1. Introduction
Turbocharging is regarded as one of the key elements in the success of downsized internal combustion engine systems, an effective strategy towards CO2 emissions reduction. These days, a turbocharger is no longer restricted to its conventional application, butinvariousotherusagessuchasturbo-compounding[1],electrically assisted [2,3] and steam turbocharging [4], where the turbine will often operate at more extreme conditions. In all cases, the process of engine-turbocharger matching during the development stage plays a significant role towards achieving the best possible system performance, in terms of minimizing fuel consumption while maintaining good transient response. In current industry practice, engine modelling does not consider the full unsteady analysis of the turbocharger turbine, but instead treats it as a quasi-steady device. While this traditional approach can provide adequate simulations of the engine’s steady state engine performance, its deficiencies become apparent when attempting to accurately predict transient response [5], especially so when the desire is to predict the benefit of turbocharger technologies such as twin
scroll turbines. Numerous unsteady turbine models have been developed over the years, yet none of these models have been widely implemented into commercial one-dimensional engine cycle simulation codes, mainly due to the associated complexity.
1.1. Background study
Commercial one-dimensional engine cycle simulation software tools model the turbocharger turbine by following a quasi-steady approach (turbine inlet and outlet are considered as the points where the flow conditions are experimentally measured). However, due to the reciprocating nature of the engine, the flow entering the turbine is of a pulsating nature, the form of which varies depending on engine speed, displacement, number of cylinders, etc. Over the last fifty years, several researchers have investigated this phenomenon, showing that during each engine cycle the instantaneous mass flow measured at the turbine inlet does not follow the steady-state characteristic, but instead forms an unsteady hysteresis loop, particularly at lower pulse flow frequencies [6–17]. The unsteady characteristic was also found (experimentally [16] and analytically [18]) to vary in accordance with turbineinletpulsefrequency.However,detailedexperimentalflow field investigations of the turbine [19] suggest that the rotor itself does operate in quasi-steady manner (compared to the turbine