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All sourcesNASA NTRSDOE OSTI
NASA NTRS2017

Determination of the Limiting Magnitude

The limiting magnitude of an optical camera system is an important property to understand since it is used to find the completeness limit of observations. Limiting magnitude depends on the hardware and software of the system, current weather conditions, and the angular speed of the objects observed. If an object exhibits a substantial angular rate during the exposure, its light spreads out over more pixels than the stationary stars. This spreading causes the limiting magnitude to be brighter when compared to the stellar limiting magnitude. The effect, which begins to become important when the object moves a full width at half max during a single exposure or video frame. For targets with high angular speeds or camera systems with narrow field of view or long exposures, this correction can be significant, up to several magnitudes. The stars in an image are often used to measure the limiting magnitude since they are stationary, have known brightness, and are present in large numbers, making the determination of the limiting magnitude fairly simple. In order to transform stellar limiting magnitude to object limiting magnitude, a correction must be applied accounting for the angular velocity. This technique is adopted in meteor and other fast-moving object observations, as the lack of a statistically significant sample of targets makes it virtually impossible to determine the limiting magnitude before the weather conditions change. While the weather is the dominant factor in observing satellites, the limiting magnitude for meteors also changes throughout the night due to the motion of a meteor shower or sporadic source radiant across the sky. This paper presents methods for determining the limiting stellar magnitude and the conversion to the target limiting magnitude.

Kingery, Aaron↗
NASA NTRS2005

Force Limited Vibration Testing

This slide presentation reviews the concept and applications of Force Limited Vibration Testing. The goal of vibration testing of aerospace hardware is to identify problems that would result in flight failures. The commonly used aerospace vibration tests uses artificially high shaker forces and responses at the resonance frequencies of the test item. It has become common to limit the acceleration responses in the test to those predicted for the flight. This requires an analysis of the acceleration response, and requires placing accelerometers on the test item. With the advent of piezoelectric gages it has become possible to improve vibration testing. The basic equations have are reviewed. Force limits are analogous and complementary to the acceleration specifications used in conventional vibration testing. Just as the acceleration specification is the frequency spectrum envelope of the in-flight acceleration at the interface between the test item and flight mounting structure, the force limit is the envelope of the in-flight force at the interface . In force limited vibration tests, both the acceleration and force specifications are needed, and the force specification is generally based on and proportional to the acceleration specification. Therefore, force limiting does not compensate for errors in the development of the acceleration specification, e.g., too much conservatism or the lack thereof. These errors will carry over into the force specification. Since in-flight vibratory force data are scarce, force limits are often derived from coupled system analyses and impedance information obtained from measurements or finite element models (FEM). Fortunately, data on the interface forces between systems and components are now available from system acoustic and vibration tests of development test models and from a few flight experiments. Semi-empirical methods of predicting force limits are currently being developed on the basis of the limited flight and system test data. A simple two degree of freedom system is shown and the governing equations for basic force limiting results for this system are reviewed. The design and results of the shuttle vibration forces (SVF) experiments are reviewed. The Advanced Composition Explorer (ACE) also was used to validate force limiting. Test instrumentation and supporting equipment are reviewed including piezo-electric force transducers, signal processing and conditioning systems, test fixtures, and vibration controller systems. Several examples of force limited vibration testing are presented with some results.

random vibration testing↗
NASA NTRS2017

Determination of the Meteor Limiting Magnitude

We present our method to calculate the meteor limiting magnitude. The limiting meteor magnitude defines the faintest magnitude at which all meteors are still detected by a given system. An accurate measurement of the limiting magnitude is important in order to calculate the meteoroid flux from a meteor shower or sporadic source. Since meteor brightness is linked to meteor mass, the limiting magnitude is needed to calculate the limiting mass of the meteor flux measurement. The mass distribution of meteoroids is thought to follow a power law, thus being slightly off in the limiting magnitude can have a significant effect on the measured flux. Sky conditions can change on fairly short timescales; therefore one must monitor the meteor limiting magnitude at regular intervals throughout the night, rather than just measuring it once. We use the stellar limiting magnitude as a proxy of the meteor limiting magnitude. Our method for determining the stellar limiting magnitude and how we transform it into the meteor limiting magnitude is presented. These methods are currently applied to NASA's wide-field meteor camera network to determine nightly fluxes, but are applicable to other camera networks.

