Temporal mode direct numerical simulation was done for the process of laminar-turbulent transition in an incompressible boundary layer on a flat plate. The analysis of the results showed that during the breakdown proc...Temporal mode direct numerical simulation was done for the process of laminar-turbulent transition in an incompressible boundary layer on a flat plate. The analysis of the results showed that during the breakdown process of laminar-turbulent transition, the modification of the mean flow profile by the disturbances led to a remarkable change in its stability characteristics, manifested in the significant enlargement of the linear unstable zone and the maximum amplification rate, and led to that many more disturbances were excited and enhanced rapidly, correspondingly the turbulent energy also increased rapidly, and the mean flow profiles evolved swiftly from laminar to turbulent. It was also found that if the oblique waves in the initial disturbances did not form symmetrical pairs, the subsequent span-wise mean velocities would, in general, be nonzero due to nonlinear interaction, which would have a great effect on the stability characteristics and also implied that the turbulence obtained by direct numerical simulation might not be fully a random process.展开更多
A numerical simulation of the interaction between laminar flow with low Reynolds number and a highly flexible elastic sheet is presented. The mathematical model for the simulation includes a three-dimensional finitevo...A numerical simulation of the interaction between laminar flow with low Reynolds number and a highly flexible elastic sheet is presented. The mathematical model for the simulation includes a three-dimensional finitevolume based fluid solver for incompressible viscous flow and a combined finite-discrete element method for the three-dimensional deformation of solid. An immersed boundary method is used to couple the simulation of fluid and solid. It is implemented through a set of immersed boundary points scattered on the solid surface. These points provide a deformable solid wall boundary for the fluid by adding body force to Navier-Stokes equations. The force from the fluid is also obtained for each point and then applied on the boundary nodes of the solid. The vortex-induced vibration of the highly flexible elastic sheet is simulated with the established mathematical model. The simulated results for both swing pattern and oscillation frequency of the elastic sheet in low Reynolds number flow agree well with experimental data.展开更多
This paper focused on the fundamental and applied research of turbulent flows encountered in the hypersonic flight of aerospace vehicles,which take place in the boundary layer and mixing layer.As to the plate boundary...This paper focused on the fundamental and applied research of turbulent flows encountered in the hypersonic flight of aerospace vehicles,which take place in the boundary layer and mixing layer.As to the plate boundary layer,LES approach has been used to simulate the flows over compression corners and incident shock waves,revealing that turbulent flows would significantly inhibit the boundary layer separation caused by shock wave-boundary layer interaction(SWBLI).The boundary layer transition over a circular cone has been analyzed through stability analysis and wind-tunnel test,by which the angle-of-attack effect in case of small angle of attack has been studied.Non-linear evolution process and secondary instability structure in the supersonic mixing layer(Mc=0.5) were initially figured out through the study of mixing layer,and knowledge of the flow control mechanism of the boundary layer and mixing enhancement mechanism of the mixing layer has been obtained through this research.Artificial boundary-layer transition technique based on subharmonic resonance has been proposed and applied to the flow control in a scramjet inlet,inhibiting the flow separation of the boundary layer while improving the inlet performance.To guarantee the mixing of kerosene and supersonic airflow in the scramjet combustor,the mixing enhancement method based on subharmonic resonance has been adopted and a concept of combustor with smooth wall and low internal drag has been proposed for ignition and stable combustion.Finally,future turbulence research and technological development of aerospace vehicles is predicted.展开更多
