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At least 739 records · Page 41

H-H, C-H, and C-C NMR spin-spin coupling constants calculated by the FP-INDO method for aromatic hydrocarbons

The FP-INDO (finite perturbation-intermediate neglect of differential overlap) method is used to calculate the H-H, C-H, and C-C coupling constants in hertz for molecules of six different benzenoid hydrocarbons: benzene, naphthalene, biphenyl, anthracene, phenanthrene, and pyrene. The calculations are based on both the actual and the average molecular geometries. It is found that only the actual molecular geometries can always yield the correct relative order of values for the H-H coupling constants. For the calculated C-C coupling constants, as for the calculated C-H coupling constants, the signs are positive (negative) for an odd (even) number of bonds connecting the two nuclei. Agreements between the calculated and experimental values of the coupling constants for all six molecules are comparable to those reported previously for other molecules.

Long, S. A. T.↗

On Calculating the Zero-Gravity Surface Figure of a Mirror

An analysis of the classical method of calculating the zero-gravity surface figure of a mirror from surface-figure measurements in the presence of gravity has led to improved understanding of conditions under which the calculations are valid. In this method, one measures the surface figure in two or more gravity- reversed configurations, then calculates the zero-gravity surface figure as the average of the surface figures determined from these measurements. It is now understood that gravity reversal is not, by itself, sufficient to ensure validity of the calculations: It is also necessary to reverse mounting forces, for which purpose one must ensure that mountingfixture/ mirror contacts are located either at the same places or else sufficiently close to the same places in both gravity-reversed configurations. It is usually not practical to locate the contacts at the same places, raising the question of how close is sufficiently close. The criterion for sufficient closeness is embodied in the St. Venant principle, which, in the present context, translates to a requirement that the distance between corresponding gravity-reversed mounting positions be small in comparison to their distances to the optical surface of the mirror. The necessity of reversing mount forces is apparent in the behavior of the equations familiar from finite element analysis (FEA) that govern deformation of the mirror.

Bloemhof, Eric E.↗

Optimized Vertex Method and Hybrid Reliability

A method of calculating the fuzzy response of a system is presented. This method, called the Optimized Vertex Method (OVM), is based upon the vertex method but requires considerably fewer function evaluations. The method is demonstrated by calculating the response membership function of strain-energy release rate for a bonded joint with a crack. The possibility of failure of the bonded joint was determined over a range of loads. After completing the possibilistic analysis, the possibilistic (fuzzy) membership functions were transformed to probability density functions and the probability of failure of the bonded joint was calculated. This approach is called a possibility-based hybrid reliability assessment. The possibility and probability of failure are presented and compared to a Monte Carlo Simulation (MCS) of the bonded joint.

Smith, Steven A.↗

Calculated scan characteristics of a large spherical reflector antenna

A previously published numerical method to calculate the radiation properties of parabolic reflectors has been modified to also include very large spherical reflectors. The method has been verified by comparing the calculated and the measured results for a 120-wavelength spherical reflector.

Agrawal, P. K.↗

Numerical Modeling of Fluid Transient in Cryogenic Fluid Network of Rocket Propulsion System

