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All sourcesNASA NTRSDOE OSTI
NASA NTRS1951

A Study of Effects of Viscosity on Flow over Slender Inclined Bodies of Revolution

The observed flow field about slender inclined bodies of revolution is compared with the calculated characteristics based upon potential theory. The comparison is instructive in indicating the manner in which the effects of viscosity are manifest. Based on this and other studies, a method is developed to allow for viscous effects on the force and moment characteristics of bodies. The calculated force and moment characteristics of two bodies of high fineness ratio are shown to be in good agreement, for most engineering purposes, with experiment. (author)

Allen, H Julian↗
NASA NTRS1943

On a new method for calculating the potential flow past a body of revolution

A new method is presented for obtaining the velocity potential of the flow about a body of revolution moving uniformly in the direction of its axis of symmetry in a fluid otherwise at rest. This method is based essentially on the fact that the form of the differential equation for the velocity potential is invariant with regard to conformal transformation of the meridian plane. By means of the conformal transformation of the meridian profile into a circle a system of orthogonal curvilinear coordinates is obtained, the main feature of which is that one of the coordinate lines is the meridian profile itself. The use of this type of coordinate system yields a simple expression of the boundary condition at the surface of the solid and leads to a rational process of iteration for the solution of the differential equation for the velocity potential. It is shown that the velocity potential for an arbitrary body of revolution may be expressed in terms of universal functions which, although not normal, are obtainable by means of simple quadratures. The general results are applied to a body of revolution obtained by revolving a symmetrical Joukowski profile about its axis of symmetry. A numerical example further serves to illustrate the theory.

Kaplan, Carl↗
NASA NTRS1976

Stability derivatives for bodies of revolution at subsonic speeds

The paper considers a rigid pointed body of revolution in a steady uniform subsonic flow. The body performs harmonic small-amplitude pitching oscillations around its zero angle of attack position. The body is assumed to be smooth and sufficiently slender so that the small perturbation concept can be applied. The basis of the method used, following Revell (1960), is the relation of a body-fixed perturbation potential to the general velocity potential. Normal force distributions as well as total force and moment coefficients are calculated for parabolic spindles and the numerical results show good agreement between Revell's second-order slender body theory and the present theory for the static stability derivatives of the parabolic spindles.

Liu, D. D.↗
NASA NTRS1990

The use of the FFT for the efficient solution of the problem of electromagnetic scattering by a body of revolution

The enhancement of the computational efficiency of the body of revolution (BOR) scattering problem is discused with a view to making it practical for solving large-body problems. The problem of EM scattering by a perfectly conducting BOR is considered, although the methods can be extended to multilayered dielectric bodies as well. Typically, the generation of the elements of the moment method matrix consumes a major portion of the computational time. It is shown how this time can be significantly reduced by manipulating the expression for the matrix elements to permit efficient FFT computation. A technique for extracting the singularity of the Green function that appears within the integrands of the matrix diagonal is also presented, further enhancing the usefulness of the FFT. The computation time can thus be improved by at least an order of magnitude for large bodies in comparison to that for previous algorithms.

Gedney, Stephen D.↗
NASA NTRS1952

Practical Calculation of Second-order Supersonic Flow past Nonlifting Bodies of Revolution

Calculation of second-order supersonic flow past bodies of revolution at zero angle of attack is described in detail, and reduced to routine computation. Use of an approximate tangency condition is shown to increase the accuracy for bodies with corners. Tables of basic functions and standard computing forms are presented. The procedure is summarized so that one can apply it without necessarily understanding the details of the theory. A sample calculation is given, and several examples are compared with solutions calculated by the method of characteristics.

Van Dyke, Milton D↗
NASA NTRS1992

Progress on hybrid finite element methods for scattering by bodies of revolution

Progress on the development and implementation of hybrid finite element methods for scattering by bodies of revolution are described. It was found that earlier finite element-boundary integral formulations suffered from convergence difficulties when applied to large and thin bodies of revolution. An alternative implementation is described where the finite element method is terminated with an absorbing termination boundary. In addition, an alternative finite element-boundary integral implementation is discussed for improving the convergence of the original code.

