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A time dependent finite difference method used to calculate blunt body flows with impinging shock is reported. The use of the method to predict maximum heat rates and pressure is discussed.
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Problems of laminar and turbulent viscous interaction near trailing edges of streamlined bodies are considered. Asymptotic expansions of the Navier-Stokes equations in the limit of large Reynolds numbers are used to describe the local solution near the trailing edge of cusped or nearly cusped airfoils at small angles of attack in compressible flow. A complicated inverse iterative procedure, involving finite-difference solutions of the triple-deck equations coupled with asymptotic solutions of the boundary values, is used to accurately solve the viscous interaction problem. Results are given for the correction to the boundary-layer solution for drag of a finite flat plate at zero angle of attack and for the viscous correction to the lift of an airfoil at incidence. A rational asymptotic theory is developed for treating turbulent interactions near trailing edges and is shown to lead to a multilayer structure of turbulent boundary layers. The flow over most of the boundary layer is described by a Lighthill model of inviscid rotational flow. The main features of the model are discussed and a sample solution for the skin friction is obtained and compared with the data of Schubauer and Klebanoff for a turbulent flow in a moderately large adverse pressure gradient.
The experimental results of steady and unsteady pressure measurements, carried out in subsonic and transonic flow on a 16 percent relative thickness supercritical aerofoil, equipped with a trailing edge flap involving 25 percent of the chord, in a sinusoidal motion are given. These experimental results are compared with those obtained by various methods of steady and unsteady inviscid flow calculations. Some calculation results in which viscous effects have been taken into account, for both steady and unsteady flows, are also presented.
The status of turbulence modeling for external aerodynamic flows is reviewed, and closure concepts for the compressible form of the Reynolds-averaged Navier-Stokes equations are briefly outlined to establish a framework for comparison. The importance of experimental requirements for developing and verifying turbulence models is emphasized. Attention is then given to three important flow categories: attached flows, separating and reattaching flows, and trailing-edge flows. Examples of comparisons between experiments and computations for twoand three-dimensional flows are presented to illustrate the status of modeling. It is shown that, for most two-dimensional attached flows, eddy viscosity concepts will probably be adequate. For attached three-dimensional flows, however, eddy-viscosity and Reynolds-stress models are both deficient, failing to predict the proper surface shear-stress in rapidly skewing boundary layers, regardless of whether they are pressure driven or strain driven.
Two-dimensional curvilinear coordinates are used to solve the incompressible Navier-Stokes equations, in conjunction with approximate factorization for the solution of the momentum equation and the successive overrelaxation by lines method for the solution of a Poisson equation for the pressure. The combined algorithm, although not fully explicit, is marginally stable at Reynolds numbers lower than 10,000 and time increments of 0.01. Pressure distributions calculated for attack angles of zero and 6 deg are of the same shape as the experimental curves, but are shifted to one side.
Report developments in the application of spectral methods to two dimensional compressible flows are reviewed. A brief introduction to spectral methods -- their history and especially their implementation -- is provided. The stress is on those techniques relevant to transonic flow computation. The spectral multigrid iterative methods are discussed with application to the transonic full potential equation. Discontinuous solutions of the Euler equations are considered. The key element is the shock fitting technique which is briefly explained.
Subsonic viscous flows through planar cascades are examined by means of a semielliptic form of the Navier-Stokes equations, which is obtained by neglecting the streamwise diffusion of momentum and energy in their respective equations and providing upstream interaction through the pressure field. The influence of downstream conditions is propagated upstream in the subsonic flow, via a streamwise implicit determination of the pressure field, in order to permit departure-free solutions for the overall flow problem. The continuity equation is thereby satisfied directly. Governing equations are written in strong conservation law form, in terms of general, nonorthogonal transformed coordinates and Cartesian velocity components.
Report developments in the application of spectral methods to two dimensional compressible flows are reviewed. A brief introduction to spectral methods - their history and especially their implementation - is provided. The stress is on those techniques relevant to transonic flow computation. The spectral multigrid iterative methods are discussed with application to the transonic full potential equation. Discontinuous solutions of the Euler equations are considered. The key element is the shock fitting technique which is briefly explained.
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A velocity-pressure-integrated mixed-interpolation Galerkin finite-element computation of the Navier-Stokes equations using the grids is presented. The velocity variables are interpolated using complete quadratic shape functions, and the pressure was interpolated using linear shape functions defined on a triangular element which is contained inside the quadratic element for velocity variables. Comprehensive computational results for a cavity flow at Reynolds number Re = 400-10,000 and a laminar backward-facing step flow at Re = 100-900 are presented. Many high-Re flows involve convection-dominated motion as well as diffusion-dominated motion in the flow domain. The computational results for both of the fluid motions compared favorably with high-accuracy finite-difference computational results and/or experimental data.
The incorporation of algebraic turbulence models in a solver for the 2-D compressible Navier-Stokes equations using triangular grids is described. A practial way to use the Cebeci Smith model, and to modify it in separated regions is proposed. The ability of the model to predict high speed, perfect gas boundary layers is investigated from a numerical point of view.
Computational fluid dynamics (CFD) codes have advanced to the point where they are effective analytical tools for solving flow fields around complex geometries. There is also a need for their use as a design tool to find optimum aerodynamic shapes. In the area of design, however, a difficulty arises due to the large amount of computer resources required by these codes. It is desired to streamline the design process so that a large number of design options and constraints can be investigated without overloading the system. There are several techniques which have been proposed to help streamline the design process. The feasibility of one of these techniques is investigated. The technique under consideration is the interaction of the geometry change with the flow calculation. The problem of finding the value of camber which maximizes the ratio of lift over drag for a particular airfoil is considered. In order to test out this technique, a particular optimization problem was tried. A NACA 0012 airfoil was considered at free stream Mach number of 0.5 with a zero angle of attack. Camber was added to the mean line of the airfoil. The goal was to find the value of camber for which the ratio of lift over drag is a maximum. The flow code used was FLOMGE which is a two dimensional viscous flow solver which uses multigrid to speed up convergence. A hyperbolic grid generation program was used to construct the grid for each value of camber.
This paper presents results of molecular dynamics computations of supersonic flow past a circular cylinder and past a flat plate perpendicular to a supersonic stream. The results are for Mach numbers of approximately 5 and 10, for several Knudsen numbers and several ratios of surface to free stream temperatures. A special feature of the computations is the use of relatively small numbers of particles in the molecular dynamics simulation, and an examination of the adequacy of using small numbers of particles to obtain physically useful results.
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