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NASA NTRS1976

Optimal reusable-tug and expendable-kickstage trajectories for high-energy planetary missions including correction for nodal precession

Equations are derived by using branched trajectory optimization techniques and the maximum principle to maximize the payload capability of a reusable tug/expendable kickstage vehicle configuration for planetary missions. The two stages and the payload are launched into a low earth orbit by a single space shuttle. The analysis includes correction for precession of the orbit. This correction is done by the tug. The tug propels the payload and the kickstage to an energy beyond earth escape and returns within a specified time to the precessed orbit. After separating from the tug, the kickstage accelerates the payload to the required injection conditions. Planetary injection conditions are specified by the mission energy and a fixed declination and right ascension of the outgoing asymptote. The multipoint boundary value problem resulting from the analysis is solved by a Newton-Raphson iteration technique. Partial derivatives of the boundary conditions are obtained by perturbing the initial conditions one at a time, integrating the trajectory and adjoint equations, and observing the changes in boundary conditions. Maximum payload capability is derived for two typical mission energies. In addition, the variations of several mission and stage parameters are also examined.

Borsody, J.↗

NASA NTRS1990

Singular perturbation analysis of AOTV-related trajectory optimization problems

The problem of real time guidance and optimal control of Aeroassisted Orbit Transfer Vehicles (AOTV's) was addressed using singular perturbation theory as an underlying method of analysis. Trajectories were optimized with the objective of minimum energy expenditure in the atmospheric phase of the maneuver. Two major problem areas were addressed: optimal reentry, and synergetic plane change with aeroglide. For the reentry problem, several reduced order models were analyzed with the objective of optimal changes in heading with minimum energy loss. It was demonstrated that a further model order reduction to a single state model is possible through the application of singular perturbation theory. The optimal solution for the reduced problem defines an optimal altitude profile dependent on the current energy level of the vehicle. A separate boundary layer analysis is used to account for altitude and flight path angle dynamics, and to obtain lift and bank angle control solutions. By considering alternative approximations to solve the boundary layer problem, three guidance laws were derived, each having an analytic feedback form. The guidance laws were evaluated using a Maneuvering Reentry Research Vehicle model and all three laws were found to be near optimal. For the problem of synergetic plane change with aeroglide, a difficult terminal boundary layer control problem arises which to date is found to be analytically intractable. Thus a predictive/corrective solution was developed to satisfy the terminal constraints on altitude and flight path angle. A composite guidance solution was obtained by combining the optimal reentry solution with the predictive/corrective guidance method. Numerical comparisons with the corresponding optimal trajectory solutions show that the resulting performance is very close to optimal. An attempt was made to obtain numerically optimized trajectories for the case where heating rate is constrained. A first order state variable inequality constraint was imposed on the full order AOTV point mass equations of motion, using a simple aerodynamic heating rate model.

Calise, Anthony J.↗

NASA NTRSDate not supplied

Towards Energy Scale Calibration and Drift Correction of TES Detectors for Athena X-IFU

The Athena X-Ray Integral Field Unit (X-IFU) comprises a 2376-pixel array of transition edge sensors (TES) read out with time-division multiplexing (TDM). X-IFU will provide spatially resolved, high-resolution spectroscopy (2.5 eV full-width-half-maximum up to 7 keV) over the energy range 0.2 to 12 keV, with an absolute energy scale accuracy of 0.4 eV. The energy scale function maps the optimally filtered pulse height, in arbitrary engineering units, to real calibrated energy. Uncertainties in the calibration can result from imperfect fitting of the energy scale between the known calibration points. Furthermore, temporal changes in the TES operating environment, such as heat-sink temperature, magnetic field and bias voltage, can cause significant variations in the detector gain function over time. If not properly corrected, this can result in degradation of the energy resolution, and systematic errors in the absolute energy scale. The non-linear nature of TES detectors, coupled with the possibility of multiple simultaneously occurring sources of drift, can make effective corrections over the full bandpass of the instrument extremely challenging. Athena X-IFU will employ an on-board calibration source that provides known reference x-ray lines. This provides real-time monitoring of the gain stability of the detector system and information that can be used to correct for gain drifts. For X-IFU the baseline approach is to measure a series of calibration curves under different environmental conditions, which bound the expected drifts the instrument is predicted to see over the course of the mission. Using the information from the in-flight calibration source, these energy scale functions can be interpolated to generate a new corrected energy scale as a function of time. In this paper we discuss progress towards demonstrating that the X-IFU energy scale requirements can be met. We present measurements on ~ 200 pixels in a prototype X-IFU array read out with 8-column x 32-row TDM. We use a rotating target source containing 12 fluorescent targets to generate x-ray lines covering the energy range 4 keV (Sc-Kα) to 12 keV (Br-Kα). We present measurements of the non-linear energy scale function and show how variations in heat-sink temperature, TES bias voltage and magnetic field affect the shape of TES energy scale differently and introduce different residual gain errors over the bandpass. We explore different drift correction algorithms that use either a single or multiple referential lines to track and correct the gain from these various sources of drift. In addition to the pulse-height, the DC ‘baseline’ level of the TES can contain information about its bias conditions. Thus, we test a multi-parameter gain correction algorithm that attempts to incorporate both the pulse height and the additional baseline information into the algorithm.

