Search NASA⌕ Search

SEARCH · Search NASA

Results for “Higher order calculations”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 145 records · Page 8

A 3D High-Order Unstructured Finite-Volume Algorithm for Solving Maxwell's Equations

A three-dimensional finite-volume algorithm based on arbitrary basis functions for time-dependent problems on general unstructured grids is developed. The method is applied to the time-domain Maxwell equations. Discrete unknowns are volume integrals or cell averages of the electric and magnetic field variables. Spatial terms are converted to surface integrals using the Gauss curl theorem. Polynomial basis functions are introduced in constructing local representations of the fields and evaluating the volume and surface integrals. Electric and magnetic fields are approximated by linear combinations of these basis functions. Unlike other unstructured formulations used in Computational Fluid Dynamics, the new formulation actually does not reconstruct the field variables at each time step. Instead, the spatial terms are calculated in terms of unknowns by precomputing weights at the beginning of the computation as functions of cell geometry and basis functions to retain efficiency. Since no assumption is made for cell geometry, this new formulation is suitable for arbitrarily defined grids, either smooth or unsmooth. However, to facilitate the volume and surface integrations, arbitrary polyhedral cells with polygonal faces are used in constructing grids. Both centered and upwind schemes are formulated. It is shown that conventional schemes (second order in Cartesian grids) are equivalent to the new schemes using first degree polynomials as the basis functions and the midpoint quadrature for the integrations. In the new formulation, higher orders of accuracy are achieved by using higher degree polynomial basis functions. Furthermore, all the surface and volume integrations are carried out exactly. Several model electromagnetic scattering problems are calculated and compared with analytical solutions. Examples are given for cases based on 0th to 3rd degree polynomial basis functions. In all calculations, a centered scheme is applied in the interior, while an upwind matching scheme is employed at material interfaces and the Engquist-Majda non-reflecting boundary condition is implemented at the numerical outer boundaries. The staggered leapfrog scheme and the Runge-Kutta methods are utilized for the time integration. Excellent agreements are found between the numerical and analytical solutions.

Liu, Yen↗

Pressure-Fed LOX/LCH4 Reaction Control System for Spacecraft: Transient Modeling and Thermal Vacuum Hotfire Test Results

