Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “DIFFERENTIAL OPERATOR”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 163 records · Page 9

Free-Spinning Characteristics of a 1/24-Scale Model of the Grumman F11F-1 Airplane, TED No. NACA AD 395

An investigation is being conducted in the Langley 20-foot free-spinning tunnel on a 1/24-scale model of the Grumman F11F-1 airplane to determine spin and recovery characteristics and the minimum-size parachute required to satisfactorily terminate the spin in an emergency. Results obtained to date are presented herein. Test results indicate that it may be difficult to obtain an erect or inverted spin on the airplane, but, if a spin is obtained, the spin will be very oscillatory and recovery from the developed erect spin by rudder reversal may not be possible. The lateral controls will have no appreciable effect on recoveries from erect.spins. Recovery from the inverted spin by merely neutralizing the rudder will be satisfactory. After recoveries by rudder reversal and after recoveries from spins without control movement (no spins), the model oftentimes rolled very rapidly about the X-axis. Based on limited preliminary tests made in this investigation to make the model recover satisfactorily, it appears that canards near the nose of the airplane or differentially operated horizontal tails may be utilized to provide rapid recoveries. The parachute test results indicate that an 11-foot-diameter (laid-out-flat) parachute with a drag coefficient of 0.650 (based on the laid- out-flat diameter) and with a towline length equal to the wing span is the minimum-size parachute required to satisfactorily terminate an erect or inverted spin in an emergency.

Bowman, James S., Jr.↗

An Extension of the Time-Spectral Method to Overset Solvers

Relative motion in the Cartesian or overset framework causes certain spatial nodes to move in and out of the physical domain as they are dynamically blanked by moving solid bodies. This poses a problem for the conventional Time-Spectral approach, which expands the solution at every spatial node into a Fourier series spanning the period of motion. The proposed extension to the Time-Spectral method treats unblanked nodes in the conventional manner but expands the solution at dynamically blanked nodes in a basis of barycentric rational polynomials spanning partitions of contiguously defined temporal intervals. Rational polynomials avoid Runge's phenomenon on the equidistant time samples of these sub-periodic intervals. Fourier- and rational polynomial-based differentiation operators are used in tandem to provide a consistent hybrid Time-Spectral overset scheme capable of handling relative motion. The hybrid scheme is tested with a linear model problem and implemented within NASA's OVERFLOW Reynolds-averaged Navier- Stokes (RANS) solver. The hybrid Time-Spectral solver is then applied to inviscid and turbulent RANS cases of plunging and pitching airfoils and compared to time-accurate and experimental data. A limiter was applied in the turbulent case to avoid undershoots in the undamped turbulent eddy viscosity while maintaining accuracy. The hybrid scheme matches the performance of the conventional Time-Spectral method and converges to the time-accurate results with increased temporal resolution.

Leffell, Joshua Isaac↗

Extended Stroke and Miniaturized Reverse-Operation DTE Thermal Switches

This paper describes two advanced thermal switches under development that are offshoots of the recently flight-qualified 2500:1 reverse-operation differential thermal expansion (DTE) thermal switch (ROD-TSW). The first is the extended stroke ROD-TSW (ES-ROD-TSW) while the second is the miniaturized ROD-TSW (mini-ROD-TSW). Each employs multiple diametrically nested DTE stages in contrast to the single-stage ROD-TSW. The ES-ROD-TSW employs two stages and a negative CTE material known as Allvar and its main purpose is to extend its stroke for use in non-vacuum planetary environments. The mini-ROD-TSW employs four stages to miniaturize its size for use in compact lunar instruments and rovers. The ES-ROD-TSW was TVAC tested at JPL and its ON/OFF ratio is 13000:1 based on a measured ON conductance of 6.89 W/K and a calculated OFF conductance of 0.00053 W/K. The mini-ROD-TSW is targeted to have an ON conductance of 1.5 W/K and an OFF conductance of 0.0015 W/K, both verified by analysis. Test verification of the mini-ROD-TSW remains to be carried out. The paper will provide design/performance details of each device.

