The spatial evolution of 2-D disturbances in supersonic sharp cone boundary layers was investigated by direct numerical simulation (DNS) in high order compact difference scheme. The results suggested that, although ...The spatial evolution of 2-D disturbances in supersonic sharp cone boundary layers was investigated by direct numerical simulation (DNS) in high order compact difference scheme. The results suggested that, although the normal velocity in the sharp cone boundary layer was not small, the evolution of amplitude and phase for small amplitude disturbances would be well in accordance with the results obtained by the linear stability theory (LST) which supposes the flow was parallel. The evolution of some finite amplitude disturbances was also investigated, and the characteristic of the evolution was shown. Shocklets were also found when the amplitude of disturbances increased over some value.展开更多
Objective In geo-marine science,the generalized bottom boundary layer(BBL)represents a layer between sediments and seawater.The BBL plays an important role in geological,geobiochemical,geophysical and geotechnical r...Objective In geo-marine science,the generalized bottom boundary layer(BBL)represents a layer between sediments and seawater.The BBL plays an important role in geological,geobiochemical,geophysical and geotechnical research because it is the connection region of hydrosphere,展开更多
The nonlinear parabolized stability equations(NPSEs)approach is widely used to study the evolution of disturbances in hypersonic boundary layers owing to its high computational efficiency.However,divergence of the NPS...The nonlinear parabolized stability equations(NPSEs)approach is widely used to study the evolution of disturbances in hypersonic boundary layers owing to its high computational efficiency.However,divergence of the NPSEs will occur when disturbances imposed at the inlet no longer play a leading role or when the nonlinear effect becomes very strong.Two major improvements are proposed here to deal with the divergence of the NPSEs.First,all disturbances are divided into two types:dominant waves and non-dominant waves.Disturbances imposed at the inlet or playing a leading role are defined as dominant waves,with all others being defined as non-dominant waves.Second,the streamwise wavenumbers of the non-dominant waves are obtained using the phase-locked method,while those of the dominant waves are obtained using an iterative method.Two reference wavenumbers are introduced in the phase-locked method,and methods for calculating them for different numbers of dominant waves are discussed.Direct numerical simulation(DNS)is performed to verify and validate the predictions of the improved NPSEs in a hypersonic boundary layer on an isothermal swept blunt plate.The results from the improved NPSEs approach are in good agreement with those of DNS,whereas the traditional NPSEs approach is subject to divergence,indicating that the improved NPSEs approach exhibits greater robustness.展开更多
The process of evolution, especially that of nonlinear evolution, of C-type instability of laminar-turbulent flow transition in nonparallel boundary layers are studied by means of a newly developed method called parab...The process of evolution, especially that of nonlinear evolution, of C-type instability of laminar-turbulent flow transition in nonparallel boundary layers are studied by means of a newly developed method called parabolic stability equations (PSE). Initial conditions, which are very important for the nonlinear problem, are investigated by computing initial solution of the harmonic waves, modifying the mean-flow-distortion, and giving initial value of TS wave and its subharmonic waves at initial station by solving linear PSE. A numerical method with high-order accuracy are developed in the text, the key normalization conditions in the PSE are satisfied, and nonlinear PSE are solved efficiently and implemented stably by the spatial marching. It has been shown that the computed process of nonlinear evolution of C-type instability in Blasius boundary layer is in good agreement with the experimental results.展开更多
The elementary task is to calculate the growth rates of disturbances when the e;method in transition prediction is performed. However, there is no unified knowledge to determine the growth rates of disturbances in thr...The elementary task is to calculate the growth rates of disturbances when the e;method in transition prediction is performed. However, there is no unified knowledge to determine the growth rates of disturbances in three-dimensional(3 D) flows. In this paper, we study the relation among the wave parameters of the disturbance in boundary layers in which the imaginary parts of wave parameters are far smaller than the real parts.The generalized growth rate(GGR) in the direction of group velocity is introduced, and the conservation relation of GGR is strictly deduced in theory. This conservation relation manifests that the GGR only depends on the real parts of wave parameters instead of the imaginary parts. Numerical validations for GGR conservation are also provided in the cases of first/second modes and crossflow modes. The application of GGR to the eN method in 3 D flows is discussed, and the puzzle of determining growth rates in 3 D flows is clarified. A convenient method is also proposed to calculate growth rates of disturbances in 3 D flows. Good agreement between this convenient method and existing methods is found except the condition that the angle between the group velocity direction and the x-direction is close to 90?which can be easily avoided in practical application.展开更多
