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NASA NTRS1995

Inertial Linear Actuators

Inertial linear actuators developed to suppress residual accelerations of nominally stationary or steadily moving platforms. Function like long-stroke version of voice coil in conventional loudspeaker, with superimposed linear variable-differential transformer. Basic concept also applicable to suppression of vibrations of terrestrial platforms. For example, laboratory table equipped with such actuators plus suitable vibration sensors and control circuits made to vibrate much less in presence of seismic, vehicular, and other environmental vibrational disturbances.

Laughlin, Darren↗

NASA NTRS1995

Linear Prediction Of Stationary Sequences Of Vectors

Report discusses direct approach to linear prediction of stationary sequence of vectors. Derives set of equations constituting minimal-order linear predictor. Using this approach, it proposes two specific computationally efficient schemes to predict vectors in sequence.

Baram, Yoram↗

NASA NTRS1995

Non-linear boundary-layer receptivity due to distributed surface roughness

The process by which a laminar boundary layer internalizes the external disturbances in the form of instability waves is known as boundary-layer receptivity. The objective of the present research was to determine the effect of acoustic excitation on boundary-layer receptivity for a flat plate with distributed variable-amplitude surface roughness through measurements with a hot-wire probe. Tollmien-Schlichting (T-S) mode shapes due to surface-roughness receptivity have also been determined, analyzed, and shown to be in agreement with theory and other experimental work. It has been shown that there is a linear relationship between the surface roughness and receptivity for certain roughness configurations with constant roughness wavelength. In addition, strong nonlinear receptivity effects exist for certain surface roughness configurations over a band where the surface roughness and T-S wavelength are matched. The results from the present experiment follow the trends predicted by theory and other experimental work for linear receptivity. In addition, the results show the existence of nonlinear receptivity effects for certain combinations of surface roughness elements.

Amer, Tahani Reffet↗

NASA NTRS1995

An approach to the development of numerical algorithms for first order linear hyperbolic systems in multiple space dimensions: The constant coefficient case

Two methods for developing high order single step explicit algorithms on symmetric stencils with data on only one time level are presented. Examples are given for the convection and linearized Euler equations with up to the eighth order accuracy in both space and time in one space dimension, and up to the sixth in two space dimensions. The method of characteristics is generalized to nondiagonalizable hyperbolic systems by using exact local polynominal solutions of the system, and the resulting exact propagator methods automatically incorporate the correct multidimensional wave propagation dynamics. Multivariate Taylor or Cauchy-Kowaleskaya expansions are also used to develop algorithms. Both of these methods can be applied to obtain algorithms of arbitrarily high order for hyperbolic systems in multiple space dimensions. Cross derivatives are included in the local approximations used to develop the algorithms in this paper in order to obtain high order accuracy, and improved isotropy and stability. Efficiency in meeting global error bounds is an important criterion for evaluating algorithms, and the higher order algorithms are shown to be up to several orders of magnitude more efficient even though they are more complex. Stable high order boundary conditions for the linearized Euler equations are developed in one space dimension, and demonstrated in two space dimensions.

Goodrich, John W.↗

NASA NTRS1995

A Large-Particle Monte Carlo Code for Simulating Non-Linear High-Energy Processes Near Compact Objects

High-energy radiation processes in compact cosmic objects are often expected to have a strongly non-linear behavior. Such behavior is shown, for example, by electron-positron pair cascades and the time evolution of relativistic proton distributions in dense radiation fields. Three independent techniques have been developed to simulate these non-linear problems: the kinetic equation approach; the phase-space density (PSD) Monte Carlo method; and the large-particle (LP) Monte Carlo method. In this paper, we present the latest version of the LP method and compare it with the other methods. The efficiency of the method in treating geometrically complex problems is illustrated by showing results of simulations of 1D, 2D and 3D systems. The method is shown to be powerful enough to treat non-spherical geometries, including such effects as bulk motion of the background plasma, reflection of radiation from cold matter, and anisotropic distributions of radiating particles. It can therefore be applied to simulate high-energy processes in such astrophysical systems as accretion discs with coronae, relativistic jets, pulsar magnetospheres and gamma-ray bursts.

