An air sparging CFD model for heap bioleaching of chalcocite

A computational fluid dynamics (CFD) solver CFX4.4 is used to implement a steady state model of heap bioleaching of chalcocite, which includes air sparging (forced aeration) based on a previous model entirely under natural convection. The model assumes the oxygen supply limits the reaction rate. A parameter analysis is performed which shows that the factors important to copper leaching are liquid and air flow rates, permeability and fraction of pyrite to chalcocite leached (FPY). The ability to control which parts of the bed received the highest extraction as a function of the liquid and air flow rates was established. Sparging is found to increase the oxygen concentration throughout the heap compared to the circumstance with no sparging (natural convection), and consequently improves the copper extraction significantly. The results show that sparging does not provide any better copper extraction for very high heap permeabilities. The arrangement and spacing of air sparging inlets is analysed in regard to the existence of oxygen starved regions between the inlets.     

Some features of the deceleration of an inhomogeneous ball in the air

A model of the deceleration of an inhomogeneous ball acted upon by the drag of the air is discussed, taking into account the interaction of the translational and rotational motions. The problem is reduced to analysing a non-linear second-order dynamical system. The steady motions of the ball, including self-oscillatory and self-rotation motions, are obtained. The bifurcation values of the parameters defining these motions are determined. The corresponding phase portraits are constructed and an interesting interpretation of them is given.     

Bifurcation analysis of the Gierer–Meinhardt system with a saturation in the activator production

The reaction–diffusion Gierer–Meinhardt system with a saturation in the activator production is considered. Stability of the unique positive constant steady state solution is analysed, and associated Hopf bifurcations and steady state bifurcations are obtained. A global bifurcation diagram of non-trivial periodic orbits and steady state solutions with respect to key system parameters is obtained, which improves the understanding of dynamics of Gierer–Meinhardt system with a saturation in different parameter regimes.     

Generative mechanism of air column oscillations in a Hartmann-Sprenger tube excited by an air jet issuing from a convergent nozzle

Summary In this paper, a theory of the origin of the air column oscillations in the Hartmann-Sprenger (HS) tube excited by an air jet issuing from a convergent nozzle is presented.For the analysis, the following basic configuration is assumed. The air jet issuing from a nozzle forms a steady stagnation flow between the nozzle and the open end of the tube, and the air column in the tube remains at rest. A massless hypothetical membrane is assumed at the open end of the tube. When a sinusoidal vibration of the membrane with very small amplitude is assumed, its radiation impedance is obtained by calculating the reactive forces of the flow field acting on the membrane on each side. If the real part of the radiation impedance is negative, the field is unstable, and the air column in the HS tube will be excited to oscillation.The analytical results can explain well the experimental observations.

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Zusammenfassung Im vorliegenden Bericht wird der Schwingungsmechanismus der Luftsäule im Hartmann-Sprenger Rohr betrachtet für den Fall, dass diese durch einen Gasstrahl von einer konvergenten Düse angeregt wird. Für die Analysis wird die folgende Fundamentalkonfiguration angenommen: Der Gasstrahl der Düse bildet die stationäre Stauströmung zwischen der Düse und der Mündung des HS Rohres, und die Luftsäule im HS Rohr ist in Ruhe. An der Rohrmündung wird eine hypothetische Membrane angenommen. Wenn diese Membrane mit einer kleinen Amplitude sinusförmig schwingt, dann ist die Strahlungsimpedanz dieser Membrane durch die Gegenkräfte auf die Membrane gegeben. Wenn der Realteil der Strahlungsimpedanz negativ ist, ist das System selbsterregend und die Luftsäuleschwingung im HS Rohr wird erzeugt.Das analytische Resultat stimmt mit dem experimentellen gut überein.

     

On the weak discontinuity surfaces and tapes of equation systems in fluid mechanics

The weak discontinuity surfaces for a system of quasi-linear differential equations of higher order are developed. The classification of equation systems in fluid mechanics is based on the propagative weak discontinuity surfaces. Types of equations for different flow models are discussed. The conclusion is as follows:(a) For incompressible nonviscous flow, incompressible viscous flow and compressible viscous flow, the types of equations are all parabolic in the unsteady case and elliptic in the steady case.(b) For compressible nonviscous flow, the type of equations is hyperbolic in the unsteady case or steady supersonic case, and the type is elliptic in the steady subsonic case.     

