ALBERT

Description: The application of computer techniques for solving Navier-Stokes equations in support of wind tunnel tests is discussed. The ILLIAC IV computer is considered for this purpose and its limitations are analyzed. The author states that improved computers will make it possible to solve many aerodynamic problems and reduce the amount of wind tunnel testing required for adequate data processing.

Description: Research within NASA relating to the nature of lift-induced vortex wakes behind large aircraft and the means whereby the hazard they represent to smaller aircraft can be alleviated is reviewed. The research, carried out in ground based facilities and in flight shows that more rapid dispersion of the wake can be effected by several means and that the modification of span-loading by appropriate flap deflection holds promise of early practical application.

Description: A thoroughly documented experiment is reported that was specifically designed to test and guide computations of the interaction of an impinging shock wave with a turbulent boundary layer. Detailed mean flow field and surface data are presented for two shock strengths which resulted in attached and separated flows, respectively. Numerical computations are used to illustrate the dependence of the computations on the particulars of the turbulence models. Models appropriate for zero pressure gradient flows predicted the overall features of the flow fields, but were deficient in predicting many of the details of the interaction regions. Improvements to the turbulence model parameters were sought through a combination of detailed data analysis and computer simulations which tested the sensitivity of the solutions to model parameter changes. Computer simulations using these improvements are presented and discussed.

Description: A method is developed for solving the laminar and turbulent compressible boundary layer equations for separating and reattaching flows. Results of this method are compared with experimental data for two laminar and three turbulent layer, shock wave interactions. Several Navier-Stokes solutions are obtained for each of the laminar boundary layer, shock wave interactions considered. Comparison of these solutions indicates a first order sensitivity in C sub f to the computational mesh selected in both the viscous and inviscid portions of the flow. Comparison of the present boundary layer solutions with the Navier-Stokes solutions and with data for a given Mach number indicates that as long as the separation bubble is small, the boundary layer approximation yields solutions whose accuracy is comparable to the Navier-Stokes solutions.

Description: Nonequilibrium phenomena in hypersonic flows are examined on the basis of theoretical models and selected experimental data, in an introduction intended for second-year graduate students of aerospace engineering. Chapters are devoted to the physical nature of gas atoms and molecules, transitions of internal states, the formulation of the master equation of aerothermodynamics, the conservation equations, chemical reactions in CFD, the behavior of air flows in nonequilibrium, experimental aspects of nonequilibrium flow, a review of experimental results, and gas-solid interaction. Diagrams, graphs, and tables of numerical data are provided.

Description: The introduction of transverse velocity fluctuations into a separated shear layer on an airfoil at high angles of attack is presently demonstrated to be an effective separation-control technique. Airfoil aerodynamic characteristics, including poststall lift and drag as well as maximum lift coefficient and stall angle, all exhibited improvements controlled forcing at 20 deg angle of attack led to an increased spreading of the mean velocity profile, together with increased turbulence activity; separation moved from the leading edge to about 80 percent of chord.

Description: The formulation of mathematical models of aeronautical systems for simulation or other purposes, involves the transformation of aerodynamic stability derivatives. It is shown that these derivatives transform like the components of a second order tensor having one index of covariance and one index of contravariance. Moreover, due to the equivalence of covariant and contravariant transformations in orthogonal Cartesian systems of coordinates, the transformations can be treated as doubly covariant or doubly contravariant, if this simplifies the formulation. It is shown that the tensor properties of these derivatives can be used to facilitate their transformation by symbolic mathematical computation, and the use of digital computers equipped with formula manipulation compilers. When the tensor transformations are mechanised in the manner described, man-hours are saved and the errors to which human operators are prone can be avoided.

Description: A closed-form solution for the sound radiation from multipole sources imbedded in an infinite cylindrical jet with an arbitrary velocity profile is obtained. It is valid in the limit where the wavelength is large compared with the jet radius. Simple formulae for the acoustic pressure field due to convected point sources are also obtained. The results show (in a simple way) how the mean flow affects the radiation pattern from the sources. For convected lateral quadrupoles it causes the exponent of the Doppler factor multiplying the far-field pressure signal to be increased from the value of 3 used by Lighthill to 5.

Description: The present investigation is an analysis of the radiation from the chemical nonequilibrium region in the shock layer about a vehicle during Venus entry. The radiation and the flow were assumed to be uncoupled. An inviscid, nonequilibrium flowfield was calculated and an effective electronic temperature was determined for the predominant radiating species. Species concentrations and electronic temperature were then input into a radiation transport code to calculate heating rates. The present results confirm earlier investigations which indicate that the radiation should be calculated using electronic temperatures for the radiating species. These temperatures are not related in a simple way to the local translational temperature. For the described mission, the nonequilibrium radiative heating rate is approximately twice the corresponding equilibrium value at peak heating.

Description: Flow characteristics in the vicinity of the flap of a single-slotted airfoil are presented and analyzed. The flow remained attached over the model surfaces, except in the vicinity of the flap trailing edge where a small region of boundary-layer separation extended over the aft 7 percent of flap chord. The airfoil configuration was tested at a Mach number of 0.09 and a chord Reynolds number of 1.8 x 10 to the 6th in the NASA Ames Research Center 7- by 10-Foot Wind Tunnel. The flow was complicated by the presence of a strong, initially inviscid, jet, emanating from the slot between airfoil and flap, and a gradual merging of the main airfoil wake and flap suction-side boundary layer.

Description: The transonic aspect of helicopter flow analysis is addressed. The equations of motion and their implementations are examined, and the computation of real rotor flows is considered. Nonlifting rotor flows, high-speed hover, high advance ratio lifting rotor flows, and strong blade/vortex interaction computations are discussed.

Description: Some of the basic finite-difference schemes that can be used to solve the nonlinear equations that describe unsteady inviscid and viscous transonic flow are reviewed. Numerical schemes for solving the unsteady Euler and Navier-Stokes, boundary-layer, and nonlinear potential equations are described. Emphasis is given to the elementary ideas used in constructing various numerical procedures, not specific details of any one procedure.

Description: A review is presented of progress in attaining technical objectives in three areas of semiautomatic airfoil development: software, hardware, and applications. Software objectives seek improved mathematical models and computer codes for flow analysis and design optimization for a variety of conditions. The 17-step iterative computer model used in designing the GA (W)-1 airfoil is effective but not yet fully automated; with present methods only single-point computer optimization is possible. Hardware objectives calling for improvement in test facilities and techniques are met in part by the introduction of the Langley (F-3C) wind tunnel for independent evaluation of transonic Mach number and Reynolds effects up to 12-16 million, and by a two-dimensional test section for the Langley 1/3 transonic cryogenic tunnel which will extend the Reynolds number to 50 million. The current status of low-speed, thin, and rotorcraft airfoil development programs is discussed.

