Comparison of two-dimensional and three-dimensional computational fluid dynamics solutions for a vectoring turbine engine exhaust nozzle

Computational fluid dynamics (CFD) solutions for vectored nozzle flow fields can be used to predict nozzle performance, design ground test facility hardware, and size nozzle instrumentation. The purpose of this research was to compare two-dimensional (2D) and three-dimensional (3D) computational fluid dynamics (CFD) solutions for a twodimensional vectoring exhaust nozzle of rectangular cross section. The motivation for using 2D CFD codes as opposed to 3D CFD codes is that 2D (planar or axisymmetric) CFD simulation results generally have less truncation and round off error, they require less labor and fewer computational resources, they are less subject to interpretive errors; and consequently, results can be provided in a more responsive and timely manner. The parameters that were compared were mass flow, axial gross thrust, and vertical gross thrust. The simulations have been performed at three nozzle pressure ratios, with uniform nozzle inlet boundary conditions. These inlet boundary conditions are based on one-dimensional turbine engine math model predictions. The assumption of uniform nozzle entrance boundary conditions is expected to negate some of the potential for three-dimensional effects; therefore this investigation represents a "best case" comparison.

The CFD codes (PARC2D and PARC3D) used to model the 2D/CD (two-dimensional convergent-divergent) nozzle flow fields are based on the finite difference form of the Reynolds-averaged Navier-Stokes equations. Usage of the PARC codes is restricted to fluids which have thermally and calorically perfect equations of state and a constant Prandtl number. The codes used to solve these equations incorporated a variant of the implicit approximate factorization algorithm of Beam and Warming. The codes also incorporated a modified Baldwin and Lomax turbulence model.

For the sake of conserving resources, and with the aim of improving simulation responsiveness, ways to obviate a full 3D treatment of 2D/CD nozzle performance predictions were investigated. These methods included;

1) Comparisons of 2D and 3D solutions at three nozzle pressure ratios (NPR) for a vectored nozzle configuration of constant area ratio and vector angle.

2) An aspect ratio (nozzle width/nozzle height at the nozzle entrance) parametric study to investigate the limits of the more economical 2D CFD performance simulation results.