# Advanced 2D Computational Fluid Dynamics Model of an External Gear Pump Considering Relief Grooves
## 1 Introduction and Motivation  
One of the most commonly used pumps in hydraulic drive practice is the external gear pump. In systems with velocity throttle control of the hydraulic motors, without high requirements regarding the flow rate ripple and the need for continuous operation at high pressure, this type of pump is most preferred. Their relatively low cost and availability in the market also contribute to their wide application not only for industrial but also for mobile applications, especially when a pump with a small displacement volume is needed [1, 2]. There are many disadvantages of external gear pumps. The most prominent disadvantages are the relatively large level of flow rate ripple, the fixed displacement volume, high noise levels, the impossibility of continuous operation at a pressure above 20 MPa, non-reparaibility, and others. But the relatively simple construction of these pumps motivated researchers years ago to look for structural modifications to overcome the listed disadvantages. To date, the development of modern software products with an engineering application makes it possible to solve complex tasks requiring not only constructive experience but also process knowledge. With the advent of computational fluid dynamics (CFD) ANSYS Fluent(r) 2019 R3 software, design modifications' influence on working characteristics of hydraulic machines has become easier to study. Of course, this is only useful if the numerical results are experimentally validated [3]. The literature review shows that the research on external gear pumps using a fluid-structural approach can be summarized in several main groups. One group is aimed at constructive improvements related to gaps in order to reduce internal volume losses(leakages) and consequently increase volumetric efficiency [4; 5; 6; 7; 8; 9]. Another significant part of the research is aimed at changing the number or geometric profile of the teeth in order to reduce the flow rate ripple [10; 11; 12; 13; 14]. Often, these studies also contribute to reducing the level or intensity of generated noise [15; 16; 17; 18; 19; 20; 21; 22; 23; 24]. Not infrequently, the goal is to create modifications for continuous work at high pressure [25; 26; 27]. This necessitates the investigation of directly related parameters-trapped volume, pressure in the inter-teeth zone, and distribution of the radial force on the gears [28; 29; 30; 31; 32; 33]. In summary, these are studies on the influence of various design parameters on the performance and universal characteristics of the machine. There is research aimed at developing specific applications based on gear pumps [34; 35; 36; 37; 38]. The cavitation phenomena are also a current research problem, which is valid not only for this gear type but also for other types of hydraulic displacement rotary machines [39; 40; 41; 32; 37; 38; 31; 32; 39; 42; 43; 8; 13; 27; 8; 13; 28; 14; 8; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33]. Creating a CFD model of newly designed or existing hydraulic machines (volumetric or turbo) is not an easy task and depends directly on the purpose for which it will be used [45; 46]. The main question to consider is whether to create a two-dimensional (2D) or three-dimensional (3D) model [47; 48; 49; 50; 51]. The answer depends on whether it is possible to create a 2D model that gives results very close to the 3D model while using significantly less computational resources. One of the main problems of external gear pumps' CFD modeling is the influence of so-called relief grooves (channels) located on the two bearing bodies (balancing plates) [52]. This has motivated the authors to design a 2D model solution beyond the possibilities of the construction, which would enable these grooves to be modeled in such a way as to properly consider their influence on the numerical results. **The general motive** for the present study is that the classical 2D models [3; 5; 8; 36; 40; 43; 44] do not consider the influence of relief grooves, although it is possible.