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Vortex-lattice subsonic method determines mean camber surface for trimmed noncoplanar planforms with minimum vortex drag. Multiple surfaces can be designed together to yield trimmed configuration with minimum induced drag at some specified lift coefficient. Program is applicable to isolated wings, wing-canard configuration, tandem wing, and wing-winglet configuration.
A numerical method is developed to predict distributed and total aerodynamic characteristics for low aspect-ratio wings with partial leading-edge separation. The flow is assumed to be steady and inviscid. The wing boundary condition is formulated by the quasi-vortex-lattice method. The leading-edge separated vortices are represented by discrete free vortex elements which are aligned with the local velocity vector at mid-points to satisfy the force free condition. The wake behind the trailing-edge is also force free. The flow tangency boundary condition is satisfied on the wing, including the leading- and trailing-edges. Comparison of the predicted results with complete leading-edge separation has shown reasonably good agreement. For cases with partial leading-edge separation, the lift is found to be highly nonlinear with angle of attack.
Sufficient instructions are provided for interfacing the Mangler-Smith, leading edge vortex rollup program with a vortex lattice (POTFAN) method and an advanced higher order, singularity linear analysis for computing the vortex effects for simple canard wing combinations.
Vortex flow modeling is used to calculate the steady inviscid incompressible flow past one, two and three delta wing configurations. The wings are modeled with vortex lattices and the leading and trailing-edge sheets are modeled by segmented straight vortex filaments. Aerodynamic characteristics are obtained for a range of geometry and angle of attack.
A theoretical study describing the effects of spanwise camber on the lift dependent drag of slender delta wings having leading-edge-vortex-flow is presented. The earlier work by Barsby, using conical flow, indicated that drag levels similar to those in attached flow could be obtained. This is reexamined and then extended to the more practical case of nonconical flow by application of the vortex-lattice method coupled with the suction-analogy and the recently developed Boeing free-vortex-sheet method. Lastly, a design code is introduced which employs the suction analogy in an attempt to define 'optimum' camber surfaces for minimum lift dependent drag for vortex flow conditions
An experimental investigation was conducted in the Langley high-speed 7- by 10-foot wind tunnel to determine the aerodynamic performance of suction applied near the wing tips above the trailing edge of a 60 deg swept Gothic wing. Moveable suction inlets were symmetrically mounted in the proximity of the trailing edge, and the amount of suction was varied to maximize wing lift. Tests were conducted at Mach 0.15, 0.30, and 0.45, and the angle of attack was varied from -4 to 50 deg. The suction augmentation increases the lift coefficient over the entire range of angle of attack. The lift improvement exceeds the unaugmented wing lift by over 20%. Moreover, the augmented lift exceeds the lift predicted by vortex lattice theory to 30 deg angle of attack. Suction augmentation is postulated to strengthen the vortex system by increasing its velocity and making it more concentrated. This causes the vortex breakdown to be delayed to a higher angle of attack
The vortex lattice method has been extended to a single bladed rotor operating at high advance ratios and encountering a free vortex from a fixed wing upstream of the rotor. The predicted unsteady load distributions on the model rotor blade are generally in agreement with the experimental results. This method has also been extended to full scale rotor flight cases in which vortex induced loads near the tip of a rotor blade were indicated. Using conformal transformation methods an exact analysis of the effects of thickness on the lift due to a two dimensional wing vortex interaction is presented.
A theoretical investigation was carried out to extend and improve an existing method for predicting the longitudinal characteristics of wing flap configurations with externally blown flaps (EBF). Two potential flow models were incorporated into the prediction method: a wing and flap lifting-surface model and a turbofan engine wake model. The wing-flap model uses a vortex-lattice approach to represent the wing and flaps. The jet wake model consists of a series of closely spaced vortex rings normal to a centerline which may have vertical and lateral curvature to conform to the local flow field beneath the wing and flaps. Comparisons of measured and predicted pressure distributions, span load distributions on each lifting surface, and total lift and pitching moment coefficients on swept and unswept EBF configurations are included. A wide range of thrust coefficients and flap deflection angles is considered at angles of attack up to the onset of stall. Results indicate that overall lift and pitching-moment coefficients are predicted reasonably well over the entire range. The predicted detailed load distributions are qualitatively correct and show the peaked loads at the jet impingement points, but the widths and heights of the load peaks are not consistently predicted.
Steady lifting flows over highly swept delta wings at large incidence were studied. After an exhaustive literature review, development of a vortex-lattice method was attempted. To demonstrate the feasibility of using such a method, an existing code was modified. A system of vortex lines to simulate the leading-edge wake was added. The coefficients predicted by the modified code were in good agreement with experimental data.
This paper deals with selected linearized-aerodynamic and vortex-flow methods as applied to aircraft design problems at high subsonic speeds. In particular, the NASA Vortex Lattice and Modified Multhopp methods are the linearized techniques employed, and the suction analogy is used to provide estimates associated with vortex-flow aerodynamics. Many examples are given as to how researchers at Langley have used these methods to design the high subsonic, wing-mean-camber shapes for various configurations such as a supersonic transport, high-aspect-ratio transport, trapezoidal fighter wing, strake wing, tandem wing, joined wing, delta wing, and slender cranked wing. Many of these have been built, tested, and have had their data compared with theory. In addition, a technique for defining efficiently performing strake planforms for use in strake-wing combinations is discussed, and further improvements in wing design are outlined. The latter may be obtained by using higher-ordered linear panel methods as well as nonlinear-transonic methods.
