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At least 775 records · Page 43

Comparison of On-Orbit Performance of Rate Sensing Gyroscopes

This work presents results from the study of a large volume of spacecraft flight data pertaining to gyroscope performance. We have examined long and short term trends of gyroscope biase of first, an exact solution for the time-dependence of the attitude part of the state error covariance, averaged over the three spacecraft axes, is given. This solution is more complete than the usual cubic polynomial for the variance in that it includes coupling among the three gyroscope axes and includes an important term arising from the initial correlations. Second, several continuous 24-hour spans of gyroscope data are examined to verify the short-term statistical model. This analysis demonstrates that in-flight data can be used to determine the strength of the white noise driving the random walk of the gyroscope bias. This may be useful for postlaunch improvement to the noise model and for diagnosing the health of the gyroscope. Third, the long-term trends in gyroscope biases show a nearly linear systematic variation over time scales of years. This has been found on three different missions. While the random walk model is adequate as a basis for onboard Kalman filters or for state estimation using relatively short time spans, these trends indicate that some applications could benefit by accounting for the secular changes in the biases. One example is a new gyroscope calibration method that is under development that allows for multi-epoch bias solutions.

Sedlak, Joseph↗

An Astronomical Test of CCD Photometric Precision

This article considers a posteriori error estimation of specified functionals for first-order systems of conservation laws discretized using the discontinuous Galerkin (DG) finite element method. Using duality techniques. we derive exact error representation formulas for both linear and nonlinear functionals given an associated bilinear or nonlinear variational form. Weighted residual approximations of the exact error representation formula are then proposed and numerically evaluated for Ringleb flow, an exact solution of the 2-D Euler equations.

Koch, David↗

A Posteriori Error Estimation for Discontinuous Galerkin Approximations of Hyperbolic Systems

This article considers a posteriori error estimation of specified functionals for first-order systems of conservation laws discretized using the discontinuous Galerkin (DG) finite element method. Using duality techniques, we derive exact error representation formulas for both linear and nonlinear functionals given an associated bilinear or nonlinear variational form. Weighted residual approximations of the exact error representation formula are then proposed and numerically evaluated for Ringleb flow, an exact solution of the 2-D Euler equations.

Larson, Mats G.↗

Age-of-Air, Tape Recorder, and Vertical Transport Schemes

A numerical-analytic investigation of the impacts of vertical transport schemes on the model simulated age-of-air and the so-called 'tape recorder' will be presented using an idealized 1-D column transport model as well as a more realistic 3-D dynamical model. By comparing to the 'exact' solutions of 'age-of-air' and the 'tape recorder' obtainable in the 1-D setting, useful insight is gained on the impacts of numerical diffusion and dispersion of numerical schemes used in global models. Advantages and disadvantages of Eulerian, semi-Lagrangian, and Lagrangian transport schemes will be discussed. Vertical resolution requirement for numerical schemes as well as observing systems for capturing the fine details of the 'tape recorder' or any upward propagating wave-like structures can potentially be derived from the 1-D analytic model.

Lin, S.-J.↗

Meshless Petrov-Galerkin Method Applied to Axisymmetric Problems

An axisymmetric Meshless Local Petrov-Galerkin (MLPG) algorithm is presented for the potential and elasticity problems. In this algorithm the trial and test functions are chosen from different spaces. By a judicious choice of these functions, the integrals involved in the weak form can be restricted to a local neighborhood. This makes the method truly meshless. The MLPG algorithm is used to study various potential and elasticity problems for which exact solutions are available. The sensitivity and effectiveness of the MLPG algorithm to various parameters such as the weight functions, basis functions and support domain radius, etc. was studied. The MLPG algorithm yielded accurate solutions for all weight functions, basis functions and support domain radii considered for all of the problems studied.

Raju, I. S.↗

Third Computational Aeroacoustics (CAA) Workshop on Benchmark Problems

The proceedings of the Third Computational Aeroacoustics (CAA) Workshop on Benchmark Problems cosponsored by the Ohio Aerospace Institute and the NASA Glenn Research Center are the subject of this report. Fan noise was the chosen theme for this workshop with representative problems encompassing four of the six benchmark problem categories. The other two categories were related to jet noise and cavity noise. For the first time in this series of workshops, the computational results for the cavity noise problem were compared to experimental data. All the other problems had exact solutions, which are included in this report. The Workshop included a panel discussion by representatives of industry. The participants gave their views on the status of applying computational aeroacoustics to solve practical industry related problems and what issues need to be addressed to make CAA a robust design tool.

Dahl, Milo D.↗

Integrated Thermal Response Modeling System For Hypersonic Entry Vehicles

We describe all extension of the Markov decision process model in which a continuous time dimension is included ill the state space. This allows for the representation and exact solution of a wide range of problems in which transitions or rewards vary over time. We examine problems based on route planning with public transportation and telescope observation scheduling.