An integrated cryogenic liquid oxygen, liquid methane (LOX/LCH4) reaction control system (RCS) was tested at NASA Glenn Research Center's Plum Brook Station in the Spacecraft Propulsion Research Facility (B-2) under vacuum and thermal vacuum conditions. The RCS is a subsystem of the Integrated Cryogenic Propulsion Test Article (ICPTA), a pressure-fed LOX/LCH4 propulsion system composed of a single 2,800 lbf main engine, two 28 lbf RCS engines, and two 7 lbf RCS engines. Propellants are stored in four 48 inch diameter 5083 aluminum tanks that feed both the main engine and RCS engines in parallel. Helium stored cryogenically in a composite overwrapped pressure vessel (COPV) flows through a heat exchanger on the main engine before being used to pressurize the propellant tanks to a design operating pressure of 325 psi. The ICPTA is capable of simultaneous main engine and RCS operation. The RCS engines utilize a coil-on-plug (COP) ignition system designed for operation in a vacuum environment, eliminating corona discharge issues associated with a high voltage lead. There are two RCS pods on the ICPTA, with two engines on each pod. One of these two engines is a heritage flight engine from Project Morpheus. Its sea level nozzle was removed and replaced by an 85:1 nozzle machined using Inconel 718, resulting in a maximum thrust of 28 lbf under altitude conditions. The other engine is a scaled down version of the 28 lbf engine, designed to match the core and overall mixture ratios as well as other injector characteristics. This engine can produce a maximum thrust of 7 lbf with an 85:1 nozzle that was additively manufactured using Inconel 718. Both engines are film-cooled and capable of limited duration gas-gas and gas-liquid operation, as well as steady-state liquid-liquid operation. Each pod contains one of each version, such that two engines of the same thrust level can be fired as a couple on opposite pods. The RCS feed system is composed of symmetrical 3/8 inch lines that tap off of the main propellant manifold to send LOX and LCH4 outboard to the RCS pods. A Thermodynamic Vent System (TVS) is used to condition propellants at each pod by venting through an orifice and then routing the cold expansion products back through tubing that is welded along a large portion of the main RCS feed lines. Prior to final installation on the ICPTA, the RCS engines were tested in a small vacuum chamber at the Johnson Space Center (JSC) Energy Systems Test Area (ESTA) to verify functionality of the new COP ignition system and check out operation of the vacuum nozzles. After engine-level testing, the RCS engines were installed on the vehicle and a series of integrated hot-fire tests were performed at JSC consisting of various pulsing and steady-state firings as well as integrated main engine/RCS operation. The ICPTA was then integrated into the Plum Brook B-2 facility for vacuum and thermal/vacuum testing. Testing in the B-2 facility was composed of multiple thermal and pressure environments. The first set of tests were performed under ambient temperature and altitude pressure conditions. These tests consisted of a range of minimum impulse bit (MIB) pulsing sequences with low duty cycle, analogous to a coast phase in which the RCS is primarily used for station keeping. The primary goal of this sequence is to understand how propellant conditions were effected without an active TVS. In this scenario, consistent gas-gas operation is desirable since it results in a smaller MIB and more efficient propellant consumption. Multiple skin thermocouples are mounted on the feedlines, in addition to a submerged thermocouple on each commodity, in order to gather thermal data on the system. Higher duty cycle pulsing tests were then performed, analogous to an ascent or landing mission phase. The primary goal of this sequence was to examine how well the engines self-conditioned without active TVS when starting from a quiescent state. The TVS was then activated during some tests to demonstrate the capability to quickly condition the engines for higher pulsing demand scenarios. A thermocouple at the TVS outlet allows for the calculation of energy absorbed by the vented propellant. Lastly, tests with longer pulses and multiple engines firing either in sequence or simultaneously were run in order to gather transient system response data on waterhammer. Six total high-speed pressure transducers are installed on the RCS system, one sensor at the end of each propellant manifold line on the pods, and one at the tap-off location for each commodity. This will allow for the accurate characterization of waterhammer in the system under various propellant conditions and firing sequences. Other instrumentation for this test series includes nozzle throat thermocouples, chamber pressure measurement, heat soakback measurement, and tank wall plume impingement temperature measurement. The next set of tests were performed to demonstrate simultaneous main engine and RCS operation. Data from this test will be used to examine if there is any change to nominal operation of the RCS as a result of feed system interaction or other phenomenon. Some of these tests began under high vacuum conditions (target ambient pressure less than 1x10(exp -3) torr) and others began at altitude conditions. The last set of tests were performed with the B-2 cold wall active. Under these tests, many of the same low duty cycle MIB tests were repeated in order to characterize how propellant conditions changed with the lower heat leak. In this scenario the RCS manifold experiences much less heat leak, resulting in a change to how well the engines self-condition. As a result, an increase in maximum waterhammer pressures and a change in natural frequency of the system was expected due to higher density propellants. The lower heat leak should also result in a change to the MIB pulse profile, and data will be examined to understand how MIB repeatability is affected in the different operating environments. Parallel to the test efforts, a set of transient model development efforts were made to predict RCS performance. The primary effort was aimed at producing a SINDA/FLUINT model to predict propellant conditioning up to the engine inlet as a function of different environmental and operating parameters, with the goal of predicting chamber pressure, TVS performance, and propellant consumption over time. Preliminary results for this effort will be presented in comparison with test data. Additional modeling efforts were made using SINDA/FLUINT to predict waterhammer in the system since the software is capable of handling multiphase transient fluid dynamics. These results will be compared with the high-speed pressure transducer test data for validation purposes.