Description: Two hypothetical vortex wakes are introduced and studied theoretically to explore whether the rollup of lift-generated vortex sheets can be suppressed. The circulation distribution across each wake is specified such that one rotates and the other translates as a unit due to their self-induced velocities. Several span loadings are constructed from these solutions and the resulting inviscid wake structure is computed for several span lengths behind the generating wing by use of the discrete vortex method wherein the vortex wake is represented by an array of vortices. The final distribution of vortices is then used to estimate the rolling moment on an encountering wing. It is found that, even though the initial specified motions are not sustained, substantial reductions in rolling moment are predicted for certain ranges of the ratio of the span of the generating wing to the following wing.

Description: Analytical solutions for inviscid supersonic corner flows are virtually nonexistent due to the complexity of the interference geometry. In view of this, numerical solutions for swept-compressive and swept-expansive corner flows are obtained. The governing equations are written in strong conservation-law form and are solved iteratively in nonorthogonal conical coordinates by use of a second-order, shock-capturing, finite-difference technique. The computed wave structure and surface pressure distributions are compared with high Reynolds number experimental data and show very good agreement. The results clearly show that supersonic corner flow at reasonably high Reynolds numbers including the effect of sweep is dominated by the inviscid field.

Description: An investigation was conducted regarding the issue of deviation from two-dimensionality in flowfield studies of a supercritical airfoil. It was found that significant three-dimensional effects occur in transonic airfoil tests, even for an aspect ratio of four. This is especially true at the supercritical Mach numbers, for which lateral propagation of disturbances is effective.

Description: The aerodynamic characteristics of the Planetary Atmosphere Experiments Test entry probe were determined experimentally in ballistic range tests over a wide range of Mach and Reynolds numbers, and were compared with full-scale flight results. The ground facility data agreed with the full-scale data within 2 to 3% in drag coefficient, and within 5 to 10% in static stability, at the higher Mach numbers. Comparisons of the flight data with conventional wind-tunnel data indicated a significant disagreement in drag coefficient in the transonic speed range suggestive of important sting or wall interference effects. Variations in drag coefficient with Mach number were very small hypersonically, but variations with Reynolds number were of the order of 15% at a free-stream Mach number of 13 over the Reynolds number range from 10,000 to 1,000,000. Variations in the lift and static-stability curves with Mach number and Reynolds number were also defined.

Description: The paper is concerned with the application of the Murman and Cole (1971) relaxation scheme to steady, inviscid transonic flow problems in two and three dimensions. This scheme, which automatically accounts for weak shock waves, uses separate difference operators in elliptic and hyperbolic regions. The details of the scheme are described in terms of the original small disturbance formulation of Murman and Cole. In particular, Murman's recent (1973) introduction of fully conservative difference operators to obtain the correct shock jumps is examined. The extension to treating the exact isentropic equation is then covered with special attention given to Jameson's (to appear) rotated difference scheme for supersonic flow regions. The bulk of the discussion is related to two-dimensional procedures, and some comparisons with experiment are made, with emphasis on the effects of viscosity and wind-tunnel walls. Application of the Murman-Cole scheme is then discussed for small disturbances in three dimensions.

Description: The paper investigates analytically the effect of multiple slot injection on skin friction for a representative fuselage shape (ogive-cylinder body) and evaluates the potential of slot injection as a drag reduction system in subsonic flow. Typical CTOL cruise flight conditions (Mach number equals 0.82 at altitudes of 11 km) were adopted for a fuselage 67.06 m in length and with maximum diameter of 7.32 m. The numerical method of Price and Harris (1972) was used to calculate the boundary-layer characteristics up to the first slot, while the finite-difference method of Beckwith and Bushnell (1971) was used to calculate the velocity profile downstream of one, three, five, or ten slots. An integral expression is proposed for characterizing skin friction reduction effectiveness, and it is seen that large reductions in viscous drag (50%) are available through slot injection. Skin friction reduction is improved by increasing the number of injection slots but at a diminishing rate.

Description: The investigation reported is concerned with questions regarding a possible Mach number influence on skin friction reduction caused by injection. The investigation shows that data considered by Danberg (1967) for the no-blowing skin friction coefficient are in error. Accurate profiles and local skin friction coefficient values are obtained when the influence of low Reynolds number amplification in the outer region of the boundary layer is included in a calculation method.

Description: The paper investigates a two-dimensional oscillating cascade with a subsonic leading edge locus in a supersonic flow. The blades are assumed to be of small thickness and camber, and are undergoing small amplitude-harmonic oscillations. The problem is reduced to the solution of a functional integral equation, and an expression is given for the kernel function.

Description: Results are presented of an experimental investigation on a nonconical wing which supports an attached shock wave over a region of the leading edge near the vertex and a detached shock elsewhere. The shock detachment point is determined from planform schlieren photographs of the flow field and discrepancies are shown to exist between this and the one calculated by applying the oblique shock equations normal to the leading edge. On a physical basis, it is argued that the shock detachment has to obey the two-dimensional law normal to the leading edges. From this, and from other measurements on conical wings, it is thought that the planform schlieren technique may not be particularly satisfactory for detecting shock detachment. Surface pressure distributions are presented and are explained in terms of the flow over related delta wings which are identified as a vertex delta wing and a local delta wing.

Description: The conical flow solution for axisymmetric supersonic flow past cones has been found to be virtually independent of the ratio of specific heats when normalized in a certain way. A simple rational approximation to this flow is derived. The important singularities and the limiting behavior of the solution are also discussed.

Description: A method for designing supersonic inlet contours is described which consists in the interpolation of the contours of two known inlets designed for different Mach numbers, thereby determining the contours for a third inlet at an intermediate design Mach number. Several similar axisymmetric inlet contours were interpolated from known inlets with design Mach numbers ranging from 2.16 to 4.0 and with design Mach numbers differing by as much as 1.0. The flowfields were calculated according to Sorensen's (1965) computer program. Shockwave structure and pressure distribution characteristics are shown for the interpolated inlets. The validity of the interpolation is demonstrated by comparing the plots of the flowfield properties across the throat station of the interpolated inlet with the known inlets which were designed iteratively. It seems possible to write a computer program so that a matrix of known inlet contours can be interpolated.

Description: The flight testing conducted over the past 10 years in the NASA laminar-flow control (LFC) will be reviewed. The LFC program was directed towards the most challenging technology application, the high supersonic speed transport. To place these recent experiences in perspective, earlier important flight tests will first be reviewed to recall the lessons learned at that time.

Description: Although most of the laminar flow airfoils recently developed at the NASA Langley Research Center were intended for general aviation applications, low-drag airfoils were designed for transonic speeds and wind tunnel performance tested. The objective was to extend the technology of laminar flow to higher Mach and Reynolds numbers and to swept leading edge wings representative of transport aircraft to achieve lower drag and significantly improved operation costs. This research involves stabilizing the laminar boundary layer through geometric shaping (Natural Laminar Flow, NLF) and active control involving the removal of a portion of the laminar boundary layer (Laminar-Flow Control, LFC), either through discrete slots or perforated surface. Results show that extensive regions of laminar flow with large reductions in skin friction drag can be maintained through the application of passive NLF boundary-layer control technologies to unswept transonic wings. At even greater extent of laminar flow and reduction in the total drag level can be obtained on a swept supercritical airfoil with active boundary layer-control.

