Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods

1Introduction 2 Static Stability and Control 3 Aircraft Equations of Motion 4 Longitudinal Motion (Stick Fixed) 5 Lateral Motion (Stick Fixed) 6 Aircraft Response to Control on Atmospheric Inputs 7 Automatic Control Theory-The Classical Approach 8 Application of Classic Control Theory to Aircraft Autopilot Design 9 Modern Control Theory 10 Applications of Modern Control Theory to Aircraft Autopilot Design Appendixes A Atmospheric Tables B Geometric, Mass, and Aerodynamic Characteristics of Selected Airplanes C Mathematical Review of Laplace Transforms and Matrix Algebra D Review of Control System Analysis Techniques

Flight Stability and Automatic Control

Vortex breakdown: a review

Finite-difference procedures are used to solve either the Euler equations or the "thin-layer" Navier-Stokes equations subject to arbitrary boundary conditions. An automatic grid generation program is employed, and because an implicit finite-difference algorithm for the flow equations is used, time steps are not severely limited when grid points are finely distributed. Computational efficiency and compatibility to vectorized computer processors is maintained by use of approximate factorization techniques. Computed results for both inviscid and viscous flow about airfoils are described and compared to viscous known solutions.

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Implicit Finite-Difference Simulation of Flow about Arbitrary Two-Dimensional Geometries

Boundary-fitted coordinate systems for numerical solution of partial differential equations—A review

Computation of turbulent supersonic flows around pointed bodies having crossflow separation

A noniterative, implicit, space-marching, finite-difference algorithm is developed for the steady thin-layer Navier-Stokes equations in conservation-law-form. The numerical algorithm is applicable to steady supersonic viscous flow over bodies of arbitrary shape. In addition, the same code can be used to compute supersonic inviscid flow or three-dimensional boundary layers. Computed results from two-dimensional and three-dimensional versions of the numerical algorithm are in good agreement with those obtained from more costly time-marching techniques.

Numerical Simulation of Steady Supersonic Viscous Flow

An experimental investigation of vortex breakdown on delta wings at high angles of attack is presented. Smoke flow visualization and the laser light sheet technique were used to obtain cross-sectional views of the leading-edge vortices as they break down for a series of flat-plate delta wings having sweep angles of 70, 75, 80, and 85 deg. At low tunnel speeds (as low as 3 m/s), details of the flow that are usually imperceptible or blurred at higher speeds can be clearly seen. A combination of lateral and longitudinal cross-sectional views provides information on the three-dimensional nature of the vortex structure before, during, and after breakdown. Whereas details of the flow are identified in still photographs, the dynamic characteristics of the breakdown process have been recorded using high-speed movies. Velocity measurements have been obtained using a laser Doppler anemometer with the 70 deg delta wing at 30 deg angle of attack. The measurements show that, when breakdown occurs, the core flow is transformed from a jet-like to a wake-like flow.

Visualization and wake surveys of vortical flow over a delta wing

A recently reported parabolized Navier-Stokes method has been extended to compute turbulent supersonic flows around cones and an ogive-cylinder body at large incidence. The algebraic eddy-viscosity turbulence model contained in the code was modified to properly account for the large regions of cross-flow separation that occur in these flows. Extensive comparisons between computed results and experimentally measured flow fields are presented. The results show good agreement for viscous-layer profiles and details of the external leeward-side vortex structure at angles of attack up to three times the cone half angles. Details of the modified turbulence model are presented and discussed.

Computation of supersonic viscous flows around pointed bodies at large incidence

The steady asymmetric vortex pattern observed on slender bodies of revolution at large angle of attack was investigated using fine-grid Navier-Stokes computations. The computed results demonstrate the marked asymmetry which has been observed in experiments. To obtain asymmetry, it was found essential to introduce a space-fixed time-invariant perturbation into the computation. The computational results suggest that vortex asymmetry is forced by amplification of small disturbances, such as those due to surface roughness, occurring within the body viscous boundary layer.

Lewis B. Schiff

Papers

Computation of turbulent supersonic flows around pointed bodies having crossflow separation

Numerical Simulation of Steady Supersonic Viscous Flow

Visualization and wake surveys of vortical flow over a delta wing

Computation of supersonic viscous flows around pointed bodies at large incidence

Numerical simulation of the effect of spatial disturbances on vortex asymmetry