## 2 Axial Turbine Loss Modelling  
The accuracy of the preliminary design process is wholly reliant on the loss predictions used to calculate stage thermodynamics and flow velocity vectors. [PERSON] [10] has compiled the most prominent loss models for axial turbines and identified the components of the total system pressure loss.  
The Soderberg correlation [11] provides the simplest three-dimensional function for blade performance. It uses the flow turning angle, basic blade geometry and the Reynolds number to predict pressure losses over a blade. The functions are based on a large amount of experimental cascade data and was considered too simplistic for the level of preliminary design aimed for.  
The second option considered was the model suggested by [PERSON] and [PERSON] [12]. They lay out a comprehensive prediction model based on summing the profile loss, secondary loss, annulus loss and tip leakage loss. Despite its accuracy, the Craig & Cox model was not considered suitable for this design process, as the intention was to fully automate the performance prediction. Due to the high number of calculations reliant on cascade data it would be very difficult and time consuming to implement the full model in an automated algorithm, as the system would have to'read' all the graphs automatically.  
[PERSON] [13] builds a total blade loss co-efficient from the same elements as the [PERSON] & Cox method and assumes pressure loss coefficients are not influenced by the flow Mach number, therefore avoiding shock losses. This means the accuracy of the model is compromised under highly supersonic conditions. Due to the conventional flow speeds and temperatures in a turbocharger, velocities significantly above the transonic range are not expected so does not preclude the use of this model. As the blade geometries anticipated from the turbocharger axial turbine involve aspect ratios near to 1, the Dunham & Came prediction allows for increased accuracy over the conventional Ainley-Mathieson model [10]. This applies a correlation for the prediction of the secondary flow loss coefficient, as opposed to basing it on cascade data as a function of annulus geometric properties.  
It also introduces a new function for evaluating the tip clearance loss. [PERSON] and [PERSON] [14] compare the most popular loss models based on their tip-leakage predictions and show that the Dunham & Came correction results in tip loss components significantly larger than the other available methods. Their review is general to all turbines, so the guidance of [PERSON] [6] and [PERSON] et al. [15] was followed for this low aspect ratio application. The 3D loss model employed for the system was the Ainley-Mathieson prediction with Dunham & Came correction.  
[PERSON] [10] found that the Craig & Cox and Ainley-Mathieson models demonstrated the same performance trends compared with experimental data, so the decision to use the simpler method should not penalise the accuracy of the obtained results. The chosen performance prediction method requires five cascade readings, from three different graphs. This was considered acceptable complexity for the automated preliminary design process.