A Kingery↗
NASA NTRS2011

Characterizing Observed Limit Cycles in the Cassini Main Engine Guidance Control System

The Cassini spacecraft dynamics-related telemetry during long Main Engine (ME) burns has indicated the presence of stable limit cycles between 0.03-0.04 Hz frequencies. These stable limit cycles cause the spacecraft to possess non-zero oscillating rates for extended periods of time. This indicates that the linear ME guidance control system does not model the complete dynamics of the spacecraft. In this study, we propose that the observed limit cycles in the spacecraft dynamics telemetry appear from a stable interaction between the unmodeled nonlinear elements in the ME guidance control system. Many nonlinearities in the control system emerge from translating the linear engine gimbal actuator (EGA) motion into a spacecraft rotation. One such nonlinearity comes from the gear backlash in the EGA system, which is the focus of this paper. The limit cycle characteristics and behavior can be predicted by modeling this gear backlash nonlinear element via a describing function and studying the interaction of this describing function with the overall dynamics of the spacecraft. The linear ME guidance controller and gear backlash nonlinearity are modeled analytically. The frequency, magnitude, and nature of the limit cycle are obtained from the frequency response of the ME guidance controller and nonlinear element. In addition, the ME guidance controller along with the nonlinearity is simulated. The simulation response contains a limit cycle with similar characterstics as predicted analytically: 0.03-0.04 Hz frequency and stable, sustained oscillations. The analytical and simulated limit cycle responses are compared to the flight telemetry for long burns such as the Saturn Orbit Insertion and Main Engine Orbit Trim Maneuvers. The analytical and simulated limit cycle characteristics compare well with the actual observed limit cycles in the flight telemetry. Both have frequencies between 0.03-0.04 Hz and stable oscillations. This work shows that the stable limit cycles occur due to the interaction between the unmodeled nonlinear elements and linear ME guidance controller.

stable limit cycle↗
DOE OSTI2025

A Two-Stage Current Limiting Control Strategy for Direct-Droop-Controlled Grid-Forming Inverters

This paper presents a two-stage current limiting control strategy with fault ride-through capability for the direct-droop-controlled grid-forming (GFM) inverters. The proposed approach comprises Stage 1 and Stage 2 current limiting controls. During faults, Stage 1 current limiting control instantly clamps the inverter output current magnitude to its maximum transient limit by blocking the switching pulses to the insulated-gate bipolar transistors (IGBTs) with the help of a hysteresis loop control, and Stage 2 current limiting control limits the inverter output current magnitude to its steady-state limit by regulating the amplitude and frequency of the modulating waveform utilizing the active and reactive current limiting control loops. By implementing the current limiting actions in two stages, this approach can effectively limit the over-current within a few cycles after the fault occurrence and ensure synchronism to the grid after long-term fault events. The efficacy of the proposed control approach is validated through electromagnetic transient (EMT) simulation results conducted on a single GFM inverter-based test system and the IEEE 39-bus test system with multiple GFM inverters in the PSCAD platform.

Mohiuddin, Sheik Mohammad↗
NASA NTRS1994

The correlation function of flux-limited X-ray clusters

We show that the spatial correlation function of a flux-limited sample of X-ray-selected clusters of galaxies will exhibit a correlation scale that is smaller than the correlation scale of a volume-limited, richness-limited sample of comparable apparent spatial density. The flux-limited sample contains clusters of different richnesses at different distances: poor groups are found nearby and rich clusters at greater distances. Since the cluster correlation strength is known to increase with richness, the flux-limited sample averages over the correlations of poor and rich clusters. On the other hand, a volume-limited, richness-limited sample has a minimum richness threshold, and a constant mixture of richnesses with redshift. Using the observed correlation scale for rich (R greater than or equal to 1) clusters, r(sub 0)(R greater than or equal to 1) = 21 +/- 2 Mpc/h, that was determined from previous volume-limited studies, we derive for the Roentgen Satellite (ROSAT) flux-limited X-ray cluster sample r(sub 0) (flux-limited) approximately equals 14 Mpc/h, in agreement with the recently observed value of 13.7 +/- 2.3 Mpc/h.

