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Solutions and parametric computer study for class of boundary value problems of time dependent temperature distribution in two layer, composite slab
The solution of the time-dependent, Reynolds-averaged, Navier-Stokes equations for unsteady, interacting flows by finite-difference algorithms is discussed. Specific examples include (1) unsteady transonic flow over a thick biconvex airfoil, (2) determination of buffet boundaries for a transonic lifting airfoil, (3) the simulation of aileron buzz and (4) dynamic stall. Algorithms considered include explicit methods, mixed (or hybrid) methods, and fully implicit methods. Consideration of time scales for computational stability, computational accuracy, and physical accuracy and the use of time-dependent adaptive meshing to realize computational efficiency are also discussed.
Context. The Cassini-Huygens mission has revealed the importance of particle precipitation in the atmosphere of Titan thanks to in-situ measurements. These ionizing particles (electrons, protons, and cosmic rays) have a strong impact on the chemistry, hence must be modeled. Aims. We revisit our computation of ionization in the atmosphere of Titan by cosmic rays. The high-energy high-mass ions are taken into account to improve the precision of the calculation of the ion production profile. Methods. The Badhwahr and O Neill model for cosmic ray spectrum was adapted for the Titan model. We used the TransTitan model coupled with the Planetocosmics model to compute the ion production by cosmic rays. We compared the results with the NAIRAS/HZETRN ionization model used for the first time for a body that differs from the Earth. Results. The cosmic ray ionization is computed for five groups of cosmic rays, depending on their charge and mass: protons, alpha, Z = 8 (oxygen), Z = 14 (silicon), and Z = 26 (iron) nucleus. Protons and alpha particles ionize mainly at 65 km altitude, while the higher mass nucleons ionize at higher altitudes. Nevertheless, the ionization at higher altitude is insufficient to obscure the impact of Saturn s magnetosphere protons at a 500 km altitude. The ionization rate at the peak (altitude: 65 km, for all the different conditions) lies between 30 and 40/cu cm/s. Conclusions. These new computations show for the first time the importance of high Z cosmic rays on the ionization of the Titan atmosphere. The updated full ionization profile shape does not differ significantly from that found in our previous calculations (Paper I: Gronoff et al. 2009, 506, 955) but undergoes a strong increase in intensity below an altitude of 400 km, especially between 200 and 400 km altitude where alpha and heavier particles (in the cosmic ray spectrum) are responsible for 40% of the ionization. The comparison of several models of ionization and cosmic ray spectra (in intensity and composition) reassures us about the stability of the altitude of the ionization peak (65 km altitude) with respect to the solar activity.
This paper describes a distributed software system for solving large-scale structural optimization problems. Distributing the software between a mainframe computer and a minicomputer takes advantage of some of the best features available on each computer. The described software system consists of a finite element structural analysis computer program, a general purpose optimizer program, and several small user-supplied problem dependent programs. Comparison with a similar system executing entirely on the mainframe computer reveals that the distributed system costs less, uses computer resources more efficiently and improves production through faster turnaround and improved user control. The system interfaces with interactive graphics software for generating models and displaying the intermediate and final results
We studied several algorithms for computing the Chebyshev spectral derivative and compare their roundoff error. For a large number of collocation points, the elements of the Chebyshev differentiation matrix, if constructed in the usual way, are not computed accurately. A subtle cause is is found to account for the poor accuracy when computing the derivative by the matrix-vector multiplication method. Methods for accurately computing the elements of the matrix are presented, and we find that if the entities of the matrix are computed accurately, the roundoff error of the matrix-vector multiplication is as small as that of the transform-recursion algorithm. Results of CPU time usage are shown for several different algorithms for computing the derivative by the Chebyshev collocation method for a wide variety of two-dimensional grid sizes on both an IBM and a Cray 2 computer. We found that which algorithm is fastest on a particular machine depends not only on the grid size, but also on small details of the computer hardware as well. For most practical grid sizes used in computation, the even-odd decomposition algorithm is found to be faster than the transform-recursion method.
