Computing of separated flow using the space-marching conservative supra-characteristics method
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The numerical solution of the Euler or Navier-Stokes equations by Lagrangian vortex methods is discussed. The mathematical background is presented in an elementary fashion and includes the relationship with traditional point-vortex studies, the convergence to smooth solutions of the Euler equations, and the essential differences between two- and three-dimensional cases. The difficulties in extending the method to viscous or compressible flows are explained. The overlap with the excellent review articles available is kept to a minimum and more emphasis is placed on the area of expertise, namely two-dimensional flows around bluff bodies. When solid walls are present, complete mathematical models are not available and a more heuristic attitude must be adopted. The imposition of inviscid and viscous boundary conditions without conformal mappings or image vortices and the creation of vorticity along solid walls are examined in detail. Methods for boundary-layer treatment and the question of the Kutta condition are discussed. Practical aspects and tips helpful in creating a method that really works are explained. The topics include the robustness of the method and the assessment of accuracy, vortex-core profiles, timemarching schemes, numerical dissipation, and efficient programming. Calculations of flows past streamlined or bluff bodies are used as examples when appropriate.
Detailed experimental surface pressure coefficient measurements, obtained for a hemisphere-cylinder-flare model in a low supersonic flow (freestream M = 1.2) at various angles of attack (0 deg to 27.5 deg), have been analyzed. The pressure values for each angle of attack were smoothed and checked against their respective oil-flow photographs. The smoothed results were then used to validate a theory which relates the number and type of singular points observed in the oil-flow patterns with local surface-pressure extrema.
Two-dimensional flow past a bluff body is presently simulated on the basis of an analysis that employs the incompressible, unsteady Navier-Stokes equations in terms of vorticity and stream function. The fully implicit, time-marching, alternating-direction, implicit-block Gaussian elimination used is a direct method with second-order spatial accuracy; this allows it to avoid the introduction of any artificial viscosity. Attention is given to the simulation of flow past a circular cylinder with and without symmetry, requiring the use of either the half or the full cylinder, respectively.
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 solution of the Euler or Navier-Stokes equations by Lagrangian vortex methods is discussed. The mathematical background is presented and includes the relationship with traditional point-vortex studies, convergence to smooth solutions of the Euler equations, and the essential differences between two and three-dimensional cases. The difficulties in extending the method to viscous or compressible flows are explained. Two-dimensional flows around bluff bodies are emphasized. Robustness of the method and the assessment of accuracy, vortex-core profiles, time-marching schemes, numerical dissipation, and efficient programming are treated. Operation counts for unbounded and periodic flows are given, and two algorithms designed to speed up the calculations are described.
The flow field surrounding a delta wing undergoing a transient pitching motion was studied experimentally. Of particular importance was the location of the leading edge vortices over the surface of the wing. The study was conducted on a 70-deg sweep flat-plate delta wing pitched about its one-half chord position. It is found that the maximum pitch rate is the key factor involved in the amount of lag experienced by the vortex breakdown during the transient pitching motion.
Flow visualization techniques have been used to investigate the complex flow in the recirculation region upstream of a rectangular jet issuing normally into a uniform cross flow. Two different flow regimes are identified. It is shown that the recirculation region upstream of the jet is unsteady and periodic. Two distinct vortical structures are found for the wake behind the jet, one dominated by a symmetric vortex pair and one with vortices shed alternately from each side of the jet.
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The effects of combustion on the turbulent structure of a flow and vice versa were studied by making simultaneous two-component laser velocimeter measurements in the turbulent flow field following an axisymmetric sudden expansion with and without combustion. Mean axial and radial velocities and Reynolds stresses were measured. In addition, simultaneous time resolved temperature measurements were made in the reacting flow using fast response thermocouples. Velocity-temperature correlations were formed from the velocity and temperature measurements.
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The invention is a method and apparatus for simultaneously detecting laminar separation and reattachment of a fluid stream such as an airstream from and to the upper surface of an airfoil by simultaneously sensing and comparing a plurality of output signals. Each signal represents the dynamic shear stress at one of an equal number of sensors spaced along a straight line on the surface of the airfoil that extends parallel to the airstream. The output signals are simultaneously compared to detect the sensors across which a reversal in phase of said output signal occurs, said detected sensors being in the region of laminar separation or reattachment.
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Numerical solutions of the Navier-Stokes equations governing shear flow in a trapezoidal enclosure have been obtained at fine grid resolutions using an efficient multigrid calculation procedure. The effects of flow Reynolds number and wall boundary conditions are studied in detail. Interesting flow patterns are observed to develop, especially at high Reynolds numbers.
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