For the purpose of investigating the influence of metastable olivine(MO) phase transformations on both deep seismicity and stagnation of slabs,we constructed a 2-dimensional finite element thermal model for a 120 Ma...For the purpose of investigating the influence of metastable olivine(MO) phase transformations on both deep seismicity and stagnation of slabs,we constructed a 2-dimensional finite element thermal model for a 120 Ma-old 50°dipping oceanic lithosphere descending at 10 cm/yr with velocity boundary layers,which would mitigate the interference of constant velocity field for the slab. The resulting temperatures show that most of intermediate and deep earthquakes occurring within the Tonga slab are occurring inside the 800℃and 1200℃isotherm,respectively.The elevation of olivine transformation near~410 km and respective persistence of metastable olivine and spinel within the transition zone and beneath 660 km would thus result in bimodal positive,zonal,negative density anomalies,respectively.These results together with the resulting pressure anomalies may reflect the stress pattern of the Tonga slab:(i) slab pull force exerts above a depth of~230 km;(ii) MO existence changes the buoyancy force within the transition zone and facilitates slab stagnation at a depth of 660 km;(iii) as the subducting materials accumulated over 660 km,deepest earthquakes occur due to MO transformation;(iv) a flattened‘slab’ may penetrate into the lower mantle due to the density increment of Sp transformation.展开更多
For direct numerical simulation (DNS) of turbulent boundary layers, generation of an appropriate inflow condition needs to be considered. This paper proposes a method, with which the inflow condition for spatial-mod...For direct numerical simulation (DNS) of turbulent boundary layers, generation of an appropriate inflow condition needs to be considered. This paper proposes a method, with which the inflow condition for spatial-mode DNS of turbulent boundary layers on supersonic blunt cones with different Mach numbers, Reynolds numbers and wall temperature conditions can be generated. This is based only on a given instant flow field obtained by a temporal-mode DNS of a turbulent boundary layer on a flat plate. Effectiveness of the method is shown in three typical examples by comparing the results with those obtained by other methods.展开更多
It is widely accepted that a robust and efficient method to compute the linear spatial amplified rate ought to be developed in three-dimensional (3D) boundary layers to predict the transition with the e^N method, es...It is widely accepted that a robust and efficient method to compute the linear spatial amplified rate ought to be developed in three-dimensional (3D) boundary layers to predict the transition with the e^N method, especially when the boundary layer varies significantly in the spanwise direction. The 3D-linear parabolized stability equation (3D- LPSE) approach, a 3D extension of the two-dimensional LPSE (2D-LPSE), is developed with a plane-marching procedure for investigating the instability of a 3D boundary layer with a significant spanwise variation. The method is suitable for a full Mach number region, and is validated by computing the unstable modes in 2D and 3D boundary layers, in both global and local instability problems. The predictions are in better agreement with the ones of the direct numerical simulation (DNS) rather than a 2D-eigenvalue problem (EVP) procedure. These results suggest that the plane-marching 3D-LPSE approach is a robust, efficient, and accurate choice for the local and global instability analysis in 2D and 3D boundary layers for all free-stream Mach numbers.展开更多
Additional equations were found based on experiments for an algebraic turbulence model to improve the prediction of the behavior of three dimensional turbulent boundary layers by taking account of the effects of press...Additional equations were found based on experiments for an algebraic turbulence model to improve the prediction of the behavior of three dimensional turbulent boundary layers by taking account of the effects of pressure gradient and the historical variation of eddy viscosity, so the model is with memory. Numerical calculation by solving boundary layer equations was carried out for the five pressure driven three dimensional turbulent boundary layers developed on flat plates, swept wing, and prolate spheroid in symmetrical plane. Comparing the computational results with the experimental data, it is obvious that the prediction will be more accurate if the proposed closure equations are used, especially for the turbulent shear stresses.展开更多
A review of former studies on the onset of sediment movement under wave action reveals that the Shields criterion obtained in unidirectional steady flow can also be applicable to oscillatory unsteady flow when the bou...A review of former studies on the onset of sediment movement under wave action reveals that the Shields criterion obtained in unidirectional steady flow can also be applicable to oscillatory unsteady flow when the boundary layer is the same. In this paper, through comparison of different boundary layers in wave and steady flow conditions, a new criterion is presented which can be used to predict the threshold of sediment movement Linder wave action. The criterion curve shows good agreement with the experimental data.展开更多
The nth-order expansion of the parabolized stability equation (EPSEn) is obtained from the Taylor expansion of the linear parabolized stability equation (LPSE) in the streamwise direction. The EPSE together with t...The nth-order expansion of the parabolized stability equation (EPSEn) is obtained from the Taylor expansion of the linear parabolized stability equation (LPSE) in the streamwise direction. The EPSE together with the homogeneous boundary conditions forms a local eigenvalue problem, in which the streamwise variations of the mean flow and the disturbance shape function are considered. The first-order EPSE (EPSE1) and the second-order EPSE (EPSE2) are used to study the crossflow instability in the swept NLF(2)-0415 wing boundary layer. The non-parallelism degree of the boundary layer is strong. Compared with the growth rates predicted by the linear stability theory (LST), the results given by the EPSE1 and EPSE2 agree well with those given by the LPSE. In particular, the results given by the EPSE2 are almost the same as those given by the LPSE. The prediction of the EPSE1 is more accurate than the prediction of the LST, and is more efficient than the predictions of the EPSE2 and LPSE. Therefore, the EPSE1 is an efficient ey prediction tool for the crossflow instability in swept-wing boundary-layer flows.展开更多
