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An analytic method was devised to predict the temperature distribution in typical antenna structural back-up members. The results are in agreement with those obtained by a numerical shooting method. The analytic method shows potential in simplifying the thermal analysis process for complex back-up antenna structures.
An analytical method has been developed to treat unsteady helicopter rotor, wake, and fuselage interaction aerodynamics. An existing lifting line/prescribed wake rotor analysis and a source panel fuselage analysis were modified to predict vibratory fuselage airloads. The analyses were coupled through the induced flow velocities of the rotor and wake on the fuselage and the fuselage on the rotor. A prescribed displacement technique was used to distort the rotor wake about the fuselage. Sensitivity studies were performed to determine the influence of wake and body geometry on the computed airloads. Predicted and measured mean and unsteady pressures on a cylindrical body in the wake of a two-bladed rotor were compared. Initial results show good qualitative agreement.
An analytical method for determining the minimum weight design of an axisymmetric supersonic inlet has been developed. The goal of this method development project was to improve the ability to predict the weight of high-speed inlets in conceptual and preliminary design. The initial model was developed using information that was available from inlet conceptual design tools (e.g., the inlet internal and external geometries and pressure distributions). Stiffened shell construction was assumed. Mass properties were computed by analyzing a parametric cubic curve representation of the inlet geometry. Design loads and stresses were developed at analysis stations along the length of the inlet. The equivalent minimum structural thicknesses for both shell and frame structures required to support the maximum loads produced by various load conditions were then determined. Preliminary results indicated that inlet hammershock pressures produced the critical design load condition for a significant portion of the inlet. By improving the accuracy of inlet weight predictions, the method will improve the fidelity of propulsion and vehicle design studies and increase the accuracy of weight versus cost studies.
Analytical studies of laminar separations using Crocco-Lees mixing parameter method
Global sensitivity analysis (GSA) of distribution systems with respect to stochastic PV and load variations plays an important role in designing optimal voltage control schemes. This paper proposes a data-driven framework for GSA of distribution systems. In particular, two representative surrogate modeling-based approaches are developed, including the traditional Gaussian process-based and the analysis of variance (ANOVA) kernel ones. The key idea is to develop a surrogate model that captures the hidden global relationship between voltage and real and reactive power injections from the historical data. With the surrogate model, the Sobol indices can be conveniently calculated through either the sampling-based method or the analytical method to assess the global sensitivity of voltage to variations of PV and load power injections. The sampling-based method approximates the Sobol indices using Monte Carlo simulations while the analytical method calculates them by resorting to the ANOVA expansion framework. Comparison results with other model-based GSA methods on the unbalanced three-phase IEEE 37-bus and 123-bus distribution systems show that the proposed framework can achieve much higher computational efficiency with negligible loss of accuracy. The results on a real 240-node distribution system using actual smart meter data further validate the feasibility and scalability of the proposed framework.
Developments in design sensitivity analysis (DSA) method have been made using two fundamentally different approaches as shown. In the first approach, a discretized structural finite element model is used to carry out DSA. There are three different methods in the discrete DSA approach: finite difference, semi-analytical, and analytical methods. The finite difference method is a popular one due to its simplicity, but a serious shortcoming of the method is the uncertainty in the choice of a perturbation step size of design variables. In the semi-analytical method, the derivatives of stiffness matrix is computed by finite differences, whereas in the analytical method, the derivatives are obtained analytically. For the shape design variable, computation of analytical derivative of stiffness matrix is quite costly. Because of this, the semi-analytical method is a popular choice in discrete shape DSA approach. However, recently, Barthelemy and Haftka presented that the semi-analytical method can have serious accuracy problems for shape design variables in structures modeled by beam, plate, truss, frame, and solid elements. They found that accuracy problems occur even for a simple cantilever beam. In the second approach, a continuum model of the structure is used to carry out DSA.
Abstract We develop a new method for analytical inversion of binned exoplanet transit spectra and for retrieval of planet parameters. The method has a geometrical interpretation and treats each observed spectrum as a single vector r → in the multidimensional spectral space of observed bin values. We decompose the observed r → into two orthogonal components: a wavelength-independent component r → ∥ corresponding to the spectral mean across all observed bins, and a transverse component r → ⊥ that is wavelength dependent and contains the relevant information about the atmospheric chemistry. The method allows us to extract, without any prior assumptions or additional information, the relative mass (or volume) mixing ratios of the absorbers in the atmosphere, the scale height to stellar radius ratio, H / R S , and the atmospheric temperature. The method is illustrated and validated with several examples of increasing complexity.
The Savannah River National Laboratory Nuclear Measurements Group was tasked by the Mark 18A Program team with developing three analytical characterization methods. These methods will support process and waste characterization of the Mark 18A program material. While methods already existed for most analytes of interest to the Mark 18A program team, the Nuclear Measurements Group developed and refined methods to quantify the Cf isotopes, 107 Pd, and 121m Sn. The results of that effort are presented in this work. Methods were successfully developed to characterize the Mark 18A samples for the needed isotopes and the NMG is ready to receive Mark 18A program samples.