Competition of multiple Gortler modes in hypersonic boundary layer flows are investigated with the local and marching methods. The wall-layer mode (mode W) and the trapped-layer mode (mode T) both occur in the com...Competition of multiple Gortler modes in hypersonic boundary layer flows are investigated with the local and marching methods. The wall-layer mode (mode W) and the trapped-layer mode (mode T) both occur in the compressible boundary layer where there exists a temperature adjustment layer near the upper edge. The mode T has the largest growth rate at a lower Gortler number while the mode W dominates at larger G/Srtler numbers. These two modes are both responsible for the flow transition in the hypersonic flows especially when Gortler number is in the high value range in which the crossover of these two modes takes place. Such high Gortler numbers are virtually far beyond the neutral regime. The nonparallel base flows, therefore, cease to influence the stability behavior of the Gortler modes. The effects of the Mach number on the multiple Gortler modes are studied within a chosen Mach number of 0.95, 2, 4 and 6. When the flow Mach number is sufficiently large, e.g., Ma ≥4, the growth rate crossover of the mode T and mode W occurs both in the conventional G-β map as well as on the route downstream for a fixed wavelength disturbance. Four particular regions (Region T, T-W, W-T and W) around the crossover point are highlighted with the marching analysis and the result matches that of the local analysis. The initial disturbance of a normal mode maintains the shape in its corresponding dominating region while a shape-transformation occurs outside this region.展开更多
This work attempts to extend the fundamental theory for classic gas dynamics to viscous compressible flow,of which aeroacoustics will naturally be a special branch.As a continuation of Part I.Unbounded fluid(Mao et al...This work attempts to extend the fundamental theory for classic gas dynamics to viscous compressible flow,of which aeroacoustics will naturally be a special branch.As a continuation of Part I.Unbounded fluid(Mao et al.,2022),this paper studies the source of longitudinal field at solid boundary,caused by the on-wall kinematic and viscous dynamic coupling of longitudinal and transverse processes.We find that at this situation the easiest choice for the two independent thermodynamic variables is the dimensionless pressure P and temperature T.The two-level structure of boundary dynamics of longitudinal field is obtained by applying the continuity equation and its normal derivative to the surface.We show that the boundary dilatation flux represents faithfully the boundary production of vortex sound and entropy sound,and the mutual generation mechanism of the longitudinal and transverse fields on the boundary does not occur symmetrically"at the samc level,but appears along a zigzag route.At the first level,it is the pressure gradient that generates vorticity unidirectionally;while at the second level,it is the vorticity that generates dilatation unidirectionally.展开更多
The nonlinear evolution of a finite-amplitude disturbance in a 3-D supersonic boundary layer over a cone was investigated recently by Liu et al. using direct numerical simulation (DNS). It was found that certain sma...The nonlinear evolution of a finite-amplitude disturbance in a 3-D supersonic boundary layer over a cone was investigated recently by Liu et al. using direct numerical simulation (DNS). It was found that certain small-scale 3-D disturbances amplified rapidly. These disturbances exhibit the characteristics of second modes, and the most amplified components have a well- defined spanwise wavelength, indicating a clear selectivity of the amplification. In the case of a cone, the three-dimensionality of the base flow and the disturbances themselves may be responsible for the rapid amplification. In order to ascertain which of these two effects are essential, in this study we carried out DNS of the nonlinear evolution of a spanwise localized disturbance (wavepacket) in a flat-plate boundary layer. A similar amplification of small-scale disturbances was observed, suggesting that the direct reason for the rapid amplification is the three-dimensionality of the disturbances rather than the three-dimensional nature of the base flow, even though the latter does alter the spanwise distribution of the disturbance. The rapid growth of 3-D waves may be attributed to the secondary instability mechanism. Further simulations were performed for a wavepacket of first modes in a supersonic boundary layer and of Tollmien-Schlichting (T-S) waves in an incompressible boundary layer. The re- suits show that the amplifying components are in the band centered at zero spanwise wavenumber rather than at a finite spanwise wavenumber. It is therefore concluded that the rapid growth of 3-D disturbances in a band centered at a preferred large spanwise wavenumber is the main characteristic of nonlinear evolution of second mode disturbances in supersonic boundary layers.展开更多
