Supercritical Ones Research Articles

Near-critical behavior of the Zhong-Zhang model.

The Zhong-Zhang (ZZ) model is a one-degree-of-freedom dynamical system describing the motion of an insulating plate of length d floating on the upper surface of a convecting fluid, with locking at the boundaries. In the absence of noise, the system away from the boundaries is described by linear differential equationswith a delay time τ. The d,τ plane consists of two domains separated by a critical curve. For asymptotically long times, subcritical orbits approach a nontrivial periodic attractor, while the supercritical ones tend to a stationary state at the origin. We investigate near-critical behavior using a modified fourth-order Runge-Kutta integration scheme. We then construct a piecewise analytic decomposition of the periodic attractor, which makes possible a far higher level of accuracy. Our results provide solid evidence for an asymptotic power-law approach to criticality of several observables. The power laws are fed back to determine the piecewise-analytic structure deep into the near-critical regime. In an Appendix, we explore the effect of introducing noise using modified order-3/2 Kloeden-Platen-Schurz stochastic integration, following several observable quantities through the near-critical parameter domain.

СТАТИЧЕСКИЙ РАСЧЕТ ОДНОПРОЛЕТНОЙ БАЛКИ ПЕРЕМЕННОЙ ЖЕСТКОСТИ МЕТОДОМ ЗАДАННЫХ ДЕФОРМАЦИЙ

This article presents a method for static calculation of a single-span beam of variable stiffness, based on the method of specified deformations, in which one of the parameters of the curved axis is used as an external influence, for example, the angle of rotation or curvature in one of the sections, and the equation of the curved axis is solved relative to the load value. When solving problems related to physical nonlinearity, it will be necessary to organize an iterative process, and the use of the method under consideration allows organizing a stable iterative process, which can be used to solve the problems of calculating bending building structures at all stages of their work, including supercritical ones. Based on the presented methodology, an algorithm and a computer program for the static calculation of a singlespan beam of variable stiffness have been developed. The angle of rotation in the reference section is set as the acting parameter on the beam. The results of the calculation of the beam are the magnitude of the load perceived by the beam, deflections, curvatures, stiffness in sections along the entire length of the beam. To test the developed method, three series of single-span hinged beams were calculated, loaded with one concentrated force in the middle of the span, having sections along the length with different bending stiffness of the sections. Analytical and graphical results of the performed calculation are presented.

The initial magnetic criticality of pre-stellar cores

ABSTRACT Direct observational measurements of the magnetic field strength in pre-stellar cores typically find supercritical mass-to-flux ratios, suggesting that the magnetic field is insufficient to prevent gravitational collapse. These measurements suffer from significant uncertainties; an alternative approach is to utilize the sensitivity of pre-stellar chemistry to the evolutionary history, and indirectly constrain the degree of magnetic support. We combine non-ideal magnetohydrodynamic simulations of pre-stellar cores with time-dependent chemistry and radiative transfer modelling, producing synthetic observations of the model cores in several commonly observed molecular lines. We find that molecules strongly affected by freeze-out, such as CS and HCN, typically have much lower line intensities in magnetically subcritical models compared to supercritical ones, due to the longer collapse time-scales. Subcritical models also produce much narrower lines for all species investigated. Accounting for a range of core properties, ages, and viewing angles, we find that supercritical models are unable to reproduce the distribution of CS and N2H+ line strengths and widths seen in an observational sample, whereas subcritical models are in good agreement with the available data. This suggests that despite presently having supercritical mass-to-flux ratios, pre-stellar cores form as magnetically subcritical objects.

Dynamics of interfacial gravity–capillary waves in three-dimensional fluids of great depth

This paper proposes a new isotropic bidirectional model for weakly nonlinear gravity–capillary waves propagating between two incompressible, inviscid, and immiscible fluids of different densities. The newly developed equation is a generalization of the celebrated two-dimensional Benjamin equation. It is derived based on the nonlocal formulation of water wave (i.e., the Ablowitz–Fokas–Musslimani formulation) and computed with the modified exponential time-differencing method. It is found that horizontally two-dimensional, fully localized traveling waves (known as lumps) exist in the model equation, and plane solitary waves are unstable subject to long transverse perturbations, which evolve into groups of lumps in the long-term dynamics. When considering topographical disturbances on the rigid upper boundary, the nonlinear effect becomes important when a uniform flow passes beneath a locally confined topography with a near-critical speed, and the phenomenon of time-periodic shedding of lumps occurs. Unlike the near-critical situation, the subcritical flows usually generate steady elevation waves, while the supercritical ones produce a V-shaped pattern of wake lines. Furthermore, it is shown that a uniformly accelerated motion can also generate lumps provided that the flow stays in the transcritical regime for a considerably long time.

