters. Less phase lag and a lower convection velocity are observed.
文摘Based on finite volume method, subsonic and transonic flow in 3-D cavity of different length-to-depth ratios are numerically investigated by using Navier-Stokes equations with k-ε SST two-equation turbulence model and coupled implicit algorithm. The cavity streamline patterns and the static pressure coefficient distributions on the cavity floor are shown, and the flow characteristics of the cavity and the floor pressure coefficient distributions are analyzed. Numerical results demon- strate that the flow characteristics of the cavity at subsonic and transonic speeds are different from that of supersonic ones; length-to-depth ratio is the main factor that affects the flow characteristics of the cavity at subsonic and transonic number has a neglectable effect on the cavity floor pressure distributions. speeds and causes changes of the cavity flow type; Mach cavity flow fields at subsonic and transonic speeds and the
文摘The fractional volumetric lattice Boltzmann method with much better stability was used to simulate two-chmensional cavity flows. Because the effective viscosity was reduced by the fraction factor, it is very effective for simulating high Reynolds number flows. Simulations were carried out on a uniform grids system. The stream lines and the velocity profiles obtained from the simulations agree well with the standard lattice Boltzmann method simulations. Comparisons of detailed flow patterns with other studies via location of vortex centers are also satisfactory.
基金supported by the Virginia Institute of Marine Science,College of William and Mary for the Study Environmentthe National Natural Science Foundation of China(Grant No.50679008)
文摘The generalized lattice Boltzmann equation(GLBE),with the addition of the standard Smagorinsky subgrid-stress(SGS) model,has been proved that it is more suitable for simulating high Reynolds number turbulent flows when compared with the lattice BGK Boltzmann equation(LBGK).However,the computing efficiency of lattice Boltzmann method(LBM) is too low to make it for practical applications,unless using a massive parallel computing clusters facility.In this study,the massive parallel computing power from an inexpensive graphic processor unit(GPU) and a typical personal computer has been developed for improving the computing efficiency,more than 100 times.This developed three-dimensional(3-D) GLBE-SGS model,with the D3Q19 scheme for simplifying collision and streaming courses,has been successfully used to study 3-D rectangular cavity flows with Reynolds number up to 10000.
基金Project supported by the National Natural Science Foundation of China （Grant No 70271069）.
文摘By coupling the non-equilibrium extrapolation scheme for boundary condition with the multi-relaxation-time lattice Boltzmann method, this paper finds that the stability of the multi-relaxation-time model can be improved greatly, especially on simulating high Reynolds number （Re） flow. As a discovery, the super-stability analysed by Lallemand and Luo is verified and the complex structure of the cavity flow is also exhibited in our numerical simulation when Re is high enough. To the best knowledge of the authors, the maximum of Re which has been investigated by direct numerical simulation is only around 50 000 in the literature; however, this paper can readily extend the maximum to 1000 000 with the above combination.
文摘In recent years, the Lattice Boltzmann Method (LBM) has developed into an alternative and promising numerical scheme for simulating fluid flows and modeling physics in fluids. In order to propose LBM for high Reynolds number fluid flow applications, a subgrid turbulence model for LBM was introduced based on standard Smagorinsky subgrid model and Lattice Bhatnagar-Gross-Krook (LBGK) model. The subgrid LBGK model was subsequently used to simulate the two-dimensional driven cavity flow at high Reynolds numbers. The simulation results including distribution of stream lines, dimensionless velocities distribution, values of stream function, as well as location of vertex center, were compared with benchmark solutions, with satisfactory agreements.
文摘Flow induced oscillation in a cavity and its suppression by means of acoustic excitation were studied both experimentally and numerically. In the experiment it was found that with the leading edge pure tone excitation at some frequencies and intensities. the flow-induced oscillation in the cavity could be greatly suppressed. Cavity flows both with and without acoustic excitation were studied by solving the 2-D time-dependent Reynolds averaged Navier Stokes equations using explicit predictor-corrector difference algorithm of MacCormack. Effects of turbulence were simulated via Cebeci-Smith turbulence mode with relaxation modification. The computational and experimental results are compared. and good agreement is obtained.