Bahcall, Neta A.↗
NASA NTRS2017

Climate Limits Across Space and Time on European Forest Structure

The impact climate has on forests has been extensively studied. However, the large scale effect climate has on forest structures, such as average diameters, heights and basal area are understudied in a spatially explicit manner. The limits, tipping points and thresholds that climate places on forest structures dictate the services a forest may provide, the vulnerability of a forest to mortality and the potential value of the timber there within. The majority of current research either investigates climate impacts on forest pools and fluxes, on a tree physiological scale or on case studies that are used to extrapolate results and potential impacts. A spatially explicit study on how climate affects forest structure over a large region would give valuable information to stakeholders who are more concerned with ecosystem services that cannot be described by pools and fluxes but require spatially explicit information - such as biodiversity, habitat suitability, and market values. In this study, we quantified the limits that climate (maximum, minimum temperature and precipitation) places on 3 forest structures, diameter at breast height, height, and basal area throughout Europe. Our results show clear climatic zones of high and low upper limits for each forest structure variable studied. We also spatially analyzed how climate restricts the potential bio-physical upper limits and creates tipping points of each forest structure variable and which climate factors are most limiting. Further, we demonstrated how the climate change has affected 8 individual forests across Europe and then the continent as a whole. We find that diameter, height and basal area are limited by climate in different ways and that areas may have high upper limits in one structure and low upper limits in another limited by different climate variables. We also found that even though individual forests may have increased their potential upper limit forest structure values, European forests as a whole have lost, on average, 5.0%, 1.7% and 6.5% in potential mean forest diameter, height and basal area, respectively.

Moreno, Adam La Salle↗
NASA NTRSDate not supplied

Shock Capturing via Limiting for High-Order Methods including Discontinuous Galerkin

High-order methods, such as discontinuous Galerkin (DG), spectral, and flux reconstruction (FR), are prone to generating unwanted oscillations near shocks and discontinuities. Conventional limiting techniques, while effective in suppressing oscillations near shocks, often compromise accuracy near extrema, where the solution is only first-order accurate. This paper introduces a novel limiting technique for these high-order schemes, aimed at effectively managing shocks while preserving accuracy. The key idea is to expand the standard monotonicity limits to provide “room” near smooth extrema, ensuring that limiting has no effect and thus preserving accuracy. Near a discontinuity, these expanded limits effectively reduce to the original monotonicity limits, suppressing oscillations. Additional motivation is drawn from a formula for the derivative of Radau polynomials, which depicts the behavior of oscillations resulting from discontinuities. This behavior leads to a simplification by applying the limits to the sum of magnitudes of all modes, linear and higher degree. Unlike typical approaches, which rely on successful detection to activate limiting, our limiter depends continuously on the data, there by avoiding potential issues if detection fails. To reduce computing time, efficient criteria for detecting smooth regions where limiting is unnecessary are presented. Combined with detection, the continuous dependence on the data is lost, but the method is more economical. A notable characteristic of the entire process is its simplicity in both concept and implementation. Numerical tests for advection and Euler equations are conducted to demonstrate the effectiveness of the proposed method.

numerical methods↗
NASA NTRSDate not supplied

Shock Capturing via Limiting for High-Order Methods including Discontinuous Galerkin

High-order methods, such as discontinuous Galerkin (DG), spectral, and flux reconstruction (FR), are prone to generating unwanted oscillations near shocks and discontinuities. Conventional limiting techniques, while effective in suppressing oscillations near shocks, often compromise accuracy near extrema, where the solution is only first-order accurate. This paper introduces a novel limiting technique for these high-order schemes, aimed at effectively managing shocks while preserving accuracy. The key idea is to expand the standard monotonicity limits to provide “room” near smooth extrema, ensuring that limiting has no effect and thus preserving accuracy. Near a discontinuity, these expanded limits effectively reduce to the original monotonicity limits, suppressing oscillations. Additional motivation is drawn from a formula for the derivative of Radau polynomials, which depicts the behavior of oscillations resulting from discontinuities. This behavior leads to a simplification by applying the limits to the sum of magnitudes of all modes, linear and higher degree. Unlike typical approaches, which rely on successful detection to activate limiting, our limiter depends continuously on the data, there by avoiding potential issues if detection fails. To reduce computing time, efficient criteria for detecting smooth regions where limiting is unnecessary are presented. Combined with detection, the continuous dependence on the data is lost, but the method is more economical. A notable characteristic of the entire process is its simplicity in both concept and implementation. Numerical tests for advection and Euler equations are conducted to demonstrate the effectiveness of the proposed method.

