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Drag Characteristics of a Low-Drag Low-Boom Supersonic Formation Flying Concept

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Drag Characteristics of a Low-Drag Low-Boom Supersonic Formation Flying Concept Drag Characteristics of a Low-Drag Low-Boom Supersonic Formation Flying Concept Yuichiro Goto∗ , Shigeru Obayashiy and Yasuaki Kohamaz Tohoku University, Sendai, Japan In this paper, a new concept for low-drag, low-boom supersonic flight, by formation flying is proposed. This concept takes advantage of the shock wave and expansion wave interactions among the aircrafts in the fleet. Drag characteristics analysis is carried out on the concept to validate the effectiveness of supersonic formation flying as a means to reduce the wave drag of the fleet of supersonic aircrafts. Analysis results indicate promising drag reduction for supersonic formation flying, and insight on the physics of wave interactions in formation flying is obtained. Nomenclature M Freestream Mach number β pM 2 1 − µ Mach angle CL Lift coefficient CDs Drag coefficient of the SST CDe Drag coefficient of the elliptic wing CDis Induced drag coefficient of the SST CDie Induced drag coefficient of the elliptic wing CDcvols Volume wave drag coefficient of the SST CDcvole Volume wave drag coefficient of the elliptic wing CDclifts Lift dependent wave drag coefficient of the SST CDclifte Lift dependent wave drag coefficient of the elliptic wing ARs Aspect ratio of the SST ARe Aspect ratio of the elliptic wing bs Span of the SST be Span of the elliptical wing cs Root chord length of the SST ce Root chord length of the elliptical wing ts Maximum thickness of the SST te Maximum thickness of the elliptical wing Ss Wing area of the SST Se Wing area of the elliptical wing rs Maximum fuselage cross-section radius of the SST Ls Fuselage length of the SST e Span efficiency factor of the SST r,θ ,xmyu Three parameters for new coordinate system ∗Graduate Student, Department of Aeronautics and Space Engineering. Student Member AIAA. yProfessor, Institute of Fluid Science. Associate Fellow AIAA. zProfessor, Institute of Fluid Science. 1 of 12 American Institute of Aeronautics and Astronautics I. Introduction n the past 50 years, although the technology for transonic flight has matured, commercially practical Icivil supersonic transport has not been realized. The two major problems that have prevented supersonic commercial transportation are wave drag and sonic boom. Wave drag, which is the dominating component of drag at supersonic speeds, leads to a deterioration in cruise efficiency. And sonic booms have a problem of public acceptance, which gives supersonic transports strict limitations on overland light. This leads to less flexible operation capabilities, reducing its profitability. Many attempts have been made to minimize the wave drag and the sonic boom in the past. Among them, many studies approached this problem by optimizing the shape of the wing body configuration. However, most studies have shown a strong trade-off between wave drag and sonic boom, making it impossible to minimize wave drag and sonic boom simultaneously, for a given aircraft overall length. The supersonic formation flying concept proposed in this paper, utilizes wave interference for the reduction of wave drag and sonic boom. For the reduction of wave drag, favorable wave interference is used for the following aircraft to extract momentum from the pressure gradients in the flow field behind the leading aircraft. And the reduction in the loudness of the sonic boom is achieved by a virtual elongation effect of the aircraft overall length, obtained from wave interference. In this paper, drag characteristics of this concept is investigated using Euler simulations. The dependence of wave drag to the relative position of the aircraft is investigated to evaluate the effectiveness of this concept and gain insight on the drag characteristics of supersonic formation flying. II. Concept The supersonic formation flying concept proposed here utilizes the benefits of multi-body favorable wave interference to reduce the volume and lift dependent wave drag of the following aircraft. When an aircraft flies through the air at supersonic speeds, they leave momentum in the air behind them. This is the cause of wave drag. Wave drag of the following aircraft is reduced by collecting this momentum as pressure gradient. Friedman et al1 carried out linear analyses on bodies of revolution, imitating a fuselage and stores. As a result they have shown that wave drag per total cross-sectional area can be reduced when placed in an optimal relative position. Positions of the stores that were favorable for wave drag reduction were positions where the stores were placed inside a shock wave, which is a positive pressure jump. The reduction