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The development of a practical method for the aerodynamic design of isolated wing and wing/body configurations is achieved through the coupling of existing computational fluid dynamics (CFD) analysis codes and a quasi-Newton numerical optimization method. The direct design method is generalized to treat three-dimensional aerodynamic optimization problems subject to inviscid, rotational, compressible flow conditions imposed by the Euler equations. The method couples either the FLO57 or the TEAM flow solver with a modified version of the QNMDIF numerical optimization algorithm. The method is applied, but is not limited, to supersonic design problems. A case study is presented illustrating the method's effectiveness in maximizing the lift-to-drag ratio, subject to a variety of constraints, of selected supersonic configurations at cruise conditions.

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.

A selection of successes and failures of Computational Fluid Dynamics (CFD) is discussed. Experiment/CFD correlations involving full potential and Euler computations of the aerodynamic characteristics of four commercial transport wings and two low aspect ratio, delta wing configurations are shown. The examples consist of experiment/CFD comparisons for aerodynamic forces, moments, and pressures. Navier-Stokes equations are not considered.

A selection of CFD successes and failures is evaluated, on the basis of experimental data/CFD result correlations involving full-potential and Euler computations of the aerodynamics of four commercial transport wings and two low aspect ratio delta wings. An effort is made to ascertain optimum values for grid density and distribution, artificial dissipation, Courant-Friedrichs-Lewy number, enthalphy damping, and a multigrid scheme for each flow condition and configuration analyzed. It is demonstrated that CFD solutions can assist the experimentalist prior to a test by indicating the locations of high pressure gradients and projecting test condition limitations due to balance design limits.

Three helicopter rotor sections were tested in the NASA Ames Research Center 2- by 2-Foot Transonic Wind Tunnel over a Mach range from 0.2 to 0.88. The sections tested had maximum thickness/chord ratios of 0.078, 0.09, and 0.10. The thickest section was of early technology and had been tested previously in other wind tunnels. This section was included in the investigation to establish a basis for comparing the two thinner sections, which were of recent design. The results of the investigation showed that the pitching-moment characteristics for the three airfoil sections were acceptable. The drag divergence Mach numbers for the three sections were 0.80, 0.825, and 0.845 in order of decreasing thickness.

A recontoured upper surface was designed to increase the maximum lift coefficient of a modified NACA 65 (0.82)(9.9) airfoil section which was tested at Mach numbers of 0.3 and 0.4 and Reynolds numbers of 2.3x10(6) and 4.3x10(6). The original 6-series section was tested for comparison with the recontoured section. The recontoured profile was found to have a higher maximum lift coefficient at all test conditions than the original airfoil. The recontoured airfoil showed less drag and nearly the same pitching moment characteristics as the original 6-series airfoil at all test conditions. The improvements found for the recontoured airfoil of the present study are similar to those found during previous investigations of recontoured 6-series airfoils with less camber.

Wind-tunnel test data for two closely related supercritical airfoils were compared with calculations obtained from a nonconservative, potential flow code over a Mach number range from 0.20 to 0.80. The potential flow code includes an iterated, integral boundary-layer correction. The theoretical pressure distributions correlated more closely with the experimental pressure distributions when the flow was entirely subsonic or subsonic with a small supersonic zone than when the flow contained a large supersonic zone. The predicted drag level was below the experimental values at nearly all test conditions and the difference in drag level for the two airfoils was not accurately predicted.

The state-of-the-art of transonic wing design by use of computer codes based on the potential flow-theory is presented. The capabilities and limitations of these codes are exemplified by several experiment-theory correlations, including an assessment of pressure distribution from isolated wing and wing-body codes. Computer codes using both conservative and nonconservative differencing schemes were used, and the effects of boundary-layer corrections were considered. Results showed that calculations from a full potential, isolated code correlate well with data from an isolated wing test, but may give poor predictions of the aerodynamic characteristics of some wing-body configurations. Boundary-layer correlations were found to have only moderate effects on experiment-theory correlation. Aeroelastic effects were considered important for high aspect ratio wings of low to moderate thickness, and viscous effects were minimal for typical cruise conditions, even for Reynold's numbers as low as two million. The effect of wind-tunnel walls on experiment-theory correlations remained inconclusive. A wing-body code was used to calculate the flow field about a wing-body configuration with body-mounted engines, typical of the transonic Biz-Jet aircraft.

