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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

A finite element based method for solution of optimal control problems

A temporal finite element based on a mixed form of the Hamiltonian weak principle is presented for optimal control problems. The mixed form of this principle contains both states and costates as primary variables that are expanded in terms of elemental values and simple shape functions. Unlike other variational approaches to optimal control problems, however, time derivatives of the states and costates do not appear in the governing variational equation. Instead, the only quantities whose time derivatives appear therein are virtual states and virtual costates. Also noteworthy among characteristics of the finite element formulation is the fact that in the algebraic equations which contain costates, they appear linearly. Thus, the remaining equations can be solved iteratively without initial guesses for the costates; this reduces the size of the problem by about a factor of two. Numerical results are presented herein for an elementary trajectory optimization problem which show very good agreement with the exact solution along with excellent computational efficiency and self-starting capability. The goal is to evaluate the feasibility of this approach for real-time guidance applications. To this end, a simplified two-stage, four-state model for an advanced launch vehicle application is presented which is suitable for finite element solution.

Bless, Robert R.↗
NASA NTRS1990

Staggered solution procedures for multibody dynamics simulation

The numerical solution procedure for multibody dynamics (MBD) systems is termed a staggered MBD solution procedure that solves the generalized coordinates in a separate module from that for the constraint force. This requires a reformulation of the constraint conditions so that the constraint forces can also be integrated in time. A major advantage of such a partitioned solution procedure is that additional analysis capabilities such as active controller and design optimization modules can be easily interfaced without embedding them into a monolithic program. After introducing the basic equations of motion for MBD system in the second section, Section 3 briefly reviews some constraint handling techniques and introduces the staggered stabilized technique for the solution of the constraint forces as independent variables. The numerical direct time integration of the equations of motion is described in Section 4. As accurate damping treatment is important for the dynamics of space structures, we have employed the central difference method and the mid-point form of the trapezoidal rule since they engender no numerical damping. This is in contrast to the current practice in dynamic simulations of ground vehicles by employing a set of backward difference formulas. First, the equations of motion are partitioned according to the translational and the rotational coordinates. This sets the stage for an efficient treatment of the rotational motions via the singularity-free Euler parameters. The resulting partitioned equations of motion are then integrated via a two-stage explicit stabilized algorithm for updating both the translational coordinates and angular velocities. Once the angular velocities are obtained, the angular orientations are updated via the mid-point implicit formula employing the Euler parameters. When the two algorithms, namely, the two-stage explicit algorithm for the generalized coordinates and the implicit staggered procedure for the constraint Lagrange multipliers, are brought together in a staggered manner, they constitute a staggered explicit-implicit procedure which is summarized in Section 5. Section 6 presents some example problems and discussions concerning several salient features of the staggered MBD solution procedure are offered in Section 7.

Park, K. C.↗
NASA NTRS1982

The Galileo Delta-VEGA mission to Jupiter

Project Galileo is to perform a more comprehensive investigation of the Jupiter system than was possible with Voyager. The Galileo spacecraft consists of both a planetary Orbiter and an atmospheric entry Probe. In connection with budgetary considerations and schedule problems, plans concerning the implementation of the project were changed a number of times. For the first seven months of 1982, the project Galileo was baselined as a Delta-VEGA transfer to be launched in 1985 by the Space Shuttle using the U.S. Air Force two-stage IUS as the upper stage augmented by a spacecraft Injection Module. The new mission and systems aspects of this 1985 Galileo Delta-VEGA baseline are compared to the prior 1985 Centaur direct transfer baseline. The techniques developed to virtually restore all the mission science in spite of greatly reduced launch vehicle performance are discussed. In July 1982, the U.S. Government reinstated the Centaur development and stipulated that Galileo be launched by Shuttle/Centaur in 1986.

Oneil, W. J.↗
NASA NTRS1972

Generating high Reynolds-number flows.

Present test facilities are seriously limited regarding investigations involving high Reynolds numbers due to financial considerations. Quasi-steady testing facilities offer a practical immediate solution to the problem of high-Re testing. A familiar example is the blowdown wind tunnel, but even more flexibility and economy may be provided by using shock-tube devices. The Ludwieg tube is the shock-tube device most often proposed as a means of generating high-Re flows. Two-stage nozzles may be used with a Ludwieg tube. Quasi-steady facilities will be useful only if the available test time exceeds that required to establish steady flow.

