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At least 811 records · Page 45
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

Development of a numerical procedure to map a general 3-d body onto a near-circle

Conformal mapping is a classical technique utilized for solving problems in aerodynamics and hydrodynamics. Conformal mapping is utilized in the construction of grids around airfoils, engine inlets and other aircraft configurations. These shapes are transformed onto a near-circle image for which the equations of fluid motion are discretized on the mapped plane and solved numerically by utilizing the appropriate techniques. In comparison to other grid-generation techniques such as algerbraic or differential type, conformal mapping offers an analytical and accurate form even if the grid deformation is large. One of the most appealing features is that the grid can be constrained to remain orthogonal to the body after the transformation. Hence, the grid is suitable for analyzing the supersonic flow past a blunt object. The associated shock as a coordinate surface adjusts its position in the course of computation until convergence is reached. The present work applied conformal mapping to 3-D bodies with no axis of symmetry such as the Aerobraking Flight Experiment (AFE) vehicle, transforming the AFE shape onto a near-circle image. A numerical procedure and code are used to generate grids around the AFE body.

Hommel, M. J.↗
NASA NTRS1989

Numerical studies of convective heat transfer in an inclined semi-annular enclosure

Natural convection heat transfer in a two-dimensional differentially heated semiannular enclosure is studied. The enclosure is isothermally heated and cooled at the inner and outer walls, respectively. A commercial software based on the SIMPLER algorithm was used to simulate the velocity and temperature profiles. Various parameters that affect the momentum and heat transfer processes were examined. These parameters include the Rayleigh number, Prandtl number, radius ratio, and the angle of inclination. A flow regime extending from conduction-dominated to convection-dominated flow was examined. The computed results of heat transfer are presented as a function of flow parameter and geometric factors. It is found that the heat transfer rate attains a minimum when the enclosure is tilted about +50 deg with respect to the gravitational direction.

Wang, L.-W.↗
NASA NTRS1993

A critical analysis of the accuracy of several numerical techniques for combustion kinetic rate equations

A detailed analysis of the accuracy of several techniques recently developed for integrating stiff ordinary differential equations is presented. The techniques include two general-purpose codes EPISODE and LSODE developed for an arbitrary system of ordinary differential equations, and three specialized codes CHEMEQ, CREK1D, and GCKP4 developed specifically to solve chemical kinetic rate equations. The accuracy study is made by application of these codes to two practical combustion kinetics problems. Both problems describe adiabatic, homogeneous, gas-phase chemical reactions at constant pressure, and include all three combustion regimes: induction, heat release, and equilibration. To illustrate the error variation in the different combustion regimes the species are divided into three types (reactants, intermediates, and products), and error versus time plots are presented for each species type and the temperature. These plots show that CHEMEQ is the most accurate code during induction and early heat release. During late heat release and equilibration, however, the other codes are more accurate. A single global quantity, a mean integrated root-mean-square error, that measures the average error incurred in solving the complete problem is used to compare the accuracy of the codes. Among the codes examined, LSODE is the most accurate for solving chemical kinetics problems. It is also the most efficient code, in the sense that it requires the least computational work to attain a specified accuracy level. An important finding is that use of the algebraic enthalpy conservation equation to compute the temperature can be more accurate and efficient than integrating the temperature differential equation.

Radhadrishnan, Krishnan↗
NASA NTRS1978

An extension of MacCormack's method for flows with higher-order equations and in different configurations

The numerical scheme for the computation of a shock discontinuity developed by MacCormack has been extended to solve a number of differential equations, including cases explicitly containing higher-order derivatives: (1) Korteweg-de Vries equation with a term of third-order derivative, (2) a system of nonlinear equations governing nonsteady one-dimensional plasma flow in cylindrical coordinate, (3) equations of solar wind. Comparisons with previous results are made, if available, to illustrate the advantages of the present method. The question of convergence of the numerical calculation is discussed.

Ying, S. J.↗
NASA NTRS1975

Nonlinear seismic analysis of a reactor structure impact between core components

The seismic analysis of the FFTF-PIOTA (Fast Flux Test Facility-Postirradiation Open Test Assembly), subjected to a horizontal DBE (Design Base Earthquake) is presented. The PIOTA is the first in a set of open test assemblies to be designed for the FFTF. Employing the direct method of transient analysis, the governing differential equations describing the motion of the system are set up directly and are implicitly integrated numerically in time. A simple lumped-nass beam model of the FFTF which includes small clearances between core components is used as a "driver" for a fine mesh model of the PIOTA. The nonlinear forces due to the impact of the core components and their effect on the PIOTA are computed.

