ALBERT

Description: The development of implicit upwind algorithms for the solution of the three-dimensional, time-dependent Euler equations on unstructured tetrahedral meshes is described. The implicit temporal discretization involves either a two-sweep Gauss-Seide relaxation procedure, a two-sweep Point-Jacobi relaxation procedure, or a single-sweep Point-Implicit procedure; the upwind spatial discretization is based on the flux-difference splitting of Roe. Detailed descriptions of the three implicit solution algorithms are given, and calculations for the Boeing 747 transport configuration are presented to demonstrate the algorithms. Advantages and disadvantages of the implicit algorithms are discussed. A steady-state solution for the 747 configuration, obtained at transonic flow conditions using a mesh of over 100,000 cells, required less than one hour of CPU time on a Cray-2 computer, thus demonstrating the speed and robustness of the general capability.

Description: Two-dimensional CFD analyses are presented related to the ground testing of hypersonic, air-breathing models which feature scramjet exhaust flow simulation. CFD analysis indicates that it is possible to test aftbody powered hypersonic airbreather configurations in a static, pumped-down environment to obtain aftbody aerodynamic performance data.

Description: The Program for Solving the General-Frequency Unsteady Two-Dimensional Transonic Small-Disturbance Equation, XTRAN2L, is used to calculate time-accurate, finite-difference solutions of the nonlinear, small-disturbance potential equation for two- dimensional transonic flow about airfoils. The code can treat forced harmonic, pulse, or aeroelastic transient type motions. XTRAN2L uses a transonic small-disturbance equation that incorporates a time accurate finite-difference scheme. Airfoil flow tangency boundary conditions are defined to include airfoil contour, chord deformation, nondimensional plunge displacement, pitch, and trailing edge control surface deflection. Forced harmonic motion can be based on: 1) coefficients of harmonics based on information from each quarter period of the last cycle of harmonic motion; or 2) Fourier analyses of the last cycle of motion. Pulse motion (an alternate to forced harmonic motion) in which the airfoil is given a small prescribed pulse in a given mode of motion, and the aerodynamic transients are calculated. An aeroelastic transient capability is available within XTRAN2L, wherein the structural equations of motion are coupled with the aerodynamic solution procedure for simultaneous time-integration. The wake is represented as a slit downstream of the airfoil trailing edge. XTRAN2L includes nonreflecting farfield boundary conditions. XTRAN2L was developed on a CDC CYBER mainframe running under NOS 2.4. It is written in FORTRAN 5 and uses overlays to minimize storage requirements. The program requires 120K of memory in overlayed form. XTRAN2L was developed in 1987.

Description: The NASCRIN program was developed for analyzing two-dimensional flow fields in supersonic combustion ramjet (scramjet) inlets. NASCRIN solves the two-dimensional Euler or Navier-Stokes equations in conservative form by an unsplit, explicit, two-step finite-difference method. A more recent explicit-implicit, two-step scheme has also been incorporated in the code for viscous flow analysis. An algebraic, two-layer eddy-viscosity model is used for the turbulent flow calculations. NASCRIN can analyze both inviscid and viscous flows with no struts, one strut, or multiple struts embedded in the flow field. NASCRIN can be used in a quasi-three-dimensional sense for some scramjet inlets under certain simplifying assumptions. Although developed for supersonic internal flow, NASCRIN may be adapted to a variety of other flow problems. In particular, it should be readily adaptable to subsonic inflow with supersonic outflow, supersonic inflow with subsonic outflow, or fully subsonic flow. The NASCRIN program is available for batch execution on the CDC CYBER 203. The vectorized FORTRAN version was developed in 1983. NASCRIN has a central memory requirement of approximately 300K words for a grid size of about 3,000 points.