numerical methods↗
DOE OSTI2024

Correlation of the L-mode density limit with edge collisionality

The "density limit'' is one of the fundamental bounds on tokamak operating space, and is commonly estimated via the empirical Greenwald scaling. This limit has garnered renewed interest in recent years as it has become clear that ITER and many tokamak pilot plant concepts must operate near or above the widely-used Greenwald limit to achieve their objectives. Evidence has also grown that the Greenwald scaling - in its remarkable simplicity - may not capture the full complexity of the disruptive density limit. In this study, we assemble a multi-machine database to quantify the effectiveness of the Greenwald limit as a predictor of the L-mode density limit and identify alternative stability metrics. We find that a two-parameter dimensionless boundary in the plasma edge, $\nu_{*\rm, edge}^{\rm limit} = 3.0 \beta_{T,{\rm edge}}^{-0.4}$, achieves significantly higher accuracy (true negative rate of 97.7\% at a true positive rate of 95\%) than the Greenwald limit (true negative rate 86.1\% at a true positive rate of 95\%) across a multi-machine dataset including metal- and carbon-wall tokamaks (AUG, C-Mod, DIII-D, and TCV). The collisionality boundary presented here can be applied for density limit avoidance in current devices and in ITER, where it can be measured and responded to in real time.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1974

Nonproportional loading limit for structures

The design of most structures involves ensuring integrity for several independent loading conditions. Often, it is rational to design these, exploiting the ductility of the materials to reduce structural costs. Then, ensuring integrity evokes the need for nonmonotonic limit analyses. A groundwork is laid for implementing these analyses. An alternate limit load characterization to that of Greenberg is provided, a mathematical statement of the problem leading to both monotonic (proportional) and nonmonotonic limit loads values is formulated, a direct limit load analysis procedure for analysis within a finite-element framework is described, and limit loads for sets of simple structures are evaluated. A direct limit analysis process is described, and monotonic limit loads are characterized. The process furnishes 'exact' values of limit loads with increasing efficiency as the number of structural elements and force redundancy decreases. Tests show that the accuracy of predicting nonmonotonic limit loads is very sensitive to the number of degrees of freedom in the analysis compared with the total number in the model.

Melosh, R. J.↗
NASA NTRS1995

New upper limits on the local metagalactic ionizing radiation density

We have obtained H-alpha observations with the Maryland-Caltech Fabry-Perot Spectrometer attached to the Cassegrain focus of the 1.5 m telescope at Palomer Observatory in order to set limits on the number of ionizing photons from the local metagalactic radiation field. We have observed the SW component of the Haynes-Giovanelli cloud H I 1225+01, an intergalactic cloud which should be optimum for measuring the metagalactic flux because it is nearly opaque to ionizing photons, it does not appear to be significantly shielded from the metagalactic radiation field, and the limits on embedded or nearby ionizing sources are unusually low. For the area of the cloud with an H I column density greater than 10(exp 19)/sq cm we set a 2 sigma limit of 1.1 x 10(exp -19) ergs/sq cm/s/sq arcsec (20 mR) for the surface brightness of diffuse H-alpha. This implies a 2 sigma upper limit on the incident one-sided ionizing flux of Phi(sub ex) is less than 3 x 10(exp 4)/sq cm/s. For a radiation field of the form J(sub nu) is approximately nu(exp -1.4), this yields a firm 2 sigma upper limit on the local metagalactic photoionization rate of Gamma is less than 2 x 10(exp -13)/s, and an upper limit for the radiation field J(sub nu) at the Lyman limit of J(sub nu0) is less than 8 x 10(exp -23) ergs/sq cm/Hz/sr. We discuss previous efforts to constrain the metagalactic ionizing flux using H-alpha surface brightness observations and also other methods, and conclude that our result places the firmest upper limit on this flux. We also observed the 7 min diameter region centered on 3C 273 in which H-alpha emission at a velocity of approximately 1700 km/s was initially reported by Williams and Schommer. In agreement with T. B. Williams (private communication) we find the initial detection was spurious. We obtain a 2 sigma upper limit of 1.8 x 10(exp -19) ergs/sq cm/s/sq arcsec (32 mR) for the mean surface brightness of diffuse H-alpha, about a factor of 6 below the published value.