A geodetic software analysis tool enables the user to analyze 2D crustal strain from geodetic ground motion, and create models of crustal deformation using a graphical interface. Users can use any geodetic measurements of ground motion and derive the 2D crustal strain interactively. This software also provides a forward-modeling tool that calculates a geodetic velocity and strain field for a given fault model, and lets the user compare the modeled strain field with the strain field obtained from the user s data. Users may change parameters on-the-fly and obtain a real-time recalculation of the resulting strain field. Four data products are computed: maximum shear, dilatation, shear angle, and principal components. The current view and data dependencies are processed first. The remaining data products and views are then computed in a round-robin fashion to anticipate view changes. When an analysis or display parameter is changed, the affected data products and views are invalidated and progressively re-displayed as available. This software is designed to facilitate the derivation of the strain fields from the GPS and strain meter data that sample it to facilitate the understanding of the strengths and weaknesses of the strain field derivation from continuous GPS (CGPS) and other geodetic data from a variety of tectonic settings, to converge on the "best practices" strain derivation strategy for the Solid Earth Science ESDR System (SESES) project given the CGPS station distribution in the western U.S., and to provide SESES users with a scientific and educational tool to explore the strain field on their own with user-defined parameters.
This paper presents a study on the impact of cirrus cloud heterogeneities on MODIS simulated thermal infrared (TIR) brightness temperatures (BTs) at the top of the atmosphere (TOA) as a function of spatial resolution from 50 meters to 10 kilometers. A realistic 3-D (three-dimensional) cirrus field is generated by the 3DCLOUD model (average optical thickness of 1.4, cloudtop and base altitudes at 10 and 12 kilometers, respectively, consisting of aggregate column crystals of D (sub eff) equals 20 microns), and 3-D thermal infrared radiative transfer (RT) is simulated with the 3DMCPOL (3-D Monte Carlo Polarized) code. According to previous studies, differences between 3-D BT computed from a heterogenous pixel and 1-D (one-dimensional) RT computed from a homogeneous pixel are considered dependent at nadir on two effects: (i) the optical thickness horizontal heterogeneity leading to the plane-parallel homogeneous bias (PPHB); and the (ii) horizontal radiative transport (HRT) leading to the independent pixel approximation error (IPAE). A single but realistic cirrus case is simulated and, as expected, the PPHB mainly impacts the low-spatial resolution results (above approximately 250 meters), with averaged values of up to 5-7 K (thousand), while the IPAE mainly impacts the high-spatial resolution results (below approximately 250 meters) with average values of up to 1-2 K (thousand). A sensitivity study has been performed in order to extend these results to various cirrus optical thicknesses and heterogeneities by sampling the cirrus in several ranges of parameters. For four optical thickness classes and four optical heterogeneity classes, we have found that, for nadir observations, the spatial resolution at which the combination of PPHB and HRT effects is the smallest, falls between 100 and 250 meters. These spatial resolutions thus appear to be the best choice to retrieve cirrus optical properties with the smallest cloud heterogeneity-related total bias in the thermal infrared. For off-nadir observations, the average total effect is increased and the minimum is shifted to coarser spatial resolutions.
Rapid Aero Modeling (RAM) applied to computational testing, RAM-C, is an approach to efficiently and automatically obtain aerodynamic models during computational investigations. RAM-C is designed to estimate models appropriate for flight dynamics studies and simulations. The approach responds to a demand for experimental efficiency and model fidelity that has increased with growing aircraft complexity and aerodynamic nonlinearities associated with hybrid and electric vertical takeoff and landing (eVTOL) aircraft. In an Urban Air Mobility (UAM) transportation system, it is expected that aircraft will embrace many features from both airplanes and rotorcraft. These vehicles present many more factors than conventional aircraft which can lead to increased computational costs and missed key factor interactions when applying traditional testing and modeling methods. RAM-C provides feedback loops around computational codes to rapidly guide testing toward aerodynamic models meeting user-defined fidelity goals. It combines and extends concepts from design of experiment theory and aircraft system identification theory that allow the user the freedom to choose, in advance of the test, a specific level of fidelity in terms of prediction error. RAM-C only collects enough data required to meet the user-specified prediction error requirements thus saving computational time and resources. The overall achievable fidelity of the final model also depends on the accuracy of the test facility, or in this case, the computational modeling approach. Previous studies to support development of the RAM-T process were conducted in wind tunnel tests to assess potential metrics, algorithms, and procedures. This paper presents results from the next steps taken and tests conducted for the development of RAM-C technology and highlights some of the unique features of RAM applied eVTOL configurations in a computational study.
