In the present study,the base pressure variations induced by the presence of a cavity,known to have a strong influence of the behaviour of supersonic projectiles,are investigated through numerical solution of the bala...In the present study,the base pressure variations induced by the presence of a cavity,known to have a strong influence of the behaviour of supersonic projectiles,are investigated through numerical solution of the balance equations for mass,momentum,and energy.An area ratio of four is considered and numerical simulations are carried out at Mach M=1.2,1.4,1.6,and 1.8 assuming no cavity or cavity locations 0.5D,1D,1.5D,and 2D.The inlet pressure of the nozzle is considered as a flow variable.The Taguchi method is also used,and the considered cases are then analyzed using a full factorial experimental design.The results show that the cavity is effective in increasing the base pressure for the conditions examined.For other nozzle pressure ratios,cavities do not lead to passive control due the change in the reattachment length.The distribution of wall pressure reveals that,in general,a cavity used to implement passive control of the base pressure does not adversely influence the flow pattern in the domain.展开更多
This work aims to compute stability derivatives in the Newtonian limit in pitch when the Mach number tends to infinity.In such conditions,these stability derivatives depend on the Ogive’s shape and not the Mach numbe...This work aims to compute stability derivatives in the Newtonian limit in pitch when the Mach number tends to infinity.In such conditions,these stability derivatives depend on the Ogive’s shape and not the Mach number.Generally,the Mach number independence principle becomes effective from M=10 and above.The Ogive nose is obtained through a circular arc on the cone surface.Accordingly,the following arc slopes are consideredλ=5,10,15,−5,−10,and−15.It is found that the stability derivatives decrease due to the growth inλfrom 5 to 15 and vice versa.Forλ=5 and 10,the damping derivative declines with an increase inλfrom 5 to 10.Yet,for the damping derivatives,the minimum location remains at a pivot position,h=0.75 for large values ofλ.Hence,whenλ=−15,the damping derivatives are independent of the cone angles for most pivot positions except in the early twenty percent of the leading edge.展开更多
We investigate the low Mach number limit for the isentropic compressible NavierStokes equations with a revised Maxwell's law(with Galilean invariance) in R^(3). By applying the uniform estimates of the error syste...We investigate the low Mach number limit for the isentropic compressible NavierStokes equations with a revised Maxwell's law(with Galilean invariance) in R^(3). By applying the uniform estimates of the error system, it is proven that the solutions of the isentropic Navier-Stokes equations with a revised Maxwell's law converge to that of the incompressible Navier-Stokes equations as the Mach number tends to zero. Moreover, the convergence rates are also obtained.展开更多
Considering droplet phenomena at low Mach numbers,large differences in the magnitude of the occurring characteristic waves are presented.As acoustic phenomena often play a minor role in such applications,classical exp...Considering droplet phenomena at low Mach numbers,large differences in the magnitude of the occurring characteristic waves are presented.As acoustic phenomena often play a minor role in such applications,classical explicit schemes which resolve these waves suffer from a very restrictive timestep restriction.In this work,a novel scheme based on a specific level set ghost fluid method and an implicit-explicit(IMEX)flux splitting is proposed to overcome this timestep restriction.A fully implicit narrow band around the sharp phase interface is combined with a splitting of the convective and acoustic phenomena away from the interface.In this part of the domain,the IMEX Runge-Kutta time discretization and the high order discontinuous Galerkin spectral element method are applied to achieve high accuracies in the bulk phases.It is shown that for low Mach numbers a significant gain in computational time can be achieved compared to a fully explicit method.Applica-tions to typical droplet dynamic phenomena validate the proposed method and illustrate its capabilities.展开更多
Mach number is a key metric in the evaluation of wind tunnel flow field performance.This complex process of wind tunnel test mainly has the problems of nonlinearity and time lag.In order to overcome the problems and c...Mach number is a key metric in the evaluation of wind tunnel flow field performance.This complex process of wind tunnel test mainly has the problems of nonlinearity and time lag.In order to overcome the problems and control the Mach number stability,this paper proposes a new method of Mach number prediction based on a nonlinear autoregressive exogenous-genetic algorithm-Elman(NARX-GA-Elman)model,which adopts NARX as the basic framework,determines the order of the input variables by using the false nearest neighbor(FNN),and uses the dynamic nonlinear network Elman to fit the model,and finally uses the global optimization algorithm GA to optimize the weight thresholds in the model to establish the Mach number prediction model with optimal performance under single working condition.By comparing with the traditional algorithm,the prediction accuracy of the model is improved by 61.5%,and the control accuracy is improved by 55.7%,which demonstrates that the model has very high prediction accuracy and good stability performance.展开更多
