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Computer code for scattering from impedance bodies of revolution. Part 3: Surface impedance with s and phi variation. Analytical and numerical results

The third phase of the development of the computer codes for scattering by coated bodies that has been part of an ongoing effort in the Electromagnetics Laboratory of the Electrical Engineering and Computer Science Department at the University of Illinois at Chicago is described. The work reported discusses the analytical and numerical results for the scattering of an obliquely incident plane wave by impedance bodies of revolution with phi variation of the surface impedance. Integral equation formulation of the problem is considered. All three types of integral equations, electric field, magnetic field, and combined field, are considered. These equations are solved numerically via the method of moments with parametric elements. Both TE and TM polarization of the incident plane wave are considered. The surface impedance is allowed to vary along both the profile of the scatterer and in the phi direction. Computer code developed for this purpose determines the electric surface current as well as the bistatic radar cross section. The results obtained with this code were validated by comparing the results with available results for specific scatterers such as the perfectly conducting sphere. Results for the cone-sphere and cone-cylinder-sphere for the case of an axially incident plane were validated by comparing the results with the results with those obtained in the first phase of this project. Results for body of revolution scatterers with an abrupt change in the surface impedance along both the profile of the scatterer and the phi direction are presented.

Uslenghi, Piergiorgio L. E.

Comparison of the Experimental and Theoretical Distribution of Lift on a Slender Inclined Body of Revolution at M = 2

Pressure distributions and force characteristics have been determined for a body of revolution consisting of a fineness ratio 5.75, circular-arc, ogival nose tangent to a cylindrical afterbody for an angle-of-attack range of 0 degrees to 35.5 degrees. The free-stream Mach number was 1.98 and the free-stream Reynolds number was approximately 0.5 x 10 sup 6, based on body diameter. Comparison of the theoretical and experimental pressure distributions shows that for zero lift, either slender-body theory or higher-order theories yield results which are in good agreement with experiment. For the lifting case, good agreement with theory is found only for low angles of attack and for the region in which the body cross-sectional area is increasing in the downstream direction. Because of the effects of cross-flow separation and the effects of compressibility due to the high cross-flow Mach numbers at large angles of attack, the experimental pressure distributions differ from those predicted by potential theory. Although the flow about the inclined body was, in general, similar to that assumed as the basis for Allen's method of estimating the forces resulting from viscous effects (NACA RM A91I26), the distribution of the forces was significantly different from that assumed. Nevertheless, the lift and pitching-moment characteristics were in fair agreement with the estimated value.

Perkins, Edward W

Calculation of stability derivatives for slowly oscillating bodies of revolution at Mach 1.0

A parabolic method for steady transonic flow is extended to bodies of revolution oscillating in a sonic flow field. A Laplace transform technique is employed to derive the dipole solution, and the Adams-Sears iterative technique is used in the stability derivative calculation. A computer program is developed to perform the stability derivative calculation for the slowly oscillating cone and parabolic ogive. Inputs for the program are body geometry thickness ratio, acceleration constant, and pitch axis location. Sample calculations were performed for the parabolic ogive and circular cone and results are compared with those obtained by using other techniques and the available experimental data for circular cones.

Ruo, S. Y.

Fuselage-drag tests in the variable-density wind tunnel: streamline bodies of revolution, fineness ratio of 5

Results are presented of the drag tests of six bodies of revolution with systematically varying shapes and with a fineness ratio of 5. The forms were derived from source-sink distributions, and formulas are presented for the calculation of the pressure distribution of the forms. The tests were made in the N.A.C.A. variable-density tunnel over a range of values of Reynolds number from about 1,500,000 to 25,000,000. The results show that the bodies with the sharper noses and tails have the lowest drag coefficients, even when the drag coefficients are based on the two-thirds power of the volume. The data shows the most important single characteristic of the body form to be the tail angle, which must be fine to obtain low drag.

Abbott, Ira H

Experimental aerodynamic characteristics for a cylindrical body of revolution with various noses at angles of attack from 0 deg to 58 deg and Mach numbers from 0.6 to 2.0

An experimental investigation was conducted to determine the effect of forebody geometry, a grit ring around the nose, Reynolds number, Mach number, and angle of attack on the aerodynamic characteristics of a body of revolution. Aerodynamic force and moment characteristics were measured for a cylindrical body with tangent ogive noses of fineness ratio 2.5, 3.0, 3.5, and 5.0. The cylindrical body was tested with an ogive nose having a rounded tip and an ogive nose with two different nose strake arrangements. Aerodynamic configurations were tested at various Mach numbers, angles of attack, and Reynolds numbers. The data demonstrate that the aerodynamic characteristics for a body of revolution can be significantly affected by changes in nose fineness ratio, nose bluntness, Reynolds number, Mach number, and, of course, angle of attack. Nose strakes increased the normal forces but had little effect on the side forces that developed at subsonic Mach numbers for alpha greater than about 25. A grit ring around the nose had little or no effect on the aerodynamic characteristics.

