Based on the investigation of mid-span local boundary layer suction and positive bowed cascade, a coupled local tailored boundary layer suction and positive bowed blade method is developed to improve the performance o...Based on the investigation of mid-span local boundary layer suction and positive bowed cascade, a coupled local tailored boundary layer suction and positive bowed blade method is developed to improve the performance of a highly loaded diffusion cascade with less suction slot. The effectiveness of the coupled method under different inlet boundary layers is also investigated.Results show that mid-span local boundary layer suction can effectively remove trailing edge separation, but deteriorate the flow fields near the endwall. The positive bowed cascade is beneficial for reducing open corner separation, but is detrimental to mid-span flow fields. The coupled method can further improve the performance and flow field of the cascade. The mid-span trailing edge separation and open corner separation are eliminated. Compared with linear cascade with suction, the coupled method reduces overall loss of the cascade by 31.4% at most. The mid-span loss of the cascade decreases as the suction coefficient increases, but increases as bow angle increases. The endwall loss increases as the suction coefficient increases. By contrast, the endwall loss decreases significantly as the bow angle increases. The endwall loss of coupled controlled cascade is higher than that of bowed cascade with the same bow angle because of the spanwise inverse ‘‘C＂ shaped static pressure distribution. Under different inlet boundary layer conditions, the coupled method can also improve the cascade effectively.展开更多
Transition prediction for boundary layers has always been one of the urgent problems waiting for a solution for the development of aero-space technology,yet there is no reliable and effective method due to the complex...Transition prediction for boundary layers has always been one of the urgent problems waiting for a solution for the development of aero-space technology,yet there is no reliable and effective method due to the complexity of the problem.The eN method has been regarded as an effective method for the transition prediction of boundary layers.However,it heavily relies on experiment or experience.And in cases with three-dimensional base flow,for instance,the boundary layer on a cone with angle of attack,the result of its application is not satisfactory.The authors have found its cause and proposed the method for its improvement,which did yield the fairly satisfactory result for a given test case,and also did not rely so much on experiment or experience.However,before people can really apply this method to practical problems,more test cases have to be studied.In this paper,more test cases for the application of the improved eN method to problems of transition prediction of supersonic and hypersonic boundary layers on cones with angle of attack will be studied.The results are compared with those obtained by experiments and/or direct numerical simulations,confirming that the improved eN method is effective and reliable.We also find that there may be more than one ZARF for each meridian plane,and which one should be chosen for the eN method has been clarified.展开更多
A singularly perturbed one-dimensional convection-diffusion problem is solved numeri- cMly by the finite element method based on higher order polynomials. Numerical solutions are obtained using S-type meshes with spec...A singularly perturbed one-dimensional convection-diffusion problem is solved numeri- cMly by the finite element method based on higher order polynomials. Numerical solutions are obtained using S-type meshes with special emphasis on meshes which are graded （based on a mesh generating function） in the fine mesh region. Error estimates in the s-weighted energy norm are proved. We derive an ＇optimal＇ mesh generating function in order to min- imize the constant in the error estimate. Two layer-adapted meshes defined by a recursive formulae in the fine mesh region are also considered and a new technique for proving er- ror estimates for these meshes is presented. The aim of the paper is to emphasize the importance of using optimal meshes for higher order finite element methods. Numerical experiments support all theoretical results.展开更多
基金supported by China Postdoctoral Science Foundationa key project of the National Natural Science Foundation of China (No. 51236006)
文摘Based on the investigation of mid-span local boundary layer suction and positive bowed cascade, a coupled local tailored boundary layer suction and positive bowed blade method is developed to improve the performance of a highly loaded diffusion cascade with less suction slot. The effectiveness of the coupled method under different inlet boundary layers is also investigated.Results show that mid-span local boundary layer suction can effectively remove trailing edge separation, but deteriorate the flow fields near the endwall. The positive bowed cascade is beneficial for reducing open corner separation, but is detrimental to mid-span flow fields. The coupled method can further improve the performance and flow field of the cascade. The mid-span trailing edge separation and open corner separation are eliminated. Compared with linear cascade with suction, the coupled method reduces overall loss of the cascade by 31.4% at most. The mid-span loss of the cascade decreases as the suction coefficient increases, but increases as bow angle increases. The endwall loss increases as the suction coefficient increases. By contrast, the endwall loss decreases significantly as the bow angle increases. The endwall loss of coupled controlled cascade is higher than that of bowed cascade with the same bow angle because of the spanwise inverse ‘‘C＂ shaped static pressure distribution. Under different inlet boundary layer conditions, the coupled method can also improve the cascade effectively.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 10632050 and 90716007)the Special Foundation for the Authors of National Excel-lent Doctoral Dissertations (Grant No. 200328)the Foundation of Liu-Hui Center of Applied Mathematics of Nankai University and Tianjin University Contributed by ZHOU Heng
文摘Transition prediction for boundary layers has always been one of the urgent problems waiting for a solution for the development of aero-space technology,yet there is no reliable and effective method due to the complexity of the problem.The eN method has been regarded as an effective method for the transition prediction of boundary layers.However,it heavily relies on experiment or experience.And in cases with three-dimensional base flow,for instance,the boundary layer on a cone with angle of attack,the result of its application is not satisfactory.The authors have found its cause and proposed the method for its improvement,which did yield the fairly satisfactory result for a given test case,and also did not rely so much on experiment or experience.However,before people can really apply this method to practical problems,more test cases have to be studied.In this paper,more test cases for the application of the improved eN method to problems of transition prediction of supersonic and hypersonic boundary layers on cones with angle of attack will be studied.The results are compared with those obtained by experiments and/or direct numerical simulations,confirming that the improved eN method is effective and reliable.We also find that there may be more than one ZARF for each meridian plane,and which one should be chosen for the eN method has been clarified.
文摘A singularly perturbed one-dimensional convection-diffusion problem is solved numeri- cMly by the finite element method based on higher order polynomials. Numerical solutions are obtained using S-type meshes with special emphasis on meshes which are graded （based on a mesh generating function） in the fine mesh region. Error estimates in the s-weighted energy norm are proved. We derive an ＇optimal＇ mesh generating function in order to min- imize the constant in the error estimate. Two layer-adapted meshes defined by a recursive formulae in the fine mesh region are also considered and a new technique for proving er- ror estimates for these meshes is presented. The aim of the paper is to emphasize the importance of using optimal meshes for higher order finite element methods. Numerical experiments support all theoretical results.
