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NASA NTRS1988

Domain decomposition methods for the parallel computation of reacting flows

Domain decomposition is a natural route to parallel computing for partial differential equation solvers. Subdomains of which the original domain of definition is comprised are assigned to independent processors at the price of periodic coordination between processors to compute global parameters and maintain the requisite degree of continuity of the solution at the subdomain interfaces. In the domain-decomposed solution of steady multidimensional systems of PDEs by finite difference methods using a pseudo-transient version of Newton iteration, the only portion of the computation which generally stands in the way of efficient parallelization is the solution of the large, sparse linear systems arising at each Newton step. For some Jacobian matrices drawn from an actual two-dimensional reacting flow problem, comparisons are made between relaxation-based linear solvers and also preconditioned iterative methods of Conjugate Gradient and Chebyshev type, focusing attention on both iteration count and global inner product count. The generalized minimum residual method with block-ILU preconditioning is judged the best serial method among those considered, and parallel numerical experiments on the Encore Multimax demonstrate for it approximately 10-fold speedup on 16 processors.

Keyes, David E.↗

NASA NTRS1990

Integrated controls-structures design methodology development for a class of flexible spacecraft

Future utilization of space will require large space structures in low-Earth and geostationary orbits. Example missions include: Earth observation systems, personal communication systems, space science missions, space processing facilities, etc., requiring large antennas, platforms, and solar arrays. The dimensions of such structures will range from a few meters to possibly hundreds of meters. For reducing the cost of construction, launching, and operating (e.g., energy required for reboosting and control), it will be necessary to make the structure as light as possible. However, reducing structural mass tends to increase the flexibility which would make it more difficult to control with the specified precision in attitude and shape. Therefore, there is a need to develop a methodology for designing space structures which are optimal with respect to both structural design and control design. In the current spacecraft design practice, it is customary to first perform the structural design and then the controller design. However, the structural design and the control design problems are substantially coupled and must be considered concurrently in order to obtain a truly optimal spacecraft design. For example, let C denote the set of the 'control' design variables (e.g., controller gains), and L the set of the 'structural' design variables (e.g., member sizes). If a structural member thickness is changed, the dynamics would change which would then change the control law and the actuator mass. That would, in turn, change the structural model. Thus, the sets C and L depend on each other. Future space structures can be roughly divided into four mission classes. Class 1 missions include flexible spacecraft with no articulated appendages which require fine attitude pointing and vibration suppression (e.g., large space antennas). Class 2 missions consist of flexible spacecraft with articulated multiple payloads, where the requirement is to fine-point the spacecraft and each individual payload while suppressing the elastic motion. Class 3 missions include rapid slewing of spacecraft without appendages, while Class 4 missions include general nonlinear motion of a flexible spacecraft with articulated appendages and robot arms. Class 1 and 2 missions represent linear mathematical modeling and control system design problems (except for actuator and sensor nonlinearities), while Class 3 and 4 missions represent nonlinear problems. The development of an integrated controls/structures design approach for Class 1 missions is addressed. The performance for these missions is usually specified in terms of (1) root mean square (RMS) pointing errors at different locations on the structure, and (2) the rate of decay of the transient response. Both of these performance measures include the contributions of rigid as well as elastic motion.

