ALBERT

Description: In the last two decades there have been extensive developments in computational unsteady transonic aerodynamics. Such developments are essential since the transonic regime plays an important role in the design of modern aircraft. Therefore, there has been a large effort to develop computational tools with which to accurately perform flutter analysis at transonic speeds. In the area of Computational Fluid Dynamics (CFD), unsteady transonic aerodynamics are characterized by the feature of modeling the motion of shock waves over aerodynamic bodies, such as wings. This modeling requires the solution of nonlinear partial differential equations. Most advanced codes such as XTRAN3S use the transonic small perturbation equation. Currently, XTRAN3S is being used for generic research in unsteady aerodynamics and aeroelasticity of almost full aircraft configurations. Use of Euler/Navier Stokes equations for simple typical sections has just begun. A brief history of the development of CFD for aeroelastic applications is summarized. The development of unsteady transonic aerodynamics and aeroelasticity are also summarized.

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: A finite difference code was implemented for the compressible Navier-Stokes equations on the Connection Machine, a massively parallel computer. The code is based on the ARC2D/ARC3D program and uses the implicit factored algorithm of Beam and Warming. The codes uses odd-even elimination to solve linear systems. Timings and computation rates are given for the code, and a comparison is made with a Cray XMP.

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 hardware and software currently used for visualization of fluid dynamics at NASA Ames is described. The software includes programs to create scenes (for example particle traces representing the flow over an aircraft), programs to interactively view the scenes, and programs to control the creation of video tapes and 16mm movies. The hardware includes high performance graphics workstations, a high speed network, digital video equipment, and film recorders.

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.

Description: Mesh generation procedures as well as solution algorithms for solving the Euler and Navier-Stokes equations on unstructured meshes are presented. The solution algorithms discussed utilize approximate Riemann solver, upwind differencing to achieve high spatial accuracy. Numerical results for Euler flow over single and multi-element airfoils are presented.

Description: The advancing front technique is being used to develop a code to generate grids around complex 3-D configurations for use in computing the invisid flow solutions by the Euler equations. By the advancing front technique points are introduced concurrently with the connectivity information so that a separate library is not required. The generation of a 3-D grid is accomplished in several steps. First the boundaries of the domain to be gridded must be described by two-, three- or four-sided surface patches. Next, a background mesh is required to control the grid spacing and stretching throughout the domain. This coarse tetrahedral grid is not required to conform to any of the boundaries. Next, each of the patches is mapped to 2-D, triangulated by the advancing front technique and mapped back to 3-D. These triangles form the initial front for the generation of the final tetrahedral mesh.

Description: A method for designing wings and airfoils at transonic speeds using a predictor/corrector approach was developed. The procedure iterates between an aerodynamic code, which predicts the flow about a given geometry, and the design module, which compares the calculated and target pressure distributions and modifies the geometry using an algorithm that relates differences in pressure to a change in surface curvature. The modular nature of the design method makes it relatively simple to couple it to any analysis method. The iterative approach allows the design process and aerodynamic analysis to converge in parallel, significantly reducing the time required to reach a final design. Viscous and static aeroelastic effects can also be accounted for during the design or as a post-design correction. Results from several pilot design codes indicated that the method accurately reproduced pressure distributions as well as the coordinates of a given airfoil or wing by modifying an initial contour. The codes were applied to supercritical as well as conventional airfoils, forward- and aft-swept transport wings, and moderate-to-highly swept fighter wings. The design method was found to be robust and efficient, even for cases having fairly strong shocks.

Description: The increased national interest in high speed flight has increased research for high speed propulsion components. The highly 3-D flows present in supersonic/hypersonic inlets are currently being studied at NASA-Lewis both experimentally and computationally using a family of steady Parabolized Navier-Stokes (PNS) and Navier-Stokes (NS) solvers and unsteady NS solvers. Some of the results of these efforts are presented with an emphasis on the comparison of the computational and experimental results. The flow in high speed inlets typically involves the interaction of compression shock waves and boundary layers on the internal surfaces. The fundamentals of these interactions have been studied experimentally for many years, while more recently, computations have been used to study these complex 3-D flow fields. Attempts to control the flow through boundary layer bleed are being investigated computationally prior to wind tunnel experiments. The ultimate goal is the higher performing inlets required for high speed flight.

Description: The feasibility was determined of incorporating the Navier-Stokes computational code, CFL3D, into the supersonic wing design process. The approach taken is of two steps. The first step was to calibrate CFL3D against existing experimental data sets obtained on thin sharp edged delta wings. The experimental data identified six flow types which are dependent on the similarity parameters of Mach number and angle of attack normal to the leading edge. The calibration showed CFL3D capable of simulating these various separated and attached flow conditions. The second step was to use CFL3D to study the initial formation of leading edge separation over delta wings at supersonic speeds. This consisted of examining solutions obtained on a 65 deg delta wing at Mach number of 1.6 with varying cross sectional shapes. Reynolds number was held constant at 1000000 and the Baldwin-Lomax turbulence model was used. The study showed that through the use of leading edge radius and/or camber, the onset of leading edge separation can be delayed to a higher angle of attack than observed on a flat sharp edged wing. Based on the geometries studied, three wind tunnel models are being designed to verify these results.

Description: An embedded grid algorithm for the Euler and/or Navier-Stokes equations is developed and applied to delta wings at high angles of attack in low speed flow. The Navier-Stokes code is an implicit, finite volume algorithm, using flux difference splitting for the convective and pressure terms and central differencing for the viscous and heat transfer terms. Calculations are compared with detailed experimental results over an angle of attack range up to and beyond the maximum lift coefficient, corresponding to vortex breakdown at the trailing edge, for a delta wing nominally of unit aspect ratio. The results indicate that the overall flowfield, including surface pressures, surface streamlines, and vortex trajectories, can be simulated accurately with the global grid version of the present algorithm. However, comparison of computed velocities and vorticity with experimentally measured off-body values at an angle of attack of 20.5 deg indicates the core region is substantially more diffuse in the computations than that measured with either a five-hole probe or a laser velocimeter. Embedded grids, used to improve the numerical discretization in the core region, are formulated within the framework of the implicit, upwind-biased multi-grid algorithm. Structured levels of local nested refinements are made. Three-dimensional results for both Euler and Navier-Stokes calculations are shown, with up to 3 levels of embedded refinement. The embedding procedure was effective in eliminating a crossflow secondary separation produced in the Euler solutions on coarse grids.

Description: The development of Short Takeoff Vertical Landing (STOVL) aircraft has historically been an empirical- and experienced-based technology. A 3-D turbulent flow CFD code was used to calculate the hot gas environment around an STOVL aircraft operating in ground proximity. Preliminary calculations are reported for a typical STOVL aircraft configuration to identify key features of the flow field, and to demonstrate and assess the capability of current 3-D CFD codes to calculate the temperature of the gases ingested at the engine inlet as a function of flow and geometric conditions.

Description: The primary objective is to expose government, industry, and academic scientists to work underway at NASA-Ames towards the application of CFD to the powered lift area. One goal is to produce the technologies which will be required in the application of numerical techniques to, for example, the Supersonic STOVL program. The progress to date on the following specific projects is presented: Jet in ground effect with crossflow; Jet in a crossflow; Delta planform with multiple jets in ground effect; Integration of CFD with thermal and acoustic analyses; Improved flow visualization techniques for unsteady flows; YAV-8B Harrier simulation program; and E-7 simulation program.