An experimental study of compressible mixing layers(CMLs)was conducted using planar laser Mie scattering(PLMS)visualizations from condensed ethanol droplets in the flow.Large ensembles of digital images were collected...An experimental study of compressible mixing layers(CMLs)was conducted using planar laser Mie scattering(PLMS)visualizations from condensed ethanol droplets in the flow.Large ensembles of digital images were collected for two flow conditions at convective Mach numbers Mc=0.11 and 0.47.The coherent vortices,braids and eruptions in the mixing zone were observed,interpreted as evidence of multi-scale,three-dimensional structures at a high Reynolds number.The mixing layers with a large visualized range present two stages along the streamwise direction,corresponding to the initial mixing and the well-developed stage.A new method,the gray level ensemble average method(GLEAM),by virtue of the similarity of the mixing layer,was applied to measure the growth rate of the CML thickness.New evidence for a nonlinear growth of CML is reported,providing an interpretation of previous observations of the scattering of the growth rate.展开更多
A new invariant, the second order potential vorticity(SPV), is derived in this paper. SPV is the dot product of vorticity and the potential vorticity(PV) gradient, and is proven conservative for a compressible, adiaba...A new invariant, the second order potential vorticity(SPV), is derived in this paper. SPV is the dot product of vorticity and the potential vorticity(PV) gradient, and is proven conservative for a compressible, adiabatic and frictionless atmosphere. Research shows that the new invariant may be used to indicate the evolution of PV, because SPV includes all the information that determines PV evolution: the wind field, and the PV gradient. Furthermore, SPV is capable of diagnosing heavy precipitation because of the strong signals it presents in areas of heavy rainfall. SPV also shows great potential as a comprehensive conserved quantity for indicating the dynamical tropopause and baroclinic instability.展开更多
When condensation occurs in a supersonic flow field, the flow is affected by the latent heat released. In the present study, a condensing flow was produced by an expansion of moist air in nozzle with circular bump mod...When condensation occurs in a supersonic flow field, the flow is affected by the latent heat released. In the present study, a condensing flow was produced by an expansion of moist air in nozzle with circular bump models and shock waves occurred in the supersonic parts of the flow fields. The experimental investigations were carried out to show the effects of initial conditions in the reservoir and nozzle geometries on the shock wave characteristics and the turbulences in the flow fields. Furthermore, in order to clarify the effect of condensation on the flow fields with shock waves, Navier-Stokes equations were solved numerically using a 3rd-order MUSCL type TVD finitedifference scheme with a second order fractional step for time integration. As a result the effect of condensation on the aspect of flow field has been clarified.展开更多
Adding a new equation to the two-equation K-turbulence model framework,this paper proposed a three-equation turbulence model to determine the density variance for high-speed aero-optics and high-speed compressible tur...Adding a new equation to the two-equation K-turbulence model framework,this paper proposed a three-equation turbulence model to determine the density variance for high-speed aero-optics and high-speed compressible turbulent flows.Simulations were performed with the new model for supersonic and hypersonic flat-plate turbulent boundary layer and hypersonic ramp flows.The results showed that the prediction with the present model agrees well with the experimental data and is significantly better than the Lutz's model in predicting the density variance for the flat-plate flows.Furthermore,the present model can produce more accurate skin pressure and skin heat flux distributions than the original K-model in simulating hypersonic compression ramp flows with separation and reattachment and shock/boundary layer interactions.Without introducing a variety of ad hoc wall damping and wall-reflection terms,the proposed three-equation turbulence model is applicable to highspeed aero-optics and turbulent flows of real vehicles of complex configuration.展开更多