Description: Aerodynamic forces and moments for a slender wing-body configuration are summarized from an investigation in the Langley National Transonic Facility (NTF). The results include both longitudinal and lateral-directional aerodynamic properties as well as slideslip derivatives. Results were selected to emphasize Reynolds number effects at a transonic speed although some lower speed results are also presented for context. The data indicate nominal Reynolds number effects on the longitudinal aerodynamic coefficients and more pronounced effects for the lateral-directional aerodynamic coefficients. The Reynolds number sensitivities for the lateral-directional coefficients were limited to high angles of attack.

Description: The objective is to provide useful engineering formulations and to instill a modest degree of physical understanding of the phenomena governing convective aerodynamic heating at high flight speeds. Some physical insight is not only essential to the application of the information presented here, but also to the effective use of computer codes which may be available to the reader. Given first is a discussion of cold-wall, laminar boundary layer heating. A brief presentation of the complex boundary layer transition phenomenon follows. Next, cold-wall turbulent boundary layer heating is discussed. This topic is followed by a brief coverage of separated flow-region and shock-interaction heating. A review of heat protection methods follows, including the influence of mass addition on laminar and turbulent boundary layers. Next is a discussion of finite-difference computer codes and a comparison of some results from these codes. An extensive list of references is also provided from sources such as the various AIAA journals and NASA reports which are available in the open literature.

Description: A co-operative testing program is in progress between the Langley Research Center (NASA) and the National Aeronautical Establishment (NAE, Canada) to validate two different techniques of airfoil testing at transonic speeds. The procedure employed is to test the same airfoil model in the NAE two-dimensional tunnel and the Langley 0.3-m Transonic Cryogenic Tunnel (0.3-m TCT). The airfoil model used in testing was CAST-10-2/DOA-2 super-critical airfoil. The Langley 0.3-m TCT has a relatively small cross section of 13 in x 13 in, giving a (h/c) ratio of 1.44 for the same 9 in chord model. The approach employed in the 0.3-m TCT aims towards eliminating the wall effects by using active walls. The top and bottom walls are flexible. By changing the wall shapes during a test in an iterative manner, the wall interference effects are reduced. The method employed to change the wall shapes is the adaptive wall technique. The current test program provided an opportunity to validate the adaptive wall technique in the 0.3-m TCT. The relatively long chord airfoil represents a severe test case to test the efficacy of the adaptive wall technique under cryogenic conditions. The program also involved removal of side wall boundary-layer thus increasing the complexity of the wall adaptation technique. This paper deals with some salient results obtained regarding repeatability of test data and possible residual interference effects.

Description: The two-dimensional (2-D) and three-dimensional Navier-Stokes equations are solved for flow over a NAE CAST-10 airfoil model. Recently developed finite-volume codes that apply a multistage time stepping scheme in conjunction with steady state acceleration techniques are used to solve the equations. Two-dimensional results are shown for flow conditions uncorrected and corrected for wind tunnel wall interference effects. Predicted surface pressures from 3-D simulations are compared with those from 2-D calculations. The focus of the 3-D computations is the influence of the sidewall boundary layers. Topological features of the 3-D flow fields are indicated. Lift and drag results are compared with experimental measurements.

Description: An experimental Adaptive Wall Test Section (AWTS) process is described. Comparisons of the ONERA T2 and the 0.3-m TCT (transonic cryogenic tunnel) AWTS data for the ONERA CAST-10 airfoil are presented. Most of the 0.3-m TCT data is new and preliminary and no sidewall boundary layer control is involved. No conclusions are given.

Description: The transonic airfoil CAST 10-2/DOA 2 was investigated in several major transonic wind tunnels at Reynolds numbers ranging from Re=1.3 x 10(exp 6) to 45 x 10(exp 6) at ambient and cryogenic temperature conditions. The main objective was to study the degree and extent of the effects of Reynolds number on both the airfoil aerodynamic characteristics and the interference effects of various model-wind-tunnel systems. The initial analysis of the CAST 10-2 airfoil results revealed appreciable real Reynolds number effects on this airfoil and showed that wall interference can be significantly affected by changes in Reynolds number thus appearing as true Reynolds number effects.

Description: Hypersonic vehicles operate in a hostile aerothermal environment which has a significant impact on their aerothermostructural performance. Significant coupling occurs between the aerodynamic flow field, structural heat transfer, and structural response creating a multidisciplinary interaction. A long term goal of the Aerothermal Loads Branch at the NASA Langley Research Center is to develop a computational capability for integrated fluid, thermal and structural analysis of aerodynamically heated structures. The integrated analysis capability includes the coupling between the fluid and the structure which occurs primarily through the thermal response of the structure, because: (1) the surface temperature affects the external flow by changing the amount of energy absorbed by the structure, and (2) the temperature gradients in the structure result in structural deformations which alter the flow field and attendant surface pressures and heating rates. In the integrated analysis, a finite element method is used to solve: (1) the Navier-Stokes equations for the flow solution, (2) the energy equation of the structure for the temperature response, and (3) the equilibrium equations of the structure for the structural deformation and stresses.

Description: Wind tunnel wall interference assessment and correction (WIAC) concepts, applications, and typical results are discussed in terms of several nonlinear transonic codes and one panel method code developed for and being implemented at NASA-Langley. Contrasts between 2-D and 3-D transonic testing factors which affect WIAC procedures are illustrated using airfoil data from the 0.3 m Transonic Cryogenic Tunnel and Pathfinder 1 data from the National Transonic Facility. Initial results from the 3-D WIAC codes are encouraging; research on and implementation of WIAC concepts continue.

Description: The stability of compressible 2-D and 3-D boundary layers is reviewed. The stability of 2-D compressible flows differs from that of incompressible flows in two important features: There is more than one mode of instability contributing to the growth of disturbances in supersonic laminar boundary layers and the most unstable first mode wave is 3-D. Whereas viscosity has a destabilizing effect on incompressible flows, it is stabilizing for high supersonic Mach numbers. Whereas cooling stabilizes first mode waves, it destabilizes second mode waves. However, second order waves can be stabilized by suction and favorable pressure gradients. The influence of the nonparallelism on the spatial growth rate of disturbances is evaluated. The growth rate depends on the flow variable as well as the distance from the body. Floquet theory is used to investigate the subharmonic secondary instability.

Description: The treatment of turbulence effects on transonic shock/turbulent boundary layer interaction is addressed within the context of a triple deck approach valid for arbitrary practical Reynolds numbers between 1000 and 10 billion. The modeling of the eddy viscosity and basic turbulent boundary profile effects in each deck is examined in detail using Law-of-the-Wall/Law-of-the-Wake concepts as the foundation. Results of parametric studies showing how each of these turbulence model aspects influences typical interaction zone property distributions (wall pressure, displacement thickness and local skin friction) are presented and discussed.

