5.1. Flow analysis: Velocity triangles

Entry and exit velocity triangles for impeller blades along the radial section with backward swept blades <sup>β</sup><sup>2</sup> <sup>¼</sup> <sup>0</sup> � are plotted as shown in Figure 2(a) and (b). Inlet Mach number is Numerical Simulations of a High-Resolution RANS-FVDM Scheme for the Design of a Gas Turbine Centrifugal… http://dx.doi.org/10.5772/intechopen.72098 107

Figure 2. (a) Inlet Mach triangles for impeller blades only in radial section with backward swept blades, β<sup>2</sup> ¼ 0 � with zero swirl at entry; (b) exit Mach triangles for impeller blades only in radial section with backward swept blades, β<sup>2</sup> ¼ 0 � with zero swirl at entry.

within the recommended range of 0.4 to 0.6. A maximum flow angle of 64� at the impeller exit and a Mach number of 1.4 are observed.

## 5.2. Blade to blade contours

diffuser vane leading edge was at a radius of 136 mm, and the trailing edge of the diffuser vanes was set at a radius of 166 mm. Blade inlets and outlet angle were set at 64�. The leading

Another method to prevent very steep velocity gradients at diffuser entry is by providing a small vane-less space (0.05d2–0.1d2) between impeller exit and diffuser entry. Therefore, a

The design methodology adapted was mainly focused aiming at decrease in Mach number and

Adapted meshing strategy for both the impeller and diffuser fluid domains was achieved using Ansys-Turbo grid module. A total node count of 7e-01 million was setup for the CFD solver, as it allows generation of refined quality hexahedral meshes required for the blade

In the present context, ANSYS tool is setup with pressure-based solver simulating a steady, three-dimensional viscous flow fields using complete set of Navier-Stokes code solving for Reynolds-averaged Navier-Stokes equations based on finite volume discretization method [7]. A high-resolution scheme is used to solve for continuity, momentum, energy, and state equations implementing a standard k-ε turbulence model. Individual compressor stage characteristics were generated by performing simulations varying back pressures. Firstly, near choke condition, flow points are run to reduce static back pressure values and later, solutions are restarted with incrementally increasing the static back pressure to compute intermediate

Inlet boundary conditions: At compressor inlet, a constant total pressure and total temperature conditions are imposed with a turbulence intensity of 1% and flow direction is marked

Outlet boundary conditions: At the outlet, an average static pressure boundary condition is implemented. Also, a circumferential symmetry condition is imposed on corresponding periodic surfaces with air-fluid medium setup as an ideal gas. A counter-rotating wall boundary is

Entry and exit velocity triangles for impeller blades along the radial section with backward

are plotted as shown in Figure 2(a) and (b). Inlet Mach number is

and trailing edge were defined by an elliptic ratio of 6 and a radius of 0.25 mm.

flow angle at diffuser exit by satisfying a diameter constraint of 340 mm.

vane-less space of 7.023 mm was allotted.

106 Numerical Simulations in Engineering and Science

points on constant speed line running toward stall.

4.4. Meshing strategy

4.5. Numerical setup

normal to the inlet plane.

given at the impeller shroud.

5. Results and discussions

swept blades <sup>β</sup><sup>2</sup> <sup>¼</sup> <sup>0</sup> �

5.1. Flow analysis: Velocity triangles

passages in turbo-machinery.

Blade to blade contours for absolute Mach number at hub, mean and tip sections are presented in below Figure 3 (a) and (c).

The absolute Mach number plots show no supersonic regions of significant volume. The hub section plot show supersonic flow near suction surface of the blade and the tip Section span plots show a supersonic region on the pressure surface of the blade. The presence of a mild bow shock in front of the leading edge of the blade can also be observed. The Mach number is around 0.6 at the leading edge of the impeller. The following plots shown in Figure 4(a–c) are the relative Mach number contours for the hub, mean and tip.

The Mach number at the leading edge in the relative frame is near 1.2 for the leading edge of the impeller blade. The regions of low Mach number can also be observed, although it is in the relative frame.

### 5.3. Circumferential contour

Circumferential relative Mach number contours at the impeller inlet and outlet are presented in Figure 5(a) and (b). The higher color temperature indicates higher values of relative Mach number.

From above Figure 5(a), corresponding inlet relative Mach number contours shows that passage area is lying in the supersonic regime. The Figure 5(b) shows the effect of lean angle of impeller blades.

5.4. Performance characteristics

5.4.1. Impeller performance characteristics

Figure 6. Mass flow versus pressure ratio by Vista CCM.

Figure 5. (a) Inlet relative Mach contour and (b) outlet relative Mach contour.

methods.

through compressor.

Individual component as well as stage performance as a whole can be gauged by different

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109

Impeller performance was evaluated by Vista-CCM and their corresponding plots are shown in below Figure 6 represents the variation of pressure ratio with varying mass flow ingested

Figure 7 represents the variation of polytropic efficiency with varying mass flow ingested to

quantify differential pressure changes occurring through compressor stage.

Figure 3. (a) Hub section absolute Mach number contour, (b) mean section absolute Mach number contour, and (c) tip section absolute Mach number contour.

Figure 4. (a) Hub section relative Mach number contour, (b) mean section relative Mach number contour, and (c) tip section relative Mach number contour.

