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The conformal mapping sequence presented transforms the potential flow about a circle into that about an airfoil with an attached flap or spoiler. It is found that adequate versatility of the flap shape for a given airfoil can usually be obtained with the indicated functions, although other transformations would expand the variety of possible flap shapes.
The necessity of having nonflammable versions of potting and encapsulating compounds and conformal coatings for space vehicles is discussed. The formulation, EPOCAST 87517 A/B, was found to have the best balance of thermal, electrical, mechanical, physical, and chemical properties of those evaluated. The requirements which this formulation did not meet are listed, and other formulations which were evaluated are summarized. Recommendations for improving EPOCAST 87517 A/B are included.
The evaluation of steady, supersonic, three-dimensional inviscid flows is considered, taking into account the construction of suitable grids on the basis of a simple conformal mapping. A description is presented of an analytical mapping technique. The technique is illustrated with the aid of examples of mappings, involving nontrivial geometries. Attention is given to a wing-fuselage cross section, a FORTRAN program for the basic mapping, the coupling of mappings, and the equations of motion.
A structure of a circularly polarized, thin conformal, antenna array which may be mounted integrally with the skin of an aircraft employs microstrip elliptical elements and interconnecting feed lines spaced from a circuit ground plane by a thin dielectric layer. The feed lines are impedance matched to the elliptical antenna elements by selecting a proper feedpoint inside the periphery of the elliptical antenna elements. Diodes connected between the feed lines and the ground plane rectify the microwave power, and microstrip filters (low pass) connected in series with the feed lines provide dc current to a microstrip bus. Low impedance matching strips are included between the elliptical elements and the rectifying and filtering elements.
A 0.15 scale model of a proposed conformal variable-ramp inlet for the Multirole Fighter was tested from Mach 0.8 to 2.2 at a wide range of angles of attack and sideslip. Inlet ramp angle was varied to optimize ramp angle as a function of engine airflow, Mach number, angle of attack, and angle of sideslip. Several inlet configuration options were investigated to study their effects on inlet operation and to establish the final flight configuration. These variations were cowl sidewall cutback, cowl lip bluntness, boundary layer bleed, and first-ramp leading edge shape. Diagnostic and engine face instrumentation were used to evaluate inlet operation at various inlet stations and at the inlet/engine interface. Pressure recovery and stability of the inlet were satisfactory for the proposed application. On the basis of an engine stability audit of the worst-case instantaneous distortion patterns, no inlet/engine compatibility problems are expected for normal operations.
A fast algorithm was developed for accurately generating boundary conforming, three dimensional, consecutively refined, computational grids applicable to arbitrary axial turbomachinery geometry. The method is based on using a single analytic function to generate two dimensional grids on a number of coaxial axisymmetric surfaces positioned between the hub and the shroud. These grids are of the "O" type and are characterized by quasi-orthogonality, geometric periodicity, and an adequate resolution throughout the flowfield. Due to the built in additional nonorthogonal coordinate stretching and shearing, the grid lines leaving the trailing of the blade end at downstream infinity, thus simplifying the numerical treatment of the three dimensional trailing vortex sheet.
A numerical procedure to compute the conformal mapping of a given n-tuply connected region onto a region with any specified boundary shapes and with several possible normalizations is developed and implemented. Procedures for calculating translation and magnification parameters are given.
A fast algorithm was developed for accurately generating boundary-conforming, three-dimensional, consecutively refined computational grids applicable to arbitrary wing-body and axial turbomachinery geometries. The method is based on using an analytic function to generate two-dimensional grids on a number of coaxial axisymmetric surfaces positioned between the centerbody and the outer radial boundary. These grids are of the O-type and are characterized by quasi-orthogonality, geometric periodicity, and an adequate resolution throughout the flow field. Because the built-in nonorthogonal coordinate stretching and shearing cause the grid lines leaving the blade or wing trailing edge to end at downstream infinity, the numerical treatment of the three-dimensional trailing vortex sheets is simplified.
Aerodynamic characteristics obtained in a rotational flow environment, utilizing a rotary balance, are presented in plotted form for a 1/12 scale conformal fuel tank equipped F-15 airplane model. The configurations tested included in the buildup of airplane components and the basic airplane with various control deflections. Data are presented for all configurations without analysis for an angle of attack range of 8 to 90 deg, and clockwise and counterclockwise rotations covering an omega b/2V range from 0 to 0.4. Selected configurations are presented over an extended omega b/2V range from 0 to 0.9.
A fast computer program, GRID3C, was developed for accurately generating periodic, boundary conforming, three dimensional, consecutively refined computational grids applicable to realistic axial turbomachinery geometries. The method is based on using two functions to generate two dimensional grids on a number of coaxial axisymmetric surfaces positioned between the centerbody and the outer radial boundary. These boundary fitted grids are of the C type and are characterized by quasi-orthogonality and geometric periodicity. The built in nonorthogonal coordinate stretchings and shearings cause the grid clustering in the regions of interest. The stretching parameters are part of the input to GRID3C. In its present version GRID3C can generate and store a maximum of four consecutively refined three dimensional grids. The output grid coordinates can be calculated either in the Cartesian or in the cylindrical coordinate system.