Vogel, Stuart N.↗
NASA NTRS2008

Gaseous Surrogate Hydrocarbons for a Hifire Scramjet that Mimic Opposed Jet Extinction Limits for Cracked JP Fuels

This paper describes, first, the top-down methodology used to define simple gaseous surrogate hydrocarbon (HC) fuel mixtures for a hypersonic scramjet combustion subtask of the HiFIRE program. It then presents new and updated Opposed Jet Burner (OJB) extinction-limit Flame Strength (FS) data obtained from laminar non-premixed HC vs. air counterflow diffusion flames at 1-atm, which follow from earlier investigations. FS represents a strain-induced extinction limit based on cross-section-average air jet velocity, U(sub air), that sustains combustion of a counter jet of gaseous fuel just before extinction. FS uniquely characterizes a kinetically limited fuel combustion rate. More generally, Applied Stress Rates (ASRs) at extinction (U(sub air) normalized by nozzle or tube diameter, D(sub n or t) can directly be compared with extinction limits determined numerically using either a 1-D or (preferably) a 2-D Navier Stokes simulation with detailed transport and finite rate chemistry. The FS results help to characterize and define three candidate surrogate HC fuel mixtures that exhibit a common FS 70% greater than for vaporized JP-7 fuel. These include a binary fuel mixture of 64% ethylene + 36% methane, which is our primary recommendation. It is intended to mimic the critical flameholding limit of a thermally- or catalytically-cracked JP-7 like fuel in HiFIRE scramjet combustion tests. Our supporting experimental results include: (1) An idealized kinetically-limited ASR reactivity scale, which represents maximum strength non-premixed flames for several gaseous and vaporized liquid HCs; (2) FS characterizations of Colket and Spadaccini s suggested ternary surrogate, of 60% ethylene + 30% methane + 10% n-heptane, which matches the ignition delay of a typical cracked JP fuel; (3) Data showing how our recommended binary surrogate, of 64% ethylene + 36% methane, has an identical FS; (4) Data that characterize an alternate surrogate of 44% ethylene + 56% ethane with identical FS and nearly equal molecular weights; this could be useful when systematically varying the fuel composition. However, the mixture liquefies at much lower pressure, which limits on-board storage of gaseous fuel; (5) Dynamic Flame Weakening results that show how oscillations in OJB input flow (and composition) can weaken (extinguish) surrogate flames up to 200 Hz, but the weakening is 2.5x smaller compared to pure methane; and finally, (6) FS limits at 1-atm that compare with three published 1-D numerical OJB extinction results using four chemical kinetic models. The methane kinetics generally agree closely at 1-atm, whereas, the various ethylene models predict extinction limits that average ~ 45% high, which represents a significant problem for numerical simulation of surrogate-based flameholding in a scramjet cavity. Finally, we continue advocating the FS approach as more direct and fundamental for assessing idealized scramjet flameholding potentials than measurements of "unstrained" premixed laminar burning velocity or blowout in a Perfectly Stirred Reactor.

Pellett, Gerald L.↗
DOE OSTI2025

Unified Model of Current-Limiting Grid-Forming Inverters for Large-Signal Analysis

Grid-forming (GFM) inverters can hardly withstand any overloading. As such, GFM inverters need a current limiter in their control system to avoid hardware damage during overloading or grid disturbances. When the current limiter is engaged for inverter protection, however, it dynamically changes the inverter output impedance, which can significantly affect the system behavior against large disturbances. For example, when the current limiter curtails the output power, the primary controller of the GFM inverter-which generates the voltage and angle reference-is prone to losing synchronization with the grid. This can cause large-signal instability in the network. This paper presents a unified GFM current-limiter model to gain a deeper understanding of the impact of the GFM inverter current limiting on large-signal instability and other system behaviors. The unified model captures several well-known current limiters for GFM inverters, and it reveals their large-signal equivalence characterized by the limiter angle. We use the unified model to present in-depth insights into the driving forces that cause large-signal instability in GFM inverter-driven grids. Further, this paper illustrates that the unified model can be used as a tool for assessing the system-level impacts of various GFM current-limiter designs during grid disturbances. Using numerical, analytical, electromagnetic transient models, and a hardware setup, the validity of the unified model is evaluated.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS2012

