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364 records · Page 21

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NASA NTRS1989

Numerical solutions of forward-flight rotor flow using an upwind method

A finite-volume upwind algorithm for solving the 3-D Euler equations with a moving grid has been developed for computing helicopter forward-flight rotor flows. The computed pressure distributions and shock positions of high-speed rotor flow are compared with various experimental data as well as with other numerical results, and the agreement is encouraging. A comparison of quasi-steady solutions with unsteady solutions reveals that when a shock occurs in the flowfield, the assumption of quasi-steady flow may fail due to the time-lag of the shock motion. Similarly, three-dimensional effects cannot be neglected. Sufficient subiterations for each time step are required to avoid numerical lag effects in using the present method. The redistribution of the residual due to the coordinate transformation is discussed. For high-order MUSCL-type schemes, a coordinate-independent solution can be obtained by interpolating primitive variables.

Chen, C. L.↗

NASA NTRS1984

Exponential-fitted methods for integrating stiff systems of ordinary differential equations: Applications to homogeneous gas-phase chemical kinetics

Conventional algorithms for the numerical integration of ordinary differential equations (ODEs) are based on the use of polynomial functions as interpolants. However, the exact solutions of stiff ODEs behave like decaying exponential functions, which are poorly approximated by polynomials. An obvious choice of interpolant are the exponential functions themselves, or their low-order diagonal Pade (rational function) approximants. A number of explicit, A-stable, integration algorithms were derived from the use of a three-parameter exponential function as interpolant, and their relationship to low-order, polynomial-based and rational-function-based implicit and explicit methods were shown by examining their low-order diagonal Pade approximants. A robust implicit formula was derived by exponential fitting the trapezoidal rule. Application of these algorithms to integration of the ODEs governing homogenous, gas-phase chemical kinetics was demonstrated in a developmental code CREK1D, which compares favorably with the Gear-Hindmarsh code LSODE in spite of the use of a primitive stepsize control strategy.

Pratt, D. T.↗

NASA NTRS1993

Particle-Gas Dynamics in the Midplane of a Protoplanetary Nebula

In this paper, we study the stage of planetary formation during which the particulate material is still dispersed as centimeter-to-meter sized primordial aggregates. During this stage, particles are able to settle toward the midplane into a layer of mass density comparable to or much greater than that of the gas. Nonlinear, coupled interactions between the particles and the nebula gas become significant and ultimately determine the vertical profiles of the particle density and the mean velocities of the particles and the nearby gas. This is the environment in which the earliest planetesimals probably form. Our numerical models rely on the Reynolds averaged Navier-Stokes equations for the gas and particles and are fully viscous and turbulent (and, for the particles. compressible). Our turbulence modeling uses a Prandtl local shear parametrization, validated by laboratory experiments. We have developed a new model for particle diffusion involving the profile of the nebula gas turbulence and the particle Schmidt number, which is a function of particle size and density. We model a cool, quiescent nebula at 1 AU (280 K) and 10 AU (90 K) and a higher temperature stage (1000 K) at 1 AU. Our main results include: (a) rapid accretion of planetesimals by gravitationally unstable fragmentation on an orbital time scale (the 'Goldreich-Ward instability') is unlikely to occur until objects have already accreted by some other process to the mass of the largest known meteorite samples, if at all; (b) from 'seeds' as small as 10 m, growth of 10- to 100-km planetesimals can proceed rapidly by drift-augmented accretion in the particle-rich midplane with orbital decay of about 1% for the growing planetesimals; (c) outward transport of vapor and small entrained chips can account for significant radial compositional and mineralogical mixing in primitive meteorite parent bodies. Other implications may be drawn concerning particle random collisional velocities and the time scales of midplane turbulence.

Cuzzi, Jeffrey N.↗

NASA NTRS1966

Fully Deuterated Aliphatic Hydrocarbons Obtained From Iron Carbide Treated with DCl and D2O

According to Oparin, Mendeleev thought that the origin of petroleum was the result of the hydrolysis of iron carbides by superheated steam under pressure from the deep interior of the Earth through geological formations where the metal carbides exist. As early as 1877, Mendeleev described the reaction leading to the synthesis of hydrocarbons according to the general equation 3Fe(sub m)C(sub n) + mH2O yields mFe3O4 + C(sub 3n)H(sub 8m). Other experimental studies on the production of hydrocarbons from cast iron have been reported. Because of the possibility that hydrocarbons may have been trapped within the carbon matrix of the cast iron, which usually has a high content of carbon, we have studied the reaction of pure iron carbide with deuterium chloride and deuterated water. This was done in order to distinguish any newly formed deuterated hydrocarbons from any possible impurities of trapped hydrocarbons. The experiments were carried out by simply allowing iron carbide to react with concentrated deuterium chloride in D2O. The volatile hydrocarbon fraction examined by gas chromatography-mass spectrometry (GC/MS), using a Finnigan 1020/OWA instrument. contained low molecular weight hydrocarbons in a range C3 to C7. Lower molecular weight hydrocarbons were not detected by GC/MS because the MS scanning mode was preset above mass 40 to exclude components of air. The identified hydrocarbons are similar to those obtained under prebiotic conditions using high frequency discharge. The hydrocarbons found in common were propane, butane, pentane, 3-methylpentane, hexane, and heptane. The percent yields decline with increasing carbon number (propane 11%, n-heptane 1%). Similar results have been obtained by the direct treatment of metal carbides by pulse laser vaporization mass spectrometry. These results show that the hydrolysis of iron carbides may have been a significant source of hydrocarbons on the primitive Earth. There appears to be a predominance of straight chain isomers, which may have been important in the prebiotic synthesis of membrane-forming compounds.

Marquez, C.↗