Hill, R. G.↗
NASA NTRS1987

Bifurcation properties of a stratospheric vacillation model

Nonlinear properties of the stratospheric vacillation model of Holton and Mass (1976) are studied numerically using bifurcation theory. Severe truncation and vertical differencing are used to obtain 81 nonlinear ordinary differential equations with time-dependent variables. Three branches of the steady solutions are determined using Powell's hybrid method and the pseudoarclength continuation method, and a multiplicity of stable steady-state solutions with different vertical structures are found to exist in some range of the bifurcation parameter. Periodic solutions are found which branch off from a steady solution by a Hopf bifurcation. It is suggested that the interannual variability of the stratospheric circulation in the middle and high latitudes during winter may be explained by the multiplicity of steady and periodic stable solutions.

Yoden, Shigeo↗
NASA NTRS1987

A new approach for shaping of dual-reflector antennas

The shaping of 2-D dual-reflector antenna systems to generate a prescribed distribution with uniform phase at the aperture of the second reflector is examined. This method is based on the geometrical nature of Cassegrain and Gregorian dual-reflector antennas. The method of syntheses satisfies the principles of geometrical optics which are the foundations of dual-reflector designs. Instead of setting up differential equations or heuristically designing the subreflector, a set of algebraic equations is formulated and solved numerically to obtain the desired surfaces. The caustics of the reflected rays from the subreflector can be obtained and examined. Several examples of 2-D dual-reflector shaping are shown to validate the study. Geometrical optics and physical optics are used to calculate the scattered fields from the reflectors.

Lee, Teh-Hong↗
NASA NTRS1989

Jupiter's Great Red Spot as a shallow water system

Voyager cloud-top velocity data for Jupiter's Great Red Spot (GRS) is used to derive the bottom topography up to a constant that depends on the unknown radius of deformation. The bottom topography is inferred from the Bernoulli streamfunction, kinetic energy per unit mass, and absolute vorticity values derived from the velocity data. The results are used to calculate potential vorticity versus latitude far from the vortex. It is found that the deep atmosphere is in differential motion and that the far-field potential vorticity gradient changes sign at several latitudes. Numerical experiments are conducted to study the time-dependent behavior of the shallow water analog of Jupiter's analog.

Dowling, Timothy E.↗
NASA NTRS1991

A simplified formulation of photon transport in leaf canopies with scatterers of finite dimensions

A formalism for photon transport in leaf canopies with finite-dimensional scattering centers that mutually cross-shade was recently proposed resulting in an equation set which is rather complicated. In this paper, we propose a simplification of the correction factors that describe the correlation in photon fates. These simplified correction factors permit the derivation of a modified integro-differential transfer equation with two additional terms that arise from considerations of finite size scatterers. A numerical procedure for the solution of this transfer equation in the framework of a successive collisions approach is also presented.

Myneni, Ranga B.↗
NASA NTRS1991

Minimum fuel coplanar aeroassisted orbital transfer using collocation and nonlinear programming

The fuel optimal control problem arising in coplanar orbital transfer employing aeroassisted technology is addressed. The mission involves the transfer from high energy orbit (HEO) to low energy orbit (LEO) without plane change. The basic approach here is to employ a combination of propulsive maneuvers in space and aerodynamic maneuvers in the atmosphere. The basic sequence of events for the coplanar aeroassisted HEO to LEO orbit transfer consists of three phases. In the first phase, the transfer begins with a deorbit impulse at HEO which injects the vehicle into a elliptic transfer orbit with perigee inside the atmosphere. In the second phase, the vehicle is optimally controlled by lift and drag modulation to satisfy heating constraints and to exit the atmosphere with the desired flight path angle and velocity so that the apogee of the exit orbit is the altitude of the desired LEO. Finally, the second impulse is required to circularize the orbit at LEO. The performance index is maximum final mass. Simulation results show that the coplanar aerocapture is quite different from the case where orbital plane changes are made inside the atmosphere. In the latter case, the vehicle has to penetrate deeper into the atmosphere to perform the desired orbital plane change. For the coplanar case, the vehicle needs only to penetrate the atmosphere deep enough to reduce the exit velocity so the vehicle can be captured at the desired LEO. The peak heating rates are lower and the entry corridor is wider. From the thermal protection point of view, the coplanar transfer may be desirable. Parametric studies also show the maximum peak heating rates and the entry corridor width are functions of maximum lift coefficient. The problem is solved using a direct optimization technique which uses piecewise polynomial representation for the states and controls and collocation to represent the differential equations. This converts the optimal control problem into a nonlinear programming problem which is solved numerically by using a modified version of NPSOL. Solutions were obtained for the described problem for cases with and without heating constraints. The method appears to be more robust than other optimization methods. In addition, the method can handle complex dynamical constraints.

