ALBERT

Description: The objective of the present investigation is to assess the effect of the spatial order of accuracy used for the evaluation of the inviscid fluxes on the resolution of higher order quantitites, such as velocity gradients. The viscous terms are computed as second-order accurate with central difference formulas, even though for the explicit part of the algorithm higher order approximations may be used. A viscous/inviscid method is used, and the outer part of the flowfield is computed with the inviscid flow equations. The viscous boundary-layer type flow region close to the body surface is computed with an algebraic eddy viscosity model. Results obtained with the conservative and nonconservative formulations and the viscous/inviscid approach are compared with available experimental data. The effect of grid refinement on the accuracy of the solution is also presented.

Description: The benefits of using a hypersonic waverider for spacecraft trajectory modification are presented. A waverider is a hypersonic vehicle specifically designed so that the undersurface bow shock is attached to the leading edge, which provides for the highest known lift-to-drag ratios achievable at high Mach number flight. Several viable space missions are suggested which could use such configurations for low-drag aero-assisted maneuvers in planetary atmospheres. It is shown that large changes in the spacecraft velocity vector can be accomplished with acceptably small losses in energy due to drag using a waverider aeroshell. The primary advantage of an aero-assist maneuver is suggested by comparison to a traditional gravity-assist trajectory. Some scaling laws are presented for comparing waveriders designed for different planetary atmospheres, and it is shown that the compositional differences between the terrestrial planets has a minimal impact on waverider design.

Description: ARC2D is a computational fluid dynamics program developed at the NASA Ames Research Center specifically for airfoil computations. The program uses implicit finite-difference techniques to solve two-dimensional Euler equations and thin layer Navier-Stokes equations. It is based on the Beam and Warming implicit approximate factorization algorithm in generalized coordinates. The methods are either time accurate or accelerated non-time accurate steady state schemes. The evolution of the solution through time is physically realistic; good solution accuracy is dependent on mesh spacing and boundary conditions. The mathematical development of ARC2D begins with the strong conservation law form of the two-dimensional Navier-Stokes equations in Cartesian coordinates, which admits shock capturing. The Navier-Stokes equations can be transformed from Cartesian coordinates to generalized curvilinear coordinates in a manner that permits one computational code to serve a wide variety of physical geometries and grid systems. ARC2D includes an algebraic mixing length model to approximate the effect of turbulence. In cases of high Reynolds number viscous flows, thin layer approximation can be applied. ARC2D allows for a variety of solutions to stability boundaries, such as those encountered in flows with shocks. The user has considerable flexibility in assigning geometry and developing grid patterns, as well as in assigning boundary conditions. However, the ARC2D model is most appropriate for attached and mildly separated boundary layers; no attempt is made to model wake regions and widely separated flows. The techniques have been successfully used for a variety of inviscid and viscous flowfield calculations. The Cray version of ARC2D is written in FORTRAN 77 for use on Cray series computers and requires approximately 5Mb memory. The program is fully vectorized. The tape includes variations for the COS and UNICOS operating systems. Also included is a sample routine for CONVEX computers to emulate Cray system time calls, which should be easy to modify for other machines as well. The standard distribution media for this version is a 9-track 1600 BPI ASCII Card Image format magnetic tape. The Cray version was developed in 1987. The IBM ES/3090 version is an IBM port of the Cray version. It is written in IBM VS FORTRAN and has the capability of executing in both vector and parallel modes on the MVS/XA operating system and in vector mode on the VM/XA operating system. Various options of the IBM VS FORTRAN compiler provide new features for the ES/3090 version, including 64-bit arithmetic and up to 2 GB of virtual addressability. The IBM ES/3090 version is available only as a 9-track, 1600 BPI IBM IEBCOPY format magnetic tape. The IBM ES/3090 version was developed in 1989. The DEC RISC ULTRIX version is a DEC port of the Cray version. It is written in FORTRAN 77 for RISC-based Digital Equipment platforms. The memory requirement is approximately 7Mb of main memory. It is available in UNIX tar format on TK50 tape cartridge. The port to DEC RISC ULTRIX was done in 1990. COS and UNICOS are trademarks and Cray is a registered trademark of Cray Research, Inc. IBM, ES/3090, VS FORTRAN, MVS/XA, and VM/XA are registered trademarks of International Business Machines. DEC and ULTRIX are registered trademarks of Digital Equipment Corporation.