The test section’s Mach number in wind tunnel testing is a significant metric for evaluating system performance.The quality of the flow field in the wind tunnel is contingent upon the system's capacity to maintai...The test section’s Mach number in wind tunnel testing is a significant metric for evaluating system performance.The quality of the flow field in the wind tunnel is contingent upon the system's capacity to maintain stability across various working conditions.The process flow in wind tunnel testing is inherently complex,resulting in a system characterized by nonlinearity,time lag,and multiple working conditions.To implement the predictive control algorithm,a precise Mach number prediction model must be created.Therefore,this report studies the method for Mach number prediction modelling in wind tunnel flow fields with various working conditions.Firstly,this paper introduces a continuous transonic wind tunnel.The key physical quantities affecting the flow field of the wind tunnel are determined by analyzing its structure and blowing process.Secondly,considering the nonlinear and time-lag characteristics of the wind tunnel system,a CNN-LSTM model is employed to establish the Mach number prediction model by combining the 1D-CNN algorithm with the LSTM model,which has long and short-term memory functions.Then,the attention mechanism is incorporated into the CNN-LSTM prediction model to enable the model to focus more on data with greater information importance,thereby enhancing the model's training effectiveness.The application results ultimately demonstrate the efficacy of the proposed approach.展开更多
By analyzing the characteristics of low Mach number perfect gas flows, a novel Slightly Compressible Model (SCM) for low Mach number perect gas flows is derived. In view of numerical calculations, this model is proved...By analyzing the characteristics of low Mach number perfect gas flows, a novel Slightly Compressible Model (SCM) for low Mach number perect gas flows is derived. In view of numerical calculations, this model is proved very efficient, for it is kept within thep-v frame but does not have to satisfy the time consuming divergence-free condition in order to get the incompressible Navier-Stokes equation solution. Writing the equations in the form of conservation laws, we have derived the characteristic systems which are necessary for numerical calculations. A cell-centered finite-volume method with flux difference upwind-biased schemes is used for the equation solutions and a new Exact Newton Relaxation (ENR) implicit method is developed. Various computed results are presented to validate the present model. Laminar flow solutions over a circular cylinder with wake developing and vortex shedding are presented. Results for inviscid flow over a sphere are compared in excellent agreement with the exact analytic incompressible solution. Three-dimensional viscous flow solutions over sphere and prolate spheroid are also calculated and compared well with experiments and other incompressible solutions. Finally, good convergent performances are shown for sphere viscous flows.展开更多
In this paper, we study the low Mach number limit of a compressible nonisothermal model for nematic liquid crystals in a bounded domain. We establish the uniform estimates with respect to the Mach number, and thus pro...In this paper, we study the low Mach number limit of a compressible nonisothermal model for nematic liquid crystals in a bounded domain. We establish the uniform estimates with respect to the Mach number, and thus prove the convergence to the solution of the incompressible model for nematic liquid crystals.展开更多
A design method was developed to specify the profile of the continuously variable Mach-number nozzle for the supersonic wind tunnel. The controllable contour design technique was applied to obtaining the original nozz...A design method was developed to specify the profile of the continuously variable Mach-number nozzle for the supersonic wind tunnel. The controllable contour design technique was applied to obtaining the original nozzle profile, while other Machnumbers were derived from the transformation of the original profile. A design scheme, covering a Mach-number range of3.0<Ma<4.0, was shown to illustrate the present design technique. To fully validate the present design method, computational fluid dynamics(CFD) analyses were carried out to study the flow quality in the test area of the nozzle. The computed results indicate that exit uniform flow is obtained with 1.19% of the maximal Mach-number deviation at the nozzle exit. The present design method achieves the continuously variable Mach-number flow during a wind tunnel running.展开更多
