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NASA NTRS1989

Preconditioning matrices for the pseudospectral approximation of first-order operators

The behavior of the eigenvalues of preconditioning matrices for the pseudospectral approximation to the derivative operator has been analyzed in one and two dimensions. The one-dimensional analysis resulted in real and positive eigenvalues for the selected tridiagonal matrices. In the two-dimensional analysis, the eigenvalues of the selected block-diagonal matrices behaved well, but the preconditioner is full and therefore not suitable for applications. The Richardson scheme has been applied in the unpreconditioned as well as the preconditioned version to find the solution of the model problem.

Funaro, D.↗

NASA NTRS1995

Coronal heating by the resonant absorption of Alfven waves: Wavenumber scaling laws.

The importance of global modes in coronal loop heating is well established. In the present work the scaling of the global-mode resonant heating rate with the perturbation wavenumbers is studied with the numerical solution of the linearized time-dependent MHD equations for a full compressible, low-beta, resistive plasma using an implicit integration scheme. The numerical simulations demonstrate that the dissipation on inhomogeneties in the background Alfven speed occurs in narrow resonant layer with the highest heating rate at the global-mode frequency. The global-mode heating rate H (sub r) was found to scale as H (Sub r) approximately k (sub y) (exp 1.03) when k (sub z) = 0.1, and as H (sub r) approximately k (sub y) (exp -1.93) when k (sub z) = 0.75, where k (sub y) and k (sub z) are the wavenumbers in the perpendicular and parallel to the magnetic field directions, respectively, while the dependence of H (sub r) on k (sub z) is more complex. The quality factor Q of the MHD resonance cavity scales as Q approximately k (sub y) (exp -1.8) for k (sub z) = 0.75 and as Q approximately k (sub y) (exp -1.46) for k (sub z) = 0.1. The numerically determined heating rate scaling, the global-mode fequency, and the quality factor are in good agreement with the analytical linear theory. The magnitude of the perturbed velocities was found to decrease with k (sub y). Assuming typical coronal loop parameters (B (sub 0) = 100-200 G, upsilon (sub A) = 2000-4000 km/s), the Alfven waves can supply the required heating to a low-Q loops.

Ofman, L.↗

NASA NTRS1990

High order filtering methods for approximating hyberbolic systems of conservation laws

In the computation of discontinuous solutions of hyperbolic systems of conservation laws, the recently developed essentially non-oscillatory (ENO) schemes appear to be very useful. However, they are computationally costly compared to simple central difference methods. A filtering method which is developed uses simple central differencing of arbitrarily high order accuracy, except when a novel local test indicates the development of spurious oscillations. At these points, the full ENO apparatus is used, maintaining the high order of accuracy, but removing spurious oscillations. Numerical results indicate the success of the method. High order of accuracy was obtained in regions of smooth flow without spurious oscillations for a wide range of problems and a significant speed up of generally a factor of almost three over the full ENO method.

Lafon, F.↗

NASA NTRS1978

Recent experiences with three-dimensional transonic potential flow calculations

Some recent experiences with computer programs capable of solving finitie-difference approximations to the full potential equation for the transonic flow past three dimensional swept wings and simple wing-fuselage combinations are discussed. The programs used are a nonconservative program for swept wings, a quasi-conservative finite-volume program capable of treating swept wings mounted on fuselages of slowly varying circular cross section, and a fully conservative finite volume scheme capable of treating swept wings and wing-cylinder combinations. The present capabilities of these codes are reviewed. The relative merits of the conservative and nonconservative formulations are discussed, and the results of calculations including corrections for the boundary-layer displacement effect are presented.