The classical formulation of sound propagation through a jet flow was found to be inadequate for computer solutions. Previous investigations selected the phase and amplitude of the acoustic pressure as dependent variables requiring the solution of a system of nonlinear algebraic equations. The nonlinearities complicated both the analysis and the computation. A reformulation of the convective wave equation in terms of a new set of dependent variables is developed with a special emphasis on its suitability for numerical solutions on fast computers. The technique is very attractive because the resulting equations are linear in nonwaving variables. The computer solution to such a linear system of algebraic equations may be obtained by well-defined and direct means which are conservative of computer time and storage space. Typical examples are illustrated and computational results are compared with available numerical and experimental data.
The computer program discussed is intended for the graphical presentation of a general dependent variable X that is a function of two independent variables, U and V. The required input to the program is the variation of the dependent variable with one of the independent variables for various fixed values of the other. The computer program is named CRP, and the output is provided by the SD 4060 plotter. Program CRP is an extremely flexible program that offers the user a wide variety of options. The dependent variable may be presented in either a linear or a logarithmic manner. Automatic centering of the plot is provided in the ordinate direction, and the abscissa is scaled automatically for a logarithmic plot. A description of the carpet plot technique is given along with the coordinates system used in the program. Various aspects of the program logic are discussed and detailed documentation of the data card format is presented.
The method is based upon molecular line parameters and makes use of a far wing scaling approximation and k distribution approach previously applied to the computation of the infrared cooling rate due to water vapor. Taking into account the wave number dependence of the incident solar flux, the solar heating rate is computed for the entire water vapor spectrum and for individual absorption bands. The accuracy of the method is tested against line by line calculations. The method introduces a maximum error of 0.06 C/day. The method has the additional advantage over previous methods in that it can be applied to any portion of the spectral region containing the water vapor bands. The integrated absorptances and line intensities computed from the molecular line parameters were compared with laboratory measurements. The comparison reveals that, among the three different sources, absorptance is the largest for the laboratory measurements.
Mathematical methods for the design of supercritical wings, which depend on the numerical solution of the partial differential equations of two-dimensional gas dynamics, are developed. The main contribution is a computer program for the design of shockless transonic airfoils using the hodograph transformation and analytic continuation into the complex domain. The mathematical theory is described, and a manual for users of the programs is provided. Numerical examples are given and computational results are discussed, and the computer programs themselves are listed. The analysis routine can be used to ascertain whether the profiles behave well at off-design conditions, or to smooth coordinates and obtain a desirable shape more quickly when perfectly shockless flow is not essential.
Understanding the high velocity impact response of polymer matrix composites with complex architectures is critical to many aerospace applications, including engine fan blade containment systems where the structure must be able to completely contain fan blades in the event of a blade-out. Despite the benefits offered by these materials, the complex nature of textile composites presents a significant challenge for the prediction of deformation and damage under both quasi-static and impact loading conditions. The relatively large mesoscale repeating unit cell (in comparison to the size of structural components) causes the material to behave like a structure rather than a homogeneous material. Impact experiments conducted at NASA Glenn Research Center have shown the damage patterns to be a function of the underlying material architecture. Traditional computational techniques that involve modeling these materials using smeared homogeneous, orthotropic material properties at the macroscale result in simulated damage patterns that are a function of the structural geometry, but not the material architecture. In order to preserve heterogeneity at the highest length scale in a robust yet computationally efficient manner, and capture the architecturally dependent damage patterns, a previously-developed subcell modeling approach where the braided composite unit cell is approximated as a series of four adjacent laminated composites is utilized. This work discusses the implementation of the subcell methodology into the commercial transient dynamic finite element code LS-DYNA (Livermore Software Technology Corp.). Verification and validation studies are also presented, including simulation of the tensile response of straight-sided and notched quasi-static coupons composed of a T700/PR520 triaxially braided [0deg/60deg/-60deg] composite. Based on the results of the verification and validation studies, advantages and limitations of the methodology as well as plans for future work are discussed.