The author surveys a few examples of boundary layers for which the Prandtl boundary layer theory can be rigorously validated.All of them are associated with the incompressible Navier-Stokes equations for Newtonian flu...The author surveys a few examples of boundary layers for which the Prandtl boundary layer theory can be rigorously validated.All of them are associated with the incompressible Navier-Stokes equations for Newtonian fluids equipped with various Dirichlet boundary conditions(specified velocity).These examples include a family of(nonlinear 3D) plane parallel flows,a family of(nonlinear) parallel pipe flows,as well as flows with uniform injection and suction at the boundary.We also identify a key ingredient in establishing the validity of the Prandtl type theory,i.e.,a spectral constraint on the approximate solution to the Navier-Stokes system constructed by combining the inviscid solution and the solution to the Prandtl type system.This is an additional difficulty besides the wellknown issue related to the well-posedness of the Prandtl type system.It seems that the main obstruction to the verification of the spectral constraint condition is the possible separation of boundary layers.A common theme of these examples is the inhibition of separation of boundary layers either via suppressing the velocity normal to the boundary or by injection and suction at the boundary so that the spectral constraint can be verified.A meta theorem is then presented which covers all the cases considered here.展开更多
基金Supported by National Natural Science Foundation of China (No.90205021)Liu Hui Center of Applied Mathematics ,Nankai Universityand Tianjin University
文摘Temporal mode direct numerical simulation was done for the process of laminar-turbulent transition in an incompressible boundary layer on a flat plate. The analysis of the results showed that during the breakdown process of laminar-turbulent transition, the modification of the mean flow profile by the disturbances led to a remarkable change in its stability characteristics, manifested in the significant enlargement of the linear unstable zone and the maximum amplification rate, and led to that many more disturbances were excited and enhanced rapidly, correspondingly the turbulent energy also increased rapidly, and the mean flow profiles evolved swiftly from laminar to turbulent. It was also found that if the oblique waves in the initial disturbances did not form symmetrical pairs, the subsequent span-wise mean velocities would, in general, be nonzero due to nonlinear interaction, which would have a great effect on the stability characteristics and also implied that the turbulence obtained by direct numerical simulation might not be fully a random process.
基金Supported by Marie Curie International Incoming Fellowship (No. PIIF-GA-2009-253453)
文摘A numerical simulation of the interaction between laminar flow with low Reynolds number and a highly flexible elastic sheet is presented. The mathematical model for the simulation includes a three-dimensional finitevolume based fluid solver for incompressible viscous flow and a combined finite-discrete element method for the three-dimensional deformation of solid. An immersed boundary method is used to couple the simulation of fluid and solid. It is implemented through a set of immersed boundary points scattered on the solid surface. These points provide a deformable solid wall boundary for the fluid by adding body force to Navier-Stokes equations. The force from the fluid is also obtained for each point and then applied on the boundary nodes of the solid. The vortex-induced vibration of the highly flexible elastic sheet is simulated with the established mathematical model. The simulated results for both swing pattern and oscillation frequency of the elastic sheet in low Reynolds number flow agree well with experimental data.
文摘This paper focused on the fundamental and applied research of turbulent flows encountered in the hypersonic flight of aerospace vehicles,which take place in the boundary layer and mixing layer.As to the plate boundary layer,LES approach has been used to simulate the flows over compression corners and incident shock waves,revealing that turbulent flows would significantly inhibit the boundary layer separation caused by shock wave-boundary layer interaction(SWBLI).The boundary layer transition over a circular cone has been analyzed through stability analysis and wind-tunnel test,by which the angle-of-attack effect in case of small angle of attack has been studied.Non-linear evolution process and secondary instability structure in the supersonic mixing layer(Mc=0.5) were initially figured out through the study of mixing layer,and knowledge of the flow control mechanism of the boundary layer and mixing enhancement mechanism of the mixing layer has been obtained through this research.Artificial boundary-layer transition technique based on subharmonic resonance has been proposed and applied to the flow control in a scramjet inlet,inhibiting the flow separation of the boundary layer while improving the inlet performance.To guarantee the mixing of kerosene and supersonic airflow in the scramjet combustor,the mixing enhancement method based on subharmonic resonance has been adopted and a concept of combustor with smooth wall and low internal drag has been proposed for ignition and stable combustion.Finally,future turbulence research and technological development of aerospace vehicles is predicted.