Maghami, P. G.↗

NASA NTRS2010

Physics-Based Methods of Failure Analysis and Diagnostics in Human Space Flight

The Integrated Health Management (IHM) for the future aerospace systems requires to interface models of multiple subsystems in an efficient and accurate information environment at the earlier stages of system design. The complexity of modern aeronautic and aircraft systems (including e.g. the power distribution, flight control, solid and liquid motors) dictates employment of hybrid models and high-level reasoners for analysing mixed continuous and discrete information flow involving multiple modes of operation in uncertain environments, unknown state variables, heterogeneous software and hardware components. To provide the information link between key design/performance parameters and high-level reasoners we rely on development of multi-physics performance models, distributed sensors networks, and fault diagnostic and prognostic (FD&P) technologies in close collaboration with system designers. The main challenges of our research are related to the in-flight assessment of the structural stability, engine performance, and trajectory control. The main goal is to develop an intelligent IHM that not only enhances components and system reliability, but also provides a post-flight feedback helping to optimize design of the next generation of aerospace systems. Our efforts are concentrated on several directions of the research. One of the key components of our strategy is an innovative approach to the diagnostics/prognostics based on the real time dynamical inference (DI) technologies extended to encompass hybrid systems with hidden state trajectories. The major investments are into the multiphysics performance modelling that provides an access of the FD&P technologies to the main performance parameters of e.g. solid and liquid rocket motors and composite materials of the nozzle and case. Some of the recent results of our research are discussed in this chapter. We begin by introducing the problem of dynamical inference of stochastic nonlinear models and reviewing earlier results. Next, we present our analytical approach to the solution of this problem based on the path integral formulation. The resulting algorithm does not require an extensive global search for the model parameters, provides optimal compensation for the effects of dynamical noise, and is robust for a broad range of dynamical models. In the following Section the strengths of the algorithm are illustrated illustrated by inferring the parameters of the stochastic Lorenz system and comparing the results with those of earlier research. Next, we discuss a number of recent results in application to the development of the IHM for aerospace system. Firstly, we apply dynamical inference approach to a solution of classical three tank problems with mixed unknown continuous and binary parameters. The problem is considered in the context of ground support system for filling fuel tanks of liquid rocket motors. It is shown that the DI algorithm is well suited for successful solution of a hybrid version of this benchmark problem even in the presence of additional periodic and stochastic perturbation of unknown strength. Secondly, we illustrate our approach by its application to an analysis of the nozzle fault in a solid rocket motor (SRM). The internal ballistics of the SRM is modelled as a set of one-dimensional partial differential equations coupled to the dynamics of the propellant regression. In this example we are specifically focussed on the inference of discrete and continuous parameters of the nozzle blocking fault and on the possibility of an application of the DI algorithm to reducing the probability of "misses" of an on-board FD&P for SRM. In the next section re-contact problem caused by first stage/upper stage separation failure is discussed. The reaction forces imposed on the nozzle of the upper stage during the re-contact and their connection to the nozzle damage and to the thrust vector control (TVC) signal are obtained. It is shown that transient impact induced torquean be modelled as a response of an effective damped oscillator. A possible application of the DI algorithm to the inference of damage parameters and predicting fault dynamics ahead of time using the actuator signal is discussed. Finally, we formulate Bayesian inferential framework for development of the IHM system for in-flight structural health monitoring (SHM) of composite materials. We consider the signal generated by piezoelectric actuator mounted on composite structure generating elastic waves in it. The signal received by the sensor is than compared with the baseline signal. The possibility of damage inference is discussed in the context of development of the SHM.

Smelyanskiy, Vadim N.↗

NASA NTRS2016

Solar Coronal Jets: Observations, Theory, and Modeling

Coronal jets represent important manifestations of ubiquitous solar transients, which may be the source of significant mass and energy input to the upper solar atmosphere and the solar wind. While the energy involved in a jet-like event is smaller than that of "nominal" solar flares and coronal mass ejections (CMEs), jets share many common properties with these phenomena, in particular, the explosive magnetically driven dynamics. Studies of jets could, therefore, provide critical insight for understanding the larger, more complex drivers of the solar activity. On the other side of the size-spectrum, the study of jets could also supply important clues on the physics of transients close or at the limit of the current spatial resolution such as spicules. Furthermore, jet phenomena may hint to basic process for heating the corona and accelerating the solar wind; consequently their study gives us the opportunity to attack a broad range of solar-heliospheric problems.

