Numerical modeling of chlorine concentration in water storage tanks

In this paper, we describe a numerical model to simulate the evolution in time of the hydrodynamics of water storage tanks, with particular emphasis on the time evolution of chlorine concentration. The mathematical model contains several ingredients particularly designed for this problem, namely, a boundary condition to model falling jets on free surfaces, an arbitrary Lagrangian–Eulerian formulation to account for the motion of the free surface because of demand and supply of water, and a coupling of the hydrodynamics with a convection–diffusion–reaction equation modeling the time evolution of chlorine. From the numerical point of view, the equations resulting from the mathematical model are approximated using a finite element formulation, with linear continuous interpolations on tetrahedra for all the unknowns. To make it possible, and also to be able to deal with convection‐dominated flows, a stabilized formulation is used. In order to capture the sharp gradients present in the chlorine concentration, particularly near the injection zone, a discontinuity capturing technique is employed. Copyright © 2015 John Wiley & Sons, Ltd.     

弹体侵彻干砂的数值模型

基于砂粒的不可压缩性假设,利用球形空腔动态收缩模型和广义Mises强度准则推导了干砂的孔隙压密演化方程;根据Hugoniot冲击突跃条件和Grüneisen系数,推导了干砂考虑孔隙演化影响的状态方程;根据关联流动法则,得到了大变形时砂的弹塑性应力应变关系;基于动力有限元计算平台,采用上述模型分析了弹体高速侵彻干砂的作用过程。结果表明,该模型能够表征高速侵彻时砂的孔隙演化对应力应变状态的反向影响,能够较准确地反映高速侵彻作用下干砂的动力响应过程。     

Numerical modeling of VOCs emission from a multi-layer carpet

A new numerical model predicting volatile organic compounds (VOCs) emission from a multi-layer carpet with activated carbon particles is developed with an aim to increase the VOCs emission rate in the carpet before it is used in an indoor environment. The influences of activated carbon particles, diffusion coefficient, material thickness and partition coefficient on the transient airside VOCs concentration and the VOCs emission from the carpet are investigated in detail.     

Numerical modeling of elastic waves in micropolar plates and shells taking into account inertial characteristics

Mathematical models of micropolar plates and shells are considered within the framework of the approximation approach. The governing equations of the theories are written in a thermodynamically consistent form of the conservation laws. This ensures hyperbolicity and correctness of the initial boundary value problems. For numerical solution, we propose parallel algorithms for supercomputers with graphics processing units. The algorithms are based on the splitting method with respect to spatial variables. We present the results of numerical computations of wave propagation in micropolar rectangular plates and cylindrical panels for media with different types of microstructure particles.     

Numerical modeling of the forming of fiber bundles from polymer melts

A mathematical model for the process of forming of synthetic fibers moving as a bundle is formulated. Three main versions are considered: forming of exposed bundles, forming in shafts with blowing, and stretching of fibers by means of an ejector. Low and high-speed forming regimes are also considered within the framework of the Maxwell model of a viscoelastic fluid. The calculations performed showed that the parameters of the fiber bundle produced depend on the method of forming used and on the local conditions in high-speed stretching, accompanied by oriented crystallization. Dnepropetrovsk State University, Dnepropetrovsk 320625. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 184–192, January–February, 1999.     

Numerical modeling of the nonstationary two-stage axisymmetric escape of a gas into a submerged space

This paper contains an exposition of the results of numerical modeling of the nonstationary two-stage flow of an underexpanded jet into the surrounding space by the method of coarse particles. A comparison is made with the results of experiment.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 153–156, July–August, 1978.     

Numerical modeling of two-dimensional nonisothermal filtration

A numerical method will be offered for the calculation of nonisothermal filtration. The model permits consideration of capillary and gravitational forces, as well as heat loss to the surrounding rock. The process of tongue formation in nonisothermal filtration will be considered.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 176–179, November–December, 1978.In conclusion the author thanks A. A. Bekserman, R. M. Kats, and M. I. Shvidler for their valuable remarks.     

