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The treatment for waste solutions containing hydrazine is presented. The invention attempts oxidation and decomposition of hydrazine in waste water in a simple and effective processing. The method adds activated charcoal to waste solutions containing hydrazine while maintaining a pH value higher than 8, and adding iron salts if necessary. Then, the solution is aerated.
Approximate solutions for potential flow past an axisymmetric slender body and past a thin airfoil are calculated using a uniform perturbation method and then compared with either the exact analytical solution or the solution obtained using a purely numerical method. The perturbation method is based upon a representation of the disturbance flow as the superposition of singularities distributed entirely within the body, while the numerical (panel) method is based upon a distribution of singularities on the surface of the body. It is found that the perturbation method provides very good results for small values of the slenderness ratio and for small angles of attack. Moreover, for comparable accuracy, the perturbation method is simpler to implement, requires less computer memory, and generally uses less computation time than the panel method. In particular, the uniform perturbation method yields good resolution near the regions of the leading and trailing edges where other methods fail or require special attention.
The response of beam and plate members to pulse and impact loading is investigated, and numerical methods are analyzed and compared. The equations of motion, the finite difference and finite element methods, the time integration/Runge-Kutta techniques, and material modeling are discussed in detail. It is found that both the finite difference and the finite element methods could be accurately employed to discretize the spatial variation in the displacements. Central differences or a fourth order Runge-Kutta algorithm could be used for the time integration. The total energy of the system would give the stability and accuracy of the solution. Results showed that the finite element method provided better efficiency in obtaining accurate solution than the finite difference method when a scalar processor is used. However, the finite difference method was more efficient on the vector processor. Therefore, the most efficient method of solution depends on the type of computer present for the analysis.
Analytic expressions have been found for Euler's Equations of Motion and for the Eulerian Angles for both symmetric and near symmetric rigid bodies under the influence of arbitrary constant body-fixed torques. These solutions have been used to solve for the secular terms in the translational delta-V equations in inertial space. This secular delta-V solution is of interest in application to spinning spacecraft in that it describes the average direction of the delta-V of the spacecraft during a spin-up maneuver. Numerical integration of the governing differential equations has verified that the secular delta-V solution is valid for large time and is accurate in many physical situations including spin-up maneuvers of the Galileo spacecraft.
Analytic error bounds are presented for the solutions of approximate models for self-excited near-symmetric rigid bodies. The error bounds are developed for analytic solutions to Euler's equations of motion. The results are applied to obtain a simplified analytic solution for Eulerian rates and angles. The results of a sample application of the range and error bound expressions for the case of the Galileo spacecraft experiencing transverse torques demonstrate the use of the bounds in analyses of rigid body spin change maneuvers.
The principle of harmonic balance is invoked in the development of an approximate analytic model for a class of nonlinear oscillators typified by a mass attached to a stretched wire. By assuming that harmonic balance will hold, solutions are devised for a steady state limit cycle and/or limit point motion. A method of slowly varying amplitudes then allows derivation of approximate solutions by determining the form of the exact solutions and substituting into them the lowest order terms of their respective Fourier expansions. The latter technique is actually a generalization of the method proposed by Kryloff and Bogoliuboff (1943).
Solution of the steady 2-D Euler equations using mesh embedding, or local grid refinement, with a cell-centered finite volume scheme is investigated. Embedded regions which are topologically similar to the global grid are considered. An isoenergetic model for the governing equations is used in Jameson's finite volume multistage scheme with modifications to the boundary conditions and smoothing. A detailed study of the embedding interface flux and smoothing formulations is conducted. Taylor expansion analysis reveals that local second order spatial accuracy is not possible if a conservative interface flux formulation is used. The analysis also gives constraints for local first order accuracy. An energy stability analysis indicates that downwind weighting of interface fluxes causes local instabilities. Analysis shows that conservative interface smoothing formulations must have a locally convective component, but that correct interface formulations allow globally dissipative smoothing. Embedded mesh solutions obtained with this scheme are presented for a transonic airfoil. They show that if embedding interfaces are close to the shocks, then small modifications in the interface location can have large effects on converge and solution accuracy.
A Blasius boundary value problem with inhomogeneous lower boundary conditions f(0) = 0 and f'(0) = - lambda with lambda strictly positive was considered. The Crocco variable formulation of this problem has a key term which changes sign in the interval of interest. It is shown that solutions of the boundary value problem do not exist for values of lambda larger than a positive critical value lambda. The existence of solutions is proven for 0 lambda lambda by considering an equivalent initial value problem. It is found however that for 0 lambda lambda, solutions of the boundary value problem are nonunique. Physically, this nonuniqueness is related to multiple values of the skin friction.
Experiments were performed to examine if the ubiquitousness of a weak magnetic component in all Martian surface fines tested with the Viking Landers can be attributed to ferric iron precipitation in aqueous solution under oxidizing conditions at neutral pH. Ferrous solutions were mixed in deionized water and various minerals were added to separate liquid samples. The iron-bearing additives included hematite, goethite, magnetite, maghemite, lepidocrocite and potassium bromide blank at varying concentrations. IR spectroscopic scans were made to identify any precipitates resulting from bubbling oxygen throughout the solutions; the magnetic properties of the precipitates were also examined. The data indicated that the lepidocrocite may have been preferentially precipitated, then aged to maghemite. The process would account for the presumed thin residue of maghemite on the present Martian surface, long after abundant liquid water on the Martian surface vanished.