Description: The problem of axisymmetric transonic flow is of interest not only because of the practical application to missile and launch vehicle aerodynamics, but also because of its relation to fully three-dimensional flow in terms of the area rule. The RAXBOD computer program was developed for the analysis of steady, inviscid, irrotational, transonic flow over axisymmetric bodies in free air. RAXBOD uses a finite-difference relaxation method to numerically solve the exact formulation of the disturbance velocity potential with exact surface boundary conditions. Agreement with available experimental results has been good in cases where viscous effects and wind-tunnel wall interference are not important. The governing second-order partial differential equation describing the flow potential is replaced by a system of finite difference equations, including Jameson's "rotated" difference scheme at supersonic points. A stretching is applied to both the normal and tangential coordinates such that the infinite physical space is mapped onto a finite computational space. The boundary condition at infinity can be applied directly and there is no need for an asymptotic far-field solution. The system of finite difference equations is solved by a column relaxation method. In order to obtain both rapid convergence and any desired resolution, the relaxation is performed iteratively on successively refined grids. Input to RAXBOD consists of a description of the body geometry, the free stream conditions, and the desired resolution control parameters. Output from RAXBOD includes computed geometric parameters in the normal and tangential directions, iteration history information, drag coefficients, flow field data in the computational plane, and coordinates of the sonic line. This program is written in FORTRAN IV for batch execution and has been implemented on a CDC 6600 computer with an overlayed central memory requirement of approximately 40K (octal) of 60 bit words. Optional plotted output can be generated for the Calcomp plotting system. The RAXBOD program was developed in 1976.

Description: Two separate and distinct theories are incorporated in this computer program to estimate the lift-induced pressures existent on a wing-body combination. These are (1) the second-order shock-expansion theory, which is used to obtain the lifting pressures on the body alone at small angles of attack, and (2) the linear-theory integral equations, which is used to evaluate the lifting pressures induced by the wing. These equations relate the local surface slope at a point on the lifting surface to the pressure differential at the point and the influence of the pressures upstream of the point. The numerical solution of these equations is effected by treating the wing-planform as a composite of elemental rectangles and applying summation techniques to satisfy the necessary integral relations. Most of the input required by this program is involved with the description of the missile planform geometry. The output consists of the computed value of the lifting pressure slope (the differential pressure coefficient per degree angle of attack) for each of the elements in the planform array. A force and moment summary is presented for the configuration under consideration.

Description: A modified strip analysis has been developed for rapidly predicting flutter of finite-span, swept or unswept wings at subsonic to hypersonic speeds. The method employs distributions of aerodynamic parameters which may be evaluated from any suitable linear or nonlinear steady-flow theory or from measured steady-flow load distributions for the underformed wing. The method has been shown to give good flutter results for a broad range of wings at Mach number from 0 to as high as 15.3. The principles of the modified strip analysis may be summarized as follows: Variable section lift-curve slope and aerodynamic center are substituted respectively, for the two-dimensional incompressible-flow values of 2 pi and quarter chord which were employed by Barmby, Cunningham, and Garrick. Spanwise distributions of these steady-flow section aerodynamic parameters, which are pertinent to the desired planform and Mach number, are used. Appropriate values of Mach number-dependent circulation functions are obtained from two-dimensional unsteady compressible-flow theory. Use of the modified strip analysis avoids the necessity of reevaluating a number of loading parameters for each value of reduced frequency, since only the modified circulation functions, and of course the reduced frequency itself, vary with frequency. It is therefore practical to include in the digital computing program a very brief logical subroutine, which automatically selects reduced-frequency values that converge on a flutter solution. The problem of guessing suitable reduced-frequency values is thus eliminated, so that a large number of flutter points can be completely determined in a single brief run on the computing machine. If necessary, it is also practical to perform the calculations manually. Flutter characteristics have been calculated by the modified strip analysis and compared with results of other calculations and with experiments for Mach numbers up to 15.3 and for wings with sweep angles from 0 degrees to 52.5 degrees, aspect ratios from 2.0 to 7.4, taper ratios from 0.2 to 1.0, and center-of-gravity positions between 34% chord and 59% chord. These ranges probably cover the great majority of wings that are of practical interest with the exception of very low-aspect-ratio surfaces such as delta wings and missile fins. This program has been implemented on the IBM 7094.