Movement of external load over free surface of fluid in the ice channel

The solution of a steady three-dimensional problem for the wave disturbances induced by a local pressure distribution moving with uniform speed on open water lead between two semi-infinite floating ice sheets (ice channel) is presented. This external load simulates an air-cushion vehicle (ACV). The problem is formulated within the linear hydroelastic theory. The fluid is assumed to be inviscid and incompressible and its motion is potential. The ice sheets are treated as viscoelastic thin plates. The solution of this problem is constructed using the Fourier transforms and the Wiener-Hopf technique. The displacements of free surface and ice sheets are determined as well as strains in ice and wave resistance acting on ACV at various speeds of its movement: subcritical and supercritical ones relative to the minimum phase velocity of flexural-gravity waves (FGW) in fluid under an ice cover. Special attention is paid to the characteristics of edge waves. It is shown that for some values of load speed, ice thickness and external pressure, ice fracture near the edge is possible.

Targeted Energy Transfers for Suppressing Regenerative Machine Tool Vibrations

We study the dynamics of targeted energy transfers in suppressing chatter instability in a single-degree-of-freedom (SDOF) machine tool system. The nonlinear regenerative (time-delayed) cutting force is a main source of machine tool vibrations (chatter). We introduce an ungrounded nonlinear energy sink (NES) coupled to the tool, by which energy transfers from the tool to the NES and efficient dissipation can be realized during chatter. Studying variations of a transition curve with respect to the NES parameters, we analytically show that the location of the Hopf bifurcation point is influenced only by the NES mass and damping coefficient. We demonstrate that application of a well-designed NES renders the subcritical limit cycle oscillations (LCOs) into supercritical ones, followed by Neimark–Sacker and saddle-node bifurcations, which help to increase the stability margin in machining. Numerical and asymptotic bifurcation analyses are performed and three suppression mechanisms are identified. The asymptotic stability analysis is performed to study the domains of attraction for these suppression mechanisms which exhibit good agreement with the bifurcations sets obtained from the numerical continuation methods. The results will help to design nonlinear energy sinks for passive control of regenerative instabilities in machining.

Experimental investigation of inclination effect on subcritical and supercritical water flows heat transfer in an internally ribbed tube

The effect of various inclination angles on heat transfer of water at subcritical and supercritical operating pressures is investigated experimentally. The test section was a SA213T12 steel six-headed internally ribbed tube with minimum inner diameter of 19.5 mm. The operating test pressures were 15, 21.5, 22.5, 25 and 28 MPa, the mass flux was 800 kg/m2 s and the heat flux was 400 kW/m2. To keep the mass flux to heat flux ratio equal to 2 kg/kJ. These operating conditions covered subcritical, near critical and supercritical water flows and also refers to low mass flux conditions. The inclination angles were 5, 20, 30, 45 and 90 (vertical) degrees respecting to horizontal plane. The heat flux was kept constant along the test tube by controlling of electric heating. As a result the inner wall temperature and convective heat transfer coefficient variations with respect to heated length and bulk enthalpy of fluid were considered in order to study the heat transfer characteristics of various flows at different inclinations. The corresponding correlation for heat transfer coefficient was developed which is applicable for wide range of inclination angles. The heat transfer enhancement was obvious for inclination angles other than 90°, however, this effect was more obvious in 5° and 20° in some operating conditions. It was also concluded that the effect of inclination on heat transfer of water was more considerable in subcritical flow conditions than supercritical ones. Also, it was observed that angle of 20° seems to be the best for subcritical flows from heat transfer point of view, but for supercritical flows 5 or 45 seem to be more advantageous. These differences could be related to different heat transfer mechanisms of subcritical and supercritical flows.

