## 4 Ricardo Wave Engine Modelling
### GT1548 Turbocharger Matching to Engine
#### 4.2.2 Compressor and Turbine Map Scaling  
The method suggested by [PERSON] et al. [15] was used for scaling the turbocharger maps, as the baseline principles yielded good results for generation of maps with similar performances but at different sizes. However, the suggested method was not followed in full, as while the method provides conclusive results based on the work conducted, it was unable to provide a methodology that would allow effective engine-operating conditions matching. The method was followed until the target parameters were identified; from then on, the method utilises an iterative process of a discontinuous function to achieve the compressor outlet and turbine inlet conditions that were tested on the model to provide the correct operating condition at the team's design point. \begin{table}
\begin{tabular}{l l l} \hline
**Reference Condition** & **Compressor** & **Turbine** \\ \hline Pressure & 100 & 101.3 \\ Temperature & 298 & 288 \\ \hline \end{tabular}
\end{table} 
Table 1: Reference conditions for conducting turbocharger maps. Figure 5: BSFC (Brake-specific fuel consumption) of Ford Eco Boost 1.6 L petrol engine at full load. To start the scaling process, both maps are required to be converted into dimensionless maps, representative of the family of compressors and turbines with similar trims [15]. Both maps are scaled using the corrected mass flow rates to obtain the mass flow coefficient in Equations (6) and (7) and the rotor tip Mach number in Equations (8) and (9) as a function of the upstream conditions. The results are shown in Figures 7 and 8. Note that the compressor map was generated using a simple MATLAB script with an interpolation function. \[\phi_{\text{C}}=\ \frac{\dot{m}_{\text{C}}\sqrt{RT_{u}}}{P_{u}D_{\text{C}}^{2}} \tag{6}\]  
\[\phi_{\text{T}}=\ \frac{\dot{m}_{\text{T}}\sqrt{RT_{u}}}{P_{u}D_{T}^{2}} \tag{7}\]  
\[C_{0,\text{ C}}=\ \Big{(}\frac{2\pi}{60}\Big{)}N_{\text{C}}\frac{D_{\text{C}}}{ \sqrt{\
u_{a}RT_{u}}} \tag{8}\]  
\[C_{0,\text{ T}}=\ \Big{(}\frac{2\pi}{60}\Big{)}N_{\text{T}}\frac{D_{\text{T}}}{ \sqrt{\
u_{e}RT_{u}}} \tag{9}\]  
With the maps now dimensionless, they can be scaled according to the diameters that match the engine. The next step in the process of scaling the turbocharger maps is to determine the scaled diameters. For this, the air mass flow rate and manifold pressure required to achieve the desired engine performance needs to be calculated [16]. The calculation is done at an engine speed of 5000 rpm. The mass flow rate was found to be 0.118 kg/s using Equation (10), and the manifold pressure was found to be 2.14 bar using Equation (11). \[\dot{m}_{air}=\ \frac{\dot{W}\,AFR}{N_{TH}E_{LHV}} \tag{10}\]  
\[P_{m}=\ \frac{120\ \dot{m}_{air}\ RT_{m}}{N_{\
u}N_{E}V_{d}} \tag{11}\]  
The next stage is to determine the inlet conditions of the turbine and outlet conditions of the compressor. This was achieved by following the instructions for calibrating a boosted model set out by  
Figure 6: Turbine Ricardo WAVE map. WAVE's help manual [16]. The compressor outlet and turbine inlet were disconnected from the model and replaced by ambient ducts. Using WAVE's built-in Design of Experiments tool (DoE) and the Box Benken method of DoE 25 simulations were conducted varying the compressor outlet conditions and turbine inlet conditions. An empirical equation was then obtained from the results using a multiple regression methodology and a MATLAB script. The script then solved the equation to identify the best combination to achieve the desired engine air mass flow rate. These conditions were then run in the WAVE model to confirm the output matched the predicted empirical response. Finally, the turbine mass flow rate was obtained using the air-to-fuel ratio (AFR), as while the fuel was combusted, the same amount of mass was expected to flow through the exhaust. The turbine mass flow rate is calculated using Equation (12). The target parameters are shown in Table 2.  
Figure 5:0