Penetration of rigid bodies into loose and layered media

Penetration and motion of rigid bodies in ground media attracts the researchers’ attention because of various problems arising as the technology evolves. In fact, there are two independent directions of studies in this field: (1) the problem of earth excavation when a rigid body of a definite shape slowly moves along a given trajectory in the ground; (2) an impact of a rapidly flying free rigid or deformable body against the ground. In the latter case, to which the proposed studies pertain, it is sometimes of interest to study the medium behavior and the motion of the free body, which moves in the medium after the impact owing to the kinetic energy of itself. In this field, a majority of studies deal with collision and penetration of bodies of various shapes into clay media. An extensive survey of these studies is given in [1]. After this survey appeared, numerous paper dealing with complicated collision conditions have been published [2]. Penetration in loose media has been studied much more rarely. The direct collision with fractured rock was studied in connection with the expected landing of spacecraft on other planets [3, 4]. In this case, the influence of grain dimensions and the density of the filling and vacuum on the penetration was studied for the initial velocities in the range of 1.7–10 m/s. On the other hand, in [5], the results of investigating the penetration of conic bodies in sand at entry velocities of 700–900 m/s are given; these velocities significantly exceed the speed of sound in this medium, which lies in the range of 100–200 m/s for dry sand. Analyzing the experimental results, the author came to the conclusion that it is necessary to use different representations of the drag force in the supersonic and subsonic modes. In the present paper, we do not consider the influence of the grain distribution, sand density, and filling methods on the penetration. But, as follows from the experiments whose results are described in [6] and [7], to represent the results of penetration of rigid bodies at velocities up to several hundreds of meters per second, in addition to the characteristics listed above, it is also required to describe the technology of the experiment preparation, because such media have the property of shape “memory.”     

Numerical calculation of storage and loss modulus from stress relaxation data for linear viscoelastic materials

Summary Numerical formulae are given for calculation of storage and loss modulus from the known course of the stress relaxation modulus for linear viscoelastic materials. These formulae involve values of the relaxation modulus at times which are equally spaced on a logarithmic time scale. The ratio between succeeding times corresponds to a factor of two.Bounds for the relative error of those formulae were derived. These bounds depend on the value of the damping, tan, at the angular frequency,. The lower the damping values, the easier is the calculation of the storage modulus. This calculation involves the value of the relaxation modulus at timet ₀=1/, and that of its derivative with respect to the logarithm of time in a rather narrow region aroundt ₀. By contrast, the calculation of the loss modulus is difficult. This calculation involves the value of the derivative of the relaxation modulus with respect to the logarithm of time in a broad interval aroundt ₀. Especially the behaviour of the relaxation modulus at timest ₀ affects the calculation of the loss modulus significantly. The consequences of this short time truncation problem for the calculation of the loss modulus are discussed.If the results of dynamic measurements are available in the short time region in addition to those of the stress relaxation measurement in the long time region, the calculation of the loss modulus from the stress relaxation measurement is considerably simplified. The short time truncation problem can then be solved by using information aboutG as obtained from the dynamic measurements at short times (high frequencies).

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Zusammenfassung Numerische Formeln werden gegeben, die die Berechnung des dynamischen Moduls aus der Spannungsrelaxationskurve ermöglichen. In diesen Formeln treten Werte der Spannungsrelaxationskurve auf, die zu logarithmisch äquidistanten Zeitpunkten gemessen wurden. Das Verhältnis zweier aufeinanderfolgender Zeitpunkte entspricht stets einem Faktor 2.Für alle Formeln werden obere und untere Schranken für den relativen Fehler abgeleitet. Diese Schranken hängen vom Werte der Dämpfung (tan) ab, die bei der Kreisfrequenz auftritt, für die die Berechnung erfolgt. Die Berechnung der Speicherkomponente des dynamischen Moduls ist desto leichter, je niedriger der Wert der Dämpfung ist. Zu dieser Berechnung benötigt man den Wert der Spannungsrelaxationsfunktion zum Zeitpunktt ₀=1/, und deren logarithmische Zeitableitung in einem ziemlich engen Zeitintervall umt ₀. Die Berechnung der Verlustkomponente des dynamischen Moduls ist umständlich, Zu dieser Berechnung benötigt man den Wert der logarithmischen Zeitableitung der Spannungsrelaxationsfunktion in einem breiten Zeitintervall umt ₀. Insbesondere erfordert diese Berechnung viel Information über den Verlauf der Spannungsrelaxationskurve bei Zeitent ₀. Die Folgerungen dieses bei der Berechnung vonG() auftretenden Kurzzeit-Verstümmelungsproblemes werden auseinandergesetzt.Wenn neben den Ergebnissen der Spannungsrelaxationsmessung im Langzeitbereich noch solche einer Schwingungsmessung im Kurzzeitbereich zur Verfügung stehen, kann das Problem der Berechnung des Verlustmoduls aus der Spannungsrelaxationskurve wesentlich vereinfacht werden.