Description: The aerodynamic characteristics for both single and twin-engine high-performance aircraft are significantly affected by shock induced flow interactions as well as other local flow interference effects which usually occur at transonic speeds. These adverse interactions can not only cause high drag, but also cause unusual aerodynamic loadings and/or severe stability and control problems. Many programs are under way to not only develop method for reducing the adverse effects, but also to develop an understanding of the basic flow conditions which are the primary contributors. It is anticipated that these programs will result in technologies which can reduce the aircraft cruise drag through improved integration as well as increase aircraft maneuverability through the application of thrust vectoring. Some of the primary integration problems for twin-engine aircraft at transonic speeds are identified, and several methods are demonstrated for reducing or eliminating the undersirable characteristics, while enhancing configuration effectiveness.

Description: Algorithms are described for the generation and adaptation of unstructured grids in two and three dimensions, as well as Euler solvers for unstructured grids. The main purpose is to demonstrate how unstructured grids may be employed advantageously for the economic simulation of both geometrically as well as physically complex flow fields.

Description: For many internal transonic flows of practical interest, some of the relevant nondimensional parameters typically are small enough that a perturbation scheme can be expected to give a useful level of numerical accuracy. A variety of steady and unsteady transonic channel and cascade flows is studied with the help of systematic perturbation methods which take advantage of this fact. Asymptotic representations are constructed for small changes in channel cross-section area, small flow deflection angles, small differences between the flow velocity and the sound speed, small amplitudes of imposed oscillations, and small reduced frequencies. Inside a channel the flow is nearly one-dimensional except in thin regions immediately downstream of a shock wave, at the channel entrance and exit, and near the channel throat. A study of two-dimensional cascade flow is extended to include a description of three-dimensional compressor-rotor flow which leads to analytical results except in thin edge regions which require numerical solution. For unsteady flow the qualitative nature of the shock-wave motion in a channel depends strongly on the orders of magnitude of the frequency and amplitude of impressed wall oscillations or fluctuations in back pressure. One example of supersonic flow is considered, for a channel with length large compared to its width, including the effect of separation bubbles and the possibility of self-sustained oscillations. The effect of viscosity on a weak shock wave in a channel is discussed.

Description: The 1980s may well be called the Euler era of applied aerodynamics. Computer codes based on discrete approximations of the Euler equations are now routinely used to obtain solutions of transonic flow problems in which the effects of entropy and vorticity production are significant. Such codes can even predict separation from a sharp edge, owing to the inclusion of artificial dissipation, intended to lend numerical stability to the calculation but at the same time enforcing the Kutta condition. One effect not correctly predictable by Euler codes is the separation from a smooth surface, and neither is viscous drag; for these some form of the Navier-Stokes equation is needed. It, therefore, comes as no surprise to observe that the Navier-Stokes has already begun before Euler solutions were fully exploited. Moreover, most numerical developments for the Euler equations are now constrained by the requirement that the techniques introduced, notably artificial dissipation, must not interfere with the new physics added when going from an Euler to a full Navier-Stokes approximation. In order to appreciate the contributions of Euler solvers to the understanding of transonic aerodynamics, it is useful to review the components of these computational tools. Space discretization, time- or pseudo-time marching and boundary procedures, the essential constituents are discussed. The subject of grid generation and grid adaptation to the solution are touched upon only where relevant. A list of unanswered questions and an outlook for the future are covered.

Description: The application of computational fluid dynamics (CFD) to fighter aircraft design and development is discussed. Methodology requirements for the aerodynamic design of fighter aircraft are briefly reviewed. The state-of-the-art of computational methods for transonic flows in the light of these requirements is assessed and the techniques found most adequate for the subject application are identified. Highlights from some proof-of-feasibility Euler and Navier-Stokes computations about a complete fighter aircraft configuration are presented. Finally, critical issues and opportunities for design application of CFD are discussed.

Description: A brief survey is given on the study of transonic shock/boundary layer effects in flight. Then the possibility of alleviating the adverse shock effects through passive shock control is discussed. A Swedish flight experiment on a swept wing attack aircraft is used to demonstrate how it is possible to reduce the extent of separated flow and increase the drag-rise Mach number significantly using a moderate amount of perforation of the surface.

Description: The paper sets forth in detail a method for the finite-difference computation of three-dimensional supersonic fields in an Eulerian mesh. First-, second-, and third-order finite difference schemes are examined. Attention is given to proper treatment of the impermeable and permeable boundaries encompassing the computational plane. Numerical results are presented for certain specific configurations: a conical wing-body combination, internal corner flow, a two-dimensional blunt body, an interfering shock problem, and three-dimensional inviscid supersonic flow past a shuttle-orbiter type vehicle.

Description: Accurate semianalytic solutions to the inverse blunt-body problem have been obtained using a method of series expansion. Rational fractions are employed for series summation and analytic continuation. Angles of incidence up to 30 deg and Mach numbers as low as 2 have been considered. The maximum-entropy streamline will not wet the body surface in asymmetric flow. It may pass either above or below the stagnation streamline. Limit lines appear in the supersonic portion of the flow field, both in the shock layer and in its upstream analytic continuation.

Description: The paper reviews the experimental data on the incipient separation characteristics of planar delta wings of 75 degree sharp leading edges, with full-span trailing edge flap deflected into the windward flow. The local Reynolds number range for these investigations covered laminar, transitional and turbulent conditions. It is shown that, while turbulent boundary layer data correlates with two dimensional results, in the laminar and transitional cases, there is a nearly parallel shift to higher flap angles for incipient separation.

Description: A forward-marching procedure for separated boundary-layer flows which permits the rapid and accurate solution of flows of limited extent is presented. The streamwise convection of vorticity in the reversed flow region is neglected, and this approximation is incorporated into a previously developed (Carter, 1974) inverse boundary-layer procedure. The equations are solved by the Crank-Nicolson finite-difference scheme in which column iteration is carried out at each streamwise station. Instabilities encountered in the column iterations are removed by introducing timelike terms in the finite-difference equations. This provides both unconditional diagonal dominance and a column iterative scheme, found to be stable using the von Neumann stability analysis.

Description: An iterative method for wall interference assessment and/or correction is presented for transonic flow conditions in wind tunnels equipped with two component velocity measurements on a single interface. The iterative method does not require modeling of the test article and tunnel wall boundary conditions. Analytical proof for the convergence and stability of the iterative method is shown in the subsonic flow regime. The numerical solutions are given for both 2-D and axisymmetrical cases at transonic speeds with the application of global Mach number correction.

Description: An intense research effort over the last few years has produced several competing and apparently diverse methods for generating meshes. Recent progress is reviewed and the central themes are emphasized which form a solid foundation for future developments in mesh generation.

