Assessment of unsteady friction coefficients in pressure transient wave simulation during water leakage from pipeline using inverse analysis

Abstract
The study of unsteady flow in leaking pipelines is important. So, in this research, first the unsteady flow in the presence of leakage in a polyethylene pipeline with a diameter of 63 mm and a length of 47 m was studied in the laboratory and then analyzed and simulated by a numerical model. During the simulation, the unknown parameters of the temporal (kut), spatial (kux) acceleration coefficients and the discharge coefficient of leak orifice (cd) were calculated up to the Reynolds number of 106000. The results showed that the kut values for leak and no-leak state were almost constant and the values of kux for a leak state was less than the kux for the no-leak state. Changes in leak location had almost no effect on the values of kut and kux. Selecting a different type of friction model to simulate the transient flow in the presence of leakage had almost no effect on the orifice discharge coefficient. Also, the minimum and maximum values of 0.97 and 4.59 for the sum of the squares of the error between the pressure wave and the simulated transient flow, indicate two coefficient unsteady friction model had a good ability in these cases.
Background and Objectives
The analysis of transient flows in closed ducts has always been one of the most important and favorite topics of hydraulic engineers. On the other hand, with operation of water supply facilities during the time, water leakage may occur anywhere in the transmission pipeline system. Haghighi and Ramos (2012) performed leak detection in pipelines using inverse transient analysis and CFO optimization method. Mohammadi and Fathi-moghadam (2013) analyzed the fast transient flow in pipelines by the unsteady friction model. Akbari et al. (2021) investigated the detection of leaks in polyethylene transmission pipelines using pressure wave reflection of transient flow. Therefore, using laboratory modeling, fast unsteady flow in leaking pipelines was investigated, and then, a computer model was coded by Visual Basic programming language, with the ability to simulate transient flow in pipelines in presence of leakage. Then the parameters of temporal and spatial acceleration coefficients kut and kux and discharge coefficient of leak orifice cd were calculated.
Methodology
In this research, a 47m long pipe that made of polyethylene with 10bar nominal pressure and diameter of 63mm was used in experiments. The transient flow was generated in it by very fast closure of the end valve. A computer numerical program was developed to simulate the hydraulic conditions in pipeline. The coded model analyzer motor analyzes the basic unsteady flow equations in pressurized ducts, and the inverse analyzer is an optimization algorithm using a defined goal function to find the best fit of the recorded pressure waves and those simulated with the least error. Also, the boundary conditions for simulating the leak in the pipeline were included in the numerical model.
Findings
The values of kut and kux coefficients related to the wave simulations was calculated. The values of kut for leakage and non-leakage state were approximately the same, and the coefficient of kux for leak state would be less than non-leakge state. In the case of leaks with different diameters, the coefficient of kut were generally the same as in the case of non-leakage. However, the values of kux coefficients for leakage with a diameter of 4 mm were greater than those for leakage with a diameter of 10 mm, and both of these values were less than non-leaking. The reason is that as the diameter of the leak increases, the damping rate of the pressure waves increases, therefore the value of the kux coefficient decreases.
The change in the leak location had almost no effect on the values of kut and kux. The coefficient of kux in the presence of leak, either at a distance of 27 m or 39 m, were less than its values in non-leak state, and both values were also approximately equal to each other. Leak orifice with a larger diameter (10 mm) had a higher discharge coefficient than leak with a smaller diameter (4 mm), due to their lower resistance and lower energy dissipation against the increase in pressure produce in the system by the transient pressure wave. The performance of the two-coefficient unsteady friction model was evaluated by statistical indexes. Also, the numerically simulated waves and the laboratory samples was compared to each other. The two-coefficient unsteady friction model had a good ability to simulate a transient pressure wave in presence of a leak.
Conclusion
The values of kut for leak and no-leak state were almost constant and the values of kux for leak state was less than the kux for the no-leak state. Changes in leak location had almost no effect on the values of kut and kux. Selecting a steady or unsteady type of friction model to simulate the transient flow in the presence of leakage had almost no effect on the orifice discharge coefficient. Two coefficient unsteady friction model had a good ability to simulate the pressure wave of transient flow in the presence of leakage.