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A small perturbation analysis, in the long wavelength regime, is used to obtain the downstream boundary condition for the pressure for the flow over a flat plate. The methodology is extendable to other geometries. Numerical results for high Reynolds number laminar flows show great improvement in convergence rate to steady state as well as the quality of the results.
The fundamental principles of the global positioning system (GPS) are reviewed, with consideration given to geological and geophysical applications and related accuracy requirements. Recent improvements are emphasized which relate to areas such as equipment cost, limitations in the GPS satellite constellation, data analysis, uncertainties in satellite orbits and propagation delays, and problems in resolving carrier phase cycle ambiguities. Earthquake processes and near-fault crustal deformation monitoring have been facilitated by advances in GPS data acquisition and analysis. Horizontal positioning capability has been improved by new satellite constellation, better models, and global tracking networks. New classes of tectonic problems may now be studied through GPS, such as kinematic descriptions of crustal deformation and the measurement of relative plate motion at convergent boundaries. Continued improvements in the GPS are foreseen.
The implementation of the finite element method on unstructured triangular grids is described and the development of centered finite element schemes for the solution of the compressible Euler equation on general triangular and tetrahedral grids is discussed. Explicit and implicit Lax-Wendroff type methods and a method based upon the use of explicit multistep timestepping are considered. In the latter case, the convergence behavior of the method is accelerated by the incorporation of a fully unstructured multigrid procedure. The advancing front method for generating unstructured grids of triangles and tetrahedra is described and the application of adaptive mesh techniques to both steady and transient flow analysis is illustrated.
Stochastic Marked Graphs are a concurrent decision free formalism provided with a powerful synchronization mechanism generalizing conventional Fork Join Queueing Networks. In some particular cases the analysis of the throughput can be done analytically. Otherwise the analysis suffers from the classical state explosion problem. Embedded in the divide and conquer paradigm, approximation techniques are introduced for the analysis of stochastic marked graphs and Macroplace/Macrotransition-nets (MPMT-nets), a new subclass introduced herein. MPMT-nets are a subclass of Petri nets that allow limited choice, concurrency and sharing of resources. The modeling power of MPMT is much larger than that of marked graphs, e.g., MPMT-nets can model manufacturing flow lines with unreliable machines and dataflow graphs where choice and synchronization occur. The basic idea leads to the notion of a cut to split the original net system into two subnets. The cuts lead to two aggregated net systems where one of the subnets is reduced to a single transition. A further reduction leads to a basic skeleton. The generalization of the idea leads to multiple cuts, where single cuts can be applied recursively leading to a hierarchical decomposition. Based on the decomposition, a response time approximation technique for the performance analysis is introduced. Also, delay equivalence, which has previously been introduced in the context of marked graphs by Woodside et al., Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's is slower, but the accuracy is generally better. Delay equivalence often fails to converge, while flow equivalent aggregation can lead to potentially bad results if a strong dependence of the mean completion time on the interarrival process exists.
Experimental results have recently demonstrated that an adaptive open loop control strategy can be highly effective in the suppression of unbalance induced vibration on rotors supported in active magnetic bearings. This algorithm, however, relies upon a predetermined gain matrix. Typically, this matrix is determined by an optimal control formulation resulting in the choice of the pseudo-inverse of the nominal influence coefficient matrix as the gain matrix. This solution may result in problems with stability and performance robustness since the estimated influence coefficient matrix is not equal to the actual influence coefficient matrix. Recently, analysis tools have been developed to examine the robustness of this control algorithm with respect to structured uncertainty. Herein, these tools are extended to produce a design procedure for determining the adaptive law's gain matrix. The resulting control algorithm has a guaranteed convergence rate and steady state performance in spite of the uncertainty in the rotor system. Several examples are presented which demonstrate the effectiveness of this approach and its advantages over the standard optimal control formulation.