This paper is concerned with the low Mach number limit for the compressible Navier-Stokes equations in an exterior domain. We present here an approach based on Strichartz estimate defined on a non trapping exterior do...This paper is concerned with the low Mach number limit for the compressible Navier-Stokes equations in an exterior domain. We present here an approach based on Strichartz estimate defined on a non trapping exterior domain and we will be able to show the compactness and strong convergence of the velocity vector field.展开更多
A novel extension to SMAC scheme is proposed for variable density flows under low Mach number approximation. The algorithm is based on a predictor—corrector time integration scheme that employs a projection method fo...A novel extension to SMAC scheme is proposed for variable density flows under low Mach number approximation. The algorithm is based on a predictor—corrector time integration scheme that employs a projection method for the momentum equation. A constant-coefficient Poisson equation is solved for the pressure following both the predictor and corrector steps to satisfy the continuity equation at each time step. The proposed algorithm has second order centrally differenced convective fluxes with upwinding based on Cell Peclet number while diffusive flux are viscous fourth order accurate. Spatial discretization is performed on a collocated grid system that offers computational simplicity and straight forward extension to curvilinear coordinate systems. The algorithm is kinetic energy preserving. Further in this paper robustness and accuracy are demonstrated by performing test on channel flow with non-Boussinesq condition on different temperature ratios.展开更多
We consider a problem of a 2-dimensional high-Mach-number dilute inelastic gas originating from infinity impinging on an oblique surface of infinite length. By analyzing probabilities of particle-particle collisions, ...We consider a problem of a 2-dimensional high-Mach-number dilute inelastic gas originating from infinity impinging on an oblique surface of infinite length. By analyzing probabilities of particle-particle collisions, we derive an analytical formula for the mean force experienced by the surface when the system is dilute. We also derive conditions for the validity of our theory.展开更多
The interaction of a shock wave with a spherical helium bubble is investigated numerically by using the high- resolution piecewise parabolic method (PPM), in which the viscous and turbulence effects are both conside...The interaction of a shock wave with a spherical helium bubble is investigated numerically by using the high- resolution piecewise parabolic method (PPM), in which the viscous and turbulence effects are both considered. The bubble is of the same size and is accelerated by a planar shock of different Mach numbers (Ma). The re- suits of low Ma cases agree quantitatively with those of experiments [G. Layes, O. Le M4tayer. Phys. Fluids 19 (2007) 042105]. With the increase of Ma, the final geometry of the bubble becomes quite different, the com- pression ratio is highly raised, and the time-dependent mean bubble velocity is also influenced. The compression ratios measured can be well normalized when Ma is low, while less agreement has been achieved for high Ma cases. In addition, the mixedness between two fluids is enhanced greatly as Ma increases. Some existed scaling laws of these quantities for the shock wave strength cannot be directly applied to high Ma cases.展开更多
On super-sonic or trans-sonic planar cascade wind tunnel of free jet intermittent type, wind blowing experiments were performed on the typical sections of stator and rotor blades in the last stage of ultra-ultra-criti...On super-sonic or trans-sonic planar cascade wind tunnel of free jet intermittent type, wind blowing experiments were performed on the typical sections of stator and rotor blades in the last stage of ultra-ultra-critical steam turbine with extra-long blade of 1200mm. The influences of attack angle and Mach number on the aerodynamic performances of these sections of the blade profiles were verified, and their operating ranges were also specified.展开更多