Description: A 3-D Navier-Stokes code was developed for analysis of turbomachinery blade rows and other internal flows. The Navier-Stokes equations are written in a Cartesian coordinate system rotating about the x-axis, and then mapped to a general body-fitted coordinate system. Streamwise viscous terms are neglected using the thin layer assumption, and turbulence effects are modelled using the Baldwin-Lomax turbulence model. The equations are discretized using finite differences on stacked C-type grids and are solved using a multistage Runge-Kutta algorithm with a spatially varying time step and implicit residual smoothing. Calculations were made of the flow around a supersonic throughflow fan blade. The fan was designed as a key component in a supersonic cruise engine. The 3-D calculations were done on a 129x29x33 grid and took 50 minutes of cpu time. Comparisons with the quasi-3-D results show minor differences in loading due to 3-D effects. Particle traces show nearly 2-D flows near the pressure surface, but large secondary flows within the suction surface boundary layer. The horseshoe vortex ahead of the leading edge is clearly seen.

Description: A numerical automation procedure was developed to be used in conjunction with an inverse hodograph method for the design of controlled diffusion blades. With this procedure a cascade of airfoils with a prescribed solidity, inlet Mach No., inlet air flow angle and air flow turning can be produced automatically. The trailing edge thickness of the airfoil, an important quantity in inverse methods, is also prescribed. The automation procedure consists of a multi-dimensional Newton iteration in which the objective design conditions are achieved by acting on the hodograph input parameters of the underlying inverse code. The method, although more general in scope, is applied to the design of axial flow turbomachinery blade sections, both compressors and turbines. A collaborative effort with U.S. Engine Companies to identify designs of interest to the industry will be described.

Description: A numerical study of the aerodynamic and thermal environment associated with axial turbine stages is presented. Computations were performed using a modification of the unsteady NASA Ames viscous code, ROTOR1, and an improved version of the NASA Lewis steady inviscid cascade system MERIDL-TSONIC coupled with boundary layer codes BLAYER and STAN5. Two different turbine stages were analyzed: the first stage of the United Technologies Research Center Large Scale Rotating Rig (LSRR) and the first stage of the Space Shuttle Main Engine (SSME) high pressure fuel turbopump turbine. The time-averaged airfoil midspan pressure and heat transfer profiles were predicted for numerous thermal boundary conditions including adiabatic wall, prescribed surface temperature, and prescribed heat flux. Computed solutions are compared with each other and with experimental data in the case of the LSRR calculations. Modified ROTOR1 predictions of unsteady pressure envelopes and instantaneous contour plots are also presented for the SSME geometry. Relative merits of the two computational approaches are discussed.

Description: Flows in turbomachinery are generally complex and do not easily lend themselves to numerical computation. The flows are three-dimensional and inherently unsteady. Complicated blade geometries and flow phenomena such as separation and periodic transition from laminar to turbulent flow add to the numerical complexity. Nevertheless, the accurate numerical analysis of such flows is a problem of considerable interest and practical importance to the turbomachinery community. Much of the early work in turbomachinery flow prediction focussed on airfoil cascades. While such analyses of flows in isolated airfoil rows have helped improve understanding of the flow phenomena and have gained widespread acceptance in the industrial community as a design tool, they do not yield any information regarding the unsteady effects arising out of rotor-stator aerodynamic interaction. These interaction effects become increasingly important as the distance between successive stator and rotor rows is decreased. Thus, the need exists for analytical tools that treat the rotor and stator airfoils as a system and provide information regarding the magnitude and the impact of the unsteady effects. The focus a three-dimensional, time-accurate, thin-layer Navier-Stokes code that was recently developed to study rotor-stator interaction problems. A system of patched and overlaid grids that move relative to each other is used to discretize the flow field and the governing equations are integrated using a third-order upwind scheme set in an iterative, implicit framework. The code was used to simulate subsonic flow through an axial turbine configuration for which considerable experimental data exists. Grid refinement studies were also conducted as part of the code validation process. The current status of the research, along with planned future directions, are also discussed.

Description: Significant advancements have been made in the last five years in the ability to model turbomachinery flows of engineering interest. This advancement can be directly attributed to the second generation of supercomputers like the Cray XMP and Cray 2 and advanced instrumentation techniques. Early on, the National Aeronautics and Space Administration Lewis Research Center recognized the potential gains in turbomachinery performance and life that could be achieved by taking advantage of this technology and instituted a comprehensive research program in turbomachinery flow modeling. This activity combined the areas of fluid flow analysis, computational fluid dynamics, and experimental fluid mechanics. As a result of this activity, Lewis has become an internationally recognized leader in turbomachinery flow modeling. Many of the research activities conducted under this program are utilized by industry. The presentation gives an overview of this program and provides sample illustration of simulation performed to date.

Description: The design of turbomachinery blades requires the prevention of flutter for all operating conditions. However, flow field predictions used for aeroelastic analysis are not well understood for all flow regimes. The present research focuses on numerical solutions of the Euler and Navier-Stokes equations using an ADI procedure to model two-dimensional, transonic flow through oscillating cascades. The model prescribes harmonic pitching motions for the blade sections for both zero and non-zero inter-blade phase angles. The code introduces the use of a deforming grid technique for convenient specification of the periodic boundary conditions. Approximate nonreflecting boundary conditions have been coded for the inlet and exit boundary conditions. Sample unsteady solutions have been performed for an oscillating cascade and compared to experimental data. Also, test cases were fun for a flat plate cascade to compare with an unsteady, small-perturbation, subsonic analysis. The predictions for oscillating cascades with non-zero inter-blade phase angles are in good agreement with experimental data and small-perturbation theory. The zero degree inter-blade phase angle cases, which were near a resonant condition, differ from the experiment and theory. Studies on reflecting versus non-reflecting inlet and exit boundary conditions show that the treatment of the boundary can have a significant effect on the first harmonic, unsteady pressure distributions for certain flow conditions. This code is expected to be used as a tool for reviewing simpler models that do not include the full nonlinear aerodynamics or as a final check for designs against flutter in turbomachinery.

Description: Three-dimensional, conjugate (solid/fluid) heat transfer analyses of new designs of the Solid Rocket Motor (SRM) nozzle/case and case field joints are described. The main focus was to predict the consequences of multiple rips (or debonds) in the ambient cure adhesive packed between the nozzle/case joint surfaces and the bond line between the mating field joint surfaces. The models calculate the transient temperature responses of the various materials neighboring postulated flow/leakpaths into, past, and out from the nozzle/case primary O-ring cavity and case field capture O-ring cavity. These results were used to assess if the design was failsafe (i.e., no potential O-ring erosion) and reusable (i.e., no excessive steel temperatures). The models are adaptions and extensions of the general purpose PHOENICS fluid dynamics code. A non-orthogonal coordinate system was employed and 11,592 control cells for the nozzle/case and 20,088 for the case field joints are used with non-uniform distribution. Physical properties of both fluid and solids are temperature dependent. A number of parametric studies were run for both joints with results showing temperature limits for reuse for the steel case on the nozzle joint being exceeded while the steel case temperatures for the field joint were not. O-ring temperatures for the nozzle joint predicted erosion while for the field joint they did not.

Description: As a result of high cycle fatigue, hydrogen embrittlement, and extended engine use, it was observed in testing that the trailing edge on the first stage nozzle plug in the High Pressure Oxygen Turbopump (HPOTP) could detach. The objective was to predict the trajectories followed by particles exiting the turbine. Experiments had shown that the heat exchanger soils, which lie downstream of the turbine, would be ruptured by particles traveling in the order of 360 ft/sec. An axisymmetric solution of the flow was obtained from the work of Lin et. al., who used INS3D to obtain the solution. The particle trajectories were obtained using the method of de Jong et. al., which employs Lagrangian tracking of the particle through the Eulerian flow field. The collision parameters were obtained from experiments conducted by Rocketdyne using problem specific alloys, speeds, and projectile geometries. A complete 3-D analysis using the most likely collision parameters shows maximum particle velocities of 200 ft/sec. in the heat exchanger region. Subsequent to this analysis, an engine level test was conducted in which seven particles passed through the turbine but no damage was observed on the heat exchanger coils.

