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

The simulation of transonic viscous flow over a modified F-16A including inlet is presented. A zonal approach is utilized which allows appropriate clustering suitable for viscous calculations on all solid surfaces. Computational efficiency is enhanced by solving the thin-layer Navier-Stokes equations in viscous zones adjacent to the aircraft and the Euler equations on those coarse zones away from the aircraft. The flow conditions for this transonic case are freestream Mach number of 0.9, angle of attack of 4.12 deg, and a Reynolds number (based on root chord) of 4.5 million. A total of 19 zones are utilized yielding a total of 350,000 grid points. This case required about 3000 iterations to reduce the residual by three orders, which takes about 10 hr of CPU time on the Cray X-MP/48 computer. Pressure distributions on the wing and on cross sections through the inlet region compare favorably with the experimental data for this transonic case.

Simulation of transonic viscous flow over a fighter-like configuration including inlet

Transonic Navier-Stokes (TNS) code solutions gathered from the literature for three-dimensional geometries, including two different wings and a complete F-16A aircraft, are presently discussed The TNS codes use a zonal grid approach whose number of zones vary from four to 54 The Euler equations are solved in zones away from no-slip surfaces, and the thin-layer TNS equations are solved in all zones immediately adjacent to no-slip surfaces In the case of 'corner' zones possessing no-slip boundary conditions on two different surfaces, a thin-layer formulation along both directions is employed Employing these features, a zonal construction with the requisite set of boundary conditions can be devised for almost any application

Navier-Stokes computations about complex configurations including a complete F-16 aircraft

Transonic flow solutions are obtained over a multielement airfoil (augmentor-wing) using the full-potential equation. Solutions obtained for a subcritical case and a strong shock case show good quantitative agreement with experiment in regions not dominated by viscous effects. In those regions where viscous effects are dominant, the results are still in good qualitative agreement. For the strong shock case, Mach number and angle-of-attack corrections were necessary to match experimental coefficient of lift. Typical results from the transonic augmentor-wing Potential Code on the Cray-1S computer require about 10 sec of CPU time for a three-order-of-magnitude drop in the maximum residual. The speed with which solutions can be generated, and the associated low cost, will make this code a practical tool for the design aerodynamicist.

Transonic solutions for a multielement airfoil using the full-potential equations

A new spatial differencing scheme for the transonic full-potential equation in conservative form has been developed. 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.

Jolen Flores

Papers

Simulation of transonic viscous flow over a fighter-like configuration including inlet

Navier-Stokes computations about complex configurations including a complete F-16 aircraft

Transonic solutions for a multielement airfoil using the full-potential equations

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

Transonic solutions for a multielement airfoil using the full-potential equation