of sonic boom of the fleet will be achieved by virtually elongating the aircraft. Marconi et al.2 showed that, instead of simple elongation of the aircraft overall length, off-axis volume addition is also effective for boom mitigation. Volume was added by placing a small keel-like forward-swept wing at the nose of the aircraft. As a result, they succeeded in reducing the amount of extension toe the fuselage by a factor of tan µ. In the concept proposed in this paper, a similar idea is applied to a fleet of aircrafts to reduce the sonic boom. It is a well known fact that the pressure sig- nature of the sonic boom is dependent on the overall length and the area distribution of the aircraft A(x). This area distribution is defined by a sweep of a plane inclined downward at the Mach angle. If aircrafts are placed in a way such that the nose of the following aircrafts i in front of this inclined plane extending from the tail of the preceding aircraft, the area distribu- tion of the aircraft will be clustered together, resulting in a longer duration time for the pres- sure wave profile. This results in the reduction in the loudness of the sonic boom perceived on the ground. A sketch of this idea is shown in Fig.1. Bahm et al.3 carried out some flight tests to measure the ground recorded sonic boom pro- duced by a formation of two F-18s. In the re- Figure 1. Sketch of area distribution continuation 2 of 12 American Institute of Aeronautics and Astronautics sults of this preliminary flight tests, it was possible to fly two aircrafts, which originally produces an N wave on the ground, and produce flattop type signatures by flying in formations. III. Computational Method Euler simulations are carried out using TAS-flow, an unstructured Euler/Navier-Stokes solver, and the computational mesh was generated using EdgeEditor and TU TetraGrid, which are CFD tools developed at Tohoku University. TAS-flow is an unstructured Euler/Navier-Stokes solver using a finite-volume cell-vertex scheme, HLLEW Riemann solver for flux computations,4 and LU-SGS implicit scheme for time integration.5 EdgeEditor is an unstructured surface mesh generation software. It takes CAD data as an input,6 and generates a surface mesh using an advancing front triangulation method.7 TU TetraGrid is an unstructured volume mesh generation software using the Delaunay triangulation algorithm.8 As for the coordinate system used in this analysis, x is in the freestream direction, y is out towards the right wing tip, and z is upward. The origin of the coordinate system is located at the half chord position along the centerline of the leading aircraft. The freestream Mach number used in this analysis is M = 1:5. This Mach number was chosen considering recent trends in the cruise Mach number of recent supersonic transports concepts. Since the objective of this study is to investigate the effectiveness of supersonic formation flying, the subject of the analysis is kept simple to extract the effect of shock wave interaction alone, and facilitate the analysis. First of all, simulations are carried out on two aircraft formations. And, the model used for this study is an elliptical planform wing with a biconvex airfoil. Although simplification of the configuration is convenient, the drag characteristic of the simplified model must be similar to that of a practical supersonic transport. The aspect ratio and thickness are determined to satisfy this condition. First, the practical supersonic transport model is approximated as a wing-body configuration consisting of an ellipsoidal wing and a Sears-Haack body of revolution as the fuselage. The drag of the components are estimated using the following equations,9 CDs = CDis + CDc vols + CDc lifts (1) where each drag component is given by, 2 CL CDis = (2) πARse 4π2r2 πr2 β2 + 2 (c =b ) t2 C = s s + s s s (3) Dc vols L2 S β2 + (c =b ) c2 s s s s s 2 2 β CL CDc lifts = (4) 2 πcs This drag model is compared with that of a single elliptical wing, expressed in the following form, CDe = CDie + CDc vole + CDc lifte (5) where each drag component is given by, 2 CL CDie = (6) πARe β2 + 2 (c =b ) t2 C = e e e (7) Dc vole β2 + (c =b ) c2 e e e 2 2 β CL CDc lifte = (8) 2 πce The numbers for the drag model are given below. Most values for the SST drag model are taken from 3 of 12 American Institute of Aeronautics and Astronautics the Concorde.10 2 bs ARs e = 1:5 = (9) π bs=2 cs=2 bs=cs = 1:5π=4 (10) ts=cs = 0:04 (11) rs=Ls = 0:0234 (12) These values are substituted into the drag model, and the drag models are compared to solve for the aspect ratio and the thickness of the simplified elliptic wing. This resulted in an elliptic wing with the following dimensions. ARe = 1:5 be=ce = 1:5π=4 te=ce = 0:04502 Se = 0:9253 A three view diagram of this configuration is given in Fig.2.
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