基金supported by the National Natural Science Foundation of China(Grant Nos.10932005 and 11202115)
文摘Competition of multiple Gortler modes in hypersonic boundary layer flows are investigated with the local and marching methods. The wall-layer mode (mode W) and the trapped-layer mode (mode T) both occur in the compressible boundary layer where there exists a temperature adjustment layer near the upper edge. The mode T has the largest growth rate at a lower Gortler number while the mode W dominates at larger G/Srtler numbers. These two modes are both responsible for the flow transition in the hypersonic flows especially when Gortler number is in the high value range in which the crossover of these two modes takes place. Such high Gortler numbers are virtually far beyond the neutral regime. The nonparallel base flows, therefore, cease to influence the stability behavior of the Gortler modes. The effects of the Mach number on the multiple Gortler modes are studied within a chosen Mach number of 0.95, 2, 4 and 6. When the flow Mach number is sufficiently large, e.g., Ma ≥4, the growth rate crossover of the mode T and mode W occurs both in the conventional G-β map as well as on the route downstream for a fixed wavelength disturbance. Four particular regions (Region T, T-W, W-T and W) around the crossover point are highlighted with the marching analysis and the result matches that of the local analysis. The initial disturbance of a normal mode maintains the shape in its corresponding dominating region while a shape-transformation occurs outside this region.
基金supported by the National Natural Science Foundation of China(Grant Nos.12102365,91752202,11472016,11621202,and 12272371).
文摘This work attempts to extend the fundamental theory for classic gas dynamics to viscous compressible flow,of which aeroacoustics will naturally be a special branch.As a continuation of Part I.Unbounded fluid(Mao et al.,2022),this paper studies the source of longitudinal field at solid boundary,caused by the on-wall kinematic and viscous dynamic coupling of longitudinal and transverse processes.We find that at this situation the easiest choice for the two independent thermodynamic variables is the dimensionless pressure P and temperature T.The two-level structure of boundary dynamics of longitudinal field is obtained by applying the continuity equation and its normal derivative to the surface.We show that the boundary dilatation flux represents faithfully the boundary production of vortex sound and entropy sound,and the mutual generation mechanism of the longitudinal and transverse fields on the boundary does not occur symmetrically"at the samc level,but appears along a zigzag route.At the first level,it is the pressure gradient that generates vorticity unidirectionally;while at the second level,it is the vorticity that generates dilatation unidirectionally.
基金supported by the National Basic Research Program of China (Grant No. 2009CB724103)
文摘The nonlinear evolution of a finite-amplitude disturbance in a 3-D supersonic boundary layer over a cone was investigated recently by Liu et al. using direct numerical simulation (DNS). It was found that certain small-scale 3-D disturbances amplified rapidly. These disturbances exhibit the characteristics of second modes, and the most amplified components have a well- defined spanwise wavelength, indicating a clear selectivity of the amplification. In the case of a cone, the three-dimensionality of the base flow and the disturbances themselves may be responsible for the rapid amplification. In order to ascertain which of these two effects are essential, in this study we carried out DNS of the nonlinear evolution of a spanwise localized disturbance (wavepacket) in a flat-plate boundary layer. A similar amplification of small-scale disturbances was observed, suggesting that the direct reason for the rapid amplification is the three-dimensionality of the disturbances rather than the three-dimensional nature of the base flow, even though the latter does alter the spanwise distribution of the disturbance. The rapid growth of 3-D waves may be attributed to the secondary instability mechanism. Further simulations were performed for a wavepacket of first modes in a supersonic boundary layer and of Tollmien-Schlichting (T-S) waves in an incompressible boundary layer. The re- suits show that the amplifying components are in the band centered at zero spanwise wavenumber rather than at a finite spanwise wavenumber. It is therefore concluded that the rapid growth of 3-D disturbances in a band centered at a preferred large spanwise wavenumber is the main characteristic of nonlinear evolution of second mode disturbances in supersonic boundary layers.
基金supported by the National Natural Science Foundation of China(Grant Nos.11172006,10572004 and 90716008)by the National Basic Research Program of China(Grant No.2009CB724100)
文摘An experimental study of compressible mixing layers(CMLs)was conducted using planar laser Mie scattering(PLMS)visualizations from condensed ethanol droplets in the flow.Large ensembles of digital images were collected for two flow conditions at convective Mach numbers Mc=0.11 and 0.47.The coherent vortices,braids and eruptions in the mixing zone were observed,interpreted as evidence of multi-scale,three-dimensional structures at a high Reynolds number.The mixing layers with a large visualized range present two stages along the streamwise direction,corresponding to the initial mixing and the well-developed stage.A new method,the gray level ensemble average method(GLEAM),by virtue of the similarity of the mixing layer,was applied to measure the growth rate of the CML thickness.New evidence for a nonlinear growth of CML is reported,providing an interpretation of previous observations of the scattering of the growth rate.