The intraseasonal variation (ISV) in the 30-60 day band, also known as Madden-Julian oscillation (MJO), has been studied for decades. Madden and Julian showed that the oscillation originated from the western Indian Ocean, propagated eastward, got enhanced over the maritime continent and weakened after passing over the dateline. Composite studies showed evidences of a signal in upper and lower level zonal wind propagating around the globe during an oscillation. Theoretical studies pointed out that the interaction with the warm ocean surface and the coupling with the convective and radiative processes in the atmosphere could manifest the oscillation, which propagates eastward via mutual feedbacks between the wave motions and the cumulus heating. Over tropical South America, no independent 30-60 day oscillation has been reported so far, despite that Amazon is the most distinct tropical convection center over the western hemisphere and the fluxes from its surface of tropical rainforests are close to that from the warm tropical ocean. Liebmann et al. showed a distinct spectral peak of 40-50 day oscillation in outgoing longwave radiation (OLR) over tropical South America and considered that was manifested by the MJO propagation. Nogues-Paegle et al. (2000) focused on a dipole pattern of the OLR anomaly with centers of action over the South Atlantic Convergence Zone (SACZ) and the subtropical plain. They used the regional 10-90 day filtered data and demonstrated this pattern could be represented by the fifth mode of the rotated empirical orthogonal function. Its principal component was further analyzed using the singular spectrum analysis. Their result showed two oscillatory modes with periods of 36-40 days and 22-28 days, of which the former was related to the MJO influence and the latter linked to the remote forcing over southwest of Australia, which produced a wave train propagating southeastward, rounding the southern tip of South America and returning back toward the northeast. The 22-28 day mode has distinct impact on SACZ, responsible for the regional seesaw pattern of alternating dry and wet conditions. In this study we will focus on the 30-60-day spectral band and investigate whether the independent oscillation source over tropical South America is existed. First, we will show the seasonal dependence of the tropical South American ISV in Section 3. Then, the leading principal modes of 30-60 day bandpass filtered 850-hPa velocity potential (VP850) will be computed to distinguish the stationary ISV over tropical South America (SISA) from the propagating MJO in the austral summertime in Section 4. The importance of SISA in representing the regional ISV over South America will be discussed. In Section 5, we will demonstrate the mass oscillation regime of SISA, which is well separated from that of MJO by the Andes, and the convective coupling with rainfall. The dynamical response of SISA and the impact on the South American summer monsoon (SASM) will be presented. Finally, we will give the concluding remarks.
The framework of Representative Key Risks (RKRs) has been adopted by the Intergovernmental Panel on Climate Change Working Group II (WGII) to categorize, assess and communicate a wide range of regional and sectoral key risks from climate change. These are risks expected to become severe due to the potentially detrimental convergence of changing climate conditions with the exposure and vulnerability of human and natural systems. Other papers in this special issue treat each of eight RKRs holistically by assessing their current status and future evolution as a result of this convergence. However, in these papers, such assessment cannot always be organized according to a systematic gradation of climatic changes. Often the big-picture evolution of risk has to be extrapolated from either qualitative effects of “low”, “medium” and “high” warming, or limited/focused analysis of the consequences of particular mitigation choices (e.g., benefits of limiting warming to 1.5 or 2C), together with consideration of the socio-economic context and possible adaptation choices. In this study we offer a representation – as systematic as possible given current literature and assessments – of the future evolution of the hazard components of RKRs. We identify the relevant hazards for each RKR, based upon the WGII authors’ assessment, and we report on their current state and expected future changes in magnitude, intensity and/or frequency, linking these changes to Global Warming Levels (GWLs) to the extent possible. We draw on the assessment of changes in climatic impact-drivers relevant to RKRs described in the 6th Assessment Report by Working Group I supplemented when needed by more recent literature. For some of these quantities - like regional trends in oceanic and atmospheric temperature and precipitation, some heat and precipitation extremes, permafrost thaw and Northern Hemisphere snow cover - a strong and quantitative relationship with increasing GWLs has been identified. For others - like frequency and intensity of tropical cyclones and extra-tropical storms, and fire weather - that link can only be described qualitatively. For some processes - like the behavior of ice sheets, or changes in circulation dynamics - large uncertainties about the effects of different GWLs remain, and for a few others - like ocean pH and air pollution - the composition of the scenario of anthropogenic emissions is most relevant, rather than the warming reached. In almost all cases, however, the basic message remains that every small increment in CO2 concentration in the atmosphere and associated warming will bring changes in climate phenomena that will contribute to increasing risk of impacts on human and natural systems, in the absence of compensating changes in these systems’ exposure and vulnerability, and in the absence of effective adaptation. Our picture of the evolution of RKR-relevant climatic impact-drivers complements and enriches the treatment of RKRs in the other papers in at least two ways: by filling in their often only cursory or limited representation of the physical climate aspects driving impacts, and by providing a fuller representation of their future potential evolution, an important component – if never the only one – of the future evolution of risk severity.
It is proposed that the study of Rusak et al. (1985), which reports numerical modeling sensitivities on longitudinal force/moment properties for a vortex-lattice method incorporating free vortex filaments to represent the leading-edge vortex separation, employs a formula that is strongly affected by the particular points of analysis chosen. This results in a narrowly applicable curve fit, where numerical sensitivities of the theory are inappropriately traded off against physical effects that are not modeled in that theory. Attention is also given to questionable drag estimate computations.