Fluid transients, also known as water hammer, can have a significant impact on the design and operation of both spacecraft and launch vehicles propulsion systems. These transients often occur at system activation and shut down. For ground safety reasons, many spacecrafts are launched with the propellant lines dry. These lines are often evacuated by the time the spacecraft reaches orbit. When the propellant isolation valve opens during propulsion system activation, propellant rushes into lines creating a pressure surge. During propellant system shutdown, a pressure surge is created due to sudden closure of a valve. During both activation and shutdown, pressure surges must be predicted accurately to ensure structural integrity of the propulsion system fluid network. The method of characteristics is the most widely used method of calculating fluid transients in pipeline [ 1,2]. The method of characteristics, however, has limited applications in calculating flow distribution in complex flow circuits with phase change, heat transfer and rotational effects. A robust cryogenic propulsion system analyzer must have the capability to handle phase change, heat transfer, chemical reaction, rotational effects and fluid transients in conjunction with subsystem flow model for pumps, valves and various pipe fittings. In recent years, such a task has been undertaken at Marshall Space Flight Center with the development of the Generalized Fluid System Simulation Program (GFSSP), which is based on finite volume method in fluid network [3]. GFSSP has been extensively verified and validated by comparing its predictions with test data and other numerical methods for various applications such as internal flow of turbo-pump [4], propellant tank pressurization [5,6], chilldown of cryogenic transfer line [7] and squeeze film damper rotordynamics [8]. The purpose of the present paper is to investigate the applicability of the finite volume method to predict fluid transient in cryogenic flow circuits.

Majumdar, Alok↗

The calculation of take-off run

A comparatively simple method of calculating length of take-off run is developed from the assumption of a linear variation in net accelerating force with air speed and it is shown that the error involved is negligible.

Diehl, Walter S↗

Estimation of Critical Temperature for Surface Ion Currents from Electron Emission Data

A method of calculating a relation for the critical surface temperature for ion current emission is presented. The method is based on the S-shaped electron emission curves for surfaces in the presence of ionizable vapors and upon the assumptions of thermodynamic equilibrium involved in the Saha-Langmuir relation. A comparison of the critical temperatures so calculated with the relation obtained from actual ion emission data on the cesium-tungsten system shows good agreement over a wide current density range. Critical temperatures for cesium ion current densities of 0.21 and 1.9 amperes per square centimeter calculated by this method are presented for surfaces of rhenium, molybdenum, tantalum, and niobium. Tentative relations of the form log j equals A (sub p) plus (B (sub p) over T) are presented for these same systems, where j is the ion current density, A (sub p) and B (sub p) are constants, and T is the temperature.

ELECTRON EMISSION↗

Calculation of Wind Compensation for Launching of Unguided Rockets

A method for calculating wind compensation for unguided missiles s derived which has a greater degree of flexibility than the previously proposed methods. Utilization of the wind-compensation technique is demonstrated by using the Shotput vehicle as a model. Postflight simulations of four of these missiles with the use of measured winds show that if the winds are known, very good accuracy can be obtained by using the proposed method.

James, Robert L., Jr.↗

Three-dimensional boundary layer calculation by a characteristic method

A numerical method for solving the three-dimensional boundary layer equations for bodies of arbitrary shape is presented. In laminar flows, the application domain extends from incompressible to hypersonic flows with the assumption of chemical equilibrium. For turbulent boundary layers, the application domain is limited by the validity of the mixing length model used. In order to respect the hyperbolic nature of the equations reduced to first order partial derivative terms, the momentum equations are discretized along the local streamlines using of the osculator tangent plane at each node of the body fitted coordinate system. With this original approach, it is possible to overcome the use of the generalized coordinates, and therefore, it is not necessary to impose an extra hypothesis about the regularity of the mesh in which the boundary conditions are given. By doing so, it is possible to limit, and sometimes to suppress, the pre-treatment of the data coming from an inviscid calculation. Although the proposed scheme is only semi-implicit, the method remains numerically very efficient.

Houdeville, R.↗

Supersonic and Moment-of-Area Rules Combined for Rapid Zero-Lift Wave-Drag Calculations

