ABSTRACT
Mixtures of liquids, which are formed due to deep penetration (mixing) in the flow of two fluids between parallel plates or turbulent mixing in the pipes, are prevalent in our everyday lives. Deep penetration of the mixture components can be considered as a combination of diffusion and physical mixing. The first process dominates in the deep penetration and the second stage the liquids are mixed. Immiscible mixing is also crucial in modern technology. It allows chemists to control chemical reactions for the production of polymeric materials with unique properties and distribution of additives that reduce the viscous friction in the pipes. However, despite its popularity, both in nature and in the production, the mixing process is still not completely clear. Researchers in different areas can not yet even set a common terminology for it by using different names. The mixing process is extremely complex and is found in a variety of systems. Theory of mixing is included, for example soluble and partially soluble, chemically active and inert liquid, slow laminar flows, and rapid turbulent flows. Not surprisingly, there is no single theory capable to explain in detail the process of mixing in fluids. Therefore, the direct calculation is impossible to cover all important aspects of this phenomenon. Nevertheless, some information about the process of mixing can be obtained both through physical experiments and using computer simulation. Typically, in certain places or local points of water pipelines exists sharp changes in pressure above atmospheric pressure. If there is a leak in the pipeline or through the valves, spaces in the plumbing lines, is filled with gaseous phase (e.g., steam at ambient temperature) or air. The complex microscopic interaction between the components of liquid-gas mixture makes the simulation extremely important. There have been several
special studies by using computer graphics in the light of immiscible mixtures. However, there are few works that deal with blending fluid. Changes in the properties of liquids in pipes and channels are due to factors such as decompression (because of the sudden opening of the discharge valve), the spread of the pulse pressure, heating or cooling, or energy production systems, mixing with the particulate matter or other body fluids (which can change the density of the liquid, specific gravity, and viscosity), the formation and collapse of vapor bubbles (cavitations) and air leak or disconnection of the system (near the vent and/or pressure wave). Changes to the boundaries of the system are due to factors such as the rapid opening or closing a valve, pipe explosion (due to high pressure) or the collapse of the tube (due to low pressure), stop the pump inlet air in the vacuum circuit breaker, the penetration of water through the valve, massive outflow valve in the discharge pressure or fire hoses, damage to the disk and/or resonance in the switching valve. Such sudden changes make the transition pressure pulse, which quickly spreads far from the place of origin of perturbations, in any possible direction, and across the sealed system. Most of the transients in water and drainage systems are the result of changes in the boundaries of the system. It happens usually near the end of the system upstream or downstream or in the local high points. Consequently, the results will help reduce the risk of system damage or failure with the proper analysis to provide a dynamic response to the shortcomings of the system, design protection equipment to manage the transition energy and determine the operational procedures to avoid transients. Analysis, design and operating procedures, that is all the benefits of computer simulations. Study of hydraulic transients began with the work of Zhukovsky [1] and Allievi [2]. Many researchers have made significant contributions in this area, including Wood [3], Angus and Parmakian [4-5], who popularized and perfected the graphical method of calculation. Benjamin Wylie and Victor Streeter [6-11], method of characteristics combined with computer modeling. Subject of transients in liquids are still growing fast around the world. Brunone et. al [12], Koelle and Luvizotto [13], Filion and Karney [14], Hamam and McCorquodale [15], Savic and Walters [16-17], Walski and Lutes [18], Wu and Simpson [19], have been developed various methods of investigation of transient pipe flow. These ranges of methods are included by approximate equations to numerical solutions of the nonlinear Navier-Stokes equations. Basic theory of unsteady fluid flow in pressure pipelines were set out in the works of Zhukovsky. He obtained the differential equations of motion of inviscid fluid formed the basis development of the theory about pressure and pressure flow of viscous fluid. With the help of this theory, it became to explanation of the physical phenomenon, known as water hammer. N. E. Zhukovsky introduced the concept of the effective sound speed. He mentioned to reducing the motion of a compressible fluid in an elastic cylindrical pipe to the motion of a compressible fluid in a rigid pipe, but with a lower modulus of elasticity of the liquid. Further study of transients in the pipelines pursuits in the works of I. A. Charny, Khristianovich, A. H. Mirzajanzadeh, M. A. Hussein-Zadeh, V. A. Yufina, H. N. Nizamova, R. F. Ganieva, L. B. Kublanovskaya, L. Polyansky, A.K. Galliamova, M.V. Lur’e, E.V. Vyazunova, A.G. Gumerova, A. Shumaylova, A. Kozak, A. A. Kandaurova, E. M. Klimovskaya, and so on. For pumps with a low inertia of moving masses with sufficient accuracy, it can be used the “method of intersecting characteristics”, proposed by
Dikarevskim [20-21]. As a result, by using the solution of characteristics, the source of perturbation of the flow, the characteristics equation of unsteady fluid motion, it can determine the pressure in the hydraulic shock caused by the quick opening valve or pump start-up. The greatest development in the theory of water hammer was analytical methods of calculation. Allievi [22-23] investigated the hydraulic shock in a simple pipeline (i.e. having a constant diameter and constant speed of propagation of shock waves), by using the general solution of differential equations of unsteady pressure flow. Zhukovsky [1] derived the equations of water hammer in finite differences, which later was called the chain of equations Allievi [2], which were subsequently was used by many researchers in the calculation of water hammer. Using the “method of characteristics” at computer simulation for transients in pressure systems was showed by Wisniewski [25-26]. In that works, water hammer was determined by the interaction between the pressure waves that occurred at the pump and reflected in the pipeline. Loss of pressure happened conditionally apart along the pipeline. This method also allows choosing the number and size of shockproof. Development of algorithms for software simulation of transients by Vishnevsky [25, 27] was made for the complex pressure systems. It included the possible formation of discontinuities flows, hydraulic resistance, structural features of the pumping of water systems (pumps, piping, valves, etc.). However, a calculation of water hammer is adapted to high-pressure water systems for household and drinking purposes. K. P. Vishnevsky used “characteristics method” for the calculation of water hammer on a computer dedicated to the work of Lyamaeva [28]. They described in detail the process of modeling the unsteady fluid flow in complex piping systems transporting drinking water. Their works were included the description of this phenomenon at discontinuities flow, unsteady friction, changes in gas content and other parameters. Much attention was paid to the way that the original data using a grid, allowing the easiest way to record all raw data for all sites for example, large and extensive network. Lyamaevym [28-29] developed a “method of characteristics” for the calculation of water hammer by using computer technology. The process of entering basic information for the calculation of water hammer is simplified for the user by the use of geo-information systems. Therefore software can be carried out for multiple calculations of unsteady flow regimes (pressurized systems) in transporting uncontaminated water. Calculations of hydraulic shock in multiphase systems, including a computer, are devoted to the work of Alysheva [30]. In that work, integration of differential equations of unsteady pressure flow is also performed by the “method of characteristics”. The works of Streater [31], Vishnevsky [25], Lyamaeva [28], Alyshev [30] use the method of calculation of water hammer. They are based on replacing the distributed along the length of the flow of gas parameters concentrated in the fictitious air-hydraulic caps installed on the boundaries of the pipeline. A fictitious elastic element is replaced by elastic deformation of the pipe walls, and the elastic deformation of the solid suspension is modeled by fictitious elastic elements of the solid suspension. However, detailed experimental studies are based on the solid component. A particular challenge in terms of calculations is a hydraulic shock, accompanied by discontinuities of the flow. This phenomenon has not been fully studied, so the works of many scientists are devoted to experimental and theoretical studies of non-stationary processes with a break of the column of liquid.
