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At least 289 records · Page 16

An Analysis of the Corridor and Guidance Requirements for Supercircular Entry into Planetary Atmospheres

The analysis of super-circular entry is developed around a new dimensionless parameter which combines certain conditions at the conic perigee altitude with certain characteristics of the vehicle; this parameter conveniently determines either deceleration-limited or heating limited corridor widths for elliptic, parabolic, or hyperbolic approach trajectories. Illustrative calculations of corridor widths and the associated guidance problems are presented for Venus, Earth, Mars, Jupiter, and Titan. Generalized curves are presented for application to various entry conditions.

Chapman, Dean R.↗

Bowles-Tatnall Wake Vortex Encounter Hazard Metric

Wake vortex spacing standards constrict the terminal area throughput and impose severe constraints on the overall capacity and efficiency of the National Airspace System. For more than two decades starting in the early 1990s, the National Aeronautics and Space Administration conducted extensive research on characterizing the formation and evolution of aircraft wakes. This multidisciplinary work included comprehensive field experiments (Pruis et al. 2016), flight tests (Vicroy et al. 1998), and wind tunnel tests (Rossow 1994; Chow et al. 1997). Parametric studies using large eddy simulations (Proctor 1998; Proctor et al. 2006) were conducted in order to develop fast-time models for the prediction of wake transport and decay (Ahmad et al. 2016). Substantial effort was spent on the formulation of acceptable vortex hazard metrics (Tatnall 1995; Hinton and Tatnall 1997). Several wake encounter severity metrics have been suggested in the past, which include the wake circulation strength, vortex-induced rolling moment coefficient (Clv), bank angle, and the roll control ratio (Tatnall 1995; Hinton and Tatnall 1997; Van der Geest 2012). The vortex-induced rolling moment coefficient introduced by Bowles and Tatnall (Tatnall 1995; Gloudemans et al. 2016) has been used extensively for risk and safety analysis of newly proposed air traffic management concepts and procedures. The original method of Bowles and Tatnall assumed a constant wing loading (the wing lift-curve slope, CL is constant), which resulted in an overestimation of the vortexinduced rolling moment coefficient. Bowles (2014) suggested a correction to the original method that provides more accurate values of Clv and which is also consistent with the underlying physics of the problem. The overestimation of Clv in the original method can be corrected by assuming an elliptical lift distribution. Figure 1.1 illustrates the correction in Clv achieved by the modified method.

Joel Malissa↗

Hypersonic bodies of maximum drag for a given lift-to-drag ratio.

The problem considered in this paper is concerned with the aerodynamic design of the forebody shape of reentry vehicles in the blunt, homothetic, elliptic transversal contour, power-law longitudinal contour, raked-off configurational set. In particular, the forebody shape which maximizes the ratio of the forebody pressure drag to the free-stream dynamic pressure for a given lift-to-drag ratio and given geometric properties is determined. This problem is considered because recent survey articles indicate that its solution will provide useful qualitative design information about manned vehicles entering the earth's atmosphere from any of the foreseeable planetary missions. Single-integral equations relating the lift and drag in Newtonian hypersonic flow to the forebody geometry are derived and used to formulate the optimization problem which is solved by a direct numerical method.

Mcmillan, W., III↗

Numerical methods for systems of conservation laws of mixed type using flux splitting

The essentially non-oscillatory (ENO) finite difference scheme is applied to systems of conservation laws of mixed hyperbolic-elliptic type. A flux splitting, with the corresponding Jacobi matrices having real and positive/negative eigenvalues, is used. The hyperbolic ENO operator is applied separately. The scheme is numerically tested on the van der Waals equation in fluid dynamics. Convergence was observed with good resolution to weak solutions for various Riemann problems, which are then numerically checked to be admissible as the viscosity-capillarity limits. The interesting phenomena of the shrinking of elliptic regions if they are present in the initial conditions were also observed.

Shu, Chi-Wang↗

On the cost of approximating and recognizing a noise perturbed straight line or a quadratic curve segment in the plane

Approximation of noisy data in the plane by straight lines or elliptic or single-branch hyperbolic curve segments arises in pattern recognition, data compaction, and other problems. The efficient search for and approximation of data by such curves were examined. Recursive least-squares linear curve-fitting was used, and ellipses and hyperbolas are parameterized as quadratic functions in x and y. The error minimized by the algorithm is interpreted, and central processing unit (CPU) times for estimating parameters for fitting straight lines and quadratic curves were determined and compared. CPU time for data search was also determined for the case of straight line fitting. Quadratic curve fitting is shown to require about six times as much CPU time as does straight line fitting, and curves relating CPU time and fitting error were determined for straight line fitting. Results are derived on early sequential determination of whether or not the underlying curve is a straight line.