The flow past a cylinder in a channel with the aspect ratio of 2 : 1 for the upper convected Maxwell (UCM) fluid and the Oldroyd-B fluid with the viscosity ratio of 0.59 is studied by using the Galerkin/Least-squar...The flow past a cylinder in a channel with the aspect ratio of 2 : 1 for the upper convected Maxwell (UCM) fluid and the Oldroyd-B fluid with the viscosity ratio of 0.59 is studied by using the Galerkin/Least-square finite element method and a p-adaptive refinement algorithm. A posteriori error estimation indicates that the stress-gradient error dominates the total error. As the Deborah number, De, approaches 0.8 for the UCM fluid and 0.9 for the Oldroyd-B fluid, strong stress boundary layers near the rear stagnation point are forming, which are characterized by jumps of the stress-profiles on the cylinder wall and plane of symmetry, huge stress gradients and rapid decay of the gradients across narrow thicknesses. The origin of the huge stress-gradients can be traced to the purely elongational flow behind the rear stagnation point, where the position at which the elongation rate is of 1/2De approaches the rear stagnation point as the Deborah number approaches the critical values. These observations imply that the cylinder problem for the UCM and Oldroyd-B fluids may have physical limiting Deborah numbers of 0.8 and 0.9, respectively.展开更多
Experimental studies which focus on flow visualization and the velocity field of a supersonic laminar/turbulent flow over a compression ramp were carried out in a Mach 3.0 wind tunnel. Fine flow structures and velocit...Experimental studies which focus on flow visualization and the velocity field of a supersonic laminar/turbulent flow over a compression ramp were carried out in a Mach 3.0 wind tunnel. Fine flow structures and velocity field structures were obtained via NPLS (nanoparticle-tracer planar laser scattering) and PIV (particle image velocimetry) techniques, time- averaged flow structures were researched, and spatiotemporal evolutions of transient flow structures were analyzed. The flow visualization results indicated that when the ramp angles were 25~, a typical separation occurred in the laminar flow, some typical flow structures such as shock induced by the boundary layer, separation shock, reversed flow and reattachment shock were visible clearly. While a certain extent separation occurred in turbulent flow, the separation region was much smaller. When the ramp angles were 28~, laminar flow separated further, and the separation region expanded evidently, flow structures in the separation region were complex. While a typical separation occurred in turbulent flow, reversed flow structures were significant, flow structures in the separation region were relatively simple. The experimental results of velocity field were corresponding to flow visualization, and the velocity field structures of both compression ramp flows agreed with the flow structures well. There were three layered structures in the U component velocity, and the V component velocity appeared like an oblique "v". Some differences between these two compression ramp flows can be observed in the velocity profiles of the shear layer and the shearing intensity.展开更多
The phenomenon of laminar-turbulent transition exists universally in nature and various engineering practice. The prediction of transition position is one of crucial theories and practical problems in fluid mechanics ...The phenomenon of laminar-turbulent transition exists universally in nature and various engineering practice. The prediction of transition position is one of crucial theories and practical problems in fluid mechanics due to the different characteristics of laminar flow and turbulent flow. Two types of disturbances are imposed at the entrance, i.e., identical amplitude and wavepacket disturbances, along the spanwise direction in the incompressible boundary layers. The disturbances of identical amplitude are consisted of one two-dimensional (2D) wave and two three-dimensional (3D) waves. The parabolized stability equation (PSE) is used to research the evolution of disturbances and to predict the transition position. The results are compared with those obtained by the numerical simulation. The results show that the PSE method can investigate the evolution of disturbances and predict the transition position. At the same time, the calculation speed is much faster than that of the numerical simulation.展开更多
Large-scale secondary motions are known to occur in turbulent flows over surfaces with spanwise roughness heterogeneity.Numerical studies often use adjacent high-and low-roughness longitudinal strips to investigate th...Large-scale secondary motions are known to occur in turbulent flows over surfaces with spanwise roughness heterogeneity.Numerical studies often use adjacent high-and low-roughness longitudinal strips to investigate these secondary rolls in boundary layers without any thermal stratification.In the present study,the effect of unstable thermal stratification on secondary rolls in a very high-Reynolds-number turbulent flow with spanwise-heterogeneous roughness is investigated by means of large-eddy simulation.The strength of the unstable stratification is systematically changed from L/h=−20 to L/h=−1,where L and h are Monin-Obukhov length and boundary-layer height,respectively.This range covers the transition from neutral stratification to unstable stratification.The results show that the positive buoyancy associated with the unstable thermal stratification acts against the roughness-induced secondary rolls.In the case of unstable stratification,secondary rolls are completely canceled out by buoyancy and replaced by new stronger convection-induced rolls rotating in opposite directions.展开更多