Farmer, Jeffery T.↗

One-shot learning for solution operators of partial differential equations

Learning and solving governing equations of a physical system, represented by partial differential equations (PDEs), from data is a central challenge in many areas of science and engineering. Traditional numerical methods can be computationally expensive for complex systems and require complete governing equations. Existing data-driven machine learning methods require large datasets to learn a surrogate solution operator, which could be impractical. Here, we propose a solution operator learning method that requires only one PDE solution, i.e., one-shot learning, along with suitable initial and boundary conditions. Leveraging the locality of derivatives, we define a local solution operator in small local domains, train it using a neural network, and use it to predict solutions of new input functions via mesh-based fixed-point iteration or meshfree neural-network based approaches. We test our method on various PDEs, complex geometries, and a practical spatial infection spread application, demonstrating its effectiveness and generalization capabilities.

97 MATHEMATICS AND COMPUTING↗

Analysis into Asymptotic Convergence to Full Nonlinear Solutions and Exploration of the Implication of Numerical Operator Mutation of Differential Systems

A robust, sufficiently accurate and practical hydrodynamic simulation toolset is required as a key component of the modeling and simulation of air-gap electrostatic discharge events. This work was performed to complement these ongoing efforts. In particular, hydrodynamic simulations must be vetted to ensure they are robust and sufficiently accurate over relevant characteristic scales. Verification models were generated in order to cultivate the technical knowledge and expertise needed to properly create, implement and execute numerical simulations. Furthermore, this effort was utilized extensively to educate students on the mathematical and numerical principles underlying hydrodynamic simulations. This education opportunity, provided in a holistic and rigorous manner, has greatly benefited developing scientists and engineers with the necessary understandings and toolsets required to excel at accomplishing the task at hand, and, more generally, it has enabled them to generate key programmatic deliverables. This report articulates several subtilties; specifically, how perturbations, nonlinear behavior, and dissipative mechanisms influence numerical stability, how to properly structure mathematical and numerical solutions, and how to properly generate error estimation/assignment. A more rigorous discussion of the consequences of such topics can be found in the body of this report in Chapters 2 and 3 with qualitative findings discussed in Chapter 4.

97 MATHEMATICS AND COMPUTING↗

The reduction of aileron operating force by differential linkage

It is shown that the control force of ordinary ailerons may be reduced to zero over a range of deflections and at a given flight condition by the use of an appropriate differential movement. Approximations to the ideal motion obtainable with a simple linkage are discussed and a chart that enables the selection of an appropriate crank arrangement is presented. Various aspects of the practical application of the system are discussed and it is concluded that a small fixed tab, deflected to trim both ailerons upward, would be advantageous.

Jones, R. T.↗

The Reduction of Aileron Operating Force by Differential Linkage

It is shown that the control force of ordinary ailerons may be reduced to zero over a range of deflections and at a given flight condition by the use of an appropriate differential movement. Approximations to the ideal motion obtainable with a simple linkage are discussed and a chart that enables the selection of an appropriate crank arrangement is presented. Various aspects of the practical application of the system are discussed and it is concluded that a small fixed tab, deflected to trim both ailerons upward, would be advantageous.

Jones, Robert T↗

Operations of the ATS-6 ion engine

The ion engine experiments on ATS 6 were operated in daylight and eclipse. The effect on particle fluxes to the spacecraft was monitored with the UCSD Auroral Particles Experiment. These data also provide information on the potential of the spacecraft with respect to the ambient plasma and on the local electric fields caused by the charge distribution on the satellite. Daylight operations of the plasma bridge neutralizer and the cesium thruster in fall, 1974, served to hold the spacecraft between -3 and -8 volts with respect to the ambient plasma. Neutralizer operation reduced differential charging effects, while operation of the thruster usually reduced the effects below the detectors sensitivity. Eclipse operations of the neutralizer reduced kilovolt negative potentials to a few volts. Operation of the thruster prevented possible charging of the satellite during substorms, making it possible to study low energy particle spectra which are at times obscured by charging during substorms.