基金supported by the National Natural Science Foundation of China (Grant Nos. 51179192, 50779069, 51139007)the Program for New Century Excellent Talents in University (NCET) (Grant No. NETC-10-0784)+1 种基金the National Hi-Tech Research and Development Program of China ("863" Project) (Grant No. 2011AA100505)the Chinese Universities Scientific Fund (Grant No. 2013RC045)
文摘A lattice Boltzmann model combined with curvilinear coordinate is proposed for lid-driven cavity three-dimensional (3D) flows. For particle velocity distribution, the particle collision process is performed in physical domain, and the particle streaming process is carried out in the corresponding computational domain, which is transferred from the physical domain using interpolation method. For the interpolation calculation, a second-order upwind interpolation method is adopted on internal lattice nodes in flow fields while a second-order central interpolation algorithm is employed at neighbor-boundary lattice nodes. Then the above-mentioned model and algorithms are used to numerically simulate the 3D flows in the lid-driven cavity at Reynolds numbers of 100, 400 and 1000 on non-uniform meshes. Various vortices on the x-y, y-z and x-z symmetrical planes are successfully predicted, and their changes in position with the Reynolds number increasing are obtained. The velocity profiles of u component along the vertical centerline and w component along the horizontal centerline are both in good agreement with the data in literature and the calculated results on uniform meshes. Besides, the velocity vector distributions on various cross sections in lid-driven cavity predicted on non-uniform meshes are compared with those simulated on uniform meshes and those in the literature. All the comparisons and validations show that the 3D lattice Boltzmann model and all the numerical algorithms on non-uniform meshes are accurate and reliable to predict effectively flow fields.
文摘An experimental study of cavity oscillating flow carried out on subsonic wall jet facilities in an anechoic room is summarized. The jet exit Mach number range is from 0.2 to 0.8. The effects of the flow Mach number ( Ma ) and the cavity depth ( D ) on the oscillation are studied. It is found that for L/D =4, (shallow cavity), the oscillation is mainly due to the self exciting of the free shear layer above the cavity opening, for L/D =2, the acoustic resonance is responsible for the oscillation. Preliminary tests are performed to study the suppression effect of the leading edge tone excitation on cavity flow, and considerable reduction of oscillation has been achieved when Ma ≤0.6.
基金supported in part by the National Science Foundation Grants No.DMS-0906440 and No.DMS-1206438.
文摘This paper investigates the chaotic lid-driven square cavity flows at extreme Reynolds numbers.Several observations have been made from this study.Firstly,at extreme Reynolds numbers two principles add at the genesis of tiny,loose counterclockwise-or clockwise-rotating eddies.One concerns the arousing of them owing to the influence of the clockwise-or counterclockwise currents nearby;the other,the arousing of counterclockwise-rotating eddies near attached to the moving(lid)top wall which moves from left to right.Secondly,unexpectedly,the kinetic energy soon reaches the qualitative temporal limit’s pace,fluctuating briskly,randomly inside the total kinetic energy range,fluctuations which concentrate on two distinct fragments:one on its upper side,the upper fragment,the other on its lower side,the lower fragment,switching briskly,randomly from each other;and further on many small fragments arousing randomly within both,switching briskly,randomly from one another.As the Reynolds number Re→∞,both distance and then close,and the kinetic energy fluctuates shorter and shorter at the upper fragment and longer and longer at the lower fragment,displaying tall high spikes which enlarge and then disappear.As the time t→∞(at the Reynolds number Re fixed)they recur from time to time with roughly the same amplitude.For the most part,at the upper fragment the leading eddy rotates clockwise,and at the lower fragment,in stark contrast,it rotates counterclockwise.At Re=109 the leading eddy-at its qualitative temporal limit’s pace—appears to rotate solely counterclockwise.
