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Free flight tests of 45-deg swept wings of 3.15 aspect ratio and 0.54 taper ratio to measure wing damping and possible transonic flutter
Gradient-based optimization requires accurate derivatives of the objective function and constraints. These gradients may have previously been obtained by manual differentiation of analysis codes, symbolic manipulators, finite-difference approximations, or existing automatic differentiation (AD) tools such as ADIFOR (Automatic Differentiation in FORTRAN). Each of these methods has certain deficiencies, particularly when applied to complex, coupled analyses with many design variables. Recently, a new AD tool called ADJIFOR (Automatic Adjoint Generation in FORTRAN), based upon ADIFOR, was developed and demonstrated. Whereas ADIFOR implements forward-mode (direct) differentiation throughout an analysis program to obtain exact derivatives via the chain rule of calculus, ADJIFOR implements the reverse-mode counterpart of the chain rule to obtain exact adjoint form derivatives from FORTRAN code. Automatically-generated adjoint versions of the widely-used CFL3D computational fluid dynamics (CFD) code and an algebraic wing grid generation code were obtained with just a few hours processing time using the ADJIFOR tool. The codes were verified for accuracy and were shown to compute the exact gradient of the wing lift-to-drag ratio, with respect to any number of shape parameters, in about the time required for 7 to 20 function evaluations. The codes have now been executed on various computers with typical memory and disk space for problems with up to 129 x 65 x 33 grid points, and for hundreds to thousands of independent variables. These adjoint codes are now used in a gradient-based aerodynamic shape optimization problem for a swept, tapered wing. For each design iteration, the optimization package constructs an approximate, linear optimization problem, based upon the current objective function, constraints, and gradient values. The optimizer subroutines are called within a design loop employing the approximate linear problem until an optimum shape is found, the design loop limit is reached, or no further design improvement is possible due to active design variable bounds and/or constraints. The resulting shape parameters are then used by the grid generation code to define a new wing surface and computational grid. The lift-to-drag ratio and its gradient are computed for the new design by the automatically-generated adjoint codes. Several optimization iterations may be required to find an optimum wing shape. Results from two sample cases will be discussed. The reader should note that this work primarily represents a demonstration of use of automatically- generated adjoint code within an aerodynamic shape optimization. As such, little significance is placed upon the actual optimization results, relative to the method for obtaining the results.
Analytical and empirical studies of a finite difference method for the solution of the transonic flow about harmonically oscillating wings and airfoils are presented. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady equations for small disturbances. Since sinusoidal motion is assumed, the unsteady equation is independent of time. Three finite difference investigations are discussed including a new operator for mesh points with supersonic flow, the effects on relaxation solution convergence of adding a viscosity term to the original differential equation, and an alternate and relatively simple downstream boundary condition. A method is developed which uses a finite difference procedure over a limited inner region and an approximate analytical procedure for the remaining outer region. Two investigations concerned with three-dimensional flow are presented. The first is the development of an oblique coordinate system for swept and tapered wings. The second derives the additional terms required to make row relaxation solutions converge when mixed flow is present. A finite span flutter analysis procedure is described using the two-dimensional unsteady transonic program with a full three-dimensional steady velocity potential.
The method for turbulent flows is a further development of an existing method; profile families with two parameters and a lag entrainment method replace the simple entrainment method and power profiles with one parameter. The method for laminar flows is a new development. Moment of momentum equations were used for the solution of the problem, the profile families were derived from similar solutions of boundary layer equations. Laminar and turbulent flows at the wings were calculated. The influence of wing tapering on the boundary layer development was shown. The turbulent boundary layer for a revolution ellipsoid is calculated for 0 deg and 10 deg incidence angles.
The linear stability of three-dimensional incompressible, isothermal, nonparallel boundary-layer flows has been investigated. The method of multiple scales is used to derive the partial-differential equations that describe the spatial modulations of the amplitude, phase and wavenumber of a disturbance. Group velocities are used to determine the disturbance growth direction. The envelope method is used to calculate the logarithmic amplitude growth rate N. The theory is applied to the flows over a swept-back tapered wing with boundary-layer suction. Results of such analysis for the X-21 wing are discussed. It is found that the nonparallel effects for this wing is substantial.
