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NASA NTRS2002

Nonlinear Dynamic Models in Advanced Life Support

To facilitate analysis, ALS systems are often assumed to be linear and time invariant, but they usually have important nonlinear and dynamic aspects. Nonlinear dynamic behavior can be caused by time varying inputs, changes in system parameters, nonlinear system functions, closed loop feedback delays, and limits on buffer storage or processing rates. Dynamic models are usually cataloged according to the number of state variables. The simplest dynamic models are linear, using only integration, multiplication, addition, and subtraction of the state variables. A general linear model with only two state variables can produce all the possible dynamic behavior of linear systems with many state variables, including stability, oscillation, or exponential growth and decay. Linear systems can be described using mathematical analysis. Nonlinear dynamics can be fully explored only by computer simulations of models. Unexpected behavior is produced by simple models having only two or three state variables with simple mathematical relations between them. Closed loop feedback delays are a major source of system instability. Exceeding limits on buffer storage or processing rates forces systems to change operating mode. Different equilibrium points may be reached from different initial conditions. Instead of one stable equilibrium point, the system may have several equilibrium points, oscillate at different frequencies, or even behave chaotically, depending on the system inputs and initial conditions. The frequency spectrum of an output oscillation may contain harmonics and the sums and differences of input frequencies, but it may also contain a stable limit cycle oscillation not related to input frequencies. We must investigate the nonlinear dynamic aspects of advanced life support systems to understand and counter undesirable behavior.

Jones, Harry↗

NASA NTRS2010

Development of a Benchmark Example for Delamination Fatigue Growth Prediction

The development of a benchmark example for cyclic delamination growth prediction is presented and demonstrated for a commercial code. The example is based on a finite element model of a Double Cantilever Beam (DCB) specimen, which is independent of the analysis software used and allows the assessment of the delamination growth prediction capabilities in commercial finite element codes. First, the benchmark result was created for the specimen. Second, starting from an initially straight front, the delamination was allowed to grow under cyclic loading in a finite element model of a commercial code. The number of cycles to delamination onset and the number of cycles during stable delamination growth for each growth increment were obtained from the analysis. In general, good agreement between the results obtained from the growth analysis and the benchmark results could be achieved by selecting the appropriate input parameters. Overall, the results are encouraging but further assessment for mixed-mode delamination is required

Krueger, Ronald↗

NASA NTRS2010

Development of a Benchmark Example for Delamination Fatigue Growth Prediction

Krueger, Ronald↗

NASA NTRS2011

Development of Benchmark Examples for Static Delamination Propagation and Fatigue Growth Predictions

The development of benchmark examples for static delamination propagation and cyclic delamination onset and growth prediction is presented and demonstrated for a commercial code. The example is based on a finite element model of an End-Notched Flexure (ENF) specimen. The example is independent of the analysis software used and allows the assessment of the automated delamination propagation, onset and growth prediction capabilities in commercial finite element codes based on the virtual crack closure technique (VCCT). First, static benchmark examples were created for the specimen. Second, based on the static results, benchmark examples for cyclic delamination growth were created. Third, the load-displacement relationship from a propagation analysis and the benchmark results were compared, and good agreement could be achieved by selecting the appropriate input parameters. Fourth, starting from an initially straight front, the delamination was allowed to grow under cyclic loading. The number of cycles to delamination onset and the number of cycles during stable delamination growth for each growth increment were obtained from the automated analysis and compared to the benchmark examples. Again, good agreement between the results obtained from the growth analysis and the benchmark results could be achieved by selecting the appropriate input parameters. The benchmarking procedure proved valuable by highlighting the issues associated with the input parameters of the particular implementation. Selecting the appropriate input parameters, however, was not straightforward and often required an iterative procedure. Overall, the results are encouraging but further assessment for mixed-mode delamination is required.

