THE COEFFICIENT OF EFFICIENCY OF A COMPLEX HYDRAULIC CIRCUIT

О.Г. Бутенко, А.В. Карамушко, Т.С. Подуфала. Коефіцієнт ефективності складної гідравлічної мережі. У статті розглядається один з можливих методів оцінки ефективності використання енергії у складній гідравлічній мережі. Показано, що для характеристики енергетичної досконалості складної гідравлічної мережі не може використовуватися лише коефіцієнт корисної дії насосної установки, оскільки він не враховує усіх можливих гідравлічних втрат та взаємного впливу елементів системи «насос − трубопровід». Для цієї мети запропоновано використовувати коефіцієнт енергетичної досконалості мережі, який є відношенням потужності потоку рідини на виході із гідравлічної мережі до потужності на валу насоса. Цей показник враховує втрати як у елементах насосної установки так і в трубопровідній системі і завдяки цьому дає об’єктивну і комплексну оцінку енергетичній ефективності цієї системи в цілому. Шляхом використання балансу потужностей елементів системи виведено формулу розрахунку цього показника для розгалуженої гідравлічної мережі, що складається із послідовних і паралельних ділянок. Проведений аналіз отриманої формули, котрий показав, що перевагою запропонованої формули є врахування прихованої взаємної залежності між величинами, що визначають коефіцієнт енергетичної досконалості. Зокрема формула враховує вплив опору складної гідравлічної мережі на робочі параметри насоса (напір і подавання) і на його коефіцієнт корисної дії. Показано, що у деяких випадках зростання гідравлічного опору мережі, а отже і втрат потужності у системі, компенсується зростанням напору, що розвиває насос, і зростанням його коефіцієнта корисної дії. Таким чином доведено, що негативна дія у трубопровідній системі може таким чином вплинути на показники насосної установки, що коефіцієнт енергетичної досконалості мережі не тільки не зменшиться, а й зросте. Формула дозволяє порівнювати енергетичну досконалість складних гідравлічних мереж з різними параметрами і різними насосними установками та дозволяє проводити оптимізацію системи за сумарними енерговитратами. Ключові слова: складна гідравлічна мережа, корисна потужність, потужність на валу, опір мережі, коефіцієнт енергетичної досконалості мережі

Introduction. In today's world, hydraulic networks have a length of millions of kilometers. They have varying degrees of complexity (branching) and provide water for both domestic and industrial needs. As a rule, fluid energy in these networks is transmitted from electrically driven pumps. Several tens of billions of kWh of electricity are consumed each year to power them. Despite such considerable amounts of electricity consumed in hydraulic networks, designers do not use any universal indicator that would generally characterize the efficiency of conversion of electrical energy into hydraulic and the efficiency of use of this hydraulic energy.

Analysis of recent publications.
To characterize the energy efficiency of hydraulic networks, the efficiency of the discharge equipment has traditionally been used. This significantly complicates the optimization of the hydraulic criterion of the hydraulic network parameters in its design or verification calculation and is methodologically incorrect [1]. Designing hydraulic networks (including branching) consists of several basic steps. According to the terms of reference, the diameters of the water sections of individual sections are selected from the standard series, then the power required to pump a given flow rate of fluid through the piping system is calculated and, finally, a discharge unit is selected that is capable of providing the specified power with maximum efficiency [2]. Even when it comes to optimizing energy costs for fluid transportation, it is only the pumping installation that is considered [3,4,5,6]. In particular, it is proposed to use as a criterion electricity costs per unit volume of pumped liquid. This is also methodologically incorrect, since the distance to which the fluid is pumped is not taken into account. This, as we see, takes into account the efficiency of the conversion of mechanical energy on the shaft into the hydraulic energy of the fluid in the pump, but does not consider the efficiency of the use of this hydraulic energy during the movement of the fluid through the pipeline to the end consumer. In other words, the performance of a system is judged by the corresponding indicator of only one element, which is a flawed approach.
The efficiency of the supercharger is the ratio of the useful power N u to the power on the shaft N s : This means that an increase in the resistance of the network and consequently a loss of energy in the pipeline part of it always leads to an increase in the useful power of the pump and in certain modesto an increase in its efficiency. Since this increase in power is spent on losses, it is impossible to find it useful. This contradiction is one example of the fact that it is not enough to use the parameters of a pumping installation alone to characterize the overall energy efficiency of a hydraulic network. In addition, in pipelines running "from the reservoir", i.e. the flow occurs under the action of hydrostatic pressure, due to the absence of the pump this indicator cannot be used in principle.
In article [7], for the general characterization of the energy efficiency of the hydraulic network, the authors introduced a new concept -the efficiency of its individual elements and, as a result, proposed the formula: where η s , η p , η п -efficiency of the hydraulic system as a whole, the pump and the n-th element of the system respectively; w i і w j -cross-sectional areas of individual sections. Formula (1) makes it possible to estimate the energy efficiency of the hydraulic system, but is not very convenient for real networks where the number of elements can reach polynomials. In addition, for example, when closing a valve, its efficiency is zero, which results in the need to divide by zero.
Alternatively, for the overall energy efficiency of the hydraulic network, work [8] proposes a network energy perfection coefficient (NEPC) ε, which is the ratio of the output power from the hy-draulic network N inp to the power input N, which is the power on the pump shaft. Since the output power is equal to the difference of the useful power and the power loss in the pipeline 3 l p N gSQ ∆ = ρ , and the power on the shaft: then NERC is obtained for a simple pipeline: The first factor in it takes into account the energy efficiency of the pump, and the second -the pipeline part of the network.
The purpose of the work is to find a general indicator of the efficiency of transportation of fluid over a complex (branched) hydraulic network, which would generally take into account the losses both in the pumping equipment and in the elements of the pipeline part of the network.
Main part. If we consider a pipeline consisting of series-connected sections in which the total resistance is the sum of the resistances of these sections, then (2): Consider a complex hydraulic network with n consecutive and k-m parallel sections (Fig. 1).
Power losses in successive sections, the volume flow of which is equal to the supply of the pump Q p , 3 where S m , S m+1 , S k -hydraulic supports of corresponding parallel sections, s 2 /m 5 ; Q m , Q m+1 , Q k -the volumetric flow in them m 3 /s. Then the total power loss in the branched hydraulic system: Based on the definition of NERC and the considerations above: The sections of the pipeline system are considered to be parallel if they have two points in common. The condition of pressure equality P m =P m+1 =…=P k . corresponds to this definition. Then: And after simple transformations: Formula (3) indicates that the efficiency of a complex hydraulic network will be greater, the greater the efficiency of converting the mechanical energy of the actuator into hydraulic energy of the fluid (greater η н ) and the smaller the loss of hydraulic energy as the fluid moves to the consumer (less network resistance). However, given that the quantities included in (3) are partially interdependent, conclusions about the value of ε can be made only on the basis of a complete analysis of the specific problem.
The pump X45/240 with a diameter of the impeller D 2 =262 mm, which is often used in systems of water supply [9]. Characteristic construction (Fig. 2) allows to obtain the following parameters: Let's replace the conditions of the example -double the resistance of the second consecutive sec-