Human exploration of the surface of Mars will require an extended powered descent phase of flight, during which aerodynamic-propulsive interference effects can be significant. Characterization of these environments to enable implementation of this technology into a flight vehicle will rely heavily on computational simulation. This work advances the understanding of retropropulsion aerodynamics through application of a massively parallel detached eddy simulation approach on a GPU-accelerated computational framework, yielding data that are largely unachievable with conventional high-performance computing resources. This work includes time-dependent and time-averaged forces and moments on a conceptual, full-scale vehicle in environments and operating conditions relevant to human Mars exploration. Conditions are examined where the engine exhaust flow transitions between over-expanded and under-expanded flow structures, and flight operation will require the ability to maintain control of the vehicle during such a transition. These transitions occur as the vehicle decelerates, and as such, this investigation includes supersonic, transonic, and subsonic flight conditions. Options for vehicle control during powered flight include differential throttling of the engines. This paper provides an overview of the computational campaign, approach, and discussion of results in characterizing the resulting aerodynamics for differential throttling with retropropulsion in atmospheric environments.
The current design of the Space Interferometry Mission (SIM) employs a 19 laser-metrology-beam system (also called L19 external metrology truss) to monitor changes of distances between the fiducials of the flight system's multiple baselines. The function of the external metrology truss is to aid in the determination of the time-variations of the interferometer baseline. The largest contributor to truss error occurs in SIM wide-angle observations when the articulation of the siderostat mirrors (in order to gather starlight from different sky coordinates) brings to light systematic errors due to offsets at levels of instrument components (which include comer cube retro-reflectors, etc.). This error is labeled external metrology wide-angle field-dependent error. Physics-based model of field-dependent error at single metrology gauge level is developed and linearly propagated to errors in interferometer delay. In this manner delay error sensitivity to various error parameters or their combination can be studied using eigenvalue/eigenvector analysis. Also validation of physics-based field-dependent model on SIM testbed lends support to the present approach. As a first example, dihedral error model is developed for the comer cubes (CC) attached to the siderostat mirrors. Then the delay errors due to this effect can be characterized using the eigenvectors of composite CC dihedral error. The essence of the linear error model is contained in an error-mapping matrix. A corresponding Zernike component matrix approach is developed in parallel, first for convenience of describing the RMS of errors across the field-of-regard (FOR), and second for convenience of combining with additional models. Average and worst case residual errors are computed when various orders of field-dependent terms are removed from the delay error. Results of the residual errors are important in arriving at external metrology system component requirements. Double CCs with ideally co-incident vertices reside with the siderostat. The non-common vertex error (NCVE) is treated as a second example. Finally combination of models, and various other errors are discussed.
The combustion process in liquid rocket engines depends on a number of complex phenomena such as atomization, vaporization, spray dynamics, mixing, and reaction mechanisms. A computational tool to study their mutual interactions is developed to help analyze these processes with a view of improving existing designs and optimizing future designs of the thrust chamber. The focus of the article is on the analysis of the Variable Thrust Engine for the Orbit Maneuvering Vehicle. This engine uses a hypergolic liquid bipropellant combination of monomethyl hydrazine as fuel and nitrogen tetroxide as oxidizer.
The fully three-dimensional, time-dependent compressible Navier-Stokes equations in cylindrical coordinates are presently used, in conjunction with the multistage Runge-Kutta numerical integration scheme for solution of the governing flow equations, to simulate complex flowfields within turbomechanical components whose pertinent effects encompass those of viscosity, compressibility, blade rotation, and tip clearance. Computed results are presented for selected cascades, emphasizing the code's capabilities in the accurate prediction of such features as airfoil loadings, exit flow angles, shocks, and secondary flows. Computations for several test cases have been performed on a Cray-YMP, using nearly 90,000 grid points.
Orbital operations in the neighborhood of other satellites or free-flying objects need the ability to see and detect such objects optically. This ability depends primarily on the brightness of the object relative to other sources present. The present analysis and computational procedure provides a means for predicting the visual brightness of a satellite when viewed from a nearby satellite in the same orbit. It is designed specifically for estimating the brightness of Spartan free-flyers from the STS Orbiters which release and later retrieve them, but the basic methods are applicable to other satellite-to-satellite visibility prediction problems. The Spartan reflector model defined herein is illuminated both by direct solar radiation and by the earth (albedo), producing a model source of defined directional intensity. The intensity in the Orbiter direction (along orbit) yields the desired maximum range directly. The required geometric and photometric calculations involve a number of angles in space, which are readily computed from the basic directions defining their sides. The time-dependent directions are determined by straightforward calculation from fundamental relationships and constants.