Description: Experimental studies have been conducted to assess Reynolds and Mach number effects on a supercritical multielement airfoil. The airfoil is representative of the stall-critical station of an advanced transport wing design. The experimental work was conducted as part of a cooperative program between the Douglas Aircraft Company and the NASA Langley Research Center to improve current knowledge of high-lift flows and to develop a validation data base with practical geometries/conditions for emerging computational methods. This article describes results obtained for both landing and takeoff multielement airfoils (four- and three-element configurations) for a variety of Mach/Reynolds number combinations up to flight conditions. Effects on maximum lift are considered for the landing configurations, and effects on both lift and drag are reported for the takeoff geometry. The present test results revealed considerable maximum lift effects on the three-element landing configuration for Reynolds number variations, and significant Mach number effects on the four-element airfoil.

Description: This paper presents an alternate approach for the generation of volumetric grids for supersonic and hypersonic flows about complex configurations. The method uses parametric two-dimensional block-face grid definitions, within the framework of GRIDGEN2D. The incorporation of a face decomposition reduces complex surfaces to simple shapes. These simple shapes are recombined to obtain the final face definition. The advantages of this method include the reduction of overall grid generation time through the use of vectorized computer code, the elimination of generating matching block faces, and simplified boundary conditions.

Description: An algorithm is described that calculates inviscid, laminar, and turbulent flows on triangular meshes with an upwind discretization. A brief description of the base solver and the multigrid implementation is given, followed by results that consist mainly of convergence rates for inviscid and viscous flows over a NACA four-digit airfoil section. The results show that multigrid does accelerate convergence when the same relaxation parameters that yield good single-grid performance are used; however, larger gains in performance can be realized by doing less work in the relaxation scheme.

Description: The SUBAERF2 program was developed to provide for the aerodynamic analysis and design of low speed wing flap systems. SUBAERF2 is based on a linearized theory lifting surface solution. It is particularly well suited to configurations which, because of high speed flight requirements, must employ thin wings with highly swept leading edges. The program is applicable to wings with either sharp or rounded leading edges. This program is a new and improved version of LAR-13116 and LAR-12987, which it replaces. The low speed aerodynamic analysis method used in SUBAERF2 provides estimates of wing performance which include the effects of attainable leading-edge thrust and vortex lift. This basic aerodynamic analysis method has been improved to provide for the convenient, efficient and accurate treatment of simple leading-edge and trailing-edge flap systems. The user inputs flap geometry directly. Solutions can be found for various combinations of leading and trailing edge flap deflections. The program provides for the simultaneous analysis of up to 25 pairs of leading-edge and trailing-edge flap deflection schedules. A revised attainable thrust algorithm improves accuracy at the low Mach numbers sometimes encountered in wind tunnel testing. Also added is a means of estimating the distribution of leading edge separation vortex forces. The revised program has been particularly useful in the subsonic analysis of vehicles designed for supersonic cruise. The SUBAERF2 program is written in FORTRAN V for batch execution and has been implemented on a CDC 175 computer operating under NOS 2.4 with a central memory requirement of approximately 115K (octal) of 60 bit words. This program was originally developed in 1983 and later revised in 1988.

Description: WAVDRAG calculates the supersonic zero-lift wave drag of complex aircraft configurations. The numerical model of an aircraft is used throughout the design process from concept to manufacturing. WAVDRAG incorporates extended geometric input capabilities to permit use of a more accurate mathematical model. With WAVDRAG, the engineer can define aircraft components as fusiform or nonfusiform in terms of non-intersecting contours in any direction or more traditional parallel contours. In addition, laterally asymmetric configurations can be simulated. The calculations in WAVDRAG are based on Whitcomb's area-rule computation of equivalent-bodies, with modifications for supersonic speed. Instead of using a single equivalent-body, WAVDRAG calculates a series of equivalent-bodies, one for each roll angle. The total aircraft configuration wave drag is the integrated average of the equivalent-body wave drags through the full roll range of 360 degrees. WAVDRAG currently accepts up to 30 user-defined components containing a maximum of 50 contours as geometric input. Each contour contains a maximum of 50 points. The Mach number, angle-of-attack, and coordinates of angle-of-attack rotation are also input. The program warns of any fusiform-body line segments having a slope larger than the Mach angle. WAVDRAG calculates total drag and the wave-drag coefficient of the specified aircraft configuration. WAVDRAG is written in FORTRAN 77 for batch execution and has been implemented on a CDC CYBER 170 series computer with a central memory requirement of approximately 63K (octal) of 60 bit words. This program was developed in 1983.

