**I. Introduction**

Smaller frontal area and high thrust to weight ratios of mixed flow compressor stage has resulted in its application for small gas turbine engines in aviation sector [1] . The efficiency and reliability of the compressor depends to a great extent on flow behavior in its flow passage and its interaction between impeller and diffuser. The complex turning of the flow not only in the impeller but also in the diagonal diffuser complicates the flow field and requires detailed study of the flow utilizing computational techniques. Stanitz [1952] gave a methodology for the design and analysis of 1-dimensional compressible flow in mixed flow compressors including effects of friction and area change [2]. The size of a compressor can be reduced by adopting the mixed flow compressor without any deterioration of performance.

In the present work, a mixed flow compressor is designed to achieve a total-to-total pressure ratio of 5:1. The compressor’s flow path consists of mixed flow impeller, diagonal vaned diffuser, and one more axial vaned diffuser. Design point operation of this compressor is summarized in Table 1.

All iterations of the present study are accomplished utilizing commercial software platform AxSTREAM™ for turbomachinery design, analysis and optimization. Although many loss models exist in the industry, Aungier’s loss mechanisms are adopted for mixed flow compressors in the present design study. Loss models for all flowpath components are listed in the Table 2. Various compressor configurations were analyzed to understand the flow field and meet design targets (Table 1)

**Table 1 The operating conditions and geometrical constraints of compressor stage**

**Table 2 Loss models**

Based on the available technical specification, using the preliminary design module of AxSTREAMTM, the mixed flow compressor stage was designed. To study effects of various parameters and geometry on the performance, the design parameters and geometrical parameters were used in ranges during the preliminary design. Nearly 15000 designs were generated during the preliminary design stage. Different compressor designs were reviewed based on blade metal & flow angles, meridional dimensions, axial lengths, etc. From the preliminary design exploration, it was observed that providing the preswirl at the impeller inlet improves the efficiency by reducing inlet Mach number and losses due to the high velocities at inlet. To turn the flow at the impeller inlet, inlet guide vanes (stationary blade row) are implemented. Figure 1(a) shows the effect of inlet flow angle on efficiency and Figure 1(b) shows the variation of efficiency with respect to impeller blade exit angle. Figure 1(c) shows the meridional flow path with pressure contours and the 3D geometry of the compressor stage. The final design selected is analyzed further in the meanline/streamline solver.

**Figure 1. Preliminary Design Explorer (a) efficiency vs. inlet flow angle; (b) efficiency vs. impeller exit blade angle; (c) 3D compressor view & meridional view with static pressure contour**

**III. Detailed compressor design**

**A. Description of Solvers**

Four different solvers were utilized in the current design: meanline, streamline, full streamline solver (FSC), and axisymmetric CFD. Meanline solver calculates kinematic and thermodynamic parameters accounting for real losses listed in Table 2. At this level, important aerodynamic criteria and experience help the designer to evaluate designs. Streamline analysis was performed adding additional conservation equations to the compressor analysis. Streamline analysis accounts for radial non-uniformity in thermodynamics, kinematics, and losses. FSC solves the compressor in meridional plane and qualitatively shows averaged velocity distribution. End-wall contours were profiled based on FSC results on a quasi-orthogonal grid. The axisymmetric CFD analysis was performed to understand the flow behavior and to compare the results with the meanline and streamline results. The losses at the hub, mean and tip sections were reviewed during each iterations of the design to achieve minimum losses in the impeller. At first, it was observed that the overall stage performance was not satisfactory and significant losses exist in the diffuser. An initial off-design analysis showed the operational margin was also not in the desired range. Hence, the authors decided to optimize the impeller first and then tackle the diffuser problems to obtain the required performance.

**B. Impeller Optimization**

End-wall contours are optimized to ensure the smooth flow through the impeller. Subsequently, the distribution of BETA & THETA are modified to increase the throat value and also to increase the total to total pressure ratio generated by the impeller. Initially a splitter with length ratio of 0.7 was used and subsequently the splitter was extended to 0.8 which resulted into better pressure ratio and operating margins. Figure 2(a) shows the slope of the impeller inlet and Figure 2(b) shows the slope angle at the impeller exit which was optimized to reduce the losses in the vaneless space as it leaves the impeller.

**Figure 2. Editing of impeller geometry at inlet/outlet station**

Figure 3(a) shows the quasi-orthogonal grid that is generated for the full streamline solver (FSC). Figure 3(b) shows the contours of Mach number for the impeller in the meridional plane for the initial impeller and the optimized impeller using full streamline (FSC) solver. To validate the FSC solver results, both impellers were also calculated using axisymmetric CFD solver and the Mach number contours for initial and optimized impeller design were presented in Figure 4 which are having good qualitative agreement with the FSC solver results.