Cooper, D. B.↗

Meteoroid capture into earth orbit by atmospheric drag

A probabilistic analysis, based on orbital mechanics, is performed to evaluate the chances of meteoroids entering into earth orbit and the potential population of such objects. The problem is addressed in terms of meteoroids on earth collision courses, slowed by atmosphere entry/exit, entering elliptical orbits with apogees above the atmosphere. The overall capture probability is derived by integrating the capture fraction dependence on velocity and size over the probability frequency distribution of the collision courses. Account is taken of eventual orbit decay, lunar infall and ejection after encounters with the moon. The results indicate that the probability that a natural 10-100 m diam object has achieved earth orbit is negligibly small.

Friedlander, A. L.↗

A method for determining the camber and twist of a surface to support a given distribution of lift

A graphical method is described for finding the shape (camber and twist) of an airfoil having an arbitrary distribution of lift. The method consists in replacing the lifting surface and its wake with an equivalent arrangement of vortices and in finding the associated vertical velocities. By a division of the vortex pattern into circular strips concentric about the downwash point instead of into the usual rectangular strips, the lifting surface is reduced for each downwash point to an equivalent loaded line for which the induced velocity is readily computed. The ratio of the vertical velocity to the stream velocity is the slope of the surface in the free-stream direction. As an illustration, the shape of the wing consistent with the pressure distribution derived from the two-dimensional theories is found for two wings: a straight elliptical wing and one with 30 degree sweepback. Application of the method to solve the reverse problem - finding the lift distribution over a given surface - is briefly discussed.

Cohen, Doris↗

The prediction of noise radiation from supersonic elliptic jets

This paper describes the prediction of noise radiation from supersonic elliptic jets. The noise is associated with the large scale structures in the jet mixing layer. These structures are described as instability waves. The local characteristics of the instability waves are determined from a compressible, linear, analysis. The jet mean velocity and density are described in elliptic cylindrical coordinates. The local eigensolution for the instability waves is determined from a finite difference solution of the non-separable boundary value problem. This inner solution which is formulated in terms of the method of multiple scales is matched with the radiated field using the method of matched asymptotic expansions. The form of the far-field directivity is derived. Predictions are presented for the noise radiation by the several modes of instability in the elliptic jet. The radiated field is not axisymmetric and certain modes radiate strongly in the directions of the major and minor axes of the jet. The extension of the present work to other geometries and flow fields is discussed.

Morris, Philip J.↗

LOOPUS Mob-D: System concept for a public mobile satellite system providing integrated digital services for the Northern Hemisphere from an elliptical orbit

A new concept for a satellite based public mobile communications system, LOOPUS Mob-D, is introduced, whereby most of the classical problems in mobile satellite systems are approached in a different way. The LOOPUS system will offer a total capacity of 6000 high rate channels in three service areas (Europe, Asia, and North America), covering the entire Northern Hemisphere with a set of group special mobile (GSM) compatible mobile services, eventually providing the 'office in the car'. Special characteristics of the LOOPUS orbit and the communications network architecture are highlighted.

Kuhlen, H.↗

A solution of the variational equations for elliptic orbits in rotating coordinates

For elliptic reference orbits, formulas are given for the perturbation state transition matrix of the two-body problem. The formulas relate perturbations expressed in a local vertical rotating coordinate system and are valid for motion in the linear neighborhood of reference orbits with e in the range of 0 to 1. The elements of the state transition matrix are expressed in terms of natural parameters (horizontal and radial velocity, radius, eccentricity, true anomaly, etc.) at the initial and final points. In addition to the general form, a simplified version, valid for small eccentricity orbits, is given.

Jones, J. B.↗

Small Gas Turbine Combustor Primary Zone Study

The combustion research program, small gas turbine combustor primary zone study is summarized. The basic elements of a design methodology program to obtain the maximum performance potential of small reverse-flow annular combustors is described. Three preferred combustion design approaches for internal flame stabilization patterns were selected. Design features are incorporated in the combustors to address the performance limiting problem areas associated with smaller annular combustors. Performance is predicted by using a 3-D aerodynamic/chemical kinetic elliptic flow analysis, initially developed by Garrett Corporation for the USARTL. It is shown that the analytical flow field predictive models provide a useful design tool for understanding the combustion performance of a small reverse flow annular combustor.

Sullivan, R. E.↗

Fluid flow and heat convection studies for actively cooled airframes

The work done during the progress report period from May-October 1992 is summarized. The effect of wall thermal boundary conditions on flows over a step or rib when repeated rib roughness is used for heating augmentation is examined. In numerical investigations of various such laminar and turbulent flows, the local heat transfer coefficients on a forward-facing step or on a rib were found to be very sensitive to the wall thermal boundary condition. For the computation of constant property laminar flow, the wall thermal boundary conditions were either a uniform heat flux or a uniform temperature. Results (Nusselt number and isotherms) of the studies are included. The second part of the work consisted of using PHOENICS to solve the conjugate heat transfer problem of flow over a rib in channel. Finally, the algebraic stress model in the TEAM (Turbulent Elliptic Algorithm-Manchester) code was tested for jet impingement flow, but there needs to be an addition of the energy equation to the code.