Description: An approximate inverse solution is presented for the nonequilibrium flow in the inviscid shock layer about a vehicle in hypersonic flight. The method is based upon a thin-shock-layer approximation and has the advantage of being applicable to both subsonic and supersonic regions of the shock layer. The relative simplicity of the method makes it ideally suited for programming on a digital computer with a significant reduction in storage capacity and computing time required by other more exact methods. Comparison of nonequilibrium solutions for an air mixture obtained by the present method is made with solutions obtained by two other methods. Additional cases are presented for entry of spherical nose cones into representative Venusian and Matrian atmospheres. A digital computer program written in FORTRAN language is presented that permits an arbitrary gas mixture to be employed in the solution. The effects of vibration, dissociation, recombination, electronic excitation, and ionization are included in the program.

Description: Small areas of high heat transfer and pressure can occur on a vehicle surface due to the influence of an impinging shock on the local flow. A method was needed to determine peak pressure and heating of these areas. This package is a system of computer programs designed to calculate two-dimensional shock interference patterns for six types of interference flows. Results also include properties of the inviscid flow field and the inviscid-viscous interaction at the surface along with peak pressure and peak heating at the impingement point. The six types of interference flow patterns considered are: 1) Type I interference patterns, occurring when two weak shocks of opposite families, BS (bow shock) and IS (impingment shock), intersect when the flow upstream of the impingement point is supersonic, or in the case of a blunt body, takes place well below the sonic point. 2) Type II interference pattern occurs when two shocks of opposite families (bow shock and impinging shock) intersect. Both shocks are weak as in type I, but are of such strength that in order to turn the flow, a Mach reflection must exist in the center of the flow field with an embedded subsonic region occurring between the intersection points (A & B) and the accompanying shear layers. Type II interference occurs on a blunt body when the impinging shock intersects the bow shock near the sonic point. 3) Type III shock interference pattern occurs when a weak impinging shock intersects a strong detached bow shock. On a blunt body the shock intersection occurs near or above the lower sonic point. 4) Type IV interference can occur when the impinging shock intersects a strong bow shock ahead of a subsonic flow region. On a blunt body this shock intersection is located between the lower sonic point and just above the body axis. The impinging shock causes a displacement of the bow shock and the formation of a supersonic jet that is embedded in the subsonic region. A jet bow shock is produced when the jet impinges on the surface, creating a small region with high stagnation heating. 5) Type V interference involves the interaction of two weak shocks of the same family. The interaction produces a shear layer, a supersonic jet, and a transmitted impinging shock. On a blunt body the shock interaction occurs near the upper sonic point. 6) Type VI interference involves the intersection of two weak shocks of the same family, which leads to an entirely supersonic flow field. This type of interference is important because it provides a means for predicting the onset of type V. Peak-heating correlations for laminar and turbulent shock-boundary-layer interactions are included in the programs for types I, II, V, and VI interference patterns. Heating correlations for laminar and turbulent reattaching shear layers obtained from separation studies are included in the program for type III interference. This program is written in FORTRAN IV for batch execution and has been implemented on a CDC 6000 Series computer. This program was developed in 1973.

Description: A computer program has been written to obtain the wave and friction drag of configurations with bodies of revolution and fins. These inviscid flow fields are superimposed and the wave drag of the configuration is obtained by integration of the surface pressures. The friction drag is obtained from the viscous flow field of the body and a flat-plate friction analysis of the fins. The numerical solution of these flow fields, superposition, and integration to obtain total drag have been programmed for high-speed digital computation. A large portion of the input required by the program is involved with the description of the configuration geometry and the specific surface positions where pressures are to be evaluated. In addition to drag forces, an output is available whereby the pressure distributions on the body and fins can be obtained.

