Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Perturbative methods”

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 1,189 records · Page 66
All sourcesNASA NTRSDOE OSTI
NASA NTRS1975

Interaction between a shock wave and a turbulent boundary layer in transonic flow

Interaction between a shock wave and an unseparated turbulent boundary layer is considered. The method of matched asymptotic expansions is used, with solutions valid in the double limit as Reynolds number tends to infinity and Mach number tends to unity. The shock is weak enough that interaction effects can be considered as perturbations to the undisturbed flow; the case considered is that where the sonic line is near the outer edge of the boundary layer. It is shown that, with order estimates for Reynolds stress perturbations, the induced wall pressure distribution can be calculated using only the two outer interaction regions, independent of a specific closure condition and that this solution is in fact a turbulent free interaction solution. A detailed analysis of the inner regions, for which an eddy viscosity model for the Reynolds shear stress is used, provides a description of the variations in velocity, temperature and density near and at the wall.

Adamson, T. C., Jr.↗
NASA NTRS1981

Development of the triplet singularity for the analysis of wings and bodies in supersonic flow

A supersonic triplet singularity was developed which eliminates internal waves generated by panels having supersonic edges. The triplet is a linear combination of source and vortex distributions which gives directional properties to the perturbation flow field surrounding the panel. The theoretical development of the triplet singularity is described together with its application to the calculation of surface pressures on wings and bodies. Examples are presented comparing the results of the new method with other supersonic methods and with experimental data.

Woodward, F. A.↗
NASA NTRS1981

The role of in-situ measurements in scintillation modelling

It is shown that the conflicting equatorial scintillation observations obtained from greatly separated ground stations can be organized in the framework of a longitudinal variation of irregularity occurrence, given satellite-borne, in situ measurements of irregularity amplitude of the global F-region irregularity morphology's general features. High-inclination satellite data are used to delineate the morphological features of the polar cap by means of such a method. The lack of diurnal and magnetic control of the irregularity morphology within the low solar flux, northern winter polar cap distinguishes this region from the auroral oval regime. A polar-orbiting communication system sensitive to phase perturbations may observe large differences in the phase-to-amplitude scintillation ratio, as it traverses the auroral oval and proceeds into the polar cap, with its sun-aligned arc system.

Basu, S.↗
NASA NTRS1984

Analysis for leakage and rotordynamic coefficients of surface roughened tapered annular gas seals

In order to soften the effects of rub, the smooth stators of turbine gas seals are sometimes replaced by a honeycomb surface. This deliberately roughened stator and smooth rotor combination retards the seal leakage and may lead to enhanced rotor stability. However, many factors determine the rotordynamic coefficients and little is known as to the effectiveness of these honeycomb seals under various changes in the independent seal parameters. An analytical-computational method to solve for the rotordynamic coefficients of this type of compressible-flow seal is developed. The governing equations for surface roughned tapered annular gas seals are based on a modified Hirs' turbulent bulk flow model. A perturbation analysis is employed to develop zeroth and first-order perturbation equations. These equations are numerically integrated to solve for the leakage, pressure, density, and velocity for small motion of the shaft about the centered position. The resulting pressure distribution is then integrated to find the corresponding rotor-dynamic coefficients.

Nelson, C. C.↗
NASA NTRS1988

A multi-element vortex lattice method for calculating the geometry and effects of a helicopter rotor wake in forward flight

A method is described for the analysis of the unsteady, incompressible potential flow associated with a helicopter rotor and it's wake in forward flight. This method is particularly useful in low advance ratio flight due to the major contribution, in the near field, of the deformed wake. The rotor geometry is prescribed and the unsteady wake geometry is computed from the local flow perturbation velocities. The wake is modeled as a full vortex lattice. The rotor geometry is arbitrary and several rotor blades can be represented. The unsteady airloads on the rotor blades are computed in the presence of the deformed rotor wake by a time-stepping technique. Solution for the load distribution on the blade surfaces is found by prescribing boundary conditions in a reference system which rotates with the blade tips. Transformation tensors are used to describe the contribution of the wake in the inertial system to the rotor in the rotating reference system. The effects of blade cyclic pitch variation are computed using a rotation tensor. The deformation of the wake is computed in the inertial frame. The wake is started impulsively from rest, allowing a natural convection of the wake with time.