Atwell, Matthew J.↗

Improved solution for potential flow about arbitrary axisymmetric bodies by the use of a higher-order surface source method

An investigation is conducted of a case of axisymmetric bodies in which the application of main interest is an inlet, possibly with centerbody and ring vanes. The technique employed makes use of curved surface elements and a source density which varies over the element. Such an approach is designated a higher-order implementation. Questions of surface element geometry are discussed along with the computation of the induced velocity matrices and the organization of the calculation. The calculated results are compared with analytic solutions.

Hess, J. L.↗

Theoretical research program to study transition metal trimers and embedded clusters

Small transition metal clusters were studied at a high level of approximation, including all the valence electrons in the calculation and extensive electron correlation, in order to understand the electronic structure of these small metal clusters. By comparison of dimers, trimers, and possibly higher clusters, the information obtained was used to provide insights into the electronic structure of bulk transition metals. Small metal clusters are currently of considerable experimental interest and some information is becomming available both from matrix electron spin resonance studies and from gas phase spectroscopy. Collaboration between theorists and experimentalists is thus expected to be especially profitable at this time since there is some experimental information which can serve to guide the theoretical work.

Walch, S. P.↗

Water loss on Venus - The role of carbon monoxide

The four-to-fivefold difference in water abundance between the earth and Venus may reflect either initial differences in the bulk volatile content of the two planets, or massive water loss mechanisms on Venus. These two possibilities were investigated by performing thermodynamic calculations on the heterogeneous system C-O-H-N-S, varying C/H upward from its 0.033 terrestrial value. While atmospheric H2O decreases as bulk C/H increases, the latter would have to rise to an improbably high value in order to account for the low water abundance on Venus through initial deficiency alone. Calculations suggest that if the outgassed C/H on Venus was higher than on earth by even a factor of 5, it would have been sufficient for CO to become competitive with FeO as a sink for oxygen. Together with the lower initial water abundance value that follows from a higher C/H ratio, water loss due to CO may have been a major factor.

Richardson, S. M.↗

An Experimental Determination of Losses in a 3-Port Wave Rotor

Wave rotors, used in a gas turbine topping cycle, offer a potential route to higher specific power and lower specific fuel consumption. In order to exploit this potential properly, it is necessary to have some realistic means of calculating wave rotor performance, taking losses into account, so that wave rotors can be designed for good performance. This in turn requires a knowledge of the loss mechanisms. The experiment reported here was designed as a statistical experiment to identify the losses due to finite passage opening time, friction, and leakage. For simplicity, the experiment used a 3-port, flow divider, wave cycle, but the results should be applicable to other cycles. A 12 inch diameter rotor was used, with two different lengths, 9 inches and 18 inches, and two different passage widths, 0.25 inch and 0.54 inch, in order to vary friction and opening time. To vary leakage, moveable end-walls were provided so that the rotor to end-wall gap could be adjusted. The experiment is described, and the results are presented, together with a parametric fit to the data. The fit shows that there will be an optimum passage width for a given wave rotor, since, as the passage width increases, friction losses decrease, but opening-time losses increase, and vice-versa. Leakage losses can be made small at reasonable gap sizes.

Wilson, Jack↗

Progress on LES of Flow Past a Circular Cylinder

The objective of the present research is to assess the usefulness of large-eddy simulation (LES) methodology for flows in complex geometries. Flow past a circular cylinder has been calculated using a central-difference based solver, and the results have been compared to those obtained by a solver that employs higher-order upwind biased schemes (Beaudan & Moin, 1994). This comparison allows us to assess the suitability of these schemes for LES in complex geometry flows.