Description: Panel method computer programs are software tools of moderate cost used for solving a wide range of engineering problems. The panel code PMARC_12 (Panel Method Ames Research Center, version 12) can compute the potential flow field around complex three-dimensional bodies such as complete aircraft models. PMARC_12 is a well-documented, highly structured code with an open architecture that facilitates modifications and the addition of new features. Adjustable arrays are used throughout the code, with dimensioning controlled by a set of parameter statements contained in an include file; thus, the size of the code (i.e. the number of panels that it can handle) can be changed very quickly. This allows the user to tailor PMARC_12 to specific problems and computer hardware constraints. In addition, PMARC_12 can be configured (through one of the parameter statements in the include file) so that the code's iterative matrix solver is run entirely in RAM, rather than reading a large matrix from disk at each iteration. This significantly increases the execution speed of the code, but it requires a large amount of RAM memory. PMARC_12 contains several advanced features, including internal flow modeling, a time-stepping wake model for simulating either steady or unsteady (including oscillatory) motions, a Trefftz plane induced drag computation, off-body and on-body streamline computations, and computation of boundary layer parameters using a two-dimensional integral boundary layer method along surface streamlines. In a panel method, the surface of the body over which the flow field is to be computed is represented by a set of panels. Singularities are distributed on the panels to perturb the flow field around the body surfaces. PMARC_12 uses constant strength source and doublet distributions over each panel, thus making it a low order panel method. Higher order panel methods allow the singularity strength to vary linearly or quadratically across each panel. Experience has shown that low order panel methods can provide nearly the same accuracy as higher order methods over a wide range of cases with significantly reduced computation times; hence, the low order formulation was adopted for PMARC_12. The flow problem is solved by modeling the body as a closed surface dividing space into two regions: the region external to the surface in which an unknown velocity potential exists representing the flow field of interest, and the region internal to the surface in which a known velocity potential (representing a fictitious flow) is prescribed as a boundary condition. Both velocity potentials are required to satisfy Laplace's equation. A surface integral equation for the unknown potential external to the surface can be written by applying Green's Theorem to the external region. Using the internal potential and zero flow through the surface as boundary conditions, the unknown potential external to the surface can be solved for. When the internal flow option, which allows the analysis of closed ducts, wind tunnels, and similar internal flow problems, is selected, the geometry is modeled such that the flow field of interest is inside the geometry and the fictitious flow is outside the geometry. Items such as wings, struts, or aircraft models can be included in the internal flow problem. The time-stepping wake model gives PMARC_12 the ability to model both steady and unsteady flow problems. The wake is convected downstream from the wake-separation line by the local velocity field. With each time step, a new row of wake panels is added to the wake at the wake-separation line. Time stepping can start from time t=0 (no initial wake) or from time t=t0 (an initial wake is specified). A wide range of motions can be prescribed, including constant rates of translation, constant rate of rotation about an arbitrary axis, oscillatory translation, and oscillatory rotation about any of the three coordinate axes. Investigators interested in a visual representation of the phenomenon they are studying with PMARC_12 may want to consider obtaining the program GVS (ARC-13361), the General Visualization System. GVS is a Silicon Graphics IRIS program which was created for the purpose of supporting the scientific visualization needs of PMARC_12. GVS is available separately from COSMIC. PMARC_12 is written in standard FORTRAN 77, with the exception of the NAMELIST extension used for input. This makes the code fairly machine independent. A compiler which supports the NAMELIST extension is required. The amount of free disk space and RAM memory required for PMARC_12 will vary depending on how the code is dimensioned using the parameter statements in the include file. The recommended minimum requirements are 20Mb of free disk space and 4Mb of RAM. PMARC_12 has been successfully implemented on a Macintosh II running System 6.0.7 or 7.0 (using MPW/Language Systems Fortran 3.0), a Sun SLC running SunOS 4.1.1, an HP 720 running HP-UX 8.07, an SGI IRIS running IRIX 4.0 (it will not run under IRIX 3.x.x without modifications), an IBM RS/6000 running AIX, a DECstation 3100 running ULTRIX, and a CRAY-YMP running UNICOS 6.0 or later. Due to its memory requirements, this program does not readily lend itself to implementation on MS-DOS based machines. The standard distribution medium for PMARC_12 is a set of three 3.5 inch 800K Macintosh format diskettes and one 3.5 inch 1.44Mb Macintosh format diskette which contains an electronic copy of the documentation in MS Word 5.0 format for the Macintosh. Alternate distribution media and formats are available upon request, but these will not include the electronic version of the document. No executables are included on the distribution media. This program is an update to PMARC version 11, which was released in 1989. PMARC_12 was released in 1993. It is available only for use by United States citizens.