泄爆诱导的湍流、旋涡和外部爆炸

基于k-ε湍流模型和Eddy-dissipation燃烧模型,采用同位网格SIMPLE算法,对充满甲烷-氧气预混气的带导管柱形泄爆容器向空气中泄爆的情形进行了数值模拟．根据计算结果,分析了泄爆后外流场中可燃云团、火焰和压力的变化过程．结果表明,外部爆炸是因射流火焰点燃高压区中的可燃云团,从而引起的剧烈湍流燃烧所致．同时还讨论了外流场湍流和涡量的分布特征．射流火焰进入外部可燃云团后,湍流主要分布在平均动能梯度较大的区域,而不在火焰阵面上．涡量分布主要受斜压效应的影响,在压力和密度梯度斜交区域,其值较大．     

Finite volume approximation of degenerate two‐phase flow model with unlimited air mobility

Models of two‐phase flows in porous media, used in petroleum engineering, lead to a coupled system of two equations, one elliptic and the other degenerate parabolic, with two unknowns: the saturation and the pressure. In view of applications in hydrogeology, we construct a robust finite volume scheme allowing for convergent simulations, as the ratio μ of air/liquid mobility goes to infinity. This scheme is shown to satisfy a priori estimates (the saturation is shown to remain in a fixed interval, and a discrete L2(0,T;H1(Ω)) estimate is proved for both the pressure and a function of the saturation), which are sufficient to derive the convergence of a subsequence to a weak solution of the continuous equations, as the size of the discretization tends to zero. We then show that the scheme converges to a two‐phase flow model whose limit, as the mobility of the air phase tends to infinity, is the “quasi‐Richards equation” (Eymard et al., Convergence of two phase flow to Richards model, F. Benkhaldoun, editor, Finite Volumes for Complex Applications IV, ISTE, London, 2005; Eymard et al., Discrete Cont Dynam Syst, 5 (2012) 93–113), which remains available even if the gas phase is not connected with the atmospheric pressure. Numerical examples, which show that the scheme remains robust for high values of μ, are finally given. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2013     

Global properties for virus dynamics model with Beddington–DeAngelis functional response

This paper investigates the global stability of virus dynamics model with Beddington–DeAngelis infection rate. By constructing Lyapunov functions, the global properties have been analysed. If the basic reproductive ratio of the virus is less than or equal to one, the uninfected steady state is globally asymptotically stable. If the basic reproductive ratio of the virus is more than one, the infected steady state is globally asymptotically stable. The conditions imply that the steady states are always globally asymptotically stable for Holling type II functional response or for a saturation response.     

Kantorovich-Bernstein polynomials

A gap between saturation and direct-converse theorems for Kantoro-vich-Bernstein polynomials will be closed for a steady rate of convergence. The present theorems unify the above-mentioned results. Furthermore, it is shown that for steady rates our converse results are an improvement on both weak-type converse theorems and strong-weak-type converse theorems for the Kantorovich-Bernstein polynomials.Communicated by George G. Lorentz.AMS classification: 41A27, 41A36, 41A40.     

Attenuation and Diffraction of Bending Waves at Gaps in Fluid Loaded Plates

The scattering of a bending wave by a finite number of parallelrectilinear gaps in an infinite fluid-loaded plate is discussed.For the purpose of analysis, the widths of the gaps are assumedto be infinitesimal, but there is no physical contact betweenabutting edges of neighbouring sections of the plate. A sectionedge may be restrained by resilient supports or loadings, eitherindividually or jointly with the neighbouring edge. The theorydetermines the attenuation of the bending wave by the gaps andthe sound radiated into the ambient fluid during the interaction.Specific results are given for a steel plate which has a singlegap in air and in water, such that either (1) the abutting edgesare free to vibrate independently, (2) both edges are clamped,or (3) one edge is clamped and the other free. In each of thesecases the coupling between the two halves of the plate is providedsolely by the fluid loading: the bending wave would be totallyreflected at the gap in vacuo. The results are relevant to thecontrol and suppression of structure-borne sound     