Raouafi, N. E.↗

NASA NTRS1990

A computational procedure for the dynamics of flexible beams within multibody systems

The dynamic analysis of three dimensional elastic beams which experience large rotational and large deformational motions are examined. The beam motion is modeled using an inertial reference for the translational displacements and a body-fixed reference for the rotational quantities. Finite strain rod theories are then defined in conjunction with the beam kinematic description which accounts for the effects of stretching, bending, torsion, and transverse shear deformations. A convected coordinate representation of the Cauchy stress tensor and a conjugate strain definition is introduced to model the beam deformation. To treat the beam dynamics, a two-stage modification of the central difference algorithm is presented to integrate the translational coordinates and the angular velocity vector. The angular orientation is then obtained from the application of an implicit integration algorithm to the Euler parameter/angular velocity kinematical relation. The combined developments of the objective internal force computation with the dynamic solution procedures result in the computational preservation of total energy for undamped systems. The present methodology is also extended to model the dynamics of deployment/retrieval of the flexible members. A moving spatial grid corresponding to the configuration of a deployed rigid beam is employed as a reference for the dynamic variables. A transient integration scheme which accurately accounts for the deforming spatial grid is derived from a space-time finite element discretization of a Hamiltonian variational statement. The computational results of this general deforming finite element beam formulation are compared to reported results for a planar inverse-spaghetti problem.

Downer, Janice Diane↗

NASA NTRS1993

Automatic specification of reliability models for fault-tolerant computers

The calculation of reliability measures using Markov models is required for life-critical processor-memory-switch structures that have standby redundancy or that are subject to transient or intermittent faults or repair. The task of specifying these models is tedious and prone to human error because of the large number of states and transitions required in any reasonable system. Therefore, model specification is a major analysis bottleneck, and model verification is a major validation problem. The general unfamiliarity of computer architects with Markov modeling techniques further increases the necessity of automating the model specification. Automation requires a general system description language (SDL). For practicality, this SDL should also provide a high level of abstraction and be easy to learn and use. The first attempt to define and implement an SDL with those characteristics is presented. A program named Automated Reliability Modeling (ARM) was constructed as a research vehicle. The ARM program uses a graphical interface as its SDL, and it outputs a Markov reliability model specification formulated for direct use by programs that generate and evaluate the model.

Liceaga, Carlos A.↗

NASA NTRS1994

Task scheduling in dataflow computer architectures

Dataflow computers provide a platform for the solution of a large class of computational problems, which includes digital signal processing and image processing. Many typical applications are represented by a set of tasks which can be repetitively executed in parallel as specified by an associated dataflow graph. Research in this area aims to model these architectures, develop scheduling procedures, and predict the transient and steady state performance. Researchers at NASA have created a model and developed associated software tools which are capable of analyzing a dataflow graph and predicting its runtime performance under various resource and timing constraints. These models and tools were extended and used in this work. Experiments using these tools revealed certain properties of such graphs that require further study. Specifically, the transient behavior at the beginning of the execution of a graph can have a significant effect on the steady state performance. Transformation and retiming of the application algorithm and its initial conditions can produce a different transient behavior and consequently different steady state performance. The effect of such transformations on the resource requirements or under resource constraints requires extensive study. Task scheduling to obtain maximum performance (based on user-defined criteria), or to satisfy a set of resource constraints, can also be significantly affected by a transformation of the application algorithm. Since task scheduling is performed by heuristic algorithms, further research is needed to determine if new scheduling heuristics can be developed that can exploit such transformations. This work has provided the initial development for further long-term research efforts. A simulation tool was completed to provide insight into the transient and steady state execution of a dataflow graph. A set of scheduling algorithms was completed which can operate in conjunction with the modeling and performance tools previously developed. Initial studies on the performance of these algorithms were done to examine the effects of application algorithm transformations as measured by such quantities as number of processors, time between outputs, time between input and output, communication time, and memory size.

Katsinis, Constantine↗

NASA NTRS1976

Sensitivity of inelastic response to numerical integration of strain energy

The exact solution to the quasi-static, inelastic response of a cantilever beam of rectangular cross section subjected to a bending moment at the tip is obtained. The material of the beam is assumed to be linearly elastic-linearly strain-hardening. This solution is then compared with three different numerical solutions of the same problem obtained by minimizing the total potential energy using Gaussian quadratures of two different orders and a Newton-Cotes scheme for integrating the strain energy of deformation. Significant differences between the exact dissipative strain energy and its numerical counterpart are emphasized. The consequence of this on the nonlinear transient responses of a beam with solid cross section and that of a thin-walled beam on elastic supports under impulsive loads are examined.