Chen, Y.-K.↗

Rapid Distortion Theory for Compressible Homogeneous Turbulence Under Isotropic Mean Strain

The case of isotropic compressible turbulence subjected to rapid isotropic compression is studied using inviscid rapid distortion theory and direct numerical simulation. An exact solution to the rapid distortion problem is given, and results are compared to those of direct numerical simulation. Implications for modelling turbulent flows are discussed.

Blaisdell, G. A.↗

Numerical Simulation of Unsteady Aerodynamic Models

This report documents the results of the numerical simulations of unsteady aerodynamic models. The results focus on numerical accuracy and efficiency, and the robustness of the numerical methods. The aerodynamic models includes the classical Wagner and Kussner functions and the Leishman-Beddoes dynamic stall model. The simulations includes the numerical approximations of the Duhamel's integrals using both indicial (step) and impulse responses, the numerical integrations of the state-space models, and the exact solutions. The report also presents the conversion among different model representations.

Nguyen, Khanh Q.↗

Towards Resolving the Crab Sigma-Problem: A Linear Accelerator?

Using the exact solution of the axisymmetric pulsar magnetosphere derived in a previous publication and the conservation laws of the associated MHD flow, we show that the Lorentz factor of the outflowing plasma increases linearly with distance from the light cylinder. Therefore, the ratio of the Poynting to particle energy flux, generically referred to as sigma, decreases inversely proportional to distance, from a large value (typically approx. greater than 10(exp 4)) near the light cylinder to sigma approx. = 1 at a transition distance R(sub trans). Beyond this distance the inertial effects of the outflowing plasma become important and the magnetic field geometry must deviate from the almost monopolar form it attains between R(sub lc), and R(sub trans). We anticipate that this is achieved by collimation of the poloidal field lines toward the rotation axis, ensuring that the magnetic field pressure in the equatorial region will fall-off faster than 1/R(sup 2) (R being the cylindrical radius). This leads both to a value sigma = a(sub s) much less than 1 at the nebular reverse shock at distance R(sub s) (R(sub s) much greater than R(sub trans)) and to a component of the flow perpendicular to the equatorial component, as required by observation. The presence of the strong shock at R = R(sub s) allows for the efficient conversion of kinetic energy into radiation. We speculate that the Crab pulsar is unique in requiring sigma(sub s) approx. = 3 x 10(exp -3) because of its small translational velocity, which allowed for the shock distance R(sub s) to grow to values much greater than R(sub trans).

Contopoulos, Ioannis↗

A Highly Accurate Technique for the Treatment of Flow Equations at the Polar Axis in Cylindrical Coordinates using Series Expansions

Numerical methods for solving the flow equations in cylindrical or spherical coordinates should be able to capture the behavior of the exact solution near the regions where the particular form of the governing equations is singular. In this work we focus on the treatment of these numerical singularities for finite-differences methods by reinterpreting the regularity conditions developed in the context of pseudo-spectral methods. A generally applicable numerical method for treating the singularities present at the polar axis, when nonaxisymmetric flows are solved in cylindrical, coordinates using highly accurate finite differences schemes (e.g., Pade schemes) on non-staggered grids, is presented. Governing equations for the flow at the polar axis are derived using series expansions near r=0. The only information needed to calculate the coefficients in these equations are the values of the flow variables and their radial derivatives at the previous iteration (or time) level. These derivatives, which are multi-valued at the polar axis, are calculated without dropping the accuracy of the numerical method using a mapping of the flow domain from (0,R)*(0,2pi) to (-R,R)*(0,pi), where R is the radius of the computational domain. This allows the radial derivatives to be evaluated using high-order differencing schemes (e.g., compact schemes) at points located on the polar axis. The proposed technique is illustrated by results from simulations of laminar-forced jets and turbulent compressible jets using large eddy simulation (LES) methods. In term of the general robustness of the numerical method and smoothness of the solution close to the polar axis, the present results compare very favorably to similar calculations in which the equations are solved in Cartesian coordinates at the polar axis, or in which the singularity is removed by employing a staggered mesh in the radial direction without a mesh point at r=0, following the method proposed recently by Mohseni and Colonius (1). Extension of the method described here for incompressible flows or for any other set of equations that are solved on a non-staggered mesh in cylindrical or spherical coordinates with finite-differences schemes of various level of accuracy is immediate.

Constantinescu, George S.↗

Meshless Local Petrov-Galerkin Method for Bending Problems

Recent literature shows extensive research work on meshless or element-free methods as alternatives to the versatile Finite Element Method. One such meshless method is the Meshless Local Petrov-Galerkin (MLPG) method. In this report, the method is developed for bending of beams - C1 problems. A generalized moving least squares (GMLS) interpolation is used to construct the trial functions, and spline and power weight functions are used as the test functions. The method is applied to problems for which exact solutions are available to evaluate its effectiveness. The accuracy of the method is demonstrated for problems with load discontinuities and continuous beam problems. A Petrov-Galerkin implementation of the method is shown to greatly reduce computational time and effort and is thus preferable over the previously developed Galerkin approach. The MLPG method for beam problems yields very accurate deflections and slopes and continuous moment and shear forces without the need for elaborate post-processing techniques.

