Simple Experiment In The Pipeline Water Hammer Calculation

Two-component flows occur in piping system in several industries, such as petroleum industries. Gases may be entrained in other liquid-carrying pipelines due to cavitation,liquid-column separation, or by an hydraulic jump. The flow in these case is , therefore, a mixture of gases and liquids. Unlike in a pure liquid in which the pressure wave velocity is constant, the wave velocity in gas-liquid mixtures varies with pressure. Thus, the coefficients of governing equations are pressure dependent and consequently the analysis of transients in the two-component flows is more complex and difficult than in single-component flows. In addition, shock waves may form due to the steepening of pressure waves limiting the use of method of characteristics, usually employed for solving the governing equations. The complexity of analysis increases if the individual components are moving with different velocities as compared to if they have the same velocity(homogeneous model). The gas-iquid mixture may be treated as a pseudo-fluid if the void fraction is small and mixtures is homogeneous. This assumption simplifies the analysis considerably and usually produces acceptable results for typical engineering applications. Thansient flow of homogeneous gas-liquid mixtures are described by a set of nonlinear hyperbolic partial differential equations. A closed-form solution of these equations is not available. Therefore, numberical methods are used for their solution. The coefficients in these equations are pressure dependent, which caused difficulties in the numrical solutions. Since wave may be produced during the transient-state conditions. The method of characteristics and a number of finite-difference shemes have been used for the analysis of transient, two-component flows. The method of characteristics requires isolation of shock and most of the other methods are first-order accurate which smears the shocks.In this paper, I treat the liquid containing a little of air as a pseudo-liquid and build up the water-hammer model in the bubbly, homogeneous, gas-liquid pipeline by using the momentum and continuity equations. Consequently, I compile the correspond program to carry out the mathematical simulation and draw the pressure-time figures. The contents in the paper are as following:To draw the pressure-time figures when the valve is closed, I adopt two finite-difference schemes, Mac Cormack and Gabuttie, which are applied inone-dimension fluid mechanics. I deduce the finite-difference schemes properly and provide the rest equations in the correspond calculation. I have make calculations when the test conditions are different. I contrast the pressure-time figures by using Mac Cormack and Gabuttie scheme with thoseby using Sβα finite-difference scheme and MOC and discuss the effects ofelasticity of pipeline and gas in the liquid on the water-hammer calculations.Two new second-order explicit finite-difference schemes are introduced for the analysis of transient two-component flows. These schemes have been used in computational fluid dynamics and have been applied recently to solve the transient problem with only liquid in the pipe. High-order methods require more computational effort per time step; however, fewer computational nodes may be used to obtain the same accuracy by using these methods.The computed results are compared with the experimental results to demonstrate validity of the simplified model and of the computational procedures.