Stern, Boris E.↗

NASA NTRS1996

Development of Torsional and Linear Piezoelectrically Driven Motors

The development of rotary and linear inchworm-motors using piezoelectric actuators is presented. The motors' design has the advantage of a macro and micro stepper motor with high load and speed. The torsional design is capable of fast angular positioning with micro level accuracy. Additionally, the rotary motor, as designed, can be used as a clutch/brake mechanism. Constructed prototype motors of both types along with their characteristics are presented. The torsional motor consists of a torsional section that provides angular displacement and torque, and two alternating clamping sections which provide the holding force. The motor relies on the principal piezoelectric coupling coefficient (d33) with no torsional elements, increasing its torque capability. The linear motor consists of a longitudinal vibrator that provides displacement and load, and two alternating clamping sections which provide the holding force. This design eliminates bending moment, tension and shear applied to the actuator elements, increase its load capability and life. Innovative flexure designs have been introduced for both motor types. Critical issues that affect the design and performance of the motors are explored and discussed. Experiments are performed demonstrating the motor prototypes based on the aforementioned design considerations.

Duong, Khanh↗

NASA NTRS1996

Soft-decision decoding techniques for linear block codes and their error performance analysis

The first paper presents a new minimum-weight trellis-based soft-decision iterative decoding algorithm for binary linear block codes. The second paper derives an upper bound on the probability of block error for multilevel concatenated codes (MLCC). The bound evaluates difference in performance for different decompositions of some codes. The third paper investigates the bit error probability code for maximum likelihood decoding of binary linear codes. The fourth and final paper included in this report is concerns itself with the construction of multilevel concatenated block modulation codes using a multilevel concatenation scheme for the frequency non-selective Rayleigh fading channel.

Lin, Shu↗

NASA NTRS1997

Identification of Linear and Nonlinear Aerodynamic Impulse Responses Using Digital Filter Techniques

This paper discusses the mathematical existence and the numerically-correct identification of linear and nonlinear aerodynamic impulse response functions. Differences between continuous-time and discrete-time system theories, which permit the identification and efficient use of these functions, will be detailed. Important input/output definitions and the concept of linear and nonlinear systems with memory will also be discussed. It will be shown that indicial (step or steady) responses (such as Wagner's function), forced harmonic responses (such as Tbeodorsen's function or those from doublet lattice theory), and responses to random inputs (such as gusts) can all be obtained from an aerodynamic impulse response function. This paper establishes the aerodynamic impulse response function as the most fundamental, and, therefore, the most computationally efficient, aerodynamic function that can be extracted from any given discrete-time, aerodynamic system. The results presented in this paper help to unify the understanding of classical two-dimensional continuous-time theories with modem three-dimensional, discrete-time theories. First, the method is applied to the nonlinear viscous Burger's equation as an example. Next the method is applied to a three-dimensional aeroelastic model using the CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code and then to a two-dimensional model using the CFL3D Navier-Stokes code. Comparisons of accuracy and computational cost savings are presented. Because of its mathematical generality, an important attribute of this methodology is that it is applicable to a wide range of nonlinear, discrete-time problems.

Silva, Walter A.↗

NASA NTRS1997

Identification of Linear and Nonlinear Aerodynamic Impulse Responses Using Digital Filter Techniques

This paper discusses the mathematical existence and the numerically-correct identification of linear and nonlinear aerodynamic impulse response functions. Differences between continuous-time and discrete-time system theories, which permit the identification and efficient use of these functions, will be detailed. Important input/output definitions and the concept of linear and nonlinear systems with memory will also be discussed. It will be shown that indicial (step or steady) responses (such as Wagner's function), forced harmonic responses (such as Theodorsen's function or those from doublet lattice theory), and responses to random inputs (such as gusts) can all be obtained from an aerodynamic impulse response function. This paper establishes the aerodynamic impulse response function as the most fundamental, and, therefore, the most computationally efficient, aerodynamic function that can be extracted from any given discrete-time, aerodynamic system. The results presented in this paper help to unify the understanding of classical two-dimensional continuous-time theories with modern three-dimensional, discrete-time theories. First, the method is applied to the nonlinear viscous Burger's equation as an example. Next the method is applied to a three-dimensional aeroelastic model using the CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code and then to a two-dimensional model using the CFL3D Navier-Stokes code. Comparisons of accuracy and computational cost savings are presented. Because of its mathematical generality, an important attribute of this methodology is that it is applicable to a wide range of nonlinear, discrete-time problems.

Silva, Walter A.↗

NASA NTRS1998

Pattern Search Methods for Linearly Constrained Minimization

We extend pattern search methods to linearly constrained minimization. We develop a general class of feasible point pattern search algorithms and prove global convergence to a Karush-Kuhn-Tucker point. As in the case of unconstrained minimization, pattern search methods for linearly constrained problems accomplish this without explicit recourse to the gradient or the directional derivative. Key to the analysis of the algorithms is the way in which the local search patterns conform to the geometry of the boundary of the feasible region.