Kruger, Ronald↗

NASA NTRS2011

Climate Change, Extreme Weather Events, and Fungal Disease Emergence and Spread

Empirical evidence from multiple sources show the Earth has been warming since the late 19th century. More recently, evidence for this warming trend is strongly supported by satellite data since the late 1970s from the cryosphere, atmosphere, oceans, and land that confirms increasing temperature trends and their consequences (e.g., reduced Arctic sea ice, rising sea level, ice sheet mass loss, etc.). At the same time, satellite observations of the Sun show remarkably stable solar cycles since the late 1970s, when direct observations of the Sun's total solar irradiance began. Numerical simulation models, driven in part by assimilated satellite data, suggest that future-warming trends will lead to not only a warmer planet, but also a wetter and drier climate depending upon location in a fashion consistent with large-scale atmospheric processes. Continued global warming poses new opportunities for the emergence and spread of fungal disease, as climate systems change at regional and global scales, and as animal and plant species move into new niches. Our contribution to this proceedings is organized thus: First, we review empirical evidence for a warming Earth. Second, we show the Sun is not responsible for the observed warming. Third, we review numerical simulation modeling results that project these trends into the future, describing the projected abiotic environment of our planet in the next 40 to 50 years. Fourth, we illustrate how Rift Valley fever outbreaks have been linked to climate, enabling a better understanding of the dynamics of these diseases, and how this has led to the development of an operational predictive outbreak model for this disease in Africa. Fifth, We project how this experience may be applicable to predicting outbreaks of fungal pathogens in a warming world. Lastly, we describe an example of changing species ranges due to climate change, resulting from recent warming in the Andes and associated glacier melt that has enabled amphibians to colonize higher elevation lakes, only to be followed shortly by the emergence of fungal disease in the new habitats.

Tucker, Compton J.↗

NASA NTRS2011

High Frequency Acoustic Response Characterization and Analysis of the Deep Throttling Common Extensible Cryogenic Engine

The Common Extensive Cryogenic Engine program demonstrated the operation of a deep throttling engine design. The program, spanning five years from August 2005 to July 2010, funded testing through four separate engine demonstration test series. Along with successful completion of multiple objectives, a discrete response of approximately 4000 Hz was discovered and explored throughout the program. The typical low-amplitude acoustic response was evident in the chamber measurement through almost every operating condition; however, at certain off-nominal operating conditions, the response became discrete with higher amplitude. This paper summarizes the data reduction, characterization, and analysis of the 4,000 Hz response for the entire program duration, using the large amount of data collected. Upon first encountering the response, new objectives and instrumentation were incorporated in future test series to specifically collect 4,000 Hz data. The 4,000 Hz response was identified as being related to the first tangential acoustic mode by means of frequency estimation and spatial decomposition. The latter approach showed that the effective node line of the mode was aligned with the manifold propellant inlets with standing waves and quasi-standing waves present at various times. Contour maps that contain instantaneous frequency and amplitude trackings of the response were generated as a significant improvement to historical manual approaches of data reduction presentation. Signal analysis and dynamic data reduction also uncovered several other features of the response including a stable limit cycle, the progressive engagement of subsequent harmonics, the U-shaped time history, an intermittent response near the test-based neutral stability region, other acoustic modes, and indications of modulation with a separate subsynchronous response. Although no engine damage related to the acoustic mode was noted, the peak-to-peak fluctuating pressure amplitude achieved 12.1% of the mean chamber pressure at its highest. The identification of this response in terms of an instability is also discussed.

