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At least 523 records · Page 29

Semigroup approximation and robust stabilization of distributed parameter systems

Theoretical results that enable rigorous statements of convergence and exponential stability of Galerkin approximations of LQR controls for infinite dimensional, or distributed parameter, systems have proliferated over the past ten years. In addition, extensive progress has been made over the same time period in the derivation of robust control design strategies for finite dimensional systems. However, the study of the convergence of robust finite dimensional controllers to robust controllers for infinite dimensional systems remains an active area of research. We consider a class of soft-constrained differential games evolving in a Hilbert space. Under certain conditions, a saddle point control can be given in feedback form in terms of a solution to a Riccati equation. By considering a related LQR problem, we can show a convergence result for finite dimensional approximations of this differential game. This yields a computational algorithm for the feedback gain that can be derived from similar strategies employed in infinite dimensional LQR control design problems. The approach described in this paper also inherits the additional properties of stability robustness common to game theoretic methods in finite dimensional analysis. These theoretical convergence and stability results are verified in several numerical experiments.

Kurdila, A. J.↗

Ozone vertical distribution retrieval from ground-based high resolution infrared solar spectra

A practical procedure for the retrieval of ozone vertical profiles from ground-based high resolution Fourier transform infrared solar spectra has been developed. The analysis is based on a multilayer line-by-line forward model and a semi-empirical version of the optimal estimation inversion method of Rodgers. The 1002.6-1003.2 cm(exp -1) spectral interval has been selected for the analysis on the basis of synthetic spectrum calculations. This interval contains numerous ozone lines covering a range of intensities and providing retrieval sensitivity from ground level to about 35 km. Characterization of the method and an error analysis have been performed. For a spectral resolution of 0.05-0.01 cm(exp -1) and a signal-to-noise ratio greater than or equal to 100 the retrieval is stable with a vertical resolution of approximately 5 km attainable near the surface degrading to approximately 10 km in the stratosphere. Synthetic spectra studies show that the a priori profile and weak constraints selected for the retrievals introduce no significant biases for a wide range of ozone profiles.

Pougatchev, N. S.↗

An Inverse Interpolation Method Utilizing In-Flight Strain Measurements for Determining Loads and Structural Response of Aerospace Vehicles

An important and challenging technology aimed at the next generation of aerospace vehicles is that of structural health monitoring. The key problem is to determine accurately, reliably, and in real time the applied loads, stresses, and displacements experienced in flight, with such data establishing an information database for structural health monitoring. The present effort is aimed at developing a finite element-based methodology involving an inverse formulation that employs measured surface strains to recover the applied loads, stresses, and displacements in an aerospace vehicle in real time. The computational procedure uses a standard finite element model (i.e., "direct analysis") of a given airframe, with the subsequent application of the inverse interpolation approach. The inverse interpolation formulation is based on a parametric approximation of the loading and is further constructed through a least-squares minimization of calculated and measured strains. This procedure results in the governing system of linear algebraic equations, providing the unknown coefficients that accurately define the load approximation. Numerical simulations are carried out for problems involving various levels of structural approximation. These include plate-loading examples and an aircraft wing box. Accuracy and computational efficiency of the proposed method are discussed in detail. The experimental validation of the methodology by way of structural testing of an aircraft wing is also discussed.

Shkarayev, S.↗

A Comprehensive Analysis of Real-World Accelerometer Data Quality in a Global Smartphone-based Seismic Network

The proliferation of low-cost sensors in smartphones has facilitated numerous applications; however, large-scale deployments often encounter performance issues. Sensing heterogeneity, which refers to varying data quality due to factors such as device differences and user behaviors, presents a significant challenge. In this research, we perform an extensive analysis of 3-axis accelerometer data from the MyShake system, a global seismic network utilizing smartphones. We systematically evaluate the quality of approximately 22 million 3-axis acceleration waveforms from over 81 thousand smartphone devices worldwide, using metrics that represent sampling rate and noise level. We explore a broad range of factors influencing accelerometer data quality, including smartphone and accelerometer manufacturers, phone specifications (release year, RAM, battery), geolocation, and time. Our findings indicate that multiple factors affect data quality, with accelerometer model and smartphone specifications being the most critical. In addition, we examine the influence of data quality on earthquake parameter estimation and show that removing low-quality accelerometer data enhances the accuracy of earthquake magnitude estimation.