A New Approach in Force-Limited Vibration Testing of Flight Hardware

The force-limited vibration test approaches discussed in NASA-7004C were developed to reduce overtesting associated with base shake vibration tests of aerospace hardware where the interface responses are excited coherently. This handbook outlines several different methods of specifying the force limits. The rationale for force limiting is based on the disparity between the impedances of typical aerospace mounting structures and the large impedances of vibration test shakers when the interfaces in general are coherently excited. Among these approaches, the semi-empirical method is presently the most widely used method to derive the force limits. The inclusion of the incoherent excitation of the aerospace structures at mounting interfaces has not been accounted for in the past and provides the basis for more realistic force limits for qualifying the hardware using shaker testing. In this paper current methods for defining the force limiting specifications discussed in the NASA handbook are reviewed using data from a series of acoustic and vibration tests. A new approach based on considering the incoherent excitation of the structural mounting interfaces using acoustic test data is also discussed. It is believed that the new approach provides much more realistic force limits that may further remove conservatism inherent in shaker vibration testing not accounted for by methods discussed in the NASA handbook. A discussion on using FEM/BEM analysis to obtain realistic force limits for flight hardware is provided.

force limiting responses↗
NASA NTRS1991

A linear control design structure to maintain loop properties during limit operation in a multi-nozzle turbofan engine

The implementation of multi-variable control systems on turbofan engines requires the use of limit protection to maintain safe engine operation. Since a turbofan engine typically encounters limits during transient operation, the use of a limit protection scheme that modifies the feedback loop may void the desired 'guarantees' associated with linear multi-variable control design methods, necessitating considerable simulation to validate the control with limited protection. An alternative control design structure is proposed that maintains the desired linear feedback properties when certain safety limits are encountered by moving the limit protection scheme outside the feedback loop. This proposed structure is compared to a structure with a limit protection scheme that modifies the feedback loop properties. The two design structures are compared using both linear and nonlinear simulations. The evaluation emphasizes responses where the fan surge margin limit is encountered.

Mattern, Duane↗
NASA NTRS1991

A linear control design structure to maintain loop properties during limit operation in a multi-nozzle turbofan engine

The implementation of multi-variable control systems on turbofan engines requires the use of limit protection to maintain safe engine operation. Since a turbofan engine typically encounters limits during transient operation, the use of a limit protection scheme that modifies the feedback loop may void the desired 'guarantees' associated with linear multi-variable control design methods, necessitating considerable simulation to validate the control with limit protection. An alternative control design structure is proposed that maintains the desired linear feedback properties when certain safety limits are encountered by moving the limit protection scheme outside of the feedback loop. This proposed structure is compared to a structure with a limit protection scheme that modifies the feedback loop properties. The two design structures are compared using both linear and nonlinear simulations. The evaluation emphasizes responses where the fan surge margin limit is encountered.

Mattern, Duane↗
NASA NTRS1999

Benefits of Force Limiting Vibration Testing

Force limited random vibration testing is used at NASA John Glenn Research Center (formerly NASA Lewis Research Center) for qualifying aerospace hardware for flight. The benefit of force limiting testing is that it limits overtesting of flight hardware, by controlling input force and acceleration from the shaker (dual control) to the test article. The purpose of force limiting is to replicate the test article resonant response for the actual flight mounting condition. The force limiting testing technology has been implemented at the Jet Propulsion Laboratory for the past 10 years on various spacecraft testing programs. The Cassini mission to Saturn, most notably, utilized force limiting vibration testing as part of the spacecraft system level vibration testing. NASA John Glenn Research Center is responsible for microgravity combustion and fluid science research on the Shuttle and the International Space Station. Qualification testing of delicate and vibration sensitive science instrumentation is particularly challenging to successfully qualify for flight. In order to facilitate the testing process, force limiting has been implemented to minimize overtesting of flight hardware. This paper will address recent flight camera testing (qualification random vibration and strength testing) for the Combustion Module-2 mission and the impact of Semi-empirical Method force limits.

McNelis, Mark E.↗