Engineering topics

Garabedian, P. R.

Publications and source records attributed to Garabedian, P. R..

10 records

NASA NTRS1987

Aspects of supercritical wing theory

Concepts and techniques that have proved successful in the computational theory of shockless airfoils are examined. Shockless airfoils have been used in the design of supercritical wings for fuel-efficient aircraft. In transonic aerodynamics, it is has been found that test data agree well with the best results obtained from CFD. This is particularly true for two-dimensional flow, where accurate experiments are difficult to perform and numerical calculations are relatively easy. However, it is important to choose reasonable models in setting up the computations. Particular attention is given to the formulation of the relevant differential equations in ways that have been found to be satisfactory in practice.

Garabedian, P. R.↗

NASA NTRS1985

A remark about pointed bubbles

The polymer expansion is a formal algebraic identity between a partition function and logarithm in statistical physics problems. The expansion gives a systematic method to control the free energy or to establish exponential tree-graph decay of connected correlations. Here, the convergence properties of the polymer expansion are analyzed in connection with three practical examples, including: intersecting bonds in chemical polymer chains; a connected closed hypersurface built from the (d-1)-faces of the d-dimensional unit cubes; and the set of Feynamn diagrams in the perturbation series of the Euclidean field theory partition function Z. The example of connected polymer chains is generalized to apply to other lattice models, including n-state Ising models at high temperature; short range lattice gases at high temperature; and weak coupling lattice field and gauge theories.

Garabedian, P. R.↗

NASA NTRS1983

Nonparametric solution of the Euler equations for steady flow

A theory is presented for formulating well-posed boundary value problems for the Euler equations for steady rotational flow. It is shown that the Euler equations of motion are equivalent to a variational principle, which is used to define a finite difference scheme for numerically solving the Euler equations. The principle is extended to MHD problems in terms of a potential energy of a perfectly conducting plasma having a minimum number of stable configurations. The flow around a cylinder is considered, noting that time-independent solutions of the Euler equations can be used to provide limits to solutions of the Navier-Stokes equations. A sample is worked out in terms of the motion of vortices inside a circle.

Garabedian, P. R.↗

NASA NTRS1980

Shockless airfoils for wings, compressors, and turbines

The major aspects of a code for the design of shockless airfoils in two-dimensional transonic flow are reviewed. The code is based on a method of analytic continuation into the domain of two complex characteristic variables, which makes it possible to associate a shockless airfoil with a given pressure distribution. This procedure is compared with another more direct method based on a two-dimensional analysis code that has had wide acceptance by the aircraft industry.

Garabedian, P. R.↗

NASA NTRS1979

Numerical design of shockless airfoils

An attempt is made to indicate and briefly discuss only the most significant achievements of the research. The most successful contribution from the contract was the code for two dimensional analysis of airfoils in transonic flow.

Garabedian, P. R.↗

NASA NTRS1979

Transonic airfoil codes

Computer codes for the design and analysis of transonic airfoils are considered. The design code relies on the method of complex characteristics in the hodograph plane to construct shockless airfoil. The analysis code uses artificial viscosity to calculate flows with weak shock waves at off-design conditions. Comparisons with experiments show that an excellent simulation of two dimensional wind tunnel tests is obtained. The codes have been widely adopted by the aircraft industry as a tool for the development of supercritical wing technology.

Garabedian, P. R.↗

NASA NTRS1976

Transonic flow theory of airfoils and wings

There are plans to use the supercritical wing on the next generation of commercial aircraft so as to economize on fuel consumption by reducing drag. Computer codes have served well in meeting the consequent demand for new wing sections. The possibility of replacing wind tunnel tests by computational fluid dynamics is discussed. Another approach to the supercritical wing is through shockless airfoils. A novel boundary value problem in the hodograph plane is studied that enables one to design a shockless airfoil so that its pressure distribution very nearly takes on data that are prescribed.

Garabedian, P. R.↗

NASA NTRS1976

Computation of wave drag for transonic flow

The paper develops a method for calculating wave drag for two-dimensional transonic flow, with particular application to the prediction of the drag rise Mach number of a supercritical wing section. The method is based on a transonic similarity model which is defined by a normalized small perturbation equation and represents shock waves by the addition of an artificial viscosity term in the region of supersonic flow to the partial differential equation. The drag formula obtained allows the computer simulation of transonic wind tunnel data taking account of boundary layer and wall effects.

Garabedian, P. R.↗

NASA NTRS1972

A theory of supercritical wing sections, with computer programs and examples.

Mathematical methods for the design of supercritical wings, which depend on the numerical solution of the partial differential equations of two-dimensional gas dynamics, are developed. The main contribution is a computer program for the design of shockless transonic airfoils using the hodograph transformation and analytic continuation into the complex domain. The mathematical theory is described, and a manual for users of the programs is provided. Numerical examples are given and computational results are discussed, and the computer programs themselves are listed. The analysis routine can be used to ascertain whether the profiles behave well at off-design conditions, or to smooth coordinates and obtain a desirable shape more quickly when perfectly shockless flow is not essential.

Bauer, F.↗

NASA NTRS1971

Analysis of transonic airfoils.

A finite difference scheme for the analysis of transonic airfoils at off-design conditions is described. It is the ultimate goal of the investigations to avoid expensive wind tunnel tests by combining the mathematical techniques in a procedure for designing supercritical airfoils so that they will be effective over a wider range of angles of attack and Mach numbers. A mathematical method is considered for computing two-dimensional transonic flows past a prescribed profile. The method can provide accurate results for a comparison with a known shockless regime. The approach gives also data of engineering reliability concerning the location and the strength of shocks at off-design conditions.

Garabedian, P. R.↗