基金the National Natural Science Foundation of China for sponsoring the research described in the current paper(No.51406204)
文摘With the aid of numerical method, both flow field and its accompanied loss mechanism within the rotating cavity are investigated in detail in the 1^(st) part of the two parts paper. For ease of comparison, rotating cavity is further classified as the rotor-stator cavity case and the rotor-rotor cavity case. Results indicate that flow within both kinds of the cavity act as the inviscid flow except that the flow near walls, neighboring the lower G region and in the vicinity of the rotating orifices. In the regions except such inviscid-flow-dominate domains, the theoretical core rotation factor can be safely used to predict the swirl ratio within the cavity. When detailed flow pattern is considered, Ekman-type flow exists near periphery of the surface's boundary layer where viscous effect is non-negligible. However, due to the complex profile of the simulated cavity case, vortices structure is varied within the cavity. By comparison, swirl ratio can be used to predict the magnitude of loss. Due to the relatively evident rotating effects of the rotor-rotor cavity, swirl ratio even increases to 1.4 in the current model, which means that flow is moving faster than the surrounding disc. Further investigation finds that this kind of highly rotating flow is accompanied with serious undesirable pressure loss. Parenthetically, unlike its counterpart, swirl ratio above 1.0 doesn't happen when fluid passes through the rotor-stator cavity. So it is suggested that rotor-rotor flow cavity with the superimposed inward throughflow should be avoided in the engine design or certain measurements should be provided when such structure design is unavoidable. Simulation done in the current paper is meaningful since these dimensional parameters are typical in the design of state-of-art. Relatively lower range of Re_φ and C_w is not considered in the current two parts paper.
基金supported by National Natural Science Foundation of China(12172308)National Key Research and Development Program of China(2020YFA0710902).
文摘Combining the detached eddy simulation(DES)method and Ffowcs Williams-Hawkings(FW-H)equation,the effect of bogie cavity end wall inclination on the flow field and aerodynamic noise in the bogie region is numerically studied.First,the simulation is conducted based on a simplified cavity-bogie model,including five cases with different inclination angles of the front and rear walls of the cavity.By comparing and analyzing the flow field and acoustic results of the five cases,the influence of the regularity and mechanism of the bogie cavity end wall inclination on the flow field and the aerodynamic noise of the bogie region are revealed.Then,the noise reduction strategy determined by the results of the simplified cavity-bogie model is applied to a three-car marshaling train model to verify its effectiveness when applied to the real train.The results reveal that the forward inclination of the cavity front wall enlarges the influence area of shear vortex structures formed at the leading edge of the cavity and intensifies the interaction between the vortex structures and the front wheelset,frontmotor,and front gearbox,resulting in the increase of the aerodynamic noise generated by the bogie itself.The backward inclination of the cavity rear wall is conducive to guiding the vortex structures flow out of the cavity and weakening the interaction between the shear vortex structures and the cavity rear wall,leading to the reduction of the aerodynamic noise generated by the bogie cavity.Inclining the rear end wall of the foremost bogie cavity of the head car is a feasible aerodynamic noise reduction measure for high-speed trains.
基金the support provided by the Department of Aerospace Engineering,IIST,Trivandrum,India,in carrying out this research work.
文摘Experimental and computational analysis has been carried out by many researchers on supersonic cavity flow,but detailed analysis based on Rossiter’s model still requires some insight.In the current study an open rectangular cavity with a length to depth ratio of 2(L/D=2)and Mach number at the inlet as 1.71,was considered as a baseline configuration for experimental analysis.Statistical techniques such as power spectral density(PSD),correlation,and overall sound pressure level(OASPL)were carried out on the unsteady pressure data,to analyze the aero-acoustic flow physics.High-speed schlieren images were processed to obtain spatially coherent modes by proper orthogonal decomposition(POD).The analysis was extended for different dimensions of subcavities on the aft,floor,and front wall.This detailed analysis of these configurations with different dimensions and combinations revealed the various flow features and mode frequencies in supersonic cavity.As the front wall subcavity act as a passive control device,reducing the overall sound pressure level inside the cavity whereas,the aft wall subcavity acts as a passive resonator with distinct harmonic fluidresonant modes,a similar phenomenon was observed for floor subcavity at different locations.A novel method was employed to analyze Rossiter’s model and its applicability in estimating experimental modes was verified,as it accurately predicted the dominant frequencies with a maximum of 2.74% uncertainty among all the configurations.