Description: The interaction of a turbulent boundary layer with rarefaction and shock waves in flows past inclined steps was investigated experimentally and theoretically. The experiments were carried out in supersonic wind tunnels with test sections of 0.6 x 0.6 m and 0.2 x 0.2 m, with adiabatic conditions on the surface model. Based on detailed measurements of pressure fields, velocity, and surface friction, combined with results of optical visualization and analysis of limiting flow lines, three characteristic flow regimes are identified. These are (1) nonseparated flow at small step angles, (2) formation of a local separation zone with a free separation point at moderate step angles, and (3) formation of a large-scale separated flow with a fixed separation point at sufficiently large step angles. The quantitative gasdynamic schemes and surface pressure distributions for these flow regimes are shown for Mach 2.85.

Description: An account is given of experimental and computational results on the mixing of single, double, and opposed rows of jets characterized by an either isothermal or variable temperature mainstream in a confined subsonic crossflow; these flow configurations are typical of gas turbine combustor dilution chambers. It is established that the momentum-flux ratio is the most significant flow variable. Combinations of flow and geometry yielding optimum mixing were identified from experimental and computational results. The orifice spacing and momentum-flux relationships affected jet structure, which was significantly different between jets injected from the inner wall of a turn and those injected from the outer wall.

Description: The essential elements of a computational fluid dynamics analysis of the HL-20/personnel launch system aerothermal environment at hypersonic speeds including surface definition, grid generation, solution techniques, and visual representation of results are presented. Examples of solution technique validation through comparison with data from ground-based facilities are presented, along with results from computations at flight conditions. Computations at flight points indicate that real-gas effects have little or no effect on vehicle aerodynamics and, at these conditions, results from approximate techniques for determining surface heating are comparable with those obtained from Navier-Stokes solutions.

Description: Definition of the aerothermal environment is critical to any vehicle such as the HL-20 Personnel Launch System that operates within the hypersonic flight regime. Selection of an appropriate thermal protection system design is highly dependent on the accuracy of the heating-environment prediction. It is demonstrated that the entry environment determines the thermal protection system design for this vehicle. The methods used to predict the thermal environment for the HL-20 Personnel Launch System vehicle are described. Comparisons of the engineering solutions with computational fluid dynamic predictions, as well as wind-tunnel test results, show good agreement. The aeroheating predictions over several critical regions of the vehicle, including the stagnation areas of the nose and leading edges, windward centerline and wing surfaces, and leeward surfaces, are discussed. Results of predictions based on the engineering methods found within the MINIVER aerodynamic heating code are used in conjunction with the results of the extensive wind-tunnel tests on this configuration to define a flight thermal environment. Finally, the selection of the thermal protection system based on these predictions and current technology is described.

Description: Experiments were conducted to observe the cross-sectional structure and streamwise growth of round transverse liquid jets injected into a highly accelerated boundary layer in supersonic flow. The accompanying shock structure was also visualized. In one case, a round jet of acetone was injected into a fully turbulent Mach 2.5 boundary layer that was subsequently accelerated and partially laminarized through a sharp Prandtl-Meyer expansion corner. In the second case, a jet was injected into the laminarized Mach 3.2 boundary layer downstream of the expansion corner at the same jet-to-freestream momentum ratio. The jet and shock structure in both cases were visualized using schlieren optics. Wall-flow patterns were visualized using paints. It was found that the lateral spreading of jets injected downstream of the expansion fan was augmented close to the wall and had a cross-sectional structure significantly different from that of the jet injected upstream: the upstream jet spreads rapidly at the expansion corner in both the lateral and vertical directions.

Description: Computational results are presented to illustrate the powered aftbody effects of representing the scramjet inlet on a generic hypersonic vehicle with a fairing, to divert the external flow, as compared to an operating flow-through scramjet inlet. This study is pertinent to the ground testing of hypersonic, airbreathing models employing scramjet exhaust flow simulation in typical small-scale hypersonic wind tunnels. The comparison of aftbody effects due to inlet representation is well-suited for computational study, since small model size typically precludes the ability to ingest flow into the inlet and perform exhaust simulation at the same time. Two-dimensional analysis indicates that, although flowfield differences exist for the two types of inlet representations, little, if any, difference in surface aftbody characteristics is caused by fairing over the inlet.

