# A New Method to Calculate Column Separation and Surge in Conduit Systems

### Significance

Cavitating flow is a phenomenon that occurs when the local pressure in a fluid drops below the vapor pressure of the liquid, causing it to vaporize and form bubbles. These bubbles then collapse, or implode, as they move downstream, creating shock waves that can cause damage to the surrounding material. As an engineer, it is important to understand cavitating flow because it can cause significant problems in pressurized systems. The formation and collapse of bubbles can create intense pressure fluctuations, which can cause erosion, vibration, noise, and even failure of system components. This can lead to decreased efficiency, increased maintenance costs, and reduced system lifespan. Cavitating flow is a common phenomenon in pressurized systems because it typically occurs when there is a rapid change in fluid velocity or pressure. This can happen in areas of a system where the flow is restricted, such as in valves, pumps, or other narrow passages. As the fluid passes through these areas, its velocity increases, causing a drop in pressure that can lead to the formation of bubbles.  Cavitating flow can occur in hydraulic systems when there is a sudden change in flow velocity or pressure, which can happen during hydraulic disconnection. Hydraulic disconnection refers to the process of disconnecting two hydraulic components, such as hoses or pipes, which can cause a rapid change in fluid velocity and pressure. When the hydraulic connection is disconnected, the fluid that was previously flowing through the system is suddenly stopped, causing a rapid decrease in pressure in the line. This drop in pressure can cause the fluid to vaporize and form bubbles, leading to cavitating flow. As the fluid continues to flow through the system, the bubbles collapse, creating shock waves that can cause damage to the surrounding material. Cavitating flow can also occur when the hydraulic connection is reconnected, as the sudden increase in pressure can cause the bubbles to collapse, creating further shock waves that can cause damage to the system. This can lead to increased maintenance costs, decreased system efficiency, and reduced lifespan of hydraulic components. To prevent cavitating flow during hydraulic disconnection, it is important for engineers to design hydraulic systems with careful attention to fluid dynamics, taking into account factors such as flow rate, pressure, and system geometry. Additionally, it is important to ensure that the hydraulic system is properly maintained and that all hydraulic connections are made and disconnected in a controlled manner to minimize the risk of cavitating flow.

Additionally, upon the complete disappearance of the cavity, the rejoining of the adjacent water columns occurs, leading to significant waterhammer pressures, which can severely damage the pipes. Column separation in pressurized pipe systems has been extensively studied. To this end, numerous numerical models have been proposed to capture essential features of column separation and to simulate both discrete and distributed cavitating flows. Additionally, two-phase flow models have been developed to simulate cavitation flow and water column separation in pipe systems. However, most of these models have various drawbacks limiting their practical applications. For example, Discrete Vapor Cavity Model (DVCM) requires a small maximum cavity size than the computational cell, resulting in invalid results.

The latest research in this direction has focused on addressing these problems. This includes tracking the boundary separating the pressurized and cavitating flows and solving the waterhammer and open channel flow equations to determine the hydraulic variables in these flow zones. Several other open-channel flow-based models have been proposed with improved results. However, none of these methods has successfully calculated column separation with satisfactory accuracy. This can be mainly attributed to the difficulty in modeling the transition from the waterhammer region to the cavitation zone.

To address these problems, Dr. David Khani and Professor Yeo Howe Lim from the University of North Dakota, in collaboration with Professor Ahmad Malekpour, the President of the Innovative Hydraulic Group, developed a novel open channel flow-based numerical model called the Modified Two Component Pressure Approach (MTPA). MTPA was a modified version of Two-Component Pressure Approach (TPA). It was designed to simultaneously calculate the waterhammer, pressurized and cavitating flow zones using single equations governing unsteady flow in open channel flow. Their work is currently published in the peer-reviewed journal, Journal of Hydraulic Engineering.

The authors showed that the present MTPA model could effectively calculate the open channel, waterhammer and cavitating flow zones simultaneously with reasonable accuracy without keeping track of the interfaces separating the regions. Consequently, unlike the shock-fitting-based models that require complex algorithms to track the interfaces separating the liquid and cavitating zones, MTPA automatically captured both flow regimes. The resulting equations were numerically solved using the first-order Godunov type finite volume method, while the fluxes were calculated at computational cell boundaries using a customized Harten, Lax and Van Leer (HLL) Riemann solver. This allowed the dissipation of the potential post-shock oscillations produced after collapsing the cavity and switching the open channel flow to pressurized flow.

In summary, Dr. David Khani and colleagues proposed an improved numerical model, called MTPA, to accurately capture the column separation physics in conduit systems. The present model uses a shock-capturing algorithm, which is easy to develop and implement, thus exhibiting superior performance than current open channel-based models that use difficult-to-implement shock-fitting algorithms. A good agreement between the experimental and simulation results was obtained, suggesting the feasibility of the proposed MTPA model. The unique features of the model were also demonstrated, including the ability to account for cavitation, waterhammer, and open channel flow regimes simultaneously. In a statement to Advances in Engineering, the authors stated that their findings would advance the safety and functionality of conduit systems.