The nonlinear evolution problem in nonparallel boundary layer stability was studied. The relative parabolized stability equations of nonlinear nonparallel boundary layer were derived. The developed numerical method, w...The nonlinear evolution problem in nonparallel boundary layer stability was studied. The relative parabolized stability equations of nonlinear nonparallel boundary layer were derived. The developed numerical method, which is very effective, was used to study the nonlinear evolution. of T-S disturbance wave at finite amplitudes. Solving nonlinear equations of different modes by using predictor-corrector and iterative approach, which is uncoupled between modes, improving computational accuracy by using high order compact differential scheme, satisfying normalization condition I determining tables of nonlinear terms at different modes, and implementing stably the spatial marching, were included in this method. With different initial amplitudes, the nonlinear evolution of T-S wave was studied. The nonlinear nonparallel results of examples compare with data of direct numerical simulations (DNS) using full Navier-Stokes equations.展开更多
Based on the study on the Mach reflection of a solitary wave in [3] , we continue to investi- gate effects of the boundary layers on the bottom and the vertical side wall. By using matched asymptotic methods, the two-...Based on the study on the Mach reflection of a solitary wave in [3] , we continue to investi- gate effects of the boundary layers on the bottom and the vertical side wall. By using matched asymptotic methods, the two-dimensional KdV equation is modified to account for effects of viscosity. Numerical simulation of the problem shows that the effects of side wall are important while the effects of the bottom can be neglected. The results including the side wall's effects agree satisfactorily with those of Melville's experiments. Finally, we establish the simplified concept of the side wall effect and conclude that it repre- sents the physical reason for the discrepancy between the experiments and the previous calculations based on the inviscid fluid flow theory.展开更多
An analysis is presented to study the dual nature of solutions for the forced convective boundary layer flow and heat transfer in a cross flow with viscous dissipation terms in the energy equation. The governing equat...An analysis is presented to study the dual nature of solutions for the forced convective boundary layer flow and heat transfer in a cross flow with viscous dissipation terms in the energy equation. The governing equations are transformed into a set of three self-similar ordinary differential equations by similarity transformations. These equations are solved numerically using the very efficient shooting method. This study reveals that the dual solutions of the transformed similarity equations for velocity and temperature distributions exist for certain values of the moving parameter, Prandtl number, and Eckert numbers. The reverse heat flux is observed for larger Eckert numbers; that is, heat absorption at the wall occurs.展开更多
The laminar-turbulent transition in boundary-layer flows is often affected by wall imperfections, because the latter may interact with either the freestream perturbations or the oncoming boundary-layer instability mod...The laminar-turbulent transition in boundary-layer flows is often affected by wall imperfections, because the latter may interact with either the freestream perturbations or the oncoming boundary-layer instability modes, leading to a modification of the accumulation of the normal modes. The present paper particularly focuses on the latter mechanism in a transonic boundary layer, namely, the effect of a two-dimensional(2 D) roughness element on the oncoming Tollmien-Schlichting(T-S) modes when they propagate through the region of the rapid mean-flow distortion induced by the roughness. The wave scattering is analyzed by adapting the local scattering theory developed for subsonic boundary layers(WU, X. S. and DONG, M. A local scattering theory for the effects of isolated roughness on boundary-layer instability and transition: transmission coefficient as an eigenvalue. Journal of Fluid Mechanics, 794, 68–108(2006)) to the transonic regime, and a transmission coefficient is introduced to characterize the effect of the roughness. In the sub-transonic regime, in which the Mach number is close to, but less than, 1, the scattering system reduces to an eigenvalue problem with the transmission coefficient being the eigenvalue;while in the super-transonic regime, in which the Mach number is slightly greater than 1, the scattering system becomes a high-dimensional group of linear equations with the transmission coefficient being solved afterward. In the largeReynolds-number asymptotic theory, the K′arm′an-Guderley parameter is introduced to quantify the effect of the Mach number. A systematical parametric study is carried out,and the dependence of the transmission coefficient on the roughness shape, the frequency of the oncoming mode, and the K′arm′an-Guderley parameter is provided.展开更多