Description: Analysis of the flow in the Space Shuttle Main Engine (SSME) high pressure oxygen turbopump (HPOTP) bearing no. 1 inlet cavity was completed in support of return-to-flight. With the incorporation of several design changes in the Phase 2 turbopump, rotordynamic stability of the pumps was enhanced, but the durability and life of the LOX-cooled bearings has decreased. During the post-Challenger SSME recertification, the causes of limited bearing durability were investigated. One topic addressed was the flow environment upstream of the pump-end bearing and the effect of seal exit swirl and a cavity anti-vortex rib on the bearing environment and life. The objective is to define the hydrodynamic environment upstream of the pump-end bearing and determine the effect of seal exit swirl and the anti-vortex rib on bearing inlet swirl. The problem was posed as an axisymmetric cavity flow with the computational domain extending from the seal exit to the bearing inlet. This domain was discretized with 22800 grid points. Boundary conditions were obtained from a 1-D model of the SSME coolant path. The inlet Mach number was 0.19 and the problem was solved with the CMINT code utilizing the Briley-McDonald/Beam-Warming algorithm with preconditioning to speed convergence at low Mach numbers. Three parametric cases with inlet swirl of 50 percent shaft speed (labyrinth seal), 20 percent shaft speed (damping seal), and no inlet swirl were considered. Computational results indicate large vortical flow structures in the cavity, with the labyrinth, damping, and no-swirl cases yielding bearing inlet swirl rates of 14, 10, and 9 percent of shaft speed, respectively. When these results were used as input to the SHABRETH bearing model, limited durability could not be explained by these small differences in swirl. Also, based on these results, a proposed design change for the cavity anti-vortex rib was not implemented by the SSME chief engineer.

Description: The CFL3D/CFL3DE CFD codes and the industrial use status of the codes are outlined. Comparison of grid density, pressure, heat transfer, and aerodynamic coefficience are presented. Future plans related to the National Aerospace Plane Program are briefly outlined.

Description: After the STS 51-L accident, an extensive review of the Space Shuttle Orbiter's ascent aerodynamic loads uncovered several questionable areas that required further analysis. The insight gained by comparing the Shuttle ascent CFD numerical simulations, obtained by the NASA Ames Space Shuttle Flow Simulation Group, to the current IVBC-3 aerodynamic loads database was instrumental in resolving uncertainties on the Orbiter payload bay doors and fuselage. Initial confidence in the numerical simulations was gained by comparing them with the limited flight data that had been obtained during the Orbiter Flight Test (OFT) program. Current CFD results exist for Mach numbers 0.6, 0.9, 1.05, 1.55, 2.0, and 2.5. Since the pre STS-1 wind tunnel test program (IA-105) often yields considerable differences when compared to STS-5 flight data, the M(sub infinity) = 1.05 transonic case is the most investigated. The IA308 mated-vehicle hot gas plume wind tunnel test, recently completed at AEDC 16T (transonic) and Lewis (hypersonic), is also used to compare with the computation where applicable.

Description: An overview of CFD activities in the Hypersonic Propulsion Branch is given. Elliptic and PNS codes that are being used for the simulation of hydrogen-air combusting flowfields for scramjet applications are discussed. Results of the computer codes are shown in comparison with those of the experiments where applicable. Two classes of experiments will be presented: parallel injection of hydrogen into vitiated supersonic air flow; and normal injection of hydrogen into supersonic crossflow of vitiated air.

Description: A steady incompressible three-dimensional (3-D) viscous flow analysis was conducted for the Space Shuttle Main Propulsion External Tank (ET)/Orbiter (ORB) propellant feed line quick separable 17-inch disconnect flapper valves for liquid oxygen (LO2) and liquid hydrogen (LH2). The main objectives of the analysis were to predict and correlate the hydrodynamic stability of the flappers and pressure drop with available water test data. Computational Fluid Dynamics (CFD) computer codes were procured at no cost from the public domain, and were modified and extended to carry out the disconnect flow analysis. The grid generator codes SVTGD3D and INGRID were obtained. NASA Ames Research Center supplied the flow solution code INS3D, and the color graphics code PLOT3D. A driver routine was developed to automate the grid generation process. Components such as pipes, elbows, and flappers can be generated with simple commands, and flapper angles can be varied easily. The flow solver INS3D code was modified to treat interior flappers, and other interfacing routines were developed, which include a turbulence model, a force/moment routine, a time-step routine, and initial and boundary conditions. In particular, an under-relaxation scheme was implemented to enhance the solution stability. Major physical assumptions and simplifications made in the analysis include the neglect of linkages, slightly reduced flapper diameter, and smooth solid surfaces. A grid size of 54 x 21 x 25 was employed for both the LO2 and LH2 units. Mixing length theory applied to turbulent shear flow in pipes formed the basis for the simple turbulence model. Results of the analysis are presented for LO2 and LH2 disconnects.

Description: The long-term goal is to develop the capability to predict chemically-reacting, multi-stream nozzle and plume flow fields. Two basic Navier-Stokes solvers, including the widely used F-3D code, are upgraded to include several upwind difference schemes and portable chemistry packages. Current computational capabilities for solving equilibrium single-stream and multi-stream, frozen gas, and finite rate chemistry problems are described. A variety of complex nozzle and plume flows were computed. Solutions presented include axisymmetric plume flow for ideal and equilibrium air, 3-D NASP nozzle/afterbody flow, and an internal nozzle calculation comparing various finite-rate chemistry packages.

Description: A new three-dimensional numerical program incorporated with comprehensive real gas property models was developed to simulate supersonic reacting flows. The code employs an implicit finite volume, Lower-Upper (LU) time-marching method to solve the complete Navier-Stokes and species equations in a fully-coupled and very efficient manner. A chemistry model with nine species and eighteen reaction steps are adopted in the program to represent the chemical reaction of H2 and air. To demonstrate the capability of the program, flow fields of underexpanded hydrogen jets transversely injected into supersonic air stream inside the combustors of scramjets are calculated. Results clearly depict the flow characteristics, including the shock structure, separated flow regions around the injector, and the distribution of the combustion products.

Description: The SPARK3D and SPARK3D-PNS computer programs were developed to model 3-D supersonic, chemically reacting flow-fields. The SPARK3D code is a full Navier-Stokes solver, and is suitable for use in scramjet combustors and other regions where recirculation may be present. The SPARK3D-PNS is a parabolized Navier-Stokes solver and provides an efficient means of calculating steady-state combustor far-fields and nozzles. Each code has a generalized chemistry package, making modeling of any chemically reacting flow possible. Research activities by the Langley group range from addressing fundamental theoretical issues to simulating problems of practical importance. Algorithmic development includes work on higher order and upwind spatial difference schemes. Direct numerical simulations employ these algorithms to address the fundamental issues of flow stability and transition, and the chemical reaction of supersonic mixing layers and jets. It is believed that this work will lend greater insight into phenomenological model development for simulating supersonic chemically reacting flows in practical combustors. Currently, the SPARK3D and SPARK3D-PNS codes are used to study problems of engineering interest, including various injector designs and 3-D combustor-nozzle configurations. Examples, which demonstrate the capabilities of each code are presented.

