Vorticity Variables Research Articles

Analysis of Turbulent Flow Past a Class of Semi-Infinite Bodies

This study was undertaken with the primary purpose of developing an analysis for flow past a class of two-dimensional and axisymmetric semi-infinite bodies. The time-averaged Navier-Stokes equations for these flows are derived in surface-oriented conformal coordinates (ξ, η) in terms of similarity-type vorticity and stream-function variables. Turbulence closure is achieved by means of a two-equation turbulence model utilizing the kinetic energy k and its dissipation rate ε which enable determination of the isotropic eddy viscosity. The coupled vorticity and stream-function equations are solved simultaneously using an incremental formulation of the factored alternating-direction implicit scheme. The turbulence equations for k and ε are solved by the standard ADI method. Numerical solutions are obtained for the thin flat plate and compared with available experimental and analytical data. Also, results are obtained for flow over a parabola and compared with the flat-plate results in order to assess the effects of longitudinal curvature on the flow results. Finally, solutions are obtained for flow past a two-dimensional semi-infinite body with a shoulder, at Red = 24,000. The computed results have the same general trend as the experimental data; possible causes for the differences within the separated-flow region are cited.

Embedded cavity drag in steady laminar flow

The numerical solution of the laminar boundary-layer flow over an embedded cavity is studied. The purpose of the study is to examine the relevant drag characteristics of laminar cavity flow. The solution field is obtained in terms of velocity and vorticity variables, with the stream function and pressure derivable from the directly computed variables. An analysis and comparison is made among four square cavities, ranging in size from 0.25 to 1.00 boundary-layer thickness deep. The dominant flow features are examined in the vicinity of the cavity by means of the stream function and isovorticity contours. The dominant physics in the overall drag characteristics of the flow are examined by an analysis of the pressure and wall shear-stress distributions in the cavity, and upstream and downstream of the cavity. Pressure forces and frictional forces in, and in the vicinity of, the cavity are determined. Stress relaxation distances, both upstream and downstream of the cavity, are calculated and analyzed. The dynamics of the boundary-layer flow over an embedded cavity are summarized. Finally, the relevance of the present results to the control of flow separation in such flows is discussed.

Investigation of the method of nets for two-dimensional equations of the Navier-Stokes and Euler type with non-negative viscosity, I

Equations of the Navier-Stokes and Euler type in stream function — vorticity variables, which are encountered in oceanology, are considered. A formulation of the problem and a difference scheme are presented. The unique solvability of the difference problem is proved, a priori estimates of the difference solution are obtained, and the convergence of a certain iterative process for solving the non-linear difference problem is proved.

Investigation of the method of nets for two-dimensional equations of the Navier-Stokes type with non-negative viscosity. II

The convergence of the solution obtained using an implicit two-layer scheme to the exact generalized solution of equations of the NavierStokes and Euler type in stream function — vorticity variables with periodic boundary conditions is proved. The approximation of the Jacobian proposed by Arakawa is used. The unique solvability of the differential problem is proved.