58 GEOSCIENCES↗

Numerical Simulations of High Enthalpy Pulse Facilities

Axisymmetric flows within shock tubes and expansion tubes are simulated including the effects of finite rate chemistry and both laminar and turbulent boundary layers. The simulations demonstrate the usefulness of computational fluid dynamics for characterizing the flows in high enthalpy pulse facilities. The modeling and numerical requirements necessary to simulate these flows accurately are also discussed. Although there is a large body of analysis which explains and quantifies the boundary layer growth between the shock and the interface in a shock tube, there is a need for more detailed solutions. Phenomena such as thermochemical nonequilibrium. or turbulent transition behind the shock are excluded in the assumptions of Mirels' analysis. Additionally there is inadequate capability to predict the influence of the boundary layer on the expanded gas behind the interface. Quantifying the gas in this region is particularly important in expansion tubes because it is the location of the test gas. Unsteady simulations of the viscous flow in shock tubes are computationally expensive because they must follow features such as a shock wave over the length of the facility and simultaneously resolve the small length scales within the boundary layer. As a result, efficient numerical algorithms are required. The numerical approach of the present work is to solve the axisymmetric gas dynamic equations using an finite-volume formulation where the inviscid fluxes are computed with a upwind TVD scheme. Multiple species equations are included in the formulation so that finite-rate chemistry can be modeled. The simulations cluster grid points at the shock and interface and translate this clustered grid with these features to minimize numerical errors. The solutions are advanced at a CFL number of less than one based on the inviscid gas dynamics. To avoid limitations on the time step due to the viscous terms, these terms are treated implicitly. This requires a block tri-diagonal matrix inversion along each line of cells normal to the wall. The cost of this inversion is more than offset by the larger allowable time step. The source terms representing the finite-rate chemical kinetics are also treated implicitly. An algebraic turbulence model for compressible flow is used. The flow in a low pressure shock tube is computed and the results are compared with Mirels'analysis. The driven gas is nitrogen at 70 Pa, and the incident shock speed is approximately 2.9 km/sec so that there is little dissociation. The simulations include a laminar boundary layer and are run until the limiting flow regime is achieved. At this limit, the shock and interface travel at the same velocity because the amount of driven gas between these two features remains the same: the mass flow across the shock is equal to the mass of gas being entrained at the interface by the boundary layer. Simulations with several grids are presented to establish the grid independence of the solution, Good agreement is achieved between Mirels' correlations and the computations. This is expected since the flow conditions are chosen to be consistent with the assumptions used in Mirels' analysis. This comparison adds credibility to the numerical approach and highlights some of the differences between the theory and the detailed simulations. In addition, simulations of the HYPULSE expansion tube are presented for two operating conditions and the computations are compared to experimental data. The operating gas for both cases is nitrogen. One test condition is at a total enthalpy of 15.2 MJ/Kg and a relatively low pressure of 2 kPa. This case is characterized by a laminar boundary layer and significant chemical nonequilibrium. in the acceleration gas. The second test condition is at a total enthalpy of 10.2 MJ/Kg and a pressure of 38 kPa and is characterized by a turbulent boundary layer. The simulations compare well with experiment and reveal that the nonuniformity in pressure observed during the test time is related to variations in the boundary layer displacement thickness.

Wilson, Gregory J.↗

Steady and unsteady incompressible free-wake analysis

The flows around highly sweptback wings and bodies of revolution at high angle of attack are described, and inviscid model approximations and mathematical formulation of the problem are given to steady and unsteady incompressible flows. A general presentation of the methods of solution is given, with emphasis on current computational techniques. Detailed descriptions of the nonlinear vortex-lattice and vortex-panel techniques are presented to show how the boundary conditions are enforced using iteration. Typical numerical results are compared with the available experimental data.

Kandil, O. A.↗

Discrete observability and numerical quadrature

The authors consider the problem of approximate observability of a one-dimensional diffusion equation on a finite spatial domain with spatial point measurements. The problem of the optimal selection of the measurement points is considered under three conditions: (1) no preassigned measurement nodes; (2) one preassigned node and; (3) two preassigned nodes. The main observation is that the optimal choice is related to three classical procedures in numerical analysis: (1) Gaussian quadrature; (2) Radau quadrature and; (3) Lobatto quadrature. It is shown that the existence of the Radau and Lobatto quadrature is closely related to classical root locus theory.

