Transonic Navier-Stokes wing solution using a zonal approach. Part 1: Solution methodology and code validation
Abstract : A fast diagonalized Beam Warming algorithm is coupled with a zonal approach to solve the three dimensional Euler/Navier Stokes equations. The computer code, called Transonic Navier Stokes (TNS), uses a total of four zones for wing configurations (or can be extended to complete aircraft configurations by adding zones). In the inner blocks near the wing surface, the thin layer Navier Stokes equations are solved, while in the outer two blocks the Euler equations are solved. The diagonal algorithm yields a speedup of as much as a factor of 40 over the original algorithm/zonal method coded. The TNS code, in addition, has the capability to model wind tunnel walls. Transonic viscous solutions are obtained on a 150,000 point mesh for a NACA 0012 wing. A three order of magnitude drop in the L2 norm of the residual requires approximately 500 iterations, which takes about 45 min of CPU time on a Cray-XMP processor. Simulations are also conducted for a different geometrical wing called WING C. All cases show good agreement with experimental data.
Zonal Navier-Stokes methodology for flow simulation about a complete aircraft
Transonic Navier-Stokes flow simulations are presented for the F-16A fighter aircraft using a zonal grid approach. This approach subdivides the physical space about the aircraft into an ensemble of simple geometric shapes, thus mitigating many of the difficulties of generating a single grid about a complex shape, e.g., providing adequate grid refinement near all body surfaces to capture the boundary layer. Information is propagated between zones via grid overlapping and a spatial interpolation procedure. Computational Cp compare well with experimental values on the wing, horizontal and vertical tails, fuselage centerline, and the inlet/diverter region. The average y+ one grid point off the wing is 3. The experimental lift is underpredicted by 2.6%, and the experimental drag is overpredicted by 1.6%. The flexibility of the zonal approach is demonstrated by adding additional zones inside the inlet up to the compressor face to model flow spillage, and downwind of the exhaust nozzle to model power-on conditions. Computations are also presented for the F-16A in sideslip. These results demonstrate that the present zonal approach provides a flexible and viable means of simulating flowfields about complex geometries.
Compact Circularly Polarized Composite Cavity-Backed Crossed Dipole for GPS Applications
In this paper, we present a circularly polarized (CP) composite cavity-backed crossed dipole antenna for global positioning system (GPS) applications. We produce the CP radiation by crossing two dipoles through a 90° phase delay line of a vacant-quarter printed ring, which also has a broadband impedance matching characteristic. Two techniques, insertion of meander lines in the dipole arm and arrowhead-shaped trace at its end, are employed to reduce the sizes of the primary radiation element. The compact radiator is backed by a cavity reflector to achieve a wide CP radiation beamwidth. The proposed antenna exhibits a measured bandwidth of 1.450～1.656 GHz for a voltage standing wave ratio (VSWR) < 2 and 1.555～1.605 GHz for AR < 3-dB. At 1.575 GHz, the antenna has a gain of 7 dBic, a frontto-back ratio of 27 dB, AR of 1.18 dB, and 3-dB AR beamwidths of 130° and 132° in the x-z and y-z planes, respectively.