Analytical methods were developed and/or adopted for calculating helicopter component noise, and these methods were incorporated into a unified total vehicle noise calculation model. Analytical methods were also developed for calculating the effects of noise reduction methodology on helicopter design, performance, and cost. These methods were used to calculate changes in noise, design, performance, and cost due to the incorporation of engine and main rotor noise reduction methods. All noise reduction techniques were evaluated in the context of an established mission performance criterion which included consideration of hovering ceiling, forward flight range/speed/payload, and rotor stall margin. The results indicate that small, but meaningful, reductions in helicopter noise can be obtained by treating the turbine engine exhaust duct. Furthermore, these reductions do not result in excessive life cycle cost penalties. Currently available main rotor noise reduction methodology, however, is shown to be inadequate and excessively costly.
Analytical studies were conducted on multiple turbine blade systems using the lumped mass method. Each blade was idealized by a two mass-two spring model whose modal values were determined from the known frequencies corresponding to the first two bending modes and the frequency corresponding to the platform lockup condition. Two friction damping models were considered namely, the blade-to-blade and the blade-damper-blade. The equations of motion derived on the basis of these models were solved by a method of harmonic balance, assuming, in effect, that under cyclic excitation the blades will exhibit cyclic response at the same frequency. The solutions for 8 blade, 16 blade, and 4 blade systems were obtained using the computer program BLADE. The levels of damping produced by the two friction damping models were compared and evaluated. The optimal values of the friction force, for which the tip amplitude of the blades had a minimum value, were determined.
An analytic perturbation method is introduced for estimating the lightning ground flash fraction in a set of N lightning flashes observed by a satellite lightning mapper. The value of N is large, typically in the thousands, and the observations consist of the maximum optical group area produced by each flash. The method is tested using simulated observations that are based on Optical Transient Detector (OTD) and Lightning Imaging Sensor (LIS) data. National Lightning Detection NetworkTM (NLDN) data is used to determine the flash‐type (ground or cloud) of the satellite-observed flashes, and provides the ground flash fraction truth for the simulation runs. It is found that the mean ground flash fraction retrieval errors are below 0.04 across the full range 0‐1 under certain simulation conditions. In general, it is demonstrated that the retrieval errors depend on many factors (i.e., the number, N, of satellite observations, the magnitude of random and systematic measurement errors, and the number of samples used to form certain climate distributions employed in the model).
This work presents probabilistic intent models for two typical vehicles in ETM operational environment. Several methods, including analytical methods for approximated solutions and a numerical method for exact solution, are presented and applied to compute the intent conflict probability for ETM operations. A comparison of these methods will be conducted in the final paper. Furthermore, simulations will be performed to verify the probabilistic intent model and verify the results of intent conflict probability from different methods.
The National Aeronautics and Space Administration (NASA) White Sands Test Facility (WSTF) was established in 1963 primarily to provide rocket engine testing services for several NASA programs. The groundwater underlying the site has been contaminated as a result of historical operations. Groundwater contaminants include several volatile organic compounds (VOCs) and two semi-volatile compounds: N-nitrosodimethylamine (NDMA) and N-nitrodimethylamine (DMN). This paper discusses some of the technical, analytical, regulatory, and health risk issues associated with the contaminant plume. The plume has moved approximately 2.5 miles downgradient of the facility industrial boundary, with evidence of continued migration. As a result, NASA has proposed a pump and treat system using air strippers and ultraviolet (UV) oxidation to stabilize future movement of the contaminant plume. The system has been designed to treat 1,076 gallons (4,073 liters) per minute, with provisions for future expansion. The UV oxidation process was selected to treat NDMA-contaminated groundwater based on successes at other NDMA-contaminated sites. Bench- and pilot-scale testing of WSTF groundwater confirmed the ability of UV oxidation to destroy NDMA and generated sufficient data to design the proposed full-scale treatment system. NDMA is acutely toxic and is a probable human carcinogen. EPA-recommended health risk criteria for the residential consumption of NDMA/DMN-contaminated groundwater was used to determine that a 1.0 x 10(exp -6) excess cancer risk corresponds to 1.7 parts per trillion (ppt). EPA analytical methods are unable to detect NDMA and DMN in the low ppt range. EPA's current Appendix IX analytical method used to screen for NDMA, Method 8270, can detect NDMA only at levels that are orders of magnitude greater than the recommended health risk level. Additionally, EPA Method 607, the most sensitive EPA approved method, has a detection limit of 150 ppt. This corresponds to an excess cancer risk of 9.0 x 10(exp -5), which exceeds the State of New Mexico's water quality standard of a cancer risk less than 1 x 10(exp -5). The treatment system has been engineered to treat contaminated groundwater to levels significantly below the New Mexico standard. However, the inability of EPA-approved analytical methods to detect NDMA and DMN at low ppt levels, and to provide verification of compliance with the 1 x 10(exp -5) cancer risk, introduces a notable risk to the long-term operation of the system. WSTF has been working with Southwest Research Institute to develop a non-EPA analytical method that can achieve a reporting limit of 1 ppt, which corresponds to an excess cancer risk of 7.6 x 10(exp -7). WSTF is currently developing a proposal to obtain approval from the New Mexico Environment Department (NMED) of this non-EPA method.