Shi, Yun Yuan↗
NASA NTRS1967

Integrating Matrix Method for Determining the Natural Vibrations of a Rotating, Unsymmetrical Beam with Application to Twisted Propeller Blades

A numerical method is Presented for determining the natural vibration frequencies, and the corresponding mode shapes, of a rotating cantilever beam which has a nonuniform, unsymmetrical cross section. Two coupled fourth-order differential equations of motion with variable coefficients are derived which govern the motion of such a beam having deformations in two directions. Through the development and utilization of the integrating matrix, the solution of the differential equations is obtained in the form of an eigenvalue problem. The solutions to the eigenvalue problem are determined by an iteration method based upon a special orthogonality relationship which is derived. Numerical examples, including an application to a twisted propeller blade, are presented with the results of the integrating matrix solutions being compared to exact solutions and experimental data.

Hunter, William F.↗
NASA NTRS2001

System Simulation by Recursive Feedback: Coupling a Set of Stand-Alone Subsystem Simulations

Conventional construction of digital dynamic system simulations often involves collecting differential equations that model each subsystem, arran g them to a standard form, and obtaining their numerical gin solution as a single coupled, total-system simultaneous set. Simulation by numerical coupling of independent stand-alone subsimulations is a fundamentally different approach that is attractive because, among other things, the architecture naturally facilitates high fidelity, broad scope, and discipline independence. Recursive feedback is defined and discussed as a candidate approach to multidiscipline dynamic system simulation by numerical coupling of self-contained, single-discipline subsystem simulations. A satellite motion example containing three subsystems (orbit dynamics, attitude dynamics, and aerodynamics) has been defined and constructed using this approach. Conventional solution methods are used in the subsystem simulations. Distributed and centralized implementations of coupling have been considered. Numerical results are evaluated by direct comparison with a standard total-system, simultaneous-solution approach.

Nixon, D. D.↗
NASA NTRS2003

Application of Satellite SAR Imagery in Mapping the Active Layer of Arctic Permafrost

The objective of this project is to map the spatial variation of the active layer over the arctic permafrost in terms of two parameters: (i) timing and duration of thaw period and (ii) differential frost heave and thaw settlement of the active layer. To achieve this goal, remote sensing, numerical modeling, and related field measurements are required. Tasks for the University of Colorado team are to: (i) determine the timing of snow disappearance in spring through changes in surface albedo (ii) simulate the freezing and thawing processes of the active layer and (iii) simulate the impact of snow cover on permafrost presence.

Zhang, Ting-Jun↗
NASA NTRS1998

Aerodynamic Design Optimization on Unstructured Meshes Using the Navier-Stokes Equations

A discrete adjoint method is developed and demonstrated for aerodynamic design optimization on unstructured grids. The governing equations are the three-dimensional Reynolds-averaged Navier-Stokes equations coupled with a one-equation turbulence model. A discussion of the numerical implementation of the flow and adjoint equations is presented. Both compressible and incompressible solvers are differentiated and the accuracy of the sensitivity derivatives is verified by comparing with gradients obtained using finite differences. Several simplifying approximations to the complete linearization of the residual are also presented, and the resulting accuracy of the derivatives is examined. Demonstration optimizations for both compressible and incompressible flows are given.

Nielsen, Eric J.↗
NASA NTRS2012

Free-Free Transitions in the Presence of Laser Fields and Debye Potential at Very Low Incident Electron Energies

We study the free-free transition in electron-helium ion in the ground state and embedded in a Debye potential in the presence of an external laser field at very low incident electron energies. The laser field is treated classically while the collision dynamics is treated quantum mechanically. The laser field is chosen as monochromatic, linearly polarized and homogeneous. The incident electron is considered to be dressed by the laser field in a nonperturbative manner by choosing Volkov wave function for it. The scattering wave function for the incident electron on the target embedded in a Debye potential is solved numerically by taking into account the effect of electron exchange. We calculate the laser-assisted differential and total cross sections for free-free transition for absorption/emission of a single photon or no photon exchange. The results will be presented at the conference.

