On the Use of the Water Hammer Equations with Time Dependent Friction during a Valve Closure, for Discharge Estimation

Abstract

The paper presents a new method for in site discharge estimation in pressured pipes. The method consists in using the water hammer equations solved with the method of characteristics with an unsteady friction factor model. The differential pressure head variation measured during a complete valve closure is used to derive the initial flow rate, similarly to the pressure-time (Gibson) method. The method is validated with a numerical experiment, and tested with experimental laboratory measurements. The results show that the proposed method can reduce the discharge estimation error by 0.6% compared to the standard pressure-time (Gibson) method for the flow rate investigation.

Measurements of Discharge through a Pump-Turbine in Both Flow Directions Using Volumetric Gauging and Pressure-Time Methods

“…These models have been confirmed experimentally-there is a high conformity between experimental and numerical results of the water hammer course [30]. With reference to the pressure-time method, the above assessment is confirmed by [27][28][29].…”

“…Owing to this factor, the geometrical characteristics of a pipeline measuring segment and impact of its flow elements on flow irregularities are taken into account. Disregarding changes in flow velocity profiles resulting from the variable shapes of pipeline elements leads to an increase in the inaccuracy of measurement using the pressure-time method, which cannot be corrected only by improving the modeling of friction losses in these elements, as discussed in [27][28][29] or by improving the computational model [22,28]. In addition, increasing the accuracy of estimation of the leakage rate through closed-flow shut-off devices is not enough [26].…”

“…A comprehensive discussion of some problems related to the computational procedures in the pressure-time method is provided in standards [4,6] as well as in monograph [11]. A description of some important problems related to the use of the pressure-time method for measuring flow rate in hydropower plants can also be found in publications [22][23][24][25][26][27][28][29]. Calculation of friction losses according to the quasi-stationary hypothesis is consistent with the conclusions presented in [30].…”

“…It was proved that the modelling of unsteady friction losses has little effect on the course of water hammer in its initial time-phase that is taken into account in the pressure-time method. Nevertheless, it should be emphasized that including the transient nature of friction losses into the calculation method, under certain circumstances, may improve predictions of the pressure-time method as described in [27][28][29].…”

On Obtaining the Young Modulus from Numerical Analysis of Composite Material Constituent

“…Future investigations shall seek to create a model capable of predicting all the elastic characteristics required in engineering design, starting from the elastic characteristics of the constituents. It is also a goal to validate the model using the numerical method of calculation with finite differences as schematized in [15].…”