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Figure 6 Turbo-component blade row definition using non-dimensional coordinates.

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Figure 1 Generic flow chart for the SOCRATES modules. The SOCRATES program, ‘coded i in FORTRAN 90, follows the 2-D SLC methodology under an iterative technique to re-calculate the streamline position, slope and curvature based on a meridional velocity estimation. Flow field solution is based on the fundamental the Newton’s Second Law or conservation of momentum. Because the conservation of momentum already considers the continuity equation, it yields in the Euler equation of motion, which considers the surface traction expressed in terms of the stress field. Due to the inviscid flow assumption, the stress tensor becomes isotropic, resulting in the simplified version of the Navier-Stokes equation for a non-viscous fluid. Within this equation, blade forces are neglected whereas centripetal and Coriolis accelerations are considered. Numerical solution in a cylindrical system, give the full REE to obtain the meridional velocity gradient in the spanwise direction. An initial mesh is generated between the intersection of the assumed initial streamline position, and the inlet and outlet blade rows. REE in set with the mass flow conservation are iteratively solved to satisfy the actual mass flow or outlet static pressure, according to the boundary condition specified. If different, the next loop begins with a new inlet meridional velocity that redefines the streamline radius, and hence, modifying the grid. Streamline radius and shape keeps moving until an agreement is found between the calculated values and specified boundary conditions within a specified error tolerance. Fig. 1 displays a general schematic of the SOCRATES aforementioned processes.

The SOCRATES GUI was coded in Python v. 3.4.3 and it is divided in three main sections: (1) model setup or pre-processing, (2) solution, and (3) visualization or post- processing, as seen in Fig. 2. Figure 2 SOCRATES GUI main window workspace.

In general, the model setup is related to the input files, the solution to the program execution, and the post-processing to the output files. Fig. 3 displays a general structure diagram of the GUI, where the different processes for the model setup and post- processing are laid out. Figure 3 SOCRATES GUI structure for model setup and post-processing.

The first step to characterize the compressor or fan model is to define the number of stages (rotor, stator), inlet guide vane (IGV), outlet guide vane (OGV), or swirler. Additional ducts can be added at the inlet or outlet to capture the flow field properties ahead or behind the active turbo-components as observed in Fig. 4. Figure 4 Compressor layout model to define the number and type of turbo-components.

Figure 5 Non-dimensional flow path coordinates definition. The compressor flow path is defined through non-dimensional x and z Cartesian coordinates that allow a potential compressor scaling, based on a maximum flow path length and maximum radius, as illustrated in Fig. 5.

To define the blade profiles, blade elements are specified by radial section, which are laid out according to a constant surface turning on a conical surface [43] and stacked along their centre-of-area. Fig. 7 shows the blade-element definition in the SOCRATES GUI. Figure 7 Blade-profile-element definition for different radial positions.

Because the solution of the REE is an interative approach, initialization values for the mean-line meridional velocities at the turbo-component inlets and outlets are specified. Additionally, endwall blockage factors can be indicated at the blade row inlets and outlets. Mean-line meridional velocities and blockage factors are given as in Fig. 8. Figure 8 Initialization values and blockage factors specification.

Figure 9 Boundary conditions for every speedline operating point specified.

Figure 10 Solution settings input. To finalize the model setup, solution settings are specified in terms of the number of streamlines for the grid, damping factor for streamline radius movement between iterations, and the different error tolerances to satisfy boundary conditions.

The SOCRATES execution can be performed directly in the GUI or through a quick launching tool developed that allows a selection of the different compressor/fan geometries available. The quick launcher allows GUI access in case a model is modified or a new compressor is defined. Figure 11 Quick launcher to directly ran SOCRATES or start the GUI.

During running time, the residuals for the steamtube inlet and outlet mass flow errors for each turbo-component are plotted to track convergence. Fig. 12 shows the residuals graphs, which are constantly updated at every iteration. Figure 12 Iteration residuals plots for the inlet and oulet of each turbo-component.

The compressor flowpath sketch is visualized in a 2-D meridional plane, where the defined turbo-components are laid out as seen in Fig. 13. Figure 13 Axial-flow compressor 2-D view in the meridional plane.

Figure 14 Blade-profile-section 2-D view in the blade-to-blade plane.

Figure 15 3-D visualization for the NASA two-stage fan [44]. Due to the blade-element layout method implemented, full 3-D coordinates are obtained for the whole compressor/fan geometry. The 3-D view of the compressor flowpath and blading can be visualized as depicted in Fig. 15.

Figure 16 2-D final grid in the meridional plane composed by converged streamlines and quasi- orthogonals.

Figure 17 Computaional 2-D grid visualization zoom at hub endwall.

Figure 18 Flow field properties plotting

Figure 19 2-D SLC NASA Two-Stage Fan [44] flow field parameters for the 1‘ stage rotor inlet and outlet. a) Absolute total temperature b) Absolute total pressure c) Static pressure d) Relative meridional flow angle e) Relative Meridional Mach number f) Meridional Velocity Fig. 19 shows the potential of the tool to compare different properties. In this case, the 1“ stage rotor inlet against the outlet behaviour at w = 34.515 kg/s and design speed is compared.

To validate the 2-D SLC flow field from the GUI, Fig. 21 shows a comparison against measured data, where consistent agreement is obtained and no significant differences are observed.

Figure 21 NASA Two-Stage Fan [44] flow field parameters comparison between experimental data and 2-D SLC for the 1“ stage rotor inlet and outlet. a) Absolute total temperature b) Absolute total pressure c) Static pressure d) Relative meridional flow angle e) Relative Meridional Mach number f) Meridional Velocity

pressure ratio fan map for the NASA Two-Stage Fan, whereas in Fig. 23, the isentropic efficiency fan map is shown. Figure 22 Fan pressure ratio map for the NASA two-stage fan [44] at 100, 90, 80, 70 and 50% of design speed.

Figure 23 Fan isentropic efficiency map for the NASA two-stage fan [44] at 100, 90, 80, 70 and 50% of design speed.

Figure 24 NASA Two-Stage Fan [44] pressure ratio map comparison between measured and 2-D SLC data.

Figure 25 NASA Two-Stage Fan [44] isentropic efficiency map comparison between measured and 2-D SLC data.