Dynamics of Nonconstant Steady States of the Sel’kov Model with Saturation Effect

In this paper, we deal with Sel’kov model with saturation law which has been applied to numerous problems in chemistry and biology. We will study the stability of the unique constant steady state, existence and nonexistence of nonconstant steady states of such models. In particular, we prove that Turing pattern may occur when the saturation coefficient is small but will not occur when the coefficient becomes large. Therefore for a Sel’kov model with saturation law, it is the saturation law that determines the formation of spatial patterns.

     

Finite element analysis of flood discharge atomization based on water–air two-phase flow

Flood discharge atomization is a phenomenon of water fog diffusion caused by the discharge of water from a spillway structure, which brings strong wind and heavy rainfall. These unnatural winds and rainfall are harmful for the safe operation of hydropower stations with high water heads. Compared to the method of prototype observations, physical models and mathematical models, which are semi-theoretical and semi-empirical, numerical simulation methods have the advantage of being not limited by a similar scale and are more economical. A finite element model is presented to simulate flood discharge atomization based on water–air two-phase flow in this paper. Equations governing flood discharge atomization are composed of partial differential equations of mass and momentum conservation laws with unknowns for pressure, velocity and the water concentration. The finite element method is used to solve the governing equations by adopting appropriate solution strategies to increase the convergence and numerical stability. Then, the finite element model is applied to a practical project, the Shuibuya hydropower station, which experienced a flood discharge in 2016. Simulation results show that the proposed model can simulate flood discharge atomization with efficient convergence and numerical stability in three dimensions, and good agreement was observed between numerical simulations and prototype observational data. Based on the simulation results, the mechanism of flood discharge atomization was analyzed.     

On the use of equations of the Fuchs class to calculate seepage from channels and irrigation ditches

Several schemes for seepage flows from the channels and ditches of irrigation systems through a layer of soil underlaid by a highly permeable artesian water-bearing table or an impermeable foundation are considered within the framework of the theory of the plane steady seepage of an incompressible liquid oblying to Darcy's law. Mixed multiparameter boundary value problems of the theory of analytic functions are formulated for their investigation, which are solved using Polubarinova–Kochina's method and integration of differential equations of the Fuchs class that are characteristic in problems of subterranean hydromechanics. On the basis of these models, algorithms are developed for calculating the dimensions of the saturation zone in cases when, in the seepage of water from channels and irrigation ditches, there is a need to estimate the combined effect on the pattern of motion of such important factors as the backwater from the underlying artesian water table or confining bed, the soil capillarity and the evaporation of ground waters from the free surface. The results of the calculations for all the flow schemes are compared for identical seepage characteristics.     

Detection of air pollutants with a tunable CO2 laser

Following a method described by Kreuzeret al., we have et up an improved spectroscopic system to detect trace pollutants in ambient air. A CO₂ laser is tuned to various transitions coincident with absorption lines or bands of pollutant gases. The laser beam is amplitude modulated at the resonant frequency of an acoustical cavity which serves as sample chamber. The pressure waves detected by sensitive microphones placed inside the cavity yield a signal proportional to the energy taken up by the absorbing gases. So far sensitivity limits of a few ppb have been achieved for some typical pollutants, together with high rejection ratios against interference among these gases and against water and CO₂.     

A note on a diffusive predator-prey model and its steady-state system

In this note, a diffusive predator-prey model subject to the homogeneous Neumann bound- ary condition is investigated and some qualitative analysis of solutions to this reaction-diffusion system and its corresponding steady-state problem is presented. In particular, by use of a Lyapunov function, the global stability of the constant positive steady state is discussed. For the associated steady state problem, a priori estimates for positive steady states are derived and some non-existence results for non-constant positive steady states are also established when one of the diffusion rates is large enough. Consequently, our results extend and complement the existing ones on this model.     