The effects of sweep and aspect ratio on the longitudinal and lateral-directional aerodynamic characteristics of low-aspect-ratio skewed (oblique) wings having separation-induced vortex flows along leading and side edges were investigated in the Langley high-speed 7- by 10-foot tunnel at a low-subsonic Mach number. The theoretical analysis used the vortex-lattice method for estimating attached-flow aerodynamic characteristics and the leading-edge suction analogy of Polhamus for estimating separation induced vortex-flow effects. Experimental results were compared with asymmetric, separated, vortex flow theory.
A method of the unsteady suction analogy is developed using the unsteady quasi-vortex-lattice method which accurately predicts unsteady leading-edge and side-edge suction forces, and applies to any reduced frequencies. The importance of vortex lag is demonstrated, and damping derivatives, including roll and pitch damping derivatives with reduced frequencies and angles of attack are accurately predicted. Agreement of predicted pitch stiffness derivatives, however, is found to depend on the Reynolds number, possible aeroelastic effect, and the degree of edge-separated vortex flow on the model. Applications to the prediction of longitudinal dynamic stability derivatives for slender wings at high angles of attack are also presented.
A user's manual is presented for a computer program in which a vortex-lattice lifting-surface method is used to model the wing and multiple flaps. The engine wake model consists of a series of closely spaced vortex rings with rectangular cross sections. The jet wake is positioned such that the lower boundary of the jet is tangent to the wing and flap upper surfaces. The two potential flow models are used to calculate the wing-flap loading distribution including the influence of the wakes from up to two engines on the semispan. The method is limited to the condition where the flow and geometry of the configurations are symmetric about the vertical plane containing the wing root chord. The results include total configuration forces and moments, individual lifting-surface load distributions, pressure distributions, flap hinge moments, and flow field calculation at arbitrary field points. The use of the program, preparation of input, the output, program listing, and sample cases are described.
A method for calculating the longitudinal aerodynamic coefficients and the pressure distributions on a body at reasonably high angles of attack is presented. The body is represented by a combination of source elements and vortex-lattice elements, including separation of the vortices at increasing angles of attack. The method is self-consistent in that the body and the separated vortex wake are treated as an integrated interacting system. The location of the separation line can be included as an arbitrary input from experimental data or can be evaluated approximately by a pressure-dependent criterion. Calculated values of the aerodynamic coefficients and pressure distributions on cone-cylinder and ogive-cylinder bodies compare well, qualitatively and quantitatively, with experimental data, including simulation of the dependence on Reynolds number.
Data obtained through very high angles of attack from a large-scale, subsonic wind-tunnel test of a close-coupled canard-delta-wing fighter model are analyzed. The canard delays wing leading-edge vortex breakdown, even for angles of attack at which the canard is completely stalled. A vortex-lattice method was applied which gave good predictions of lift and pitching moment up to an angle of attack of about 20 deg, where vortex-breakdown effects on performance become significant. Pitch-control inputs generally retain full effectiveness up to the angle of attack of maximum lift, beyond which, effectiveness drops off rapidly. A high-angle-of-attack prediction method gives good estimates of lift and drag for the completely stalled aircraft. Roll asymmetry observed at zero sideslip is apparently caused by an asymmetry in the model support structure.
The advanced propeller developed for high Mach number cruise incorporates swept blades to reduce compressibility losses. In order to evaluate the induced flow-field vortex lattice methods are applied to a swept propeller blade. The blade is modeled by a radial distribution of helical horseshoe vortices with a single swept bound vortex at the quarter chord and the control point at the three-quarter chord of each radial section. The results of numerical calculations show that the power coefficient decreases as the blade is swept and the power loading distribution shifts inboard.
A procedure based on vortex lattice theory to interpret the lift and torque measured on a following model in a wind tunnel is developed to retrieve the velocity distribution in the vortex wake that caused the induced forces. It is concluded that the retrieval procedure has a potential for reliably determining the structure of vortex wakes that trail from the wings of subsonic transport aircraft. Tests using idealized theoretical models show that the procedure is highly reliable and accurate. However, certain difficulties are found in the retrieval procedure when applied to actual data measured with following wings of various sizes in a wind tunnel.
The effect of wingtip modifications on the stability and control characteristics of an agricultural airplane has been studied by means of a nonplanar quasi-vortex-lattice method. The method is used to compute the changes in steady state and perturbed state lateral-directional stability and control derivatives produced by wingtip mounted winglets, vortex diffuser vanes, and tip extensions. The study shows that the combination of the excessive positive dihedral effect produced by the winglets and adverse yaw due to aileron deflection can have a detrimental effect on the roll control characteristics of the airplane. Introduction of an aileron-rudder-interconnect, and reduction of the effective dihedral by canting-in of the winglets, or addition of a lower winglet can eliminate the roll control problems.