**Figure 3. Contours of Mach number of the initial and optimized flow path using FSC solver**

**Figure 4. a) axisymmetric mesh; b) axisymmetric CFD solution -- Mach number contours**

The performance of the impeller at both design and off-design operation was calculated for the initial impeller and for the final impeller. The results are presented in Figure 5. Charts show that not only there is improvement in efficiency but also the improvement in pressure ratio and operational range. The final compressor characteristic shifted to the right which resulted in establishing sufficient choke margin comparing to the earlier design.

**Figure 5. Comparison of old design and improved design after editing of impeller**

To analyze the flow structure and also to obtain the performance map in 3D CFD, full RANS based CFD analysis was performed in CFD module of the AxSTREAMTM. Profiling was done prior to CFD analysis and Figure 6(a) shows the distribution of the BETA, THETA and thickness at the mean section of the impeller. Red, blue and green color curves represent the BETA, THETA and thickness distribution, respectively. The angle values represented in Figure 6(a) are with respect to meridional plane. Figure 6(b) shows the 3D view of the blade profile for both splitter and main blade. 3D CFD analysis of the final impeller geometry is compared with the streamline calculation results in Figure 7. The choke mass flow difference between streamline solver and CFD is about 1.35% whereas the efficiency at design point differed by about 1.2% when compared between the streamline solver and CFD solver. Streamline and 3D performance predictions show good agreement.

**Figure 6. (a) THETA, BETA & Thickness distribution for impeller (b) 3D view of the profile**

**Figure 7. Impeller performance: a) pressure ratio (total-total) versus corrected mass flow rate; b) efficiency versus corrected mass flow rate**

The blade loading distribution at hub, mean and tip section for the main blade and splitter blade is show in Figure 8. The local static pressure is normalized with inlet total pressure. The loading looks smooth and within norm.

**Figure 8. Blade loading**

As the next step, diffuser was introduced for the optimized impeller and performance was calculated using the streamline solver. It was observed that the losses in diffuser were significantly high resulting in lower performance of the stage.**C. Diagonal Diffuser optimization**

The major constraint on the diagonal diffuser was the maximal tip diameter. The flow at the exit of impeller was transonic and this resulted in shock formation at the diffuser inlet. 3D CFD analysis was performed to understand the flow interaction between the impeller, vaneless space and diffuser. Figure 9, shows the various configurations of diffusers studied during this phase. It was observed that total pressure loss in initial diffuser was very high. Initial diffuser design has 20% total pressure loss and the modified diffuser pressure loss is 8%. The losses were reduced by optimizing the inlet and outlet angle of the diffuser, varying the axial length of the diffuser, the channel height ratio at the inlet and outlet, and the profile.

**Figure 9. Diagonal diffuser shapes**

While calculating the stage with initial diagonal diffuser, some blockage at design point was noticed in the streamline results and later verified with CFD results. In streamline solver, losses due to blockage and flow separation can be predicted by the separated flow mix loss factor [3], om_mix, which was equal to 0.00033 at design point and increases in the direction of stall condition which reduces the stage stall margin. CFD calculation was performed for the point slightly left to the design point and analysis showed the huge blockage in the diagonal diffuser passage. The reason was improper diffuser profile. To overcome this, profile of the diffuser was edited using BETA & THETA distribution of the diffuser vane and separated flow mix loss factor [3] dropped to 0.00021. Figure 10 shows the diffuser geometry. While making the adjustments in the profile, throat area was reduced which resulted in diagonal diffuser passage additional choking losses. Such type of choke losses of the components can be predicted by the choke loss factor [3], om_ch, in AxSTREAM. To avoid the choke losses at the design point, number of diffuser vanes was reduced from 14 to 12 along with the blade thickness. The number of diffuser vanes can be reduced even further and implement diffuser splitter vanes to control the choke loss and to provide the better flow turning in the diffuser passage. The desired performance was achieved with the optimized diffuser and the author did not implement diffuser splitter vanes.

**Figure 10. Diagonal diffuser profile, BETA, and THETA curves**

Since the required velocity was not achieved at the exit of the vaned diffuser, an additional axial stator was introduced at the exit of diagonal diffuser vane. DCA profiling was used for the axial stator blades with the main objective of reducing the swirl at the exit and recovering the static pressure to maximum