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Figure from:Characterization of the Performance of a Turbocharger Centrifugal Compressor by Component Loss Contributions

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In order to predict centrifugal compressor performance using mean-line analysis, it is necessary to analyze its components, including inlet duct, impeller, diffuser and volute. To do so, requires marching through the compressor in the flow direction; the ideal stream being modeled by thermodynamic and fluid mechanic relations, then, by implementing loss mechanism relations and correlations, the mode becomes more realistic. To do so, a set of empirical models was selected. In this study, models that were physically based were preferred rather than models that were based solely on mathematica correlations. Under the specified geometry, inlet conditions, rotational speed and mass flow rate, stream properties could be calculated at discharge of each component and set for the next component inlet. From the model, velocities, static and total temperature, static and total pressure, efficiency and pressure loss of each component could be calculated.

Figure 1 In order to predict centrifugal compressor performance using mean-line analysis, it is necessary to analyze its components, including inlet duct, impeller, diffuser and volute. To do so, requires marching through the compressor in the flow direction; the ideal stream being modeled by thermodynamic and fluid mechanic relations, then, by implementing loss mechanism relations and correlations, the mode becomes more realistic. To do so, a set of empirical models was selected. In this study, models that were physically based were preferred rather than models that were based solely on mathematica correlations. Under the specified geometry, inlet conditions, rotational speed and mass flow rate, stream properties could be calculated at discharge of each component and set for the next component inlet. From the model, velocities, static and total temperature, static and total pressure, efficiency and pressure loss of each component could be calculated.

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The friction coefficient, Cy is calculated by following the relation based on the Reynolds number, Skin friction loss: This is due to shear stresses from impeller channel surfaces. Friction losses in impellers have a similar mechanism to total pressure drop in straight pipes based on a channel with hydraulic diameter and length of dy and Ly respectively, so skin friction loss is calculated by [5]: in which the diffusion factor, D, is as below [28].
The friction coefficient, Cy is calculated by following the relation based on the Reynolds number, Skin friction loss: This is due to shear stresses from impeller channel surfaces. Friction losses in impellers have a similar mechanism to total pressure drop in straight pipes based on a channel with hydraulic diameter and length of dy and Ly respectively, so skin friction loss is calculated by [5]: in which the diffusion factor, D, is as below [28].
Figure 2. Flowchart of the 1D procedure algorithm.
Figure 2. Flowchart of the 1D procedure algorithm.
Figure 3. Sketch of the impeller (dimensions in mm and degrees). Table 1. Geometric specifications of the compressor. 4. 3D Modeling
Figure 3. Sketch of the impeller (dimensions in mm and degrees). Table 1. Geometric specifications of the compressor. 4. 3D Modeling
Table 2. Mesh independency analysis.
Table 2. Mesh independency analysis.
Mesh independency analysis results are shown in Table 2, performed based on the compressor pressure ratio and isentropic efficiency values at 60k rpm rotational speed and 0.09 kg/s mass flow rate. Increasing mesh resolution shows the minimum elements required for giving near constant performance values. Around 750,000 elements per passage were used from the inlet section to vaneless diffuser discharge and near two million elements were used for the volute.
Mesh independency analysis results are shown in Table 2, performed based on the compressor pressure ratio and isentropic efficiency values at 60k rpm rotational speed and 0.09 kg/s mass flow rate. Increasing mesh resolution shows the minimum elements required for giving near constant performance values. Around 750,000 elements per passage were used from the inlet section to vaneless diffuser discharge and near two million elements were used for the volute.
Figure 5. Pressure ratio versus mass flow rate.
Figure 5. Pressure ratio versus mass flow rate.
Figure 6. Isentropic efficiency versus mass flow rate.
Figure 6. Isentropic efficiency versus mass flow rate.
Figure 7. Effect of the impeller blade height at the outlet on the pressure ratio.
Figure 7. Effect of the impeller blade height at the outlet on the pressure ratio.
Figure 8. Effect of the impeller inlet diameter at the shroud on the pressure ratio.
Figure 8. Effect of the impeller inlet diameter at the shroud on the pressure ratio.
Figure 9. Effect of the impeller blade angle at the inlet on the pressure ratio.
Figure 9. Effect of the impeller blade angle at the inlet on the pressure ratio.
Figure 10. Effect of the impeller blade angle at the outlet on the pressure ratio.
Figure 10. Effect of the impeller blade angle at the outlet on the pressure ratio.
Figure 11. Effect of the diffuser diameter at the outlet on the pressure ratio. As shown in Figure 9 increasing the impeller blade angle at the inlet increased the pressure ratio around the design point region, which was due to a reduction in the incidence loss. Increasing the blade angle at the outlet increased the pressure ratio as can easily be seen in Figure 10 but it increased the impeller outflow velocity so gas static pressure was low, which is not favorable, also the operation range was decreased.
Figure 11. Effect of the diffuser diameter at the outlet on the pressure ratio. As shown in Figure 9 increasing the impeller blade angle at the inlet increased the pressure ratio around the design point region, which was due to a reduction in the incidence loss. Increasing the blade angle at the outlet increased the pressure ratio as can easily be seen in Figure 10 but it increased the impeller outflow velocity so gas static pressure was low, which is not favorable, also the operation range was decreased.
Figure 12. Each loss impact, 60k rpm rotational speed. Figure 13. Each loss impact, 80k rpm rotational speed.
Figure 12. Each loss impact, 60k rpm rotational speed. Figure 13. Each loss impact, 80k rpm rotational speed.
clearance loss. Significant reduction in pressure ratio was probably the reason of decreasing leakage flow and the clearance loss in the high mass flow rates.
clearance loss. Significant reduction in pressure ratio was probably the reason of decreasing leakage flow and the clearance loss in the high mass flow rates.
Figure 14. Each loss impact, 92k rpm rotational speed (nominal). 6. Conclusions
Figure 14. Each loss impact, 92k rpm rotational speed (nominal). 6. Conclusions
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