Description: A detailed description of the bow-shock behavior associated with a conical-walled cavity with a flat circular base at M(infinity) = 10 is presented. An experimental test was performed on this configuration, and measurements of shock-oscillation frequency and amplitude, as well as shock shape, were recorded by a number of techniques. A laser-interferometer system was used for the first time during this test to determine bow-shock oscillation frequency in a nonintrusive manner. The primary behavior was a stable, periodically oscillating bow shock. Attention is also given to a violent bow-shock instability.

Description: Hypersonic reactive flowfield results are presented for the flow about an axisymmetric representation of a three-dimensional aeroassisted vehicle using the viscous shock-layer (VSL) and Navier-Stokes (NS) equations for low- and high-altitude entry conditions, respectively. Solutions are limited to the stagnation region. The NS results have been obtained by employing the surface recombination boundary condition for an 11-species air model, whereas the VSL calculations are carried out by using a 5-species model. Three widely used surface recombination rate models are implemented with these two flowfield calculation procedures. The low-density (or high altitude) NS solutions are obtained with surface slip equations and compare quite well with the direct simulation Monte Carlo predictions. For higher densities (or lower altitudes), the no-slip VSL solutions are considered adequate. Results from this study highlight the effect of surface catalyticity on surface heating and electron number density.

Description: Qualitative features of the inviscid instability characteristics of hypersonic boundary-layer flows over a flat plate are considered. The instability of a viscous hypersonic boundary layer which exists far downstream from the leading edge of the plate. It is shown that the vorticity mode of instability operates on a different lengthscale from that obtained using a Chapman viscosity law. The growth rate predicted by a linear viscosity law is found to overestimate the size of the growth rate. The inviscid instability of the boundary layer near the leading edge interaction zone is discussed focusing on the strong-interaction zone which occurs sufficiently close to the leading edge. The vorticity mode in this regime is found to be unstable.

Description: The edge technique is a new and powerful method for measuring small frequency shifts such as the Doppler shift of an atmospheric backscattered signal from a pulsed laser. The edge technique can be used for high spatial resolution, high accuracy ground and airborne wind measurements as well as high accuracy spaceborne wind measurements. We have recently made our first ground based wind measurements. These have a spatial resolution of 15 m and an accuracy of 25 cm/s and these measurements are presented in this paper. This is a unique capability and provides valuable information for studies of turbulent processes in the lower atmosphere. It could also be used for high sensitivity detection of wind shear and microbursts in the vicinity of airports. In addition, global wind measurements can be made with the edge technique from space with an accuracy of 1 m/s and a vertical resolution as high as 150 m in the boundary layer and 1 km through the troposphere. Such a system could make eyesafe wind measurements using well developed diode pumped solid state laser technology at 1.06 micron. Multi-pulse averaging would provide a spatially representative wind measurement.

Description: This paper is on the control of nonlinear-nonstationary vibration of a frame-stringer structure resulting from high levels of excitaation from a nearby supersonic jet exhaust. The structure exhibits periodic, chaotic, or random behaviors when forced by high-intensity sound from a supersonic jet exhaust with shock loading superimposed on the broadband response. The time history of the pressure, showing the rotation and flapping of the shock structure in the jet column due to large-scale instabilities, indicates that the response is not only nonlinear but also nonstationary. The acoustic pressure radiated by the structure also contains shocks and the formation of harmonics with distance. Control of the structural response is achieved by actively forcing the structure with an actuator at the shock oscillation frequency whose amplitude is locked into a self-control cycle. Results show that the peak power level is reduced by a factor of 63, or 18 dB. As a result, new broadband components emerge with at least four harmonics. At accelerating and decelerating supersonic speeds, the exhaust from the jet induces higher transient loading on the nearby flexible structure due to the occurence of multiple shocks from the jet.

Description: Prandtl's theory is used to determine the airflow over bodies and wings adapted to supersonic flight. By making use of these results, and by incorporating in them an allowance for the probable skin friction, some estimates of expected lift-drag ratios are made for various flight speeds with the best configuration. At each speed a slender body and wings having the best angle of sweepback are considered. For the range of supersonic speeds shown an airplane of normal density and loading would be required to operate at an altitude of the order of 60,000 feet. The limiting value of 1-1/2 times the speed of sound corresponds to a flight speed of 1000 miles per hour. At this speed about 1.5 miles per gallon of fuel are expected. It is interesting to note that this value corresponds to a value of more than 15 miles per gallon when the weight is reduced to correspond to that of an ordinary automobile.

