Engineering topics

Hogan, Robert C.

Publications and source records attributed to Hogan, Robert C..

7 records

NASA NTRS2003

Blowing in the Wind: Velocities of Chondrule-Sized Particles in a Turbulent Protoplanetary Nebula - 1

Small but macroscopic particles-chondrules, higher temperature mineral inclusions, metal grains and their like-dominate the fabric of primitive meteorites. The properties of these constituents, and their relationship to the fine dust grains which surround them, suggest that they led an extended existence in a gaseous protoplanetary nebula prior to their incorporation into their parent primitive bodies. In this paper we explore in some detail the velocities acquired by such particles in a turbulent nebula. We treat velocities in inertial space (relevant to diffusion), velocities relative to the gas entrained microscopic dust (relevant to accretion of dust rims), and velocities relative to each other (relevant to collisions). We extend previous work by presenting explicit, closed-form solutions for the magnitude and size dependence of these velocities in this important particle size regime, and we compare these expressions with new numerical calculations. The magnitude and size dependence of these velocities have immediate applications to chondrule and CAI rimming by fine dust and to their diffusion in the nebula, which we explore separately.

Cuzzi, Jeffrey N.↗

NASA NTRS2003

Blowing in the Wind: I. Velocities of Chondrule-sized Particles in a Turbulent Protoplanetary Nebula

Small but macroscopic particles - chondrules, higher temperature mineral inclusions, metal grains, and their like - dominate the fabric of primitive meteorites. The properties of these constituents, and their relationship to the fine dust grains which surround them, suggest that they led an extended existence in a gaseous protoplanetary nebula prior to their incorporation into their parent primitive bodies. In this paper we explore in some detail the velocities acquired by such particles in a turbulent nebula. We treat velocities in inertial space (relevant to diffusion), velocities relative to the gas and entrained microscopic dust (relevant to accretion of dust rims), and velocities relative to each other (relevant to collisions). We extend previous work by presenting explicit, closed-form solutions for the magnitude and size dependence of these velocities in this important particle size regime, and compare these expressions with new numerical calculations. The magnitude and size dependence of these velocities have immediate applications to chondrule and CAI rimming by fine dust, and to their diffusion in the nebula, which we explore separately.

Cuzzi, Jeffrey N.↗

NASA NTRS2000

Size-Selective Concentration of Chondrules and Other Small Particles in Protoplanetary Nebula Turbulence

Size-selective concentration of particles in a weakly turbulent protoplanetary nebula may be responsible for the initial collection of chondrules and other constituents into primitive bodY precursors. This paper presents the main elements of this process of turbulent concentration. In the terrestrial planet region. both the characteristic size and size distribution of chondrules are explained. "Fluffier" particles would be concentrated in nebula regions which were at a lower density and/or more intensely turbulent. The spatial distribution of concentrated particle density obeys multifractal scaling, suggesting a close tie to the turbulent cascade process. This scaling behavior allows predictions of the probability distributions for concentration in the protoplanetary nebula to be made. Large concentration factors (less than 10(exp 5)) are readily obtained, implying that numerous zones of particle density significantly exceeding the gas density could exist. If most of the available solids were actually in chondrule sized particles, the ensuing particle mass density would become so large that the feedback effects on gas turbulence due to mass loading could no longer be neglected. This paper describes the process, presenting its basic elements and some implications, without including the effects of mass loading.

Cuzzi, Jeffrey N.↗

NASA NTRS1999

Turbulent Concentration of Chondrules: Size Distribution and Multifractal Scaling

Size-selective concentration of particles in 3D turbulence may be related to collection of chondrules and other constituents into primitive bodies in a weakly turbulent protoplanetary nebula. In the terrestrial planet region, both the characteristic size and narrow size distribution of chondrules are explained, whereas "fluffier" particles would be concentrated in lower density, or more intensely turbulent, regions of the nebula. The spatial distribution of concentrated particle density obeys multifractal scaling, suggesting a dose tie to the turbulent cascade process. This scaling behavior allows predictions of the concentration probabilities to be made in the protoplanetary nebula, which are so large (> 10(exp 3) - 10(exp 4)) that further studies must be made of the role of mass loading.

