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At least 109 records · Page 6

Dynamic characteristics of a hydrostatic gas bearing driven by oscillating exhaust pressure

Vibration of a statically loaded, inherently compensated hydrostatic journal bearing due to oscillating exhaust pressure is investigated. Both angular and radial vibration modes are analyzed. The time-dependent Reynolds equation governing the pressure distribution between the oscillating journal and sleeve is solved together with the journal equation of motion to obtain the response characteristics of the bearing. The Reynolds equation and the equation of motion are simplified by applying regular perturbation theory for small displacements. The numerical solutions of the perturbation equations are obtained by discretizing the pressure field using finite-difference aproximations with a discrete, nonuniform line-source model which excludes effects due to feeding hole volume. An iterative scheme is used to simultaneously satisfy the equations of motion for the journal. The results presented include Bode plots of bearing-oscillation gain and phase for a particular bearing configuration for various combinations of parameters over a range of frequencies, including the resonant frequency.

Watkins, C. B.↗

On the Lagrangian description of unsteady boundary layer separation. Part 1: General theory

Although unsteady, high-Reynolds number, laminar boundary layers have conventionally been studied in terms of Eulerian coordinates, a Lagrangian approach may have significant analytical and computational advantages. In Lagrangian coordinates the classical boundary layer equations decouple into a momentum equation for the motion parallel to the boundary, and a hyperbolic continuity equation (essentially a conserved Jacobian) for the motion normal to the boundary. The momentum equations, plus the energy equation if the flow is compressible, can be solved independently of the continuity equation. Unsteady separation occurs when the continuity equation becomes singular as a result of touching characteristics, the condition for which can be expressed in terms of the solution of the momentum equations. The solutions to the momentum and energy equations remain regular. Asymptotic structures for a number of unsteady 3-D separating flows follow and depend on the symmetry properties of the flow. In the absence of any symmetry, the singularity structure just prior to separation is found to be quasi 2-D with a displacement thickness in the form of a crescent shaped ridge. Physically the singularities can be understood in terms of the behavior of a fluid element inside the boundary layer which contracts in a direction parallel to the boundary and expands normal to it, thus forcing the fluid above it to be ejected from the boundary layer.

Vandommelen, Leon L.↗

On the Lagrangian description of unsteady boundary-layer separation. I - General theory

Although unsteady, high-Reynolds number, laminar boundary layers have conventionally been studied in terms of Eulerian coordinates, a Lagrangian approach may have significant analytical and computational advantages. In Lagrangian coordinates the classical boundary layer equations decouple into a momentum equation for the motion parallel to the boundary, and a hyperbolic continuity equation (essentially a conserved Jacobian) for the motion normal to the boundary. The momentum equations, plus the energy equation if the flow is compressible, can be solved independently of the continuity equation. Unsteady separation occurs when the continuity equation becomes singular as a result of touching characteristics, the condition for which can be expressed in terms of the solution of the momentum equations. The solutions to the momentum and energy equations remain regular. Asymptotic structures for a number of unsteady 3-D separating flows follow and depend on the symmetry properties of the flow. In the absence of any symmetry, the singularity structure just prior to separation is found to be quasi 2-D with a displacement thickness in the form of a crescent shaped ridge. Physically the singularities can be understood in terms of the behavior of a fluid element inside the boundary layer which contracts in a direction parallel to the boundary and expands normal to it, thus forcing the fluid above it to be ejected from the boundary layer.

Van Dommelen, Leon L.↗

Matched asymptotic expansion of the Hamilton-Jacobi-Bellman equation for aeroassisted plane-change maneuvers

In this paper we develop a general procedure for constructing a matched asymptotic expansion of the Hamilton-Jacobi-Bellman equation based on the method of characteristics. The development is for a class of perturbation problems whose solution exhibits two-time-scale behavior. A regular expansion for problems of this type is inappropriate since it is not uniformly valid over a narrow range of the independent variable. Of particular interest here is the manner in which matching and boundary conditions are enforced when the expansion is carried out to first order. Two cases are distinguished - one where the left boundary condition coincides with or lies to the right of the singular region and one where the left boundary condition lies to the left of the singular region. A simple example is used to illustrate the procedure, and its potential application to aeroassisted plane change is described.