Thermomechanical effects in supercritical binary fluids

Thermomechanical effects, i.e., Piston effect (PE), Soret effect (SE), and Dufour effect (DE), occur in supercritical binary fluids when subjected to boundary thermal perturbation due to the diverging compressibility, vanishing thermal diffusivity and mass diffusion. We numerically study those effects in a 1-D slab with a size of 10mm by solving a complete set of governing equations, which are derived considering the supercritical hydrodynamics, mass transfer and energy conservation simultaneously. The characteristics of these thermomechanical effects in the supercritical binary fluid and liquid binary fluid on different timescales (acoustic and diffusion timescales) are clarified, respectively. Because of the existence of the strong PE in the supercritical binary fluid, the fluid bulk is heated up uniformly, and the SE appears on both sides simultaneously. The direction of mass diffusion is determined by the relative magnitude between concentration gradient and temperature gradient, i.e., gradient ratio γ, and there is a balance gradient ratio γb in each specific binary fluid under a certain condition. The DE is verified by comparing the results of binary fluid and the corresponding pseudo-pure fluid with the same thermo-physical properties. The DE is considerable in supercritical binary fluid, but negligibly small in liquid ethanol/water binary fluid because of the weak SE. These thermomechanical effects in different binary fluids (including supercritical, liquid and gaseous ones) mainly differ in the relative magnitudes and the traveling speed of thermoacoustic wave.

Cycle configuration analysis and techno-economic sensitivity of biomass externally fired gas turbine with bottoming ORC

This paper focuses on the energy analysis of a combined cycle composed by a topping 1.3MW Externally Fired Gas Turbine (EFGT) with direct combustion of biomass and a bottoming Organic Rankine Cycle (ORC). A non recuperative scheme is assumed for the EFGT in order to avoid the costs of the recuperator. This scheme presents lower conversion efficiency in comparison to a recuperative one, however the heat available for the bottoming cycle is at a higher temperature (about 400°C). In the present work, evaporation pressure and superheating temperature of ORC cycle are ranged in order to examine different bottoming cycles, including supercritical ones. Different organic fluids are investigated, such as siloxanes and toluene, aiming to analyze how the fluid choice influences both the plant performance and important features for the ORC turbine design. On the basis of the results of the thermodynamic simulation, a thermo-economic assessment is proposed, to investigate the profitability of the bottoming ORC in comparison to only topping EFGT, and the most influencing techno-economic factors that influence the selection of the optimal cycle. In order to propose real case studies, the Italian bioenergy subsidy framework is assumed, and the sensitivity assessment includes the options of only electricity and CHP, at different biomass cost, thermal energy demand and heat selling price values.

Investigation of not fully stable fluids by the method of controlled pulse heating. 1. Experimental approach

We are developing an experimental approach to investigation of the properties of not fully stable fluids based on the procedure of controlled pulse heating of a thin wire probe using pulse lengths from 1 to 10ms. We shall use the term “not fully stable” to refer to fluids that lose their stability in the course of heating (superheated liquids and thermally unstable ones), as well as to initially unstable systems (nanofluids and supercritical ones). In this paper, the peculiarities of the technique and the device operation are discussed. The applicability of the approach is illustrated by demonstration experiments with not fully stable fluids using the constant heating power mode.

Viscous flows in corner regions: Singularities and hidden eigensolutions

AbstractNumerical issues arising in computations of viscous flows in corners formed by a liquid–fluid free surface and a solid boundary are considered. It is shown that on the solid a Dirichlet boundary condition, which removes multivaluedness of velocity in the ‘moving contact‐line problem’ and gives rise to a logarithmic singularity of pressure, requires a certain modification of the standard finite‐element method. This modification appears to be insufficient above a certain critical value of the corner angle where the numerical solution becomes mesh‐dependent. As shown, this is due to an eigensolution, which exists for all angles and becomes dominant for the supercritical ones. A method of incorporating the eigensolution into the numerical method is described that makes numerical results mesh‐independent again. Some implications of the unavoidable finiteness of the mesh size in practical applications of the finite‐element method in the context of the present problem are discussed. Copyright © 2009 John Wiley & Sons, Ltd.

Complete and Systematic Simulation Tools<newline/> for Frequency Divider Design

In this study, a two-stage simulation method is presented for the efficient design of frequency dividers using harmonic balance. The first stage uses a modified conversion matrix approach to select the subharmonic loads of the active element enabling the frequency division by a given order N. The second stage makes use of an auxiliary generator to obtain and modify the sub-harmonic-power curve versus the input power or input frequency. Systematic simulation tools are used to eliminate common hysteresis phenomena, which require additional constraints to minimize the disturbance of the original frequency-division bands and output power. A harmonic-balance technique to distinguish between subcritical flip bifurcations, associated with hystereses, and supercritical ones is presented, to our knowledge, for the first time. A technique is also derived to transform subcritical bifurcations into supercritical ones. The techniques have been successfully applied to a frequency divider by 2 at 630 MHz.