Stephen J Smith↗

NASA NTRS1978

Solar thermal collectors using planar reflector

Specular reflectors have been used successfully with flat-plate collectors to achieve exceptionally high operating temperatures and high delivered energy per unit collector area. Optimal orientation of collectors and reflectors can result in even higher performance with an improved relationship between energy demand and supply. This paper reports on a study providing first order optimization of collector-reflector arrays in which single- and multiple-faceted reflectors in fixed or singly adjustable configurations provide delivered energy maxima in either summer or winter.

Espy, P. N.↗

NASA NTRS1985

Improved Specific Energy Ni-h2 Cell

Design optimization activities which have evolved and validated the necessary technology to produce Ni-H2 battery cells exhibiting a specific energy of 75-80 Whr/Kg (energy density approximately 73 Whr/L are summarized. Final design validation is currently underway with the production of battery cells for qualification and life testing. The INTELSAT type Ni-H2 battery cell design has been chosen for expository purposes. However, it should be recognized portions of the improved technology could be applied to the Air Force type Ni-H2 battery cell design with equal benefit.

Miller, L.↗

NASA NTRS2010

Fuel-Cell-Powered Vehicle with Hybrid Power Management

Figure 1 depicts a hybrid electric utility vehicle that is powered by hydrogenburning proton-exchange-membrane (PEM) fuel cells operating in conjunction with a metal hydride hydrogen-storage unit. Unlike conventional hybrid electric vehicles, this vehicle utilizes ultracapacitors, rather than batteries, for storing electric energy. This vehicle is a product of continuing efforts to develop the technological discipline known as hybrid power management (HPM), which is oriented toward integration of diverse electric energy-generating, energy-storing, and energy- consuming devices in optimal configurations. Instances of HPM were reported in five prior NASA Tech Briefs articles, though not explicitly labeled as HPM in the first three articles: "Ultracapacitors Store Energy in a Hybrid Electric Vehicle" (LEW-16876), Vol. 24, No. 4 (April 2000), page 63; "Photovoltaic Power Station With Ultracapacitors for Storage" (LEW- 17177), Vol. 27, No. 8 (August 2003), page 38; "Flasher Powered by Photovoltaic Cells and Ultracapacitors" (LEW-17246), Vol. 27, No. 10 (October 2003), page 37; "Hybrid Power Management" (LEW-17520), Vol. 29, No. 12 (December 2005), page 35; and "Ultracapacitor-Powered Cordless Drill" (LEW-18116-1), Vol. 31, No. 8 (August 2007), page 34. To recapitulate from the cited prior articles: The use of ultracapacitors as energy- storage devices lies at the heart of HPM. An ultracapacitor is an electrochemical energy-storage device, but unlike in a conventional rechargeable electrochemical cell or battery, chemical reactions do not take place during operation. Instead, energy is stored electrostatically at an electrode/electrolyte interface. The capacitance per unit volume of an ultracapacitor is much greater than that of a conventional capacitor because its electrodes have much greater surface area per unit volume and the separation between the electrodes is much smaller.

Eichenberg, Dennis J.↗

NASA NTRS1992

Flight-test guidance for airbreathing hypersonic vehicles

A guidance solution for aerospace planes is given based on a family of energy-heading extremal solutions that can be used for feedback implementations. Test conditions are developed as steady-cruise solutions by means of energy-heading extremal solutions to a time/fuel-range flight-optimization problem. Feedback charts are derived that give control as a function of energy and heading-to-go, and the reduced-order model is compared to numerically optimized point-mass solutions for flight optimization. The energy-heading model is shown to provide feedback-control charts that yield fuel-efficient turn/acceleration maneuvers with significant weight-change as compared to the point-mass solutions. Such variables as Mach number, dynamic pressure, and lift are found to influence the solutions significantly.