New algorithms were derived for computing terrain corrections, all components of the attraction of the topography at the topographic surface and the gradients of these attractions. These algoriithms utilize fast Fourier transforms, but, in contrast to methods currently in use, all divergences of the integrals are removed during the analysis. Sequential methods employing a smooth intermediate reference surface were developed to avoid the very large transforms necessary when making computations at high resolution over a wide area. A new method for the numerical solution of Molodensky's problem was developed to mitigate the convergence difficulties that occur at short wavelengths with methods based on a Taylor series expansion. A trial field on a level surface is continued analytically to the topographic surface, and compared with that predicted from gravity observations. The difference is used to compute a correction to the trial field and the process iterated. Special techniques are employed to speed convergence and prevent oscillations. Three different spectral methods for fitting a point-mass set to a gravity field given on a regular grid at constant elevation are described. Two of the methods differ in the way that the spectrum of the point-mass set, which extends to infinite wave number, is matched to that of the gravity field which is band-limited. The third method is essentially a space-domain technique in which Fourier methods are used to solve a set of simultaneous equations.
A steady incompressible three-dimensional viscous flow analysis has been conducted for the Space Shuttle external tank/orbiter propellant feed line disconnect flapper valves with upstream elbows. The Navier-Stokes code, INS3D, is modified to handle interior obstacles and a simple turbulence model. The flow solver is tested for stability and convergence in the presence of interior flappers. An under-relaxation scheme has been incorporated to improve the solution stability. Important flow characteristics such as secondary flows, recirculation, vortex and wake regions, and separated flows are observed. Computed values for forces, moments, and pressure drop are in satisfactory agreement with water flow test data covering a maximum tube Reynolds number of 3.5 million. The predicted hydrodynamical stability of the flappers correlates well with the measurements.
Bi-Level Integrated System Synthesis (BLISS) is a method for optimization of an engineering system, e.g., an aerospace vehicle. BLISS consists of optimizations at the subsystem (module) and system levels to divide the overall large optimization task into sets of smaller ones that can be executed concurrently. In the initial version of BLISS that was introduced and documented in previous publications, analysis in the modules was kept at the early conceptual design level. This paper reports on the next step in the BLISS development in which the fidelity of the aerodynamic drag and structural stress and displacement analyses were upgraded while the method's satisfactory convergence rate was retained.
Bi-Level Integrated System Synthesis (BLISS) is a method for optimization of an engineering system, e.g., an aerospace vehicle. BLISS consists of optimizations at the subsystem (module) and system levels to divide the overall large optimization task into sets of smaller ones that can be executed concurrently. In the initial version of BLISS that was introduced and documented in previous publications, analysis in the modules was kept at the early conceptual design level. This paper reports on the next step in the BLISS development in which the fidelity of the aerodynamic drag and structural stress and displacement analyses were upgraded while the method's satisfactory convergence rate was retained.
Bi-Level Integrated System Synthesis (BLISS) is a method for optimization of an engineering system, e.g., an aerospace vehicle. BLISS consists of optimizations at the subsystem (module) and system levels to divide the overall large optimization task into sets of smaller ones that can be executed concurrently. In the initial version of BLISS that was introduced and documented in previous publications, analysis in the modules was kept at the early conceptual design level. This paper reports on the next step in the BLISS development in which the fidelity of the aerodynamic drag and structural stress and displacement analyses were upgraded while the method's satisfactory convergence rate was retained.
At the NASA Glenn Research Center, NASA Langley Research Center's Flight Optimization System (FLOPS) and the design optimization testbed COMETBOARDS with regression and neural-network-analysis approximators have been coupled to obtain a preliminary aircraft design methodology. For a subsonic aircraft, the optimal design, that is the airframe-engine combination, is obtained by the simulation. The aircraft is powered by two high-bypass-ratio engines with a nominal thrust of about 35,000 lbf. It is to carry 150 passengers at a cruise speed of Mach 0.8 over a range of 3000 n mi and to operate on a 6000-ft runway. The aircraft design utilized a neural network and a regression-approximations-based analysis tool, along with a multioptimizer cascade algorithm that uses sequential linear programming, sequential quadratic programming, the method of feasible directions, and then sequential quadratic programming again. Optimal aircraft weight versus the number of design iterations is shown. The central processing unit (CPU) time to solution is given. It is shown that the regression-method-based analyzer exhibited a smoother convergence pattern than the FLOPS code. The optimum weight obtained by the approximation technique and the FLOPS code differed by 1.3 percent. Prediction by the approximation technique exhibited no error for the aircraft wing area and turbine entry temperature, whereas it was within 2 percent for most other parameters. Cascade strategy was required by FLOPS as well as the approximators. The regression method had a tendency to hug the data points, whereas the neural network exhibited a propensity to follow a mean path. The performance of the neural network and regression methods was considered adequate. It was at about the same level for small, standard, and large models with redundancy ratios (defined as the number of input-output pairs to the number of unknown coefficients) of 14, 28, and 57, respectively. In an SGI octane workstation (Silicon Graphics, Inc., Mountainview, CA), the regression training required a fraction of a CPU second, whereas neural network training was between 1 and 9 min, as given. For a single analysis cycle, the 3-sec CPU time required by the FLOPS code was reduced to milliseconds by the approximators. For design calculations, the time with the FLOPS code was 34 min. It was reduced to 2 sec with the regression method and to 4 min by the neural network technique. The performance of the regression and neural network methods was found to be satisfactory for the analysis and design optimization of the subsonic aircraft.