Calise, Anthony J.↗

Massively Parallel Algorithms for Real-Time Wavefront Control of a Dense Adaptive Optics System

In this paper massively parallel algorithms and architectures for real-time wavefront control of a dense adaptive optic system (SELENE) are presented. We have already shown that the computation of a near optimal control algorithm for SELENE can be reduced to the solution of a discrete Poisson equation on a regular domain. Although this represents an optimal computation, due the large size of the system and the high sampling rate requirement, the implementation of this control algorithm poses a computationally challenging problem since it demands a sustained computational throughput of the order of 10 GFlops. We develop a novel algorithm, designated as Fast Invariant Imbedding algorithm, which offers a massive degree of parallelism with simple communication and synchronization requirements. Due to these features, our algorithm is significantly more efficient than other Fast Poisson Solvers for implementation on massively parallel architectures.

massively↗

An inverse method with regularity condition for transonic airfoil design

It is known from Lighthill's exact solution of the incompressible inverse problem that in the inverse design problem, the surface pressure distribution and the free stream speed cannot both be prescribed independently. This implies the existence of a constraint on the prescribed pressure distribution. The same constraint exists at compressible speeds. Presented here is an inverse design method for transonic airfoils. In this method, the target pressure distribution contains a free parameter that is adjusted during the computation to satisfy the regularity condition. Some design results are presented in order to demonstrate the capabilities of the method.

Zhu, Ziqiang↗

On a fourth order accurate implicit finite difference scheme for hyperbolic conservation laws. II - Five-point schemes

This paper presents a family of two-level five-point implicit schemes for the solution of one-dimensional systems of hyperbolic conservation laws, which generalized the Crank-Nicholson scheme to fourth order accuracy (4-4) in both time and space. These 4-4 schemes are nondissipative and unconditionally stable. Special attention is given to the system of linear equations associated with these 4-4 implicit schemes. The regularity of this system is analyzed and efficiency of solution-algorithms is examined. A two-datum representation of these 4-4 implicit schemes brings about a compactification of the stencil to three mesh points at each time-level. This compact two-datum representation is particularly useful in deriving boundary treatments. Numerical results are presented to illustrate some properties of the proposed scheme.

Harten, A.↗

A time-accurate high-resolution TVD scheme for solving the Navier-Stokes equations

A total variation diminishing (TVD) scheme has been developed and incorporated into an existing time-accurate high-resolution Navier-Stokes code. The accuracy and the robustness of the resulting solution procedure have been assessed by performing many calculations in four different areas: shock tube flows, regular shock reflection, supersonic boundary layer, and shock boundary layer interactions. These numerical results compare well with corresponding exact solutions or experimental data.

Kim, Hyun Dae↗

A time-accurate high-resolution TVD scheme for solving the Navier-Stokes equations

A total variation diminishing (TVD) scheme has been developed and incorporated into an existing time-accurate high-resolution Navier-Stokes code. The accuracy and the robustness of the resulting solution procedure have been assessed by performing many calculations in four different areas: shock tube flows, regular shock reflection, supersonic boundary layer, and shock boundary layer interactions. These numerical results compare well with corresponding exact solutions or experimental data.

Kim, Hyun D.↗

Recursive analytical solution describing artificial satellite motion perturbed by an arbitrary number of zonal terms

An analytical first order solution has been developed which describes the motion of an artificial satellite perturbed by an arbitrary number of zonal harmonics of the geopotential. A set of recursive relations for the solution, which was deduced from recursive relations of the geopotential, was derived. The method of solution is based on Von-Zeipel's technique applied to a canonical set of two-body elements in the extended phase space which incorporates the true anomaly as a canonical element. The elements are of Poincare type, that is, they are regular for vanishing eccentricities and inclinations. Numerical results show that this solution is accurate to within a few meters after 500 revolutions.

