A Navier‐Stokes code for S‐shaped diffusers—a review

Abstract

SUMMARYThree-dimensional, compressible, internal flow solutions obtained using a thin-layer Navier-Stokes code are presented. The code, formulated by P.D. Thomas, is based on the Beam-Warming implicit factorization scheme; the boundary conditions also are formulated implicitly. Turbulent flow is treated through the use of the Baldwin-Lomax two-layer, algebraic eddy viscosity model. Steady-state solutions are obtained by solving numerically the time-dependent equations from given initial conditions until the time-dependent terms become negligible. The configuration considered is a rectangular cross-section, S-shaped centreline diffuser duct with an exit/inlet area ratio of 2.25. The Mach number at the duct entrance is 0.9, with a Reynolds number of 5.82 x lo5. Convergence to the final results required about 2700 time steps or 11 hours of CPU time on our CRAY-1M computer. The averaged residuals were reduced by about two orders of magnitude during the computations. Several regions of separated flow exist within the diffuser. The separated flow region on the upper wall, downstream of the second bend, is by far the largest and extends to the exit plane. KEY WORDS Viscous Turbulent Subsonic Duct Diffuser Navier-Stokes INTRODUCTONIn the past decade numerous schemes have arisen for solving the Navier-Stokes equations or approximations to these equations. Most of these methods have been for external flows. For application to propulsive systems, however, internal and combination internal-external flows are of paramount importance but, so far, little work has been done in solving the Navier-Stokes equations for this class of problem.' The work that has been done is mostly for simple duct geometries, and much of it has been for parabolized equations, thereby ruling out possibilities of flow separation.' It is the purpose of this paper to examine the application of a 'thin-layer' approximated Navier-Stokes code to a complex three-dimensional internal flow-namely, an S-shaped, rectangular cross-section diffuser flow. The equations used in this code retain all terms important in boundary layers, both separated and attached, and the code should therefore be able to handle flow separation. DESCRIPTION OF CODEThe Navier-Stokes code used in this work was formulated by P. D.It is based on the Beam-Warming6 implicit factorization scheme. The boundary conditions also are formulated in an implicit fashion consistent with the implicit difference equations for interior grid points. An elliptic grid generation technique is used to construct a boundary-conforming curvilinear co-