# Influence of the Radial Gap on the External Gear Pump Performance
## 1 Introduction and Motivation  
External gear pumps are one of the most commonly applied in the practice of hydraulic drives. They are used in both mobile and industrial hydraulic systems [1]. The reason for this wide applicability is their large number of advantages: a relatively simple construction, a wide range of variation in the displacement volume (most often between 1 and 200 cm\({}^{3}\)) [2], the possibility of coupling up to three pumps with different displacement volumes to one drive shaft, the ability to implement a similar design to hydraulic motors, and last but not least, a low cost compared to other types of displacement rotary pumps. Along with the listed advantages, there are also disadvantages: a higher level of flow ripple, a fixed displacement volume, a relatively lower overall efficiency, the impossibility of continuous operation at high pressures (over 20 MPa), a high level of noise, impossible repair in the case of wear in the housing or the rotating pair, etc. [3]. The listed disadvantages have motivated a number of researchers and manufacturers' development divisions to improve the external gear pump design. Usually, the goal is to improve the performance, where the corresponding indicator is the overall efficiency. Often, the goal of developments is to increase overall efficiency, and in achieving this, some of the other listed disadvantages are also overcome, such as reducing noise and vibrations in the hydraulic system, etc. There is a large number of published developments devoted to increasing the overall gear pump efficiency. They can be summarized into several groups depending on the way this goal is achieved. A large group of studies is dedicated to the inter-mesh zone design parameters [4; 5; 6; 7; 8; 9]. Sometimes, this is associated with changes in the tooth profile, which is most often involute, but attempts have been made with the use of non-involute or non-symmetrical profiles [10]. Another group of studies is dedicated to the influence of the radial and axial gap sizes on the volumetric and overall efficiency [11; 12; 13]. Some studies have aimed at evaluating the influence of operating mode parameters, such as rotation frequency and the pressure load on the pump efficiency [14; 15; 16; 17]. When the focus is on the performance and efficiency affecting processes, a significant place is occupied by the influence of cavitation phenomena [18; 19; 20; 21; 22]. There is also a body of research devoted to the influence of working fluid parameters on pump efficiency [23; 24; 25; 26]. This implies a study of the working process when using special hydraulic oils as well as the influence of temperature changes [27]. For sure, this unification is conditional, as research often covers the influence of a combination of parameters--design, mode, process, etc. [28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38]. With the increase in IT computational capabilities, fluid simulations software products are also being improved. This is a prerequisite for deepening the CFD studies of the flow process in hydraulic machines, devices, and systems. The transition from 2D [39; 40; 41] to three-dimensional (3D) CFD models [29; 42] has further improved the possibilities of fluid-structure theory. In this aspect, it has also increased the possibilities for researching the working process of gear pumps in order to study the influence of various design parameters. Moreover, reaching an experimentally verified CFD model of the hydraulic machine makes it possible to study in simulation conditions specific design parameters whose influence is not possible to study through a real experiment [43]. The authors created a 2D CFD model of a certain specimen of an external gear pump based on the Ansys Fluent(r) ver. 2019 R3 software product. A detailed description of the model is presented in [41], and its advancement and verification are presented in [44].