C201 MRA-POD解析による開水路水面波紋の挙動評価

In this study, water surface fluctuations along the lateral direction of an open-channel flow were examined by using the multi-resolution approximation (MRA) and proper orthogonal decomposition (POD). The water surface fluctuations were measured by supersonic wave displacement sensors. In the experimental conditions, we kept the Reynolds number a constant, and systematically changed the Froude number from sub-critical flows to supercritical ones to examine differences in the water surface fluctuation characteristics with respect to the Froude number. The measurement time-series of the water surface fluctuations showed that there precisely existed high and low frequency signals. In the MRA and POD analysis of the fluctuations, it turned out that the predominant mode of the water surface fluctuations along the lateral direction was approximated to a constant spatial distribution. Therefore, the predominant surface fluctuation seemed to propagate two-dimensionally in the longitudinal direction.

Supercritical density relaxation as a new approach of droplet vaporization

The isobaric density relaxation of a cold, slightly supercritical, fluid package in a hotter atmosphere of this same fluid at a near critical pressure is studied in this paper. We solve the Navier–Stokes equations describing the evolution of an initial density inhomogeneity in a supercritical van der Waals fluid. These numerical simulations allow exploring the whole range of surrounding conditions, including the slightly supercritical ones. Strong discrepancies are found from the classical decay of the squared diameter of the droplet observed in clearly subcritical conditions. We present a quasisteady analysis that allows neglecting unsteady terms in the equations that describe the problem, provided that the moving reference frame is well defined. The strong density gradient that follows the “droplet” as well as the time dependant mass flow rate location are considered with a particular attention. The obtained solutions of the equations match with the numerical results and generalize to near critical conditions the classical subcritical quasisteady analysis of droplet vaporization performed in the combustion science field.

Titanium Dissolution-Passivation in Highly Chloridic and Oxygenated Aqueous Solutions: Reaction Mechanism Extended to Supercritical Water Conditions

The principal objective of this paper is to show that we developed an experimental setup and a dissolution-passivation monitoring technique for use in super critical water oxidation (SCWO) conditions MPa). The principal barrier to this technology development is the corrosion of the reactor materials. High corrosion rates were experienced in industrial plants. A major goal is to develop effective tools to determine and control the electrochemical and corrosion parameters. Until now, electrochemical data concerning metallic materials submitted to aqueous solutions at pressures and temperatures beyond the critical point are scarce. This research, in the context of organic wastes SCWO, first proposes, for both sub and supercritical conditions, technical solutions for an electrochemical cell able to give access to quantitative electrochemical information in aggressive solutions and chloride ions content of 1 g/L). Its second purpose is to obtain information on a titanium alloy (T60 grade) behavior in such conditions. The present study leads to a model establishing a reaction mechanism, which operates under normal conditions of pressure and temperature and can be extended to supercritical ones. The limits of use of this material as a plant reactor material for supercritical water oxidation (SCWO) are evaluated. © 2004 The Electrochemical Society. All rights reserved.

17O Chemical shift and spin-lattice relaxation measurements of water in liquid and supercritical states by using high-resolution multinuclear NMR

Special high-temperature and -pressure multinuclear NMR equipments were constructed, and used for the measurements of 17O-NMR chemical shift and spin-lattice relaxation time ( T 1) in water over the range from liquid to supercritical (SC) states. The chemical shift could be interpreted in terms of the extent of hydrogen bonding. Although the cleavage of hydrogen bonding of water proceeds continuously from liquid to SC conditions, the hydrogen bonding was found to still remain even under SC conditions. It was confirmed that the spin-lattice relaxation of 17O is mainly controlled by the quadrupole interaction and the T 1 values of 17O are related with the values of the molecular reorientational correlation time ( τ c) over the range from liquid to SC states. It was found that the τ c values decrease drastically with increasing temperature and decreasing density in lower temperature and higher density regions (25⩽ T<250 °C and 1.1⩾ ρ>0.6 g/cm 3) and are close to the τ c corresponding to a free-rotor in sub-critical and SC ones (250⩽ T⩽425 °C and 0.6⩾ ρ⩾0.1 g/cm 3). It was considered from this result that a decrease of viscosity with increasing temperature and decreasing density leads to acceleration of molecular rotation in lower temperature and higher density regions, and on the other hand the rotational motions of water in sub-critical and SC regions are comparable to those of monometric water molecule. Accordingly, it was concluded that the principal contributions to the molecular rotational motions of water are the variation of the intermolecular hydrogen bonding interactions in lower temperature and higher density regions, and are that of the dipole moment of a water molecule in sub-critical and SC regions, respectively.