Description: A comparative study was made with four different codes for solving the compressible Navier-Stokes equations using three different test problems. The first of these cases was hypersonic flow through the P8 inlet, which represents inlet configurations typical of a hypersonic airbreathing vehicle. The free-stream Mach number in this case was 7.4. This 2-D inlet was designed to provide an internal compression ratio of 8. Initial calculations were made using two state-of-the-art finite-volume upwind codes, CFL3D and USA-PG2, as well as NASCRIN, a code which uses the unsplit finite-difference technique of MacCormack. All of these codes used the same algebraic eddy-viscosity turbulence model. In the experiment, the cowl lip was slightly blunted; however, for the computations, a sharp cowl leading edge was used to simplify the construction of the grid. The second test problem was the supersonic (Mach 3.0) flow in a three-dimensional corner formed by the intersection of two wedges with equal wedge angles of 9.48 degrees. The flow in such a corner is representative of the flow in the corners of a scramjet inlet. Calculations were made for both laminar and turbulent flow and compared with experimental data. The three-dimensional versions of the three codes used for the inlet study (CFL3D, USA-PG3, and SCRAMIN, respectively) were used for this case. For the laminar corner flow, a fourth code, LAURA, which also uses recently-developed upwind technology, was also utilized. The final test case is the two-dimensional hypersonic flow over a compression ramp. The flow is laminar with a free-stream Mach number of 14.1. In the experiment, the ramp angle was varied to change the strength of the ramp shock and the extent of the viscous-inviscid interaction. Calculations were made for the 24-degree ramp configuration which produces a large separated-flow region that extends upstream of the corner.

Description: It is now known that Batchelor's trailing-line vortex is extremely unstable to small amplitude disturbances for swirl numbers in the neighborhood of 0.83. The results of numerical calculations are presented that show the response of the vortex in this range of swirl numbers to finite amplitude, temporal, helical disturbances. Phenomena observed include: (1) ejection of axial vorticity and momentum from the core resulting in the creation of secondary, separate vortices; (2) a great intensification of core axial vorticity and a weakening of core momentum; and (3) the production of azimuthal vorticity in the form of a tightly wrapped spiral wave. The second phenomenon eventually stablizes the vortex, which then smooths and gradually returns to an axisymmetric state. The calculations are mixed spectral-finite-difference, fourth-order accurate, and have been carried out at Reynolds numbers of 1000 to 2000. Some linearized results are also discussed in an attempt to explain the process of vortex intensification.

Description: The NASA-Lewis aircraft icing analysis program is composed of three major sub-programs. These sub-programs are ice accretion simulation, performance degradation evaluation, and ice protection system evaluation. These topics cover all areas of concern related to the simulation of aircraft icing and its consequences. The motivation for these activities is twofold, reduction of time and effort required in experimental programs and the ability to provide reliable information for aircraft certification in icing, over the complete range of environmental conditions. In addition to the analytical activities associated with development of these codes, several experimental programs are underway to provide verification information for existing codes. These experimental programs are also used to investigate the physical processes associated with ice accretion and removal for improvement of present analytical models. The NASA-Lewis icing analysis program is thus striving to provide a full range of analytical tools necessary for evaluation of the consequences of icing and of ice protection systems.

Description: The state-of-the-art in rotor blade drag prediction involves the use of two-dimensional airfoil tables to calculate the drag force on the blade. One of the most serious problems with the current methods is that they cannot be used for airfoils that have yet to be tested. Most of the drag prediction methods also do not take the Reynolds number or the rotational effects of the blade into account, raising doubts about the accuracy of the results. These problems are addressed with the development of an analytical method which includes the shape of airfoil, the effects of Reynolds number, and the rotational motion of the blade.

Description: Interactions between the rotors and wing of a rotary wing aircraft in hover have a significant detrimental effect on its payload performance. The reduction of payload results from the wake of lifting rotors impinging on the wing, which is at 90 deg angle of attack in hover. This vertical drag, often referred as download, can be as large as 15 percent of the total rotor thrust in hover. The rotor wake is a three-dimensional, unsteady flow with concentrated tip vortices. With the rotor tip vortices impinging on the upper surface of the wing, the flow over the wing is not only three-dimensional and unsteady, but also separated from the leading and trailing edges. A simplified two-dimensional model was developed to demonstrate the stability of the methodology. The flow model combines a panel method to represent the rotor and the wing, and a vortex method to track the wing wake. A parametric study of the download on a 20 percent thick elliptical airfoil below a rotor disk of uniform inflow was performed. Comparisons with experimental data are made where the data are available. This approach is now being extended to three-dimensional flows. Preliminary results on a wing at 90 deg angle of attack in free stream is presented.

Description: TranAir is a computer code which solves the full-potential equation for transonic flow about very general and complex configurations. Piecewise flat surface panels are used to describe the surface geometry. This paneled definition is then embedded in an unstructured cartesian flow field grid. Finite elements are used in the discretization of the flow field grid in a manner which is fully conservative and second-order accurate. Since geometries may be defined with relative ease, and since the user is not involved in the generation of the flow field grid, computational results may be generated rather quickly for a wide range of geometries. For transonic cases in the cruise angle-of-attack range, TranAir has generated results which are in generally good agreement with both Euler results and wind tunnel data. A typical transonic case runs in 1 to 2 CPU hours on a Cray X-MP. For subcritical cases, the code runs in 15 to 30 CPU minutes, even for geometries in which several thousand surface panels are used in the definition. This ability to rapidly and accurately provide both subsonic and transonic predictions about very complex aircraft configurations gives TranAir the potential of being a very powerful and widely used design tool.

Description: The objective is developing CFD capabilities to obtain solutions for viscous flows about generic configurations of internally and externally carried stores. The emphasis is placed on the supersonic flow regime with extensions being made to the transonic regime. The project is broken into four steps: (1) Cavity flows for internal carriage configurations; (2) High angle of attack flows, which may be experienced during the separation of the stores: (3) Flows about a body near a flat plate for external carriage configurations; and (4) Flows about a body inside or in the proximity of a cavity. Three-dimensional unsteady cavity flow solutions are obtained by an explicit, MacCormack algorithm, EMCAV3, for open, close, and transitional cavities. High angle of attack flows past cylinders are solved by an implicit, upwind algorithm. All the results compare favorably with the experimental data. For flows about multiple body configurations, the Chimera embedding scheme is modified for finite-volume and multigrid algorithms, MaGGiE. Then a finite volume, implicit, upwind, multigrid Navier-Stokes solver which uses on overlapped/embedded and zonal grids, VUMXZ3, is developed from the CFL3D code. Supersonic flows past a cylinder near a flat plate are computed using this code. The results are compared with the experimental data. Currently the VUMXZ3 code is being modified to accomplish step 4 of this project. Wind tunnel experiments are also being conducted for validation purposes.

Description: Three-dimensional viscous flow computations are presented for the F/A-18 forebody-LEX (Leading Edge EXtensions) geometry. Solutions are obtained from an algorithm for the compressible Navier-Stokes equations which incorporates an upwind-biased, flux-difference-splitting approach along with longitudinally-patched grids. Results are presented for both laminar and fully turbulent flow assumptions and include correlations with wind tunnel as well as flight-test results. A good quantitative agreement for the forebody surface pressure distribution is achieved between the turbulent computations and wind tunnel measurements at Mach number 0.6. The computed turbulent surface flow patterns on the forebody qualitatively agree well with in-flight surface flow patterns obtained on an F/A-18 aircraft at Mach number 0.34.

Description: Fine-grid Navier-Stokes solutions were obtained for flow over the fuselage forebody and wing leading edge extension of the F/A-18 High Alpha Research Vehicle at large incidence. The resulting flows are complex, and exhibit cross flow separation from the sides of the forebody and from the leading edge extension. A well-defined vortex pattern is observed in the leeward-side flow. Results obtained for laminar flow show good agreement with flow visualizations obtained in ground-based experiments. Further, turbulent flows computed at high Reynolds-number flight-test conditions show good agreement with surface and off-surface visualizations obtained in flight.

