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The vortex flow over an arrow wing is theoretically investigated using the free-vortex-sheet method. The sectional lift coefficient and accumulated span loadings, which are important in determining the root bending moment, are calculated. The longitudinal stability variation is also estimated.
Vortex shedding from an oscillating circular cylinder was numerically investigated at Re = 100 with the Navier-Stokes equations and the new boundary conditions. The detailed shedding patterns are characterized by means of streakline plotting and lift-coefficient curves. A parameter map is presented which distinguishes the synchronized shedding from the asynchronous and the double vortices shedding from the single vortex shedding. The computational result is in good agreement with earlier experimental results.
The transonic flowfield around an F-16A fighter configuration at a moderate incidence angle is simulated by solving the Navier-Stokes equations on a single-block grid. The numerical solution matches experimental freestream conditions with a mach number of 0.85, 16 degrees angle of attack, and a characteristic Reynolds number of 12.75 million. MacCormack's explicit algorithm is used in conjuction with a local time step and consecutive mesh refinement procedure to accelerate numerical convergence. The Baldwin-Lomax algebraic model provides turbulent closure. Computed surface pressure distributions and the aircraft lift coefficient compare favorably with wind tunnel data. The drag coefficient in the simulation overpredicts the experimental value by 8 percent.
A fundamentally new approach to the aircraft minimum induced drag problem is presented. The method, a 'viscous lifting line', is based on the minimum entropy production principle and does not require the planar wake assumption. An approximate, closed form solution is obtained for several wing configurations including a comparison of wing extension, winglets, and in-plane wing sweep, with and without a constraint on wing-root bending moment. Like the classical lifting-line theory, this theory predicts that induced drag is proportional to the square of the lift coefficient and inversely proportioinal to the wing aspect ratio. Unlike the classical theory, it predicts that induced drag is Reynolds number dependent and that the optimum spanwise circulation distribution is non-elliptic.
A subsonic and a transonic airfoil are presented for application in a high-altitude long-endurance aircraft and a very-high-altitude aircraft, respectively. The subsonic airfoil is designed for a lift coefficient c(l) = 1.4 at a chord Reynolds number Re = 700,000 and a very low Mach number. The transonic airfoil is designed for c(l) = 1.0 at Re = 500,000 and a transonic Mach number M = 0.7. Both airfoils are developed to perform as well or better than previously designed airfoils. However, the present airfoils are developed for a constrained pitching moment to reduce aircraft trim drag and to relieve, to some extent, the torsional loads in the typically high-aspect-ratio wings. The beneficial effects of a cruise flap and of boundary-layer transition control on the off-design performance characteristics are illustrated.
An embedded grid algorithm for the Euler and/or Navier-Stokes equations is developed and applied to delta wings at high angles of attack in low speed flow. The Navier-Stokes code is an implicit, finite volume algorithm, using flux difference splitting for the convective and pressure terms and central differencing for the viscous and heat transfer terms. Calculations are compared with detailed experimental results over an angle of attack range up to and beyond the maximum lift coefficient, corresponding to vortex breakdown at the trailing edge, for a delta wing nominally of unit aspect ratio. The results indicate that the overall flowfield, including surface pressures, surface streamlines, and vortex trajectories, can be simulated accurately with the global grid version of the present algorithm. However, comparison of computed velocities and vorticity with experimentally measured off-body values at an angle of attack of 20.5 deg indicates the core region is substantially more diffuse in the computations than that measured with either a five-hole probe or a laser velocimeter. Embedded grids, used to improve the numerical discretization in the core region, are formulated within the framework of the implicit, upwind-biased multi-grid algorithm. Structured levels of local nested refinements are made. Three-dimensional results for both Euler and Navier-Stokes calculations are shown, with up to 3 levels of embedded refinement. The embedding procedure was effective in eliminating a crossflow secondary separation produced in the Euler solutions on coarse grids.
A number of vehicles are currently being proposed for a manned mission to Mars. One of these vehicles has a modified blunt-nosed cone configuration. Experimental results were obtained for this vehicle in 1968. They show lift-over-drag ratios comparable to those needed for Mars entry. Computations are performed to verify the earlier results and to further describe the flight characteristics of this vehicle. An analytical method is used to define the surface of this vehicle. A single-block volume grid is generated around the vehicle using the algebraic Two-Boundary Grid Generation algorithm (TBGG) and transfinite interpolation. Euler solutions are then obtained from a Langley Aerodynamic Upward Relaxation Algorithm (LAURA) at Mach 6.0 and angles of attack of 0, 6, and 12 deg. The lift coefficient determined from the LAURA code agree very well with the experimental results. The drag and pitching moment coefficients, however, are underestimated by the code since viscous effects are not considered. Contour plots of the flowfield show no evidence of separation for angles of attack up to 12 deg.