The method of computing the Whitham F function using distributions of downwash and sidewash angles was evaluated with two different models. F functions which were calculated for a half angle cone cylinder at M infinites = 2.01, using theoretically and experimentally derived flow angles, show that the method is sensitive to small inaccuracies in the measured flow angles. An oblique wing transport model was tested at 0 deg angle of attack at M infinitely = 2.01. In this test, two different probes were used at two different distances from the model. The pressure signature derived from the F function was extrapolated and compared to the pressure signature measured at the distance of 0.87 body lengths with the static pressure probe. The agreement between the two pressure signatures was poor due to the many inaccuracies involved in using a probe designed to measure flow angularity.

A practical procedure for the design of low drag, transonic airfoils is demonstrated. The procedure uses an optimization program, based on a gradient algorithm coupled with an aerodynamic analysis program, that solves the full, non-linear potential equation for transonic flow. The procedure is useful for the design of retrofit modifications for drag reduction of existing aircraft as well as for the design of low drag profiles for new aircraft. Results are presented for the modification of four different airfoils to decrease the drag at a given transonic Mach number.

Two different forward contour modifications designed to increase the maximum lift coefficient of the NACA 64 sub 1-212 airfoil section were evaluated experimentally at low speeds. One modification consisted of a slight droop of the leading edge with an increased leading-edge radius; the other modification incorporated increased thickness over the forward 35 percent of the upper surface of the profile. Both modified airfoil sections were found to provide substantially higher maximum lift coefficients than the 64 sub 1-212 section. The drooped leading-edge modification incurred a drag penalty of approximately 10 percent at low and moderate lift coefficients and exhibited a greater nosedown pitching moment than the 64 sub 1-212 profile. The upper surface modification produced about the same drag level as the 64 sub 1-212 section at low and moderate lift coefficients and less nosedown pitching moment than the 64 sub 1-212 profile. Both modified airfoil sections had lower drag coefficients than the 64 sub 1-212 section at high lift coefficients.

A practical procedure for the optimum design of low-speed airfoils is demonstrated. The procedure uses an optimization program based on a gradient algorithm coupled with an aerodynamic analysis program that uses a relaxation solution of the inviscid, full-potential equation. The analysis program is valid for both incompressible and compressible flow, thereby making optimum design of high-speed, shock-free airfoils possible. Results are presented for the following three constrained optimization problems at fixed angle of attack and Mach number: (1) adverse pressure-gradient minimization, (2) pitching-moment minimization; and (3) lift maximization. All three optimization problems were studied with various aerodynamic and geometric constraints.

A practical procedure for the optimum design of low-speed airfoils is demonstrated. The procedure uses an optimization program based on the method of feasible directions coupled with an aerodynamic analysis program that uses a relaxation solution of the inviscid, full potential equation. Results are presented for airfoils designed to have small adverse pressure gradients, high maximum lift, and low pitching moment.

A practical procedure for optimum design of aerodynamic shapes is demonstrated. The proposed procedure uses an optimization program based on the method of feasible directions coupled with an analysis program that uses a relaxation solution of the inviscid, transonic, small-disturbance equations. Results are presented for low-drag, nonlifting transonic airfoils. Extension of the method to lifting airfoils, other speed regimes, and to three dimensions if feasible.

The wind tunnel performance of a 10-percent thick helicopter rotor section design by numerical optimization is presented. The model was tested at Mach number from 0.2 to 0.84 with Reynolds number ranging from 1,900,000 at Mach 0.2 to 4,000,000 at Mach numbers above 0.5. The airfoil section exhibited maximum lift coefficients greater than 1.3 at Mach numbers below 0.45 and a drag divergence Mach number of 0.82 for lift coefficients near 0. A moderate 'drag creep' is observed at low lift coefficients for Mach numbers greater than 0.6.