Structural Disorder in Supercritical Aqueous Ionic Solutions as seen by MD-EXAFS

Because of their inherent structural disorder, liquids are challenging systems for structural studies. This is even more so for high temperature/high pressure fluids such as supercritical (SC) ones. By combining Molecular Dynamics simulations with Extended X-ray Absorption Fine Structure spectroscopy, we have recently elucidated the structure of the Br m hydration shell in low concentrated solutions from ambient to supercritical conditions [1]. The densities explored correspond to pressures up to 450 bar. In this paper, we show that this combination of techniques has been an essential tool to correctly interpret the experimental signals. Indeed, the occurrence of drastic different local environment of the ions in solutions, typical of liquids and magnified in supercritical conditions, can be seriously misleading if not taken into account.

Supercritical-fluid cell with device of variable optical path length giving fringe-free terahertz spectra

An optical cell suitable for supercritical fluids was constructed for measurements of far infrared absorption spectra with terahertz radiation as a light source. It was designed to withstand temperature up to 400 K and pressure up to 15 MPa. The cell has two characteristic devices; one is diamond windows set in the Brewster angle to the incident far infrared light and the other is a variable optical path length from 30 μm to 20 mm under high pressure conditions. Using the cell, fringe-free spectra of CHF3 ranging from low-density gaseous states to high-density supercritical ones were measured in a low-energy region of 10–100 cm−1.

Effect of short- and long-range forces on the structure of water: temperature and density dependence

The individual effects of short-range and long-range forces on the structure of water, a prerequisite for developing a perturbation theory, are assessed using a decomposition of realistic water—water potential models into trial potentials. Computer simulations for one typical liquid density and a number of temperatures ranging from the freezing temperature up to supercritical ones, and for several densities on a supercritical isotherm were performed. The trial potentials were constructed from the ST2 and TIP4P potentials and it is shown that for both potentials the results are practically identical. It is shown that (i) regardless of the thermo-dynamic conditions and potential models used, the structure of water and the mutual orientational arrangement of water molecules, given by a set of site—site correlation functions, are determined nearly exclusively only by the short range forces, and (ii) for high density states the effect of the short range electrostatic part of the intermolecular potential on the spatial arrangement of the water molecules rapidly decreases with increasing temperature but does not become negligible.

Star Formation in Magnetic Clouds

This paper reexamines the widely accepted assumption that low-mass stars form mainly in magnetically subcritical cloud cores and high-mass stars form in magnetically supercritical ones. Cloud cores, as well as molecular clouds, are shown to be magnetically supercritical because although the cores are generally observed as portions of a molecular cloud having considerably higher column densities than their surroundings, magnetically subcritical condensations embedded in a cloud are not very likely to have higher column densities than their surroundings, and because it is difficult to maintain the nonthermal velocity dispersions widely observed in the cores for a significant fraction of their lifetimes if the cores are magnetically subcritical. In a magnetically supercritical condensation, which we call a core, for the pressure Ps of the surrounding medium there is a critical value Pcr above which the core cannot be in magnetohydrostatic equilibrium and collapses; Pcr depends sharply on the core mass, on the effective sound velocity in the core, which includes the effect of turbulence, and on the effective coefficient aeff for the gravity diluted by magnetic force. The cloud core begins dynamical contraction when Pcr has decreased below Ps by some mechanism. Dissipation of turbulence is the most important process in reducing Pcr. Therefore, in most cases, the timescale of star formation in each core is the dissipation time of turbulence, which is several times the free-fall time of the core. For the cores of magnetic flux Φ very close to the critical flux Φcr or with small aeff ≈ 1 - (Φ/Φcr)2, Pcr will not decrease below Ps even when turbulence has completely dissipated; this will happen only in very low mass cores because of the sharp mass dependence of Pcr. Such cores begin dynamical contraction after aeff has increased somewhat because of magnetic flux loss from their central parts by ambipolar diffusion; for this to happen, only a slight loss of magnetic flux is needed because of sharp dependence of Pcr on Φ at Φ ≈ Φcr. The timescale of star formation in this case is not much different from the dissipation time of the turbulence, though the probability that the cores have Φ ≈ Φcr must be low. It is shown to be implausible that cloud cores form from magnetically subcritical condensations via ambipolar diffusion.