Russell, D. A.↗
NASA NTRS1980

Status of the DOE/NASA critical gas turbine R & T Project

The purpose of the DOE/NASA CRT (Critical Research and Technology) Project at the Lewis Research Center is to provide an R&T data base for utility gas turbine systems burning coal-derived fuels. Coal-derived fuels present difficult problems in combustion (because of the high organically-bound nitrogen in the fuel), and materials (because of the trace metal contaminant levels in the fuels, leading to corrosion and deposition in the turbine hot section). The combustion task includes (1) an effort to model the rich-lean combustion process, to predict NOx emissions; (2) a two-stage flame tube experiment to study the effects of combustion operating conditions and fuel properties on NOx conversion; and (3) scaled combustor tests to evaluate the NOx-reduction potential of several staged-combustion concepts. The materials-corrosion resistance effort attacks the problem on three sides.

Clark, J. S.↗
NASA NTRS1983

Quantum/classical mode evolution in free electron laser oscillators

The problem of oscillator evolution and mode competition in free electron lasers is studied. Relativistic quantum field theory is used to calculate electron wave functions, the angular distribution of spontaneous emission, and the transition rates for stimulated emission and absorption in each mode. The photon rate equation for the weakfield regime is presented. This rate equation is applied to oscillator evolution with a conventional undulator, a two-stage optical klystron, and a tapered undulator. The effects of noise are briefly discussed.

Bosco, P.↗
NASA NTRS1990

Explicit-implicit staggered procedure for multibody dynamics analysis

An explicit-implicit staggered time-integration procedure is presented for the solution of multibody dynamical equations involving large rotations and constraints. The algorithms adopts a two-stage modification of the central difference algorithm for integrating the translational coordinates and the angular velocity vector, and the midpoint implicit algorithm to solve the kinematical relation in terms of the Euler parameters for updating the angular orientations. The Lagrange multipliers to enforce the system constraints are obtained by implicitly integrating a parabolically regularized differential equation for the multipliers. The performance of the present procedure has been evaluated to applying the procedure to solve several sample problems. The results indicate that the procedure is robust in dealing with a variety of constraints and spatial kinematic motions, hence it is recommended for applications to general multibody dynamics analyses.

Park, K. C.↗
NASA NTRS1992

Finite element method for optimal guidance of an advanced launch vehicle

A temporal finite element based on a mixed form of Hamilton's weak principle is summarized for optimal control problems. The resulting weak Hamiltonian finite element method is extended to allow for discontinuities in the states and/or discontinuities in the system equations. An extension of the formulation to allow for control inequality constraints is also presented. The formulation does not require element quadrature, and it produces a sparse system of nonlinear algebraic equations. To evaluate its feasibility for real-time guidance applications, this approach is applied to the trajectory optimization of a four-state, two-stage model with inequality constraints for an advanced launch vehicle. Numerical results for this model are presented and compared to results from a multiple-shooting code. The results show the accuracy and computational efficiency of the finite element method.

Hodges, Dewey H.↗
NASA NTRS1992

On the evolution of slowly accreting neutron stars

In the light of recent calculations of pycnonuclear reaction rates for light elements, we consider the problem of slow interstellar accretion onto old, possibly magnetized neutron stars. We argue that accretion will occur at the Hoyle-Lyttleton rate after the star has spun down in less than about 10 exp 9 yr. A deep ocean of liquid hydrogen and helium, extending down to depths about 100 m, will cover the surface of the star once it has accreted about 10 exp 25 g of gas. Beneath the ocean will be a layer of almost pure solid O-16 which undergoes two-stage electron capture to C-16 above a pressure 2.7 x 10 exp 28 dyne/sq cm, corresponding to an accreted mass of about 10 exp 27 g. Taking into account the presence of multiple layers of distinct chemical composition, we conclude that the crust will be stable to small perturbations under the conditions envisaged for instellar accretion. A thick layer of up to 10 exp 27 g of metastable C-16 will then accumulate. We discuss the implications of these results to old Galactic neutron stars as sources of gamma-ray bursts.