The application of abruptly enlarged flows to adjust the drag of aerodynamic vehicles using machine learning models has not been investigated previously.The process variables(Mach number(M),nozzle pressure ratio(η),a...The application of abruptly enlarged flows to adjust the drag of aerodynamic vehicles using machine learning models has not been investigated previously.The process variables(Mach number(M),nozzle pressure ratio(η),area ratio(α),and length to diameter ratio(γ))were numerically explored to address several aspects of this process,namely base pressure(β)and base pressure with cavity(βcav).In this work,the optimal base pressure is determined using the PCA-BAS-ENN based algorithm to modify the base pressure presetting accuracy,thereby regulating the base drag required for smooth flow of aerodynamic vehicles.Based on the identical dataset,the GA-BP and PSO-BP algorithms are also compared to thePCA-BAS-ENNalgorithm.The data for training and testing the algorithmswas derived using the regression equation developed using the Box-Behnken Design(BBD).The results show that the PCA-BAS-ENN model delivered highly accurate predictions when compared to the other two models.As a result,the advantages of these results are two-fold,providing:(i)a detailed examination of the efficiency of different neural network algorithms in dealing with a genuine aerodynamic problem,and(ii)helpful insights for regulating process variables to improve technological,operational,and financial factors,simultaneously.展开更多
文摘In the present study,the base pressure variations induced by the presence of a cavity,known to have a strong influence of the behaviour of supersonic projectiles,are investigated through numerical solution of the balance equations for mass,momentum,and energy.An area ratio of four is considered and numerical simulations are carried out at Mach M=1.2,1.4,1.6,and 1.8 assuming no cavity or cavity locations 0.5D,1D,1.5D,and 2D.The inlet pressure of the nozzle is considered as a flow variable.The Taguchi method is also used,and the considered cases are then analyzed using a full factorial experimental design.The results show that the cavity is effective in increasing the base pressure for the conditions examined.For other nozzle pressure ratios,cavities do not lead to passive control due the change in the reattachment length.The distribution of wall pressure reveals that,in general,a cavity used to implement passive control of the base pressure does not adversely influence the flow pattern in the domain.
文摘This work aims to compute stability derivatives in the Newtonian limit in pitch when the Mach number tends to infinity.In such conditions,these stability derivatives depend on the Ogive’s shape and not the Mach number.Generally,the Mach number independence principle becomes effective from M=10 and above.The Ogive nose is obtained through a circular arc on the cone surface.Accordingly,the following arc slopes are consideredλ=5,10,15,−5,−10,and−15.It is found that the stability derivatives decrease due to the growth inλfrom 5 to 15 and vice versa.Forλ=5 and 10,the damping derivative declines with an increase inλfrom 5 to 10.Yet,for the damping derivatives,the minimum location remains at a pivot position,h=0.75 for large values ofλ.Hence,whenλ=−15,the damping derivatives are independent of the cone angles for most pivot positions except in the early twenty percent of the leading edge.
基金Yuxi HU was supported by the NNSFC (11701556)the Yue Qi Young Scholar ProjectChina University of Mining and Technology (Beijing)。
文摘We investigate the low Mach number limit for the isentropic compressible NavierStokes equations with a revised Maxwell's law(with Galilean invariance) in R^(3). By applying the uniform estimates of the error system, it is proven that the solutions of the isentropic Navier-Stokes equations with a revised Maxwell's law converge to that of the incompressible Navier-Stokes equations as the Mach number tends to zero. Moreover, the convergence rates are also obtained.
基金support provided by the Deutsche Forschun-gsgemeinschaft(DFG,German Research Foundation)through the project GRK 2160/1“Droplet Interaction Technologies”and through the project no.457811052
文摘Considering droplet phenomena at low Mach numbers,large differences in the magnitude of the occurring characteristic waves are presented.As acoustic phenomena often play a minor role in such applications,classical explicit schemes which resolve these waves suffer from a very restrictive timestep restriction.In this work,a novel scheme based on a specific level set ghost fluid method and an implicit-explicit(IMEX)flux splitting is proposed to overcome this timestep restriction.A fully implicit narrow band around the sharp phase interface is combined with a splitting of the convective and acoustic phenomena away from the interface.In this part of the domain,the IMEX Runge-Kutta time discretization and the high order discontinuous Galerkin spectral element method are applied to achieve high accuracies in the bulk phases.It is shown that for low Mach numbers a significant gain in computational time can be achieved compared to a fully explicit method.Applica-tions to typical droplet dynamic phenomena validate the proposed method and illustrate its capabilities.
基金funded by the National Natural Science Foundation of China(No.61503069)the Fundamental Research Funds for the Central Universities(N150404020).