Caughey, D. A.↗

NASA NTRS1994

Navier-Stokes Flowfield Simulation of Boeing 747-200 as Platform for SOFIA

Steady and unsteady viscous, three-dimensional flowfields are calculated using a thin layer approximation of Navier-Stokes equations in conjunction with Chimera overset grids. The finite-difference numerical scheme uses structured grids and a pentadiagonal flow solver called "OVERFLOW". The configuration of Boeing 747-200 has been chosen as one of configurations to be used as a platform for the SOFIA (Stratospheric Observatory For Infrared Astronomy). Initially, the steady flowfield of the full aircraft is calculated for the clean configuration (without a cavity to house telescope). This solution is then used to start the unsteady flowfield of a configuration containing cavity housing the observation telescope and its peripheral units. Analysis of unsteady flowfield in the cavity and its influence on the tail empennage, as well as the noise due to turbulence and optical quality of the flow are the main focus of this study. For the configuration considered here, the telescope housing cavity is located slightly downstream of the portwing. The entire flow-field is carefully constructed using 45 overset grids and consists of nearly 4 million grid points. All the computations axe done at one freestream flow condition of M(sub infinity) = 0.85, alpha = 2.5deg, and a Reynolds of Re = 1.85x10deg

Srinivasan, G.R.↗

NASA NTRS1992

Investigation of upwind, multigrid, multiblock numerical schemes for three dimensional flows. Volume 1: Runge-Kutta methods for a thin layer Navier-Stokes solver

A state-of-the-art computer code has been developed that incorporates a modified Runge-Kutta time integration scheme, upwind numerical techniques, multigrid acceleration, and multi-block capabilities (RUMM). A three-dimensional thin-layer formulation of the Navier-Stokes equations is employed. For turbulent flow cases, the Baldwin-Lomax algebraic turbulence model is used. Two different upwind techniques are available: van Leer's flux-vector splitting and Roe's flux-difference splitting. Full approximation multi-grid plus implicit residual and corrector smoothing were implemented to enhance the rate of convergence. Multi-block capabilities were developed to provide geometric flexibility. This feature allows the developed computer code to accommodate any grid topology or grid configuration with multiple topologies. The results shown in this dissertation were chosen to validate the computer code and display its geometric flexibility, which is provided by the multi-block structure.

Cannizzaro, Frank E.↗

NASA NTRS1990

Control of an aircraft in downbursts

Guidance schemes are designed to approximate the optimal survival and optimal performance paths through downbursts, which were determined in the previous paper. Specifically, climb-rate command following is used to achieve performance, and altitude command following is used to enhance survivability. Nonlinear simulations are conducted to investigate the effects of the climb-rate command and altitude command. Takeoff flight is considered and full thrust is assumed. In a mild to moderate downburst, an aircraft can follow a constant, smaller-than-nominal climb rate without stall. Better survival capability is achieved by climbing at a lower rate accompanied by lower altitude, and vice versa. In a severe downbursts, the aircraft must descend to avoid stall. The farther it descends, the higher the survival capability, but the poorer the performance. If the downburst is very severe, the best strategy is to descend immediately to the lowest safe altitude. Since the intensity of a downbursts is hard to evaluate prior to penetration, it is advisable to keep a high airspeed. Therefore, use of the survival strategy is recommended that employs maximum thrust and allows the aircraft to descend to a safe minimum altitude immediately upon entering a downburst on takeoff.

Zhao, Yiyuan↗

NASA NTRS1992

Electron impact polarization of atomic spectral lines. I - A general theoretical scheme

A suitable theoretical scheme able to describe, in a wide variety of astrophysical situations, the phenomenon of atomic line polarization by electron impact is developed. Starting from the general principles of quantum mechanics and assuming the Born approximation, the rate equations for the density matrix elements of a multilevel atomic system, interacting with a nonrelativistic electron beam having any kind of angular distribution, are derived in full generality. The resulting theory generalizes the previous ones by accounting for the collisional rates and the cross sections concerning both inelastic and superelastic collisions (in any geometrical situation), and, moreover, by taking into account the coherences among Zeeman sublevels split by a magnetic field. As an example of particular relevance, the general formulas derived in the first sections of the paper are subsequently particularized to the case of the electric dipole interaction.