Description: This program determines the supersonic flowfield surrounding three-dimensional wing-body configurations of a delta wing. It was designed to provide the numerical computation of three dimensional inviscid, flowfields of either perfect or real gases about supersonic or hypersonic airplanes. The governing equations in conservation law form are solved by a finite difference method using a second order noncentered algorithm between the body and the outermost shock wave, which is treated as a sharp discontinuity. Secondary shocks which form between these boundaries are captured automatically. The flowfield between the body and outermost shock is treated in a shock capturing fashion and therefore allows for the correct formation of secondary internal shocks . The program operates in batch mode, is in CDC update format, has been implemented on the CDC 7600, and requires more than 140K (octal) word locations.

Description: This theoretical aerodynamics program, TAD, was developed to predict the aerodynamic characteristics of vehicles with sounding rocket configurations. These slender, axisymmetric finned vehicle configurations have a wide range of aeronautical applications from rockets to high speed armament. Over a given range of Mach numbers, TAD will compute the normal force coefficient derivative, the center-of-pressure, the roll forcing moment coefficient derivative, the roll damping moment coefficient derivative, and the pitch damping moment coefficient derivative of a sounding rocket configured vehicle. The vehicle may consist of a sharp pointed nose of cone or tangent ogive shape, up to nine other body divisions of conical shoulder, conical boattail, or circular cylinder shape, and fins of trapezoid planform shape with constant cross section and either three or four fins per fin set. The characteristics computed by TAD have been shown to be accurate to within ten percent of experimental data in the supersonic region. The TAD program calculates the characteristics of separate portions of the vehicle, calculates the interference between separate portions of the vehicle, and then combines the results to form a total vehicle solution. Also, TAD can be used to calculate the characteristics of the body or fins separately as an aid in the design process. Input to the TAD program consists of simple descriptions of the body and fin geometries and the Mach range of interest. Output includes the aerodynamic characteristics of the total vehicle, or user-selected portions, at specified points over the mach range. The TAD program is written in FORTRAN IV for batch execution and has been implemented on an IBM 360 computer with a central memory requirement of approximately 123K of 8 bit bytes. The TAD program was originally developed in 1967 and last updated in 1972.

Description: This program, which is called 'AOFA', determines the complete viscous and inviscid flow around a body of revolution at a given angle of attack and traveling at supersonic speeds. The viscous calculations from this program agree with experimental values for surface and pitot pressures and with surface heating rates. At high speeds, lee-side flows are important because the local heating is difficult to correlate and because the shed vortices can interact with vehicle components such as a canopy or a vertical tail. This program should find application in the design analysis of any high speed vehicle. Lee-side flows are difficult to calculate because thin-boundary-layer theory is not applicable and the concept of matching inviscid and viscous flow is questionable. This program uses the parabolic approximation to the compressible Navier-Stokes equations and solves for the complete inviscid and viscous regions of flow, including the pressure. The parabolic approximation results from the assumption that the stress derivatives in the streamwise direction are small in comparison with derivatives in the normal and circumferential directions. This assumption permits the equation to be solved by an implicit finite difference marching technique which proceeds downstream from the initial data point, provided the inviscid portion of flow is supersonic. The viscous cross-flow separation is also determined as part of the solution. To use this method it is necessary to first determine an initial data point in a region where the inviscid portion of the flow is supersonic. Input to this program consists of two parts. Problem description is conveyed to the program by namelist input. Initial data is acquired by the program as formatted data. Because of the large amount of run time this program can consume the program includes a restart capability. Output is in printed format and magnetic tape for further processing. This program is written in FORTRAN IV and has been implemented on a CDC 7600 with a central memory requirement of approximately 35K (octal) of 60 bit words.