Description: A cell-vertex scheme is outlined for solving the flow about a delta wing with M (sub infinity) is greater than 1. Embedded regions of mesh refinement allow solutions to be obtained which have much higher resolution than those achieved to date. Effects of mesh refinement and artificial viscosity on the solutions are studied, to determine at what point leading-edge vortex solutions are grid-converged. A macroscale and a microscale for the size of the vortex are defined, and it is shown that the macroscale (which includes the wing surface properties) is converged on a moderately refined grid, while the microscale is very sensitive to grid spacing. The level of numerical diffusion in the core of the vortex is found to be substantial. Comparisons with the experiment are made for two cases which have transonic cross-flow velocities.

Description: A computer analysis was developed for calculating steady (or unsteady) three-dimensional aircraft component flow fields. This algorithm, called ENS3D, can compute the flow field for the following configurations: diffuser duct/thrust nozzle, isolated wing, isolated fuselage, wing/fuselage with or without integrated inlet and exhaust, nacelle/inlet, nacelle (fuselage) afterbody/exhaust jet, complete transport engine installation, and multicomponent configurations using zonal grid generation technique. Solutions can be obtained for subsonic, transonic, or hypersonic freestream speeds. The algorithm can solve either the Euler equations for inviscid flow, the thin shear layer Navier-Stokes equations for viscous flow, or the full Navier-Stokes equations for viscous flow. The flow field solution is determined on a body-fitted computational grid. A fully-implicit alternating direction implicit method is employed for the solution of the finite difference equations. For viscous computations, either a two layer eddy-viscosity turbulence model or the k-epsilon two equation transport model can be used to achieve mathematical closure.

Description: The use of computational methods for three dimensional transonic flow design and analysis at the Boeing Company is presented. A range of computational tools consisting of production tools for every day use by project engineers, expert user tools for special applications by computational researchers, and an emerging tool which may see considerable use in the near future are described. These methods include full potential and Euler solvers, some coupled to three dimensional boundary layer analysis methods, for transonic flow analysis about nacelle, wing-body, wing-body-strut-nacelle, and complete aircraft configurations. As the examples presented show, such a toolbox of codes is necessary for the variety of applications typical of an industrial environment. Such a toolbox of codes makes possible aerodynamic advances not previously achievable in a timely manner, if at all.

Description: Progress in a recently started project aimed at the prediction of transition to turbulence in hypersonic flow is briefly discussed. The prediction of transition to turbulence is a very important issue in the design of space vessels. Two space vehicles currently under investigation, namely the aeroassisted transfer vehicle (AOTV) and the trans-atmospheric vehicle (TAV), suffer from strong aerodynamic heating. This heating is strongly influenced by the boundary layer structure. These aerospace vehicles fly in the upper atmospheric layer at a Mach number between 10 and 30 at very low atmospheric pressures. At very high altitudes the flow is laminar, but when the space vessel returns to a lower orbit, the flow becomes turbulent and the heating is dramatically increased. The prediction of this transition process is commonly done by means of experiments. The experimental facilities available nowadays cannot model the hypersonic flow field accurately enough by limitations in Mach and Reynolds number. These facilities also have a large free stream disturbance level which makes it very difficult to investigate transition accurately. An alternative approach is to study transition by theoretical means. Up to now numerical studies of hypersonic flow only discussed steady laminar or turbulent flow. This theoretical approach is extended to the study of transition in hypersonic flow by means of direct numerical simulations and additional theoretical investigations to explain the mechanisms leading to transition. A brief outline of how this research is to be performed is given.

Description: In the past decade, there has been much activity in the development of computational methods for the analysis of unsteady transonic aerodynamics about airfoils and wings. Significant features are illustrated which must be addressed in the treatment of computational transonic unsteady aerodynamics. The flow regimes for an aircraft on a plot of lift coefficient vs. Mach number are indicated. The sequence of events occurring in air combat maneuvers are illustrated. And further features of transonic flutter are illustrated. Also illustrated are several types of aeroelastic response which were encountered and which offer challenges for computational methods. The four cases illustrate problem areas encountered near the boundaries of aircraft envelopes, as operating condition change from high speed, low angle conditions to lower speed, higher angle conditions.

Description: A unified formulation is presented based on the full potential framework coupled with an appropriate structural model to compute steady and unsteady flows over rigid and flexible configurations across the Mach number range. The unsteady form of the full potential equation in conservation form is solved using an implicit scheme maintaining time accuracy through internal Newton iterations. A flux biasing procedure based on the unsteady sonic reference conditions is implemented to compute hyperbolic regions with moving sonic and shock surfaces. The wake behind a trailing edge is modeled using a mathematical cut across which the pressure is satisfied to be continuous by solving an appropriate vorticity convection equation. An aeroelastic model based on the generalized modal deflection approach interacts with the nonlinear aerodynamics and includes both static as well as dynamic structural analyses capability. Results are presented for rigid and flexible configurations at different Mach numbers ranging from subsonic to supersonic conditions. The dynamic response of a flexible wing below and above its flutter point is demonstrated.

Description: One of the most important uses of method that calculate unsteady aerodynamic loads is to predict and analyze the aeroelastic responses of flight vehicles. Currently, methods based on transonic small disturbance potential aerodynamics are the primary tools for aeroelastic analysis. Flow solutions obtained using isentropic potential theory can be highly inaccurate and even multivalued, because they do not model the effects of entropy that is produced when shock waves are in the flow field. From the results that are presented, it is concluded that nonisentropic potential methods more accurately model Euler solutions than do isentropic methods. The primary effects of modeling shock generated entropy are: (1) to eliminate mulitple flow solutions when strong shock waves are in the flow field; and (2) to bring the strengths and locations of computed shock waves into better agreement with those calculated using Euler method and those measured during experiments.

Description: A finite difference technique is used to solve the transonic small disturbance flow equation making use of shock capturing to treat wave discontinuities. Thus the nonlinear effects of thickness and angle of attack are considered. Such an approach is made feasible by the development of a new code called CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance), and is based on a fully implicit approximate factorization (AF) finite difference method to solve the time dependent transonic small disturbance equation. The application of the CAP-TSD code to the calculation of low to moderate supersonic steady and unsteady flows is presented. In particular, comparisons with exact linear theory solutions are made for steady and unsteady cases to evaluate shock capturing and other features of the current method. In addition, steady solutions obtained from an Euler code are used to evaluate the small disturbance aspects of the code. Steady and unsteady pressure comparisons are made with measurements for an F-15 wing model and for the RAE tailplane model.

Description: Two wind tunnel investigations were conducted to assess two different wall interference alleviation/correction techniques: adaptive test section walls and classical analytical corrections. The same airfoil model has been tested in the adaptive wall test section of the NASA-Langley 0.3 m Transonic Cryogenic Tunnel (TCT) and in the National Aeronautical Establishment (NAE) High Reynolds Number 2-D facility. The model has a 9 in. chord and a CAST 10-2/DOA 2 airfoil section. The 0.3 m TCT adaptive wall test section has four solid walls with flexible top and bottom walls. The NAE test section has porous top and bottom walls and solid side walls. The aerodynamic results corrected for top and bottom wall interference at Mach numbers from 0.3 to 0.8 at a Reynolds number of 10 by 1,000,000. Movement of the adaptive walls was used to alleviate the top and bottom wall interference in the test results from the NASA tunnel.