Solutions of the Navier-Stokes equations with chemical nonequilibrium and multicomponent surface slip are presented along the stagnation streamline under low-density hypersonic flight conditions. The conditions analyzed are those encountered by the nose region of the Space Shuttle Orbiter during reentry. A detailed comparison of the Navier-Stokes (NS) results is made with the viscous shock-layer (VSL) and Direct Simulation Monte Carlo (DSMC) predictions. With the inclusion of surface-slip boundary conditions in NS calculations, the surface heat transfer and other flow field quantities adjacent to the surface are predicted favorably with the DSMC calculations from 75 km to 115 km in altitude. Therefore, the practical range for the applicability of Navier-Stokes solutions is much wider than previously thought. This is appealing because the continuum (NS and VSL) methods are commonly used to solve the fluid flow problems and are less demanding in terms of computer resource requirements than the noncontinuum (DSMC) methods. The NS solutions agree well with the VSL results for altitudes less than 92 km. An assessment is made of the frozen flow approximation employed in the VSL calculations.
A Program for an Iterative Aeroelastic Solution (PIAS) is discussed. This will be a modular computer program that combines the use of a finite-element structural analysis code with any linear or nonlinear aerodynamic code. At this point in time, PIAS has been designed but the software has not been written. The idea for this development originated with P. J. (Bud) Bobbitt of the NASA Langley Research Center. There was initial interest in an aeroelastic solution for a separation-induced leading-edge vortex. Some examples of the flow patterns for a low aspect ratio wing are shown. The Leading-Edge Vortex Program, which calculates pressure distributions including the effects of a separation-induced leading-edge vortex, uses an iterative solution method. This led to the concept of an iteration cycle on configuration shape external to the aerodynamic code.
Numerically solving the incompressible Navier-Stokes equations is known to be time consuming and expensive. Testing of the INS3D computers code, which solves these equations with the use of the pseudocompressibility method, shows this method to be an efficient way to obtain the steady state solution. The effects of the waves introduced by the pseudocompressibility method are analyzed and criteria are set and tested for the choice of the pseudocompressibility parameter which governs the artificial sound speed. The code is tested using laminar flow over a two dimensional backward-facing step, and laminar flow over a two dimensional circular cylinder. The results of the computations over the backward-facing step are in excellent agreement with experimental results. The transient solution of the flow over the cylinder impulsively started from rest is in good agreement with experimental results. However, the computed frequency of periodic shedding of vortices behind the cylinder is not in agreement with the experimental value. For a three dimensional test case, computations were conducted for a cylinder end wall junction. The saddle point separation and horseshoe vortex system appear in the computed field. The solution also shows secondary vortex filaments which wrap around the cylinder and spiral up in the wake.
Solutions for transonic viscous and inviscid flows using a composite velocity procedure are presented. The velocity components of the compressible flow equations are written in terms of a multiplicative composite consisting of a viscous or rotational velocity and an inviscid, irrotational, potential-like function. This provides for an efficient solution procedure that is locally representative of both asymptotic inviscid and boundary layer theories. A modified conservative form of the axial momentum equation that is required to obtain rotational solutions in the inviscid region is presented and a combined conservation/nonconservation form is applied for evaluation of the reduced Navier-Stokes (RNS), Euler and potential equations. A variety of results is presented and the effects of the approximations on entropy production, shock capturing, and viscous interaction are discussed.
Two-dimensional systems of linear hyperbolic equations are studied with regard to their behavior under a solution strategy that in alternate time-steps solves exactly the component one-dimensional operators. The initial data is a step function across an oblique discontinuity. The manner in which this discontinuity breaks up under repeated applications of the split operator is analyzed, and it is shown that the split solution will fail to match the true solution in any case where the two operators do not share all their eigenvectors. The special case of the fluid flow equations is analyzed in more detail, and it is shown that arbitrary initial data gives rise to pseudo acoustic waves and a non-physical stationary wave. The implications of these findings for the design of high-resolution computing schemes are discussed.
The KI solution for a finite length single-edge notch specimen loaded under fixed-end displacements is derived using a crack compliance analysis. Numerical and experimental checks of the KI solution are provided. Good agreement between the experimental and numerical solutions is observed. The applicability of conventional fracture mechanics to correlate crack growth data generated under displacement control is discussed.
A solution for transonic flow past a twisted rotor blade in hover is obtained using a modified version of the full-potential code ROT22 and a circular wake. The flow is also evaluated for a fixed-wing-type straight wake. The solutions for the straight wake and circular wake, and the circular wake and a two-dimensional wake are compared. The data reveal that the circular wake and the general two-dimensional wake solutions have similar characteristics.
The first subsonic solutions of the bi-Maxwellian-based 16-moment set of transport equations for stable auroral red (SAR) arc conditions are presented. These are compared with the solutions obtained from the Maxwellian-based 13-moment transport equations for the same boundary conditions. Close agreement between the 16-moment and 13-moment solutions was obtained for the drift velocity, total electron temperature, total proton heat flow, and total electron heat flow profiles. On the other hand, significant discrepancies were found. Thus, the 16-moment density profile falls off more rapidly with increasing altitude than that computed with the 13-moment equations; the total proton temperature is less in the 16-moment case than in the 13-moment case by several thousand degrees at most altitudes; and differences exist in the ratios of the proton and electron temperature anisotropies with the altitude. A simplified set of transport equations was obtained by dropping terms which remain relatively small at all altitudes.
The equations of motion in the steady laminar flow past a sudden expansion at large Reynolds number, R, reduce to the boundary layer equations as R tends to the freestream valve, when the longitudinal length scale of the separated eddy increases linearly and indefinitely with R. A global Newton method is presently used to obtain finite difference solutions to the steady Navier-Stokes equations up to R of 1000 for a uniform inflow past a cascade of sudden expansions. For large expansion ratio values, the eddy length increases linearly with R; for smaller values, however, where boundary layer equation solutions could not be found, the steady solutions to the Navier-Stokes equations approach the limit of an inviscid eddy in length with increasing R.