Casiano, M. J.↗

NASA NTRSDate not supplied

Modeling and Simulation of Rotary Sloshing in Launch Vehicles

The nonlinear dynamics of propellant sloshing during orbital ascent are usually neglected in the flight control analysis of large boost vehicles under the assumption that the viscous damping of the fluid is sufficient to suppress nonlinear phenomena and confine the fluid to small, planar free surface displacements. In this case, the sloshing dynamics can be modeled using a spring-mass-damper or linearized pendulum mechanical analog. However, large, smooth-wall tanks without significant internal hardware or ring baffles are still susceptible to nonlinear effects. In particular, rotary sloshing can present a risk to flight control as it involves the formation of a stable limit cycle which can lead to undesirable roll coupling. The underlying phenomena of jump resonance does not manifest in linear models, but can be reproduced using a nonlinear spherical pendulum or the Bauer paraboloid model developed during the Apollo/Saturn program. In this paper, a detailed analysis of the rotary sloshing dynamics of these mechanical analogs is presented, and discussed in the context of flight control stability. High-fidelity simulations of a representative boost vehicle are used to verify the semi-analytical predictions of the nonlinear dynamic response.

Modeling↗

NASA NTRS1988

34S/32S fractionation in sulfur cycles catalyzed by anaerobic bacteria

Stable isotopic distributions in the sulfur cycle were studied with pure and mixed cultures of the anaerobic bacteria, Chlorobium vibrioforme and Desulfovibrio vulgaris. D. vulgaris and C. vibrioforme can catalyze three reactions constituting a complete anaerobic sulfur cycle: reduction of sulfate to sulfide (D. vulgaris), oxidation of sulfide to elemental sulfur (C. vibrioforme), and oxidation of sulfur to sulfate (C. vibrioforme). In all experiments, the first and last reactions favored concentration of the light 32S isotope in products (isotopic fractionation factor epsilon = -7.2 and -1.7%, respectively), whereas oxidation of sulfide favored concentration of the heavy 34S isotope in products (epsilon = +1.7%). Experimental results and model calculations suggest that elemental sulfur enriched in 34S versus sulfide may be a biogeochemical marker for the presence of sulfide-oxidizing bacteria in modern and ancient environments.

Non-NASA Center↗

NASA NTRS2010

Closed-Loop Control of Vortex Formation in Separated Flows

In order to phase lock the flow at the desired shedding cycle, particularly at Phi,best, We designed a feedback compensator. (Even though the open-loop forcing at Wf below Wn can lead to phase-locked limit cycles with a high average lift,) This feedback controller resulted in the phase-locked limit cycles that the open-loop control could not achieve for alpha=30 and 40 Particularly for alpha=40, the feedback was able to stabilize the limit cycle that was not stable with any of the open-loop periodic forcing. This results in stable phase-locked limit cycles for a larger range of forcing frequencies than the open-loop control. Also, it was shown that the feedback achieved the high-lift unsteady flow states that open-loop control could not sustain even after the states have been achieved for a long period of time.

Colonius, Tim↗

NASA NTRS2021

High Temperature W-band Complex Permittivity Measurements of Thermally Cycled Ceramic-Metal Composites: AlN:Mo with 0.25 vol% to 4.0 vol% Mo from 25 °C to 1000 °C in Air

An apparatus for measuring the W-band (75-110GHz) complex permittivity of dielectrics at 1000 °C was developed. This apparatus allows for measurements at approximately twice the temperature of previously published high temperature free-space measurement systems while maintaining similar precision. Challenges were addressed related to high temperature measurements, including temperature uniformity, the accuracy of temperature measurements, and preventing temperature related changes to mm-wave measurement systems. The details of complex permittivity extraction from the measured S-parameters are discussed. Sources of error related to permittivity measurement and mathematical models were identified and are discussed in detail herein. Thermally-cycled, mm-wave absorbing, aluminum nitride ceramic composites containing varying levels of molybdenum additives were measured over the range of 25-1000 °C. These measurements were compared to the same composites before thermal cycling. It was found that ceramic composites are largely stable after thermal cycling in terms of dielectric properties despite the presence of visible surface modifications.

