No abstract

No abstract

No abstract

Boundary-fitted curvilinear coordinate systems are optimized for viscous flows about arbitrary airfoils at angles of attack such that boundary-layer-dependent grid systems for high Reynolds numbers are generated efficiently. The grid systems are utilized in implicit finite-difference solutions. Solution of a one-dimensional model equation is compared with the theoretical solution. The unsteady Navier-Stokes equations are solved for the incompressible flow around a cylinder and around NACA airfoils approaching stall. The predicted flows around a NACA 6412 airfoil near stall at Reynolds numbers of 4x 10 4 and 2x 10 5 are compared with the experimental observations obtained in a smoke tunnel. Nomenclature= amplitude coefficients for contracting mesh systems = drag coefficient = lift coefficient = pressure coefficient = contours in a doubly connected region = velocity divergence = coordinate-transformation parameter, Eq.(11) = decay coefficients for contracting mesh systems = number of £ lines in transformed plane = Jacobian determinant = number of 17 lines in transformed plane = number of points in boundary layer = characteristic length = nondimensional pressure (C p /2) = summations of exponential functions for contraction of mesh systems = two-dimensional physical region = Reynolds number = Strouhal number based on thickness = nondimensional time (Ut/L ) = nondimensional velocity component in x direction = freestream velocity magnitude = nondimensional velocity component in y direction = nondimensional physical field coordinates = coordinate-transformation parameter, Eq.(2) = coordinate-transformation parameter, Eq.(2) (2) 17 = transformed coordiante £ = tranformed coordinate a = coordinate-transformation parameter, Eq. (U) r = coordinate-transformation parameter, Eq. (U) 0 = angle of attack . = acceleration parameter IJL = function definition, Eq. (6) Superscripts N (s) * Subscripts U cs = time step index = iterate number = the transformed plane = field position in mesh systems = central-space difference = first partial differentiation = second partial differentiation = cross partial differentiation = value at infinity

No abstract