Description: The Comprehensive Analytical Model of Rotorcraft Aerodynamics, CAMRAD, program is designed to calculate rotor performance, loads, and noise; helicopter vibration and gust response; flight dynamics and handling qualities; and system aeroelastic stability. The analysis is a consistent combination of structural, inertial, and aerodynamic models applicable to a wide range of problems and a wide class of vehicles. The CAMRAD analysis can be applied to articulated, hingeless, gimballed, and teetering rotors with an arbitrary number of blades. The rotor degrees of freedom included are blade/flap bending, rigid pitch and elastic torsion, and optionally gimbal or teeter motion. General two-rotor aircrafts can be modeled. Single main-rotor and tandem helicopter and sideby-side tilting proprotor aircraft configurations can be considered. The case of a rotor or helicopter in a wind tunnel can also be modeled. The aircraft degrees of freedom included are the six rigid body motion, elastic airframe motions, and the rotor/engine speed perturbations. CAMRAD calculates the load and motion of helicopters and airframes in two stages. First the trim solution is obtained; then the flutter, flight dynamics, and/or transient behavior can be calculated. The trim operating conditions considered include level flight, steady climb or descent, and steady turns. The analysis of the rotor includes nonlinear inertial and aerodynamic models, applicable to large blade angles and a high inflow ratio, The rotor aerodynamic model is based on two-dimensional steady airfoil characteristics with corrections for three-dimensional and unsteady flow effects, including a dynamic stall model. In the flutter analysis, the matrices are constructed that describe the linear differential equations of motion, and the equations are analyzed. In the flight dynamics analysis, the stability derivatives are calculated and the matrices are constructed that describe the linear differential equations of motion. These equations are analyzed. In the transient analysis, the rigid body equations of motion are numerically integrated, for a prescribed transient gust or control input. The CAMRAD program product is available by license for a period of ten years to domestic U.S. licensees. The licensed program product includes the CAMRAD source code, command procedures, sample applications, and one set of supporting documentation. Copies of the documentation may be purchased separately at the price indicated below. CAMRAD is written in FORTRAN 77 for the DEC VAX under VMS 4.6 with a recommended core memory of 4.04 megabytes. The DISSPLA package is necessary for graphical output. CAMRAD was developed in 1980.

Description: ARC2D is a computational fluid dynamics program developed at the NASA Ames Research Center specifically for airfoil computations. The program uses implicit finite-difference techniques to solve two-dimensional Euler equations and thin layer Navier-Stokes equations. It is based on the Beam and Warming implicit approximate factorization algorithm in generalized coordinates. The methods are either time accurate or accelerated non-time accurate steady state schemes. The evolution of the solution through time is physically realistic; good solution accuracy is dependent on mesh spacing and boundary conditions. The mathematical development of ARC2D begins with the strong conservation law form of the two-dimensional Navier-Stokes equations in Cartesian coordinates, which admits shock capturing. The Navier-Stokes equations can be transformed from Cartesian coordinates to generalized curvilinear coordinates in a manner that permits one computational code to serve a wide variety of physical geometries and grid systems. ARC2D includes an algebraic mixing length model to approximate the effect of turbulence. In cases of high Reynolds number viscous flows, thin layer approximation can be applied. ARC2D allows for a variety of solutions to stability boundaries, such as those encountered in flows with shocks. The user has considerable flexibility in assigning geometry and developing grid patterns, as well as in assigning boundary conditions. However, the ARC2D model is most appropriate for attached and mildly separated boundary layers; no attempt is made to model wake regions and widely separated flows. The techniques have been successfully used for a variety of inviscid and viscous flowfield calculations. The Cray version of ARC2D is written in FORTRAN 77 for use on Cray series computers and requires approximately 5Mb memory. The program is fully vectorized. The tape includes variations for the COS and UNICOS operating systems. Also included is a sample routine for CONVEX computers to emulate Cray system time calls, which should be easy to modify for other machines as well. The standard distribution media for this version is a 9-track 1600 BPI ASCII Card Image format magnetic tape. The Cray version was developed in 1987. The IBM ES/3090 version is an IBM port of the Cray version. It is written in IBM VS FORTRAN and has the capability of executing in both vector and parallel modes on the MVS/XA operating system and in vector mode on the VM/XA operating system. Various options of the IBM VS FORTRAN compiler provide new features for the ES/3090 version, including 64-bit arithmetic and up to 2 GB of virtual addressability. The IBM ES/3090 version is available only as a 9-track, 1600 BPI IBM IEBCOPY format magnetic tape. The IBM ES/3090 version was developed in 1989. The DEC RISC ULTRIX version is a DEC port of the Cray version. It is written in FORTRAN 77 for RISC-based Digital Equipment platforms. The memory requirement is approximately 7Mb of main memory. It is available in UNIX tar format on TK50 tape cartridge. The port to DEC RISC ULTRIX was done in 1990. COS and UNICOS are trademarks and Cray is a registered trademark of Cray Research, Inc. IBM, ES/3090, VS FORTRAN, MVS/XA, and VM/XA are registered trademarks of International Business Machines. DEC and ULTRIX are registered trademarks of Digital Equipment Corporation.

