The paper examines computational schemes for calculating the gradient of fluid dynamic quantities using grids of various types.The Green–Gaussmethod and the least squares method(LSM)used to develop a hybrid gradient ...The paper examines computational schemes for calculating the gradient of fluid dynamic quantities using grids of various types.The Green–Gaussmethod and the least squares method(LSM)used to develop a hybrid gradient calculation scheme are considered.It is demonstrated that the accuracy of gradient calculations may vary depending on the geometry of the control volume:the Green–Gauss method exhibits lower errors for strongly elongated thin cells and cells with curved edges,while for cells with orthogonal edges,it is preferable to use LSM.In order to improve the accuracy of calculations on unstructured grids,a hybrid gradient calculation scheme is proposed.This scheme computes the gradient by summing values derived from both the Green–Gauss method and LSM,given the weight function that incorporates the geometry of the control volume.The paper presents a formula for the weight function,which determines the contribution of each method within the hybrid scheme.The developed scheme is applied to the problem of supersonic flow around a cylinder with a needle on two unstructured grids,namely truncated hexagons and tetrahedra.It is shown that the proposed hybrid scheme reduces the error in calculating the aerodynamic characteristics of a streamlined object.展开更多
A solution to a multi-point optimization problem of a wing airfoil for a Long Endurance Mars Exploration Flying Vehicle(LEMFEV)under various constraints is considered.Formulated is the problem of multi-point optimizat...A solution to a multi-point optimization problem of a wing airfoil for a Long Endurance Mars Exploration Flying Vehicle(LEMFEV)under various constraints is considered.Formulated is the problem of multi-point optimization of the airfoil shape,based on level flight conditions of LEMFEV,with an additional condition related to flight Reynolds number variation of the LEMFEVwing.This problem formulationmakes possible the airfoil optimization taking into account the studied vehiclewing loading.The airfoil is optimized for a wide range of flight lift coefficients C_(L)and Reynolds’numbers.It has been shown that taking into account the Reynolds’number makes possible quality improvement of the obtained optimization results,which are physically better justified against existing optimization techniques.Computational Fluid Dynamics(CFD)are applied to validate the obtained aerodynamic coefficients.The most popular CFD simulation methods are based on Reynolds averaged Navier-Stocks equations with semi-empirical turbulence models,such as k−εand k−ω.In this regard,investigated is Ansys Fluent ability to predict the airfoils lift and drag coefficients in Martian atmospheric conditions.Experimental data are used to validate the numerical simulation.The flow around NACA0012-34 airfoil with a chord length c~50 mm is simulated at angles of attack ranging−5…15°using different turbulence models.It has been shown that turbulent Prandtl numberσk in turbulence kinetic energy equation significantly influences on the aerodynamic coefficient prediction accuracy.展开更多
基金support of the national project“Science and Universities”within the framework of the pro-gram of the Ministry of Science and Higher Education of the Russian Federation for the creation of laboratories for young scientists No.FSWE-2024-0001(scientific topic:“Development of numerical methods,models and algorithms for description of fluid flows under natural conditions and normal and critical operating conditions of industrial facilities using exa-and zetta-scale supercomputers”)the program for development of the world-class scientific center“Supersonic”in 2020-2025 with the financial support of the Ministry of Science and Higher Education of the Russian Federation(Agreement dated April 20,2022,No.075-15-2022-309).
文摘The paper examines computational schemes for calculating the gradient of fluid dynamic quantities using grids of various types.The Green–Gaussmethod and the least squares method(LSM)used to develop a hybrid gradient calculation scheme are considered.It is demonstrated that the accuracy of gradient calculations may vary depending on the geometry of the control volume:the Green–Gauss method exhibits lower errors for strongly elongated thin cells and cells with curved edges,while for cells with orthogonal edges,it is preferable to use LSM.In order to improve the accuracy of calculations on unstructured grids,a hybrid gradient calculation scheme is proposed.This scheme computes the gradient by summing values derived from both the Green–Gauss method and LSM,given the weight function that incorporates the geometry of the control volume.The paper presents a formula for the weight function,which determines the contribution of each method within the hybrid scheme.The developed scheme is applied to the problem of supersonic flow around a cylinder with a needle on two unstructured grids,namely truncated hexagons and tetrahedra.It is shown that the proposed hybrid scheme reduces the error in calculating the aerodynamic characteristics of a streamlined object.
基金supported by the Russian Science Fund under the Agreement No 22–49-02047 from 09.03.2022.
文摘A solution to a multi-point optimization problem of a wing airfoil for a Long Endurance Mars Exploration Flying Vehicle(LEMFEV)under various constraints is considered.Formulated is the problem of multi-point optimization of the airfoil shape,based on level flight conditions of LEMFEV,with an additional condition related to flight Reynolds number variation of the LEMFEVwing.This problem formulationmakes possible the airfoil optimization taking into account the studied vehiclewing loading.The airfoil is optimized for a wide range of flight lift coefficients C_(L)and Reynolds’numbers.It has been shown that taking into account the Reynolds’number makes possible quality improvement of the obtained optimization results,which are physically better justified against existing optimization techniques.Computational Fluid Dynamics(CFD)are applied to validate the obtained aerodynamic coefficients.The most popular CFD simulation methods are based on Reynolds averaged Navier-Stocks equations with semi-empirical turbulence models,such as k−εand k−ω.In this regard,investigated is Ansys Fluent ability to predict the airfoils lift and drag coefficients in Martian atmospheric conditions.Experimental data are used to validate the numerical simulation.The flow around NACA0012-34 airfoil with a chord length c~50 mm is simulated at angles of attack ranging−5…15°using different turbulence models.It has been shown that turbulent Prandtl numberσk in turbulence kinetic energy equation significantly influences on the aerodynamic coefficient prediction accuracy.
