Wing-body Junction Research Articles

Time-depeiident and time-averaged turbulence structure near the nose of a wing-body junction

The behaviour of a turbulent boundary layer on a flat surface as it encounters the nose of a cylindrical wing mounted normal to that surface is being investigated. A three-component laser anemometer has been developed to measure this highly turbulent three-dimensional flow. Measurements of all the non-zero mean-velocity and Reynolds-stress components have been made with this instrument in the plane of symmetry upstream of the wing. These data have been used to estimate some of the component terms of the turbulence kinetic energy equation. Histograms of velocity fluctuations and short-time cross-correlations between the laser anemometer and a hot-wire probe have also been measured in the plane of symmetry. In all, these results reveal much of the time-dependent and time-averaged turbulence structure of the flow here.Separation occurs in the plane of symmetry because of the adverse pressure gradient imposed by the wing. In the time mean the resulting separated flow consists of two fairly distinct regions: a thin upstream region characterized by low mean backflow velocities and a relatively thick downstream region dominated by the intense recirculation of the mean junction vortex. In the upstream region the turbulence stresses develop in a manner qualitatively similar to those of a two-dimensional boundary layer separating in an adverse pressure gradient. In the vicinity of the junction vortex, though, the turbulence stresses are much greater and reach’ values many times larger than those normally observed in turbulent flows. These large stresses are associated with bimodal (double-peaked) histograms of velocity fluctuations produced by a velocity variation that is bistable. These observations are consistent with large-scale low-frequency unsteadiness of the instantaneous flow structure associated with the junction vortex. This unsteadiness seems to be produced by fluctuations in the momentum and vorticity of fluid from the outer part of the boundary layer which is recirculated as it impinges on the leading edge of the wing. Though we would expect these fluctuations to be produced by coherent structures in the boundary layer, frequencies of the large-scale unsteadiness are substantially lower than the passage frequency of such structures. It therefore seems that only a fraction of the turbulent structures are recirculated in this way.

Measurements of turbulent flow behind a wing-body junction

This paper describes measurements in the turbulent shear flow behind a wing that is mounted on a flat plate at 30Deg. of angle attack. Various physical aspects of the flow are illuminated by the experimental data that include the skin-friction coefficient and pattern, the static pressure coefficient, and two mean velocity components.

An Experimental Study of the Flow and Wall Pressure Field Around a Wing-Body Junction

The flow and wall-pressure field around a wing-body junction has been experimentally investigated in a quiet, low-turbulence wind tunnel. Measurements were made along the centerline in front of the wing and along several spanwise locations. The flow field data indicated that the strong adverse pressure gradient on the upstream centerline causes three-dimensional flow separation at approximately one wing thickness upstream and this induced the formation of the horseshoe root vortex which wrapped around the wing and became deeply embedded within the boundary layer. The wall-pressure fluctuations were measured for their spectral content and the data indicate that the effect of the adverse pressure gradient is to increase the low-frequency content of the wall pressure and to decrease the high-frequency content. The wall pressure data in the separated region, which is dominated by the horseshoe vortex, shows a significant increase in the low-frequency content and this characteristic feature prevails around the corner of the wing. The outer edge of the horseshoe vortex is clearly identified by the locus of maximum values of RMS wall pressure.

A study of wing-fuselage interaction

The problem addressed is that of the initial profile appropriate for the calculation of the boundary layer on the wing at a wing-body junction. The geometry considered is such that the fuselage boundary layer reaches the interaction region still attached and it is shown that when the wing has curvature the boundary-layer component of velocity normal to the wing is turned inviscidly through a right angle to provide a (in general) non-zero profile to initiate the wing calculation.

The position of points of maximum and minimum shear stress upstream of cylinders mounted normal to flat plates

Boundary layer separation upstream of cylinders mounted normal to a flat plate leads to the formation of horseshoe vortices around the bases of these cylinders, which can be either laminar or turbulent, depending upon the state of the upstream boundary layer. Therefore, a point of zero shear stress (at the separation position) and a point of maximum shear stress (beneath the main vortex) exists upstream of such cylinders. These particular points are of interest in many fields of fluid mechanics (flow in heat exchangers, wing body junctions, etc.). In this paper, formulae are presented which relate these positions to the following parameters: 1. (a) a boundary layer displacement thickness Reynolds number; 2. (b) the ratio of boundary layer displacement thickness to cylinder diameter; 3. (c) the ratio of cylinder height to cylinder diameter; 4. (d) the ratio of the boundary layer form parameter to the equivalent zero pressure gradient form parameter. Data from a number of experimental and theoretical investigations of low Mach number laminar and turbulent vortex systems are used in the derivation of these formulae.

Computation of three-dimensional turbulent shear flows in corners

A numerical technique developed for the solution of the steady Navier-Stokes equations using a space marching algorithm has been used to predict a complex, three-dimensional turbulent flow. The scheme has been designed to calculate flows with a dominant flow direction, in three-dimensional geometries, and has been used successfully to predict laminar flows. This paper is concerned with the extension of this technique to calculate turbulent flows in the corner region of the wingbody junction using both the algebraic eddy viscosity and the A>e turbulence models. The effects of different boundary conditions for the streamwise velocity at a solid boundary, used in many turbulent flow computations, are also considered. In the flow cases computed in this paper using a law of the wall boundary condition at solid boundaries, the A>e model showed no distinct advantages over the simpler algebraic viscosity model. However, the k-€ model provided much better results for the cases computed with the more realistic no-slip boundary condition.