A computer program HADY-I for calculating the linear incompressible or compressible stability characteristics of the laminar boundary layer on swept and tapered wings is described. The eigenvalue problem and its adjoint arising from the linearized disturbance equations with the appropriate boundary conditions are solved numerically using a combination of Newton-Raphson interative scheme and a variable step size integrator based on the Runge-Kutta-Fehlburh fifth-order formulas. The integrator is used in conjunction with a modified Gram-Schmidt orthonormalization procedure. The computer program HADY-I calculates the growth rates of crossflow or streamwise Tollmien-Schlichting instabilities. It also calculates the group velocities of these disturbances. It is restricted to parallel stability calculations, where the boundary layer (meanflow) is assumed to be parallel. The meanflow solution is an input to the program.
Recent progress in the development of implicit algorithms for the Euler equations using the flux-vector splitting method is described. Comparisons of the relative efficiency of relaxation and spatially-split approximately factored methods on a vector processor for two-dimensional flows are made. For transonic flows, the higher convergence rate per iteration of the Gauss-Seidel relaxation algorithms, which are only partially vectorizable, is amply compensated for by the faster computational rate per iteration of the approximately factored algorithm. For supersonic flows, the fully-upwind line-relaxation method is more efficient since the numerical domain of dependence is more closely matched to the physical domain of dependence. A hybrid three-dimensional algorithm using relaxation in one coordinate direction and approximate factorization in the cross-flow plane is developed and applied to a forebody shape at supersonic speeds and a swept, tapered wing at transonic speeds.
Development of a computational method for prediction of external store carriage characteristics at transonic speeds is described. The geometric flexibility required for treatment of pylon-mounted stores is achieved by computing finite difference solutions on a five-level embedded grid arrangement. A completely automated grid generation procedure facilitates applications. Store modeling capability consists of bodies of revolution with multiple fore and aft fins. A body-conforming grid improves the accuracy of the computed store body flow field. A nonlinear relaxation scheme developed specifically for modified transonic small disturbance flow equations enhances the method's numerical stability and accuracy. As a result, treatment of lower aspect ratio, more highly swept and tapered wings is possible. A limited supersonic freestream capability is also provided. Pressure, load distribution, and force/moment correlations show good agreement with experimental data for several test cases. A detailed computer program description for the Transonic Store Carriage Loads Prediction (TSCLP) Code is included.
A computational method for prediction of external store carriage loads at transonic speeds is described. The geometric flexibility required for treatment of isolated and underwing, pylon-mounted stores is achieved by computing solutions on a five-level embedded grid arrangement. A completely automated grid generation procedure facilitates applications. Store modeling capability consists of bodies of revolution with multiple fore and aft fins. A body-conforming grid improves the accuracy of the computed store body flow field. A nonlinear finite difference relaxation scheme, developed specifically for modified transonic small disturbance flow equations, enhances numerical stability and accuracy. As a result, more accurate treatment of low aspect ratio, highly swept and tapered wing planforms is possible. A limited supersonic freestream capability is also provided. Pressure, load distribution, force and moment correlations show good agreement for several test cases.
Improvements to the XTRAN3S computer program are summarized. Work on this code, for steady and unsteady aerodynamic and aeroelastic analysis in the transonic flow regime has concentrated on the following areas: (1) Maintenance of the XTRAN3S code, including correction of errors, enhancement of operational capability, and installation on the Cray X-MP system; (2) Extension of the vectorization concepts in XTRAN3S to include additional areas of the code for improved execution speed; (3) Modification of the XTRAN3S algorithm for improved numerical stability for swept, tapered wing cases and improved computational efficiency; and (4) Extension of the wing-only version of XTRAN3S to include pylon and nacelle or external store capability.