Cliff, Eugene M.↗

NASA NTRS1983

Energetics and optimum motion of oscillating lifting surfaces

Low-frequency, unsteady, lifting-line theory is used to characterize the energetics and optimum motion of an unswept rigid wing oscillating harmonically in an inviscid, incompressible flow. The energetics calculations account for the leading edge suction force, the power absorbed in the wing oscillations, and the energy loss rate produced by vortex shedding. Optimization is achieved by minimizing the average energy loss rate in relation to a given thrust, and a unique solution is found in the three dimensional case for low, reduced frequencies. The two-dimensional solution is nonunique, a condition which is examined in terms of the normal modes of the energy loss rate matrix. An invisible mode with a hydrodynamic efficiency of 100 pct is obtained in the two-dimensional case, causing the nonuniqueness of the solution by yielding no fixed positive thrust through perfect unsteady feathering.

Ahmadi, A. R.↗

NASA NTRS1992

Membrane triangles with corner drilling freedoms. II - The ANDES element

This is the second article in a three-part series on the construction of 3-node, 9-dof membrane elements with normal-to-its-plane rotational freedoms (the so-called drilling freedoms) using parametrized variational principles. In this part, one such element is derived within the context of the assumed natural deviatoric strain (ANDES) formulation. The higher-order strains are obtained by constructing three parallel-to-sides pure-bending modes from which natural strains are obtained at the corner points and interpolated over the element. To attain rank sufficiency, an additional higher-order 'torsional' mode, corresponding to equal hierarchical rotations at each corner with all other motions precluded, is incorporated. The resulting formulation has five free parameters. When these parameters are optimized against pure bending by energy balance methods, the resulting element is found to coalesce with the optimal EFF element derived in Part I. Numerical integration as a strain filtering device is found to play a key role in this achievement.

Felippa, Carlos A.↗

NASA NTRSDate not supplied

Evaluation of Regional Water and Energy Balance in Contemporary Reanalyses

Regional to continental water and energy balance in reanalyses provide crucial information on the climate and climate variations in that region and can contrast other regions. Reanalyses are a valuable tool in piecing together the complete balance owing to the incorporation of the budgets in the background model and the assimilation of observation. On the other hand, the background model has its own biases and observational assimilation can lead to non-negligible tendencies within the budgets, and these can vary over space and time. Here, we will compare the balance within several reanalyses and how they have evolved over recent decades. Several observational data products will provide reference points in the comparison. In addition, a recent project has integrated observations of the water and energy budgets in an optimization that aims to reduce the imbalance of regional budgets in using observational terms from disparate sources. In evaluating the regional balances, we will incorporate, when available, the water and energy convergence terms as well as their analysis increments (which may be diagnosed as residuals). The reanalyses considered here include: Japanese Reanalyses for Three Quarters Century (JRA3Q), ECMWF Reanalysis version 5 (ERA5), Modern Era Retrospective-analysis for Research and Applications version 2 (MERRA-2) and the NCEP Reanalysis II (NCEPR2). NCEPR2 is representative of the late 90s technology, while the others represent the contemporary climate reanalyses presently available. We will discuss the regional balances over key river basins (e.g. Mississippi and Amazon), and a range of continents including those well observed (North America and Europe) and those with fewer consistent observations (e.g. Africa). These contrasting regions show the degree of advancement in reanalyses and expose areas in need of improvement. The results also demonstrate the usefulness of producing complete atmospheric water and energy budgets as part of the diagnostic output.