Description: The objective of the research is to develop and validate accurate, user-oriented viscous CFD codes (with inviscid options) for three-dimensional, unsteady aerodynamic flows about arbitrary rotorcraft configurations. Unsteady, three-dimensional Euler and Navier-Stokes codes are developed, adapted, and extended to rotor-body combinations. Flow solvers are coupled with zonal grid topologies, including rotating and nonrotating blocks. Special grid clustering and wave-fitting techniques were developed to capture low-level radiating acoustic waves. Significant progress was made in computing the propagation of acoustic waves due to the interaction of a concentrated vortex and a helicopter airfoil. The need for higher-order schemes was firmly established in relatively inexpensive two-dimensional calculations. In three dimensions, the number of grid points required to capture the low-level acoustic waves becomes very large, so that large supercomputer memory becomes essential. Good agreement was obtained between the numerical results obtained with a thin-layer Navier-Stokes code and experimental data from a model rotor. In addition, several nonrotating configurations that are sometimes proposed to simulate rotor blade tips in conventional wind tunnels were examined, and the complex flow around the radical tip shape of the world's fastest helicopter is under investigation. These studies demonstrate the flexibility and power of CFD to gain physical insight, study novel ideas, and examine various possibilities that might be difficult or impossible to set up in physical experiments. As a prelude to studies of rotor-body aerodynamic interactions, a preliminary grid topology and moving-interface strategy were developed. A new Euler/Navier-Stokes code using these techniques computes the vortical wake directly, rather than modeling it, as in most previous rotorcraft studies. Several hover cases were run for conventional and advanced-geometry blades. Numerical schemes using multi-zones and/or adaptive grids appear to be necessary to simulate the complex vortical flows in rotor wakes.

Description: The thin layer, Reynolds-averaged, Navier-Stokes equations are used to simulate the transonic viscous flow about the complete F-16A fighter aircraft. These computations demonstrate how computational fluid dynamics can be used to simulate turbulent viscous flow about realistic aircraft geometries. A zonal grid approach is used to provide adequate viscous grid clustering on all aircraft surfaces. Zonal grids extend inside the F-16A inlet and up to the compressor face while power on conditions are modeled by employing a zonal grid extending from the exhaust nozzle to the far field. Computations are compared with existing experimental data and are in fair agreement. Computations for the F-16A in side slip are also presented.

Description: Grid generation and Euler flow about fighter aircraft are described. A fighter aircraft geometry is specified by an area ruled fuselage with an internal duct, cranked delta wing or strake/wing combinations, canard and/or horizontal tail surfaces, and vertical tail surfaces. The initial step before grid generation and flow computation is the determination of a suitable grid topology. The external grid topology that has been applied is called a dual-block topology which is a patched C (exp 1) continuous multiple-block system where inner blocks cover the highly-swept part of a cranked wing or strake, rearward inner-part of the wing, and tail components. Outer-blocks cover the remainder of the fuselage, outer-part of the wing, canards and extend to the far field boundaries. The grid generation is based on transfinite interpolation with Lagrangian blending functions. This procedure has been applied to the Langley experimental fighter configuration and a modified F-18 configuration. Supersonic flow between Mach 1.3 and 2.5 and angles of attack between 0 degrees and 10 degrees have been computed with associated Euler solvers based on the finite-volume approach. When coupling geometric details such as boundary layer diverter regions, duct regions with inlets and outlets, or slots with the general external grid, imposing C (exp 1) continuity can be extremely tedious. The approach taken here is to patch blocks together at common interfaces where there is no grid continuity, but enforce conservation in the finite-volume solution. The key to this technique is how to obtain the information required for a conservative interface. The Ramshaw technique which automates the computation of proportional areas of two overlapping grids on a planar surface and is suitable for coding was used. Researchers generated internal duct grids for the Langley experimental fighter configuration independent of the external grid topology, with a conservative interface at the inlet and outlet.

Description: Information on time dependent incompressible Navier-Stokes equations is given in viewgraph form. Information is given on streamfunction equations for unsteady incompressible flow, the streamfunction algorithm for unsteady incompressible flow, and a multigrid solver for the laminar implicit equations.

Description: The purpose is to describe the development of unstructured grid methods which have several advantages when compared to methods which make use of structured grids. Unstructured grids, for example, easily allow the treatment of complex geometries, allow for general mesh movement for realistic motions and structural deformations of complete aircraft configurations which is important for aeroelastic analysis, and enable adaptive mesh refinement to more accurately resolve the physics of the flow. Steady Euler calculations for a supersonic fighter configuration to demonstrate the complex geometry capability; unsteady Euler calculations for the supersonic fighter undergoing harmonic oscillations in a complete-vehicle bending mode to demonstrate the general mesh movement capability; and vortex-dominated conical-flow calculations for highly-swept delta wings to demonstrate the adaptive mesh refinement capability are discussed. The basic solution algorithm is a multi-stage Runge-Kutta time-stepping scheme with a finite-volume spatial discretization based on an unstructured grid of triangles in 2D or tetrahedra in 3D. The moving mesh capability is a general procedure which models each edge of each triangle (2D) or tetrahedra (3D) with a spring. The resulting static equilibrium equations which result from a summation of forces are then used to move the mesh to allow it to continuously conform to the instantaneous position or shape of the aircraft. The adaptive mesh refinement procedure enriches the unstructured mesh locally to more accurately resolve the vortical flow features. These capabilities are described in detail along with representative results which demonstrate several advantages of unstructured grid methods. The applicability of the unstructured grid methodology to steady and unsteady aerodynamic problems and directions for future work are discussed.

Description: SAGE is a user-friendly, highly efficient, two-dimensional self-adaptive grid code based on Nakahashi and Deiwert's variational principles method. Grid points are redistributed into regions of high flowfield gradients while maintaining smoothness and orthogonality of the grid. Efficiency is obtained by splitting the adaption into 2 directions and applying one-sided torsion control, thus producing a 1-D elliptic system that can be solved as a set of tridiagonal equations.

Description: Strong interactions of structures and fluids are common in many engineering environments. Such interactions can give rise to physically important phenomena such as those occurring for aircraft due to aeroelasticity. Aeroelasticity can significantly influence the safe performance of aircraft. At present exact methods are available for making aeroelastic computations when flows are in either the linear subsonic or supersonic range. However, for complex flows containing shock waves, vortices and flow separations, computational methods are still under development. Several phenomena that can be dangerous and limit the performance of an aircraft occur due to the interaction of these complex flows with flexible aircraft components such as wings. For example, aircraft with highly swept wings experience vortex induced aeroelastic oscillations. Correct understanding of these complex aeroelastic phenomena requires direct coupling of fluids and structural equations. Here, a summary is presented of the development of such coupled methods and applications to aeroelasticity since about 1978 to present. The successful use of the transonic small perturbation theory (TSP) coupled with structures is discussed. This served as a major stepping stone for the current stage of aeroelasticity using computational fluid dynamics. The need for the use of more exact Euler/Navier-Stokes (ENS) equations for aeroelastic problems is explained. The current development of unsteady aerodynamic and aeroelastic procedures based on the ENS equations are discussed. Aeroelastic results computed using both TSP and ENS equations are discussed.