Berry, John D.↗
NASA NTRS2001

Resonances in Positronium Hydride

Recently, Ho and his colleagues have calculated the positions and widths of a series of resonances in the Ps+H scattering system, using the complex -rotation method and have compared them with estimates that I made many years ago using a quite different technique. I assumed that the resonance mechanism was the existence in the rearrangement channel [e+ + H-] of an infinite series of perturbed Coulomb bound states. Although these must be broadened and shifted by coupling with the open scattering channel, I expected them to lie very close to the actual resonance positions. To verify this, I did a model calculation for S-waves, including the coupling, and found that the first two resonances were not shifted very far from their unperturbed position. The new, detailed calculation agrees with this result, but when the P-wave was examined it was found, surprisingly, that the lowest resonance indeed moved up in energy by a large amount. With the help of Joseph DiRienzi of the College of Notre Dame of Maryland I am now extending the old calculation to P- and D-waves, in an attempt to understand this unexpected energy shift. Results will be presented at the Workshop.

Drachman, Richard J.↗
NASA NTRS2001

Short-Term Dynamical Interactions Among Extrasolar Planets

We show that short-term perturbations among massive planets in multiple planet systems can result in radial velocity variations of the central star which differ substantially from velocity variations derived assuming the planets are executing independent Keplerian motions. We discuss two alternate fitting methods which can lead to an improved dynamical description of multiple planet systems. In the first method, the osculating orbital elements are determined via a Levenberg-Marquardt minimization scheme driving an N-body integrator. The second method is an improved analytic model in which orbital elements such as the periods and longitudes of periastron are allowed to vary according to a simple model for resonant interactions between the planets. Both of these methods can potentially determine the true masses for the planets by eliminating the sin(i) degeneracy inherent in fits that assume independent Keplerian motions. As more radial velocity data is accumulated from stars such as GJ876, these methods should allow for unambiguous determination of the planetary masses and relative inclinations.

Laughlin, Gregory↗
NASA NTRS2008

Space Technology 5 Observations of Auroral Field-Aligned Currents

During its three month long technology validation mission, Space Technology 5 (ST-5) returned high quality multi-point measurements of the near-Earth magnetic field. Its three micro-satellites were launched into a 300 x 4500 km, dawn - dusk, sun synchronous orbit (inclination = 105.60) orbit with a period of 138 min by a Pegasus launch vehicle on March 22, 2006. The spacecraft were maintained in a "pearls on a sting" constellation with controlled spacings ranging from just over 5000 km down to under 50 km. The individual micro-satellites were 48 cm tall octagons with diameters of 50 cm. They were spin-stabilized at approximately 20 rpm at deployment and slowly spun-down to about 15 rpm by the end of the mission. Each spacecraft carried a miniature tri-axial fluxgate magnetometer (MAG) provided by the University of California at Los Angeles mounted at the end of a ultra-low mass 72 cm boom. These data allow, for the first time, the separation of temporal and spatial variations in field-aligned current (FAC) perturbations measured in low-Earth orbit on time scales of 10 sec to 10 min. The constellation measurements are used to directly determine field-aligned current sheet motion, thickness. and current density. Two multi-point methods for the inference of FAC current density that have not previously been possible in low-Earth orbit are demonstrated: 1) the -standard method." based upon s/c velocity, but corrected for FAC current sheet motion. and 2) the "gradiometer method" which uses simultaneous magnetic field measurements at two points with known separation. Future studies will apply these methods to the entire ST-5 data sct and expand to include horizontal ionospheric currents. ULF waves and geomagnetic field gradient analyses.

Slavin, James↗
NASA NTRS2018

Assessment and Verification of SLS Block 1-B Exploration Upper Stage State and Stage Disposal Performance