Description: In theory, the most efficient wing shape for transonic and low supersonic speeds is simply a long narrow straight subsonic wing turned at an oblique angle to the flight direction. This theory has been verified by tests at Mach numbers from .6 to 1.4 in supersonic wind tunnel and by comparative studies of transonic transport designs.

Description: Recent theoretical and experimental work in supersonic aerodynamics is reviewed with its practical application in mind. Several arrangements of supporting surfaces and bodies are discussed and in some cases comparisons of theory and experiment are made. Finally, certain phenomena connected with lift and drag in a rarefied medium are considered briefly.

Description: A method is reported for determining mathematically the combined disturbance field, and in certain cases the minimum drag, of wings at supersonic speeds. The simplest analytic example is provided by the wing of elliptic planform, which achieves its minimum drag when the lift is distributed uniformly over the surface. With a symmetrical distribution of thickness, the requirement of minimum drag for a given total volume is found to lead to profiles of constant curvature.

Description: The assumptions of the thin airfoil theory are found to provide certain necessary conditions for the minimum drag of airfoils having a given total lift, a given maximum thickness, or a given volume. The conditions are applicable to steady or unsteady motions and to subsonic or supersonic speeds without restriction on the planform. The computation of drag and the statement of the conditions for minimum drag depend on the consideration of a combined flow field, which is obtained by superimposing the disturbance velocities in forward and reversed motions. If the planform of the airfoil and its total lift are given, it is found that, for minimum drag, the lift must be distributed in such a way that the downwash in the combined field is constant over the entire planform. If the planform is given and the thickness of the airfoil is required to contain a specified volume, then the thickness must be distributed over the planform in such a way that the pressure gradient of the combined field in the direction of flight is constant at all points of the wing.

Description: The application of mathematical advances made in electricity and other branches to problems of airplane dynamics is demonstrated. The Heaviside-Bromwich methods of solution of linear differential equations are described and it is shown how these methods avoid the consideration of boundary conditions and of particular or complementary integrals. It is pointed out that if the solution of the differential equation is obtained for the case of a unit disturbance, the effect of varying disturbances may be found therefrom by Carson's theorem. A graphical solution of Carson's integral for irregular disturbances is given. The procedure of obtaining unit solutions of the equations is then taken up and the analogy between Heaviside's symbolic series solution and a physical procedure of approximation is shown. It is suggested that a fictitious impulsive disturbance be used in the treatment of initial motions.

Description: Accounts are presented of tangential, semisubmerged, and internal store carriage drag, as well as of the results to date of stores-separation investigations employing both computational and experimental methods. It is demonstrated that CFD can contribute to the data base needed for internal stores carriage design and trade studies. Attention is given to the case of an internally carried store separating from its bay at supersonic speeds, where various kinds of interference are encountered. A code is developed for the simulation of these unsteady flows through time-accurate computations; computation results are noted to closely reproduce experiment data.

Description: A development status evaluation is presented for the aerodynamics of missile configurations with noncircular cross-sections and bank-to-turn maneuvering systems, giving attention to cases with elliptical and square cross-sections, as well as bodies with variable cross-sections. The assessment of bank-to-turn missile performance notes inherent stability/control problems. A summary and index are provided for aerodynamic data on monoplanar configurations, including those which incorporate airbreathing propulsion systems.

Description: A survey is conducted of the results of investigations into the flowfields and aerodynamic forces associated with low aspect ratio wings at high angles of attack. Attention is given to criteria for the cataloging of these flowfields, the phenomenon of vortex breakdown, with varying wing incidence and Mach number, and the effects of aspect ratio and compressibility. The planforms treated are of rectangular, clipped-delta, and strake-wing combination geometries. Extensive graphic representations of performance trends with varying parameters are furnished.