Description: A thin-layer Navier-Stokes has been developed for solving high Reynolds number, turbulent flows past aircraft components under transonic flow conditions. The computer code has been validated through data comparisons for flow past isolated wings, wing-body configurations, prolate spheroids and wings mounted inside wind-tunnels. The basic code employs an explicit Runge-Kutta time-stepping scheme to obtain steady state solution to the unsteady governing equations. Significant gain in the efficiency of the code has been obtained by implementing a multigrid acceleration technique to achieve steady-state solutions. The improved efficiency of the code has made it feasible to conduct grid-refinement and turbulence model studies in a reasonable amount of computer time. The non-equilibrium turbulence model of Johnson and King has been extended to three-dimensional flows and excellent agreement with pressure data has been obtained for transonic separated flow over a transport type of wing.

Description: The INS3D family of computational fluid dynamics computer codes is presented. These codes are used to as tools in developing and assessing algorithms for solving the incompressible Navier-Stokes equations for steady-state and unsteady flow problems. This work involves applying the codes to real-world problems involving complex three-dimensional geometries. The algorithms utilized include the method of pseudocompressibility including both central and upwind differencing, several types of artificial dissipation schemes, approximate factorization, and an implicit line-relaxation scheme. These codes have been validated using a wide range of problems including flow over a backward-facing step, driven cavity flow, flow through various types of ducts, and steady and unsteady flow over a circular cylinder. Many diverse flow applications have been solved using these codes including parts of the Space Shuttle Main Engine, problems in naval hydrodynamics, low-speed aerodynamics, and biomedical fluid flows. The presentation details several of these, including the flow through a Space Shuttle Main Engine inducer, vortex shedding behind a circular cylinder, and flow through an artificial heart.

Description: Significant improvements in predictive accuracies for off-design conditions are achievable through better turbulence modeling; and, without necessarily adding any significant complication to the numerics. One well established fact about turbulence is it is slow to respond to changes in the mean strain field. With the 'equilibrium' algebraic turbulence models no attempt is made to model this characteristic and as a consequence these turbulence models exaggerate the turbulent boundary layer's ability to produce turbulent Reynolds shear stresses in regions of adverse pressure gradient. As a consequence, too little momentum loss within the boundary layer is predicted in the region of the shock wave and along the aft part of the airfoil where the surface pressure undergoes further increases. Recently, a 'nonequilibrium' algebraic turbulence model was formulated which attempts to capture this important characteristic of turbulence. This 'nonequilibrium' algebraic model employs an ordinary differential equation to model the slow response of the turbulence to changes in local flow conditions. In its original form, there was some question as to whether this 'nonequilibrium' model performed as well as the 'equilibrium' models for weak interaction cases. However, this turbulence model has since been further improved wherein it now appears that this turbulence model performs at least as well as the 'equilibrium' models for weak interaction cases and for strong interaction cases represents a very significant improvement. The performance of this turbulence model relative to popular 'equilibrium' models is illustrated for three airfoil test cases of the 1987 AIAA Viscous Transonic Airfoil Workshop, Reno, Nevada. A form of this 'nonequilibrium' turbulence model is currently being applied to wing flows for which similar improvements in predictive accuracy are being realized.

Description: Presented here are several direct simulations of one 2-D second mode perturbation wave, superimposed upon a prescribed mean flow. Periodicity is assumed in the streamwise direction (Fourier) and the variables are expanded in Chebyshev series in the direction normal to the flat plate. The code is fully explicit and is time advanced with a 3rd order Runge-Kutta scheme. The second mode wave (R delta prime = 8000), interacts with itself to generate higher streamwise harmonics. Physical parameters are chosen to maximize the linear growth rate at the prescribed Reynolds number. Initial results indicate that the nonlinear processes begin in the critical layer region and are the result of the cubic interactions in the momentum equations, rather than due to the higher streamwise harmonics. Analysis of the various terms in the momentum equations combined with numerical experiments in which various modes are artificially suppressed, lead to the conclusion that asymptotic methods will produce the saturated state in one or two order of magnitude less computer time than that required by the direct numerical simulations.

Description: Direct simulations consist in solving the full Navier-Stokes equations, without any turbulence model, and describing all the detailed features of the flow. Usually the flows are three-dimensional and time-dependent and contain both coarse and fine structures, which makes the numerical task very challenging in terms of both the algorithm and the computational effort. Most of the work until now has involved spectral methods, which are highly accurate but not very flexible in terms of geometry or complex equations. For that reason, future work will also rely on high-order finite-difference or other methods. Direct simulations complement experimental work, and both contribute to the theory and the empirical knowledge of turbulence. Once such a simulation has been shown to be accurate, the flow field is completely known in three dimensions and time, including the pressure, the vorticity and any other quantity. On the other hand, most simulations to date solved the incompressible equations in rather simple geometries, and direct simulations will always be limited to moderate Reynolds numbers. Extensive simulations have been conducted in homogeneous turbulence, channel flows, boundary layers, and mixing layers. Much effort is devoted to addressing flows with compressibility and chemical reactions, and to new geometries such as a backward-facing step.

Description: Recent applications and development of CFD technology have focused on flow problems that are critically important to the operation and design of space flight vehicles. The main effort is spent on the Space Shuttle in order to provide an understanding of the cryogenic fluid in the duct connecting the External Tank and the Main Engines, the subsonic flow surrounding the Orbiter during crew egress maneuvers, the transonic aerodynamic forces on the Orbiter fuselage and wing, the high angle-of-attack abort flight, and the aerodynamic heating during entry. To provide in-depth analyses for such diverse problems within a timely schedule, matured panel codes and a state-of-the-art incompressible turbulent flow code were adapted. Collaboration with Ames Research Center has resulted in a Shuttle ascent aerodynamic code; and a viscous chemical nonequilibrium code is being developed for predicting Orbiter real-gas aerodynamics and finite-catalytic heating. The remaining activities are devoted to the prediction of the flow environment around the Aeroassist Flight Experiment vehicle at hypersonic speeds and high altitudes. A thermochemical nonequilibrium Navier-Stokes code has been developed on the basis of two- temperature and 11-species models for solving both the shock layer and near wake. After validating the code against wind-tunnel aerodynamic, pressure and heating data, the code is being used to supplement the ground test facilities in predicting a more realistic flight environment. CFD technology is being relied upon by other programs as well in the consideration of candidate configurations.

Description: Several direct simulations of 3-D homogeneous, compressible turbulence are presented with emphasis on the differences with incompressible turbulent simulations. A fully spectral collocation algorithm, periodic in all directions coupled with a 3rd order Runge-Kutta time discretization scheme is sufficient to produce well-resolved flows at Taylor Reynolds numbers below 40 on grids of 128x128x128. A Helmholtz decomposition of velocity is useful to differentiate between the purely compressible effects and those effects solely due to vorticity production. In the context of homogeneous flows, this decomposition in unique. Time-dependent energy and dissipation spectra of the compressible and solenoidal velocity components indicate the presence of localized small scale structures. These structures are strongly a function of the initial conditions. Researchers concentrate on a regime characterized by very small fluctuating Mach numbers Ma (on the order of 0.03) and density and temperature fluctuations much greater than sq Ma. This leads to a state in which more than 70 percent of the kinetic energy is contained in the so-called compressible component of the velocity. Furthermore, these conditions lead to the formation of curved weak shocks (or shocklets) which travel at approximately the sound speed across the physical domain. Various terms in the vorticity and divergence of velocity production equations are plotted versus time to gain some understanding of how small scales are actually formed. Possible links with Burger turbulence are examined. To visualize better the dynamics of the flow, new graphic visualization techniques have been developed. The 3-D structure of the shocks are visualized with the help of volume rendering algorithms developed in-house. A combination of stereographic projection and animation greatly increase the number of visual cues necessary to properly interpret the complex flow.