Fineschi, Silvano↗

NASA NTRS1990

Integral solution of unsteady full-potential equation for a transonic pitching airfoil

The unsteady full-potential equation formulation in a moving frame of reference has been has been developed and used to solve unsteady transonic flow problems. An unsteady integral-equation shock-capturing (IE-SC) scheme has been developed. The resulting unsteady IE-SC scheme is applied to a NACA 0012 airfoil undergoing a pitching oscillation. The numerical results are compared with those of an implicit, approximately factored, finite-volume Euler scheme. The present scheme is efficient in terms of the number of iterations as compared to the other existing schemes, which use finite-difference or finite-volume methods.

Kandil, Osama A.↗

NASA NTRS2011

Allowing for Horizontally Heterogeneous Clouds and Generalized Overlap in an Atmospheric GCM

While fully accounting for 3D effects in Global Climate Models (GCMs) appears not realistic at the present time for a variety of reasons such as computational cost and unavailability of 3D cloud structure in the models, incorporation in radiation schemes of subgrid cloud variability described by one-point statistics is now considered feasible and is being actively pursued. This development has gained momentum once it was demonstrated that CPU-intensive spectrally explicit Independent Column Approximation (lCA) can be substituted by stochastic Monte Carlo ICA (McICA) calculations where spectral integration is accomplished in a manner that produces relatively benign random noise. The McICA approach has been implemented in Goddard's GEOS-5 atmospheric GCM as part of the implementation of the RRTMG radiation package. GEOS-5 with McICA and RRTMG can handle horizontally variable clouds which can be set via a cloud generator to arbitrarily overlap within the full spectrum of maximum and random both in terms of cloud fraction and layer condensate distributions. In our presentation we will show radiative and other impacts of the combined horizontal and vertical cloud variability on multi-year simulations of an otherwise untuned GEOS-5 with fixed SSTs. Introducing cloud horizontal heterogeneity without changing the mean amounts of condensate reduces reflected solar and increases thermal radiation to space, but disproportionate changes may increase the radiative imbalance at TOA. The net radiation at TOA can be modulated by allowing the parameters of the generalized overlap and heterogeneity scheme to vary, a dependence whose behavior we will discuss. The sensitivity of the cloud radiative forcing to the parameters of cloud horizontal heterogeneity and comparisons of CERES-derived forcing will be shown.

Lee, D.↗

NASA NTRS1992

Numerical simulation of turbomachinery flows with advanced turbulence models

A three dimensional full Navier-Stokes (FNS) code is used to simulate complex turbomachinery flows. The code incorporates an explicit multistep scheme and solves a conservative form of the density averaged continuity, momentum, and energy equations. A compressible low Reynolds number form of the k-epsilon turbulence model, and a q-omega model and an algebraic Reynolds stress model have been incorporated in a fully coupled manner to approximate Reynolds stresses. The code is used to predict the viscous flow field in a backswept transonic centrifugal compressor for which laser two focus data is available. The code is also used to simulate the tip clearance flow in a cascade. The code has been extended to include unsteady Euler solutions for predicting the unsteady flow through a cascade due to incoming wakes, simulating rotor-stator interactions.

Lakshminarayana, B.↗

NASA NTRS1999

Martian Meteor Ionization Layers

Small interplanetary grains bombard Mars, like all the solar system planets, and, like all the planets with atmospheres, meteoric ion and atom layers form in the upper atmosphere. We have developed a comprehensive one-dimensional model of the Martian meteoric ionization layer including a full chemical scheme. A persistent layer of magnesium ions should exist around an altitude of 70 km. Unlike the terrestrial case, where the metallic ions are formed via charge-exchange with the ambient ions, Mg(+) in the Martian atmosphere is produced by photoionization. Nevertheless, the predicted metal layer peak densities for Earth and Mars are similar. Diffusion solutions, such as those presented here, should be a good approximation of the metallic ions in regions where the magnetic field is negligible and may provide a significant contribution to the nightside ionosphere. The low ultraviolet absorption of the Martian atmosphere may make Mars an excellent laboratory in which to study meteoric ablation. Resonance lines not seen in the spectra of terrestrial meteors may be visible to a surface observatory in the Martian highlands.