Cuzzi, Jeffrey N.↗

NASA NTRS1998

Scaling Properties of Particle Density Fields Formed in Simulated Turbulent Flows

Direct numerical simulations (DNS) of particle concentrations in fully developed 3D turbulence were carried out in order to study the nonuniform structure of the particle density field. Three steady-state turbulent fluid fields with Taylor microscale Reynolds numbers (Re(sub lambda)) of 40, 80 and 140 were generated by solving the Navier-Stokes equations with pseudospectral methods. Large scale forcing was used to drive the turbulence and maintain temporal stationarity. The response of the particles to the fluid was parameterized by the particle Stokes number St, defined as the ratio of the particle's stopping time to the mean period of eddies on the Kolmogorov scale (eta). In this paper, we consider only passive particles optimally coupled to these eddies (St approx. = 1) because of their tendency to concentrate more than particles with lesser or greater St values. The trajectories of up to 70 million particles were tracked in the equilibrated turbulent flows until the particle concentration field reached a statistically stationary state. The nonuniform structure of the concentration fields was characterized by the multifractal singularity spectrum, f(alpha), derived from measures obtained after binning particles into cells ranging from 2(eta) to 15(eta) in size. We observed strong systematic variations of f(alpha) across this scale range in all three simulations and conclude that the particle concentration field is not statistically self similar across the scale range explored. However, spectra obtained at the 2(eta), 4(eta), and 8(eta) scales of each flow case were found to be qualitatively similar. This result suggests that the local structure of the particle concentration field may be flow-Independent. The singularity spectra found for 2n-sized cells were used to predict concentration distributions in good agreement with those obtained directly from the particle data. This Singularity spectrum has a shape similar to the analogous spectrum derived for the inertial-range energy dissipation fields of experimental turbulent flows at Re(sub lambda) = 110 and 1100. Based on this agreement, and the expectation that both dissipation and particle concentration are controlled by the same cascade process, we hypothesize that singularity spectra similar to the ones found in this work provide a good characterization of the spatially averaged statistical properties of preferentially concentrated particles in higher Re(sub lambda) turbulent flows.

Hogan, Robert C.↗

NASA NTRS1998

Turbulence, Chondrules, and Planetesimals

It has been shown both numerically and experimentally that 3-D turbulence concentrates aerodynamically size-selected particles by orders of magnitude. In a previous review chapter, in "Chondrules and the protoplanetary disk" we illustrated the initial predictions of Turbulent Concentration (TC) as applied to the solar nebula. We predicted the particle size which will be most effectively concentrated by turbulence; it is the particle which has a gas drag stopping time equal to the overturn time of the smallest (Kolmogorov scale) eddy. The primary uncertainty is the level of nebula turbulence, or Reynolds number Re, which can be expressed in terms of the standard nebula eddy viscosity parameter alpha = Re(nu)(sub m)/cH, where nu(sub m) is molecular viscosity, c is sound speed, and H is vertical scale height. Several studies, and observed lifetimes of circumstellar disks, have suggested that the level of nebula turbulence can be described by alpha = 10(exp -2) - 10(exp -4). There is some recent concern about how energy is provided to maintain this turbulence, but the issue remains open. We adopt a canonical minimum mass nebula with a range of alpha > 0. We originally showed that chondrule-sized particles are selected for concentration in the terrestrial planet region if alpha = 10(exp -3) - 10(exp -4). In addition, Paque and Cuzzi found that the size distribution of chondrules is an excellent match for theoretical predictions. One then asks by what concentration factor C these particles can be concentrated; our early numerical results indicated an increase of C with alpha, and were supported by simple scaling arguments, but the extrapolation range was quite large and the predictions (C ~ 10(exp 5) - 10(exp 6) not unlikely) uncertain. The work presented here, which makes use of our recent demonstration that the particle density field is a multifractal with flow-independent properties provides a far more secure ground for such predictions. We also indicate how fine-grained dust rims on chondrules might enter into constraining the situation.

Cuzzi, Jeffrey↗

NASA NTRS1994

Turbulent Diffusion and Concentration of "Chondrules" in the Protoplanetary Nebula

Turbulence is known to possess structure on many scales. The largest or integral scale L is usually taken to be the largest relevant dimension of the system; for the nebula as a whole, it would be on the order of a vertical gas scale height H approximately 0.1R where R is the distance from the sun. Turbulent kinetic energy cascades towards smaller scales; for fully developed, homogeneous turbulence, the turbulent kinetic energy peaks at the integral scale and is distributed within its "inertial range" according to the Kolmogorov energy spectrum dE(k) = E(sub 0)(kL)(sup -5/3)dk where k is the wavenumber or inverse wavelength. The smallest scale in a turbulent regime is the Kolmogorov scale (n)(sometimes referred to as the inner scale). On this scale, molecular viscosity can dissipate turbulent kinetic energy . Turbulent flows are characterized by their Reynolds number Re = UL/v, where U is a characteristic velocity scale and v is molecular viscosity. More energetic (higher Re) flows drive turbulence to smaller Kolmogorov scales: n = LRe(sup -3/4). Two different turbulent regimes are likely to be of importance; early stage convective turbulence in a hot nebula probably extends over the entire nebula scale height, and probably has typical eddy frequency comparable to the orbit frequency. At a later stage, midplane shear layer turbulence can be driven by the presence of a differentially rotating, densely settled particle layer, with different length and time scales.

Cuzzi, Jeffrey N.↗