This paper investigates a specific case of one of the most popular fluid dynamic simulations,the incompressible flow around an airfoil(NACA 0012 here)at a high Reynolds number(6×10^(6)).OpenFOAM software was used...This paper investigates a specific case of one of the most popular fluid dynamic simulations,the incompressible flow around an airfoil(NACA 0012 here)at a high Reynolds number(6×10^(6)).OpenFOAM software was used to study the effect of domain size and four common choices of boundary conditions on airfoil lift,drag,surface friction,and pressure.We also examine the relation between boundary conditions and the velocity,pressure,and vorticity distributions throughout the domain.In addition to the common boundary conditions,we implement the“point vortex”boundary condition that was introduced many years ago but is now rarely used.We also applied the point vortex condition for the outlet pressure instead of using the traditional Neumann condition.With the airfoil generating significant lift at incidence angles of 5°,10°,and 14°,we confirm a previous finding that the boundary conditions combine with domain size to produce an induced(pressure)drag.The change in the pressure drag with domain size is significant for the commonly-used boundary conditions but is much smaller for the point vortex alternative.The point vortex boundary condition increases the execution time,but this is more than offset by the reduction in domain size needed to achieve a specified accuracy in the lift and drag.This study also estimates the error in total drag and lift due to domain size and shows it can be almost eliminated using the point vortex boundary condition.We also used the impulse form of the momentum equations to study the relation between drag and lift and spurious vorticity,which is generated as a result of using non-exact boundary conditions.These equations reveal that the spurious vorticity throughout the domain is associated with cancelling circulation around the domain boundaries.展开更多
This study focuses on the trailing-edge separation of a symmetrical airfoil at a low Rey-nolds number. Finite volume method is adopted to solve the unsteady Reynolds-averaged Navier-Stokes （RANS） equation. Flow of t...This study focuses on the trailing-edge separation of a symmetrical airfoil at a low Rey-nolds number. Finite volume method is adopted to solve the unsteady Reynolds-averaged Navier-Stokes （RANS） equation. Flow of the symmetrical airfoil SD8020 at a low Reynolds number has been simulated. Laminar separation bubble in the flow field of the airfoil is observed and process of unsteady bubble burst and vortex shedding from airfoil surfaces is investigated. The time-dependent lift coefficient is characteristic of periodic fluctuations and the lift curve varies nonlinearly with the attack of angle. Laminar separation occurs on both surfaces of airfoil at small angles of attack. With the increase of angle of attack, laminar separation occurs and then reattaches near the trailing edge on the upper surface of airfoil, which forms laminar separation bubble. When the attack of angle reaches certain value, the laminar separation bubble is unstable and produces two kinds of large scale vortex, i.e. primary vortex and secondary vortex. The periodic processes that include secondary vortex production, motion of secondary vortex and vortex shedding cause fluctuation of the lift coefficient. The periodic time varies with attack of angle. The secondary vortex is relatively stronger than the primary vortex, which means its influence is relatively stronger than the primary vortex.展开更多
基金This work is supported by NSERC Discovery Grant RGPIN/04886-2017the Schulich endowment to the University of Calgary.
文摘This paper investigates a specific case of one of the most popular fluid dynamic simulations,the incompressible flow around an airfoil(NACA 0012 here)at a high Reynolds number(6×10^(6)).OpenFOAM software was used to study the effect of domain size and four common choices of boundary conditions on airfoil lift,drag,surface friction,and pressure.We also examine the relation between boundary conditions and the velocity,pressure,and vorticity distributions throughout the domain.In addition to the common boundary conditions,we implement the“point vortex”boundary condition that was introduced many years ago but is now rarely used.We also applied the point vortex condition for the outlet pressure instead of using the traditional Neumann condition.With the airfoil generating significant lift at incidence angles of 5°,10°,and 14°,we confirm a previous finding that the boundary conditions combine with domain size to produce an induced(pressure)drag.The change in the pressure drag with domain size is significant for the commonly-used boundary conditions but is much smaller for the point vortex alternative.The point vortex boundary condition increases the execution time,but this is more than offset by the reduction in domain size needed to achieve a specified accuracy in the lift and drag.This study also estimates the error in total drag and lift due to domain size and shows it can be almost eliminated using the point vortex boundary condition.We also used the impulse form of the momentum equations to study the relation between drag and lift and spurious vorticity,which is generated as a result of using non-exact boundary conditions.These equations reveal that the spurious vorticity throughout the domain is associated with cancelling circulation around the domain boundaries.
文摘This study focuses on the trailing-edge separation of a symmetrical airfoil at a low Rey-nolds number. Finite volume method is adopted to solve the unsteady Reynolds-averaged Navier-Stokes （RANS） equation. Flow of the symmetrical airfoil SD8020 at a low Reynolds number has been simulated. Laminar separation bubble in the flow field of the airfoil is observed and process of unsteady bubble burst and vortex shedding from airfoil surfaces is investigated. The time-dependent lift coefficient is characteristic of periodic fluctuations and the lift curve varies nonlinearly with the attack of angle. Laminar separation occurs on both surfaces of airfoil at small angles of attack. With the increase of angle of attack, laminar separation occurs and then reattaches near the trailing edge on the upper surface of airfoil, which forms laminar separation bubble. When the attack of angle reaches certain value, the laminar separation bubble is unstable and produces two kinds of large scale vortex, i.e. primary vortex and secondary vortex. The periodic processes that include secondary vortex production, motion of secondary vortex and vortex shedding cause fluctuation of the lift coefficient. The periodic time varies with attack of angle. The secondary vortex is relatively stronger than the primary vortex, which means its influence is relatively stronger than the primary vortex.