The instability of the Mack mode is destabilized by wall-cooling in a high speed boundary layer. The aim of this paper is to study the mechanism of the wall cooling effect on the Mack mode instability by numerical met...The instability of the Mack mode is destabilized by wall-cooling in a high speed boundary layer. The aim of this paper is to study the mechanism of the wall cooling effect on the Mack mode instability by numerical methods. It is shown that the wall-cooling can destabilize the Mack mode instability, similar to the previous conclusions with the exception that the Mack mode instability can be stabilized by wall-cooling if the wall temperature is extremely low. The reversed wall temperature is related to a freestream condition. If the Mach number increases to a large enough value, e.g., about 7, the reversed wall temperature will tend to be zero. It seems that the Mack mode instability is determined by the region between the boundary layer edge and the critical layer. When the wall temperature decreases, this region becomes wider, and the boundary layer becomes more unstable. Additionally, a relative supersonic unstable mode can be observed when the velocity of the critical layer is less than 1 - liMa or is cancelled by the wall-cooling effect. These results provide a deeper understanding on the wall-cooling effect in high speed boundary layers.展开更多
基金Project supported by the National Natural Science Foundation of China (Nos. 10232020 and 90205021)the Special Foundation for the Authors of National Excellent Doctoral Dissertations (No.200328)
文摘The spatial evolution of 2-D disturbances in supersonic sharp cone boundary layers was investigated by direct numerical simulation (DNS) in high order compact difference scheme. The results suggested that, although the normal velocity in the sharp cone boundary layer was not small, the evolution of amplitude and phase for small amplitude disturbances would be well in accordance with the results obtained by the linear stability theory (LST) which supposes the flow was parallel. The evolution of some finite amplitude disturbances was also investigated, and the characteristic of the evolution was shown. Shocklets were also found when the amplitude of disturbances increased over some value.
基金supported by the National Natural Science Foundation of China (grants No.41427803 amd 41272316)
文摘Objective In geo-marine science,the generalized bottom boundary layer(BBL)represents a layer between sediments and seawater.The BBL plays an important role in geological,geobiochemical,geophysical and geotechnical research because it is the connection region of hydrosphere,
基金the National Natural Science Foundation of China(Grant Nos.12072232 and 11672351)the National Key Project of China(Grant No.GJXM92579).
文摘The nonlinear parabolized stability equations(NPSEs)approach is widely used to study the evolution of disturbances in hypersonic boundary layers owing to its high computational efficiency.However,divergence of the NPSEs will occur when disturbances imposed at the inlet no longer play a leading role or when the nonlinear effect becomes very strong.Two major improvements are proposed here to deal with the divergence of the NPSEs.First,all disturbances are divided into two types:dominant waves and non-dominant waves.Disturbances imposed at the inlet or playing a leading role are defined as dominant waves,with all others being defined as non-dominant waves.Second,the streamwise wavenumbers of the non-dominant waves are obtained using the phase-locked method,while those of the dominant waves are obtained using an iterative method.Two reference wavenumbers are introduced in the phase-locked method,and methods for calculating them for different numbers of dominant waves are discussed.Direct numerical simulation(DNS)is performed to verify and validate the predictions of the improved NPSEs in a hypersonic boundary layer on an isothermal swept blunt plate.The results from the improved NPSEs approach are in good agreement with those of DNS,whereas the traditional NPSEs approach is subject to divergence,indicating that the improved NPSEs approach exhibits greater robustness.
文摘The process of evolution, especially that of nonlinear evolution, of C-type instability of laminar-turbulent flow transition in nonparallel boundary layers are studied by means of a newly developed method called parabolic stability equations (PSE). Initial conditions, which are very important for the nonlinear problem, are investigated by computing initial solution of the harmonic waves, modifying the mean-flow-distortion, and giving initial value of TS wave and its subharmonic waves at initial station by solving linear PSE. A numerical method with high-order accuracy are developed in the text, the key normalization conditions in the PSE are satisfied, and nonlinear PSE are solved efficiently and implemented stably by the spatial marching. It has been shown that the computed process of nonlinear evolution of C-type instability in Blasius boundary layer is in good agreement with the experimental results.
基金Project supported by the National Natural Science Foundation of China(Nos.11672351 and11332007)the National Key R&D Plan(No.2016YFA0401200)the FengLei Youth Innovation Fund of China Aerodynamics Research and Development Center(No.KT-FLJJ-201803)
文摘The elementary task is to calculate the growth rates of disturbances when the e;method in transition prediction is performed. However, there is no unified knowledge to determine the growth rates of disturbances in three-dimensional(3 D) flows. In this paper, we study the relation among the wave parameters of the disturbance in boundary layers in which the imaginary parts of wave parameters are far smaller than the real parts.The generalized growth rate(GGR) in the direction of group velocity is introduced, and the conservation relation of GGR is strictly deduced in theory. This conservation relation manifests that the GGR only depends on the real parts of wave parameters instead of the imaginary parts. Numerical validations for GGR conservation are also provided in the cases of first/second modes and crossflow modes. The application of GGR to the eN method in 3 D flows is discussed, and the puzzle of determining growth rates in 3 D flows is clarified. A convenient method is also proposed to calculate growth rates of disturbances in 3 D flows. Good agreement between this convenient method and existing methods is found except the condition that the angle between the group velocity direction and the x-direction is close to 90?which can be easily avoided in practical application.