Description: Computational Fluid Dynamics (CFD) activities at Marshall Space Flight Center (MSFC) have been focused on hardware specific and research applications with strong emphasis upon benchmark validation. The purpose here is to provide insight into the MSFC CFD related goals, objectives, current hardware related CFD activities, propulsion CFD research efforts and validation program, future near-term CFD hardware related programs, and CFD expectations. The current hardware programs where CFD has been successfully applied are the Space Shuttle Main Engines (SSME), Alternate Turbopump Development (ATD), and Aeroassist Flight Experiment (AFE). For the future near-term CFD hardware related activities, plans are being developed that address the implementation of CFD into the early design stages of the Space Transportation Main Engine (STME), Space Transportation Booster Engine (STBE), and the Environmental Control and Life Support System (ECLSS) for the Space Station. Finally, CFD expectations in the design environment will be delineated.

Description: Lewis is a multidisciplinary Center with strong research and development programs in aeronautical and space propulsion, power, space communications, space experiments and materials. Computational fluid dynamics (CFD) is playing an important and growing role in most of these areas. Described here is how CFD is integrated into these programs and highlights elements of the CFD activities. Examples are presented of codes developed to predict flow fields in advanced propulsion systems and several of the code validation experiments are described. The CFD effort at Lewis ranges from basic research on new and improved algorithms through code development to the application of these codes to specific engineering problems. Because of the substantial improvement in CFD's predictive capability, its use at Lewis is on a steep growth path, spreading rapidly into new areas which had not traditionally taken advantage of the techniques of numerical simulation. Multidisciplinary codes and the future direction of CFD at Lewis are discussed.

Description: Information on computational fluid dynamics (CFD) research and applications carried out at the NASA Langley Research Center is given in viewgraph form. The Langley CFD strategy, the five-year plan in CFD and flow physics, 3-block grid topology, the effect of a patching algorithm, F-18 surface flow, entropy and vorticity effects that improve accuracy of unsteady transonic small disturbance theory, and the effects of reduced frequency on first harmonic components of unsteady pressures due to airfoil pitching are among the topics covered.

Description: The Computational Fluid Dynamics (CFD) Program at NASA Ames Research Center is reviewed and discussed. The technical elements of the CFD Program are listed and briefly discussed. These elements include algorithm research, research and pilot code development, scientific visualization, advanced surface representation, volume grid generation, and numerical optimization. Next, the discipline of CFD is briefly discussed and related to other areas of research at NASA Ames including experimental fluid dynamics, computer science research, computational chemistry, and numerical aerodynamic simulation. These areas combine with CFD to form a larger area of research, which might collectively be called computational technology. The ultimate goal of computational technology research at NASA Ames is to increase the physical understanding of the world in which we live, solve problems of national importance, and increase the technical capabilities of the aerospace community. Next, the major programs at NASA Ames that either use CFD technology or perform research in CFD are listed and discussed. Briefly, this list includes turbulent/transition physics and modeling, high-speed real gas flows, interdisciplinary research, turbomachinery demonstration computations, complete aircraft aerodynamics, rotorcraft applications, powered lift flows, high alpha flows, multiple body aerodynamics, and incompressible flow applications. Some of the individual problems actively being worked in each of these areas is listed to help define the breadth or extent of CFD involvement in each of these major programs. State-of-the-art examples of various CFD applications are presented to highlight most of these areas. The main emphasis of this portion of the presentation is on examples which will not otherwise be treated at this conference by the individual presentations. Finally, a list of principal current limitations and expected future directions is given.

Description: The present investigation has focused on a computational methodology for the fundamental case of transition in channel flow, in which recently published experimental data are utilized both as a stimulus and as a measure of merit of the method. The research has proceeded along three avenues in parallel. The first task has consisted of the development and verification of a computer code which calculates the mean evolution of flow in a channel similar to the one employed experimentally by Blair and Anderson. An analytical test case was created for the dual purposes of code verification and of highlighting the interactions between the Reynolds stress and the mean velocity profile. This test case generated a Reynolds stress by the residue in the momentum equation which is produced by a typical analytical velocity profile. By a substitution of this Reynolds stress into the appropriate code module, the correctness of the code may be verified, along with the accuracy of the computational method. The second task pursued has involved the development of a triple layer model for the Reynolds stress profile, which was suggested and derived from experimental velocity profiles. It is demonstrated that the innermost length scale is based on the local friction velocity, the intermediate layer corresponds to the usual logarithmic law of the wall region in which the normalized Reynolds stress is approximately unity, and the outermost layer is represented by a closed mathematical form depending explicitly on the velocity profile in the wake region. The third task was comprised of scrutiny of the excellent databases developed by Blair and others, and the planning of its incorporation into the transition analysis. These extensive measurements indicate that turbulent statistics in the transition regime may be considered to alternate between laminar and fully turbulent types, the proportions of which are quantified by a measured intermittency function.

Description: Numerous experimental studies were conducted on the steady, three-dimensional boundary layer over a disk rotating at constant angular speed in an otherwise undisturbed fluid. The subject flow geometry is of interest because it provides a relatively simple way to study the cross-flow instability phenomenon which occurs in three-dimensional boundary layers, as on swept wings. This flow instability results in the formation of a stationary spiral vortex flow field over the disk, as shown by Wilkinson and Malik. Using a hot-wire probe, the spatial wave pattern of stationary vortices, which filled the entire circumference of the disk was mapped. The subject flow instability caused transition-to-turbulent flow as the periphery of the disk was approached. The effect on receptivity and transition of discrete disturbance modes, such as three-dimensional toughness elements and acoustic excitation was investigated. The present study (an extension of the work of Wilkinson and Malik) is focused on the effect of pulsed point suction on flow instability and transition, and consequently, on the classical stationary vortical flow pattern.

Description: In 1978, the Russian mathematician V. Kharitonov published a remarkably simple necessary and sufficient condition in order that a rectangular parallelpiped of polynomials be a stable set. Here, stable is taken to mean that the polynomials have no roots in the closed right-half of the complex plane. The possibility of generalizing this result was studied by numerous authors. A set, Q, of polynomials is given and a necessary and sufficient condition that the set be stable is sought. Perhaps the most general result is due to Barmish who takes for Q a polytope and proceeds to construct a complicated nonlinear function, H, of the points in Q. With the notion of stability which was adopted, Barmish asks that the boundary of the closed right-half plane be swept, that the set G is considered = to (j(omega)(bar) - infinity is less than omega is less than infinity) and for each j(omega)(sigma)G, require H(delta) is greater than 0. Barmish's scheme has the merit that it describes a true generalization of Kharitonov's theorem. On the other hand, even when Q is a polyhedron, the definition of H requires that one do an optimization over the entire set of vertices, and then a subsequent optimization over an auxiliary parameter. In the present work, only the case where Q is a polyhedron is considered and the standard definition of stability described, is used. There are straightforward generalizations of the method to the case of discrete stability or to cases where certain root positions are deemed desirable. The cases where Q is non-polyhedral are less certain as candidates for the method. Essentially, a method of geometric programming was applied to the problem of finding maximum and minimum angular displacements of points in the Nyquist locus (Q(j x omega)(bar) - infinity is less than omega is less than infinity). There is an obvious connection with the boundary sweeping requirement of Barmish.

