## 1 Introduction  
The flow behavior of radial turbines has attracted the attention of many researchers [1]. Twisting the blade along the span and the passage produces an inherently three-dimensional (3D) flow. Different admission conditions add extra complexity in the case of dual volute turbines. Double entry turbines are used in automotive turbochargers for preserving the pulsating exhaust flow energy [2]. Dual entry turbines work most of the time with the unbalanced flow. In the partial admission situation, only one entry is fed [3]. Several studies have been published over the years regarding the effects of unequal admission effects on turbine performance. [PERSON] et al. [4; 5; 6] and [PERSON] [7] performed detailed studies on a double volute turbine. Their results showed that increasing the inequality between the internal mass flows of the entries leads to an efficiency drop, especially at the lower powers. [PERSON] [7] found some dependency between the two entries of the dual volute, even when they were kept entirely separate. They reported that a significant interaction of two entries also adds considerable dissipation in the interspace region between the stator and the rotor [6]. The results showed that the flow developing from high-pressure entry into this region checks the flow from the other entry with the low-pressure fluid. [PERSON] et al. [8] focused on the loss generation in a partial admission case. They found that the entropy produced in the non-flowing section of the rotor wheel had the same magnitude as that in the working section. Also, they showed that when the vortices in the non-flowing area entered into the flowing part of the volute, further losses will be created. When the primary objective is to increase turbine efficiency and the total pressure ratio, secondary flow should be defined and controlled [9]. Secondary flow regions are always the origin of higher losses. The cascade passage vortex, corner vortex, tip clearance vortex, horseshoe vortex, and annulus end wall boundary layer are some of the well-known vortex structures in axial turbines; they are not independent mechanisms, and as can be observed in experiments, they overlap and interact [9]. [PERSON] studied the secondary flows in turbines [10]. Blade loading, load distribution, the incidence, and the inlet boundary layer affect the secondary flow characteristics. Classic secondary flows in axial turbines are known [9]. However, there is a lack of knowledge regarding the understanding of the physical origin of the correlated \"secondary loss\" also in the effects of the upstream non-uniform flow conditions on the formation of secondary flows [11]. Several studies investigated the secondary vortices in a linear cascade. [PERSON] compared a linear and an annular cascade with the same two-dimensional blade geometry that was employed [12]. He showed that the radial pressure gradient in the annular cascades changes the pressure loss distribution compared to the linear passage, which experiences no such pressure gradient. A radial pressure gradient is added to the flow everywhere in the annular passage, because the flow area in the cascade passage increases from the hub to the tip of the adjacent blades [13]. From the pressure side to the suction side, the radial pressure gradient increases [14]. Flow visualization studies by [PERSON] and [PERSON] [15], [PERSON] et al. [16], [PERSON] and [PERSON] [17], and [PERSON] et al. [18] have indicated that the pressure-side leg of the horseshoe vortex is a dominant constituent of the passage vortex system. [PERSON] et al. investigated the effect of periodically incoming wakes on the axial loss development [19]. They found higher front-loading results in a lower intensity of the secondary flow downstream of the trailing edge. Also, there are lots of research studies about radial turbines. [PERSON] et al. [20] presented an investigation of secondary flow phenomena in a radial one-entry scroll turbine nozzle.