**1. Introduction**

The viscous flow between rotating disks has received special attention for its wide applications, including wet clutches in automatic transmission [1], in hydro-viscous drive [2], and in turbomachinery [3]. The theoretical research of the two-disk flow was first proposed by Von Karman in 1921 [4]. Later, the fundamental flow behaviors of the counter-rotating and the rotor-stator disks were investigated theoretically by Batchelor [5] and Stewartson [6]. Most of the literature on the two-disk flow dealt with the shrouded disk systems, forming the theoretical foundation of the turbomachinery [7]. However, studies on an open disk system are also important, since the theory is the foundation of many applications, such as wet clutches. In the open disk configuration, the flow field becomes a Stewartson-type flow [8]. It has been found that annular or spiral rolls and an Ekman layer exist on a rotor disk [9]. Moreover, traditional research of a flat disk flow field is also focused on the laminar–turbulent transition [10].

In applications of the open disk system, such as mechanical seals and thrust bearings, the disks are featured with complicated surface texture. The load-carrying capacity and the cooling effect are improved by various groove structures on the surface [11–15]. The radial single-phase flow between a grooved rotating disk and a flat stationary disk was investigated analytically and experimentally [16]. Additionally, the effect of grooves on lubricant flow and thermal characteristics was examined for engagement of wet clutches [17,18]. The cooling capacity was notably affected by the single or the

two phase flow patterns of the flow field with grooved plates [19,20]. The influence of flow dynamic behavior inside the grooved rotating-disk system on the disk temperature distribution was also demonstrated [21]. A rotating disk model, which is the topological geometry of bearing rotating parts, was established, and the volume of fluid (VOF) method was used to instantaneously track the interface between the oil film and the air on the disk surface [22]. For open wet clutches, the flow changed from single-phase to multi-phase flow in the gap at high speed. The commonly used simplified analytical model was constituted by the multi-phase flow theory of open grooved two-disk systems [23,24]. The flow field of the oil film based on the VOF model was simulated numerically by fluid dynamics simulation software to study the two-phase flow of a hydro-viscous drive [25]. The flow behavior was found to have an enormous effect on mass and heat transfer in the multiphase flows [26,27]. The effects of radial grooves and waffle-shape grooves on disk thermal and torque responses were studied [28]. Several other models were formulated to determine the flow impact on the heat exchange and the temperature distribution in the grooved two-disk system [29,30], including a computational fluid dynamics (CFD) model [31]. The drag torque and the flow pattern in the grooved rotating-disk system also received special focus [1,32–34]. It was found that the efficiency of the grooved rotating-disk system varied with flow field parameters [35–37]. From the above review, it could be concluded that the flow field would be dramatically affected by the disk configuration and the operation status in the grooved rotating-disk system. The variation of the flow field has a tremendous effect on the operation performance of the grooved rotating-disk system. However, the details of the flow pattern variation under different parametric conditions are still not clear. The heat dissipation characteristics of the flow field in a two-disk system remains to be further studied. Thus, a deeper insight into the interaction between the flow field characteristics and the grooved two-disk system enables potential improvements in practical applications, such as wet clutches.

In this paper, the flow pattern and the heat dissipation of the flow field inside the grooved rotating-disk system is studied. Different from the single phase studies before, the air–oil two-phase flow is investigated. The air–oil phase distribution in the flow field is presented in detail and compared with visualization experimental results. The effects of angular speed of grooved disk, oil flow rate at inlet, and disk spacing on the flow pattern and the oil phase distribution are analyzed. The local and the average Nusselt number was utilized to investigate the heat dissipation capacity of the two-disk system. This research aims to propose a quantitative method for the advanced precision cooling mechanism design of the clutch disk.