Olsen, R. C.↗

Deep transfer operator learning for partial differential equations under conditional shift

Transfer learning enables the transfer of knowledge gained while learning to perform one task (source) to a related but different task (target), hence addressing the expense of data acquisition and labelling, potential computational power limitations and dataset distribution mismatches. Here, we propose a new transfer learning framework for task-specific learning (functional regression in partial differential equations) under conditional shift based on the deep operator network (DeepONet). Task-specific operator learning is accomplished by fine-tuning task-specific layers of the target DeepONet using a hybrid loss function that allows for the matching of individual target samples while also preserving the global properties of the conditional distribution of the target data. Inspired by conditional embedding operator theory, we minimize the statistical distance between labelled target data and the surrogate prediction on unlabelled target data by embedding conditional distributions onto a reproducing kernel Hilbert space. We demonstrate the advantages of our approach for various transfer learning scenarios involving nonlinear partial differential equations under diverse conditions due to shifts in the geometric domain and model dynamics. Our transfer learning framework enables fast and efficient learning of heterogeneous tasks despite considerable differences between the source and target domains.

42 ENGINEERING↗

Cycloidal wave energy converter using fixed differential buoyancy to control operating torques

A floating mooring system for a single CycWEC applies counter forces and torques to keep a generator suitably stationary for power generation without requiring fixed attachments to the ocean floor or requiring a large frame interconnecting multiple CycWECs. The mooring system uses floats or floatation structure with differential ballasting to counter operating torque and drag plates to counter reactive forces. The floatation structures may be used to float the CycWEC for transport to a deployment location, where changing the overall ballasting of the floatation structures submerges the CycWEC to a desired depth and differential ballasting in the floatation structures counts expected operating torques.

Siegel, Stefan G.↗

Learning Only on Boundaries: A Physics-Informed Neural Operator for Solving Parametric Partial Differential Equations in Complex Geometries

Recently, deep learning surrogates and neural operators have shown promise in solving partial differential equations (PDEs). However, they often require a large amount of training data and are limited to bounded domains. In this work, we present a novel physics-informed neural operator method to solve parameterized boundary value problems without labeled data. By reformulating the PDEs into boundary integral equations (BIEs), we can train the operator network solely on the boundary of the domain. This approach reduces the number of required sample points from $O(N^d)$ to $O(N^{d-1}$), where $d$ is the domain’s dimension, leading to a significant acceleration of the training process. Additionally, our method can handle unbounded problems, which are unattainable for existing physics-informed neural networks (PINNs) and neural operators. Finally, our numerical experiments show the effectiveness of parameterized complex geometries and unbounded problems.

97 MATHEMATICS AND COMPUTING↗

Doppler and Reflectivity Measurements at Two Closely-Spaced Frequencies

Spaceborne and airborne radars are limited with a respect to the mass and size of the instrument and the power available to operate it. As a consequence, dual-wavelength radars that require separate antennas and power amplifiers are expensive and often impractical. However, if the frequency difference can be reduced so that a single antenna and the same radio-frequency subsystem can be used for both frequencies, dual- wavelength Doppler measurements can be made with a radar of about the same size and mass as its single-frequency counterpart. In the first part of the paper we present calculations of the reflectivity factor differences as functions of the center frequency from 10 to 35 GHz and for frequency differences between -10% and 10% of the center frequency. The results indicate that differential-frequency operation at Ka-band frequencies (26.5 - 40 GHz) provides relatively strong differential signals if the frequencies can be separated by at least 5%. Unlike lower frequency operation, the differential signals at Ka-band (both reflectivity and Doppler) are directly related to the median mass diameter. An important feature of the differential mean Doppler is that it depends only on the drop-size dependent part of the radial velocity. In principle, the mean and mean differential Doppler data from a nadir-looking platform can be used to infer vertical air motion and characteristics of the particle size distribution. To test the instrument concept, the ER-2 Doppler radar was modified for differential frequency operation. Measurements by the modified radar, operating at frequencies of 9.1 GHz and 10 GHz, were made using an 8 degree zenith-pointing offset parabolic antenna. Simultaneous data were taken with an optical rain gauge and an impact disdrometer. Measured and DSD-estimated values of the differential dBZ mean Doppler are presented.

Meneghini, Robert↗