Grebowsky, J. M.↗

NASA NTRS2005

Probabilistic Design of a Wind Tunnel Model to Match the Response of a Full-Scale Aircraft

approach is presented for carrying out the reliability-based design of a plate-like wing that is part of a wind tunnel model. The goal is to design the wind tunnel model to match the stiffness characteristics of the wing box of a flight vehicle while satisfying strength-based risk/reliability requirements that prevents damage to the wind tunnel model and fixtures. The flight vehicle is a modified F/A-18 aircraft. The design problem is solved using reliability-based optimization techniques. The objective function to be minimized is the difference between the displacements of the wind tunnel model and the corresponding displacements of the flight vehicle. The design variables control the thickness distribution of the wind tunnel model. Displacements of the wind tunnel model change with the thickness distribution, while displacements of the flight vehicle are a set of fixed data. The only constraint imposed is that the probability of failure is less than a specified value. Failure is assumed to occur if the stress caused by aerodynamic pressure loading is greater than the specified strength allowable. Two uncertain quantities are considered: the allowable stress and the thickness distribution of the wind tunnel model. Reliability is calculated using Monte Carlo simulation with response surfaces that provide approximate values of stresses. The response surface equations are, in turn, computed from finite element analyses of the wind tunnel model at specified design points. Because the response surface approximations were fit over a small region centered about the current design, the response surfaces were refit periodically as the design variables changed. Coarse-grained parallelism was used to simultaneously perform multiple finite element analyses. Studies carried out in this paper demonstrate that this scheme of using moving response surfaces and coarse-grained computational parallelism reduce the execution time of the Monte Carlo simulation enough to make the design problem tractable. The results of the reliability-based designs performed in this paper show that large decreases in the probability of stress-based failure can be realized with only small sacrifices in the ability of the wind tunnel model to represent the displacements of the full-scale vehicle.

Mason, Brian H.↗

NASA NTRS1982

A conservative finite difference algorithm for the unsteady transonic potential equation in generalized coordinates

An implicit, approximate-factorization, finite-difference algorithm has been developed for the computation of unsteady, inviscid transonic flows in two and three dimensions. The computer program solves the full-potential equation in generalized coordinates in conservation-law form in order to properly capture shock-wave position and speed. A body-fitted coordinate system is employed for the simple and accurate treatment of boundary conditions on the body surface. The time-accurate algorithm is modified to a conventional ADI relaxation scheme for steady-state computations. Results from two- and three-dimensional steady and two-dimensional unsteady calculations are compared with existing methods.

Bridgeman, J. O.↗

NASA NTRS2015

Airborne Simulation of Launch Vehicle Dynamics

In this paper we present a technique for approximating the short-period dynamics of an exploration-class launch vehicle during flight test with a high-performance surrogate aircraft in relatively benign endoatmospheric flight conditions. The surrogate vehicle relies upon a nonlinear dynamic inversion scheme with proportional-integral feedback to drive a subset of the aircraft states into coincidence with the states of a time-varying reference model that simulates the unstable rigid body dynamics, servodynamics, and parasitic elastic and sloshing dynamics of the launch vehicle. The surrogate aircraft flies a constant pitch rate trajectory to approximate the boost phase gravity turn ascent, and the aircraft's closed-loop bandwidth is sufficient to simulate the launch vehicle's fundamental lateral bending and sloshing modes by exciting the rigid body dynamics of the aircraft. A novel control allocation scheme is employed to utilize the aircraft's relatively fast control effectors in inducing various failure modes for the purposes of evaluating control system performance. Sufficient dynamic similarity is achieved such that the control system under evaluation is configured for the full-scale vehicle with no changes to its parameters, and pilot-control system interaction studies can be performed to characterize the effects of guidance takeover during boost. High-fidelity simulation and flight-test results are presented that demonstrate the efficacy of the design in simulating the Space Launch System (SLS) launch vehicle dynamics using the National Aeronautics and Space Administration (NASA) Armstrong Flight Research Center Fullscale Advanced Systems Testbed (FAST), a modified F/A-18 airplane (McDonnell Douglas, now The Boeing Company, Chicago, Illinois), over a range of scenarios designed to stress the SLS's Adaptive Augmenting Control (AAC) algorithm.

