## 1 Introduction  
Along with the growing interest in global environmental issues, the automotive manufacturers are facing increasing challenges to reduce the gaseous emissions [1] coming from internal combustion engines as well as to meet the strict emission legislation year by year [2]. Despite the rapid growth of electric car sales in recent years, internal combustion engines will continue to be active until at least 2050, according to recent studies [3]. Moreover, nowadays, battery electric vehicles have heavy CO\({}_{2}\) footprints when analyzed from cradle to grave [4, 5]. It is foreseen that plug-in hybrid powertrains, and small capacity turbocharged engines will cover the major part of passenger cars needs in decades ahead [6]. To compete with an electric powertrain, automotive engineers are developing new internal combustion engines to be environmentally friendly, while keeping the vehicle performance and having sufficiently attractive fuel consumption to satisfy the customers' requirements. Over the years, automotive OEMs are increasingly downsizing their engines, which has been demonstrated to be an efficient way in reducing the engine CO\({}_{2}\) emissions with promising cost-to-benefit ratios compared with many other advanced ICE technologies [7]. To assure the same engine brake output power and performance with the reduction in cylinder displacement, downsizing technologies need to use forced induction-turbocharging. The traditional single entry turbine is widely used in turbochargers, due to its straightforward construction. This has given many advantages in terms of fuel consumption and emissions reductions with the previous and current regulations. However, concerning the future legal requirements for low emissions (Euro 6d Full and Euro 7 regulations) with fuel efficiency, there is still need and potential for optimization. Nevertheless, a turbocharger turbine always confronts high unsteadiness of flows coming from the reciprocating internal combustion engine [8]. In recent years, automotive OEMs are seeing much interest in using the double entry turbines, especially for four cylinders turbocharged petrol engines with wide valves overlap period in their timing diagram or in six-cylinder compression ignition engines [9]. They have the advantages of utilizing the pulse energy coming from the engine exhaust and minimizing the interferences between the cylinders during the exhaust process (engine pumping losses). Some engine manufacturers choose twin-entry turbines (where the turbine scroll is meridionally divided, as shown in Figure 1a); others opt for the dual-volute turbine (turbine scroll is circumferentially divided, as shown in Figure 1b). The comparison of performance parameters between these two types of double entry turbines has been extensively discussed since [PERSON] and [PERSON] [10] until more recently, such as in the work by [PERSON] et al. [11]. Moreover, both turbines (twin-entry/dual-volute) have different geometries due to their designs, merely by the type of flow division, as explained below:  
* Twin-entry turbine (T#1 TE): The scroll has a single wall around the entire perimeter of the turbine housing such that each entry admits the exhaust gas over the whole circumference of the turbine wheel. The entry closer to the turbine outlet is named as Shroud (Sh), and the entry which is closer to the bearing housing side is called as Hub (H), and the same is shown in Figure 1a. * Dual-volute turbine (T#2 DV): The scroll is divided in a way that each scroll admits the exhaust gas at a separate section of the rotor. The turbine scroll which has a longer volute is named as Long Volute (LV), and the scroll which has a shorter volute is named as Short Volute (SV), as shown in Figure 1b. Hereafter, the respective turbocharger turbine entries/scroll are referred to by their names.