Solutions of the navier-stokes equations in various flow regimes on fields containing any number of arbitrary bodies using boundary-fitted coordinate systems

Thompson, J. F.; Thames, Frank C.; Hodge, J. K.; Shanks, S. P.; Reddy, R. N.; Mastin, C. W.

doi:10.1007/3-540-08004-x_349

Cited by 8 publications

(2 citation statements)

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“…Grid systems at Re = 2x 10 6 were also generated using only 100 s of GDG 6600 computer time for each case. The earlier automated procedure 3 was used to generate the grid systems for the flow about a NAGA 0018 airfoil and a NAGA 6412 airfoil at a Reynolds number of 4.4xl0 4 . The new boundary-layerdependent procedure was used for the solution of a onedimensional model equation at a Reynolds number of 2x 10 6 , for a circular cylinder at a Reynolds number of 67, and for a NAGA 6412 airfoil at a Reynolds number of 1.67 x 10 5 .…”

Section: Curvilinear Grid Systemsmentioning

confidence: 99%

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Numerical Solution for Airfoils near Stall in Optimized Boundary-Fitted Curvilinear Coordinates

1979

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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

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Section: Curvilinear Grid Systemsmentioning

confidence: 99%

“…The implicit method was successful for a time step of 0.001 and a maximum of two iterations per time step. 4 Approximately 2 h of CDC 6600 computer time was required to obtain a converged solution.…”

Section: Naca0018mentioning

confidence: 99%