Algorithm for cavity flow in a new-born goaf and experimental verification

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.

Mode transition and oscillation suppression in supersonic cavity flow

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.

Transition to chaos in lid-driven square cavity flow

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.

Model reduction for supersonic cavity flow using proper orthogonal decomposition(POD)and Galerkin projection

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.

SUPG finite element method based on penalty function for lid-driven cavity flow up to Re = 27500

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.

Numerical investigation of cavity flow at subsonic and transonic speeds

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

Effect of Bogie Cavity End Wall Inclination on Flow Field and Aerodynamic Noise in the Bogie Region of High-Speed Trains

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.

Effects of multiple subcavities with floor subcavity in supersonic cavity flow

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.

Simulating high Reynolds number flow in two-dimensional lid-driven cavity by multi-relaxation-time lattice Boltzmann method

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.

A LATTICE BOLTZMANN SUBGRID MODEL FOR LID-DRIVEN CAVITY FLOW

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.

EXPERIMENTAL AND NUMERICAL INVESTIGATIONS OF BOTH FLOW INDUCED CAVITY OSCILLATION AND ITS SUPPRESSION BY ACOUSTIC 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.

EXPERIMENTAL STUDY OF HIGH SUBSONIC CAVITY FLOW OSCILLATION AND ITS SUPPRESSION BY ACOUSTIC EXCITATION

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.

Self-sustained oscillation for compressible cylindrical cavity flows

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.

Development and Application of a Reduced Order Model for the Control of Self-Sustained Instabilities in Cavity Flows

Flow around a cavity is characterized by a self-sustained mechanism in which the shear layer impinges on the downstream edge of the cavity resulting in a feedback mechanism.Direct Numerical Simulations of the flow at low Reynolds number has been carried out to get pressure and velocity fluctuations,for the case of un-actuated and multi frequency actuation.A Reduced Order Model for the isentropic compressible equations based on the method of Proper Orthogonal Decomposition has been constructed.The model has been extended to include the effect of control.The Reduced Order dynamical system shows a divergence in time integration.A method of calibration based on the minimization of a linear functional of error,to the sensitivity of the modes,is proposed.The calibrated low order model is used to design a feedback control of cavity flows based on an observer design.For the experimental implementation of the controller,a state estimate based on the observed pressure measurements is obtained through a linear stochastic estimation.Finally the obtained control is introduced into the Direct Numerical Simulation to obtain a decrease in spectra of the cavity acoustic mode.

Chaotic Lid-Driven Square Cavity Flows at Extreme Reynolds Numbers

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.

Numerical Simulation of Flow over an Open Cavity with Self-Sustained Oscillation Mode Switching

Numerical simulations are used to investigate the self-sustained oscillating flows past an open cavity. The two-dimensional incompressible Navier-Stokes equations are solved directly by using the finite difference method for cavities with an upstream laminar boundary layer. A series of simulations are performed for a variety of cavity length-to-depth ratio. The results show the switching among some flow modes including non-oscillation mode, shear layer mode and wake mode. The variation of the Strouhal number is in favorable agreement with available experimental data. The results of flow fields in the cavity reveal the relationship between the cavity shear layer oscillation modes and recirculating vortices in the cavity.

FLOW FIELD AT COLLAPSE OF A CAVITY

Employing Rayleigh's method, the collapse of a vaporous bubble in an incompressible liquid with surface tension is analysed. The expressions of time versus radius, bubble-wall velocity and pressure developed at collapse are thus introduced.Finally, the numerical solution of velocity and pressure field in the liquid surrounding the cavity is also given.

An artificial viscosity augmented physics-informed neural network for incompressible flow

Physics-informed neural networks(PINNs)are proved methods that are effective in solving some strongly nonlinear partial differential equations(PDEs),e.g.,Navier-Stokes equations,with a small amount of boundary or interior data.However,the feasibility of applying PINNs to the flow at moderate or high Reynolds numbers has rarely been reported.The present paper proposes an artificial viscosity(AV)-based PINN for solving the forward and inverse flow problems.Specifically,the AV used in PINNs is inspired by the entropy viscosity method developed in conventional computational fluid dynamics(CFD)to stabilize the simulation of flow at high Reynolds numbers.The newly developed PINN is used to solve the forward problem of the two-dimensional steady cavity flow at Re=1000 and the inverse problem derived from two-dimensional film boiling.The results show that the AV augmented PINN can solve both problems with good accuracy and substantially reduce the inference errors in the forward problem.

Multiple solutions and hysteresis in the flows driven by surface with antisymmetric velocity profile

Multiple steady solutions and hysteresis phenomenon in the square cavity flows driven by the surface with antisymmetric velocity profile are investigated by numerical simulation and bifurcation analysis.A high order spectral element method with the matrix-free pseudo-arclength technique is used for the steady-state solution and numerical continuation.The complex flow patterns beyond the symmetry-breaking at Re≈320 are presented by a bifurcation diagram for Re<2500.The results of stable symmetric and asymmetric solutions are consistent with those reported in literature,and a new unstable asymmetric branch is obtained besides the stable branches.A novel hysteresis phenomenon is observed in the range of 2208<Re<2262,where two pairs of stable and two pairs of unstable asymmetric steady solutions beyond the stable symmetric state coexist.The vortices near the sidewall appear when the Reynolds number increases,which correspond to the bifurcation of topology structure,but not the bifurcation of Navier-Stokes equations.The hysteresis is proposed to be the result of the combined mechanisms of the competition and coalescence of secondary vortices.

Experimental Investigation on Cavitating Flow Shedding over an Axisymmetric Blunt Body

Nowadays,most researchers focus on the cavity shedding mechanisms of unsteady cavitating flows over different objects,such as 2D/3D hydrofoils,venturi-type section,axisymmetric bodies with different headforms,and so on.But few of them pay attention to the differences of cavity shedding modality under different cavitation numbers in unsteady cavitating flows over the same object.In the present study,two kinds of shedding patterns are investigated experimentally.A high speed camera system is used to observe the cavitating flows over an axisymmetric blunt body and the velocity fields are measured by a particle image velocimetry（PIV）technique in a water tunnel for different cavitation conditions.The U-type cavitating vortex shedding is observed in unsteady cavitating flows.When the cavitation number is 0.7,there is a large scale cavity rolling up and shedding,which cause the instability and dramatic fluctuation of the flows,while at cavitation number of 0.6,the detached cavities can be conjunct with the attached part to induce the break-off behavior again at the tail of the attached cavity,as a result,the final shedding is in the form of small scale cavity and keeps a relatively steady flow field.It is also found that the interaction between the re-entrant flow and the attached cavity plays an important role in the unsteady cavity shedding modality.When the attached cavity scale is insufficient to overcome the re-entrant flow,it deserves the large cavity rolling up and shedding just as that at cavitation number of 0.7.Otherwise,the re-entrant flow is defeated by large enough cavity to induce the cavity-combined process and small scale cavity vortexes shedding just as that of the cavitation number of0.6.This research shows the details of two different cavity shedding modalities which is worthful and meaningful for the further study of unsteady cavitation.