Description: Recently, NASA, FAA, and other organizations have focused their attention upon the possible effects of rain on airfoil performance. Rhode carried out early experiments and concluded that the rain impacting the aircraft increased the drag. Bergrum made numerical calculation for the rain effects on airfoils. Luers and Haines did an analytic investigation and found that heavy rain induces severe aerodynamic penalties including both a momentum penalty due to the impact of the rain and a drag and lift penalty due to rain roughening of the airfoil and fuselage. More recently, Hansman and Barsotti performed experiments and declared that performance degradation of an airfoil in heavy rain is due to the effective roughening of the surface by the water layer. Hansman and Craig did further experimental research at low Reynolds number. E. Dunham made a critical review for the potential influence of rain on airfoil performance. Dunham et al. carried out experiments for the transport type airfoil and concluded that there is a reduction of maximum lift capability with increase in drag. There is a scarcity of published literature in analytic research of two-phase boundary layer around an airfoil. Analytic research is being improved. The following assumptions are made: the fluid flow is non-steady, viscous, and incompressible; the airfoil is represented by a two-dimensional flat plate; and there is only a laminar boundary layer throughout the flow region. The boundary layer approximation is solved and discussed.

Description: An experimental simulation of an in-flight wingtip vortical flow visualization technique uses infrared imaging to observe strong and concentrated vortices. This experiment is phase 1 of a two-phase infrared evaluation program. The system includes a vortex generator (model 320 Vortec Vortex Tube) which generates the required vortex. The mouth of the unit is mounted close to the free end of a half-inch diameter, sixteen and a half foot long stainless steel tubing (sized after tubing currently installed in the wings of an experimental Beechcraft Sundowner 180 aircraft). Dichloro difluoromethane (Freon-12) is entrained into the generated vortex. A breakdown of the vortices is indicated by the rapid diffusion and the resulting pattern is tracked using the infrared imager and video systems. Flow rates (volume and mass) are estimated at the laboratory and proposed flight conditions. The nominal flight altitude is expected to be 2500 feet.

Description: Researchers started their studies on the development and application of computational methods for compressible flows. Particular attention was given to proper numerical treatment of sharp layers occurring in such problems and to general mesh generation capabilities for intricate computational geometries. Mainly finite element methods enhanced with several state-of-the art techniques (such as the streamline-upwind/Petrov-Galerkin, discontinuity capturing, adaptive implicit-explicit, and trouped element-by-element approximate factorization schemes) were employed.

Description: A self-consistent derivation of the conservation laws is given for flows of a fluid-solid mixture. A unified analytical framework for obtaining constitutive relations is provided. This analysis uses a control volume/control surface approach that is widely used in fluid mechanics. All terms in the governing equations and the constitutive relations are written in terms of the mass-weighted averages except solid concentration. It is believed that the mass-weighted average is the natural bridge between micromechanics and constitutive relations. The derived momentum equations contain terms that differ from all existing models except that of Prosperetti and Jones (1984). However, their assumptions are not needed here. Special attention is given to the solid phase pressure. The physical basis of the previously assumed form for this pressure (Givler 1987) becomes clear. A number of related phenomena are also discussed. These include the anti-diffusion and anisotropic normal stresses. The energy equations are also different from existing models.

Description: A common airfoil model with the CAST 10-2/DOA-2 profile and 228 mm (9 inches) chord length was tested. The tests performed in NAE covered the Mach numbers from 0.3 to 0.8 and Reynolds numbers from 10 to 30 million. The model was tested with transition free and with transition fixed at 5 percent chord for both the upper and the lower surfaces. The data obtained were analyzed for the effects of Reynolds number, transition fixing and Mach number. The role of the boundary layer on the displacement effect, the interaction with the shock wave and the trailing edge separation are examined. The results are summarized as follows: (1) the airfoil performance depends strongly on Reynolds number and transition fixing; (2) with transition fixed, the aerodynamic quantities such as lift, pitching moment and drag show a monotonic variation with Reynolds number; (3) with transition free, the aerodynamic quantities vary less regularly with Reynolds number and a slight parametric dependency is shown. The weak dependency is due to the compensatory effect of the forward shift of the transition position and the thinning of the turbulent boundary layer as Reynolds number increases; (4) the shock Mach number and the shock position are weakly dependent on Reynolds number; and (5) the long extent of the laminar boundary layer at transonic speeds reduces the drag appreciably at low Reynolds numbers. The drag bucket around the design Mach number can be observed below Reynolds number 15 million.

Description: The aim of this cooperative NASA/DFVLR/ONERA project was to examine the performance of the CAST-10 airfoil in the T2 cryogenic wind tunnel. Tests included general characteristics of the CAST-10 airfoil and fundamental studies on Reynold number effects. Good T2 cryogenic operation was observed. Improvements should be done for moisture elimination and for side wall boundary layer effects.

Description: The development of missiles from early history up to about 1970 is discussed. Early unpowered missiles beyond the rock include the spear, the bow and arrow, the gun and bullet, and the cannon and projectile. Combining gunpowder with projectiles resulted in the first powered missiles. In the early 1900's, the development of guided missiles was begun. Significant advances in missile technology were made by German scientists during World War II. The dispersion of these advances to other countries following the war resulted in accelerating the development of guided missiles. In the late 1940's and early 1950's there was a proliferation in the development of missile systems in many countries. These developments were based primarily on experimental work and on relatively crude analytical techniques. Discussed here are some of the missile systems that were developed up to about 1970; some of the problems encountered; the development of an experimental data base for use with missiles; and early efforts to develop analytical methods applicable to missiles.

Description: Results of the simulation of the viscous flow past the CAST-10 airfoil were shown for different flow conditions. Since the experiments provide only surface pressures and force coefficients, the comparison to the numerical results relies on these. Good agreement of these results is found for the lower Mach number cases except for the shock position. As numerical experiments indicate, this seems to be due to the turbulent shock boundary layer interaction which is not correctly modelled by the algebraic turbulence model employed. For the lower Mach number case the influence of the transition location was investigated, too. Changing the transition location at the lower surface has much more influence on the pressure distribution than changing it on the upper side. For the higher Mach number case the double shock structure found in the experiment for the lower Reynolds numbers was not reproduced by the numerical solutions. The reason for this is unknown though it may be due to the turbulence modelling. For the higher Reynolds number a better resolution of the boundary layer is needed in the computation in order to recover the experimental pressure plateau; but then the shock position is still found downstream of the experimental one.

Description: Some features of two recent approaches of two-phase potential flow are presented. The first approach is based on a set of progressive examples that can be analyzed using common techniques, such as conservation laws, and taken together appear to lead in the direction of a general theory. The second approach is based on variational methods, a classical approach to conservative mechanical systems that has a respectable history of application to single phase flows. This latter approach, exemplified by several recent papers by Geurst, appears generally to be consistent with the former approach, at least in those cases for which it is possible to obtain comparable results. Each approach has a justifiable theoretical base and is self-consistent. Moreover, both approaches appear to give the right prediction for several well-defined situations.

Description: The main characteristics and the potential advantages of generalized drift flux models are presented. In particular it is stressed that the issue on the propagation properties and on the mathematical nature (hyperbolic or not) of the model and the problem of closure are easier to tackle than in two fluid models. The problem of identifying the differential void-drift closure law inherent to generalized drift flux models is then addressed. Such a void-drift closure, based on wave properties, is proposed for bubbly flows. It involves a drift relaxation time which is of the order of 0.25 s. It is observed that, although wave properties provide essential closure validity tests, they do not represent an easily usable source of quantitative information on the closure laws.

Description: Numerical techniques for solving the compressible Euler and Navier-Stokes equations are discussed with an emphasis on characteristic-based schemes. Two popular approaches, flux difference splitting and flux vector splitting, are described in one-dimensional Cartesian coordinates and then extended to three-dimensional generalized coordinates. A technique for increasing the spatial accuracy is presented, followed by a discussion of numerical dissipation mechanisms. An introduction to the use of implicit time integration schemes for accelerating the convergence rate to steady-state solutions including Newton's method, relaxation strategies, and approximate factorization techniques and their implementation on a vector processor concludes the chapter.