基金supported by the Key Research Program of the Chinese Academy of Sciences(Grant No.KZZD-EW-05-01)the National Natural Science Foundation of China(Grant Nos.40921160379,40930950 and 40775031)
文摘A new invariant, the second order potential vorticity(SPV), is derived in this paper. SPV is the dot product of vorticity and the potential vorticity(PV) gradient, and is proven conservative for a compressible, adiabatic and frictionless atmosphere. Research shows that the new invariant may be used to indicate the evolution of PV, because SPV includes all the information that determines PV evolution: the wind field, and the PV gradient. Furthermore, SPV is capable of diagnosing heavy precipitation because of the strong signals it presents in areas of heavy rainfall. SPV also shows great potential as a comprehensive conserved quantity for indicating the dynamical tropopause and baroclinic instability.
文摘When condensation occurs in a supersonic flow field, the flow is affected by the latent heat released. In the present study, a condensing flow was produced by an expansion of moist air in nozzle with circular bump models and shock waves occurred in the supersonic parts of the flow fields. The experimental investigations were carried out to show the effects of initial conditions in the reservoir and nozzle geometries on the shock wave characteristics and the turbulences in the flow fields. Furthermore, in order to clarify the effect of condensation on the flow fields with shock waves, Navier-Stokes equations were solved numerically using a 3rd-order MUSCL type TVD finitedifference scheme with a second order fractional step for time integration. As a result the effect of condensation on the aspect of flow field has been clarified.
基金supported by the National Natural Science Foundation of China (Grant No. 11102079)the Aeronautical Science Foundation of China (Grant No. 20111456005)
文摘Adding a new equation to the two-equation K-turbulence model framework,this paper proposed a three-equation turbulence model to determine the density variance for high-speed aero-optics and high-speed compressible turbulent flows.Simulations were performed with the new model for supersonic and hypersonic flat-plate turbulent boundary layer and hypersonic ramp flows.The results showed that the prediction with the present model agrees well with the experimental data and is significantly better than the Lutz's model in predicting the density variance for the flat-plate flows.Furthermore,the present model can produce more accurate skin pressure and skin heat flux distributions than the original K-model in simulating hypersonic compression ramp flows with separation and reattachment and shock/boundary layer interactions.Without introducing a variety of ad hoc wall damping and wall-reflection terms,the proposed three-equation turbulence model is applicable to highspeed aero-optics and turbulent flows of real vehicles of complex configuration.
基金Project supported by the National Science Foundation,the 111 Project from the Ministry of Education of China at Fudan University and the COFRS award from Florida State University
文摘The author surveys a few examples of boundary layers for which the Prandtl boundary layer theory can be rigorously validated.All of them are associated with the incompressible Navier-Stokes equations for Newtonian fluids equipped with various Dirichlet boundary conditions(specified velocity).These examples include a family of(nonlinear 3D) plane parallel flows,a family of(nonlinear) parallel pipe flows,as well as flows with uniform injection and suction at the boundary.We also identify a key ingredient in establishing the validity of the Prandtl type theory,i.e.,a spectral constraint on the approximate solution to the Navier-Stokes system constructed by combining the inviscid solution and the solution to the Prandtl type system.This is an additional difficulty besides the wellknown issue related to the well-posedness of the Prandtl type system.It seems that the main obstruction to the verification of the spectral constraint condition is the possible separation of boundary layers.A common theme of these examples is the inhibition of separation of boundary layers either via suppressing the velocity normal to the boundary or by injection and suction at the boundary so that the spectral constraint can be verified.A meta theorem is then presented which covers all the cases considered here.