A three-dimensional, inviscid, full-potential lifting rotor code was used to demonstrate that pressure distributions on both advancing and retreating blades could be significantly improved by perturbing local airfoil sections. The perturbations were described by simple geometric shape functions. To illustrate the procedure, an example calculation was made at a forward flight speed of 85 m/sec (165 knots) and an advance ratio of 0.385. It was found that a minimum of three shape functions was required to improve the pressures without producing undesirable secondary effects in high-speed forward flight on a hypothetical modern rotor blade initially having an NLR-1 supercritical airfoil. Reductions in the shock strength on the advancing blade could be achieved, while simultaneously lessening leading-edge pressure gradients on the retreating blade. The major blade section modifications required were blunting of the upper surface leading edge and some reshaping of the blade's upper surface resulting in moderately thicker airfoils.

The thickness of the upper surface of 64 airfoils was increased from the leading edge to the position of maximum thickness. The modifications were generated using a numerical optimization routine coupled with an aerodynamic analysis code. The type of modification presented can be used for aircraft design or for the retrofit of current aircraft to improve the stall characteristics and climb performance. The coordinates of the modified airfoils are presented with plots of the forward 45% of the profiles and pressure distributions for both the modified and unmodified sections at an angle of attack of 14 degrees.

An upper surface modification designed to increase the maximum lift coefficient of a 63 sub 2 - 215 airfoil section was tested at Mach numbers of 0.2, 0.3, and 0.4 Reynolds numbers of 1.3 x 1 million, 2 x 10 sub 6 and 2.5 x 1 million. Comparisons of the aerodynamic coefficients before and after the modification were made. The upper surface modification increased the maximum lift coefficient of the airfoil significantly at all conditions.

A practical procedure for the optimum design of transonic wings is demonstrated. The procedure uses an optimization program based on the method of feasible directions coupled with an aerodynamic analysis program which solves the three-dimensional potential equation for subsonic through transonic flow. Two new wings for the A-7 aircraft were designed by using the optimization procedure to achieve specified surface pressure distributions. The new wings, along with the existing A-7 wing, were tested in the Ames 11-foot transonic wind tunnel. The experimental data show that all of the performance goals were met.

A numerical minimization scheme is used in conjunction with two-dimensional and three-dimensional inviscid transonic flow analysis codes to provide procedures for wing leading edge aerodynamic design. The procedures are demonstrated in the design of a new leading edge to improve C-141 cruise performance. For the high aspect ratio moderately swept C-141 wing, the 2-D procedure is shown to yield results which are in close agreement with those obtained using the 3-D technique. Although the 2-D approach uses much less computation time than the 3-D technique, the latter requires fewer manhours than the former. Comparisons of predicted and wind tunnel measured performance improvements are presented which verify the design procedures.

An application of numerical optimization to the design of advanced airfoils for transonic aircraft showed that low-drag sections can be developed for a given design Mach number without an accompanying drag increase at lower Mach numbers. This is achieved by imposing a constraint on the drag coefficient at an off-design Mach number while minimizing the drag coefficient at the design Mach number. This multiple design-point numerical optimization has been implemented with the use of airfoil shape functions which permit a wide range of attainable profiles during the optimization process. Analytical data for the starting airfoil shape, a single design-point optimized shape, and a double design-point optimized shape are presented. Experimental data obtained in the NASA Ames two-by two-foot wind tunnel are also presented and discussed.

A computer program developed for the automated design of low speed airfoils utilizes a generalized Joukowski method for aerodynamic analysis coupled with a conjugate gradient, penalty function, numerical optimization algorithm to give an efficient calculation technique for use with minicomputers. The program designs airfoils with a prescribed pressure distribution as well as those which minimize or maximize some aerodynamic force coefficient. At present the method is restricted to inviscid, incompressible flow. A typical design problem will execute in 4.5 hr on an HP 9830 minicomputer.

