Features of modelling the head losses on regulating locks in the processof calculating the transients of pump stations
It is common in design practice to install check valves and regulating valves at penstocks of pumping stations.The peculiarity of the valves characteristics is essential increase in the coefficient of resistance with a decreasing rotary disc angle. In order to describe the flow characteristic around zero opening of the valve, this characteristic can be presented as the connection of flow coefficient and the angle of the disc rotation. At small angles the disc flow coefficient tends to zero.In case of transient calculations, the work of the gate can be modeled by one of three algorithms. In algorithm 1 the loss at the gate is determined by solving the chain equations of water hammer on the areas adjacent to the gate using the flow characteristics of the valve as boundary conditions.The distinguishing feature is that the boundary condition has to be written in two forms: with the positive flow direction for turbine mode and with negative — for pump mode. For the solution adequacy the radical expression in the flow formula is required to remain positive with the opposite directions of flow. This is achieved by changing the dependencies used to drop the gate.In both cases, the solution will be a quadratic equation with opposite signs of the coefficients. One of the roots gives the correct value of the head loss. The second root is parasitic, it shows significantly overestimated values of pressure loss, and should be ignored.The disadvantage of the algorithm 1 is its buildup in the transition flow through zero due to the delay in switching algorithm from one branch to another, and taking into account parasitic square equation root.The algorithms 2 and 3 are devoid of this disadvantage. Substitution of water hammer of head losses in them is made in the chain equation. The losses are calculated with the help of variable resistance coefficient, which depends on the position of the valve disc and the velocity head.In the algorithm 2 the velocity head is calculated with the help of the known data of flow at the previous step. In the algorithm 3 the losses are calculated more precisely with the flow through the gate and the known flow at the previous step.The analysis of the calculation conditions of pressure loss in the process of simulating water hammer in pressure control valve systems showed that the most stable and consistent result is provided by the method for calculating losses according to the algorithm 3. The system of partial differential equations is reduced to a linear form, providing stability of the solution at high values of the resistance coefficient, as well as during the flow transition through zero.