Lewis, Robert Michael↗

NASA NTRS1998

The Control System for the X-33 Linear Aerospike Engine

The linear aerospike engine is being developed for single-stage -to-orbit (SSTO) applications. The primary advantages of a linear aerospike engine over a conventional bell nozzle engine include altitude compensation, which provides enhanced performance, and lower vehicle weight resulting from the integration of the engine into the vehicle structure. A feature of this integration is the ability to provide thrust vector control (TVC) by differential throttling of the engine combustion elements, rather than the more conventional approach of gimballing the entire engine. An analysis of the X-33 flight trajectories has shown that it is necessary to provide +/- 15% roll, pitch and yaw TVC authority with an optional capability of +/- 30% pitch at select times during the mission. The TVC performance requirements for X-33 engine became a major driver in the design of the engine control system. The thrust level of the X-33 engine as well as the amount of TVC are managed by a control system which consists of electronic, instrumentation, propellant valves, electro-mechanical actuators, spark igniters, and harnesses. The engine control system is responsible for the thrust control, mixture ratio control, thrust vector control, engine health monitoring, and communication to the vehicle during all operational modes of the engine (checkout, pre-start, start, main-stage, shutdown and post shutdown). The methodology for thrust vector control, the health monitoring approach which includes failure detection, isolation, and response, and the basic control system design are the topic of this paper. As an additional point of interest a brief description of the X-33 engine system will be included in this paper.

Jackson, Jerry E.↗

NASA NTRS1998

Linear Aerospike SR-71 Experiment (LASRE): Aerospace Propulsion Hazard Mitigation Systems

A major hazard posed by the propulsion system of hypersonic and space vehicles is the possibility of fire or explosion in the vehicle environment. The hazard is mitigated by minimizing or detecting, in the vehicle environment, the three ingredients essential to producing fire: fuel, oxidizer, and an ignition source. The Linear Aerospike SR-71 Experiment (LASRE) consisted of a linear aerospike rocket engine integrated into one-half of an X-33-like lifting body shape, carried on top of an SR-71 aircraft. Gaseous hydrogen and liquid oxygen were used as propellants. Although LASRE is a one-of-a-kind experimental system, it must be rated for piloted flight, so this test presented a unique challenge. To help meet safety requirements, the following propulsion hazard mitigation systems were incorporated into the experiment: pod inert purge, oxygen sensors, a hydrogen leak detection algorithm, hydrogen sensors, fire detection and pod temperature thermocouples, water misting, and control room displays. These systems are described, and their development discussed. Analyses, ground test, and flight test results are presented, as are findings and lessons learned.

Mizukami, Masashi↗

NASA NTRS1998

Flight Stability and Control and Performance Results from the Linear Aerospike SR-71 Experiment (LASRE)

The Linear Aerospike SR-71 Experiment (LASRE) is presently being conducted to test a 20-percent-scale version of the Linear Aerospike rocket engine. This rocket engine has been chosen to power the X-33 Single Stage to Orbit Technology Demonstrator Vehicle. The rocket engine was integrated into a lifting body configuration and mounted to the upper surface of an SR-71 aircraft. This paper presents stability and control results and performance results from the envelope expansion flight tests of the LASRE configuration up to Mach 1.8 and compares the results with wind tunnel predictions. Longitudinal stability and elevator control effectiveness were well-predicted from wind tunnel tests. Zero-lift pitching moment was mispredicted transonically. Directional stability, dihedral stability, and rudder effectiveness were overpredicted. The SR-71 handling qualities were never significantly impacted as a result of the missed predictions. Performance results confirmed the large amount of wind-tunnel-predicted transonic drag for the LASRE configuration. This drag increase made the performance of the vehicle so poor that acceleration through transonic Mach numbers could not be achieved on a hot day without depleting the available fuel.