Mittal, R.↗

Evaluation of Magnet Configurations for Magnetohydrodynamic Trajectory Control during Planetary Entry

Magnetohydrodynamics is a phenomenon that can be harnessed during planetary entry to augment aerodynamic drag and may enable higher mass payloads to safely reach the surface. The magnetohydrodynamic force is quantified over a wide range of freestream conditions using computational fluid dynamics results from a previous study. The force is calculated for an array of small electromagnets, a large non-superconducting magnet, a large superconducting magnet, and a uniform field. The superconducting magnet produces a magnetohydrodynamic force within an order of magnitude of aerodynamic drag for velocities higher than 10 km/s, indicating that it may have a reasonable impact on the trajectory for some cases. The array of small magnets and non-superconducting magnet produced a magnetohydrodynamic force that is less than 1% of the aerodynamic drag, so their magnetic fields are not strong enough to affect an entry trajectory. Additionally, the magnet placement plays an important role in magnetohydrodynamic force magnitude, with a magnet located near the shoulder producing approximately eight times more force than a magnet placed on the axis of symmetry. A mass and power budget for each magnet configuration is given assuming current state-of-the-art magnet technology. This study also discusses implementation challenges for each type of magnet on a spacecraft.

Magnetohydrodynamics↗

The energy dependence of the ratios of secondary to primary elements in the cosmic radiation

The secondary to primary ratios B/C, N/O and (Sc-Mn)/Fe in the galactic cosmic rays have been measured in the overall energy interval 30-180 MeV/n with the University of Chicago cosmic ray telescope on board the satellite IMP-8 during the period 1974-1978. These results, together with the values of the same ratios measured at higher energies, have been compared to the results of cosmic ray propagation calculations using different pathlength distributions (PLD) and different levels of solar modulation, in order to select a single set of parameters consistent with all the measured ratios.

Garcia-Munoz, M.↗

Algorithm development with applications to aerodynamics and aeroelasticity

The development of a streamwise upwind algorithm is presented. Applications of this algorithm to steady flow over a delta wing and unsteady flow over an oscillating wing, respectively, are covered. An extension to higher order accuracy for upwind methods is discussed. This scheme will use the compatibility relations for the extension. The use of multiple zones in the calculation of unsteady flows is considered. Multiple zones are one way to treat complex configurations, such as complete aircraft. Aeroelastic calculations are discussed. A procedure for aeroelastic calculations is described that simultaneously solves the aerodynamic and structural equations of motion. Sample calculations are given to illustrate the above.

Goorjian, P. M.↗

An Exact Separation of the Spin-Free and Spin-Dependent Terms of the Dirac-Coulomb-Breit Hamiltonian

The Dirac Hamiltonian is transformed by extracting the operator (sigma x p)/2mc from the small component of the wave function and applying it to the operators of the original Hamiltonian. The resultant operators contain products of Paull matrices that can be rearranged to give spin-free and spin-dependent operators. These operators are the ones encountered in the Breit-Pauli Hamiltonian, as well as some of higher order in alpha(sup 2). However, since the transformation of the original Dirac Hamiltonian is exact, the new Hamiltonian can be used in variational calculations, with or without the spin-dependent terms. The new small component functions have the same symmetry properties as the large component. Use of only the spin-free terms of the new Hamiltonian permits the same factorization over spin variables as in nonrelativistic theory, and therefore all the post-Self-Consistent Field (SCF) machinery of nonrelativistic calculations can be applied. However, the single-particle functions are two-component orbitals having a large and small component, and the SCF methods must be modified accordingly. Numerical examples are presented, and comparisons are made with the spin-free second-order Douglas-Kroll transformed Hamiltonian of Hess.

Dyall, Kenneth G.↗

Thermocapillary Bubble Migration: Thermal Boundary Layers for Large Marangoni Numbers

The migration of an isolated gas bubble in an immiscible liquid possessing a temperature gradient is analyzed in the absence of gravity. The driving force for the bubble motion is the shear stress at the interface which is a consequence of the temperature dependence of the surface tension. The analysis is performed under conditions for which the Marangoni number is large, i.e. energy is transferred predominantly by convection. Velocity fields in the limit of both small and large Reynolds numbers are used. The thermal problem is treated by standard boundary layer theory. The outer temperature field is obtained in the vicinity of the bubble. A similarity solution is obtained for the inner temperature field. For both small and large Reynolds numbers, the asymptotic values of the scaled migration velocity of the bubble in the limit of large Marangoni numbers are calculated. The results show that the migration velocity has the same scaling for both low and large Reynolds numbers, but with a different coefficient. Higher order thermal boundary layers are analyzed for the large Reynolds number flow field and the higher order corrections to the migration velocity are obtained. Results are also presented for the momentum boundary layer and the thermal wake behind the bubble, for large Reynolds number conditions.

