https://ntrs.nasa.gov/api/citations/19880020687/downloads/19880020687.pdf

An analysis of finite-difference and finite-volume formulations of conservation laws

An Euler solution algorithm is presented for unsteady aerodynamic analysis of complex-aircr aft configurations. The flow solver involves a multistage Runge-Kutta time-stepping scheme that uses a finite-volume spatial discretization on an unstructured grid made up of tetrahedra. A significant contribution of the research is the development and implementation of a moving mesh algorithm that is employed for problems involving static or dynamic deformation of the aircraft. The mesh algorithm is a general procedure that can treat realistic motions and deformations of complex-aircraft configurations. Steady and unsteady results are presented for a supersonic fighter configuration to demonstrate applications of the Euler solver and dynamic mesh algorithm. The unsteady flow results were obtained for the aircraft oscillating harmonically in a complete-vehicle bending mode. Effects of angle of attack and reduced frequency on instantaneous pressures and force responses were investigated. The paper presents descriptions of the Euler solver and dynamic mesh algorithm along with results that assess the capability.

Unsteady euler algorithm with unstructured dynamic mesh for complex – aircraft aerodynamic analysis

In finite difference flow field simulations the use of a single well-ordered body-conforming curvilinear mesh can lead to efficient solution procedures. However, it is generally impractical to build a single grid of this type for complex three-dimensional aircraft configurations. As a result, a trend in computational aerodynamics has been toward the use of composite grids. Composite grids use more than one grid to mesh an overall configuration with each individual subgrid of the system patched or overset together. Because each individual subgrid in the system is well ordered, the overall grid is suitable for efficient finite difference solution using vectorized or multitasking computers. Some of the advantages and difficulties of using various composite grid schemes are reviewed in this paper.

On the use of composite grid schemes in computational aerodynamics

Review of numerical simulations for high-speed, turbulent cavity flows

A procedure to solve simultaneously the Euler flow equations and modal structural equations of motion is presented for computing aeroelastic responses of wings. The Euler flow equations are solved by a finite-difference scheme with dynamic grids. The coupled aeroelastic equations of motion are solved using the linear-acceleration method. The aeroelastic configuration adaptive dynamic grids are time-accurately generated using the aeroelastically deformed shape of the wing. The unsteady flow calculations are validated with the experiment, both for a semi-infinite wing and a wall-mounted cantilever rectangular wing. Aeroelastic responses are computed for a rectangular wing using the modal data generated by the finite-element method. The robustness of the present approach in computing unsteady flows and aeroelastic responses that are beyond the capability of earlier approaches using potential equations are demonstrated.

Unsteady aerodynamic and aeroelastic calculations for wings using Euler equations

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.

/pdf/zonal-navier-stokes-methodology-for-flow-simulation-about-a-2mfd68m20e.pdf

Zonal Navier-Stokes methodology for flow simulation about a complete aircraft

The Transonic Navier-Stokes wing code is extended to a 16-zone TNS wing-fuselage code and used to solve the transonic viscous flow over a modified F-16A. The computer code, called Transonic Navier-Stokes Wing/Fuselage uses a zonal approach to solve the three-dimensional Euler and Navier-Stokes equations. With the zonal implementation, clustering suitable for viscous calculations is achieved on all solid surfaces. The transonic case has flow conditions of free-stream M = 0.9, alpha = 4.12 deg, and a Reynolds number based on root chord of 4.5 million. This case required about 3,000 iterations to reduce the L2-norm of the residual by three orders, which takes about 15 hr of cpu time on the Cray X-MP/48 processor. Pressure distributions, as well as separaton patterns, compare favorably with experiment for this transonic case.

Transonic Navier-Stokes solutions for a fighter-like configuration

The thin-layer, Reynolds-averaged, Navier-Stokes equations are used to simulate the transonic viscous flow about the complete F-16A fighter aircraft. These computations demonstrate how computational fluid dynamics (CFD) can be used to simulate turbulent viscous flow about realistic aircraft geometries. A zonal grid approach is used to provide adequate viscous grid clustering on all aircraft surfaces. Zonal grids extend inside the F-16A inlet and up to the compressor face while power on conditions are modeled by employing a zonal grid extending from the exhaust nozzle to the far field. A simple solution adaptive grid procedure is used on the wing surface and good agreement with experimental data is obtained. Computations for the F-16A in side slip are also presented.

The numerical simulation of transonic separated flow about the complete F-16A

A fast diagonal algorithm is coupled with a zonal approach to solve the three-dimensional Euler/Navier-Stokes equations. Transonic viscous solutions are obtained on a 150,000 point mesh for a NACA 0012 wing. The new computational approach yields a speedup by as much as a factor of 40 over the standard Beam-Warming algorithm/zonal method originally coded. 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. The numerically computed solutions are in good agreement with experimental results. Effects on convergence rate owing to increasing the zonal boundary overlap regions, different stretching distributions in the viscous regions, and different CFL values are also explored.

Convergence acceleration for a three-dimensional Euler/Navier-Stokes zonal approach

A new spatial differencing scheme for the transonic full-potential equation in conservative form has been developed. Three consistency conditions for the full-potential equations are derived and are satisifed by the new scheme. This scheme guarantees zero truncation error on any curvilinear mesh for freestream flows in either two- or three-space dimensions. Solutions obtained with this new differencing scheme, away from freestream regions, exhibit greatly improved accuracy, especially for nonsmooth or singular meshes. The computing times associated with the new scheme are approximately the same as the less accurate old scheme when computations are performed on the same mesh.

Jolen Flores

Papers

Zonal Navier-Stokes methodology for flow simulation about a complete aircraft

Transonic Navier-Stokes solutions for a fighter-like configuration

The numerical simulation of transonic separated flow about the complete F-16A

Convergence acceleration for a three-dimensional Euler/Navier-Stokes zonal approach

A new consistent spatial differencing scheme for the transonic full-potential equation