Description: A central artificial-viscosity and an upwind-biased difference method are contrived to solve the Euler equations for flowfields over typical spacecrafts. The spatial discretization is based on either nodal or cell-vertex formulation in the domain extending from free stream to the end of the vehicle. The outer boundary is treated as a bow shock in the first method but is placed in the free stream in the second, which captures both bow and internal shocks using an approximate Riemann solver based on high-order extrapolation to the cell face. These methods were tested for the Shuttle and Hermes orbiters at wind-tunnel conditions and angles of attack ranging from 0 to 60 deg. The artificial-viscosity method incorporated with a shock-fitting procedure shows smeared crossflow and wing-shock positions and required 15 percent more CPU per node than the upwind method. Greater flexibility and robustness is demonstrated by the latter on a fixed grid for all cases considered.

Description: Three-dimensional Navier-Stokes simulations have been done for transonic and low supersonic flow past a nonaxisymmetric nozzle typical of those advocated for advanced fighter airplanes. The jet exhaust is included in the calculations. The investigation compares the performance of the unmodified Baldwin-Lomax turbulence model with its performance when enhanced by the Degani-Schiff and the Goldberg modifications. Solutions are presented for Mach numbers of 0.80, 0.94, and 1.20 at 0-deg angle of attack and a Reynolds number of 20 x 10 to the 6th. The numerical results, which are compared to the wind-tunnel data, show that the three turbulence models predict considerably different shock locations, separated-flow regions, and flowfields.

Description: A new kind of C-type grid is proposed, this grid is non-periodic on the wake and allows minimum skewness for cascades with high turning and large camber. Reynolds-averaged Navier-Stokes equations are solved on this type of grid using a finite volume discretization and a full multigrid method which uses Runge-Kutta stepping as the driving scheme. The Baldwin-Lomax eddy-viscosity model is used for turbulence closure. A detailed numerical study is proposed for a highly loaded transonic blade. A grid independence analysis is presented in terms of pressure distribution, exit flow angles, and loss coefficient. Comparison with experiments clearly demonstrates the capability of the proposed procedure.

Description: The flow through a highly offset subsonic diffuser with cross-sectional profiles that varied from rectangular at the duct entrance to circular at the engine face was numerically simulated. A multizonal approach combined with a two-grid topology was used to represent both the internal and external flowfields, and an implicit, approximately-factored, partially flux-split finite-difference algorithm was used to solve the three-dimensional thin-layer Navier-Stokes equations. The computed static pressures along the inlet wall and total pressures on the engine face were compared with experimental data. In addition, the overall flowfield within the duct was examined in detail. Good agreement is shown between experiment and computations, with the limiting factor being the lack of a reliable turbulence model for internal flow problems.

Description: This paper discusses NASA's Computational Aerosciences (CAS) Project of the High Performance Computing and Communications Program (HPCCP). The project is aimed at developing advanced, multidisciplinary simulation capabilities for aerospace vehicle and propulsion system design. It is also aimed at overcoming computational performance barriers by accelerating the development of parallel computer technology. The goals and approach of the CAS Project are described and the challenges to its implementation are addressed. Specific vehicle class simulations to be demonstrated and the principal mutidisciplinary modeling approaches to be emphasized are described. The computational speed and memory requirements for representative multidisciplinary applications are estimated. Finally, the state of parallel computer technology including programming issues and the results of performance measurements are explored.

Description: Previous work on the use of a vortex trapped above a wing in order to produce high lift at low angles of attack is extended here. It is first postulated that the optimum way to trap a vortex is to design the airfoil section and wing so that the flow along the vortex core is minimized. It is then shown that a vertical fence both in front of and behind the separation bubble generated by the trapped vortex is an effective way to reduce the mass flow removal and its associated drag to a negligible amount. In order to show that vertical surfaces upstream and downstream of the vortex separation bubble have an opposite effect on the source requirements for vortex trapping, conformal mapping methods are used to obtain the solutions for a variety of simple two-dimensional, inviscid, incompressible flow configurations. Trapped-vortex flowfield solutions for the flow over flat plate and Clark-Y airfoils are then used to demonstrate that the heights of the fences can be tailored to make the required mass withdrawal (and therefore, the drag due to trapping) to be vanishingly small.