Quasi 2D analysis of Column separation and Bubbles Growth in Water Hammer

Numerical Investigation of Column separation and Bubbles Growth in Water Hammer
Maryam Mousavifard‎, Assistant Professor, Department of Civil Engineering‎, Faculty of engineering‎, Fasa University, Fasa, Iran
Reza Roohi‎, Assistant Professor, Department of Mechanical Engineering‎, Faculty of engineering‎, Fasa University, Fasa, Iran
Introduction
In modern hydraulic systems, when a sudden change occurs in fluid velocity because of any reasons (sudden pump stroke, valve closure, etc.), it will be followed by intense pressure fluctuations in the system, which is referred to water hemmer. If the fluctuations decrease to less than the vapor pressure of the fluid, the separation column will occur. In general, two cases can be distinguished: either the pressure drops below the saturation pressure but keeps above the vapor pressure, or the pressure drops to the vapor pressure of the liquid. In the former case, gaseous cavitation takes place, characterized by the presence of a large number of gas nuclei. When the pressure drops suddenly, a significant gas release may occur. In the latter case, vaporous cavitation takes place, and when the fluid pressure drops to its vapor pressure, a sudden growth of the nuclei containing vapor occurs.
In general, there are two basic assumptions to describe the phenomenon of cavitation: discrete and distributed cavitation. In discrete cavitation, the vapor or gas cavities create discontinuity in fluid. In this case, it is assumed that the vapor and gas cavities occur at computational nodes, when the pressure reaches less than the vapor pressure of the fluid or the saturation pressure. In distributed cavitation, the two phases of the liquid and the vapor (or the gas) are simultaneously solved, and the vapor (or gas) cavities are continuously exist all over the fluid.
Methodology
In this paper, the column separation in pressurized pipes affected by water hammer is numerically investigated using one-dimensional and quasi-two-dimensional models of gas cavity. A one-dimensional model is modeled based on the method of characteristics, and the energy dissipation is simulated using the summation of the Brunone unsteady friction and quasi-steady friction. In the proposed quasi-two-dimensional model, the characteristic equations along the pipeline axis and the finite difference equations along the pipe radius are used to simulate water hammer, and then the governing equations of discrete gas cavity model is coupled with the primary model, and the five-layer turbulence model was also used to simulate the energy dissipation. It should be noted that, in the quasi two dimensional model of separation column, like the one-dimensional model, the velocity on the upstream and downstream of each computing node will not be equal. Free gas distribution throughout liquid in a homogeneous mix in a pipeline yields a wave propagation velocity that is strongly pressure dependent.
Results and Discussion
After verifying the developed models by experimental data, the total shear stress is studied in some initial cycles of water hammer. In the second part of the paper, the dynamics of bubble growth and the process of temperature and pressure variation within the bubbles are also analyzed using the Rayleigh-Plesset equation. The growth of bubbles in the fluid is a function of a variety of variables such as applied pressure, fluid surface tension, evaporation pressure in fluid temperature and viscosity.
Conclusion
- the quasi-two-dimensional model has been more successful in calculating energy depreciation, especially in the final cycles of water hammer.
- Regarding the head oscillation shape, it can be evaluated that the quasi 2D DGCM improved the energy losses reproduction, and reproduces the experimental spikes successfully even in final cycles of experimental runs.
- The 1D model of DGCM reproduce the first oscillations of the experimental data successfully, but in final cycles, does not predict the shape of head oscillations successfully and does not stay in phase with experimental data.
- According to the shear stress diagrams it can be concluded that in high pressure pulses, the total shear stress is negative and it is positive in low pressure pulses.
- The difference between the minimum and maximum radius is about 0.5 μm. Considering the average radius of the bubbles and the relationship between the radius of the bubbles and the gas phase volume, the 85 to 125% increase in the volume of the gas phase in the fluid during the periodic pressure fluctuations process, is visible.
- It should be noted that in spite of the fact that the maximum pressure inside the bubbles (the driving force for the growth of bubbles) is greater than the external pressure, the high dependence of the internal gas pressure on the radius of the bubbles and the dynamic behavior of the system, lead to periodic changes. In other words, the strong growth of the resistive force by reducing the radius of the bubbles prevents significant contraction in them, and again, by reducing the pressure head in the fluid, the growth of the bubbles will be renewed to reach the initial radius.
Keywords: Water hammer; Column separation; unsteady friction; quasi two Dimensional model; shear stress; Rayleigh Plesset equation