## 2 Modelling Methodology
### Computational Fluid Dynamics  
AxSTREAM provides tools that generate geometries based on 1D meanline design and allows analysis using higher fidelity models ranging from streamline analysis, axi-symmetric 2D and 3D computational fluid dynamics (CFD). AxCFD is the tool used for pre-processing, mesh generation, calculation and results post-processing. This step allows for the evaluation of the designed flow path, the comparison of results between the different calculation models (meanline, streamline, 3D CFD), and the understanding of flow mechanisms within the turbine.  
The turbine domain employing a mixing plane halfway between stator trailing edge and rotor leading edge is simulated using AxCFD. Boundary conditions, of P\({}_{0_{in}}\) = 297 bar, T\({}_{0_{in}}\) = 1173 K and P\({}_{out}\) = 54.0 bar, and working parameters are taken directly from the AxSTREAM project case saved  
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Parameter** & **Unit** & **Constraint** \\ \hline Power & MW & \(\geq\)_W_ from cycle Section 3.1 \\ Efficiency & \% & \(\geq\)80 \\ Flow coefficient & - & \(<\)1 \\ Rotor inlet blade speed & m/s & \(\approx\)450 \\ Rotor outlet absolute flow angle & \(\circ\) & \(\approx\)0 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Design space explorer constraints.  
after the 2D analysis with values taken as spanwise averages of quantities at hub, mean and tip sections. Rotational speed and mass flow rate are also automatically inherited from the project database but are altered for off-design simulations. Like other CFD tools, AxCFD solves decomposed Reynolds-Stress-Averaged Navier Stokes (RANS) equations with time-averaged density, pressure and energy conservation, and mass-averaged velocity equations in discretised fluid domains.  
Passage mesh creation is required before any aerodynamic assessment of the turbine. The way of defining the size and number of the mesh elements in AxCFD is through mesh quality, a value ranging between 1 (coarsest) and 10 (finset). A mesh sensitivity study is performed, with results discussed in Section 3.3.1, to allow for a compromise between accuracy (mesh refinement) and computational time. Structured HO-type mesh elements with the same quality in hub-to-shroud and blade-to-blade directions are used in all cases with additional parameters for mesh adjustment; values are taken based on recommendations by SoftInWay.  
The meshing zones defined by points on leading edge (LE) and trailing edge (TE) are modified manually over the blade profile contour for hub and tip sections. A mesh quality check is performed; good quality elements are described as those with no Jacobian determinant less than 0.3 and no (or minimal) angle parameter less than 12\({}^{\circ}\).  
The k-\(\omega\) SST turbulence model is used for its suitability in viscous turbomachinery simulations based on previous experience [23; 24; 25], with a medium turbulence intensity of 5%. The first order upwind scheme is employed due to convergence difficulties when using second-order. Slightly fluctuating trends and considerably high value criteria for some residuals in the range of 10\({}^{-5}\) are accepted for simulations of similar applications shown in [26; 27], but convergence is also checked against inlet/outlet mass imbalance of within 0.2%. AxCFD also allows calculations over 2D spanwise fluid domain sections via axi-symmetric modelling which is used of off-design performance map generation.