Zane W Cohick↗

NASA NTRS1972

Planetary resonances, bi-stable oscillation modes, and solar activity cycles

The natural resonance structure of the planets in the solar system yields resonance periods of 11.08 and 180 years. The 11.08 year period is due to resonance of the sidereal periods of the three inner planets. The 180-year period is due to synodic resonances of the four major planets. These periods are also observed in the sunspot time series. The 11-year sunspot cycles from 1 to 19 are separated into categories of positive and negative cycles, Mode 1 and Mode 2 cycles, and typical and anomalous cycles. Each category has a characteristic shape, magnitude, or duration, so that statistical prediction techniques are improved when a cycle can be classified in a given category. These categories provide evidence for bistable modes of solar oscillation. The next minimum is expected in 1977 and the next maximum in 1981 or later. These epoch values are 2.5 years later than those based on typical cycle characteristics.

Sleeper, H. P., Jr.↗

NASA NTRS1985

Bifurcation techniques for nonlinear dynamic analysis of compressor stall phenomena

Compressor stall phenomena is analyzed from nonlinear control theory viewpoint, based on bifurcation-catastrophe techniques. This new approach appears promising and offers insight into such well known compressor instability problems as surge and rotating stall; furthermore it suggests strategies for recovery from stall. Three interlocking dynamic nonlinear state space models are developed. It is shown that the problem of rotating stall can be viewed as an (induced) bifurcation of solution of the unstalled model. Hysteresis effect is shown to exist in the stall/recovery process. Surge cycles are observed to develop for some critical parameter values. It is shown that the oscillatory behavior is due to development of limit cycles, generated by Hopf bifurcation of solutions. Both stable and unstable limit cycles are observed. To further illustrate the usefulness of the methodology some partial computation of domains of attraction of equilibria is carried out, and parameter sensitivity analysis is performed.

Razavi, H. C.↗

NASA NTRS1983

Moderate temperature rechargeable sodium batteries

Cells utilizing the organic electrolyte, NaI in triglyme, operated at approx. 130 C with Na(+) - intercalating cathodes. However, their rate and stability were inadequate. NaAlCl4 was found to be a highly useful electrolyte for cell operation at 165-190 C. Na(+) intercalating chalcogenides reacted with NaAlCl4 during cycling to form stable phases. Thus, VS2 became essentially VS2Cl, with reversible capacity of approx 2.8 e(-)/V, and a mid-discharge voltage of approx 2.5V and 100 deep discharge cycles were readily achieved. A positive electrode consisting of VCl3 and S plus NaAlCl4 was subjected to deep-discharge cycles 300 times and it demonstrated identity with the in-situ-formed BSxCly cathode. NiS2 and NiS which are not Na(+)-intercalating structures formed highly reversible electrodes in NaAlCl4. The indicated discharge mechanism implies a theoretical capacity 4e(-)/Ni for NiS2 and 2e(-)/Ni for NiS. The mid-discharge potentials are, respectively, 2.4V and 2.1V. A Na/NiS2 cell cycling at a C/5 rate has exceeded 500 deep discharge cycles with 2.5e(-)/Ni average utilization. A 4 A-hr nominal capacity prototype Na/NiS2 cell was tested at 190 C. It was voluntarily terminated after 80 cycles. Further development, particularly of cathode structure and hardware should produce a battery capable of at least 50-W-hr/lb and more than 1000 cycles.

Abraham, K. M.↗

NASA NTRS1987

A low-power arcjet cyclic lifetest

A cyclic lifetest of a low power dc arcjet thruster using a hydrogen/nitrogen propellant mixture simulating hydrazine is currently in progress. Over 300 hr of operation have been accumulated to date in 2 hr duty cycles at a power level of about 1.15 kW, approximating that available on commercial communications satellites. A burn-in period was carried out before consistent operation was attained. After this period, the arcjet operated in a very stable fashion from cycle to cycle. At the beginning of each cycle, there was a brief starting transient followed by a rapid rise to a steady-state voltage. The steady-state voltage increased by about 5 V over the first 95 cycles. After this, it increased by only 1 V through the remainder of the test. Thrust measurements taken before the life test and again after the completion of the 144th cycle showed that both thrust, specific impulse, and arc voltage had increased over this period of operation. No life limiting mechanisms were observed during the course of the testing.

