The transition criterion in the improved eN method is that transition would occur whenever the velocity amplitude of disturbance reaches 1%-2% of the free stream velocity,while in the conventional eN method,the N fact...The transition criterion in the improved eN method is that transition would occur whenever the velocity amplitude of disturbance reaches 1%-2% of the free stream velocity,while in the conventional eN method,the N factor is an empirical factor.In this paper the reliability of this key assumption in the improved eN method is checked by results of transition prediction by using the Parabolized Stability Equations(PSE).Transition locations of an incompressible boundary layer and a hypersonic boundary layer at Mach number 6 on a flat plate are predicted by both the improved eN method and the PSE method.Results from both methods agree fairly well with each other,implying that the transition criterion proposed in the improved eN method is reliable.展开更多
Pitot probes enable a simple and convenient way of measuring mean velocity in air flow. The contrastive numerical simulation between free supersonic airflow and pitot tube at different positions in supersonic air flow...Pitot probes enable a simple and convenient way of measuring mean velocity in air flow. The contrastive numerical simulation between free supersonic airflow and pitot tube at different positions in supersonic air flow was performed using Navier-Stokes equations, the ENN scheme with time-dependent boundary conditions （TDBC） and the Spalart-Allmaras turbulence model. The physical experimental results including pitot pressure and shadowgraph are also presented. Numerical results coincide with the experimental data. The flow characteristics of the pitot probe on the supersonic flow structure show that the measure- ment gives actually the total pressure behind the detached shock wave by using the pitot probe to measure the total pressure. The measurement result of the distribution of the total pressure can still represent the real free jet flow. The similar features of the intersection and reflection of shock waves can be identified. The difference between the measurement results and the actual ones is smaller than 10%. When the pitot probe is used to measure the region of L=0-4D, the measurement is smaller than the real one due to the increase of the shock wave strength. The difference becomes larger where the waves intersect. If the pitot probe is put at L=SD-10D, where the flow changes from supersonic to subsonic, the addition of the pitot probe turns the original supersonic flow region subsonic and causes bigger measurement errors.展开更多
When an upstream steady uniform supersonic flow impinges onto a symmetric straight-sided wedge,governed by the Euler equations,there are two possible steady oblique shock configurations if the wedge angle is less than...When an upstream steady uniform supersonic flow impinges onto a symmetric straight-sided wedge,governed by the Euler equations,there are two possible steady oblique shock configurations if the wedge angle is less than the detachment angle—the steady weak shock with supersonic or subsonic downstream flow(determined by the wedge angle that is less than or greater than the sonic angle)and the steady strong shock with subsonic downstream flow,both of which satisfy the entropy condition.The fundamental issue—whether one or both of the steady weak and strong shocks are physically admissible solutions—has been vigorously debated over the past eight decades.In this paper,we survey some recent developments on the stability analysis of the steady shock solutions in both the steady and dynamic regimes.For the static stability,we first show how the stability problem can be formulated as an initial-boundary value type problem and then reformulate it into a free boundary problem when the perturbation of both the upstream steady supersonic flow and the wedge boundary are suitably regular and small,and we finally present some recent results on the static stability of the steady supersonic and transonic shocks.For the dynamic stability for potential flow,we first show how the stability problem can be formulated as an initial-boundary value problem and then use the self-similarity of the problem to reduce it into a boundary value problem and further reformulate it into a free boundary problem,and we finally survey some recent developments in solving this free boundary problem for the existence of the PrandtlMeyer configurations that tend to the steady weak supersonic or transonic oblique shock solutions as time goes to infinity.Some further developments and mathematical challenges in this direction are also discussed.展开更多
基金supported by the National Natural Science Foundation of China (Grant No.11002098)the National Basic Research Program of China (Grant No.2009CB724103)the Specialized Research Fund for the Doctoral Program of Higher Education
文摘The transition criterion in the improved eN method is that transition would occur whenever the velocity amplitude of disturbance reaches 1%-2% of the free stream velocity,while in the conventional eN method,the N factor is an empirical factor.In this paper the reliability of this key assumption in the improved eN method is checked by results of transition prediction by using the Parabolized Stability Equations(PSE).Transition locations of an incompressible boundary layer and a hypersonic boundary layer at Mach number 6 on a flat plate are predicted by both the improved eN method and the PSE method.Results from both methods agree fairly well with each other,implying that the transition criterion proposed in the improved eN method is reliable.
基金supported by the National Natural Science Foundation of China (Grant No. 30970822)
文摘Pitot probes enable a simple and convenient way of measuring mean velocity in air flow. The contrastive numerical simulation between free supersonic airflow and pitot tube at different positions in supersonic air flow was performed using Navier-Stokes equations, the ENN scheme with time-dependent boundary conditions （TDBC） and the Spalart-Allmaras turbulence model. The physical experimental results including pitot pressure and shadowgraph are also presented. Numerical results coincide with the experimental data. The flow characteristics of the pitot probe on the supersonic flow structure show that the measure- ment gives actually the total pressure behind the detached shock wave by using the pitot probe to measure the total pressure. The measurement result of the distribution of the total pressure can still represent the real free jet flow. The similar features of the intersection and reflection of shock waves can be identified. The difference between the measurement results and the actual ones is smaller than 10%. When the pitot probe is used to measure the region of L=0-4D, the measurement is smaller than the real one due to the increase of the shock wave strength. The difference becomes larger where the waves intersect. If the pitot probe is put at L=SD-10D, where the flow changes from supersonic to subsonic, the addition of the pitot probe turns the original supersonic flow region subsonic and causes bigger measurement errors.
基金supported by the US National Science Foundation (Grant Nos. DMS0935967 and DMS-0807551)the UK Engineering and Physical Sciences Research Council (Grant Nos. EP/E035027/1 and EP/L015811/1)+1 种基金National Natural Science Foundation of China (Grant No. 10728101)the Royal Society-Wolfson Research Merit Award (UK)
文摘When an upstream steady uniform supersonic flow impinges onto a symmetric straight-sided wedge,governed by the Euler equations,there are two possible steady oblique shock configurations if the wedge angle is less than the detachment angle—the steady weak shock with supersonic or subsonic downstream flow(determined by the wedge angle that is less than or greater than the sonic angle)and the steady strong shock with subsonic downstream flow,both of which satisfy the entropy condition.The fundamental issue—whether one or both of the steady weak and strong shocks are physically admissible solutions—has been vigorously debated over the past eight decades.In this paper,we survey some recent developments on the stability analysis of the steady shock solutions in both the steady and dynamic regimes.For the static stability,we first show how the stability problem can be formulated as an initial-boundary value type problem and then reformulate it into a free boundary problem when the perturbation of both the upstream steady supersonic flow and the wedge boundary are suitably regular and small,and we finally present some recent results on the static stability of the steady supersonic and transonic shocks.For the dynamic stability for potential flow,we first show how the stability problem can be formulated as an initial-boundary value problem and then use the self-similarity of the problem to reduce it into a boundary value problem and further reformulate it into a free boundary problem,and we finally survey some recent developments in solving this free boundary problem for the existence of the PrandtlMeyer configurations that tend to the steady weak supersonic or transonic oblique shock solutions as time goes to infinity.Some further developments and mathematical challenges in this direction are also discussed.