基金supported by the National Natural Science Foundation of China(Nos.40574047 and 40628004)
文摘For the purpose of investigating the influence of metastable olivine(MO) phase transformations on both deep seismicity and stagnation of slabs,we constructed a 2-dimensional finite element thermal model for a 120 Ma-old 50°dipping oceanic lithosphere descending at 10 cm/yr with velocity boundary layers,which would mitigate the interference of constant velocity field for the slab. The resulting temperatures show that most of intermediate and deep earthquakes occurring within the Tonga slab are occurring inside the 800℃and 1200℃isotherm,respectively.The elevation of olivine transformation near~410 km and respective persistence of metastable olivine and spinel within the transition zone and beneath 660 km would thus result in bimodal positive,zonal,negative density anomalies,respectively.These results together with the resulting pressure anomalies may reflect the stress pattern of the Tonga slab:(i) slab pull force exerts above a depth of~230 km;(ii) MO existence changes the buoyancy force within the transition zone and facilitates slab stagnation at a depth of 660 km;(iii) as the subducting materials accumulated over 660 km,deepest earthquakes occur due to MO transformation;(iv) a flattened‘slab’ may penetrate into the lower mantle due to the density increment of Sp transformation.
基金the National Natural Science Foundation of China(Nos.10632050,90716007)the Special Foundation for the Authors of National Excellent Doctoral Dissertations(No.200328)
文摘For direct numerical simulation (DNS) of turbulent boundary layers, generation of an appropriate inflow condition needs to be considered. This paper proposes a method, with which the inflow condition for spatial-mode DNS of turbulent boundary layers on supersonic blunt cones with different Mach numbers, Reynolds numbers and wall temperature conditions can be generated. This is based only on a given instant flow field obtained by a temporal-mode DNS of a turbulent boundary layer on a flat plate. Effectiveness of the method is shown in three typical examples by comparing the results with those obtained by other methods.
基金Project supported by the National Natural Science Foundation of China(Nos.11272183,11572176,11402167,11202147,and 11332007)the National Program on Key Basic Research Project of China(No.2014CB744801)
文摘It is widely accepted that a robust and efficient method to compute the linear spatial amplified rate ought to be developed in three-dimensional (3D) boundary layers to predict the transition with the e^N method, especially when the boundary layer varies significantly in the spanwise direction. The 3D-linear parabolized stability equation (3D- LPSE) approach, a 3D extension of the two-dimensional LPSE (2D-LPSE), is developed with a plane-marching procedure for investigating the instability of a 3D boundary layer with a significant spanwise variation. The method is suitable for a full Mach number region, and is validated by computing the unstable modes in 2D and 3D boundary layers, in both global and local instability problems. The predictions are in better agreement with the ones of the direct numerical simulation (DNS) rather than a 2D-eigenvalue problem (EVP) procedure. These results suggest that the plane-marching 3D-LPSE approach is a robust, efficient, and accurate choice for the local and global instability analysis in 2D and 3D boundary layers for all free-stream Mach numbers.
基金National Natural Science F oundation of China !( No.91880 10 )National Defense Science Foundation!( 95 J13 A .1.2 )
文摘Additional equations were found based on experiments for an algebraic turbulence model to improve the prediction of the behavior of three dimensional turbulent boundary layers by taking account of the effects of pressure gradient and the historical variation of eddy viscosity, so the model is with memory. Numerical calculation by solving boundary layer equations was carried out for the five pressure driven three dimensional turbulent boundary layers developed on flat plates, swept wing, and prolate spheroid in symmetrical plane. Comparing the computational results with the experimental data, it is obvious that the prediction will be more accurate if the proposed closure equations are used, especially for the turbulent shear stresses.
文摘A review of former studies on the onset of sediment movement under wave action reveals that the Shields criterion obtained in unidirectional steady flow can also be applicable to oscillatory unsteady flow when the boundary layer is the same. In this paper, through comparison of different boundary layers in wave and steady flow conditions, a new criterion is presented which can be used to predict the threshold of sediment movement Linder wave action. The criterion curve shows good agreement with the experimental data.