Martin, Clyde F.↗

The remarkable ability of turbulence model equations to describe transition

This paper demonstrates how well the k-omega turbulence model describes the nonlinear growth of flow instabilities from laminar flow into the turbulent flow regime. Viscous modifications are proposed for the k-omega model that yield close agreement with measurements and with Direct Numerical Simulation results for channel and pipe flow. These modifications permit prediction of subtle sublayer details such as maximum dissipation at the surface, k approximately y(exp 2) as y approaches 0, and the sharp peak value of k near the surface. With two transition specific closure coefficients, the model equations accurately predict transition for an incompressible flat-plate boundary layer. The analysis also shows why the k-epsilon model is so difficult to use for predicting transition.

Wilcox, David C.↗

Microscopic and Metallurgical Aspects of the Space Shuttle Columbia Accident Investigation and Reconstruction

The Space Shuttle Columbia was descending for a landing at the Kennedy Space Center (KSC) on February 1, 2003. Approximately 20 minutes prior to touchdown, the Columbia began disintegrating over the western United States; the majority of debris eventually impacted in eastern Texas and western Louisiana. A monumental effort eventually recovered approximately 84,000 pieces of debris, approximately 38% of the Orbiter's original dry weight. The debris was transported to KSC, where the items were catalogued and evaluated. Critical areas of interest, such as the left and right leading edge surfaces and the underside of the ship, were placed upon a grid to aid in the reconstruction. Items of interest included metallic structures, reinforced carbon-carbon composites, and ceramic heat insulation tiles. Many of the leading edge elements had re-solidified metallic deposits spattered on them. These deposits became known as slag and were one of the main focuses of the investigation. In order to help determine the sequence of events inside the left wing during the accident, the slag's composition, layering order, and directionality of deposition were studied. A myriad of analytical tests were performed in an attempt to ascertain the compositional and depositional characteristics of selected slag deposits, including the ordering of deposited layers within each individual slag deposit harvested. Initially, Scanning Electron Microscopy and Energy Dispersive X-Ray Spectroscopy (SEM/EDX) were performed to quickly characterize the overall composition of individual slag deposits: SEM utilizes a narrowlyfocused high-energy electron beam impinging upon a specimen. The incident beam excites and liberates lower energy secondary electrons, which are detected and analyzed, providing a visual representation of the sample's surface topography. EDX also relies on an incident electron beam, except an EDX unit measures X-ray energies generated by the impinging beam. Each element generates a unique X-ray signature; the EDX detector measures these discreet energies. EDX actually penetrates approximately 2 microns into the bulk of the sample. However, random examination of various portions of slag, coupled with the semiquantitative nature of the SEM/EDX analysis, did not yield convincingly pertinent data. Therefore, X-ray dot mapping was conducted, which provided more understandable data, both in terms of slag layering and composition. An X-ray dot map is generated by performing numerous EDX scans for individual elements, then compiling the scans in a visual representation. Eventually, specimens consisting of not only the slag, but of the adjacent RCC substrate as well were cross-sectioned. X-Ray dot mapping of the materialographicallymounted and -polished cross- sections provided a visual representation of both the layering sequence and compositional characteristics of the slag. Contemporaneously, Electron Spectroscopy for Chemical Analysis/X-Ray Photoelectron Spectroscopy (ESCA/XPS) and powdered X-Ray Diffraction (XRD) were performed to further characterize the deposits and to attempt to identify what, if any, compounds were present. The ESCA/XPS analysis allowed the analyst to "sputter" into the sample with an electron gun, aiding in the identification of the layering sequence. XPS uses photons, rather than electrons, which impinge upon the surface of the sample. XPS measures the electrons emitted from within the first 5 nm of the sample's surface. The XRD measures the scatter angles of incident X-rays; the angle and intensity of scatter depend upon the crystalline structure of the pulverized sample. XRD is considered a qualitative rather than quantitative technique. ESCA/XPS revealed that the final layer to deposit was predominantly carbonaceous. XRD was successful in identifying specific compounds, such as Al 2O3, Al and/or Al3 21SiO47, mullite (3(Al2)O3 -SiO2), and nickel-aluminides. Eventually, Electron MicroProbe Analysis (EMPA) was conducted on the marialographically-prepared cross- sections of selected slag deposits. Microprobe combines SEM and Wavelength Dispersive X-Ray Spectroscopy (WDS), and, like EDX, uses a narrowly-focused high-energy electron beam impinging upon a specimen to elicit, in the case of EPMA, characteristic X-rays with specific wavelengths. This quantitative, analytical tool proved the most useful in determining depositional layering and composition of the slag deposits. This information was utilized in verifying the location of the breach in the left leading edge of the wing of the Columbia.