Flow past wing-body junctions

The three-dimensional laminar flow past a junction formed by a thin wing protruding normally from a locally flat body surface is considered for wings of finite span but short or long chord. The Reynolds number is taken to be large. The leading-edge interaction for a long wing has the triple-deck form, with the pressure due to the wing thickness forcing a three-dimensional flow response on the body surface alone. The same interaction describes the flow past an entire short wing. Linearized solutions are presented and discussed for long and short two-dimensional wings and for certain three-dimensional wings of interest. The trailing-edge interaction for a long wing is different, however, in that the three-dimensional motions on the wing and on the body are coupled together and in general the coupling is nonlinear. Linearized properties are retrieved only for reduced chord lengths. The overall flow structure for a long wing is also discussed, including the traditional three-dimensional corner layer, which is shown to have an unusual singular starting form near the leading edge. Qualitative comparisons with experiments are made.

Remarks on the vortex model of wing-body interference.

W the framework of slender body theory, wingbody c mbinations of complicated configurations may be analyzed approximately by the vortex method.' In such an approach to the interference problem, the body is assumed to be a circular cylinder represented by a doublet, and the wing panels are represented by a finite number of vortices. The doublet and the vortices satisfy the linear Laplace equation in the cross-flow plane. It remains to satisfy the boundary conditions. The condition of a vanishing normal velocity component on the body is satisfied by the image vortices in the circle. For a given number N of vortices for each wing panel, we have at our disposal the strength and the spacing of each vortex, which are to be determined by further restraining conditions. The purpose of the present note is to point out the correct image system and to recommend the appropriate conditions for the vortex model. For a vortex of strength 7 at the point z = x + iy outside the circular cylinder \z = a, the boundary condition is satisfied by the method of images, which consists of a vortex of strength —7 at the inverse point az and a vortex of strength 7 at the center. This statement can be rigorously proved by the circle theorem of Milne-Thomson. The image system most commonly usedconsists of only the vortex at the inverse point, but not the vortex at the center. Although both systems satisfy the boundary condition of vanishing normal velocity on the circle, the latter system, unfortunately, does not obey the Kelvin theorem on the constancy of circulation. If the original vortices outside the circle add up to zero in strength, the vortices at the center cancel out. Thus, neglect of the center vortex is applicable only to symmetric configuration for which the sum of external vortices is zero. In general, it is important to include the image vortex system at the center. For example, in a recent work of Barnes, the two trailing vortices outside the cylinder do not cancel each other; the correct image system should include a vortex of strength equal to the sum of the two external vortices at the center as well as two vortices at the inverse points. However, Ref. 4 did not have the vortex system at the center, the effect of which would be of interest. As mentioned previously, the strengths and the locations of wing vortices are at our disposal. Consequently, there is certain arbitrariness in the vortex method. To determine these quantities, Nielsen suggested the following conditions: 1) the sum of the strengths of the wing vortices equals the circulation at the wing-body juncture; 2) the centroid of the vortices remains at rest. For N discrete vortices, there are 2N unknowns; these two conditions are certainly not sufficient, unless N = I. Besides, the circulation at the wingbody juncture and the centroid of the vortices are usually not known in advance. The number of unknowns is halved if one arbitrarily specifies the strength or location of each of the N vortices. The remaining N unknowns are determined from no-flow boundary conditions across the wing panel at N control points. For a given geometry, it is convenient to specify the vortex locations as being evenly distributed over the exposed wing span. The control points may be located midway between two neighboring vortices. This method is suggested by Campbell and has been found convenient for machine computation when N is large. Once the strengths of vortices at the specified locations are solved, the aerodynamic loading, normal force, side force5 and rolling moment may be readily evaluated.

UNIFORMLY VALID SECOND-ORDER SOLUTION FOR SUPERSONIC FLOW OVER CRUCIFORM SURFACES

Abstract : Second-order supersonic flow over a cruciform configuration is sudied for supersonic inlets, wing-body junctions and vehicle fins. Severe local failures are identified and adjusted for the ordinary second-order theory. For wings with discontinuous slopes, discontinuous potentials occur across the planar shock and squareroot singularities in the velocities occur at the intersection of these shocks with the ruciform surfaces. second-order solution uniformly valid to first order is constructed by adjustment of the ordinary second-order solution obtained first. The uniformly valid solution has two different series representations in the thickness parameter. This solution gives the detailed wave structure and shows a flow regime upstream of the vertex-centered undisturbed Mach cone not predicted by the ordinary theory. The wave structure consists of a pyramidal arrangement of planar shocks adjacent to and upstream of the above cone, followed by weaker oblique expansion fans and finally by two extremely weak shocks coincident with the vertex-centered undisturbed Mach cone. Results are given for the case of two iAD-287 426Div. 9 U (TITA/SEB) Bell Aerosystems Co., Buffalo, N. Y. THERMOELASTIC EFFECTS ON HYPERSONIC STABILITY AND CONTROL. PART II. VOLUME I. ELASTIC RESPONSE DETERINATIONS FOR SEVERELY HEATED WINGS. Final rept., by Richard H. Gllagher and Rolland D. Huff. Aug 62, 160p. incl. illus. tersecting wedges. (uthor)