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Figure from:Design Procedure of Centrifugal Compressors

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Mach number M., known as C,/a, can be developed to the following expression:

Figure 2 Mach number M., known as C,/a, can be developed to the following expression:

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Figure 2. Effect of the exit blade angle on the work factor for different flow coefficients. Figure 1. Main component of a centrifugal compressor with velocity triangles at inlet and exit. 2.1.2 Compressor efficiency
Figure 2. Effect of the exit blade angle on the work factor for different flow coefficients. Figure 1. Main component of a centrifugal compressor with velocity triangles at inlet and exit. 2.1.2 Compressor efficiency
where y, is the impeller efficiency and equal to 80%. number, M,., through the specification of a range of
where y, is the impeller efficiency and equal to 80%. number, M,., through the specification of a range of
Figure 3. Relation between discharge Mach number and tangential blade Mach number with various exit blade angles and different pressure ratios The non-dimensional speed of the impeller (tangential Mach number M_,) for a range of blade backsweep angles (0 to -60°) together with the discharge Mach number M, are shown in Figure 3 using equations 3 and 5. The efficiency is assumed to be 80% and a, =65° for a pressure ratio ranging from 1.5 to 5. The clear advantage of the blade backward is illustrated through the reduction in the discharge Mach number of the fluid. This is accompanied by an increase in the non-dimensional speed of the impeller, which leads to an increase in the stress levels. The results obtained by Whitfield [25] and Abdel Hafiz and Bayomi [16] for pressure ratios 2, 3, 4 and 6 are also presented in Figure 3 for comparison. Good agreements in trends are shown between the present results and the other authors’ results. Figure 3 for comparison. Good agreements in trends
Figure 3. Relation between discharge Mach number and tangential blade Mach number with various exit blade angles and different pressure ratios The non-dimensional speed of the impeller (tangential Mach number M_,) for a range of blade backsweep angles (0 to -60°) together with the discharge Mach number M, are shown in Figure 3 using equations 3 and 5. The efficiency is assumed to be 80% and a, =65° for a pressure ratio ranging from 1.5 to 5. The clear advantage of the blade backward is illustrated through the reduction in the discharge Mach number of the fluid. This is accompanied by an increase in the non-dimensional speed of the impeller, which leads to an increase in the stress levels. The results obtained by Whitfield [25] and Abdel Hafiz and Bayomi [16] for pressure ratios 2, 3, 4 and 6 are also presented in Figure 3 for comparison. Good agreements in trends are shown between the present results and the other authors’ results. Figure 3 for comparison. Good agreements in trends
Figure 4. Variation of inlet relative Mach number with tangential blade Mach number with various exit blade angle and different impeller radius ratios at a pressure ratio of 1.5. This equation, together with equation (9), is used to represent the aerodynamic characteristics in relation to the corresponding impeller dimensions for different pressure ratios. The typical plot for a pressure ratio of 1.5 is presented in Figure 4 taking an inlet relative flow angle, B,=- 60°. This was carried out for a radial blade i.e. B, = 0° up to high exit blade angle §,=-40° and -60°. It can be concluded that increasing the blade backsweep B, and the accompanying increase in non-dimensional impeller speed M,, leads to an increase in the inlet relative Mach number for any specified radius ratio. In order to decrease the inlet relative Mach number, the impeller radius ratio has to be reduced. This means a larger sized impeller. If the designer is free to select the non-dimensional impeller speed, then a range of impeller radius ratios and blade backsweep are available. Increasing the blade backsweep has a beneficial effect on the impeller discharge M, as shown in Figure 3. Whitfield and Baines [24] showed that the inlet absolute and relative Mach numbers are related to the mass flowrate per unit frontal area through this equation:
Figure 4. Variation of inlet relative Mach number with tangential blade Mach number with various exit blade angle and different impeller radius ratios at a pressure ratio of 1.5. This equation, together with equation (9), is used to represent the aerodynamic characteristics in relation to the corresponding impeller dimensions for different pressure ratios. The typical plot for a pressure ratio of 1.5 is presented in Figure 4 taking an inlet relative flow angle, B,=- 60°. This was carried out for a radial blade i.e. B, = 0° up to high exit blade angle §,=-40° and -60°. It can be concluded that increasing the blade backsweep B, and the accompanying increase in non-dimensional impeller speed M,, leads to an increase in the inlet relative Mach number for any specified radius ratio. In order to decrease the inlet relative Mach number, the impeller radius ratio has to be reduced. This means a larger sized impeller. If the designer is free to select the non-dimensional impeller speed, then a range of impeller radius ratios and blade backsweep are available. Increasing the blade backsweep has a beneficial effect on the impeller discharge M, as shown in Figure 3. Whitfield and Baines [24] showed that the inlet absolute and relative Mach numbers are related to the mass flowrate per unit frontal area through this equation:
Figure 6. Compressor maps for a pressure ratio of 3 with various exit blade angles f, at different prewhirl angle ©., ¢ Representing the minimum inlet relative Mach number.
Figure 6. Compressor maps for a pressure ratio of 3 with various exit blade angles f, at different prewhirl angle ©., ¢ Representing the minimum inlet relative Mach number.
Figure 7. Compressor maps for pressure a ratio of 5 with various exit blade angles B, at different prewhirl angles o., ¢ Representing the minimum inlet relative Mach number.
Figure 7. Compressor maps for pressure a ratio of 5 with various exit blade angles B, at different prewhirl angles o., ¢ Representing the minimum inlet relative Mach number.
Figure 8. Diffusion factors against minimum inlet relative Macl number for different exit blade angle and prewhirl angle at different pressure ratios.
Figure 8. Diffusion factors against minimum inlet relative Macl number for different exit blade angle and prewhirl angle at different pressure ratios.
Figure 9. Flow-chart for the design process of centrifugal compressors.
Figure 9. Flow-chart for the design process of centrifugal compressors.
TABLE 1: Permissible parameters of compressors at a pressure ratio of 1.5 TABLE 2: Permissible parameters of compressors at a pressure ratio of 3.
TABLE 1: Permissible parameters of compressors at a pressure ratio of 1.5 TABLE 2: Permissible parameters of compressors at a pressure ratio of 3.
TABLE 3: Permissible parameters of compressors at a pressure ratio of 5.
TABLE 3: Permissible parameters of compressors at a pressure ratio of 5.