Kamat, M. P.↗

NASA NTRS1980

Development of tunable high pressure CO2 laser for lidar measurements of pollutants and wind velocities

The problem of laser energy extraction at a tunable monochromatic frequency from an energetic high pressure CO2 pulsed laser plasma, for application to remote sensing of atmospheric pollutants by Differential Absorption Lidar (DIAL) and of wind velocities by Doppler Lidar, was investigated. The energy extraction principle analyzed is based on transient injection locking (TIL) at a tunable frequency. Several critical experiments for high gain power amplification by TIL are presented.

Levine, J. S.↗

NASA NTRS1991

Formulation of the nonlinear analysis of shell-like structures, subjected to time-dependent mechanical and thermal loading

The object of the research reported herein was to develop a general mathematical model and solution methodologies for analyzing the structural response of thin, metallic shell structures under large transient, cyclic, or static thermomechanical loads. Among the system responses associated with these loads and conditions are thermal buckling, creep buckling, and ratcheting. Thus geometric and material nonlinearities (of high order) can be anticipated and must be considered in developing the mathematical model. The methodology is demonstrated through different problems of extension, shear, and of planar curved beams. Moreover, importance of the inclusion of large strain is clearly demonstrated, through the chosen applications.

Simitses, George J.↗

NASA NTRS1990

Improved boundary layer heat transfer calculations near a stagnation point

A thermal design of a solar receiver has been developed for the solutions of problems involving phase-change thermal energy storage and natural convection loss. Two dimensional axisymmetrical solidification and melting of materials contained between two concentric cylinders of finite length has been studied for thermal energy storage analysis. For calculation of free convection loss inside receiver cavity, two dimensional axisymmetrical, laminar, transient free convection including radiation effects has been studied using integral/finite difference method. Finite difference equations are derived for the above analysis subject to constant or variable material properties, initial conditions, and boundary conditions. The validity of the analyses has been substantiated by comparing results of the present general method with available analytic solutions or numerical results reported in the literature. Both explicit and implicit schemes are tested in phase change analysis with different number of nodes ranging from 4 to 18. The above numerical methods have been applied to the existing solar receiver analyzing computer code as additional subroutines. The results were computed for one of the proposed Brayton cycle solar receiver models running under the actual environmental conditions. Effect of thermal energy storage on the thermal behavior of the receiver has been estimated. Due to the thermal energy storage, about 65% reduction on working gas outlet temperature fluctuation has been obtained; however, maximum temperature of thermal energy storage containment has been increased about 18%. Also, effect of natural convection inside a receiver cavity on the receiver heat transfer has been analyzed. The finding indicated that thermal stratification occurs during the sun time resulting in higher receiver temperatures at the outlet section of the gas tube, and lower temperatures at the inlet section of the gas tube when compared with the results with no natural convection. Due to heat supply from the air during the shade time, minimum temperature has been increased, while maximum temperature has been reduced due to convection loss to air. Consequently, cyclic temperature fluctuation has been reduced 29% for working gas and 16% for thermal energy storage containment. On the other hand, despite the presence of the natural convection the time-averaged temperatures for receiver components were found to be similar for two cases with/without natural convection (maximum difference was 1.8%).

Ahn, Kyung Hwan↗

NASA NTRS1987

Efficient numerical simulation of an electrothermal de-icer pad

In this paper, a new approach to calculate the transient thermal behavior of an iced electrothermal de-icer pad was developed. The method of splines was used to obtain the temperature distribution within the layered pad. Splines were used in order to create a tridiagonal system of equations that could be directly solved by Gauss elimination. The Stefan problem was solved using the enthalpy method along with a recent implicit technique. Only one to three iterations were needed to locate the melt front during any time step. Computational times were shown to be greatly reduced over those of an existing one dimensional procedure without any reduction in accuracy; the curent technique was more than 10 times faster.