Description: Nonintrusive measurements were made of a normal shock wave/boundary layer interaction. Two dimensional measurements were made throughout the interaction region while 3-D measurements were made in the vicinity of the shock wave. The measurements were made in the corner of the test section of a continuous supersonic wind tunnel in which a normal shock wave had been stabilized. Laser Doppler Anemometry, surface pressure measurement and flow visualization techniques were employed for two freestream Mach number test cases: 1.6 and 1.3. The former contained separated flow regions and a system of shock waves. The latter was found to be far less complicated. The results define the flow field structure in detail for each case.

Description: Three dimensional linear secondary instability theory is extended for compressible boundary layers on a flat plate in the presence of finite amplitude Tollmien-Schlichting waves. The focus is on principal parametric resonance responsible for strong growth of subharmonics in low disturbance environment.

Description: A review is made of the performance of a variety of turbulence models in the evaluation of a particular well documented transonic flow. This is done to supplement a previous attempt to calibrate and verify transonic airfoil codes by including many more turbulence models than used in the earlier work and applying the calculations to an experiment that did not suffer from uncertainties in angle of attack and was free of wind tunnel interference. It is found from this work, as well as in the earlier study, that the Johnson-King turbulence model is superior for transonic flows over simple aerodynamic surfaces, including moderate separation. It is also shown that some field equation models with wall function boundary conditions can be competitive with it.

Description: Computational fluid dynamics has an increasingly important role in the design and analysis of aircraft as computer hardware becomes faster and algorithms become more efficient. Progress is being made in two directions: more complex and realistic configurations are being treated and algorithms based on higher approximations to the complete Navier-Stokes equations are being developed. The literature indicates that linear panel methods can model detailed, realistic aircraft geometries in flow regimes where this approximation is valid. As algorithms including higher approximations to the Navier-Stokes equations are developed, computer resource requirements increase rapidly. Generation of suitable grids become more difficult and the number of grid points required to resolve flow features of interest increases. Recently, the development of large vector computers has enabled researchers to attempt more complex geometries with Euler and Navier-Stokes algorithms. The results of calculations for transonic flow about a typical transport and fighter wing-body configuration using thin layer Navier-Stokes equations are described along with flow about helicopter rotor blades using both Euler/Navier-Stokes equations.

Description: Computational results are presented for three advanced configurations: the F-16A with wing tip missiles and under wing fuel tanks, the Oblique Wing Research Aircraft, and an Advanced Turboprop research model. These results were generated by the latest version of the TranAir full potential code, which solves for transonic flow over complex configurations. TranAir embeds a surface paneled geometry definition in a uniform rectangular flow field grid, thus avoiding the use of surface conforming grids, and decoupling the grid generation process from the definition of the configuration. The new version of the code locally refines the uniform grid near the surface of the geometry, based on local panel size and/or user input. This method distributes the flow field grid points much more efficiently than the previous version of the code, which solved for a grid that was uniform everywhere in the flow field. TranAir results are presented for the three configurations and are compared with wind tunnel data.

Description: Vector potential and related methods, for the simulation of both inviscid and viscous flows over aerodynamic configurations, are briefly reviewed. The advantages and disadvantages of several formulations are discussed and alternate strategies are recommended. Scalar potential, modified potential, alternate formulations of Euler equations, least-squares formulation, variational principles, iterative techniques and related methods, and viscous flow simulation are discussed.

Description: Advancements have occurred in transonic numerical simulation that place aerodynamic performance design into a relatively well developed status. Efficient broad band operating characteristics can be reliably developed at the conceptual design level. Recent aeroelastic and separated flow simulation results indicate that systematic consideration of an increased range of design problems appears promising. This emerging capability addresses static and dynamic structural/aerodynamic coupling and nonlinearities associated with viscous dominated flows.

Description: A review of several applications of Computational Fluid Dynamics (CFD) to various aspects of aerodynamic design recently carried out at Grumman is presented. The emphasis is placed on project-oriented applications where the ease of use of the methods and short start-to-completion times are required. Applications cover transonic wing design/optimization, wing mounted stores load prediction, transonic buffet alleviation, fuselage loads estimation, and compact offset diffuser design for advanced aircraft configurations. Computational methods employed include extended transonic small disturbance (automatic grid embedding) formulation for analysis/design/optimization and a thin layer Navier-Stokes formulation for both external and internal flow analyses.

Description: Numerous computational fluid dynamics (CFD) codes are available that solve any of several variations of the transonic flow equations from small disturbance to full Navier-Stokes. The design philosophy at General Dynamics Fort Worth Division involves use of all these levels of codes, depending on the stage of configuration development. Throughout this process, drag calculation is a central issue. An overview is provided for several transonic codes and representative test-to-theory comparisons for fighter-type configurations are presented. Correlations are shown for lift, drag, pitching moment, and pressure distributions. The future of applied CFD is also discussed, including the important task of code validation. With the progress being made in code development and the continued evolution in computer hardware, the routine application of these codes for increasingly more complex geometries and flow conditions seems apparent.

Description: Flight research and testing form a critical link in the aeronautic research and development chain. Brilliant concepts, elegant theories, and even sophisticated ground tests of flight vehicles are not sufficient to prove beyond a doubt that an unproven aeronautical concept will actually perform as predicted. Flight research and testing provide the ultimate proof that an idea or concept performs as expected. Ever since the Wright brothers, flight research and testing were the crucible in which aeronautical concepts were advanced and proven to the point that engineers and companies are willing to stake their future to produce and design aircraft. This is still true today, as shown by the development of the experimental X-30 aerospace plane. The Dryden Flight Research Center (Ames-Dryden) continues to be involved in a number of flight research programs that require understanding and characterization of the total airplane in all the aeronautical disciplines, for example the X-29. Other programs such as the F-14 variable-sweep transition flight experiment have focused on a single concept or discipline. Ames-Dryden also continues to conduct flight and ground based experiments to improve and expand the ability to test and evaluate advanced aeronautical concepts. A review of significant aeronautical flight research programs and experiments is presented to illustrate both the progress being made and the challenges to come.

Description: Present flutter analysis methods do not accurately predict the flutter speeds in the transonic flow region for wings with supercritical airfoils. Aerodynamic programs using computational fluid dynamic (CFD) methods are being developed, but these programs need to be verified before they can be used with confidence. A wind tunnel test was performed to obtain all types of data necessary for correlating with CFD programs to validate them for use on high aspect ratio wings. The data include steady state and unsteady aerodynamic measurements on a nominal stiffness wing and a wing four times that stiffness. There is data during forced oscillations and during flutter at several angles of attack, Mach numbers, and tunnel densities.