McDaniels, Steven J.↗

Unsteady Analysis of Blade and Tip Heat Transfer as Influenced by the Upstream Momentum and Thermal Wakes

The effect of the upstream wake on the blade heat transfer has been numerically examined. The geometry and the flow conditions of the first stage turbine blade of GE s E3 engine with a tip clearance equal to 2 percent of the span was utilized. Based on numerical calculations of the vane, a set of wake boundary conditions were approximated, which were subsequently imposed upon the downstream blade. This set consisted of the momentum and thermal wakes as well as the variation in modeled turbulence quantities of turbulence intensity and the length scale. Using a one-blade periodic domain, the distributions of unsteady heat transfer rate on the turbine blade and its tip, as affected by the wake, were determined. Such heat transfer coefficient distribution was computed using the wall heat flux and the adiabatic wall temperature to desensitize the heat transfer coefficient to the wall temperature. For the determination of the wall heat flux and the adiabatic wall temperatures, two sets of computations were required. The results were used in a phase-locked manner to compute the unsteady or steady heat transfer coefficients. It has been found that the unsteady wake has some effect on the distribution of the time averaged heat transfer coefficient on the blade and that this distribution is different from the distribution that is obtainable from a steady computation. This difference was found to be as large as 20 percent of the average heat transfer on the blade surface. On the tip surface, this difference is comparatively smaller and can be as large as four percent of the average.

Ameri, Ali A.↗

An efficient numerical model for predicting residual stress and strain in parts manufactured by laser powder bed fusion

Abstract Computational modeling of additively manufactured structures plays an increasingly important role in product design and optimization. For laser powder bed fusion processes, the accurate modeling of stress and distortion requires large amount of computational cost due to very localized heat input and evolving complex geometries. The current study takes advantage of a graphics processing unit accelerated explicit finite element analysis code and approximated heat conduction analysis to predict the macroscopic thermo-mechanical behavior in laser selective melting. Adjacent layers and tracks were lumped to reduce the number of time steps and elements in the finite element model. The effects of track and layer grouping on prediction accuracy and solution efficiency are investigated to provide a guidance for a cost-effective simulation. Thin-wall builds from Inconel alloy 625 (IN625) powders were simulated by applying the developed modeling approach to get the detailed residual stress and distortion at a computational speed 50 times higher than conventional approach. Under repeated heating and cooling cycles, a high tensile stress was produced near surfaces of a build due to a larger shrinkage on surface than that in central area. It is also shown that horizontal stresses concentrate near the root and top layers of the IN625 build. The predicted residual elastic strain distribution was validated by the experimental measurement using x-ray synchrotron diffraction.

36 MATERIALS SCIENCE↗

An efficient full potential implicit method based on characteristics for analysis of supersonic flows

A nonlinear aerodynamic prediction technique based on the full potential equation in conservation form has been developed for the treatment of supersonic flows. The method uses the theory of characteristic signal propagation to accurately simulate the flow structure, which includes shock waves and mixed elliptic-hyperbolic crossflow. An implicit approximate factorization scheme is employed to solve the finite-differenced equation. The necessary body-fitted grid system in every marching plane is generated numerically, using an elliptic grid solver. Results are shown for conical and nonconical wing-body combinations and compared with experimental data and Euler calculations. The method demonstrates an enormous savings in execution time and memory requirements over Euler methods.

Shankar, V.↗

Two dimensional analysis of a high temperature gaseous radiation receiver

The characteristics of the Flowing Gas Radiation Receiver (FGRR), a device that absorbs solar radiation volumetrically in a gas to produce high temperatures for space propulsion and power applications, are analyzed using a two-dimensional axisymmetric numerical model of the flow and radiation fields within a diffusely reflecting channel. The results show that an FGRR system is capable of generating temperatures in excess of 3000 K with collection efficiencies of approximately 75 percent for a channel with a reflectivity of 0.9. For a collinear radiation source, outflow temperatures of 3193 and 3092 K were achieved for axial and radial flow inputs, respectively, with receiver efficiencies of 0.82 and 0.76.

