A stabilized and convergent finite element formulation for the generalized Stokes problem is proposed and a posteriori analysis is performed to produce an error indicator. On this basis adaptive numerical method for s...A stabilized and convergent finite element formulation for the generalized Stokes problem is proposed and a posteriori analysis is performed to produce an error indicator. On this basis adaptive numerical method for solying the problem is developed . Numerical calculations are performed to confirm the reliability and effectiveness of the method.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
The problem of transition prediction for hypersonic boundary layers over a sharp cone has been studied in this work. The Mach number of the oncoming flow is 6, the cone half-angle is 5°, and the angle of attack i...The problem of transition prediction for hypersonic boundary layers over a sharp cone has been studied in this work. The Mach number of the oncoming flow is 6, the cone half-angle is 5°, and the angle of attack is 1°. The conventional e N method is used, but the transition location so obtained is obviously incorrect. The reason is that in the conventional method, only the amplifying waves are taken into account, while in fact, for different meridians the decay processes of the disturbances before they begin to grow are different. Based on our own previous work, new interpretation and essential improvement for the e N method are proposed. Not only the amplification process but also the decay process is considered. The location, where by linear stability theory, the amplitude of disturbance wave is amplified from its initial small value to 1%, is considered to be the transition location. The new result for transition prediction thus obtained is found to be fairly satisfactory. It is also indicated that for the calculation of base flow, boundary layer equations can be used for a small angle of attack. Its computational cost is much smaller than those for DNS.展开更多
文摘A stabilized and convergent finite element formulation for the generalized Stokes problem is proposed and a posteriori analysis is performed to produce an error indicator. On this basis adaptive numerical method for solying the problem is developed . Numerical calculations are performed to confirm the reliability and effectiveness of the method.
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 (Grant Nos. 10632050 and 90716007)the Special Foundation for the Authors of National Excellent Doctoral Dissertations (Grant No. 200328)the Foundation of Liu-Hui Center of Applied Mathematics of Nankai University and Tianjin University
文摘The problem of transition prediction for hypersonic boundary layers over a sharp cone has been studied in this work. The Mach number of the oncoming flow is 6, the cone half-angle is 5°, and the angle of attack is 1°. The conventional e N method is used, but the transition location so obtained is obviously incorrect. The reason is that in the conventional method, only the amplifying waves are taken into account, while in fact, for different meridians the decay processes of the disturbances before they begin to grow are different. Based on our own previous work, new interpretation and essential improvement for the e N method are proposed. Not only the amplification process but also the decay process is considered. The location, where by linear stability theory, the amplitude of disturbance wave is amplified from its initial small value to 1%, is considered to be the transition location. The new result for transition prediction thus obtained is found to be fairly satisfactory. It is also indicated that for the calculation of base flow, boundary layer equations can be used for a small angle of attack. Its computational cost is much smaller than those for DNS.