A computational method for prediction of external store carriage loads at transonic speeds is described. The geometric flexibility required for treatment of isolated and underwing, pylon mounted stores is achieved by computing solutions on a five level embedded grid arrangement. A completely automated grid generation procedure facilitates applications. Store modeling capability consists of bodies of revolution with multiple fore and aft fins. A body conforming grid improves the accuracy of the computed store body flow field. A nonlinear finite difference relaxation scheme, developed specifically for modified transonic small disturbance flow equations, enhances numerical stability and accuracy. As a result, more accurate treatment of low aspect ratio, highly swept and tapered wing planforms is possible. A limited supersonic freestream capability is also provided. Pressure, load distribution, force and moment correlation show good agreement for several test cases.
The results of tests of six airfoils having the N.A.C.A. 230 mean line and varying in thickness from 0.06c to 0.21c are presented. These results agree with previous findings in showing that aerodynamically the best section is one of moderate thickness. The data are of value mainly in connection with the design of tapered wings having sections based on the N.A.C.A. 230 mean line.
An empirical method is given for estimating the aerodynamic effect of ordinary and split flaps on airfoils similar to the Clark Y. The method is based on a series of charts that have been derived from an analysis of existing wind-tunnel data. Factors are included by which such variables as flap location, flap span, wing aspect ratio, and wing taper may be taken into account. A series of comparisons indicate that the method would be suitable for use in making preliminary performance calculations and in structural design.
The force variation along the wing span under combined normal and angular accelerations is considered. Non dimensional curves of section load, shear, and moment are given for: (1) the air load that produces a normal acceleration; (2) the accompanying wing weight and normal inertia loads; (3) aileron and gust air loads that produce angular acceleration; (4) the angular inertia load of the wing. The required aerodynamic load distributions have been obtained by use of wing theory, and the wing inertia distributions are based on an analysis of wing-weight data. Several examples are included to illustrate the effect of wing taper and aileron span on the total shears and moments at any section along the span.
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An investigation has been conducted in the Langley 4- by 4-foot supersonic tunnel at Mach numbers 1.40 and 1.59 to determine the effect of aileron profile on the aerodynamic characteristics of a complete model of a supersonic aircraft configuration. The model had a 40 degree sweptback tapered wing with 10-percent-thick circular-arc sections normal to the quarter-chord line. The ailerons were 20-percent chord and were located on the outboard 50 percent of the wing semispans. The various ailerons investigated included the basic circular-arc profile and three flat-sided ailerons having ratios of trailing-edge thickness to hinge-line thickness t of 0, 0.5, and 1.0. Low aileron effectiveness was obtained with the circular-arc and t = 0 profiles. Increasing the trailing-edge thickness (t = 0.5 and 1.0) resulted in increased effectiveness as well as increased hinge moments with only a slight increase in drag.
The results of the basic flutter theory originally devised in 1934 and published as NACA Technical Report no. 496 are presented in a simpler and more complete form convenient for further studies. The paper attempts to facilitate the judgement of flutter problems by a systematic survey of the theoretical effects of the various parameters. A large number of experiments were conducted on cantilever wings, with and without ailerons, in the NACA high-speed wind tunnel for the purpose of verifying the theory and to study its adaptability to three-dimensional problems. The experiments included studies on wing taper ratios, nacelles, attached floats, and external bracings. The essential effects in the transition to the three-dimensional problem have been established. Of particular interest is the existence of specific flutter modes as distinguished from ordinary vibration modes. It is shown that there exists a remarkable agreement between theoretical and experimental results.
The primary goal in designing the Blue Emu was to provide an airline with a cost efficient and profitable means of transporting passengers between the major cities in Aeroworld. The design attacks the market where a demand for inexpensive transportation exists and for this reason the Blue Emu is an attractive investment for any airline. In order to provide a profitable aircraft, special attention was paid to cost and economics. For example, in manufacturing, simplicity was stressed in structural design to reduce construction time and cost. Aerodynamic design employed a tapered wing which reduced the induced drag coefficient while also reducing the weight of the wing. Even the propulsion system was selected with cost effectiveness in mind, yet also to maintain the marketability of the aircraft. Thus, in every aspect of the design, consideration was given to economics and marketability of the final product.