Blaes, O. M.↗
NASA NTRS1987

The Large Deployable Reflector (LDR) - Plans and progress

The program history, scientific aims, design, and projected performance of the LDR, a 20-m-primary two-stage four-mirror orbiting sub-mm/FIR astronomical observatory under NASA development, are reviewed. It is shown that the LDR would provide capabilities complementary to those of IRAS, the Kuiper Airborne Observatory, the IRTF, the Hubble Space Telescope, and the planned Space IR Telescope Facility for observations of small-scale background anisotropies, high-redshift galaxies, and objects at temperatures of a few times 10 K or lower. The current design concept is illustrated with extensive drawings, diagrams, and tables of instrument parameters. Particular attention is given to the graphite-epoxy facing and Al-honeycomb core of the primary structure, the focal-plane instruments, and outstanding technological problems.

Swanson, Paul N.↗
NASA NTRS1990

A computational procedure for the dynamics of flexible beams within multibody systems

The dynamic analysis of three dimensional elastic beams which experience large rotational and large deformational motions are examined. The beam motion is modeled using an inertial reference for the translational displacements and a body-fixed reference for the rotational quantities. Finite strain rod theories are then defined in conjunction with the beam kinematic description which accounts for the effects of stretching, bending, torsion, and transverse shear deformations. A convected coordinate representation of the Cauchy stress tensor and a conjugate strain definition is introduced to model the beam deformation. To treat the beam dynamics, a two-stage modification of the central difference algorithm is presented to integrate the translational coordinates and the angular velocity vector. The angular orientation is then obtained from the application of an implicit integration algorithm to the Euler parameter/angular velocity kinematical relation. The combined developments of the objective internal force computation with the dynamic solution procedures result in the computational preservation of total energy for undamped systems. The present methodology is also extended to model the dynamics of deployment/retrieval of the flexible members. A moving spatial grid corresponding to the configuration of a deployed rigid beam is employed as a reference for the dynamic variables. A transient integration scheme which accurately accounts for the deforming spatial grid is derived from a space-time finite element discretization of a Hamiltonian variational statement. The computational results of this general deforming finite element beam formulation are compared to reported results for a planar inverse-spaghetti problem.

Downer, Janice Diane↗
NASA NTRS1969

Dynamic characteristics of a variable-mass flexible missile: Dynamics of a two-stage variable-mass flexible rocket

The dynamic characteristics of two-stage slender elastic body were investigated. The first stage, containing a solid-fuel rocket, possesses variable mass while the second stage, envisioned as a flexible case, contains packaged instruments of constant mass. The mathematical formulation was in terms of vector equations of motion transformed by a variational principle into sets of scalar differential equations in terms of generalized coordinates. Solutions to the complete equations were obtained numerically by means of finite difference techniques. The problem has been programmed in the FORTRAN 4 language and solved on an IBM 360/50 computer. Results for limited cases are presented showing the nature of the solutions.

Meirovitch, L.↗
NASA NTRS1974

Feasibility and tradeoff study of an aeromaneuvering orbit-to-orbit shuttle (AMOOS)

This study establishes that configurations satisfying the aeromaneuvering orbit-to-orbit shuttle (AMOOS) requirements can be designed with performance capabilities in excess of the purely propulsive space tug. In view of this improved potential of the AMOOS vehicle over the propulsive space tug concept it is recommended that the AMOOS studies be advanced to a stage comparable to those performed for the space tug. This advancement is needed in particular in areas that are either peculiar to AMOOS or not addressed in sufficient detail in these studies to date. These areas include the thermodynamics problems, navigation and guidance, operations and economics analyses, subsystems and interfaces. The aeromaneuvering orbit-to-orbit shuttle (AMOOS) is evaluated as a candidate reusable third stage to the two-stage earth-to-orbit shuttle (EOS). AMOOS has the potential for increased payload capability over the purely propulsive space tug by trading a savings in consumables for an increase in structural and thermal protection system (TPS) mass.

White, J.↗
NASA NTRS1976

Noise comparisons of single and two stage demonstrator fans for advanced technology aircraft

A high-speed single-stage and a low-speed two-stage fan were designed, fabricated and tested to demonstrate their predicted low noise performance for an advanced 0.85-0.90 cruise Mach number aircraft requiring a 1.8-1.9 pressure ratio fan. Acoustic tests were made with both unsuppressed and suppressed configurations. The two-stage fan demonstrated that quiet fan technology developed for low-speed single-stage fan is applicable to two-stage designs. The unsuppressed two-stage fan was 3-5 dB quieter than the high-speed single-stage fan at the same pressure ratio. The unsuppressed high-speed single-stage fan demonstrated that significant reductions in inlet noise can be achieved from the sonic blockage caused by supersonic flow in the rotor blading. Both fans demonstrated suppressed inlet noise levels with treated sonic inlets that met advanced technology goals. Suppressed aft noise levels did not meet expectations for either fan. The aft noise problem is attributed to both excessive source noise and ineffective treatment performance.