基金supported by the National Natural Science Foundation of China(No.11332007)
文摘The nth-order expansion of the parabolized stability equation (EPSEn) is obtained from the Taylor expansion of the linear parabolized stability equation (LPSE) in the streamwise direction. The EPSE together with the homogeneous boundary conditions forms a local eigenvalue problem, in which the streamwise variations of the mean flow and the disturbance shape function are considered. The first-order EPSE (EPSE1) and the second-order EPSE (EPSE2) are used to study the crossflow instability in the swept NLF(2)-0415 wing boundary layer. The non-parallelism degree of the boundary layer is strong. Compared with the growth rates predicted by the linear stability theory (LST), the results given by the EPSE1 and EPSE2 agree well with those given by the LPSE. In particular, the results given by the EPSE2 are almost the same as those given by the LPSE. The prediction of the EPSE1 is more accurate than the prediction of the LST, and is more efficient than the predictions of the EPSE2 and LPSE. Therefore, the EPSE1 is an efficient ey prediction tool for the crossflow instability in swept-wing boundary-layer flows.
基金The project supported by the National Natural Science Foundation of China(50335010 and 20274041)the MOLDFLOW Comp.Australia.
文摘The flow past a cylinder in a channel with the aspect ratio of 2 : 1 for the upper convected Maxwell (UCM) fluid and the Oldroyd-B fluid with the viscosity ratio of 0.59 is studied by using the Galerkin/Least-square finite element method and a p-adaptive refinement algorithm. A posteriori error estimation indicates that the stress-gradient error dominates the total error. As the Deborah number, De, approaches 0.8 for the UCM fluid and 0.9 for the Oldroyd-B fluid, strong stress boundary layers near the rear stagnation point are forming, which are characterized by jumps of the stress-profiles on the cylinder wall and plane of symmetry, huge stress gradients and rapid decay of the gradients across narrow thicknesses. The origin of the huge stress-gradients can be traced to the purely elongational flow behind the rear stagnation point, where the position at which the elongation rate is of 1/2De approaches the rear stagnation point as the Deborah number approaches the critical values. These observations imply that the cylinder problem for the UCM and Oldroyd-B fluids may have physical limiting Deborah numbers of 0.8 and 0.9, respectively.
基金supported by the National Natural Science Foundation of China(Grant Nos.11172326 and 11302256)
文摘Experimental studies which focus on flow visualization and the velocity field of a supersonic laminar/turbulent flow over a compression ramp were carried out in a Mach 3.0 wind tunnel. Fine flow structures and velocity field structures were obtained via NPLS (nanoparticle-tracer planar laser scattering) and PIV (particle image velocimetry) techniques, time- averaged flow structures were researched, and spatiotemporal evolutions of transient flow structures were analyzed. The flow visualization results indicated that when the ramp angles were 25~, a typical separation occurred in the laminar flow, some typical flow structures such as shock induced by the boundary layer, separation shock, reversed flow and reattachment shock were visible clearly. While a certain extent separation occurred in turbulent flow, the separation region was much smaller. When the ramp angles were 28~, laminar flow separated further, and the separation region expanded evidently, flow structures in the separation region were complex. While a typical separation occurred in turbulent flow, reversed flow structures were significant, flow structures in the separation region were relatively simple. The experimental results of velocity field were corresponding to flow visualization, and the velocity field structures of both compression ramp flows agreed with the flow structures well. There were three layered structures in the U component velocity, and the V component velocity appeared like an oblique "v". Some differences between these two compression ramp flows can be observed in the velocity profiles of the shear layer and the shearing intensity.
基金Project supported by the National Basic Research Program of China (No.2009CB724103)
文摘The phenomenon of laminar-turbulent transition exists universally in nature and various engineering practice. The prediction of transition position is one of crucial theories and practical problems in fluid mechanics due to the different characteristics of laminar flow and turbulent flow. Two types of disturbances are imposed at the entrance, i.e., identical amplitude and wavepacket disturbances, along the spanwise direction in the incompressible boundary layers. The disturbances of identical amplitude are consisted of one two-dimensional (2D) wave and two three-dimensional (3D) waves. The parabolized stability equation (PSE) is used to research the evolution of disturbances and to predict the transition position. The results are compared with those obtained by the numerical simulation. The results show that the PSE method can investigate the evolution of disturbances and predict the transition position. At the same time, the calculation speed is much faster than that of the numerical simulation.
基金P.F.thanks the Aarhus University Research Foundation(AUFF)for the financial support.M.A.acknowledges the financial support from the Aarhus University Centre for Digitalisation,Big Data and Data Analytics(DIGIT).
文摘Large-scale secondary motions are known to occur in turbulent flows over surfaces with spanwise roughness heterogeneity.Numerical studies often use adjacent high-and low-roughness longitudinal strips to investigate these secondary rolls in boundary layers without any thermal stratification.In the present study,the effect of unstable thermal stratification on secondary rolls in a very high-Reynolds-number turbulent flow with spanwise-heterogeneous roughness is investigated by means of large-eddy simulation.The strength of the unstable stratification is systematically changed from L/h=−20 to L/h=−1,where L and h are Monin-Obukhov length and boundary-layer height,respectively.This range covers the transition from neutral stratification to unstable stratification.The results show that the positive buoyancy associated with the unstable thermal stratification acts against the roughness-induced secondary rolls.In the case of unstable stratification,secondary rolls are completely canceled out by buoyancy and replaced by new stronger convection-induced rolls rotating in opposite directions.