The concepts of the supersonic area rule and the moment-of-area rule are combined to develop a new method for calculating zero-lift wave drag which is amenable to the use of ordinary desk calculators. The total zero-lift wave drag of a configuration is calculated by the new method as the sum of the wave drag of each component alone plus the interference between components. In calculating the separate contributions each component or pair of components is analyzed over the smallest allowable length in order to improve the convergence of the series expression for the wave drag. The accuracy of the present method is evaluated by comparing the total zero-lift wave-drag solutions for several simplified configurations obtained by the present method with solutions given by slender-body and linearized theory. The accuracy and computational time required by the present method are also evaluated relative to the supersonic area rule and the moment-of-area rule. The results of the evaluation indicate that total zero-lift wave-drag solutions for simplified configurations can be obtained by the present method which differ from solutions given by slender-body and linearized theory by less than 6 percent. This accuracy for simplified configurations was obtained from only nine terms of the series expression for the wave drag as a result of calculating the total zero-lift wave drag by parts. For the same number of terms these results represent an accuracy greater than that for solutions obtained by either of the two methods upon which the present method is based, except in a few isolated cases. For the excepted cases, solutions by the present method and the supersonic area rule are identical. Solutions by the present method are obtained in one fifth the computing time required by the supersonic area rule. This difference in computing time of course would be substantially reduced if the complete procedures for both methods were programmed on electronic computing machines.

Levy, Lionel L., Jr.↗

Application of a full potential method to AGARD standard airfoils

One of the most important uses of method that calculate unsteady aerodynamic loads is to predict and analyze the aeroelastic responses of flight vehicles. Currently, methods based on transonic small disturbance potential aerodynamics are the primary tools for aeroelastic analysis. Flow solutions obtained using isentropic potential theory can be highly inaccurate and even multivalued, because they do not model the effects of entropy that is produced when shock waves are in the flow field. From the results that are presented, it is concluded that nonisentropic potential methods more accurately model Euler solutions than do isentropic methods. The primary effects of modeling shock generated entropy are: (1) to eliminate mulitple flow solutions when strong shock waves are in the flow field; and (2) to bring the strengths and locations of computed shock waves into better agreement with those calculated using Euler method and those measured during experiments.

Whitlow, Woodrow, Jr.↗

Preconditioned minimal residual methods for Chebyshev spectral calculations

The problem of preconditioning the pseudospectral Chebyshev approximation of an elliptic operator is considered. The numerical sensitiveness to variations of the coefficients of the operator are investigated for two classes of preconditioning matrices: one arising from finite differences, the other from finite elements. The preconditioned system is solved by a conjugate gradient type method, and by a Dufort-Frankel method with dynamical parameters. The methods are compared on some test problems with the Richardson method and with the minimal residual Richardson method.

Canuto, C.↗

Calculation of two dimensional vortex/surface interference using panel methods

The application of panel methods to the calculation of vortex/surface interference characteristics in two dimensional flow was studied over a range of situations starting with the simple case of a vortex above a plane and proceeding to the case of vortex separation from a prescribed point on a thick section. Low order and high order panel methods were examined, but the main factor influencing the accuracy of the solution was the distance between control stations in relation to the height of the vortex above the surface. Improvements over the basic solutions were demonstrated using a technique based on subpanels and an applied doublet distribution.

Maskew, B.↗

Calculation of guaranteed mean power from wind turbine generators

A method for calculating the 'guaranteed mean' power output of a wind turbine generator is proposed. The term 'mean power' refers to the average power generated at specified wind speeds during short-term tests. Correlation of anemometers, the method of bins for analyzing non-steady data, the PROP Code for predicting turbine power, and statistical analysis of deviations in test data from theory are discussed. Guaranteed mean power density for the Clayton Mod-OA system was found to be 8 watts per square meter less than theoretical power density at all power levels, with a confidence level of 0.999. This amounts to 4 percent of rated power.

Spera, D. A.↗

Calculation of aerodynamic heat transfer for blunt-nosed thin wings at different angles of attack at supersonic speeds

A method for calculating aerodynamic heat transfer on thin wings at angles of attack is provided, based on the assumption of small cross flow and the calculation of an infinite cylinder. It is valid in the range of supersonic and hypersonic speeds. The method does not require calculation of the details of the stream lines and can be used for various swept wings at moderate angle of attack or yaw angle. A comparison between theoretical and experimental results is given.

Xu, Shuxuan↗