Numerical investigation on a transition prediction model

A new transition prediction model is introduced, which couples the intermittency effect into the turbulence transport equations and takes the characteristics of fluid transition into consideration to mimic the exact process of transition. Test cases include a two-dimensional incompressible plate and a two-dimensional NACA0012 airfoil. Performance of this transition model for incompressible flows is studied, with numerical results consistent to experimental data. The requirement of grid resolution for this transition model is also studied.

Two-Dimensional Hillslope Scale Soil Erosion Model

On a hillslope, overland flow first generates sheet erosion and then, with increasing flux, it causes rill erosion. Sheet erosion (interrill erosion) and rill erosion are commonly observed to coexist on hillslopes. Great differences exist between both the intensities and incidences of rill and interrill erosion. In this paper, a two-dimensional rill and interrill erosion model is developed to simulate the details of the soil erosion process on hillslopes. The hillslope is treated as a combination of a two-dimensional interrill area and a one-dimensional rill. The rill process, the interrill process, and the joint occurrence of rill and interrill areas are modeled, respectively. Thus, the process of sheet flow replenishing rill flow with water and sediment can be simulated in detail, which may possibly render more truthful results for rill erosion. The model was verified with two sets of data and the results seem good. Using this model, the characteristics of soil erosion on hillslopes are investigated. Study results indicate that (1) the proposed model is capable of describing the complex process of interrill and rill erosion on hillslopes; (2) the spatial distribution of erosion is simulated on a simplified two-dimensional hillslope, which shows that the distribution of interrill erosion may contribute to rill development; and (3) the quantity of soil eroded increases rapidly with the slope gradient, then declines, and a critical slope gradient exists, which is about 15-20 degrees for the accumulated erosion amount.

A numerical model for predicting the jump of lift force on an oscillating cylinder

The fluid force coefficients on a transversely oscillating cylinder are calculated by applying two- dimensional large eddy simulation method. Considering the ‘‘jump’’ phenomenon of the amplitude of lift coefficient is harmful to the security of the submarine slender structures, the characteristics of this ‘‘jump’’ are dissertated concretely. By comparing with experiment results, we establish a numerical model for predicting the jump of lift force on an oscillating cylinder, providing consultation for revising the hydrodynamic parameters and checking the fatigue life scale design of submarine slender cylindrical structures.

Asymptotic scaling in the two-dimensional O(3) Nonlinear sigma model: a Monte Carlo study on parallel computers

We investigate the 2d O(3) model with the standard action by Monte Carlo simulation at couplings β up to 2.05. We measure the energy density, mass gap and susceptibility of the model, and gather high statistics on lattices of size L ≤ 1024 using the Floating Point Systems T-series vector hypercube and the Thinking Machines Corp.'s Connection Machine 2. Asymptotic scaling does not appear to set in for this action, even at β = 2.10, where the correlation length is 420. We observe a 20% difference between our estimate m/Λ^─_(Ms) = 3.52(6) at this β and the recent exact analytical result . We use the overrelaxation algorithm interleaved with Metropolis updates and show that decorrelation time scales with the correlation length and the number of overrelaxation steps per sweep. We determine its effective dynamical critical exponent to be z' = 1.079(10); thus critical slowing down is reduced significantly for this local algorithm that is vectorizable and parallelizable.

We also use the cluster Monte Carlo algorithms, which are non-local Monte Carlo update schemes which can greatly increase the efficiency of computer simulations of spin models. The major computational task in these algorithms is connected component labeling, to identify clusters of connected sites on a lattice. We have devised some new SIMD component labeling algorithms, and implemented them on the Connection Machine. We investigate their performance when applied to the cluster update of the two dimensional Ising spin model.

Finally we use a Monte Carlo Renormalization Group method to directly measure the couplings of block Hamiltonians at different blocking levels. For the usual averaging block transformation we confirm the renormalized trajectory (RT) observed by Okawa. For another improved probabilistic block transformation we find the RT, showing that it is much closer to the Standard Action. We then use this block transformation to obtain the discrete β-function of the model which we compare to the perturbative result. We do not see convergence, except when using a rescaled coupling β_E to effectively resum the series. For the latter case we see agreement for m/ Λ^─_(Ms) at , β = 2.14, 2.26, 2.38 and 2.50. To three loops m/Λ^─_(Ms) = 3.047(35) at β = 2.50, which is very close to the exact value m/ Λ^─_(Ms) = 2.943. Our last point at β = 2.62 disagrees with this estimate however.

