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Murman, E. M.

Publications and source records attributed to Murman, E. M..

43 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

Application of finite element approach to transonic flow problems

A variational finite element model for transonic small disturbance calculations is described. Different strategy is adopted in subsonic and supersonic regions. Blending elements are introduced between different regions. In the supersonic region, no upstream effect is allowed. If rectangular elements with linear shape functions are used, the model is similar to Murman's finite difference operators. Higher order shape functions, non-rectangular elements and discontinuous approximation of shock waves are also discussed.

Hafez, M. M.↗
NASA NTRS1974

An assessment of airfoil design by numerical optimization

A practical procedure for optimum design of aerodynamic shapes is demonstrated. The proposed procedure uses an optimization program based on the method of feasible directions coupled with an analysis program that uses a relaxation solution of the inviscid, transonic, small-disturbance equations. Results are presented for low-drag, nonlifting transonic airfoils. Extension of the method to lifting airfoils, other speed regimes, and to three dimensions if feasible.

Hicks, R. M.↗
NASA NTRS1974

Inviscid drag at transonic speeds

A systematic asymptotic expansion procedure is introduced into the Euler equations to obtain the transonic, small-disturbance potential equation and corresponding relation for the drag. The relation consists of an integral around any contour enclosing the body and an integral along all shocks contained within the contour. Interpretations are given for the origin of the pressure drag due to shock waves, lift, and wind-tunnel boundaries. Numerical procedures are discussed for evaluating these quantities from finite-difference relaxation calculations. Computed results are included for various contours, and results are compared with some experimental data.

Murman, E. M.↗
NASA NTRS1973

Analysis of embedded shock waves calculated by relaxation methods.

The requirements for uniqueness of the calculated jump conditions across embedded shock waves are investigated for type-dependent difference systems used in transonic flow studies. A mathematical analysis shows that sufficient conditions are (1) the equations should be differenced in conservative form and (2) a special difference operator should be used when switching from a hyperbolic to an elliptic operator. The latter results in a consistency condition on the integral equations, rather than the differential, at these points. Calculated jump conditions for several embedded and detached shock waves are analyzed in the physical and hodograph planes. Comparisons are made with previous results, a time-dependent calculation, and data.

Murman, E. M.↗
NASA NTRS1973

A relaxation method for calculating transonic flows with detached bow shocks

The use of Murman and Krupp's (1971) method for calculating steady, inviscid, transonic flows with imbedded shock waves is discussed in application to two-dimensional problems for transonic flows past sharp and moderately blunt nosed geometries. A relaxation algorithm is used to solve the equations.

Murman, E. M.↗
NASA NTRS1972

Computation of wall effects in ventilated transonic wind tunnels.

A method for computing interference effects due to ventilated wind-tunnel walls on lifting transonic airfoils is presented. Differences between the present method based on nonlinear transonic theory and the classical correction formulae from linear subsonic theory are discussed. Computed results are presented for an NACA 0012 in solid and perforated wall tunnels. The solid wall calculations are compared with data.

Murman, E. M.↗