airborne simulation↗

NASA NTRS1981

Full potential solution of transonic quasi-3-D flow through a cascade using artificial compressability

The three-dimensional flow in a turbomachinery blade row was approximated by correcting for streamtube convergence and radius change in the throughflow direction. The method is a fully conservative solution of the full potential equation incorporating the finite volume technique on body fitted periodic mesh, with an artificial density imposed in the transonic region to insure stability and the capture of shock waves. Comparison of results for several supercritical blades shows good agreement with their hodograph solutions. Other calculations for these profiles as well as standard NACA blade sections indicate that this is a useful scheme analyzing both the design and off-design performance of turbomachinery blading.

Farrell, C.↗

NASA NTRS1986

Upwind relaxation algorithms for Euler/Navier-Stokes equations

A description of and results from a solution algorithm for the compressible Navier-Stokes equations are presented. The main features of the algorithm are second or third order accurate upwind discretization of the convection and pressure derivatives and a relaxation scheme for the unfactored implicit backward Euler time method, implemented in a finite-volume formulation. Upwind methods were successfully used to obtain solutions to the Euler equations for flows with strong shock waves. The particular upwind method being used is based on the flux vector splitting technique developed by Van Leer and both second and third order accurate discretizations were developed. Currently, the most widely used implicit solution technique for the Navier-Stokes equations use approximate factorization (AF) methods to treat multidimensional problems. The time integration scheme being used in the present algorithm corresponds to a line Gauss-Seidel relaxation method. This method produces good convergence rates for steady-state flows, and most of the algorithm was vectorized on the NASA Langley VPS 32 computer. The Navier-Stokes algorithm was tested for several two-dimensional flow problems. Solutions for the problems gave excellent results. The presented effort is directed toward the extension of the scheme to the full three-dimensional Navier-Stokes equations.

Thomas, J. L.↗

NASA NTRS2014

Airborne Simulation of Launch Vehicle Dynamics

In this paper we present a technique for approximating the short-period dynamics of an exploration-class launch vehicle during flight test with a high-performance surrogate aircraft in relatively benign endoatmospheric flight conditions. The surrogate vehicle relies upon a nonlinear dynamic inversion scheme with proportional-integral feedback to drive a subset of the aircraft states into coincidence with the states of a time-varying reference model that simulates the unstable rigid body dynamics, servodynamics, and parasitic elastic and sloshing dynamics of the launch vehicle. The surrogate aircraft flies a constant pitch rate trajectory to approximate the boost phase gravity-turn ascent, and the aircraft's closed-loop bandwidth is sufficient to simulate the launch vehicle's fundamental lateral bending and sloshing modes by exciting the rigid body dynamics of the aircraft. A novel control allocation scheme is employed to utilize the aircraft's relatively fast control effectors in inducing various failure modes for the purposes of evaluating control system performance. Sufficient dynamic similarity is achieved such that the control system under evaluation is optimized for the full-scale vehicle with no changes to its parameters, and pilot-control system interaction studies can be performed to characterize the effects of guidance takeover during boost. High-fidelity simulation and flight test results are presented that demonstrate the efficacy of the design in simulating the Space Launch System (SLS) launch vehicle dynamics using NASA Dryden Flight Research Center's Full-scale Advanced Systems Testbed (FAST), a modified F/A-18 airplane, over a range of scenarios designed to stress the SLS's adaptive augmenting control (AAC) algorithm.

Gilligan, Eric T.↗