Numerical Simulations of a High-Resolution RANS-FVDM Scheme for the Design of a Gas Turbine Centrifugal… http://dx.doi.org/10.5772/intechopen.72098 109

Figure 5. (a) Inlet relative Mach contour and (b) outlet relative Mach contour.

### 5.4. Performance characteristics

Individual component as well as stage performance as a whole can be gauged by different methods.

## 5.4.1. Impeller performance characteristics

Figure 3. (a) Hub section absolute Mach number contour, (b) mean section absolute Mach number contour, and (c) tip

Figure 4. (a) Hub section relative Mach number contour, (b) mean section relative Mach number contour, and (c) tip

section absolute Mach number contour.

108 Numerical Simulations in Engineering and Science

section relative Mach number contour.

Impeller performance was evaluated by Vista-CCM and their corresponding plots are shown in below Figure 6 represents the variation of pressure ratio with varying mass flow ingested through compressor.

Figure 7 represents the variation of polytropic efficiency with varying mass flow ingested to quantify differential pressure changes occurring through compressor stage.

Figure 6. Mass flow versus pressure ratio by Vista CCM.

Figure 7. Mass flow versus polytropic efficiency by Vista CCM.

### 5.4.2. Stage performance characteristics

Compressor stage performance can be evaluated by obtaining individual characteristic curves as plotted in Figures 8–10. The compressor performance is presented only for a functional design speed of 38,000 rpm. Variables like total pressure ratio, adiabatic efficiency, and power requirement of compressor are plotted against varying mass flow rate as shown in Figures 8– 10. The maximum achieved pressure ratio is 5.4 while allowing a fixed mass flow rate of 5.73 kg/s.

5.5. Validation studies

Figure 10. Power versus mass flow.

Figure 11. Comparison with compressor in [8].

Figure 9. Efficiency versus mass flow.

various stages.

The obtained results presented in the Figures 11 and 12 shows state-of-the-art validity of

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111

The design methodology adapted in current framework uses a backswept angle of 0 and does not follow the design trend established for validation in above figures. Above deviations in the performance trends can be attributed to the structural size and rotational specifications of

current design with design performance work stated in the literature.

A peak efficiency of 75.8% is obtained at a pressure ratio of 5.73. The design point efficiency is predicted to be around 74.5%. Possible reasons for loss in efficiency may be owing to primary and secondary losses.

The impeller works with power a power requirement in the range of 1350–1360 kW on its 100% speed line over the range of total pressure ratio 4.5–5.4.

Figure 8. Pressure ratio versus mass flow.

Numerical Simulations of a High-Resolution RANS-FVDM Scheme for the Design of a Gas Turbine Centrifugal… http://dx.doi.org/10.5772/intechopen.72098 111

Figure 9. Efficiency versus mass flow.

Figure 10. Power versus mass flow.

### 5.5. Validation studies

5.4.2. Stage performance characteristics

110 Numerical Simulations in Engineering and Science

Figure 7. Mass flow versus polytropic efficiency by Vista CCM.

speed line over the range of total pressure ratio 4.5–5.4.

5.73 kg/s.

and secondary losses.

Figure 8. Pressure ratio versus mass flow.

Compressor stage performance can be evaluated by obtaining individual characteristic curves as plotted in Figures 8–10. The compressor performance is presented only for a functional design speed of 38,000 rpm. Variables like total pressure ratio, adiabatic efficiency, and power requirement of compressor are plotted against varying mass flow rate as shown in Figures 8– 10. The maximum achieved pressure ratio is 5.4 while allowing a fixed mass flow rate of

A peak efficiency of 75.8% is obtained at a pressure ratio of 5.73. The design point efficiency is predicted to be around 74.5%. Possible reasons for loss in efficiency may be owing to primary

The impeller works with power a power requirement in the range of 1350–1360 kW on its 100%

The obtained results presented in the Figures 11 and 12 shows state-of-the-art validity of current design with design performance work stated in the literature.

The design methodology adapted in current framework uses a backswept angle of 0 and does not follow the design trend established for validation in above figures. Above deviations in the performance trends can be attributed to the structural size and rotational specifications of various stages.

Figure 11. Comparison with compressor in [8].

[3] Wilson DG, Korakianitis TH. The Design of High Efficiency Turbomachinery and Gas

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113

[4] Srinivasa Rao P: Modeling of turbulent flows and boundary layer. In: Hyoung Woo Oh, editor. Computational Fluid Dynamics. London, United Kingdom: InTech; 2010. p. 285-306.

[5] Moorthy CHVKNSN, Bharadwajan K, Srinivas V. Computational studies on aerothermodynamic design and performance of centrifugal turbo-machinery. International

[6] Philip P Walsh, Fletcher P. Gas Turbine Performance. 2nd ed. Oxford: John Wiley & Sons;

[7] Moorthy CHVKNSN, Srinivas V, Prasad VVSH. Computational analysis of a CD nozzle with 'SED' for a rocket air ejector in space applications. International Journal of Mechani-

[8] Zahed AH, Bayomi NN. Design procedure of centrifugal compressors. ISESCO Journal of

[9] Hideaki T, Masaru U, Hirata KT. Aerodynamic design of centrifugal compressor for AT14

cal and Production Engineering Research and Development. 2017;7(1):53-60

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ISBN: 978-953-7619-59-6

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turbocharger. IHI Engineering Review. 2010;43(2):70-76

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Figure 12. Comparison with trend established in paper [9].