Description: The model wing consists of a set of fiberglass panels mounted on a steel spar that spans the 8 ft test section of the UTRC Large Subsonic Wind Tunnel. The first use of this system was to measure surface pressures and flow conditions for a series of constant pitch rate ramps and sinusoidal oscillations a Mach number range, a Reynolds number range, and a pitch angle range. It is concluded that an increased pitch rate causes stall events to be delayed, strengthening of the stall vortex, increase in vortex propagation, and increase in unsteady airloads. The Mach number range causes a supersonic zone near the leading edge, stall vortex to be weaker, and a reduction of unsteady airloads.

Description: Steady and unsteady pressures were measured on a 14 percent supercritical airfoil at transonic Mach numbers at Reynolds numbers from 6,000,000 to 35,000,000. Instrumentation techniques were developed to measure unsteady pressures in a cryogenic tunnel at flight Reynolds numbers. Experimental steady data, corrected for wall effects show very good agreement with calculations from a full potential code with an interacted boundary layer. The steady and unsteady pressures both show a shock position that is dependent on Reynolds number. For a supercritical pressure distribution at a chord Reynolds number of 35,000,000 laminar flow was observed between the leading edge and the shock wave at 45 percent chord.

Description: In transonic flutter problems where shock motion plays an important part, it is believed that accurate predictions of the flutter boundaries will require the use of codes based on the Euler equations. Only Euler codes can obtain the correct shock location and shock strength, and the crucially important shock excursion amplitude and phase lag. The present study is based on the finite volume scheme developed by Jameson and Venkatakrishnan for the 2-D unsteady Euler equations. The equations are solved in integral form on a moving grid. The variable are pressure, density, Cartesian velocity components, and total energy.

Description: The initial application of the CAP-TSD computer program for wing flutter analysis is presented. Computational Aeroelasticity Program - Transonic Small Disturbance (CAP-TSD) is based on an approximate factorization (AF) algorithm that is stable and efficient on supercomputers with vector arithmetic. CAP-TSD was used to calculate steady and unsteady pressures on wings and configurations at subsonic, transonic, and supersonic Mach numbers. However, the CAP-TSD code has been developed primarily for aeroelastic analysis. The initial efforts for validation of the aeroelastic analysis capability is presented. The initial applications include two series of symmetric, planar wing planforms. Well defined modal properties are available for these wings. In addition, transonic flutter boundaries are available for evaluation of the transonic capabilities of CAP-TSD.

Description: The DAST Aeroelastic Research Wing had been previously in the NASA Langley TDT and an unusual instability boundary was predicted based upon supercritical response data. Contrary to the predictions, no instability was found during the present test. Instead a region of high dynamic wing response was observed which reached a maximum value between Mach numbers 0.92 and 0.93. The amplitude of the dynamic response increased directly with dynamic pressure. The reponse appears to be related to chordwise shock movement in conjunction with flow separation and reattachment on the upper and lower wing surfaces. The onset of flow separation coincided with the occurrence of strong shocks on a surface. A controller was designed to suppress the wing response. The control law attenuated the response as compared with the uncontrolled case and added a small but significant amount of damping for the lower density condition.

Description: One aircraft configuration that shows great promise in achieving high performance is that of an asymmetrically swept wing. When compared to conventional swept wings, these advantages include higher lift to drag ratios and reduced takeoff and landing speeds, which translate into greater performance in terms of fuel comsumption, loiter time, and range. However, the oblique wing has a number of disadvantages because of its asymmetric configuration. The question is how to best achieve maximum stability and roll equilibrium without compromising performance. Using aeroelastic tailoring to enhance aeroelastic stability and control has been demonstrated in several analyses, especially for the forward swept wing. The advantages and disadvantages for the oblique wing configuration are discussed.

Description: The advantages of oblique wings have been the subject of numerous theoretical studies, wind tunnel tests, low speed flight models, and finally a low speed manned demonstrator, the AD-1. The specific objectives of the OWRA program are: (1) to establish the necessary technology base required to translate theoretical and experimental results into practical mission oriented designs; (2) to design, fabricate and flight test an oblique wing aircraft throughout a realistic flight envelope, and (3) to develop and validate design and analysis tools for asymmetric aircraft configurations. The preliminary design phase of the project is complete and has resulted in a wing configuration for which construction is ready to be initiated.

Description: A finite volume implicit approximate factorization method which solves the thin layer Navier-Stokes equations was used to predict unsteady turbulent flow airfoil behavior. At a constant angle of attack of 16 deg, the NACA 0012 airfoil exhibits an unsteady periodic flow field with the lift coefficient oscillating between 0.89 and 1.60. The Strouhal number is 0.028. Results are similar at 18 deg, with a Strouhal number of 0.033. A leading edge vortex is shed periodically near maximum lift. Dynamic mesh solutions for unstalled airfoil flows show general agreement with experimental pressure coefficients. However, moment coefficients and the maximum lift value are underpredicted. The deep stall case shows some agreement with experiment for increasing angle of attack, but is only qualitatively comparable past stall and for decreasing angle of attack.

Description: The application of unsteady 3-D Euler and Navier-Stokes equations to transonic flow past rotor blades, and wing-alone configurations is described. A promising approach for the numerical solution of these equations is examined. Additional work is needed for improving the efficiency of the present procedure. It is hoped that the techniques presented will find use in fixed and rotary wing aircraft analysis.

Description: The Euler code is used extensively for computation of transonic unsteady aerodynamics. The boundary layer code solves the 3-D, compressible, unsteady, mean flow kinetic energy integral boundary layer equations in the direct mode. Inviscid-viscous coupling is handled using porosity boundary conditions. Some of the advantages and disadvantages of using the Euler and boundary layer equations for investigating unsteady viscous-inviscid interaction is examined.

Description: Recent experience in calculating unsteady transonic flow by means of viscous-inviscid interactions with the XTRAN2L computer code is examined. The boundary layer method for attached flows is based upon the work of Rizzetta. The nonisentropic corrections of Fuglsang and Williams are also incorporated along with the viscous interaction for some cases and initial results are presented. For unsteady flows, the inverse boundary layer equations developed by Vatsa and Carter are used in a quasi-steady manner and preliminary results are presented.

Description: Since emphasis is on the transonic speed range, special importance is placed on configurations for which available data are sufficient to define accurately a transonic flutter boundary. Only configurations with clean, smooth surfaces are considered suitable. Segmented models or models with surface-slope discontinuities are inappropriate. Excluded also, in general, are configurations and data sets that involve behavior that is uncertain or not well understood, uncertain model properties, or know sensitivities to small variations in model properties. In order to assess the suitability of configurations already tested and the associated data for designation as standard, a survey of AGARD member countries was conducted to seek candidates for the prospective set. The results of that survey are given and summarized along with the initial selection of a standard configuration.