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Paper presented at the Symposium at Leende of De Nederlandse Rheologische Vereniging on 21st and 22nd May 1970.     

Numerical modeling of the process of oil displacement from reservoirs with zonal nonuniformity

In extracting oil from nonuniform reservoirs a considerable fraction remains unrecovered from the zones of lesser permeability. The mechanism of displacement of oil from reservoirs with zonal nonuniformity is investigated within the framework of the two-dimensional Muskat-Meres model of combined oil, water and gas flow [1]. A wholly conservative difference scheme implicit in the saturations and pressure is used for the calculations. Various reservoir exploitation regimes are considered with the object of seeking means of improving the characteristics of the process.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 177–180, September–October, 1987.     

Numerical modeling of carbon monoxide neutralization by metered water injection into a high-temperature mixture of combustion products

A closed mathematical model of the flow of a two-phase mixture consisting of evaporating water droplets and a chemically reacting multicomponent gas is described. The effect of the real droplet heating and evaporationkinetics on the gas-phase chemical reactions in a mixture of combustion products is studied within the framework of this model.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 96–106, November–December, 1993.     

Numerical modeling of deposition-release mechanisms in long-term filtration: validation from experimental data

A numerical phenomenological filtration model based on the combination of existing modeling approaches for simulating the transport of suspended particles in saturated porous medium is presented. The model accounts for the decreased physical straining with the distance from the inlet and the amount of deposited particles in the deposition kinetics. The particle release flux is a function of the local shear stress exerted by the flow on the pore surfaces. The proposed model is validated by interpreting a series of experimental data, realized in a laboratory sand column. The results show that the present model allows simulating the presence of a plateau in the breakthrough curves in the light of the shear stress conditions, and the spatial profile of deposited particles in the porous medium in the light of the straining profile.     

Numerical modeling of incline plate LiBr absorber

Among major components of LiBr–H₂O absorption chillers is the absorber, which has a direct effect on the chillier size and whose characteristics have significant effects on the overall efficiency of absorption machines. In this article, heat and mass transfer process in absorption of refrigerant vapor into a lithium bromide solution of water-cooled incline plate absorber in the Reynolds number range of 5 < Re < 150 is performed numerically. The boundary layer assumptions are used for the mass, momentum and energy transport equations and the fully implicit finite difference method is employed to solve the governing equations. Dependence of lithium bromide aqueous properties to the temperature and concentration is employed as well as dependence of film thickness to vapor absorption. An analysis for linear distribution of wall temperature condition carries out to investigate the reliability of the present numerical method through comparing with previous investigation. The effect of plate angle on heat and mass transfer parameters is investigated and the results show that absorption mass flux and heat and mass transfer coefficient increase as the angle of the plate increase. The main parameters of absorber design, namely Nusselt and Sherwood numbers, are correlated as a function of Reynolds Number and the plate angle.     

Numerical modeling of turbulent boundary layer suction

For the problem of gas suction from the turbulent flow over a plate, the results of numerically solving the Navier-Stokes equations complemented by a differential model of turbulence are presented. On the range of Mach numbers from 0.8 to 1, the effect of suction of various intensities on the flow parameters in the neighborhood of the suction region and downstream is considered.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 45–49, November–December, 1996.