One of the SLS Navigation System's key performance requirements is a constraint on the payload system's delta-v allocation to correct for insertion errors due to vehicle state uncertainty at payload separation. The SLS navigation team has developed a Delta-Delta-V analysis approach to assess the effect on trajectory correction maneuver (TCM) design needed to correct for navigation errors. This approach differs from traditional covariance analysis based methods and makes no assumptions with regard to the propagation of the state dynamics. This allows for consideration of non-linearity in the propagation of state uncertainties. The Delta-Delta-V analysis approach re-optimizes perturbed SLS mission trajectories by varying key mission states in accordance with an assumed state error. The state error is developed from detailed vehicle 6-DOF Monte Carlo analysis or generated using covariance analysis. These perturbed trajectories are compared to a nominal trajectory to determine necessary TCM design. To implement this analysis approach, a tool set was developed which combines the functionality of a 3-DOF trajectory optimization tool, Copernicus, and a detailed 6-DOF vehicle simulation tool, Marshall Aerospace Vehicle Representation in C (MAVERIC). In addition to delta-v allocation constraints on SLS navigation performance, SLS mission requirement dictate successful upper stage disposal. Due to engine and propellant constraints, the SLS Exploration Upper Stage (EUS) must dispose into heliocentric space by means of a lunar fly-by maneuver. As with payload delta-v allocation, upper stage disposal maneuvers must place the EUS on a trajectory that maximizes the probability of achieving a heliocentric orbit post Lunar fly-by considering all sources of vehicle state uncertainty prior to the maneuver. To ensure disposal, the SLS navigation team has developed an analysis approach to derive optimal disposal guidance targets. This approach maximizes the state error covariance prior to the maneuver to develop and re-optimize a nominal disposal maneuver (DM) target that, if achieved, would maximize the potential for successful upper stage disposal. For EUS disposal analysis, a set of two tools was developed. The first considers only the nominal pre-disposal maneuver state, vehicle constraints, and an a priori estimate of the state error covariance. In the analysis, the optimal nominal disposal target is determined. This is performed by re-formulating the trajectory optimization to consider constraints on the eigenvectors of the error ellipse applied to the nominal trajectory. A bisection search methodology is implemented in the tool to refine these dispersions resulting in the maximum dispersion feasible for successful disposal via lunar fly-by. Success is defined based on the probability that the vehicle will not impact the lunar surface and will achieve a characteristic energy (C3) relative to the Earth such that it is no longer in the Earth-Moon system. The second tool propagates post-disposal maneuver states to determine the success of disposal for provided trajectory achieved states. This is performed using the optimized nominal target within the 6-DOF vehicle simulation. This paper will discuss the application of the Delta-Delta-V analysis approach for performance evaluation as well as trajectory re-optimization so as to demonstrate the system's capability in meeting performance constraints. Additionally, further discussion of the implementation of assessing disposal analysis will be provided.

Patrick, Sean↗
NASA NTRS1979

Long period perturbations of earth satellite orbits

All the equations involved in extending the PS phi solution to include the long periodic and second order secular effects of the zonal harmonics are presented. Topics covered include DSphi elements and relations for their conconical transformation into the PS phi elements; the solution algorithm based on the Von Zeipel method; and the elimination of long periodic terms and analytical integration of primed variables. The equations were entered into the ASOP program, checked out, and verified. Comparisons with numerical integrations show the long period theory to be accurate within several meters after 800 revolutions.

Wang, K. C.↗
NASA NTRS2000

Theory of the lattice Boltzmann Method: Dispersion, Dissipation, Isotropy, Galilean Invariance, and Stability

The generalized hydrodynamics (the wave vector dependence of the transport coefficients) of a generalized lattice Boltzmann equation (LBE) is studied in detail. The generalized lattice Boltzmann equation is constructed in moment space rather than in discrete velocity space. The generalized hydrodynamics of the model is obtained by solving the dispersion equation of the linearized LBE either analytically by using perturbation technique or numerically. The proposed LBE model has a maximum number of adjustable parameters for the given set of discrete velocities. Generalized hydrodynamics characterizes dispersion, dissipation (hyper-viscosities), anisotropy, and lack of Galilean invariance of the model, and can be applied to select the values of the adjustable parameters which optimize the properties of the model. The proposed generalized hydrodynamic analysis also provides some insights into stability and proper initial conditions for LBE simulations. The stability properties of some 2D LBE models are analyzed and compared with each other in the parameter space of the mean streaming velocity and the viscous relaxation time. The procedure described in this work can be applied to analyze other LBE models. As examples, LBE models with various interpolation schemes are analyzed. Numerical results on shear flow with an initially discontinuous velocity profile (shock) with or without a constant streaming velocity are shown to demonstrate the dispersion effects in the LBE model; the results compare favorably with our theoretical analysis. We also show that whereas linear analysis of the LBE evolution operator is equivalent to Chapman-Enskog analysis in the long wave-length limit (wave vector k = 0), it can also provide results for large values of k. Such results are important for the stability and other hydrodynamic properties of the LBE method and cannot be obtained through Chapman-Enskog analysis.

Lallemand, Pierre↗
NASA NTRS1973

Differential transformation for satellite injection.

This paper provides an analytical method for computing the required orbital inclination change when the nominal orbital node rate is slightly modified to meet satellite mission requirements. A first-order theory retaining up to J sub 2 terms of the earth-oblateness perturbation has been found adequate to generate a four-decimal digit accuracy for required orbital changes. A numerical example of an actual ITOS series prelaunch analysis has been given to illustrate computational steps.

Sugai, I.↗
NASA NTRS1975

Analysis of transonic flow about lifting wing-body configurations

An analytical solution was obtained for the perturbation velocity potential for transonic flow about lifting wing-body configurations with order-one span-length ratios and small reduced-span-length ratios and equivalent-thickness-length ratios. The analysis is performed with the method of matched asymptotic expansions. The angles of attack which are considered are small but are large enough to insure that the effects of lift in the region far from the configuration are either dominant or comparable with the effects of thickness. The modification to the equivalence rule which accounts for these lift effects is determined. An analysis of transonic flow about lifting wings with large aspect ratios is also presented.