Heidmann, M. F.↗
NASA NTRS1977

Thermochemical water decomposition

At present, nearly all of the hydrogen consumed in the world is produced by reacting hydrocarbons with water. As the supply of hydrocarbons diminishes, the problem of producing hydrogen from water alone will become increasingly important. Furthermore, producing hydrogen from water is a means of energy conversion by which thermal energy from a primary source, such as solar or nuclear fusion of fission, can be changed into an easily transportable and ecologically acceptable fuel. The attraction of thermochemical processes is that they offer the potential for converting thermal energy to hydrogen more efficiently than by water electrolysis. A thermochemical hydrogen-production process is one which requires only water as material input and mainly thermal energy, or heat, as an energy input. Attention is given to a definition of process thermal efficiency, the thermodynamics of the overall process, the single-stage process, the two-stage process, multistage processes, the work of separation and a process evaluation.

Funk, J. E.↗
NASA NTRS1989

Flux splitting algorithms for two-dimensional viscous flows with finite-rate chemistry

The Roe flux-difference splitting method has been extended to treat two-dimensional 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-stage 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.

Shuen, Jian-Shun↗
NASA NTRS1990

Gamma guidance of trajectories for coplanar, aeroassisted orbital transfer

The optimization and guidance of trajectories for coplaner, aeroassisted orbital transfer (AOT) from high Earth orbit (HEO) to low Earth orbit (LEO) are examined. In particular, HEO can be a geosynchronous Earth orbit (GEO). It is assumed that the initial and final orbits are circular, that the gravitational field is central and is governed by the inverse square law, and that at most three impulses are employed: one at HEO exit, one at atmospheric exit, and one at LEO entry. It is also assumed that, during the atmospheric pass, the trajectory is controlled via the lift coefficient. The presence of upper and lower bounds on the lift coefficient is considered. First, optimal trajectories are computed by minimizing the total velocity impulse (hence, the propellant consumption) required for AOT transfer. The sequential gradient-restoration algorithm (SGRA) is used for optimal control problems. The optimal trajectory is shown to include two branches: a relatively short descending flight branch (branch 1) and a long ascending flight branch (branch 2). Next, attention is focused on guidance trajectories capable of approximating the optimal trajectories in real time, while retaining the essential characteristics of simplicity, ease of implementation, and reliability. For the atmospheric pass, a feedback control scheme is employed and the lift coefficient is adjusted according to a two-stage gamma guidance law. Further improvements are possible via a modified gamma guidance which is more stable with respect to dispersion effects arising from navigation errors, variations of the atmospheric density, and uncertainties in the aerodynamic coefficients than gamma guidance trajectory. A byproduct of the studies on dispersion effects is the following design concept. For coplaner aeroassisted orbital transfer, the lift-range-to-weight ratio appears to play a more important role than the lift-to-drag ratio. This is because the lift-range-to-weight ratio controls mainly the minimum altitude (hence, the peak heating rate) of the guidance trajectory; on the other hand, the lift-to-drag ratio controls mainly the duration of the atmospheric pass of the guidance trajectory.

Miele, A.↗
NASA NTRS1992

CFD applications in pump flows

The objective of the proposed paper is to develop a computational procedure that solves incompressible Navier-Stokes equations for pump flows. The solution method is based on the pseudo-compressibility approach and uses an implicit-upwind differencing scheme together with the Gauss-Seidel line relaxation method. The equations are solved in steadily rotating reference frames and the centrifugal force and the Coriolis force are added to the equation of motion. As a benchmark problem, the flow through the Rocketdyne inducer is numerically simulated. A coarse grid solution is obtained with a single zone by using an algebraic turbulence model. In multi-zone fine grid computation, a one-equation Baldwin-Barth turbulence model is utilized. Numerical results are compared with experimental measurements and a good agreement is found between the two. The resulting computer code is then applied to the flow analysis inside a two-stage fuel pump impeller operating at 80 percent, 100 percent, and 120 percent of design flow.

Kiris, Cetin↗