A finite analytic (FA) numerical solution is developed for unsteady two-dimensional Navier-Stokes equations. The FA method utilizes the analytic solution in a small local element to formulate the algebraic representation of partial differential equations. The combination of linear and exponential functions that satisfy the governing equation is adopted as the boundary function, thereby improving the accuracy of the finite analytic solution. Two flows, one a starting cavity flow and the other a vortex shedding flow behind a rectangular block, are solved by the FA method. The starting square cavity flow is solved for Reynolds number of 400, 1000, and 2000 to show the accuracy and stability of the FA solution. The FA solution for flow over a rectangular block (H x H/4) predicts the Strouhal number for Reynolds numbers of 100 and 500 to be 0.156 and 0.125. Details of the flow patterns are given. In addition to streamlines and vorticity distribution, rest-streamlines are given to illustrate the vortex motion downstream of the block.
Building structures and spacecraft in orbit will require technologies for positioning, docking/berthing, and joining orbital structures. A fundamental problem underlying the operation of docking and berthing is that of controlling the contact dynamics of mechanical structures actuated by active mechanisms such as robotic devices. Control systems must be designed to control these active mechanisms so that both the free space motions and contact motions are stable and satisfy specifications on position accuracy and bounds on contact forces. For the large orbital structures of the future, the problem of interactive dynamics and control is fundamentally different in several ways than it was for spacecraft docking in the past. First, future space structures must be treated as flexible structures - the operations of docking, berthing, and assembly will need to respect the vibrations of the structures. Second, the assembly of these structures will require multiple-point contact, rather than the essentially single-point positioning of conventional spacecraft docking. Third, some assembly operations require the subassemblies to be brought and held in contact so that successful joining can be accomplished. A preliminary study of contact stability and compliance control design has resulted in the development of an analytical method and a design method to analyze stability. The analytical method analyzes the problem of stability when an actively-controlled structure contacts a passive structure. This method makes it possible to accurately estimate the stiffness of the passive structures with which the contact motion will become unstable. The analytic results suggest that passivity is neither achievable in practice, nor necessary as a design concept. A contact control system need only be passive up to a certain frequency; beyond that frequency the system can be stabilized with sufficiently small gains. With this concept the Center developed a design methodology for achieving desired compliant contact motions. This design method is based on H-infinity norm optimization, which makes it possible to consider both driving point mechanical impedance and systems robustness to modeling uncertainty. A laboratory facility was set up to verify experimentally the analytical and design theory.
Analytical and numerical methods of calculation of the energy and three dimensional EPS characteristics are reported. The angular and lateral functions of electrons in EPS have been obtained by the Landau and small angle approximations A and B and compared with earlier data. A numerical method of solution of cascade equations for the EPS distribution function moments has been constructed. Considering the equilibrium rms angle as an example, errors appearing when approximating the elementary process cross sections by their asymptotic expressions are analyzed.
The JPL Control/Structure Interaction Program is developing new analytical methods for designing micro-precision spacecraft with controlled structures. One of these, the Conceptual Design Tool, will illustrate innovative new approaches to the integration of multi-disciplinary analysis and design methods. The tool will be used to demonstrate homogeneity of presentation, uniform data representation across analytical methods, and integrated systems modeling. The tool differs from current 'integrated systems' that support design teams most notably in its support for the new CSI multi-disciplinary engineer. The design tool will utilize a three dimensional solid model of the spacecraft under design as the central data organization metaphor. Various analytical methods, such as finite element structural analysis, control system analysis, and mechanical configuration layout, will store and retrieve data from a hierarchical, object oriented data structure that supports assemblies of components with associated data and algorithms. In addition to managing numerical model data, the tool will assist the designer in organizing, stating, and tracking system requirements.
An analytical method is presented for determining the oxygen consumption rate of the intact heart working (as opposed to empty but beating) human left ventricle. Use is made of experimental recordings obtained for the chamber pressure and the associated dimensions of the LV. LV dimensions are determined by cineangiocardiography, and the chamber pressure is obtained by means of fluid-filled catheters during retrograde or transeptal catheterization. An analytical method incorporating these data is then employed for the evaluation of the LV coronary oxygen consumption in five subjects. Oxygen consumption for these subjects was also obtained by the conventional clinical method in order to evaluate the reliability of the proposed method.