A major goal of NASA during the last 15 years has been the development of laminar flow technology for aircraft drag reduction. Of equal importance is achieving a state of readiness that will allow the successful application of this technology by industry to large, long-range aircraft. Recent progress in achieving extensive laminar flow with limited suction on the Boeing 757 has raised the prospects from practical application of the hybrid laminar flow control (HLFC) concept to subsonic aircraft. Also, better understanding of phenomena affecting laminar flow stability and response to disturbances has encouraged consideration of natural laminar flow (NLF), obtained without suction or active mechanical means, for application to transport aircraft larger than previously thought feasible. These ideas have inspired the current NASA/ASEE project with goals as follows: explore the feasibility of extensive NLF for aircraft at high Reynolds number under realistic flight conditions; determine the potential applications of NLF technology and the conditions under which they may be achieved; and identify existing aircraft that could be adapted to carry out flight experiments to validate NLF technology application. To achieve these objectives, understanding of the physical limits to natural laminar flow and possible ways to extend these limits was sought. The primary factors involved are unit Reynolds number, Mach number, wing sweep, thickness, and lift coefficients as well as surface pressure gradients and curvature. Based on previous and ongoing studies using laminar boundary layer stability theory, the interplay of the above factors and the corresponding transition limits were postulated.
Results of correlative and design studies for transition location, laminar and turbulent boundary-layer parameters, and wake drag for forward swept and aft swept wings are presented. These studies were performed with the use of an improved integral-type boundary-layer and transition-prediction methods. Theoretical predictions were compared with flight measurements at subsonic and transonic flow conditions for the variable aft swept wing F-14 aircraft for which experimental pressure distributions, transition locations, and turbulent boundary-layer velocity profiles were measured. Flight data were available at three spanwise stations for several values of sweep, freestream unit Reynolds number, Mach numbers, and lift coefficients. Theory/experiment correlations indicate excellent agreement for both transition location and turbulent boundary-layer parameters. The results of parametric studies performed during the design of a laminar glove for the forward swept wing X-29 aircraft are also presented. These studies include the effects of a spanwise pressure gradient on transition location and wake drag for several values of freestream Reynolds numbers at a freestream Mach number of 0.9.
Guidance trajectories for coplanar aeroassisted orbital transfer (AOT) from high earth orbit to LEO are presently optimized under the assumption of trajectory control during its endoatmospheric phase by alpha-dependent lift coefficient. Optimal trajectories are first computed by minimizing the total velocity impulse required for AOT; attention is then given to guidance trajectories capable of approximating such key properties of the optimal trajectories as minimum altitude, exit velocity, and exit path inclination, in real time. A switch is made from target-altitude guidance to target path inclination-guidance according to the velocity depletion required for optimum flight.
The thin-layer Navier-Stokes equations are solved for the flow about a coplanar close-coupled canard-wing-body configuration at a transonic Mach number of 0.90 and at angles of attack ranging from 0 to 12 degrees. The influence of the canard on the wing flowfield, including canard-wing vortex interaction and wing vortex breakdown, is investigated. A study of canard downwash and canard leading-edge vortex effects, which are the primary mechanisms of the canard-wing interaction, is emphasized. Comparisons between the computations and experimental measurements of surface pressure coefficients, lift, drag and pitching moment data are favorable. A grid refinement study for configurations with and without canard shows that accurate results are obtained using a refined grid for angles of attack where vortex burst is present. At an angle of attack of approximately 12 deg, favorable canard-wing interaction which delays wing vortex breakdown is indicated by the computations and is in good agreement with experimental findings.
This paper presents the exact dimensionless equation of motion and the necessary conditions for the computation of the optimal trajectories of a hypervelocity vehicle flying through a non-rotating spherical planetary atmosphere. Numerical solution is then presented for the case when the vehicle makes several passages through the atmosphere near the perigee of its orbit. While the orbit is slowly contracting, aerodynamic maneuver is performed to obtain the maximum plane change. Several plots were presented to show the optimal variations of the lift coefficient and the bank angle and the various elements of the orbit.
An experimental study has been performed to assess the maximum lift capability of a supercritical multielement airfoil representative of an advanced transport aircraft wing. The airfoil model was designed with a leading-edge slat and single or two-segment trailing-edge flaps. Optimization work was performed at various slat/flap deflections as well as gap/overhang positions. Landing configurations and the attainment of maximum lift coefficients of 4.5 with single-element flaps and 5.0 with two-segment flaps was emphasized. Test results showed a relatively linear variation of the optimum gap/overhang positioning of the slat versus slat deflection, considerable differences in optimum rigging between single and double segment flaps, and large Reynolds number effects on multielement airfoil optimization.
