Engineering topics
Publications and source records attributed to Jameson, A..
Several algorithms to calculate a rain-rate profile from a single-frequency air- or space-borne radar backscatter profile and a given path-integrated attenuation have been proposed.
This paper describes the implementation of optimization techniques based on control theory for airfoil design. In previous studies it was shown that control theory could be used to devise an effective optimization procedure for two-dimensional profiles in which the shape is determined by a conformal transformation from a unit circle, and the control is the mapping function. The goal of our present work is to develop a method which does not depend on conformal mapping, so that it can be extended to treat three-dimensional problems. Therefore, we have developed a method which can address arbitrary geometric shapes through the use of a finite volume method to discretize the potential flow equation. Here the control law serves to provide computationally inexpensive gradient information to a standard numerical optimization method. Results are presented, where both target speed distributions and minimum drag are used as objective functions.
A Navier-Stokes algorithm for use on unstructured triangular meshes is presented. Spatial discretization of the governing equations is achieved using a finite element Galerkin approximation, which can be shown to be equivalent to a finite volume approximation for regular equilateral triangular meshes. Integration steady-state is performed using a multistage time-stepping scheme, and convergence is accelerated by means of implicit residual smoothing and an unstructured multigrid algorithm. Directional scaling of the artificial dissipation and the implicit residual smoothing operator is achieved for unstructured meshes by considering local mesh stretching vectors at each point. The accuracy of the scheme for highly stretched triangular meshes is validated by comparing computed flat-plate laminar boundary layer results with the well known similarity solution, and by comparing laminar airfoil results with those obtained from various well-established structured quadrilateral-mesh codes. The convergence efficiency of the present method is also shown to be competitive with those demonstrated by structured quadrilateral-mesh algorithms.
A new Navier-Stokes algorithm for use on unstructured triangular meshes is presented. Spatial discretization of the governing equations is achieved using a finite-element Galerkin approximation, which can be shown to be equivalent to a finite-volume approximation for regular equilateral triangular meshes. Integration to steady-state is performed using a multistage time-stepping scheme, and convergence is accelerated by means of implicit residual smoothing and an unstructured multigrid algorithm. The convergence efficiency of the present method is shown to be competitive with those demonstrated by structured quadrilateral-mesh algorithms.
An unstructured mesh of tetrahedra offers an attractive approach to mesh generation for complex three dimensional shapes. The combination of a method for constructing tetrahedral meshes and a finite element technique for solving the Euler equations has resulted in a powerful new approach to the problem of calculating flows over complex geometries. Recent progress and improvements to the authors' aircraft Euler method are described and results presented to demonstrate its capability.
A numerical method is developed to analyze the inviscid flowfield of a high speed inlet by the solution of the Euler equations. The LU implicit scheme in conjunction with adaptive dissipation proves to be an efficient and robust nonoscillatory shock capturing technique for high Mach number flows as well as for transonic flows.
A numerical method is developed to analyze the inviscid flowfield of a high speed inlet by the solution of the Euler equations. The lower-upper implicit scheme in conjunction with adaptive dissipation proves to be an efficient and robust nonoscillatory shock capturing technique for high Mach number flows as well as for transonic flows.
A new interacting boundary layer approach for computing the viscous transonic flow over airfoils is described. The theory includes a complete treatment of viscous interaction effects induced by the wake and accounts for normal pressure gradient effects across the boundary layer near trailing edges. The method is based on systematic expansions of the full Reynolds equation of turbulent flow in the limit of Reynolds numbers, Reynolds infinity. Procedures are developed for incorporating the local trailing edge solution into the numerical solution of the coupled full potential and integral boundary layer equations. Although the theory is strictly applicable to airfoils with cusped or nearly cusped trailing edges and to turbulent boundary layers that remain fully attached to the airfoil surface, the method was successfully applied to more general airfoils and to flows with small separation zones. Comparisons of theoretical solutions with wind tunnel data indicate the present method can accurately predict the section characteristics of airfoils including the absolute levels of drag.
A method of adaptive grid refinement for the solution of the steady Euler equations for transonic flow is presented. Algorithm automatically decides where the coarse grid accuracy is insufficient, and creates locally uniform refined grids in these regions. This typically occurs at the leading and trailing edges. The solution is then integrated to steady state using the same integrator (FL052) in the interior of each grid. The boundary conditions needed on the fine grids are examined and the importance of treating the fine/coarse grid interface conservatively is discussed. Numerical results are presented.