文摘The nonlinear evolution problem in nonparallel boundary layer stability was studied. The relative parabolized stability equations of nonlinear nonparallel boundary layer were derived. The developed numerical method, which is very effective, was used to study the nonlinear evolution. of T-S disturbance wave at finite amplitudes. Solving nonlinear equations of different modes by using predictor-corrector and iterative approach, which is uncoupled between modes, improving computational accuracy by using high order compact differential scheme, satisfying normalization condition I determining tables of nonlinear terms at different modes, and implementing stably the spatial marching, were included in this method. With different initial amplitudes, the nonlinear evolution of T-S wave was studied. The nonlinear nonparallel results of examples compare with data of direct numerical simulations (DNS) using full Navier-Stokes equations.
文摘Based on the study on the Mach reflection of a solitary wave in [3] , we continue to investi- gate effects of the boundary layers on the bottom and the vertical side wall. By using matched asymptotic methods, the two-dimensional KdV equation is modified to account for effects of viscosity. Numerical simulation of the problem shows that the effects of side wall are important while the effects of the bottom can be neglected. The results including the side wall's effects agree satisfactorily with those of Melville's experiments. Finally, we establish the simplified concept of the side wall effect and conclude that it repre- sents the physical reason for the discrepancy between the experiments and the previous calculations based on the inviscid fluid flow theory.
文摘An analysis is presented to study the dual nature of solutions for the forced convective boundary layer flow and heat transfer in a cross flow with viscous dissipation terms in the energy equation. The governing equations are transformed into a set of three self-similar ordinary differential equations by similarity transformations. These equations are solved numerically using the very efficient shooting method. This study reveals that the dual solutions of the transformed similarity equations for velocity and temperature distributions exist for certain values of the moving parameter, Prandtl number, and Eckert numbers. The reverse heat flux is observed for larger Eckert numbers; that is, heat absorption at the wall occurs.
基金Project supported by the National Natural Science Foundation of China(No.11772224)。
文摘The laminar-turbulent transition in boundary-layer flows is often affected by wall imperfections, because the latter may interact with either the freestream perturbations or the oncoming boundary-layer instability modes, leading to a modification of the accumulation of the normal modes. The present paper particularly focuses on the latter mechanism in a transonic boundary layer, namely, the effect of a two-dimensional(2 D) roughness element on the oncoming Tollmien-Schlichting(T-S) modes when they propagate through the region of the rapid mean-flow distortion induced by the roughness. The wave scattering is analyzed by adapting the local scattering theory developed for subsonic boundary layers(WU, X. S. and DONG, M. A local scattering theory for the effects of isolated roughness on boundary-layer instability and transition: transmission coefficient as an eigenvalue. Journal of Fluid Mechanics, 794, 68–108(2006)) to the transonic regime, and a transmission coefficient is introduced to characterize the effect of the roughness. In the sub-transonic regime, in which the Mach number is close to, but less than, 1, the scattering system reduces to an eigenvalue problem with the transmission coefficient being the eigenvalue;while in the super-transonic regime, in which the Mach number is slightly greater than 1, the scattering system becomes a high-dimensional group of linear equations with the transmission coefficient being solved afterward. In the largeReynolds-number asymptotic theory, the K′arm′an-Guderley parameter is introduced to quantify the effect of the Mach number. A systematical parametric study is carried out,and the dependence of the transmission coefficient on the roughness shape, the frequency of the oncoming mode, and the K′arm′an-Guderley parameter is provided.
基金Project supported by the State Key Program of National Natural Science Foundation of China(No.11332007)the Young Scientists Fund of the National Natural Science Foundation of China(No.11402167)
文摘The instability of the Mack mode is destabilized by wall-cooling in a high speed boundary layer. The aim of this paper is to study the mechanism of the wall cooling effect on the Mack mode instability by numerical methods. It is shown that the wall-cooling can destabilize the Mack mode instability, similar to the previous conclusions with the exception that the Mack mode instability can be stabilized by wall-cooling if the wall temperature is extremely low. The reversed wall temperature is related to a freestream condition. If the Mach number increases to a large enough value, e.g., about 7, the reversed wall temperature will tend to be zero. It seems that the Mack mode instability is determined by the region between the boundary layer edge and the critical layer. When the wall temperature decreases, this region becomes wider, and the boundary layer becomes more unstable. Additionally, a relative supersonic unstable mode can be observed when the velocity of the critical layer is less than 1 - liMa or is cancelled by the wall-cooling effect. These results provide a deeper understanding on the wall-cooling effect in high speed boundary layers.