The results of an aircraft parameters identification study conducted on the National Aeronautics and Space Administration/Ames Research Center Advanced Concepts Flight Simulator (ACFS) in conjunction with the Navy-NASA Joint Institute of Aeronautics are given. The ACFS is a commercial airline simulator with a design based on future technology. The simulator is used as a laboratory for human factors research and engineering as applied to the commercial airline industry. Parametric areas examined were engine pressure ratio (EPR), optimum long range cruise Mach number, flap reference speed, and critical take-off speeds. Results were compared with corresponding parameters of the Boeing 757 and 767 aircraft. This comparison identified two areas where improvements can be made: (1) low maximum lift coefficients (on the order of 20-25 percent less than those of a 757); and (2) low optimum cruise Mach numbers. Recommendations were made to those anticipated with the application of future technologies.
The fuel optimal control problem arising in coplanar orbital transfer employing aeroassisted technology is addressed. The mission involves the transfer from high energy orbit (HEO) to low energy orbit (LEO) without plane change. The basic approach here is to employ a combination of propulsive maneuvers in space and aerodynamic maneuvers in the atmosphere. The basic sequence of events for the coplanar aeroassisted HEO to LEO orbit transfer consists of three phases. In the first phase, the transfer begins with a deorbit impulse at HEO which injects the vehicle into a elliptic transfer orbit with perigee inside the atmosphere. In the second phase, the vehicle is optimally controlled by lift and drag modulation to satisfy heating constraints and to exit the atmosphere with the desired flight path angle and velocity so that the apogee of the exit orbit is the altitude of the desired LEO. Finally, the second impulse is required to circularize the orbit at LEO. The performance index is maximum final mass. Simulation results show that the coplanar aerocapture is quite different from the case where orbital plane changes are made inside the atmosphere. In the latter case, the vehicle has to penetrate deeper into the atmosphere to perform the desired orbital plane change. For the coplanar case, the vehicle needs only to penetrate the atmosphere deep enough to reduce the exit velocity so the vehicle can be captured at the desired LEO. The peak heating rates are lower and the entry corridor is wider. From the thermal protection point of view, the coplanar transfer may be desirable. Parametric studies also show the maximum peak heating rates and the entry corridor width are functions of maximum lift coefficient. The problem is solved using a direct optimization technique which uses piecewise polynomial representation for the states and controls and collocation to represent the differential equations. This converts the optimal control problem into a nonlinear programming problem which is solved numerically by using a modified version of NPSOL. Solutions were obtained for the described problem for cases with and without heating constraints. The method appears to be more robust than other optimization methods. In addition, the method can handle complex dynamical constraints.
An experimental investigation was conducted at the ARC 11- by 11-Foot Transonic Wind Tunnel as part of the Oblique Wing Research Aircraft Program to study the aerodynamic performance and stability characteristics of a 0.087-scale model of an F-8 airplane fitted with an oblique wing designed by Rockwell International. The 10.3 aspect ratio, straight-tapered wing of 0.14 thickness/chord ratio was tested at two different mounting heights above the fuselage. Additional tests were conducted to assess low-speed behavior with and without flaps, aileron effectiveness at representative flight conditions, and transonic drag divergence with 0 degree wing sweep. Longitudinal stability data were obtained at sweep angles of 0, 30, 45, 60, and 65 degrees, at Mach numbers ranging from 0.25 to 1.40. Test Reynolds numbers varied from 3.2 to 6.6 x 10 exp 6/ft. and angle of attack ranged from -5 to +18 degrees. Most data were taken at zero sideslip, but a few runs were at sideslip angles of +/- 5 degrees. The raised wing position proved detrimental overall, although side force and yawing moment were reduced at some conditions. Maximum lift coefficient with the flaps deflected was found to fall short of the value predicted in the preliminary design document. The performance and trim characteristics of the present wing are generally inferior to those obtained for a previously tested wing designed at ARC.
A twin-engine, low-wing transport model, with a supercritical wing designed for a cruise Mach number of 0.77 and a lift coefficient of 0.55 was tested in the 16-Foot Transonic Tunnel at NASA Langley Research Center. The purpose of this test was to compare the wing/nacelle interference effects of superfans (BPR 18) with the interference effects of advanced turbofans (BPR 6). Flow-through nacelles were used. Forces and moments on the complete model were measured using a strain gage balance, and extensive surface static pressure measurements were made on the model's wing, nacelles, and pylons. Results of the investigation indicate that superfan nacelles can be installed with approximately the same drag penalty as conventional turbofan nacelles.
Detailed measurements of all three mean velocity components and five of the six Reynolds stresses have been made around a model of a lifting-wing/body junction. The body was the flat working section floor of a small blower wind tunnel. Measurements of the surface pressure distribution on the NACA 0012 wing showed that the lift coefficient at the body surface was reduced by only 16 percent from the freestream value. It is shown that the near constancy of the bound vorticity requires the formation of aixal vorticity within the body boundary layer. This vorticity was concentrated in the two legs of the necklace vortex formed near the leading edge of the wing. The magnitude of the vorticity was always greater in the leg that developed on the suction surface. By four chord lengths downstream of the trailing edge, the turbulence structure of the suction leg was qualitatively similar to that of a single vortex imbedded in a turbulent boundary layer.