Description: An implicit, two factor, split flux, finite volume Euler equations solution algorithms is applied to the time accurate solution of transonic flow about an NACA 0012 airfoil and a rectangular planform supercritical wing undergoing pitch oscillations. Accuracy for Courant numbers greater than one is analyzed. Freezing the flux Jacobians can result in significant savings for steady state solutions; the accuracy of freezing flux Jacobians for unsteady results is investigated. The Euler algorithm results are compared with experimental results for an NACA 0012 and a rectangular planform supercritical wing.

Description: The method of flux vector splitting used is that of Van Leer. The fluxes split in this manner have the advantage of being continuously differentiable at eigenvalue sign changes and this allows normal shocks to be captured with at most two interior zones, although in practice only one zone is usually observed. The fluxes as originally derived, however did not include the necessary terms appropriate for calculations on a dynamic mesh. The extension of the splitting to include these terms while retaining the advantages of the original splitting is the main purpose of this investigation. In addition, the use of multiple grids to reduce the computer time is investigated. A subiterative procedure to eliminate factorization and linearization error so that larger time steps can be used is also investigated.

Description: An efficient and accurate transonic unsteady aerodynamic method is needed for predicting flight loads, flutter and aeroelastic stability for advanced aircraft. There have been new developments and many improvements to older codes. XTRAN3S was improved and is a useful code for the near term. However, to predict the unsteady aerodynamics for high performance maneuvering aircraft, the Euler/Navier-Stokes codes must be extended and improved for complex 3-D configurations. The long term goal is development of Euler/Navier-Stokes unsteady aerodynamic methods for aeroelastic analysis.

Description: Since ground based flow simulations are presently unable to model flight conditions expected for AOTVs (Aeroassist Orbital Transfer Vehicle) and other hypersonic space vehicles, computer codes are being developed to provide design parameters necessary for structure, guidance, and control aspects. Over the past four years, VRFLO (Viscous Reactive Flow) has been written to model finite-rate chemistry and viscous effects for a variety of aerobrake bodies. VRFLO includes a number of unique features that are summarized as follows: (1) Grid generation is an integral part of the code for several aerobrake configurations which includes the wake flow region; (2) The formulation is valid for three air chemical models; (3) An ADI central difference technique is used to solve the Navier-Stokes and species continuity equations in split groups; and (4) Grid density and numerical damping are minimized by shock-fitting and conformal mapping of body points.

Description: As the capability of the space transportation vehicles (STV's) expand to meet the requirements for future space exploration and utilization, the effects of rarefied hypersonic flows will play a more significant role in defining the aerodynamic and aerothermodynamic performance of STV's. This is particularly true of the low lift/drag aeroassisted STV's where aerobraking occurs at relatively high altitudes and high velocity. Because of the limitations of the continuum description as expressed by the Navier-Stokes equations and the difficulties of solving the Boltzmann equation, the particle of molecular approach has been developed over the last three decades for modeling rarefied gas effects. The direct simulation Monte Carlo (DSMC) method of Bird is the most used method today for simulating rarefied flows. The DSMC method provides a direct physical simulation as opposed to a numerical solution of a set of model equations. This is accomplished by developing phenomenological models of the relevant physical events. The DSMC method accounts for translational, thermal, chemical, and radiative nonequilibrium effects. The general features of the DSMC method, the numerical requirements for obtaining meaningful results, the modeling used to simulate high temperature gas effects, and applications of the method to calculate the flow about an aeroassist flight experiment vehicle (AFE) are reviewed. The AFE simulates a geosynchronous return while entering the Earth's upper atmosphere at approximately 10 km/s. Results obtained using a general 3-D code are presented for the more rarefied portion of the atmospheric encounter (altitudes of 200 to 100 km) emphasizing surface, flowfield, and aerodynamic characteristics of the AFE. Finally, results obtained using axisymmetric and 1-D versions of the code are presented for lower altitude conditions.

Description: The code development and application program for the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA), with emphasis directed toward support of the Aeroassist Flight Experiment (AFE) in the near term and Aeroassisted Space Transfer Vehicle (ASTV) design in the long term is reviewed. LAURA is an upwind-biased, point-implicit relaxation algorithm for obtaining the numerical solution to the governing equations for 3-D, viscous, hypersonic flows in chemical and thermal nonequilibrium. The algorithm is derived using a finite volume formulation in which the inviscid components of flux across cell walls are described with Roe's averaging and Harten's entropy fix with second-order corrections based on Yee's Symmetric Total Variation Diminishing scheme. Because of the point-implicit relaxation strategy, the algorithm remains stable at large Courant numbers without the necessity of solving large, block tri-diagonal systems. A single relaxation step depends only on information from nearest neighbors. Predictions for pressure distributions, surface heating, and aerodynamic coefficients compare well with experimental data for Mach 10 flow over an AFE wind tunnel model. Predictions for the hypersonic flow of air in chemical and thermal nonequilibrium over the full scale AFE configuration obtained on a multi-domain grid are discussed.

Description: Several conceptual designs for vehicles that would fly in the atmosphere at hypersonic speeds have been developed recently. For the proposed flight conditions the air in the shock layer that envelops the body is at a sufficiently high temperature to cause chemical reaction, vibrational excitation, and ionization. However, these processes occur at finite rates which, when coupled with large convection speeds, cause the gas to be removed from thermo-chemical equilibrium. This non-ideal behavior affects the aerothermal loading on the vehicle and has ramifications in its design. A numerical method to solve the equations that describe these types of flows in 2-D was developed. The state of the gas is represented with seven chemical species, a separate vibrational temperature for each diatomic species, an electron translational temperature, and a mass-average translational-rotational temperature for the heavy particles. The equations for this gas model are solved numerically in a fully coupled fashion using an implicit finite volume time-marching technique. Gauss-Seidel line-relaxation is used to reduce the cost of the solution and flux-dependent differencing is employed to maintain stability. The numerical method was tested against several experiments. The calculated bow shock wave detachment on a sphere and two cones was compared to those measured in ground testing facilities. The computed peak electron number density on a sphere-cone was compared to that measured in a flight test. In each case the results from the numerical method were in excellent agreement with experiment. The technique was used to predict the aerothermal loads on an Aeroassisted Orbital Transfer Vehicle including radiative heating. These results indicate that the current physical model of high temperature air is appropriate and that the numerical algorithm is capable of treating this class of flows.

Description: The Roe flux difference splitting method was extended to treat 2-D viscous flows with nonequilibrium chemistry. The derivations have avoided unnecessary assumptions or approximations. For spatial discretization, the second-order Roe upwind differencing is used for the convective terms and central differencing for the viscous terms. An upwind-based TVD scheme is applied to eliminate oscillations and obtain a sharp representation of discontinuities. A two-state Runge-Kutta method is used to time integrate the discretized Navier-Stokes and species transport equations for the asymptotic steady solutions. The present method is then applied to two types of flows: the shock wave/boundary layer interaction problems and the jet in cross flows.