The application of conforming mixed finite element methods to obtain approximate solutions of linearized Navier-Stokes equations is examined. Attention is given to the convergence rates of various finite element approximations of the pressure and the velocity field. The optimality of the convergence rates are addressed in terms of comparisons of the approximation convergence to a smooth solution in relation to the best approximation available for the finite element space used. Consideration is also devoted to techniques for efficient use of a Gaussian elimination algorithm to obtain a solution to a system of linear algebraic equations derived by finite element discretizations of linear partial differential equations.
A research study was initiated to systematically determine the impact of selected blade tip geometric parameters on aeroelasticity conformable rotor performance and loads characteristics. The model articulated rotors included baseline and torsionally soft blades with interchangeable tips. Seven blade tip designs were evaluated on the baseline rotor and three tip designs were tested on the torsionally soft blades. The designs incorporated a systematic variation in three geometric parameters: sweep, taper, and anhedral. The rotors were evaluated in the NASA Langley Transonic Dynamics Tunnel at several advance ratios, lift and propulsive force values, and tip Mach numbers. Based on the test results, tip parameter variations generated significant rotor performance and loads difference for both baseline and torsionally soft blades. Azimuthal variation of elastic twist generated by the tip parameters strongly correlated with rotor performance and loads, but the magnitude of advancing blade elastic twist did not correlate.
The structure, torsional potentials, vibrational spectra, and harmonic force fields for s-cis and s-trans isomers of methacryloyl fluoride are examined to understand the conformational properties of the molecules and their relationship to macroscopic polymer properties. The structure is found to be in good agreement with experiment. It is shown by calculations that the energy difference between the cis and the transisomers is less than 1 kcal/mol at both the split valence and the split valence polarized levels, with the trans form favored. Analysis of the torsional potentials indicates that a rigid rotor model provides a reasonable description of the motion of the COF group in the molecule. The torsional barrier to interconvert the s-trans to the s-cis form is found to be 7.0 kcal/mol. A fit of the data to a three-term Fourier series shows that it is possible to reproduce the experimentally derived barrier, even though a direct determination indicates that the barrier is higher.
During periods of extravehicular activity it is obviously important that communication and telemetry systems continue to function independently of the astronaut. A system of antennas must therefore be designed that will provide the necessary isotropic coverage using circular polarization over both the transmit and receive frequency bands. To avoid the inherent physical limitations to motion that would be incurred with any sort of protruding antenna, it is necessary that the radiator be essentially flush-mounted or conformable to the structure on which it is attached. Several individual antenna elements are needed for the desired coverage. Both the particular elements chosen and their location determine the ultimate radiation pattern of the overall system. For these reasons a two-fold research plan was undertaken. First, individual elements were investigated and designed. Then various mounting locations were considered and the radiation patterns were predicted taking into account the effects of the astronaut's backpack.
A method for computing a new body conforming grid at each time step of an unsteady flow calculation is presented. The method is based on a spring system analogy. It simply updates the grid from the previous time step, hence it requires that an initial grid be created using another method. The method is designed to be independent of the flow equations used, so it can be easily transferred between aerodynamic codes with the same type of initial grid (i.e., O-type). The initial development was done using an O-type grid. It was then extended to C-type grids which required only minor changes to the routine. Results are presented for both O-type and C-type grids. The quality of the updated grids were examined by observing their movement and the flow results they produced. The effect due to the shape of the prescribed grid lines for the O-type grids was examined for a NACA 0012 airfoil undergoing harmonic pitch. The time history of the pressure coefficients of this case was compared with the interpolation scheme and experimental data.
The complete, exact exterior solution for a static, spherically symmetric source in locally conformal invariant Weyl gravity is presented. The solution includes the familiar exterior Schwarzschild solution as a special case and contains an extra gravitational potential term which grows linearly with distance. The obtained solution provides a potential explanation for observed galactic rotation curves without the need for dark matter. The solution also has some interesting implications for cosmology.
Wind tunnel tests were conducted on monoplanar circular missile configurations with low-profile quadriform tail fins to provide an aerodynamic data base to study and evaluate air-launched missile candidates for efficient conformal carriage on supersonic-cruise-type aircraft. The tests were conducted at Mach numbers from 1.70 to 2.86 for a constant Reynolds number per foot of 2,000,000. Selected test results are presented to show the effects of tail-fin dihedral angle, wing longitudinal and vertical location, and nose-body strakes on the static longitudinal and lateral-directional aerodynamic stability and control characteristics.
The Euclidian Einstein equations with a cosmological constant and a conformally coupled scalar field are solved, taking the metric to be of the Robertson-Walker type. In the case Lambda = 0, solutions are found which represent a wormhole connecting two asymptotically flat Euclidian regions. In the case Lambda greater than 0, the solutions represent tunneling from a small Tolman-like universe to a large Robertson-Walker universe.