文摘Mach number is a key metric in the evaluation of wind tunnel flow field performance.This complex process of wind tunnel test mainly has the problems of nonlinearity and time lag.In order to overcome the problems and control the Mach number stability,this paper proposes a new method of Mach number prediction based on a nonlinear autoregressive exogenous-genetic algorithm-Elman(NARX-GA-Elman)model,which adopts NARX as the basic framework,determines the order of the input variables by using the false nearest neighbor(FNN),and uses the dynamic nonlinear network Elman to fit the model,and finally uses the global optimization algorithm GA to optimize the weight thresholds in the model to establish the Mach number prediction model with optimal performance under single working condition.By comparing with the traditional algorithm,the prediction accuracy of the model is improved by 61.5%,and the control accuracy is improved by 55.7%,which demonstrates that the model has very high prediction accuracy and good stability performance.
基金funded by the National Natural Science Foundation of China(No.61503069)the Fundamental Research Funds for the Central Universities(N150404020).
文摘The test section’s Mach number in wind tunnel testing is a significant metric for evaluating system performance.The quality of the flow field in the wind tunnel is contingent upon the system's capacity to maintain stability across various working conditions.The process flow in wind tunnel testing is inherently complex,resulting in a system characterized by nonlinearity,time lag,and multiple working conditions.To implement the predictive control algorithm,a precise Mach number prediction model must be created.Therefore,this report studies the method for Mach number prediction modelling in wind tunnel flow fields with various working conditions.Firstly,this paper introduces a continuous transonic wind tunnel.The key physical quantities affecting the flow field of the wind tunnel are determined by analyzing its structure and blowing process.Secondly,considering the nonlinear and time-lag characteristics of the wind tunnel system,a CNN-LSTM model is employed to establish the Mach number prediction model by combining the 1D-CNN algorithm with the LSTM model,which has long and short-term memory functions.Then,the attention mechanism is incorporated into the CNN-LSTM prediction model to enable the model to focus more on data with greater information importance,thereby enhancing the model's training effectiveness.The application results ultimately demonstrate the efficacy of the proposed approach.
基金The project supported by the Basic Research on Frontier Problems in Fluid and Aerodynamics in Chinathe National Natural Science Foundation of China (19772069)
文摘By analyzing the characteristics of low Mach number perfect gas flows, a novel Slightly Compressible Model (SCM) for low Mach number perect gas flows is derived. In view of numerical calculations, this model is proved very efficient, for it is kept within thep-v frame but does not have to satisfy the time consuming divergence-free condition in order to get the incompressible Navier-Stokes equation solution. Writing the equations in the form of conservation laws, we have derived the characteristic systems which are necessary for numerical calculations. A cell-centered finite-volume method with flux difference upwind-biased schemes is used for the equation solutions and a new Exact Newton Relaxation (ENR) implicit method is developed. Various computed results are presented to validate the present model. Laminar flow solutions over a circular cylinder with wake developing and vortex shedding are presented. Results for inviscid flow over a sphere are compared in excellent agreement with the exact analytic incompressible solution. Three-dimensional viscous flow solutions over sphere and prolate spheroid are also calculated and compared well with experiments and other incompressible solutions. Finally, good convergent performances are shown for sphere viscous flows.
基金supported by NSFC(11171154)supported in part by by NSFC(11671193)A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘In this paper, we study the low Mach number limit of a compressible nonisothermal model for nematic liquid crystals in a bounded domain. We establish the uniform estimates with respect to the Mach number, and thus prove the convergence to the solution of the incompressible model for nematic liquid crystals.
基金Project(11072264)supported by the National Natural Science Foundation of China
文摘A design method was developed to specify the profile of the continuously variable Mach-number nozzle for the supersonic wind tunnel. The controllable contour design technique was applied to obtaining the original nozzle profile, while other Machnumbers were derived from the transformation of the original profile. A design scheme, covering a Mach-number range of3.0<Ma<4.0, was shown to illustrate the present design technique. To fully validate the present design method, computational fluid dynamics(CFD) analyses were carried out to study the flow quality in the test area of the nozzle. The computed results indicate that exit uniform flow is obtained with 1.19% of the maximal Mach-number deviation at the nozzle exit. The present design method achieves the continuously variable Mach-number flow during a wind tunnel running.