Jorgensen, L. H.

Determination of Shapes of Boattail Bodies of Revolution for Minimum Wave Drag

By use of an approximate equation for the wave drag of slender bodies of revolution in a supersonic flow field, the optimum shapes of certain boattail bodies are determined for minimum wave drag. The properties of three specific families of bodies are determined, the first family consisting of bodies having a given length and base area and a contour passing through a prescribed point between the nose and base, the second family having fixed length, base area, and maximum area, and the third family having given length, volume, and base area. The method presented is easily generalized to determine minimum-wave-drag profile shapes which have contours that must pass through any prescribed number of points. According to linearized theory, the optimum profiles are found to have infinite slope at the nose but zero radius of curvature so that the bodies appear to have pointed noses, a zero slope at the body base, and no variation of wave drag with Mach number. For those bodies having a specified intermediate.diameter (that is, location and magnitude given), the maximum body diameter is shown to be larger, in general, than the specified diameter. It is also shown that, for bodies having a specified maximum diameter, the location of the maximum diameter is not arbitrary but is determined from the ratio of base diameter to maximum diameter.

Adams, Mac C.

Effect of Tail Surfaces on the Base Drag of a Body of Revolution at Mach Numbers of 1.5 and 2.0

Wind-tunnel tests were performed at Mach numbers of 1.5 and 2.0 to investigate the influence of tail surfaces on the base drag of a body of revolution without boattailing and having a turbulent boundary layer. The tail surfaces were of rectangular plan form of aspect ratio 2.33 and has symmetrical, circular-arc airfoil section. The results of the investigation showed that the addition of these tail surfaces with the trailing edges at or near the body base incurred a large increase in the base-drag coefficient. For a cruciform tail having a 10-percent-thick airfoil section, this increase was about 70 percent at a Mach number of 1.5 and 35 percent at a Mach number of 2.0. As the trailing edge of the tail was moved forward or rearward of the base by about one tail-chord length, the base-drag increment was reduced to nearly zero. The increments in base-drag coefficient due to the presence of 10-percent-thick tail surfaces were generally twice those for 5-percent-thick surfaces. The base-drag increments due to the presence of a cruciform tail were less than twice those for a plane tail. An estimate of the change in base pressure due to the tail surfaces was made, based on a simple superposition of the airfoil-pressure field onto the base-pressure field behind the body. A comparison of the results with the experimental values indicated that in most cases the trend in the variation of the base-drag increment with changes in tail position could be predicted by this approximate method but that the quantitative agreement at most tail locations was poor.

BOUNDARY LAYER - BODIES OF REVOLUTION

Drag measurements on a laminar-flow body of revolution in the 13-inch magnetic suspension and balance system

Low speed wind tunnel drag force measurements were taken on a laminar flow body of revolution free of support interference. This body was tested at zero incidence in the NASA Langley 13 in. Magnetic Suspension and Balance System (MSBS). The primary objective of these tests was to substantiate the drag force measuring capabilities of the 13 in. MSBS. The drag force calibrations and wind-on repeatability data provide a means of assessing these capabilities. Additional investigations include: (1) the effects of fixing transition; (2) the effects of fins installed in the tail; and (3) surface flow visualization using both liquid crystals and oil flow. Also two simple drag prediction codes were used to assess their usefulness in estimating overall body drag.

Dress, David A.

Transonic wall interference effects on bodies of revolution.

Efforts to develop a near sonic transport have placed renewed emphasis on obtaining accurate aerodynamic force and pressure data in the near sonic speed range. Comparison of wind-tunnel and flight data obtained for a blunt-nose body of revolution showed significant discrepancies in drag levels near Mach 1 - apparently due to wind-tunnel wall interference. Subsequent tests of geometrically similar bodies of revolution showed that increasing the model-to-test-section blockage ratio from 0.00017 to 0.0043 resulted in altered drag curve shapes, delayed drag divergence, and 'transonic creep' from subsonic drag levels due to increased wall interference.

Couch, L. M.

A second-order shock-expansion method applicable to bodies of revolution near zero lift

A second-order shock-expansion method applicable to bodies of revolution is developed by the use of the predictions of the generalized shock-expansion method in combination with characteristics theory. Equations defining the zero-lift pressure distributions and the normal-force and pitching-moment derivatives are derived. Comparisons with experimental results show that the method is applicable at values of the similarity parameter, the ratio of free-stream Mach number to nose fineness ratio, from about 0.4 to 2.

