Centrifugal Compressor

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  • Introduction In this project the analysis of a centrifugal compressor was carried out. This compressor was a part of a turbocharger, which was to be designed according to the various parameters mentioned in the problem statement. These parameters are displayed in the next section. This project also includes optimization of certain parameters and other structural geometries. They are optimized in order to obtain maximum work done on air, within constraints.

    Given Data

    Design Procedure The whole project was divided in to analysis of three different parts of the compressor. Associated results of analysis and assumptions made will be stated in each section. All the calculations and graphs associated with the analysis were carried out in EES.

    Inducer The analysis of the Inducer began by assuming isentropic conditions and inlet isentropic velocity. The inlet isentropic conditions were used, to find temperature at inlet. After this a relationship was derived between inlet isentropic velocity and Mach number. This was done by varying the value of inlet isentropic velocity and recording the values of Mach number. The analysis was carried out to pin point the inlet velocity at which lowest inlet Mach number is achieved. The following graph shows this relation.

  • It was observed that the lowest value of Mach number was achieved at 137.6 m/s. Thus this was value was selected and the calculations were repeated. Furthermore, this velocity was used to find out the isentropic enthalpy. The isentropic enthalpy along with the inducer efficiency were used to find out the real thermodynamic state at the inlet. This helped us to calculate the radii of the hub and the tip of the blade. Finally, the actual inlet velocity triangle and Mach number were found. These values can be seen in the table below and also in appendix-4. The equations used to carry out these calculations can be seen in Appendix-1 in a step wise manner.

    Parameter Value Optimized inlet isentropic velocity (c1s) 137.6 m/s

    Mach Number at isentropic velocity (Ma1stip) 0.7749 Actual inlet absolute velocity (c1) 135.5 m/s

    Mach Number at actual inlet velocity (Ma1tip) 0.7713 Radius of hub (rhub) 0.005288 m Radius of hub (rtip) 0.0187 m

    Impeller The next component which was analyzed in this project was the Impeller. Our goal in this stage of the analysis is calculate velocity triangles and find out the cross-sectional geometry of the impeller. Since the blade speed was not given in the problem statement, its value was calculated from the compressor efficiency and pressure ratio. The values of radius of tip and radius at hub were used to calculate the value of inlet relative velocity. The value of blade speed at the outlet an along with the flow and blade loading coefficients were used to calculate the outlet velocity triangle. This in-turn helped is calculate the radius of cross-section of the Impeller. After, calculation of the velocity triangle the next geometric parameter calculated was the width of the impeller. A problem was encountered in this part of the analysis. The Mach number at the exit of the impeller was more than one. Thus, to rectify this situation the values of both Blade and Flow loading coefficients were changed to achieve a Mach number of less than one. Moreover, the number of Blades were optimized by selecting a number for which the tangential component of absolute velocity at the outlet of the Impeller was the highest. The important results are shown in the table below. The equation used towards calculating these values are shown in a step-wise manner in Appendix-2.

    Parameter Value Actual inlet relative velocity (w1) 198.1 m/s Blade speed at mean radius (u1m) 144.1 m/s

    Outlet absolute velocity (c2) 299.0 m/s Outlet relative velocity (w2) -93.76 m/s

    Blade speed outlet (u2) 382.2 m/s Radius of Impeller cross-section (r2) 0.03174 m

    Width of Impeller (b2) 0.0109 m Corrected Value of Blade Loading Coefficient () 0.776 (original = 0.7)

    Corrected Value of Flow Coefficient () 0.1 (original = 0.15) Optimized number of Blades (Z) 30

  • Diffuser In the third and final part of the analysis, the Diffuser is analyzed. The goal of this analysis is to determine the dimensions of the Diffuser and also to obtain the final thermodynamic stage of the Centrifugal compressor. From the value of Diffuser recovery coefficient and the static and stagnation enthalpies of state-2, the static enthalpy of state-3 is obtained. Finally by applying the conservation of angular momentum the width and the radius of the Diffuser are determined. The important results are displayed in the following table. Moreover, the equation used to calculate this part of the analysis can be seen in Appendix-3.

    Parameter Value Stagnation Enthalpy at State -3 (h03) 411.8 kJ/kg

    Static Enthalpy at State -3 (h3) 387.2 kJ/kg Entropy at State 3 (s03) 5.758 kJ/kg-K

    Diffuser velocity (c3) 221.8 m/s Radius of Diffuser cross-section (r3) 0.04256 m

    Width of Diffuser (b3) 0.0189 m

    Summary After, analyzing the all the components a highly optimized system was reached. The optimization was done in manner, where the outlet velocity at the impeller had a very high tangential component. The value of Power required to compress the air was found to be 17 kW.

    Velocity Triangles

  • Thermodynamic Diagram

    Figure with main dimensions of the compressor

  • Appendices Appendix-1

  • Appendix-2

  • Appendix-3

  • Appendix-4

    IntroductionGiven DataDesign ProcedureInducerImpeller

    DiffuserSummaryVelocity TrianglesThermodynamic DiagramFigure with main dimensions of the compressorAppendicesAppendix-1Appendix-2Appendix-3Appendix-4