Barnwell, R. W.↗
NASA NTRS1992

Numerical models for the collapse and fragmentation of centrally condensed molecular cloud cores

The gravitational collapse and fragmentation of centrally condensed molecular cloud cores are investigated using a new hydrodynamical code. The numerical scheme is second-order accurate and uses explicit finite difference methods to advance the fluid variables on a 3D Cartesian grid. Two initial power-law density profiles, rho varies as r exp -1 and rho varies as r exp -2, are considered, as well as two initial density perturbations in the azimuthal coordinate theta, rho-i - rho(1 + a cos 2theta) where a = 0.1 and 0.5. Fragmentation is found to be possible in these centrally condensed cores if the initial conditions also include differential rotation. Models which collapse with initial uniform rotation do not produce fragments. If molecular cloud cores are indeed centrally condensed, as suggested by observations of star-forming regions and by studies of ambipolar diffusion, then differential rotation may be a mechanism for producing binary protostars during gravitational collapse.

Myhill, Elizabeth A.↗
NASA NTRS1995

Sensitivity analysis of frictional contact response of axisymmetric composite structures

A computational procedure is presented for evaluating the sensitivity coefficients of the static frictional contact response of axisymmetric composite structures. The structures are assumed to consist of an arbitrary number of perfectly bonded homogeneous anisotropic layers. The material of each layer is assumed to be hyperelastic, and the effect of geometric nonlinearity is included. The sensitivity coefficients measure the sensitivity of the response variations in different material, lamination and geometric parameters of the structure. A displacement finite element model is used for the discretization. The normal contact conditions are incorporated into the formulation by using a perturbed Lagrangian approach with the fundamental unknowns consisting of nodal displacements, and Lagrange multipliers associated with the contact conditions. The Lagrange multipliers are allowed to be discontinuous at interelement boundaries. Tangential contact conditions are incorporated by using a penalty method in conjunction with the classical Coulomb's friction model. The Newton-Raphson iterative scheme is used for the solution of the resulting nonlinear algebraic equations, and for the determination of the contact region, contact conditions (sliding or sticking), and the contact pressures. The sensitivity coefficients are evaluated by using a direct differentiation approach. Numerical results are presented for the frictional contact of a composite spherical cap pressed against a rigid plate.

Karaoglan, I.↗
NASA NTRS2000

Generation and Radiation of Acoustic Waves from a 2-D Shear Layer

A parallel numerical simulation of the radiation of sound from an acoustic source inside a 2-D jet is presented in this paper. This basic benchmark problem is used as a test case for scattering problems that are presently being solved by using the Impedance Mismatch Method (IMM). In this technique, a solid body in the domain is represented by setting the acoustic impedance of each medium, encountered by a wave, to a different value. This impedance discrepancy results in reflected and scattered waves with appropriate amplitudes. The great advantage of the use of this method is that no modifications to a simple Cartesian grid need to be made for complicated geometry bodies. Thus, high order finite difference schemes may be applied simply to all parts of the domain. In the IMM, the total perturbation field is split into incident and scattered fields. The incident pressure is assumed to be known and the equivalent sources for the scattered field are associated with the presence of the scattering body (through the impedance mismatch) and the propagation of the incident field through a non-uniform flow. An earlier version of the technique could only handle uniform flow in the vicinity of the source and at the outflow boundary. Scattering problems in non-uniform mean flow are of great practical importance (for example, scattering from a high lift device in a non-uniform mean flow or the effects of a fuselage boundary layer). The solution to this benchmark problem, which has an acoustic wave propagating through a non-uniform mean flow, serves as a test case for the extensions of the IMM technique.

Agarwal, Anurag↗
NASA NTRS1989

Beat to beat variability in cardiovascular variables: noise or music?

Cardiovascular variables such as heart rate, arterial blood pressure, stroke volume and the shape of electrocardiographic complexes all fluctuate on a beat to beat basis. These fluctuations have traditionally been ignored or, at best, treated as noise to be averaged out. The variability in cardiovascular signals reflects the homeodynamic interplay between perturbations to cardiovascular function and the dynamic response of the cardiovascular regulatory systems. Modern signal processing techniques provide a means of analyzing beat to beat fluctuations in cardiovascular signals, so as to permit a quantitative, noninvasive or minimally invasive method of assessing closed loop hemodynamic regulation and cardiac electrical stability. This method promises to provide a new approach to the clinical diagnosis and management of alterations in cardiovascular regulation and stability.

Non-NASA Center↗