Mills, A. F.↗

Canonical forms of multidimensional steady inviscid flows

Canonical forms and canonical variables for inviscid flow problems are derived. In these forms the components of the system governed by different types of operators (elliptic and hyperbolic) are separated. Both the incompressible and compressible cases are analyzed, and their similarities and differences are discussed. The canonical forms obtained are block upper triangular operator form in which the elliptic and non-elliptic parts reside in different blocks. The full nonlinear equations are treated without using any linearization process. This form enables a better analysis of the equations as well as better numerical treatment. These forms are the analog of the decomposition of the one dimensional Euler equations into characteristic directions and Riemann invariants.

Taasan, Shlomo↗

Investigation of a Technique for Measuring Dynamic Ground Effect in a Subsonic Wind Tunnel

To better understand the ground effect encountered by slender wing supersonic transport aircraft, a test was conducted at NASA Langley Research Center's 14 x 22 foot Subsonic Wind Tunnel in October, 1997. Emphasis was placed on improving the accuracy of the ground effect data by using a "dynamic" technique in which the model's vertical motion was varied automatically during wind-on testing. This report describes and evaluates different aspects of the dynamic method utilized for obtaining ground effect data in this test. The method for acquiring and processing time data from a dynamic ground effect wind tunnel test is outlined with details of the overall data acquisition system and software used for the data analysis. The removal of inertial loads due to sting motion and the support dynamics in the balance force and moment data measurements of the aerodynamic forces on the model is described. An evaluation of the results identifies problem areas providing recommendations for future experiments. Test results are validated by comparing test data for an elliptical wing planform with an Elliptical wing planform section with a NACA 0012 airfoil to results found in current literature. Major aerodynamic forces acting on the model in terms of lift curves for determining ground effect are presented. Comparisons of flight and wind tunnel data for the TU-144 are presented.

Graves, Sharon S.↗

Numerical Study of Multigrid Methods with Various Smoothers for the Elliptical Grid Generation Equations

A robust solver for the elliptic grid generation equations is sought via a numerical study. The system of PDEs is discretized with finite differences, and multigrid methods are applied to the resulting nonlinear algebraic equations. Multigrid iterations are compared with respect to the robustness and efficiency. Different smoothers are tried to improve the convergence of iterations. The methods are applied to four 2D grid generation problems over a wide range of grid distortions. The results of the study help to select smoothing schemes and the overall multigrid procedures for elliptic grid generation.

Golik, W. L.↗

A two-dimensional unsteady Euler-equation solver for flow regions with arbitrary boundaries

A new technique is described for solving supersonic fluid dynamic problems containing multiple regions of continuous flow, each bounded by a permeable or impermeable surface. Region boundaries are, in general, arbitrarily shaped and time dependent. Discretization of such a region for solution by conventional finite difference procedures is accomplished using an elliptic solver which alleviates the dependence on a particular base coordinate system. Multiple regions are coupled together through the boundary conditions. The technique has been applied to a variety of problems including the shock diffraction and pointed wedge with detached bow shock.

Hindman, R. G.↗

Two-Dimensional Unsteady Euler-Equation Solver for Arbitrarily Shaped Flow Regions

A new technique is described for solving supersonic fluid dynamics problems containing multiple regions of continuous flow, each bounded by a permeable or impermeable surface. Region boundaries are, in general, arbitrarily shaped and time dependent. Discretization of such a region for solution by conventional finite difference procedures is accomplished using an elliptic solver which alleviates the dependence on a particular base coordinate system. Multiple regions are coupled together through the boundary conditions. The technique has been applied to a variety of problems including a shock diffraction problem and supersonic flow over a pointed ogive.

Hindman, R. G.↗

Nonlinear aerodynamics and the design of wing tips

This contract began in April 1990 with studies on the effect of wingtip shape on induced drag. That work considered problems of determining induced drag from computational aerodynamic methods and examined effects of wake roll up on the induced drag of elliptical and crescent wings. The research contract was continued in April 1991 and again in April 1992 with scope augmented to include considerations other than induced drag. The idea was to develop methods for comparing wing tip shapes on the basis of their effects on total drag, structural weight, and high lift performance. To accomplish this, work was done to improve methods for multidisciplinary analysis and optimization of wings. This report describes results of research conducted from April 1992 through March 1993. The general objective was to improve an existing wing optimization method and apply the method to specific problems of interest. The method, while a valuable tool for wing tip design studies, can be applied to more general problems, and has been applied to some of these other problems during its development. Specific goals that were accomplished are listed below and are explained in more detail in attached reports: analysis methods were improved in the area of structural modeling; small improvements to the high lift model were made, and ideas were collected on how clean wing c(sub l(sub max)) should vary with sweep - these ideas should provide a guide for future examination of high lift with experiment or CFD; and a calculation for drag due to the loss of leading edge suction was added to the wing analysis.

Kroo, Ilan↗