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At least 397 records · Page 22

An investigation of the transient thermal analysis of spur gears

A finite element computer program is developed for evaluating the transient behavior of surface temperature in high performance spur gears. The time dimension is implemented using two and three point finite difference schemes. The different schemes are provided for the purpose of numerical stability and convergence studies. A detailed explanation of the gear cooling process leading to the establishment of a modified Blok model is also included. Other conventional models for approximating the heat transfer coefficients are available for comparison. Preliminary results are given showing snap shots of gear temperature contours at the initial stages of tooth engagement.

El-Bayoumy, L. E.↗

Selection of optimum frequencies for atmospheric electric path length measurement by satellite-borne microwave radiometers

Numerical experiments using regressions by leaps and bounds have been performed to determine the optimum frequencies for satellite-borne microwave radiometers to estimate atmospheric electrical path length over the sea. The frequency range 5-40 GHz was searched. The effect of surface wind speed, sea surface temperature, and clouds was considered in the optimum frequency selection. The analysis indicates that approximately 0.6-cm rms accuracy is possible for one-way path length measurement using a proper pair of frequencies. The best two-channel subset selected by the leaps and bounds techniques is (16.0, 21.0) GHz.

Pandey, P. C.↗

A nonlinear analysis of an equilibrium craze. I - Problem formulation and solution. II - Simulations of craze and crack growth

A numerical method is developed for the determinations of the equilibrium shape of a craze in an infinite elastic plane whose fibrils exhibit very general nonlinear force-displacement behavior. The problem formulation is based on the superposition of the relevant elasticity Green's function; the solution of the resulting nonlinear problem is obtained by using Picard's successive approximation scheme. The model is used to investigate the effect of nonlinear fibril behavior on the mechanics of craze and crack growth, and the results are compared with the Dugdale model.

Ungsuwarungsri, T.↗

Energetic Consistency and Coupling of the Mean and Covariance Dynamics

The dynamical state of the ocean and atmosphere is taken to be a large dimensional random vector in a range of large-scale computational applications, including data assimilation, ensemble prediction, sensitivity analysis, and predictability studies. In each of these applications, numerical evolution of the covariance matrix of the random state plays a central role, because this matrix is used to quantify uncertainty in the state of the dynamical system. Since atmospheric and ocean dynamics are nonlinear, there is no closed evolution equation for the covariance matrix, nor for the mean state. Therefore approximate evolution equations must be used. This article studies theoretical properties of the evolution equations for the mean state and covariance matrix that arise in the second-moment closure approximation (third- and higher-order moment discard). This approximation was introduced by EPSTEIN [1969] in an early effort to introduce a stochastic element into deterministic weather forecasting, and was studied further by FLEMING [1971a,b], EPSTEIN and PITCHER [1972], and PITCHER [1977], also in the context of atmospheric predictability. It has since fallen into disuse, with a simpler one being used in current large-scale applications. The theoretical results of this article make a case that this approximation should be reconsidered for use in large-scale applications, however, because the second moment closure equations possess a property of energetic consistency that the approximate equations now in common use do not possess. A number of properties of solutions of the second-moment closure equations that result from this energetic consistency will be established.

Cohn, Stephen E.↗

Engineering analysis of drooped leading-edge wings near stall

Numerical results obtained with a three-dimensional vortex panel computer program for the calculation of inviscid, incompressible (potential) flow over infinitely thin finite wings with camber are presented. The program, which is designed for wings with drooped leading edge discontinuities, is essentially a numerical representation of lifting surface theory, involving both spanwise and chordwise distributions of vorticity. The results also include two engineering approximations. First, the effect of the leading-edge discontinuities is modeled by assuming that the vortices emanating from the discontinuities aerodynamically divide the wing into three distinct sections of lower aspect ratio. Secondly, the effect of the separated flow at high angle of attack is modeled by applying rectangular vortex panels with a varying vortex strength over the portions of the wing with attached flow.

Anderson, J. D., Jr.↗

Experimental results and numerical modeling of solidification during aircraft high-g arcs

The question of how the Coriolis and gravity gradient forces during high-gravity maneuvers compare to that for common centrifuges is addressed. Microstructural examination of samples solidified during high-gravity arcs reveals no evidence of convection dampening. As a first approximation, the high-gravity arc is modeled as a centrifuge with a radius of 20,480 ft and angular speed of 0.318 rpm. Scaling analysis indicates that the Coriolis and gravity gradient expected on the aircraft high gravity arc are less than that for the centrifuges by a factor of 100. Detailed Navier-Stokes analysis of the fluid flow and thermal fields during solidification of aluminum and Cd-Te during KC-135 high gravity show that convective flows of about 1 mm/s are induced. The thermal field is only slightly modified by the convection. Coriolis and gravity gradient during solidification in KC-135 high-gravity arcs, even at accelerations that have been shown to produce significant convective flow dampening in the centrifuge systems, are found to have no significant influence on the melt thermal and flowfields.

Curreri, P. A.↗

Analysis of temperature distribution in liquid-cooled turbine blades

The temperature distribution in liquid-cooled turbine blades determines the amount of cooling required to reduce the blade temperature to permissible values at specified locations. This report presents analytical methods for computing temperature distributions in liquid-cooled turbine blades, or in simplified shapes used to approximate sections of the blade. The individual analyses are first presented in terms of their mathematical development. By means of numerical examples, comparisons are made between simplified and more complete solutions and the effects of several variables are examined. Nondimensional charts to simplify some temperature-distribution calculations are also given.

Livingood, John N B↗

On least squares approximations to indefinite problems of the mixed type

A least squares method is presented for computing approximate solutions of indefinite partial differential equations of the mixed type such as those that arise in connection with transonic flutter analysis. The method retains the advantages of finite difference schemes namely simplicity and sparsity of the resulting matrix system. However, it offers some great advantages over finite difference schemes. First, the method is insensitive to the value of the forcing frequency, i.e., the resulting matrix system is always symmetric and positive definite. As a result, iterative methods may be successfully employed to solve the matrix system, thus taking full advantage of the sparsity. Furthermore, the method is insensitive to the type of the partial differential equation, i.e., the computational algorithm is the same in elliptic and hyperbolic regions. In this work the method is formulated and numerical results for model problems are presented. Some theoretical aspects of least squares approximations are also discussed.

Fix, G. J.↗

The parallel diffusion of cosmic rays in a random magnetic field.

Within the quasi-linear approximation, the existence of the parallel diffusion coefficient for cosmic rays in a random magnetic field (homogeneous, isotropic), despite the slow decay of the interaction between particles and random field, is demonstrated. As an example, the results of a numerical calculation of the parallel diffusion coefficient for a Gaussian random-field correlation function are presented. The numerical results are corroborated by asymptotic analysis and are compared to those of other theories.

Klimas, A.↗

The optimization of convergence for Chebyshev polynomial methods in an unbounded domain

Grosch and Orszag (1977) have performed a numerical analysis of the problem of solving differential equations in a semiinfinite or infinite domain using Chebyshev polynomials. The principal limitation of the conducted study was that it was entirely empirical. Various differential equations were solved in different ways and the numbers were compared. The present investigation has the objective to extend the studies conducted by Grosch and Orszag by deriving asymptotic approximations to the Chebyshev coefficients of simple model functions. This approach makes it possible to conduct more systematic comparisons of different methods, extend the range of comparisons, and, perhaps most important, give simple analytic formulas for choosing the optimum domain size or mapping parameter L for various situations.

Boyd, J. P.↗

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.↗

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.↗