Description: Panel methods are moderate cost tools for solving a wide range of engineering problems. PMARC (Panel Method Ames Research Center) is a potential flow panel code that numerically predicts flow fields around complex three-dimensional geometries. PMARC's predecessor was a panel code named VSAERO which was developed for NASA by Analytical Methods, Inc. PMARC is a new program with many additional subroutines and a well-documented code suitable for powered-lift aerodynamic predictions. The program's open architecture facilitates modifications or additions of new features. Another improvement is the adjustable size code which allows for an optimum match between the computer hardware available to the user and the size of the problem being solved. PMARC can be resized (the maximum number of panels can be changed) in a matter of minutes. Several other state-of-the-art PMARC features include internal flow modeling for ducts and wind tunnel test sections, simple jet plume modeling essential for the analysis and design of powered-lift aircraft, and a time-stepping wake model which allows the study of both steady and unsteady motions. PMARC is a low-order panel method, which means the singularities are distributed with constant strength over each panel. In many cases low-order methods can provide nearly the same accuracy as higher order methods (where the singularities are allowed to vary linearly or quadratically over each panel). Low-order methods have the advantage of a shorter computation time and do not require exact matching between panels. The flow problem is solved by assuming that the body is at rest in a moving flow field. The body is modeled as a closed surface which divides space into two regions -- one region contains the flow field of interest and the other contains a fictitious flow. External flow problems, such as a wing in a uniform stream, have the external region as the flow field of interest and the internal flow as the fictitious flow. This arrangement is reversed for internal flow problems where the internal region contains the flow field of interest and the external flow field is fictitious. In either case it is assumed that the velocity potentials in both regions satisfy Laplace's equation. PMARC has extensive geometry modeling capabilities for handling complex, three-dimensional surfaces. As with all panel methods, the geometry must be modeled by a set of panels. For convenience, the geometry is usually subdivided into several pieces and modeled with sets of panels called patches. A patch may be folded over on itself so that opposing sides of the patch form a common line. For example, wings are normally modeled with a folded patch to form the trailing edge of the wing. PMARC also has the capability to automatically generate a closing tip patch. In the case of a wing, a tip patch could be generated to close off the wing's third side. PMARC has a simple jet model for simulating a jet plume in a crossflow. The jet plume shape, trajectory, and entrainment velocities are computed using the Adler/Baron jet in crossflow code. This information is then passed back to PMARC. The wake model in PMARC is a time-stepping wake model. The wake is convected downstream from the wake separation line by the local velocity flowfield. With each time step, a new row of wake panels is added to the wake at the wake separation line. PMARC also allows an initial wake to be specified if desired, or, as a third option, no wakes need be modeled. The effective presentation of results for aerodynamics problems requires the generation of report-quality graphics. PMAPP (ARC-12751), the Panel Method Aerodynamic Plotting Program, (Sterling Software), was written for scientists at NASA's Ames Research Center to plot the aerodynamic analysis results (flow data) from PMARC. PMAPP is an interactive, color-capable graphics program for the DEC VAX or MicroVAX running VMS. It was designed to work with a variety of terminal types and hardcopy devices. PMAPP is available separately from COSMIC. PMARC was written in standard FORTRAN77 using adjustable size arrays throughout the code. Redimensioning PMARC will change the amount of disk space and memory the code requires to be able to run; however, due to its memory requirements, this program does not readily lend itself to implementation on MS-DOS based machines. The program was implemented on an Apple Macintosh (using 2.5 MB of memory) and tested on a VAX/VMS computer. The program is available on a 3.5 inch Macintosh format diskette (standard media) or in VAX BACKUP format on TK50 tape cartridge or 9-track magnetic tape. PMARC was developed in 1989.