Balasubramaniam, R.↗

Higher-Order Statistical Moments of Predicted Sonic Boom Waveforms Through Turbulence

Sonic booms generated by supersonic aircraft are affected by turbulence in the atmospheric boundary layer through which they propagate. Turbulence effects lead to random variability of the sonic boom waveforms measured on the ground, complicating the prediction of such waveforms. As an initial effort to predict the waveform variability, the solution of the coherent or mean sonic boom waveform has previously been formulated by the author. The current paper extends the formulation to derive an expression of the second-order statistical moment necessary to calculate the variance of the spectral amplitudes. Since the derivation uses a full wave equation, results using the derived expression will be compared with those obtained using a parabolic approximation. In order to fully quantify the uncertainty of our predictions, the higher order statistical moments are also formulated and are shown to be approximately zero. Consequently, the probability density function (pdf) of the spectral amplitudes is predicted to be Gaussian. The formulation is further extended to determine the pdf of the loudness of sonic booms and quantify the uncertainties associated with the loudness prediction. Results from the formulation are compared with available flight test data.

sonic booms↗

Nonlinear diffusion in the solid phase

A Fourier series expansion method has been used to develop simple and relatively accurate solutions for nonlinear Fickian diffusion in the solid phase. For the fundamental harmonic, the first term in the Fourier expansion is qualitatively similar but quantitatively quite different from the conventional exponential function. In contrast, the Fourier coefficients of the higher order harmonics are combinations of fast-decay and slow-decay components. The simple analytical results agree well with numerical solutions for one sample calculation.

Tsang, Tung↗

The prediction of nonlinear longitudinal combustion instability in liquid propellant rockets

An analytical technique was developed to solve nonlinear longitudinal combustion instability problems. The analysis yields the transient and limit cycle behavior of unstable motors and the threshold amplitude required to trigger a linearly stable motor into unstable operation. The limit cycle waveforms were found to exhibit shock wave characteristics for most unstable engine operating conditions. A method of correlating the analytical solutions with experimental data was developed. Calculated results indicate that a second-order solution adequately describes the behavior of combustion instability oscillations over a broad range of engine operating conditions, but that higher order effects must be accounted for in order to investigate engine triggering.

Lores, M. E.↗

The role of higher-multipolar and repulsive forces in the calculation of collision-broadened line-widths of linear molecules

Collision-broadened line widths in CO-CO2 and CO-O2 collisions have been calculated by incorporating interactions due to octopoles and hexadecapoles and short-range repulsive interactions into Anderson's (1949) theory. It is shown how these higher-order interactions can be manipulated to yield good agreement with experimental data. A critical evaluation of this totally empirical manipulation suggests that a thorough revision of the theory is required for all but simple dipole-dipole interactions. In the process of the evaluation, the values of the multipole moments are discussed.

Varanasi, P.↗

On essentially non-oscillatory schemes on unstructured meshes: Analysis and implementation

A few years ago, the class of Essentially Non-Oscillatory Schemes for the numerical simulation of hyperbolic equations and systems was constructed. Since then, some extensions have been made to multidimensional simulations of compressible flows, mainly in the context of very regular structured meshes. In this paper, we first recall and improve the results of an earlier paper about non-oscillatory reconstruction on unstructured meshes, emphasizing the effective calculation of the reconstruction. Then we describe a class of numerical schemes on unstructured meshes and give some applications for its third order version. This demonstrates that a higher order of accuracy is indeed obtained, even on very irregular meshes.

Abgrall, R.↗