The role of sonic shocks between two- and three-phase states in porous media

Flowof threefluids in porousmedia is governed by a systemof two conservation laws. Shock solutions are described by curves in state space, which is the saturation triangle of the fluids. We study a certain bifurcation locus of these curves, which is relevant for certain injection problems. Such structure arises, for instance, when water and gas are injected in a mature reservoir either to dislodge oil or to sequestrate CO₂. The proof takes advantage of a certain wave curve to ensure that the waves in the flow are a rarefaction preceded by a shock, which is in turn preceded by a constant two-phase state (i.e., it lies at the boundary of the saturation triangle). For convex permeability models of Corey type, the analysis reveals further details, such as the number of possible two-phase states that correspond to the above mentioned shock, whatever the left state of the latter is within the saturation triangle.     

A single server queue with cyclically indexed arrival and service rates

In this paper we consider a queueing model that results from at least two apparently unrelated areas. One motivation to study a system of this type results from a test case of a computer simulation factor screening technique calledfrequency domain methodology. A second motivation comes from manufacturing, where due to cyclic scheduling of upstream machines, the arrival process to downstream machines is periodic. The model is a single server queue with FIFO service discipline and exponential interarrival and service times where the arrival and/or service rates are deterministic cyclic functions of the customer sequence number. We provide steady state results for the mean number in the system for the model with cyclic arrival and fixed service rates and for the model with fixed arrival and cyclic service rates. For the model with both cyclic arrival and service rates, upper and lower bounds are developed for the steady state mean waiting time in the system. Throughout the paper various implications and/or insights derived from the results of this study are discussed for frequency domain methodology.The authors acknowledge the financial support of the CBA/GSB Faculty Research Committee of the College of Business Administration, The University of Texas at Austin.     

A dynamic evaluation framework for ambient air pollution monitoring

Accurate real-time prediction of urban air quality is one of the most important problems in control and improve ambient air condition globally. Therefore, the modeling and applications of air pollutant forecasting and evaluation has attracted the attention of researchers in recent years. Based on the method of fuzzy mathematical synthetic evaluation, this paper built a dynamic evaluation model for the purpose of mastering the future air quality immediately. A newly proposed computational intelligence optimization algorithm is improved to optimize the least square support vector machine, which can generate rolling forecasts of six air pollutants concentration. The information of future air quality status is built by the fuzzy synthetic assessment model based on entropy weighing method. The results and analysis of air quality monitoring show that accurate and reliable forecast of urban air pollutants concentration are possible and the air quality conditions can be evaluated objectively. Through the simulation design, it proves that the proposed dynamic evaluation model can provide a practical tool for ambient air ambient quality evaluation.     

CFD application for coal/air balancing in power plants

Unbalanced coal/air flow in the pipe systems of coal-fired power plants will lead to non-uniform combustion in the furnace, and hence a overall lower efficiency of the boiler. A common solution to this problem is to put orifices in the pipe systems to balance the flow. It is well known that if the orifices are sized to balance clean air flow to individual burners connected to a pulverizer, the coal/air flow would still be unbalanced and vice versa. However, the current power industry practice throughout the world is to size orifices for balancing the clean air flow and accept the resulting imbalance in coal/air flow. Field tests are mostly conducted to verify a balanced clean air flow.     

Resonant Interactions between Vortical Flows and Water Waves. Part I: Deep Water

Any weak, steady vortical flow is a solution to leading order of the inviscid fluid equations with a free surface, so long as this flow has horizontal streamlines coinciding with the undisturbed free surface. This work considers the propagation of irrotational surface gravity waves when such a vortical flow is present. In particular, when the vortical flow and the irrotational surface waves are both periodic, resonant interactions can occur between the various components of the flow. The periodic vortical component of the flow is proposed as a model for more complicated vortical flows that would affect surface waves in the ocean, such as the turbulence in the wake of a ship. These resonant interactions are studied in two dimensions, both in the limit of deep water (Part I) and shallow water (Part II). For deep water, the resonant set of surface waves is governed by “triad-like” ordinary differential equations for the wave amplitudes, whose coefficients depend on the underlying rotational flow. These coefficients are calculated explicitly and the stability of various configurations of waves is discussed. The effect of three dimensionality is also briefly mentioned.