## 1 Introduction  
The cost of fuel in the UK over the last fifteen years is presented in Figure 1. The price of fuel increases faster than inflation, suggesting it will be a greater factor in the consumers' thought process on purely economic grounds. Because of this, automotive manufacturers are implementing and researching methods to improve the fuel economy of their vehicles. One way to do this is by reducing the size of engines in the fleet, known as downsizing. Smaller engines are intrinsically more fuel efficient, demonstrated experimentally by [PERSON] et al. [1], also leading to an overall reduction in CO\({}_{2}\) emissions. Downsizing the engine in a vehicle will reduce its power output and performance, therefore additional boosting technologies that can increase the power density of an engine are vital in sustaining  
Figure 1: UK fuel prices at pump and UK inflation rates normalised to fuel prices (consumer price indexing), data from Department for Business, Energy & Industrial Strategy (2018) and Rate Inflation (2018) [2,3]. the downsizing trend; turbochargers are one such boost device. A study by [PERSON] and [PERSON] [4] suggests turbochargers accounted for 33% of net fuel savings from all technologies among new vehicles sold over two representative years in the United States. This is a multi-faceted benefit, as it incentivises turbocharged vehicles as a financially responsible option, as well as playing to the social pressures towards more environmentally friendly transport. Turbo-lag is the primary target for improvement by current day turbocharger manufacturers. It has become such a focus in the industry because of the poor reputation it has with drivers, making them feel less connected to the vehicle and reducing the quality of the driving experience, particularly in high performance turbocharged vehicles. 'Boost on demand' is a concept that resonates with the manufacturers of high-performance vehicles, needing immediate and predictable responses to the drivers control inputs [5]. While improving the turbine power output is one method to tackle turbo lag, the other is to decrease the rotational moment of inertia of the turbochargers rotating assembly. The inertia of the system represents the amount of torque needed to produce a level of angular acceleration around the rotational axis. By decreasing this quantity an equivalent power generation will spool the turbocharger up faster, providing increased boost to the engine, faster. Focusing on the turbine as a route to better inertia, replacing the conventional, bulky radial turbine with an advanced, lightweight axial device has potential to improve the transient response of the boost system and the whole vehicle, while not sacrificing steady-state performance. This defines the problem with current turbocharging technology and highlights the necessity for research on the axial turbine in the automotive environment. Despite the dominance of radial devices in small automotive turbine applications, there is clear evidence to indicate the benefits the axial turbine can offer. The specific speed and specific diameter is a useful way of normalising a turbine for a direct performance comparison with devices of completely different scales. [PERSON] and [PERSON] [6] suggest that radial turbines significantly drop off in efficiency above specific speeds of 0.8. [PERSON] et al. [7] show that for the modelled operating conditions of a Ford eco-boost 1.6 litre petrol engine, lead to a turbine specific speed and specific diameter that support the implementation of an axial device. In addition to potential performance benefits, the rotational moment of inertia of the axial turbine is intrinsically lower than a radial equivalent. Early testing by [PERSON] [8] demonstrated that the turbocharger equipped with an axial turbine reached full boost pressure 25-40% faster than the radial equivalent. This potential for improvement in transient performance was a significant motivating factor for the current research programme.