Collins, Jeffery D.↗
NASA NTRS1953

An Exploratory Investigation of Some Types of Aeroelastic Instability of Open and Closed Bodies of Revolution Mounted on Slender Struts

Aeroelastic instability phenomena of isolated open and closed rigid bodies of revolution free to move under elastic restraint have been investigated experimentally at low speeds by means of models suspended at zero angles of attack and yaw on slender flexible struts from a wind tunnel ceiling. Three types of instability were observed - flutter similar to classical bending-torsion flutter, divergence, and an uncoupled oscillatory instability which consists in nonviolent continuous or intermittent small-amplitude oscillations involving only angular deformations. The speeds at which this oscillatory instability starts were found to be as low as about one-third of the speed at flutter or divergence and to depend on the shape of the body, particularly that of the afterbody, and on the relative location of the elastic axis. An attempt has been made to calculate the airspeeds and, in the case of the oscillatory phenomena, the frequencies at which these instabilities occur by using slender-body theory for the aerodynamic forces on the bodies and neglecting the aerodynamic forces on the struts. However, the agreement between the speeds and frequencies calculated in this manner and those actually observed has been found to be generally unsatisfactory; with the exception of the frequencies of the uncoupled oscillations which could be predicted with fair accuracy. The nature of the observed phenomena and of the forces on bodies of revolution suggests that a significant improvement in the accuracy of analytical predictions of these aeroelastic instabilities can be had only by taking into account the effects of boundary-layer separation on the aerodynamic forces.

Clevenson, S. A.↗
NASA NTRS1979

Investigation of the asymmetric aerodynamic characteristics of cylindrical bodies of revolution with variations in nose geometry and rotational orientation at angles of attack to 58 degrees and Mach numbers to 2

Wind-tunnel tests were conducted to investigate the side forces and yawing moments that can occur at high angles of attack and zero sideslip for cylindrical bodies of revolution. Two bodies having several tangent ogive forebodies with fineness ratios of 0.5, 1.5, 2.5, and 3.5 were tested. The forebodies with fineness ratios of 2.5 and 3.5 had several bluntnesses. The cylindrical afterbodies had fineness ratios of 7 and 13. The model components - tip, forebody, and afterbody - were tested in various rotational positions about their axes of symmetry. Most of the tests were conducted at a Mach number of 0.25, a Reynolds number of 0.32 x 10 to the 6th power, and with the afterbody that had a fineness ratio of 7 and with selected forebodies. The effect of Mach number was determined with the afterbody that had a fineness ratio of 13 and with selected forebodies at mach numbers from 0.25 to 2 at Reynolds number = 0.32 X 10 to the 6th power. Maximum angle of attack was 58 deg.

Kruse, R. L.↗
NASA NTRS1951

Wind-tunnel investigation of the descent characteristics of bodies of revolution simulating anti-personnel bombs

An investigation has been conducted in the Langley 20-foot free spinning tunnel to study the relative behavior in descent of a number of homogeneous balsa bodies of revolution simulating anti-personnel bombs with a small cylindrical exploding device suspended approximately 10 feet below the bomb. The bodies of revolution included hemispherical, near-hemispherical, and near-paraboloid shapes. The ordinates of one near-paraboloid shape were specified by the Office of the Chief of Ordnance, U. S. Army. The behavior of the various bodies without the cylinder was also investigated. The results of the investigation indicated that several of the bodies descended vertically with their longitudinal axis, suspension line, and small cylinder in a vertical attitude,. However, the body, the ordinates of which had been specified by the Office of the Chief of Ordnance, U. S. Army, oscillated considerably from a vertical attitude while descending and therefore appeared unsuitable for its intended use. The behavior of this body became satisfactory when its center of gravity was moved well forward from its original position. In general, the results indicated that the descent characteristics of the bodies of revolution become more favorable as their shapes approached that of a hemisphere.

Sher, S. H.↗
NASA NTRS1936

Circular motion of bodies of revolution

The circular motion for airship-like bodies has thus far been calculated only for a prolate ellipsoid of revolution (reference 1, p.133 and reference 2). In this paper, however, the circular motion of elongated bodies of revolution more nearly resembling airships will be investigated. The results will give the effect of rotation on the pressure distribution and thus yield some information as to the stresses set up in an airship in circular flight.

Kaplan, Carl↗