Roelke, R. J.↗

NASA NTRS1991

Control design variable linking for optimization of structural/control systems

In this study a method is presented to integrate the design space of structural/control system optimization problems in the case of state feedback control. Conventional structural sizing variables and elements of the feedback gain matrix are both treated as strictly independent design variables in the optimization by extending design variable linking concepts to the control gains. Examples which involve a variety of behavior constraints, including dynamic transient response and control force limits, are effectively solved by using the method presented.

Jin, I. M.↗

NASA NTRS1991

Laminar flames in premixed gases

Numerical simulation of laminar flames in premixed gases is addressed. Various efforts to solve the laminar flame problem are briefly described, and basic equations to be modeled in a comprehensive description of laminar flames are discussed along with the physical and chemical processes represented by these equations and the numerical requirements to model them. Two flame methods are discussed in some detail: a numerical model for studying transient phenomena and its 2D counterpart method. The various input parameters needed for the models are addressed, and the use of the models is illustrated in several studies of laminar flames in premixed gases. Flammability limits and multidimensional flame propagation are also examined.

Kailasanath, K.↗

NASA NTRS1974

Theoretical study of the effects of refraction on the noise produced by turbulence in jets

The production of noise by turbulence in jets is an extremely complex problem. One aspect of that problem, the transmission of acoustic disturbances from the interior of the jet through the mean velocity profile and into the far field is studied. The jet (two-dimensional or circular cylindrical) is assumed infinitely long with mean velocity profile independent of streamwise location. The noise generator is a sequence of transient sources drifting with the surrounding fluid and confined to a short length of the jet.

Graham, E. W.↗

NASA NTRS1974

Ultrasonic attenuation - Q measurements on 70215,29

Ultrasonic attenuation measurements have been made on an aluminum alloy, obsidian, and rock samples including lunar sample 70215,29. The measurement technique is based on a combination of the pulse transmission method and the forced resonance method. The technique is designed to explore the problem of defining experimentally, the Q of a medium or sample in which mode conversion may occur. If modes are coupled, the measured attenuation is strongly dependent on individual modes of vibration, and a range of Q-factors may be measured over various resonances or from various portions of a transient signal. On 70215,29, measurements were made over a period of a month while the sample outgassed in hard varuum. During this period, the highest measured Q of this sample increased from a few hundred into the range of 1000-1300.

Warren, N.↗

NASA NTRS1982

Mixed time integration methods for transient thermal analysis of structures, appendix 5

Mixed time integration methods for transient thermal analysis of structures are studied. An efficient solution procedure for predicting the thermal behavior of aerospace vehicle structures was developed. A 2D finite element computer program incorporating these methodologies is being implemented. The performance of these mixed time finite element algorithms can then be evaluated employing the proposed example problem.

Liu, W. K.↗

NASA NTRS1988

Dynamics of two fluids under periodic acceleration

The evolution of the interface between two fluids confined in a rectangular cavity is investigated numerically to predict its transient behavior. These computations address mixing characteristics of fluids under microgravity conditions, particularly g-jitter conditions resulting from aircraft vibration or crew motion, and have applications in solution crystal growth. The two-dimensional formulation employs the Boussinesq approximation and treats the mixing of two fluids as an initial value problem with a prescribed concentration field. For fluid mixing of practical applications inside a cavity, it is shown that nonlinear convective transport can dominate over both viscous and molecular diffusion. However, viscous diffusion can become important for low Reynolds number or certain cavity sizes. A stacking phenomenon is shown to occur for aspect ratios (Ar) approximately between 5 to 10. For aspect ratios in the neighborhood of 0.1 to 0.2, inner cells evolve at the interface with increasing time. For a square cavity of Ar = 1, chaotic mixing of the fluid appears to occur for a Stokes-Reynolds number greater than about 5.

Duval, Walter M. B.↗