Evaluation of Two Alternative Carbon Capture and Storage Technologies: A Stochastic Model

30 p.

I. The effects of variations in certain parameters upon the efficiency of in vivo hemodialysis with a Kiil dialyzer. II. Interfacial structure of concurrent air-water flow in a two-inch diameter horizontal tube.

Part I

Regression analyses are performed on in vivo hemodialysis data for the transfer of creatinine, urea, uric acid and inorganic phosphate to determine the effects of variations in certain parameters on the efficiency of dialysis with a Kiil dialyzer. In calculating the mass transfer rates across the membrane, the effects of cell-plasma mass transfer kinetics are considered. The concept of the effective permeability coefficient for the red cell membrane is introduced to account for these effects. A discussion of the consequences of neglecting cell-plasma kinetics, as has been done to date in the literature, is presented.

A physical model for the Kiil dialyzer is presented in order to calculate the available membrane area for mass transfer, the linear blood and dialysate velocities, and other variables. The equations used to determine the independent variables of the regression analyses are presented. The potential dependent variables in the analyses are discussed.

Regression analyses were carried out considering overall mass-transfer coefficients, dialysances, relative dialysances, and relative permeabilities for each substance as the dependent variables. The independent variables were linear blood velocity, linear dialysate velocity, the pressure difference across the membrane, the elapsed time of dialysis, the blood hematocrit, and the arterial plasma concentrations of each substance transferred. The resulting correlations are tabulated, presented graphically, and discussed. The implications of these correlations are discussed from the viewpoint of a research investigator and from the viewpoint of patient treatment.

Recommendations for further experimental work are presented.

Part II

The interfacial structure of concurrent air-water flow in a two-inch diameter horizontal tube in the wavy flow regime has been measured using resistance wave gages. The median water depth, r.m.s. wave height, wave frequency, extrema frequency, and wave velocity have been measured as functions of air and water flow rates. Reynolds numbers, Froude numbers, Weber numbers, and bulk velocities for each phase may be calculated from these measurements. No theory for wave formation and propagation available in the literature was sufficient to describe these results.

The water surface level distribution generally is not adequately represented as a stationary Gaussian process. Five types of deviation from the Gaussian process function were noted in this work. The presence of the tube walls and the relatively large interfacial shear stresses precludes the use of simple statistical analyses to describe the interfacial structure. A detailed study of the behavior of individual fluid elements near the interface may be necessary to describe adequately wavy two-phase flow in systems similar to the one used in this work.

Fluid-structure Interactions of Inverted Leaves and Flags

Interactions between fluid flows and elastic bodies are ubiquitous in nature. One such phenomena that is encountered on a daily basis is the flapping and fluttering of leaves in the wind. The fluid-structure interaction that governs the physics of a leaf in the wind is poorly understood at best and has potential applications in biomechanics, vehicle design, and energy conversion. We build upon previous work on the flapping dynamics of inverted flags, which are cantilevered elastic sheets with free leading edge and fixed trailing edge that display unique large amplitude oscillatory behaviors. We model a leaf in the laboratory using modified inverted flags, experimentally probing the governing parameters behind leaf fluttering as well as shedding light on the physics behind the inverted flag phenomena. The behavior of these "inverted leaves" studied here display sensitive dependence on two biomechanically relevant parameters, stem-to-leaf rigidity and stem-to-leaf length. In addition, leaves on a tree are not often found alone. We seek to understand the complex interactions of multiple fluttering and flapping leaves by way of examining the interactions between pairs of inverted flags. Coupling through their flow fields, pairs of inverted flags exhibit striking emergent phenomena. We report these observed dynamical behaviors and the conditions upon which they arise.