文摘This paper is concerned with the low Mach number limit for the compressible Navier-Stokes equations in an exterior domain. We present here an approach based on Strichartz estimate defined on a non trapping exterior domain and we will be able to show the compactness and strong convergence of the velocity vector field.
文摘A novel extension to SMAC scheme is proposed for variable density flows under low Mach number approximation. The algorithm is based on a predictor—corrector time integration scheme that employs a projection method for the momentum equation. A constant-coefficient Poisson equation is solved for the pressure following both the predictor and corrector steps to satisfy the continuity equation at each time step. The proposed algorithm has second order centrally differenced convective fluxes with upwinding based on Cell Peclet number while diffusive flux are viscous fourth order accurate. Spatial discretization is performed on a collocated grid system that offers computational simplicity and straight forward extension to curvilinear coordinate systems. The algorithm is kinetic energy preserving. Further in this paper robustness and accuracy are demonstrated by performing test on channel flow with non-Boussinesq condition on different temperature ratios.
基金supported by the Research Grants Council of Hong Kong Special Administrative Region,China(CityU 103509)
文摘We consider a problem of a 2-dimensional high-Mach-number dilute inelastic gas originating from infinity impinging on an oblique surface of infinite length. By analyzing probabilities of particle-particle collisions, we derive an analytical formula for the mean force experienced by the surface when the system is dilute. We also derive conditions for the validity of our theory.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11232011 and 11402262the 111 Project under Grant No B07033the China Postdoctoral Science Foundation Funded Project under Grant No 2014M561833
文摘The interaction of a shock wave with a spherical helium bubble is investigated numerically by using the high- resolution piecewise parabolic method (PPM), in which the viscous and turbulence effects are both considered. The bubble is of the same size and is accelerated by a planar shock of different Mach numbers (Ma). The re- suits of low Ma cases agree quantitatively with those of experiments [G. Layes, O. Le M4tayer. Phys. Fluids 19 (2007) 042105]. With the increase of Ma, the final geometry of the bubble becomes quite different, the com- pression ratio is highly raised, and the time-dependent mean bubble velocity is also influenced. The compression ratios measured can be well normalized when Ma is low, while less agreement has been achieved for high Ma cases. In addition, the mixedness between two fluids is enhanced greatly as Ma increases. Some existed scaling laws of these quantities for the shock wave strength cannot be directly applied to high Ma cases.
文摘On super-sonic or trans-sonic planar cascade wind tunnel of free jet intermittent type, wind blowing experiments were performed on the typical sections of stator and rotor blades in the last stage of ultra-ultra-critical steam turbine with extra-long blade of 1200mm. The influences of attack angle and Mach number on the aerodynamic performances of these sections of the blade profiles were verified, and their operating ranges were also specified.
基金This research is supported by the Structures and Materials(S&M)Research Lab of Prince Sultan University.
文摘The application of abruptly enlarged flows to adjust the drag of aerodynamic vehicles using machine learning models has not been investigated previously.The process variables(Mach number(M),nozzle pressure ratio(η),area ratio(α),and length to diameter ratio(γ))were numerically explored to address several aspects of this process,namely base pressure(β)and base pressure with cavity(βcav).In this work,the optimal base pressure is determined using the PCA-BAS-ENN based algorithm to modify the base pressure presetting accuracy,thereby regulating the base drag required for smooth flow of aerodynamic vehicles.Based on the identical dataset,the GA-BP and PSO-BP algorithms are also compared to thePCA-BAS-ENNalgorithm.The data for training and testing the algorithmswas derived using the regression equation developed using the Box-Behnken Design(BBD).The results show that the PCA-BAS-ENN model delivered highly accurate predictions when compared to the other two models.As a result,the advantages of these results are two-fold,providing:(i)a detailed examination of the efficiency of different neural network algorithms in dealing with a genuine aerodynamic problem,and(ii)helpful insights for regulating process variables to improve technological,operational,and financial factors,simultaneously.