Moes, Timothy R.↗

NASA NTRS1998

Flight Testing the Linear Aerospike SR-71 Experiment (LASRE)

The design of the next generation of space access vehicles has led to a unique flight test that blends the space and flight research worlds. The new space vehicle designs, such as the X-33 vehicle and Reusable Launch Vehicle (RLV), are powered by linear aerospike rocket engines. Conceived of in the 1960's, these aerospike engines have yet to be flown, and many questions remain regarding aerospike engine performance and efficiency in flight. To provide some of these data before flying on the X-33 vehicle and the RLV, a spacecraft rocket engine has been flight-tested atop the NASA SR-71 aircraft as the Linear Aerospike SR-71 Experiment (LASRE). A 20 percent-scale, semispan model of the X-33 vehicle, the aerospike engine, and all the required fuel and oxidizer tanks and propellant feed systems have been mounted atop the SR-71 airplane for this experiment. A major technical objective of the LASRE flight test is to obtain installed-engine performance flight data for comparison to wind-tunnel results and for the development of computational fluid dynamics-based design methodologies. The ultimate goal of firing the aerospike rocket engine in flight is still forthcoming. An extensive design and development phase of the experiment hardware has been completed, including approximately 40 ground tests. Five flights of the LASRE and firing the rocket engine using inert liquid nitrogen and helium in place of liquid oxygen and hydrogen have been successfully completed.

Stephen Corda↗

NASA NTRS1961

A Linear Theory for Inflatable Plates of Arbitrary Shape

A linear small-deflection theory is developed for the elastic behavior of inflatable plates of which Airmat is an example. Included in the theory are the effects of a small linear taper in the depth of the plate. Solutions are presented for some simple problems in the lateral deflection and vibration of constant-depth rectangular inflatable plates.

McComb, Harvey G., Jr.↗

NASA NTRS1961

Analysis of a Linear System for Variable-Thrust Control in the Terminal Phase of Rendezvous

A linear system for applying thrust to a ferry vehicle in the 3 terminal phase of rendezvous with a satellite is analyzed. This system requires that the ferry thrust vector per unit mass be variable and equal to a suitable linear combination of the measured position and velocity vectors of the ferry relative to the satellite. The variations of the ferry position, speed, acceleration, and mass ratio are examined for several combinations of the initial conditions and two basic control parameters analogous to the undamped natural frequency and the fraction of critical damping. Upon making a desirable selection of one control parameter and requiring minimum fuel expenditure for given terminal-phase initial conditions, a simplified analysis in one dimension practically fixes the choice of the remaining control parameter. The system can be implemented by an automatic controller or by a pilot.

Hord, Richard A.↗

NASA NTRS1998

Performance of an Axisymmetric Rocket Based Combined Cycle Engine During Rocket Only Operation Using Linear Regression Analysis

The all rocket mode of operation is shown to be a critical factor in the overall performance of a rocket based combined cycle (RBCC) vehicle. An axisymmetric RBCC engine was used to determine specific impulse efficiency values based upon both full flow and gas generator configurations. Design of experiments methodology was used to construct a test matrix and multiple linear regression analysis was used to build parametric models. The main parameters investigated in this study were: rocket chamber pressure, rocket exit area ratio, injected secondary flow, mixer-ejector inlet area, mixer-ejector area ratio, and mixer-ejector length-to-inlet diameter ratio. A perfect gas computational fluid dynamics analysis, using both the Spalart-Allmaras and k-omega turbulence models, was performed with the NPARC code to obtain values of vacuum specific impulse. Results from the multiple linear regression analysis showed that for both the full flow and gas generator configurations increasing mixer-ejector area ratio and rocket area ratio increase performance, while increasing mixer-ejector inlet area ratio and mixer-ejector length-to-diameter ratio decrease performance. Increasing injected secondary flow increased performance for the gas generator analysis, but was not statistically significant for the full flow analysis. Chamber pressure was found to be not statistically significant.

Smith, Timothy D.↗

NASA NTRS1998

On the Numerical Formulation of Parametric Linear Fractional Transformation (LFT) Uncertainty Models for Multivariate Matrix Polynomial Problems

Robust control system analysis and design is based on an uncertainty description, called a linear fractional transformation (LFT), which separates the uncertain (or varying) part of the system from the nominal system. These models are also useful in the design of gain-scheduled control systems based on Linear Parameter Varying (LPV) methods. Low-order LFT models are difficult to form for problems involving nonlinear parameter variations. This paper presents a numerical computational method for constructing and LFT model for a given LPV model. The method is developed for multivariate polynomial problems, and uses simple matrix computations to obtain an exact low-order LFT representation of the given LPV system without the use of model reduction. Although the method is developed for multivariate polynomial problems, multivariate rational problems can also be solved using this method by reformulating the rational problem into a polynomial form.

Belcastro, Christine M.↗