Particle fluid mechanics in shear flows, acoustic waves, and shock waves

Three different categories of flow problems of a fluid containing small particles are being considered here. They are: (i) a fluid containing small, non-reacting particles (Parts I and II); (ii) a fluid containing reacting particles (Parts III and IV); and (iii) a fluid containing particles of two distinct sizes with collisions between two groups of particles (Part V).

Part I

A numerical solution is obtained for a fluid containing small particles flowing over an infinite disc rotating at a constant angular velocity. It is a boundary layer type flow, and the boundary layer thickness for the mixture is estimated. For large Reynolds number, the solution suggests the boundary layer approximation of a fluid-particle mixture by assuming W = W_p. The error introduced is consistent with the Prandtl’s boundary layer approximation. Outside the boundary layer, the flow field has to satisfy the “inviscid equation” in which the viscous stress terms are absent while the drag force between the particle cloud and the fluid is still important. Increase of particle concentration reduces the boundary layer thickness and the amount of mixture being transported outwardly is reduced. A new parameter, β = 1/Ω τ_v, is introduced which is also proportional to μ. The secondary flow of the particle cloud depends very much on β. For small values of β, the particle cloud velocity attains its maximum value on the surface of the disc, and for infinitely large values of β, both the radial and axial particle velocity components vanish on the surface of the disc.

Part II

The “inviscid” equation for a gas-particle mixture is linearized to describe the flow over a wavy wall. Corresponding to the Prandtl-Glauert equation for pure gas, a fourth order partial differential equation in terms of the velocity potential ϕ is obtained for the mixture. The solution is obtained for the flow over a periodic wavy wall. For equilibrium flows where λ_v and λ_T approach zero and frozen flows in which λ_v and λ_T become infinitely large, the flow problem is basically similar to that obtained by Ackeret for a pure gas. For finite values of λ_v and λ_T, all quantities except v are not in phase with the wavy wall. Thus the drag coefficient C_D is present even in the subsonic case, and similarly, all quantities decay exponentially for supersonic flows. The phase shift and the attenuation factor increase for increasing particle concentration.

Part III

Using the boundary layer approximation, the initial development of the combustion zone between the laminar mixing of two parallel streams of oxidizing agent and small, solid, combustible particles suspended in an inert gas is investigated. For the special case when the two streams are moving at the same speed, a Green’s function exists for the differential equations describing first order gas temperature and oxidizer concentration. Solutions in terms of error functions and exponential integrals are obtained. Reactions occur within a relatively thin region of the order of λ_D. Thus, it seems advantageous in the general study of two-dimensional laminar flame problems to introduce a chemical boundary layer of thickness λ_D within which reactions take place. Outside this chemical boundary layer, the flow field corresponds to the ordinary fluid dynamics without chemical reaction.

Part IV

The shock wave structure in a condensing medium of small liquid droplets suspended in a homogeneous gas-vapor mixture consists of the conventional compressive wave followed by a relaxation region in which the particle cloud and gas mixture attain momentum and thermal equilibrium. Immediately following the compressive wave, the partial pressure corresponding to the vapor concentration in the gas mixture is higher than the vapor pressure of the liquid droplets and condensation sets in. Farther downstream of the shock, evaporation appears when the particle temperature is raised by the hot surrounding gas mixture. The thickness of the condensation region depends very much on the latent heat. For relatively high latent heat, the condensation zone is small compared with Ʌ_D.

For solid particles suspended initially in an inert gas, the relaxation zone immediately following the compression wave consists of a region where the particle temperature is first being raised to its melting point. When the particles are totally melted as the particle temperature is further increased, evaporation of the particles also plays a role.

The equilibrium condition downstream of the shock can be calculated and is independent of the model of the particle-gas mixture interaction.

Part V

For a gas containing particles of two distinct sizes and satisfying certain conditions, momentum transfer due to collisions between the two groups of particles can be taken into consideration using the classical elastic spherical ball model. Both in the relatively simple problem of normal shock wave and the perturbation solutions for the nozzle flow, the transfer of momentum due to collisions which decreases the velocity difference between the two groups of particles is clearly demonstrated. The difference in temperature as compared with the collisionless case is quite negligible.