Michael G Bosilovich↗

NASA NTRSDate not supplied

Evaluation of Regional Water and Energy Balance in Contemporary Reanalyses

Michael Bosilovich↗

NASA NTRS2016

Transient Growth Analysis of Compressible Boundary Layers with Parabolized Stability Equations

The linear form of parabolized linear stability equations (PSE) is used in a variational approach to extend the previous body of results for the optimal, non-modal disturbance growth in boundary layer flows. This methodology includes the non-parallel effects associated with the spatial development of boundary layer flows. As noted in literature, the optimal initial disturbances correspond to steady counter-rotating stream-wise vortices, which subsequently lead to the formation of stream-wise-elongated structures, i.e., streaks, via a lift-up effect. The parameter space for optimal growth is extended to the hypersonic Mach number regime without any high enthalpy effects, and the effect of wall cooling is studied with particular emphasis on the role of the initial disturbance location and the value of the span-wise wavenumber that leads to the maximum energy growth up to a specified location. Unlike previous predictions that used a basic state obtained from a self-similar solution to the boundary layer equations, mean flow solutions based on the full Navier-Stokes (NS) equations are used in select cases to help account for the viscous-inviscid interaction near the leading edge of the plate and also for the weak shock wave emanating from that region. These differences in the base flow lead to an increasing reduction with Mach number in the magnitude of optimal growth relative to the predictions based on self-similar mean-flow approximation. Finally, the maximum optimal energy gain for the favorable pressure gradient boundary layer near a planar stagnation point is found to be substantially weaker than that in a zero pressure gradient Blasius boundary layer.

Compressible boundary layer↗

NASA NTRS2020

Extension of the energy range accessible with a TES using bath temperature variations

The energy range of transition-edge sensor (TES) X-ray microcalorimeters with a multiplexed readout depends upon the width and shape of the TES superconducting transition, and also on the dynamic range of the readout. In many detector systems, the multiplexed readout slew rate capability will be the limiting factor for the energy range. In these cases, if we are willing to accept some energy resolution degradation, we can significantly extend the energy range by increasing the bath temperature of operation, essentially creating a second â€œextended energy rangeâ€ mode of operation. For example, if we require the very highest energy resolution up to 7 keV, and wish to optimize the design up to this energy, for some measurements it could be very beneficial to have a mode where we can extend the energy range to 15â€“20 keV even if some energy resolution is sacrificed. In this paper, we explore the trade-off between dynamic range and energy resolution from changing the bath temperature of the TES. We present measurements of TES resolution and slew rate as a function of bath temperature and compare to numerical simulations.

S Beaumont↗

NASA NTRS1981

The application of simulation modeling to the cost and performance ranking of solar thermal power plants

A computer simulation code was employed to evaluate several generic types of solar power systems (up to 10 MWe). Details of the simulation methodology, and the solar plant concepts are given along with cost and performance results. The Solar Energy Simulation computer code (SESII) was used, which optimizes the size of the collector field and energy storage subsystem for given engine-generator and energy-transport characteristics. Nine plant types were examined which employed combinations of different technology options, such as: distributed or central receivers with one- or two-axis tracking or no tracking; point- or line-focusing concentrator; central or distributed power conversion; Rankin, Brayton, or Stirling thermodynamic cycles; and thermal or electrical storage. Optimal cost curves were plotted as a function of levelized busbar energy cost and annualized plant capacity. Point-focusing distributed receiver systems were found to be most efficient (17-26 percent).

Rosenberg, L. S.↗

NASA NTRS1993

Minimizing distortion in truss structures -- a Hopfield network solution

Distortions in truss structures can result from random errors in elemental lengths that are typical of a manufacturing process. These distortions may be minimized by an optimal selection of elements from those available for placement between the prescribed nodes -- a combinatorial optimization problem requiring significant investment of computational resource for all but the smallest problems. The present paper describes a formulation in which near-optimal element assignments are obtained as minimum energy, stable states, of an analogous Hopfield neural network. This requires mapping of the optimization problem into an energy function of the appropriate Lyapunov form. The computational architecture is ideally suited to a parallel processor implementation and offers significant savings in computational effort. A numerical implementation of the approach is discussed with reference to planar truss problems.

Fu, B.↗

NASA NTRS1996

Application of Hybrid Optimization-Expert System for Optimal Power Management on Board Space Power Station