Source record

Supersonic flow past nonlifting bumped and indented bodies of revolution

Linear-theory values of the supersonic pressure field and wave drag of nonlifting bumped and indented bodies of revolution are presented and compared with the corresponding properties of a smooth body. The comparisons indicate that relatively small surface irregularities cause large pressure disturbances and changes in wave drag. The interference drag produced by bumps and indentations is discussed and a correction for the curvature of the characteristics is applied.

FLOW, SUPERSONIC

Effect of the Acceleration of Elongated Bodies of Revolution Upon the Resistance in a Compressible Flow

The problem of the motion of an elongated body of revolution in an incompressible fluid may, as is known, be solved approximately with the aid of the distribution of sources along the axis of the body. In determining the velocity field, the question of whether the body moves uniformly or with an acceleration is no factor in the problem. The presence of acceleration must be taken into account in determining the pressures acting on the body. The resistance of the body arising from the accelerated motion may be computed either directly on the basis of these pressures or with the aid of the so-called associated masses (inertia coefficients). A different condition holds in the case of the motion of bodies in a compressible gas. In this case the finite velocity of sound must be taken into account.

Frankl, F. I.

Drag measurements on a laminar flow body of revolution in Langley's 13 inch magnetic suspension and balance system

Low-speed wind tunnel drag force measurements were taken on a laminar flow body of revolution free of support interference. This body was tested at zero incidence in the NASA Langley 13 inch Magnetic Suspension and Balance System (MSBS). The primary objective of these tests was to substantiate the drag force measuring capabilities of the 13 inch MSBS. A secondary objective was to obtain support interference free drag measurements on an axisymmetric body of interest. Both objectives were met. The drag force calibrations and wind-on repeatability data provide a means of assessing the drag force measuring capabilities of the 13 inch MSBS. The measured drag coefficients for this body are of interest to researchers actively involved in designing minimum drag fuselage shapes. Additional investigations included: the effects of fixing transition; the effects of fins installed in the tail; surface flow visualizations using both liquid crystals and oil flow; and base pressure measurements using a one-channel telemetry system. Two drag prediction codes were used to assess their usefulness in estimating overall body drag. These theoretical results did not compare well with the measured values because of the following: incorrect or non-existent modeling of a laminar separation bubble on the body and incorrect of non-existent estimates of base pressure drag.

Dress, David A.

Arrangement of Bodies of Revolution in Supersonic Flow to Reduce Wave Drag

The wave drag of a combination of slender bodies of revolution at zero angle of attack is studied with a view to determining the arrangements for which the total drag is a minimum.Linearized theory is used to calculate the pressure distribution in the field surrounding the bodies. The interference drag coefficient is computed for different arrangements. The special cases of two bodies and of a three-body combination with bilateral symmetry are considered. The bodies treated are of the form determined by Sears and Haack as having minimum wave drag for prescribed volume and length. They also have equal fineness ratios. Numerical calculations of the drag coefficient of interference are carried out and curves are drawn which show the relative positions at which minimum drag occurs. A three-body configuration is found for which the total wave drag is about 35 percent less than the sum of the individual wave drags of the three bodies.

Friedman, Morris D

Wall Interference Study of the NTF Slotted Tunnel Using Bodies of Revolution Wall Signature Data

This paper is a description of the analysis of blockage corrections for bodies of revolution for the slotted-wall configuration of the National Transonic Facility (NTF) at the NASA Langley Research Center (LaRC). A wall correction method based on the measured wall signature is used. Test data from three different-sized blockage bodies and four wall ventilation settings were analyzed at various Mach numbers and unit Reynolds numbers. The results indicate that with the proper selection of the boundary condition parameters, the wall correction method can predict blockage corrections consistent with the wall measurements for Mach numbers as high as 0.95.

Iyer, Venkit

Wall Interference Study of the NTF Slotted Tunnel Using Bodies of Revolution Wall Signature Data

This paper is a description of the analysis of blockage corrections for bodies of revolution for the slotted-wall configuration of the National Transonic Facility (NTF) at the NASA Langley Research Center (LaRC). A wall correction method based on the measured wall signature is used. Test data from three different-sized blockage bodies and four wall ventilation settings were analyzed at various Mach numbers and unit Reynolds numbers. The results indicate that with the proper selection of the boundary condition parameters, the wall correction method can predict blockage corrections consistent with the wall measurements for Mach numbers as high as 0.95.

Iyer, Venkit