I. Phosphorescence and the true lifetime of triplet states in fluid solutions. II. Why is condensed oxygen blue?

I. PHOSPHORESCENCE AND THE TRUE LIFETIME OF TRIPLET STATES IN FLUID SOLUTIONS

Phosphorescence has been observed in a highly purified fluid solution of naphthalene in 3-methylpentane (3-MP). The phosphorescence lifetime of C₁₀H₈ in 3-MP at -45 °C was found to be 0.49 ± 0.07 sec, while that of C₁₀D₈ under identical conditions is 0.64 ± 0.07 sec. At this temperature 3-MP has the same viscosity (0.65 centipoise) as that of benzene at room temperature. It is believed that even these long lifetimes are dominated by impurity quenching mechanisms. Therefore it seems that the radiationless decay times of the lowest triplet states of simple aromatic hydrocarbons in liquid solutions are sensibly the same as those in the solid phase. A slight dependence of the phosphorescence lifetime on solvent viscosity was observed in the temperature region, -60° to -18°C. This has been attributed to the diffusion-controlled quenching of the triplet state by residual impurity, perhaps oxygen. Bimolecular depopulation of the triplet state was found to be of major importance over a large part of the triplet decay.

The lifetime of triplet C₁₀H₈ at room temperature was also measured in highly purified benzene by means of both phosphorescence and triplet-triplet absorption. The lifetime was estimated to be at least ten times shorter than that in 3-MP. This is believed to be due not only to residual impurities in the solvent but also to small amounts of impurities produced through unavoidable irradiation by the excitation source. In agreement with this idea, lifetime shortening caused by intense flashes of light is readily observed. This latter result suggests that experiments employing flash lamp techniques are not suitable for these kinds of studies.

The theory of radiationless transitions, based on Robinson's theory, is briefly outlined. A simple theoretical model which is derived from Fano's autoionization gives identical result.

Il. WHY IS CONDENSED OXYGEN BLUE?

The blue color of oxygen is mostly derived from double transitions. This paper presents a theoretical calculation of the intensity of the double transition (a ¹Δ_g) (a ¹Δ_g)←(X ³Σ_g^-) (X ³Σ_g^-), using a model based on a pair of oxygen molecules at a fixed separation of 3.81 Å. The intensity enhancement is assumed to be derived from the mixing (a ¹Δ_g) (a ¹Δ_g) _~~~ (X ³Σ_g^-) (X ³Σ_u^-) and (a ¹Δ_g) (¹Δ_u) _~~~ (X ³Σ_g^-) (X ³Σ_g^-). Matrix elements for these interactions are calculated using a π-electron approximation for the pair system. Good molecular wavefunctions are used for all but the perturbing (B ³Σ_u^-) state, which is approximated in terms of ground state orbitals. The largest contribution to the matrix elements arises from large intramolecular terms multiplied by intermolecular overlap integrals. The strength of interaction depends not only on the intermolecular separation of the two oxygen molecules, but also as expected on the relative orientation. Matrix elements are calculated for different orientations, and the angular dependence is fit to an analytical expression. The theory therefore not only predicts an intensity dependence on density but also one on phase at constant density. Agreement between theory and available experimental results is satisfactory considering the nature of the approximation, and indicates the essential validity of the overall approach to this interesting intensity enhancement problem.

Observational constraints on the unified dark matter and dark energy model based on the quark bag model

In this work we investigate if a small fraction of quarks and gluons, which escaped hadronization and survived as a uniformly spread perfect fluid, can play the role of both dark matter and dark energy. This fluid, as developed in [1], is characterized by two main parameters: beta, related to the amount of quarks and gluons which act as dark matter; and gamma, acting as the cosmological constant. We explore the feasibility of this model at cosmological scales using data from type Ia Supernovae (SNeIa), Long Gamma-Ray Bursts (LGRB) and direct observational Hubble data. We find that: (i) in general, beta cannot be constrained by SNeIa data nor by LGRB or H(z) data; (ii) gamma can be constrained quite well by all three data sets, contributing with approximate to 78% to the energy matter content; (iii) when a strong prior on (only) baryonic matter is assumed, the two parameters of the model are constrained successfully. (C) 2014 The Authors. Published by Elsevier B.V.