Mcfall, K. A.↗

Navier-Stokes analysis of three-dimensional unsteady flows inside turbine stages

This study presents a numerical method for solving the 3D Navier-Stokes equations for unsteady, viscous flow through multiple turbomachinery blade rows. The method solves the fully 3D Navier-Stokes equations with an implicit scheme which is based on a control volume approach. A two-equation turbulence model with a low Reynolds number modification is employed. A third-order accurate upwinding scheme is used to approximate convection terms, while a second order accurate central difference scheme is used for the discretization of viscous terms. A second-order accurate scheme is employed for the temporal discretization. The numerical method is applied to study the unsteady flowfield of the High Pressure Fuel side Turbo-Pump (HPFTP) of the Space Shuttle Main Engine (SSME). The stage calculation is performed by coupling the stator and the rotor flowfields at each time step through an over-laid grid. Numerical results for the complete geometry with the vane trailing edge cutback are presented and compared with the available experimental data.

Hah, C.↗

Non-numeric computation for high eccentricity orbits

Geocentric orbits of large eccentricity (e = 0.9 to 0.95) are significantly perturbed in cislunar space by the sun and moon. The time-history of the height of perigee, subsequent to launch, is particularly critical. The determination of 'launch windows' is mostly concerned with preventing the height of perigee from falling below its low initial value before the mission lifetime has elapsed. Between the extremes of high accuracy digital integration of the equations of motion and of using an approximate, but very fast, stability criteria method, this paper is concerned with the developement of a method of intermediate complexity using non-numeric computation. The computer is used as the theory generator to generalize Lidov's theory using six osculating elements. Symbolic integration is completely automatized and the output is a set of condensed formulae well suited for repeated applications in launch window analysis. Examples of applications are given.

Sridharan, R.↗

An analysis of turbulent diffusion flame in axisymmetric jet

The kinetic theory of turbulent flow was employed to study the mixing limited combustion of hydrogen in axisymmetric jets. The integro-differential equations in two spatial and three velocity coordinates describing the combustion were reduced to a set of hyperbolic partial differential equations in the two spatial coordinates by a binodal approximation. The MacCormick's finite difference method was then employed for solution. The flame length was longer than that predicted by the flame-sheet analysis, and was found to be in general agreement with a recent experimental result. Increase of the turbulence energy and scale resulted in an enhancement of the combustion rate and, hence, in a shorter flame length. Details of the numerical method as well as of the physical findings are discussed.

Chung, P. M.↗

Instability and transition in rotating disk flow

The stability of three-dimensional rotating disk flow is investigated, including the effects of Coriolis forces and streamline curvature. The numerical results show that the critical Reynolds number for establishment of stationary vortex flow is 287. These vortices spiral outward at an angle of about 11.2 deg, and transition to turbulence occurs when their total amplification is about e to the 11th. New experimental results are also reported on the spatial growth rates of the stationary vortices. It is shown that the analysis gives growth rates that compare much better with the experimental results than do results obtained using the Orr-Sommerfeld equation. The experimental results tend to support the numerical prediction that the number of stationary vortices varies directly with the Reynolds number. The calculations also indicate the existence of weakly unstable propagating (type II) modes at low Reynolds numbers (Critical Reynolds Number being approximately equal to 49).

Malik, M. R.↗

Multigrid properties of upwind-biased data reconstructions

The multigrid properties of two data reconstruction methods used for achieving second-order spatial accuracy when solving the two-dimensional Euler equations are examined. The data reconstruction methods are used with an implicit upwind algorithm which uses linearized backward-Euler time-differencing. The solution of the resulting linear system is performed by an iterative procedure. In the present study only regular quadrilateral grids are considered, so a red-black Gauss-Seidel iteration is used. Although the Jacobian is approximated by first-order upwind extrapolation, two alternative data reconstruction techniques for the flux integral that yield higher-order spatial accuracy at steady state are examined. The first method, probably most popular for structured quadrilateral grids, is based on estimating the cell gradients using one-dimensional reconstruction along curvilinear coordinates. The second method is based on Green's theorem. Analysis and numerical results for the two dimensional Euler equations show that data reconstruction based on Green's theorem has superior multigrid properties as compared to the one-dimensional data reconstruction method.

Warren, Gary P.↗