Mueller, A. C.↗

Over-relaxation applied to the MacCormack finite-difference scheme

An over-relaxation procedure is applied to the MacCormack finite-difference scheme in order to reduce the computation time required to obtain a steady-state solution. The implementation of this acceleration procedure to an existing computer program using the regular MacCormack method is extremely simple and does not require additional storage. The over-relaxation procedure does not alter the steady-state solution, which is second-order accurate. The method is first applied to Burgers' equation. A stability condition and an expression for the increase in the rate of convergence are derived. The method is then applied to the calculation of the hypersonic viscous flow over a flat plate, using the complete Navier-Stokes equations, and the inviscid flow over a wedge. Reductions in computing time by factors of 3 and 1.5, respectively, are obtained by over-relaxation.

Desideri, J.-A.↗

Euler procedure for three-dimensional transonic wall interference

Based on an optimization formulation, a procedure has been developed to evaluate Mach number and angle-of-attack corrections. The Euler equations are assumed to be the flow governing equations. To obtain efficient solutions for the optimization problem, the iterative solutions for the flow variables and the design parameters are simultaneously updated. In addition to the model lift and geometry, the procedure requires pressure measurements near the tunnel walls. The tunnel boundary conditions are based on the introduction of Reimann invariants for a one-dimensional flow normal to the boundary. Computations are performed to verify that the errors introduced by this approximate boundary-condition formulation are acceptably small. The correction scheme is applied to an aircraft configuration in an open jet. The results indicate that the optimization scheme is highly efficient with the rate of convergence of the flow solution nearly equal to the corresponding rate of a regular analysis problem.

Rizk, Magdi H.↗

Regularized Chapman-Enskog expansion for scalar conservation laws

Rosenau has recently proposed a regularized version of the Chapman-Enskog expansion of hydrodynamics. This regularized expansion resembles the usual Navier-Stokes viscosity terms at law wave-numbers, but unlike the latter, it has the advantage of being a bounded macroscopic approximation to the linearized collision operator. The behavior of Rosenau regularization of the Chapman-Enskog expansion (RCE) is studied in the context of scalar conservation laws. It is shown that thie RCE model retains the essential properties of the usual viscosity approximation, e.g., existence of traveling waves, monotonicity, upper-Lipschitz continuity..., and at the same time, it sharpens the standard viscous shock layers. It is proved that the regularized RCE approximation converges to the underlying inviscid entropy solution as its mean-free-path epsilon approaches 0, and the convergence rate is estimated.

Schochet, Steven↗

Optimal guidance law development for an advanced launch system

The proposed investigation on a Matched Asymptotic Expansion (MAE) method was carried out. It was concluded that the method of MAE is not applicable to launch vehicle ascent trajectory optimization due to a lack of a suitable stretched variable. More work was done on the earlier regular perturbation approach using a piecewise analytic zeroth order solution to generate a more accurate approximation. In the meantime, a singular perturbation approach using manifold theory is also under current investigation. Work on a general computational environment based on the use of MACSYMA and the weak Hamiltonian finite element method continued during this period. This methodology is capable of the solution of a large class of optimal control problems.

Calise, Anthony J.↗

Generative Representations for Computer-Automated Evolutionary Design

With the increasing computational power of computers, software design systems are progressing from being tools for architects and designers to express their ideas to tools capable of creating designs under human guidance. One of the main limitations for these computer-automated design systems is the representation with which they encode designs. If the representation cannot encode a certain design, then the design system cannot produce it. To be able to produce new types of designs, and not just optimize pre-defined parameterizations, evolutionary design systems must use generative representations. Generative representations are assembly procedures, or algorithms, for constructing a design thereby allowing for truly novel design solutions to be encoded. In addition, by enabling modularity, regularity and hierarchy, the level of sophistication that can be evolved is increased. We demonstrate the advantages of generative representations on two different design domains: the evolution of spacecraft antennas and the evolution of 3D objects.