The ability of the method to compute wing transonic performance was determined by comparing computed results with both experimental data and results computed by other theoretical procedures. Both pressure distributions and aerodynamic forces were evaluated. Comparisons indicated that the method is a significant improvement in transonic wing analysis capability. In particular, the computational method generally calculated the correct development of three-dimensional pressure distributions from subcritical to transonic conditions. Complicated, multiple shocked flows observed experimentally were reproduced computationally. The ability to identify the effects of design modifications was demonstrated both in terms of pressure distributions and shock drag characteristics.

This paper discusses the application of three-dimensional computational transonic flow methods to several different types of transport wing designs. The purpose of these applications is to evaluate the basic accuracy and limitations associated with such numerical methods. The use of such computational methods for practical engineering problems can only be justified after favorable evaluations are completed. The paper summarizes a study of both the small-disturbance and the full potential technique for computing three-dimensional transonic flows. Computed three-dimensional results are compared to both experimental measurements and theoretical results. Comparisons are made not only of pressure distributions but also of lift and drag forces. Transonic drag rise characteristics are compared. Three-dimensional pressure distributions and aerodynamic forces, computed from the full potential solution, compare reasonably well with experimental results for a wide range of configurations and flow conditions.

A study was conducted to assess the feasibility of performing computerized wing design by numerical optimization. The design program combined a full potential, inviscid aerodynamics code with a conjugate gradient optimization algorithm. Three design problems were selected to demonstrate the design technique. The first involved modifying the upper surface of the inboard 50% of a swept wing to reduce the shock drag subject to a constraint on wing volume. The second involved modifying the entire upper surface of the same swept wing (except the tip section) to increase the lift-drag ratio subject to constraints on wing volume and lift coefficient. The final problem involved modifying the inboard 50% of a low-speed wing to achieve good stall progression. Results from the three cases indicate that the technique is sufficiently accurate to permit substantial improvement in the design objectives.

Recent applications of numerical optimization to the design of advanced airfoils for transonic aircraft have shown that low-drag sections can be developed for a given design Mach number without an accompanying drag increase at lower Mach numbers. This is achieved by imposing a constraint on the drag coefficient at an off-design Mach number while the drag at the design Mach number is the objective function. Such a procedure doubles the computation time over that for single design-point problems, but the final result is worth the increased cost of computation. The ability to treat such multiple design-point problems by numerical optimization has been enhanced by the development of improved airfoil shape functions. Such functions permit a considerable increase in the range of profiles attainable during the optimization process.

A method is presented for numerical airfoil optimization whereby a reduced number of design coordinates are used to define the airfoil shape. The approach is to define the airfoil as a linear combination of shapes. These basic shapes may be analytically or numerically defined, allowing the designer to use his insight to propose candidate designs. The design problem becomes one of determining the participation of each such function in defining the optimum airfoil. Examples are presented for two-dimensional airfoil design and are compared with previous results based on a polynomial representation of the airfoil shape. Four existing NACA airfoils are used as basic shapes. Solutions equivalent to previous results are achieved with a factor of more than 3 improvements in efficiency, while superior designs are demonstrated with an efficiency greater than 2 over previous methods. With this shape definition, the optimization process is shown to exploit the simplifying assumptions in the inviscid aerodynamic analysis used here, thus demonstrating the need to use more advanced aerodynamics for airfoil optimization.

A practical procedure for the design of low drag, transonic airfoils is demonstrated. The procedure uses an optimization program, based on a gradient algorithm coupled with an aerodynamic analysis program, that solves the full, non-linear potential equation for transonic flow. The procedure is useful for the design of retrofit modifications for drag reduction of existing aircraft as well as for the design of low drag profiles for new aircraft. Results are presented for the modification of four different airfoils to decrease the drag at a given transonic Mach number.

Supersonic skin friction measurements in grit type boundary layer transition trips with zero heat transfer

Mach number and geometry effects on level of sonic boom overpressure and applicability of Whitham theory to calculation of sonic boom

Aerodynamic characteristics of leading-edge sweep wing-body combinations

Guidelines applicable to grit-type boundary layer transition trips near leading edges of wind tunnel models