Phillips, Dawn R.↗

Vortex Reconnection or Breakdown Subsequent to Perpendicular Collision With A Solid Body

This paper analytically examines the unsteady fluid dynamics of a vortex filament subsequent to a normal collision of the vortex with a solid body. In particular, the breakdown or reconnection phenomena, post-collision, for a vortex filament is studied. The paper does not investigate the collision dynamics process itself. The derived exact solution is based upon the laminar viscous form of the Helmholtz equations.

Young, Larry A.↗

A Meshless Local Petrov-Galerkin Method for Euler-Bernoulli Beam Problems

An accurate and yet simple Meshless Local Petrov-Galerkin (MLPG) formulation for analyzing beam problems is presented. In the formulation, simple weight functions are chosen as test functions. The use of these functions shows that the weak form can be integrated with conventional Gaussian integration. The MLPG method was evaluated by applying the formulation to a variety of patch test and thin beam problems. The formulation successfully reproduced exact solutions to machine accuracy when test functions with C2 continuity and an appropriate order of basis functions are used.

Raju, I. S.↗

A Time Integration Algorithm Based on the State Transition Matrix for Structures with Time Varying and Nonlinear Properties

A variable order method of integrating the structural dynamics equations that is based on the state transition matrix has been developed. The method has been evaluated for linear time variant and nonlinear systems of equations. When the time variation of the system can be modeled exactly by a polynomial it produces nearly exact solutions for a wide range of time step sizes. Solutions of a model nonlinear dynamic response exhibiting chaotic behavior have been computed. Accuracy of the method has been demonstrated by comparison with solutions obtained by established methods.

Bartels, Robert E.↗

Further Developments in the MLPG Method for Beam Problems

An accurate and yet simple Meshless Local Petrov-Galerkin (MLPG) formulation for analyzing beam problems is presented. In the formulation, simple weight functions are chosen as test functions as in the conventional MLPG method. Linear test functions are also chosen, leading to a variation of the MLPG method that is computationally efficient compared to the conventional implementation. The MLPG method is evaluated by applying the formulation to a variety of patch tests, thin beam problems, and problems with load discontinuities. The formulation successfully reproduces exact solutions to machine accuracy when higher order power and spline functions are chosen as test functions or when the linear test function is used, and when constructing the trial functions, the order of the basis function is properly balanced by the order of the weight function. For mixed boundary value problems, deflections, slopes, moments, and shear forces are calculated to the same accuracy by the MLPG method without the use of elaborate post-processing techniques. Problems with load discontinuities require special care - when a reasonable number of nodes are used, the method yields very accurate results.

Raju, I. S.↗

A Computationally Efficient Meshless Local Petrov-Galerkin Method for Axisymmetric Problems

The Meshless Local Petrov-Galerkin (MLPG) method is one of the recently developed element-free methods. The method is convenient and can produce accurate results with continuous secondary variables, but is more computationally expensive than the finite element method. To overcome this disadvantage, a simple Heaviside test function is chosen. The computational effort is significantly reduced by eliminating the domain integral for the axisymmetric potential problems and by simplifying the domain integral for the axisymmetric elasticity problems. The method is evaluated through several patch tests for axisymmetric problems and example problems for which the exact solutions are available. The present method yielded very accurate solutions. The sensitivity of several parameters of the method is also studied.

Raju, I. S.↗

Surface Pressures and Heat Transfer on Unswept Blunt Plates in Helium at High Mach Numbers

Pressure distributions and local convective heat-transfer coefficients on a flat plate at zero angle of attack were measured in helium. Data were obtained with various amounts of leading-edge bluntness at Mach numbers of 12.5 and 14.7. The pressures on a sharp leading-edged plate were not influenced by the leading edge and were predicted by the first-order, hypersonic, weak-interaction theory. Pressures on blunt plates were correlated by introducing the leading-edge Reynolds number as a parameter. Measured heat-transfer coefficients on the sharp plate agreed with predictions obtained form existing exact solutions for hear transfer across the laminar boundary layer. For the blunt plates a comparison of theory with experiment indicated that more knowledge of the flow field between the sock wave and plate surface is necessary before an adequate prediction of convective heat transfer can be made. Shock-wave shapes for the blun plates at a Mach number 12.5 and zero angle of attack were measured. At distances between 2 and 60 leading-edge thicknesses from the shock vertex, the shock-wave shapes were found to be represented by a modified form of the blast-wave analogy.

Marvin, Joseph G.↗