Experimental study of the polytropic coefficient for hydraulic shock from a decrease in pressure

Abstract

The article provides an analysis of scientific papers on the study of a hydraulic shock absorber - an air-hydraulic cap, shows that at present there is no consensus on the choice of the numerical value of the polytropic coefficient n. In practice, during the operation of pumping stations with long pressure pipelines, in the event of a sudden power outage, water hammer often occurs to the motors of the main pumps. To prevent this phenomenon, it is convenient to apply a hydraulic shock absorber. The accuracy of calculating the shock absorber depends on the reliable value of the coefficient n. The correct selection of the numerical value of the polytropic coefficient n provides for determining the optimal dimensions of the proposed hydraulic shock absorber. There are different opinions about the choice of the numerical value of n among scientists. N.E. Zhukovsky, when calculating the hydraulic shock absorber, takes n = 1.41. V.S. Dikarevsky accepts n=1.0. Therefore, the rationale for the correct choice of the numerical value of the polytropic coefficient for calculating the absorber in the case of water hammer is very relevant. The paper presents the results of experimental studies of the polytropic coefficient n in a hydraulic shock absorber from a decrease in pressure. When conducting experiments on the study of the absorber, modern scientific instrumentation was used. At the same time, the obtained results of the experiments confirm that the variability of the value of the polytropic coefficient during hydraulic shock in the cap and the correctness of the recommendation of D.A. Fox. The conducted studies prove that the polytropic coefficient has a strictly polytropic character.

Anti-shock pneumohydraulic damper

“…The above equations have the following notation: ϑ and H are flow velocity and the absolute pressure in the pipeline at the damper installation site at time t; Q is flow rate of the fluid during steady motion; β is coefficient of momentum; x is coordinate along the length of the pipeline; ρ is liquid density; R is hydraulic radius of the pipe; τ nu is shear stress at the pipe wall in unsteady flow; g is acceleration of gravity; V is volume of air in the damper at the moment t; V 1 is increase in the volume of air in the damper; V г is volume of air in the damper at the absolute geodetic head H o-a (Fig. 1); n is polytropic index [3,4].…”

“…The accuracy of calculating the hydraulic shock damper depends on the reliable value of the polytropic index n [3,4]. In engineering practice, there is a problem with the selection of the numerical value of the polytropic index n, which considers the law of compression and expansion of air in the hydraulic shock damper [3,4]. So, for example, N.E.…”

“…Currently, to dampen the force of hydraulic shock that occurs in a long pressure pipeline, pneumohydraulic dampers are widely used [1][2][3][4][5][6][7]. Similar anti-shock devices (dampers) can protect water supply pipelines from water hammers.…”

“…Similar anti-shock devices (dampers) can protect water supply pipelines from water hammers. When installing a damper at the beginning of pressure pipelines of pumping stations, their dimensions are determined by the conditions for starting and stopping pumps [3,4,7,8,9]. Dampers are calculated in different ways according to the conditions for stopping the pumps.…”

“…However, these graphs are calculated only for a very small change interval in the main parameters of pressure pipelines of pumping stations during hydraulic shock in the presence of dampers. There is no general solution in Evangelisti's work; therefore, in many cases, this method is not applicable [4][5][6].…”