The nonuniqueness problem occurring at transonic speeds with the conservative potential equation is investigated numerically. The study indicates that the problem is not an inviscid phenomenon, but results from approximate treatment of shock waves inherent in the conservative potential model. A new bound on the limit of validity of the conservative potential model is proposed.
A method for modifying the third order dissipative terms by the introduction of flux limiters is proposed. The first order dissipative terms can then be eliminated entirely, and in the case of a scalar conservation law the scheme is converted into a total variation diminishing scheme provided that an appropriate value is chosen for the dissipative coefficient. Particular attention is given to: (1) the treatment of the scalar conservation law; (2) the treatment of the Euler equations for inviscid compressible flow; (3) the boundary conditions; and (4) multistage time stepping and multigrid schemes. Numerical results for transonic flows suggest that a central difference scheme augmented by flux limited dissipative terms can lead to an effective nonoscillatory shock capturing method.
An effort is made to develop a satisfactory numerical method for the calculation of steady solutions of the Euler equations for inviscid compressible gas flows. The intended application is the prediction of the aerodynamic properties of aircraft flying at transonic speeds. Particular consideration is given to the modification of the equations to improve convergence to a steady state; finite volume formulation; adaptive dissipation; schemes designed to improve the resolution of shock waves; hybrid multistage time stepping schemes; residual averaging; a multigrid scheme; and trials with Burgers' equation. Results clearly demonstrate that the convergence of a time-dependent hyperbolic system to a steady state can be substantially accelerated by the introduction of multiple grids.
A multigrid scheme for solving the Euler equations is presented. The method has been successfully applied to two-dimensional airfoil calculations on both O-type and C-type meshes. In three dimensions the scheme has proved equally effective and calclations of flows over wing/body combinations are possible with convergence achieved in less than 100 cycles.
A method of adaptive grid refinement for the solution of the steady Euler equations for transonic flow is presented. Algorithm automatically decides where the coarse grid accuracy is insufficient, and creates locally uniform refined grids in these regions. This typically occurs at the leading and trailing edges. The solution is then integrated to steady state using the same integrator (FLO52) in the interior of each grid. The boundary conditions needed on the fine grids are examined and the importance of treating the fine/coarse grid inerface conservatively is discussed. Numerical results are presented.
An improved version of the 'GRUMFOIL' code has been developed for the computation of airfoil flows. The method employs a conservative difference scheme for the potential equation, integral methods for the boundary layer, and viscous coupling conditions that fully account for the wake and strong interaction effects at trailing edges. The improved version uses Jameson's 'MAD' scheme to accelerate convergence of the inviscid solution, an improved 2nd order artificial viscosity and far field 'TARE' correction to reduce spatial truncation errors and Carter's semi-inverse method for the viscous solution. Results are presented which demonstrate a factor of ten reduction in computing cost.
The nonuniqueness problem occurring at transonic speeds with the conservative potential equation is reviewed. Additional evidence supporting the idea that the nonuniqueness problem is inherent to the differential equation is given. An extensive, comparative study between potential and Euler calculations is presented. The results of the study indicate that the nonuniqueness problem is not an inviscid phenomenon, but a result of the conservative potential approximate treatment of shock waves. A new bound on the limit of validity of the potential formulation is discussed.
Transonic viscous-inviscid interaction is considered using the Euler and inverse compressible turbulent boundary-layer equations. Certain improvements in the inverse boundary-layer method are mentioned, along with experiences in using various Runge-Kutta schemes to solve the Euler equations. Numerical conditions imposed on the Euler equations at a surface for viscous-inviscid interaction using the method of equivalent sources are developed, and numerical solutions are presented and compared with experimental data to illustrate essential points. Previously announced in STAR N83-17829
Transonic viscous-inviscid interaction is considered using the Euler and inverse compressible turbulent boundary-layer equations. Certain improvements in the inverse boundary-layer method are mentioned, along with experiences in using various Runge-Kutta schemes to solve the Euler equations. Numerical conditions imposed on the Euler equations at a surface for viscous-inviscid interaction using the method of equivalent sources are developed, and numerical solutions are presented and compared with experimental data to illustrate essential points.