Hornby, Gregory S.↗

Conjunction Assessment and Deconfliction Paradigm for Co-Located Satellite Constellations With on-Spacecraft “Autonomous” Flight Dynamics Control

Satellite constellations that employ on-spacecraft flight dynamics and conjunction assessment (CA) approaches face particular challenges. First, they must arrange to obtain and upload to the constellation satellite close approach information, such as Conjunction Data Messages, so that their on-board systems will have the data they need to make informed CA decisions. Second, given current latencies in obtaining CA screening information, such systems often cannot obtain dedicated screenings of their proposed maneuvers before they are executed. Third, they usually cannot engage in real time with owner/operators (O/Os) with whom they may come into conjunction, relying instead on pre-arranged courses of action that may or may not fit a given situation well. Despite these difficulties, it is nonetheless possible, as operators such as SpaceX have demonstrated, to operate safely using on-board CA calculations, in the presence of a largely collaborative operating environment. The situation breaks down, however, when two constellations that operate with such a paradigm are placed in the same orbital region and will experience conjunctions with each other. Each may have a vague idea of where the other’s satellites are, or perhaps even a somewhat precise idea if they exchange O/O ephemerides, but neither will know the other’s more immediate maneuver intentions, especially for situations in which they are in a high-risk conjunction with each other and a mitigation maneuver is required. As there is no formalized way for these automated systems to ascertain each other’s intentions for this type of conjunction, it is quite possible that each spacecraft may choose a maneuver that results in the two objects’ colliding. An opportunity to develop a solution to this problem was presented by the NASA “Starling” project, a small experimental constellation developed to demonstrate autonomous satellite control and constellation reconfiguration and for which a launch was obtained that, serendipitously, will place this constellation close to the SpaceX Starlink constellation. Because the NASA constellation is experimental, an extended mission part of the mission has been negotiated to implement and test mechanisms for resolving the problem of co-located constellations with on-board flight dynamics control. For the last eighteen months, a consortium among NASA Ames (the Starling satellite providers), NASA CARA (the Agency organization responsible for conjunction assessment), Space X, and the Department of Commerce (in observer status) has met regularly to assemble a concept of operations for a robust solution to this problem and has developed a prototype ground node that will serve as a needed CA screening and information dispensary. The approach and methods, as well as the active employment of the developed ground node, will be tested both in simulation before actual use and then in actual spacecraft operations, which are anticipated to begin in January 2024. This paper will describe the co-located autonomously-controlled constellation problem and the developed solution in detail, outlining what ground node (i.e., government) infrastructure and features are required, what particular capabilities are needed by the constellations themselves in order to make use of this deconfliction paradigm, and the migration path forward to allow such a capability set to be incorporated by the Department of Commerce’s space traffic coordination system.

Conjunction Assessment↗

Initial Results of an MDO Method Evaluation Study

The NASA Langley MDO method evaluation study seeks to arrive at a set of guidelines for using promising MDO methods by accumulating and analyzing computational data for such methods. The data are collected by conducting a series of re- producible experiments. In the first phase of the study, three MDO methods were implemented in the SIGHT: framework and used to solve a set of ten relatively simple problems. In this paper, we comment on the general considerations for conducting method evaluation studies and report some initial results obtained to date. In particular, although the results are not conclusive because of the small initial test set, other formulations, optimality conditions, and sensitivity of solutions to various perturbations. Optimization algorithms are used to solve a particular MDO formulation. It is then appropriate to speak of local convergence rates and of global convergence properties of an optimization algorithm applied to a specific formulation. An analogous distinction exists in the field of partial differential equations. On the one hand, equations are analyzed in terms of regularity, well-posedness, and the existence and unique- ness of solutions. On the other, one considers numerous algorithms for solving differential equations. The area of MDO methods studies MDO formulations combined with optimization algorithms, although at times the distinction is blurred. It is important to

Alexandrov, Natalia M.↗

Influence of Alloying upon Grain-Boundary Creep

Grain-boundary displacement, occurring in bicrystals during creep at elevated temperature (350 degrees c), has been measured as a function of the copper content (0.1 to 3 percent) in a series of aluminum-rich aluminum-copper solid-solution alloys. The minimums in stress and temperature, below which grain-boundary motion does not occur, increase regularly with the copper content as would be expected if recovery is necessary for movement. Otherwise, the effects, if any, of the copper solute upon grain-boundary displacement and its rate are too small for identification by the experimental technique employed. It was shown, additionally, that grain-boundary displacement appears regular and proceeds at a constant rate if observed parallel to the stress axis, whereas the motion is seen to occur in a sequence of surges and the rate to diminish with time if the observations are made perpendicular to the stress axis.

Rhines, F N↗