Bhatia, Anand↗
NASA NTRS2018

Instability Wave–Streak Interactions in a High Mach Number Boundary Layer at Flight Conditions

The interaction of stationary streaks undergoing nonmodal growth with modally unstable instability waves in a hypersonic boundary-layer flow is studied using numerical computations. The geometry and flow conditions are selected to match a relevant trajectory location from the ascent phase of the HIFiRE-1 flight experiment; namely, a 7 degree half-angle, circular cone with 2.5 mm nose radius, freestream Mach number equal to 5.30, unit Reynolds number equal to 13.42 m -1 , and wall-to-adiabatic temperature ratio of approximately 0.35 over most of the vehicle. This paper investigates the nonlinear evolution of initially linear optimal disturbances that evolve into finite-amplitude streaks, followed by an analysis of the modal instability characteristics of the perturbed, streaky boundary-layer flow. The investigation is performed with stationary direct numerical simulations (DNS) and plane-marching parabolized stability equations (PSE), in conjunction with partial-differential-equation-based planar eigenvalue analysis. The overall effect of streaks is to reduce the peak amplification factors of instability waves, indicating a possible downstream shift in the onset of laminar-turbulent transition. The present study confirms previous findings that the mean flow distortion of the nonlinear streak perturbation reduces the amplification rates of the Mack-mode instability. More importantly, however, the present results demonstrate that the spanwise varying component of the streak can produce a larger effect on the Mack-mode amplification. The study with selected azimuthal wavenumbers for the stationary streaks reveals that a wavenumber of approximately 1.4 times larger than the optimal wavenumber is more effective in stabilizing the planar Mack-mode instabilities. In the absence of unstable first-mode waves for the present cold-wall condition, transition onset is expected to be delayed until the peak streak amplitude increases to nearly 35 percent of the freestream velocity, when intrinsic instabilities of the boundary-layer streaks begin to dominate the transition process. For streak amplitudes below that limit a significant net stabilization is achieved, yielding a potential transition delay that can exceed 100 percent of the length of the laminar region in the uncontrolled case.

Boundary layer stability↗
NASA NTRS1987

Factorization and the synthesis of optimal feedback kernels for differential-delay systems

A combination of ideas from the theories of operator Riccati equations and Volterra factorizations leads to the derivation of a novel, relatively simple set of hyperbolic equations which characterize the optimal feedback kernel for the finite-time regulator problem for autonomous differential-delay systems. Analysis of these equations elucidates the underlying structure of the feedback kernel and leads to the development of fast and accurate numerical methods for its computation. Unlike traditional formulations based on the operator Riccati equation, the gain is characterized by means of classical solutions of the derived set of equations. This leads to the development of approximation schemes which are analogous to what has been accomplished for systems of ordinary differential equations with given initial conditions.

Milman, Mark M.↗
NASA NTRS2003

Multibody Parachute Flight Simulations for Planetary Entry Trajectories Using "Equilibrium Points"

A method has been developed to reduce numerical stiffness and computer CPU requirements of high fidelity multibody flight simulations involving parachutes for planetary entry trajectories. Typical parachute entry configurations consist of entry bodies suspended from a parachute, connected by flexible lines. To accurately calculate line forces and moments, the simulations need to keep track of the point where the flexible lines meet (confluence point). In previous multibody parachute flight simulations, the confluence point has been modeled as a point mass. Using a point mass for the confluence point tends to make the simulation numerically stiff, because its mass is typically much less that than the main rigid body masses. One solution for stiff differential equations is to use a very small integration time step. However, this results in large computer CPU requirements. In the method described in the paper, the need for using a mass as the confluence point has been eliminated. Instead, the confluence point is modeled using an "equilibrium point". This point is calculated at every integration step as the point at which sum of all line forces is zero (static equilibrium). The use of this "equilibrium point" has the advantage of both reducing the numerical stiffness of the simulations, and eliminating the dynamical equations associated with vibration of a lumped mass on a high-tension string.

Raiszadeh, Ben↗