ESDA 2012-82332 DRAFT : EXPERIMENTAL STUDY OF VERY LOW ASPECT RATIO WINGS IN SLENDER BODIES

The dynamics of very low aspect ratio wings (or strakes) vortices in slender bodies are complex due to the interaction of the shed vortex sheet and the body vortex. For missiles at supersonic speeds these interactions are not easily predicted using engineering level tools. To shed some new light onto this problem, an experimental study in a water channel for moderate Reynolds number (Re=1000) was performed for a 19D body and strake configuration with strakes having a span to body diameter ratio of 1.25. Comparisons to numerical simulations in supersonic flow are also performed. Flow visualisation has been carried out to characterize the vortex dynamics at different angles of attack; these being 11◦, 16◦, 22◦and 27◦. The comparison between a slender body without strakes and the body-strake configuration has given some key indicators in relation to the vortex position ∗Address all correspondence to this author. of the core. Furthermore, unsteady wing-body interference has been observed at angles of attack above 20◦for both experimental and numerical simulations. Consequently, the average position of the vortex core is located at larger distances from the missile in comparison to the body without strakes. The numerical simulations show good correlation with the experimental tests even though the dynamic convective interactions between the body vortex and strake vortex sheet are not predicted. NOMENCLATURE AT S Area of the tunnel test section D Body diameter KBW Wing-to-body carryover factor Re Reynolds number T Temperature V Body velocity 1 Copyright c ⃝ 2012 by ASME (x,y,z) Experimental Coordinate System (ECS) (x’,y’,z’) Body Coordinate System (BCS) z Non-dimensional axial distance (z/D) zM Non-dimensional axial distances at which the wing-body vortices merge α Angle of Attack ν Kinematic viscosity INTRODUCTION The interaction between wings and bodies for slender body configurations has been the subject of numerous studies in the past [1] [2]. Potential methods have in the past, and still remain the only theoretical methods for determining these interactions. At an engineering prediction level the theoretical methods suffice for wings of low to moderate aspect ratio. For wing body combinations with very low aspect ratio wings having side edges which are a significant length of the configuration, the overall body loads are not reasonably predicted. Current methods accounting for these effects are based on experimental databases [3] [2], and unfortunately, the limitations of the experimental configurations. Studies in the past [4] [5] have only peripherally touched on the aerodynamic phenomena causing this discrepancy between the original formulations based on slender body theory and the observed loads. One of the traditional methods for predicting gross loads of a body and wing combination is to algebraically sum the individual components i.e. body and wing, and their interactions i.e. wing-to-body and body-to-wing. At the gross loads level, the wing-to-body carryover factor, KBW , is poorly predicted [4] [5]. A previous numerical study by Tuling and Dala [5] on these interactions has indicated possible complex vortex interactions of the body with very low aspect ratio wings or strakes. The configuration of the strakes are dominated by its side edge that makes the strake a rectangular wing for all intensive purposes except for the leading. To this end, experimental studies of the flow phenomena and their dynamics is intended to shed some light on the possible reason for the observed discrepancies. In addition to this fewer studies are concerned about the three dimensional velocity field measurements of vortex dynamics [6] or flow visualisation [7] for such configurations. Expected flow regimes as a function of angle of attack are symmetric, unsteady, or non-symmetric and unsteady. For slender body wing combinations, the dominant speed regime of application is transonic to supersonic, as reflected in by the work performed by Tuling and Dala. The experimental study executed in this paper was performed at low speed because the slender body assumption where the changes in the dominant flow direction are small compared to other two dimensions are applicable. The geometry used in this work is the same as that used by Tuling and Dala [5], which is a 19D tangent-ogive body with cruciform 11.25D strakes with a span to body diameter ration of 1.25. The nose and aft body are 3D in length, whilst the strakes had a 45◦leading edge sweep. The strakes are tested in the ’+’ configuration. For the configuration of reference [5] the diameter of 80mm was used. For the experimental study a body diameter of 16mm was used. NUMERICAL SIMULATIONS For comparison purposes and because this work follows on from the numerical studies of reference [5], additional numerical simulations were performed to match the experimental conditions of this study. In summary, the numerical simulations were performed using Fluent with the Spalart-Allmaras turbulence model with near wall treatment. These simulations were performed at the supersonic speeds of Mach 2.0, 2.5 and 3.0. Little difference between the flow structures between Mach 2.0, 2.5 and 3.0 were observed, and all the comparisons presented are for the Mach number 2.0. The vortex positions of shed vortices of the numerical simulations (for comparison to the experimental tests) were determined by extracting the local minimum of the λ2−criterion [8] at any plane of interest perpendicular to the body axes of the configuration. EXPERIMENTAL SETUP AND TEST CONDITIONS The experiments were carried out in a water towing tank with a working section of 0.5m x 0.5m and 5m long installed at the Laboratory of Aero-Hydrodynamics of Vehicles at the University of Málaga. The test section is made of Plexiglas to allow for optical visualisation. A sketch of the experimental set up is depicted in 1. FIGURE 1. EXPERIMENTAL SETUP OVERVIEW The missile is attached to a specially manufactured device 2 Copyright c ⃝ 2012 by ASME that allows the angle of attack to be changed. This detail is presented in 2, where both the anchor devices and the missile are shown. The body moves through the towing tank by means of a controlled linear guide rail and is driven by a DC motor with an encoder and controlled by a PC. FIGURE 2. MISSILE WITHOUT STRAKES AND MOUNTING SYSTEM The values of the angle of attack are typically the ones used in missile aerodynamics (from 5 to 30 degrees). A set of five different angles of attack where used (6.5◦±0.3, 11◦±0.3, 16◦±0.2, 22◦±0.05 and 27◦±0.05). The velocity imposed to the missile is about 57 mm/s ±1 mm/s. The water temperature is measured with a PT100 probe to within ±0.1 ◦C. The Reynolds number is defined as Re = V D/ν and reaches a constant value of 1040 ±3 . Special care was taken to obtain a steady state regime with no velocity fluctuations. The missile was thus smoothly accelerated until it reached a constant velocity and the results were checked to ensure that they were not dependent on the acceleration. The two configurations of body alone and body plus strakes were tested in an attempt to understand the change in leeside vortex behaviour and compare the results to the numerical simulations. Flow visualisation was carried out using a green fluorescent dye (Rhodamine 6G) mixed with a retardant gel. The dye was applied on the forebody zone. This area was found to better highlight the fluid dynamics. The test area was illuminated normally to the mean flow with a laser sheet from a green laser of 500mW (wavelength = 532nm). A set of lens and optics were used to create a thin laser sheet. A 1Mpixel video-camera was used to capture the vortex images at a frame rate of 1/25s. The frame rate was found to be well suited to have enough accuracy in the axial resolution of the flow structures which can be resolved to an axial step below 0.15D. The processed images were extracted from a video and then postprocessed to quantify the vortex core position from both the body and the strakes. FLOW VISUALISATION The comparison of different frames between the missile with and without strakes is presented in this section. First, we will discuss the different coordinate systems used in this study to compare the results with those presented in [5]. Experimental and Body Coordinate Systems Due to the experimental setup, flow visualisations were performed in a x-y plane, which corresponds to an experimental coordinate system (ECS). The origin of this system being the rocket nose. The results were converted to the body coordinate system (BCS); this being a more common axes system for missile aerodynamics. This is shown in 3.