The space power system has two sources of energy: photo-voltaic blankets and batteries. The optimal power management problem on-board has two broad operations: off-line power scheduling to determine the load allocation schedule of the next several hours based on the forecast of load and solar power availability. The nature of this study puts less emphasis on speed requirement for computation and more importance on the optimality of the solution. The second category problem, on-line power rescheduling, is needed in the event of occurrence of a contingency to optimally reschedule the loads to minimize the 'unused' or 'wasted' energy while keeping the priority on certain type of load and minimum disturbance of the original optimal schedule determined in the first-stage off-line study. The computational performance of the on-line 'rescheduler' is an important criterion and plays a critical role in the selection of the appropriate tool. The Howard University Center for Energy Systems and Control has developed a hybrid optimization-expert systems based power management program. The pre-scheduler has been developed using a non-linear multi-objective optimization technique called the Outer Approximation method and implemented using the General Algebraic Modeling System (GAMS). The optimization model has the capability of dealing with multiple conflicting objectives viz. maximizing energy utilization, minimizing the variation of load over a day, etc. and incorporates several complex interaction between the loads in a space system. The rescheduling is performed using an expert system developed in PROLOG which utilizes a rule-base for reallocation of the loads in an emergency condition viz. shortage of power due to solar array failure, increase of base load, addition of new activity, repetition of old activity etc. Both the modules handle decision making on battery charging and discharging and allocation of loads over a time-horizon of a day divided into intervals of 10 minutes. The models have been extensively tested using a case study for the Space Station Freedom and the results for the case study will be presented. Several future enhancements of the pre-scheduler and the 'rescheduler' have been outlined which include graphic analyzer for the on-line module, incorporating probabilistic considerations, including spatial location of the loads and the connectivity using a direct current (DC) load flow model.

Momoh, James↗

NASA NTRSDate not supplied

A Multiphysics Study to Improve Specific Energy of Primary Batteries for Low Temperature Operation for Deep Space Missions

Several lander missions on the outer planets such as Europa, Enceladus, and Titan require electrical power to operate scientific and communication equipment. The traditional power generation methods, such as a photovoltaic array, are not feasible as their efficiency drops significantly at these vast distances. The novel radioisotope power systems are not practical today based on current lander designs and the effectiveness of these systems. To perform in situ science on distant planets, a high specific energy battery (>700 Wh/kg) needs to operate for about 480 hours under cold temperatures (-40C or 0C) [1]. While a primary battery such as Li-CFx can provide high specific energy at room temperature, its specific capacity decreases significantly at low temperatures. One of the causes for this drop is low ion and electrical conductivity, and slower reaction kinetics. Slower transport and facile kinetics lead to an increase in the battery’s resistance and higher voltage drops during the cell operation, thus reducing specific capacity. Both the transport and kinetics show a strong dependence on temperature. Thus, a small temperature rise can lead to an increase in the reaction rate and ion conductivity; since the temperature, cell resistance, and specific capacity are interdependent. A conventional battery model accounts for ohmic, thermodynamic, and, electrochemical, and chemical decomposition heating. The ohmic heating can be controlled by designing a resistive microstructure and varying the ratios of the active materials [2]. The kinetics can be improved by increasing the surface area, reducing the particle size, or adding a catalyst. These parameters are often optimized to achieve high specific energy at room temperatures. A similar optimization study is not available at low temperatures and for a primary (high specific energy) battery. For this presentation, we will explore the effect of geometrical, microstructural, and material properties on optimal specific capacity at low temperatures through multiphysics simulations. The ion transport resistance depends on the porosity and the tortuosity of an electrode and the separator.

M. Mehta↗

NASA NTRS1995

Minimization of the Vibration Energy of Thin-Plate Structures and the Application to the Reduction of Gearbox Vibration

While the vibration analysis of gear systems has been developed, a systematic approach to the reduction of gearbox vibration has been lacking. The technique of reducing vibration by shifting natural frequencies is proposed here for gearboxes and other thin-plate structures using the theories of finite elements, modal analysis, and optimization. A triangular shell element with 18 degrees of freedom is developed for structural and dynamic analysis. To optimize, the overall vibration energy is adopted as the objective function to be minimized at the excitation frequency by varying the design variable (element thickness) under the constraint of overall constant weight. Modal analysis is used to determine the sensitivity of the vibration energy as a function of the eigenvalues and eigenvectors. The optimum design is found by the gradient projection method and a unidimensional search procedure. By applying the computer code to design problems for beams and plates, it was verified that the proposed method is effective in reducing vibration energy. The computer code is also applied to redesign the NASA Lewis gear noise rig test gearbox housing. As one example, only the shape of the top plate is varied, and the vibration energy levels of all the surfaces are reduced, yielding an overall reduction of 1/5 compared to the initial design. As a second example, the shapes of the top and two side plates are varied to yield an overall reduction in vibration energy of 1/30.

Inoue, Katsumi↗