Curran, Francis M.↗

NASA NTRS2004

Eight-Channel Continuous Timer

A custom laboratory electronic timer circuit measures the durations of successive cycles of nominally highly stable input clock signals in as many as eight channels, for the purpose of statistically quantifying the small instabilities of these signals. The measurement data generated by this timer are sent to a personal computer running software that integrates the measurements to form a phase residual for each channel and uses the phase residuals to compute Allan variances for each channel. (The Allan variance is a standard statistical measure of instability of a clock signal.) Like other laboratory clock-cycle-measuring circuits, this timer utilizes an externally generated reference clock signal having a known frequency (100 MHz) much higher than the frequencies of the input clock signals (between 100 and 120 Hz). It counts the number of reference-clock cycles that occur between successive rising edges of each input clock signal of interest, thereby affording a measurement of the input clock-signal period to within the duration (10 ns) of one reference clock cycle. Unlike typical prior laboratory clock-cycle-measuring circuits, this timer does not skip some cycles of the input clock signals. The non-cycle-skipping feature is an important advantage because in applications that involve integration of measurements over long times for characterizing nominally highly stable clock signals, skipping cycles can degrade accuracy. The timer includes a field-programmable gate array that functions as a 20-bit counter running at the reference clock rate of 100 MHz. The timer also includes eight 20-bit latching circuits - one for each channel - at the output terminals of the counter. Each transition of an input signal from low to high causes the corresponding latching circuit to latch the count at that instant. Each such transition also sets a status flip-flop circuit to indicate the presence of the latched count. A microcontroller reads the values of all eight status flipflops and then reads the latched count for each channel for which the flip-flop indicates the presence of a count. Reading the count for each channel automatically causes the flipflop of that channel to be reset. The microcontroller places the counts in time order, identifies the channel number for each count, and transmits these data to the personal computer.

Cole, Steven↗

NASA NTRS1970

Load cell for thermionic converter tests

Stable, low duty cycle transistorized emitter follower load cell controls and absorbs large currents at low voltages. The use of energy storage in capacitors reduces auxiliary power source requirements. Low duty cycle pulse mode of operation reduces the average power handling requirement of all components.

Breitwieser, R.↗

NASA NTRS1974

Stability analysis of nonlinear systems by multiple time scaling

The asymptotic solution for the transient analysis of a general nonlinear system in the neighborhood of the stability boundary was obtained by using the multiple-time-scaling asymptotic-expansion method. The nonlinearities are assumed to be of algebraic nature. Terms of order epsilon to the 3rd power (where epsilon is the order of amplitude of the unknown) are included in the solution. The solution indicates that there is always a limit cycle which is stable (unstable) and exists above (below) the stability boundary if the nonlinear terms are stabilizing (destabilizing). Extension of the solution to include fifth order nonlinear terms is also presented. Comparisons with harmonic balance and with multiple-time-scaling solution of panel flutter equations are also included.

Morino, L.↗

NASA NTRS1977

F-8C adaptive flight control laws

Three candidate digital adaptive control laws were designed for NASA's F-8C digital flyby wire aircraft. Each design used the same control laws but adjusted the gains with a different adaptative algorithm. The three adaptive concepts were: high-gain limit cycle, Liapunov-stable model tracking, and maximum likelihood estimation. Sensors were restricted to conventional inertial instruments (rate gyros and accelerometers) without use of air-data measurements. Performance, growth potential, and computer requirements were used as criteria for selecting the most promising of these candidates for further refinement. The maximum likelihood concept was selected primarily because it offers the greatest potential for identifying several aircraft parameters and hence for improved control performance in future aircraft application. In terms of identification and gain adjustment accuracy, the MLE design is slightly superior to the other two, but this has no significant effects on the control performance achievable with the F-8C aircraft. The maximum likelihood design is recommended for flight test, and several refinements to that design are proposed.

Hartmann, G. L.↗