Electric-motor powered aircraft possess the ability to operate with efficient energy delivery, but lack the operational range of internal combustion engine powered aircraft. This range limitation requires the use of high aspect ratio, thin-chord wings to minimize aerodynamic drag losses, which results in highly loaded composite spar structures. High aspect ratio wings are required to increase mission durations for a NASA-developed experimental multi-rotor electric powered aircraft denoted as the Scalable Convergent Electric Propulsion Technology and Operations Research (SCEPTOR) or “X-57”. This paper examines the structural performance of the composite main wing spars to validate spar strength using ply-based laminate finite element methods. Geometric scaling of a main spar test-section was initially proposed for proof-testing but sacrificed stability. Ply-based structures modeling with local structural features was implemented as a risk-reduction methodology. Ply-based modeling was selected to augment the conventional “building block” approach to reduce risk, and leverage a “performance-based” approval processes encouraged in Federal Aviation Administration (FAA) design guidance. Therefore, ply-based laminate modeling of the full-scale main spar and forward spar shear-web attachments were subsequently undertaken to determine load path complexity with predicted flight loads. Ply-based modeling included stress concentrations and interlaminate behavior at interface locations that can be obscured in traditional finite element sizing models. Analysis of the wing spar laminate ply-based models compared with bearing test coupon performance was used to reduce future wing assembly proof-testing burden and facilitate performance-based flight hardware safety for the X-57 experimental aircraft.
A computer program is presented which was developed for the combined compression and shear of stiffened variable thickness orthotropic composite panels on discrete springs: boundary conditions are general and include elastic boundary restraints. Buckling solutions are obtained by using a newly developed trigonometric finite difference procedure which improves the solution convergence rate over conventional finite difference methods. The classical general shear buckling results which exist only for simply supported panels over a limited range of orthotropic properties, were extended to the complete range of these properties for simply supported panels and, in addition, to the complete range of orthotropic properties for clamped panels. The program was also applied to parametric studies which examine the effect of filament orientation upon the buckling of graphite-epoxy panels. These studies included an examination of the filament orientations which yield maximum shear or compressive buckling strength for panels having all four edges simply supported or clamped over a wide range of aspect ratios. Panels with such orientations had higher buckling loads than comparable, equal weight, thin skinned aluminum panels. Also included among the parameter studies were examinations of combined axial compression and shear buckling and examinations of panels with rotational elastic edge restraints.
A power series expansion in the damping parameter, epsilon, of the limit cycle of the free van der Pol equation is constructed and analyzed. Coefficients in the expansion are computed in exact rational arithmetic using the symbolic manipulation system MACSYMA and using a FORTRAN program. The series is analyzed using Padeapproximants. The convergence of the series for the maximum amplitude of the limit cycle is limited by two pair of complex conjugate singularities in the complex epsilon-plane. A new expansion parameter is introduced which maps these singularities to infinity and leads to a new expansion for the amplitude which converges for all real values of epsilon. Amplitudes computed from this transformed series agree very well with reported numerical and asymptotic results. For the limit cycle itself, convergence of the series expansion is limited by three pair of complex conjugate branch point singularities. Two pair remain fixed throughout the cycle, and correspond to the singularities found in the maximum amplitude series, while the third pair moves in the epsilon-plane as a function of t from one of the fixed pairs to the other. The limit cycle series is transformed using a new expansion parameter, which leads to a new series that converges for larger values of epsilon.
This slide presentation reviews the use of OVERFLOW, a flow solver, to analyze the effect of separation for a launch abort vehicle (i.e., Orion capsule) if required. Included in the presentation are views of the geometry, and the Overset grids, listing of the assumptions, the general run strategy, inputs into the Overflow solver, the required computational resources, the results of the convergence study. Charts and graphics are presented to show the results.