Papiernička’2006 Kosprdová Jindra, Vlček Petr 1 THE INFLUENCE OF RADIAL IMPELLER BLADE GEOMETRY ON ITS COMPRESSION AND BLADE LOADING KOSPRDOVÁ Jindra, Ing., ČKD NOVÉ ENERGO, a.s., Klečákova 1947, 192 02 Praha 9 Czech Republic Department 12107, Faculty of Mechanical Engineering, CTU in Prague, Czech Republic [email protected]VLČEK Petr, Ing., ČKD NOVÉ ENERGO, a.s., Klečákova 1947, 192 02 Praha 9 Czech Republic [email protected]Abstract: This paper is concerned with the influence of 2D radial blade geometry on its compression, static pressure and relative velocity distributions along the blade. The other basic geometric parameters are held constant. The change of the blade geometry was carried out through the selection of the camber line angle as a function of the radius, i.e. b = f(R). The influence of the blade geometry change on the observed values was determined from numerical solution of the flow in the impeller with help of the CFX software. The numerical solution was performed for original impeller geometry from the series of stages produced by ČKD NOVÉ ENERGO, a. s. and for designed variants. 1. Introduction Gas static pressure increase flowing through the impeller is determined by the quantity A stat for which the following equation is valid: loss dyn stat A - A - A A , where Astat represents work required for static pressure increase in the impeller A represents total amount of work delivered to the gas in the impeller dyn A represents work required for absolute kinetic energy increase in the impeller loss A represents work lost due to viscous friction in the impeller On the basis of these quantities we can define: R A A - A dyn as a degree of reaction and A A - A loss as impeller efficiency. Framework in which these quantities range comes from „1D“ design. With the help of this „1D“ design fundamental impeller geometry (D 1 , D 2 , b 1 , b 2 , 1b , 2b ) and impeller revolutions are determined for prescribed static pressure increase (in the stage), mass flow rate and inlet conditions. However actual values of A , R , depend on the impeller meridional cross section geometry and on the impeller blade geometry (determined by the functions R f b and t = f(R) = const. in this case). Thus after „1D“ design is done it only remains to determine the best meridional cross section and impeller blade geometry. Here we are concerned only with the impeller blade geometry while meridional cross section remains the same (see Figure1). Four variants of R f b were proposed and are depicted in Figure2 along with the original distribution. Variants that lie below the curve „original“ result in longer blades than those that lie above. Thus when t = const. variants 2 and 3 have smaller flow area than variants 1 and 4. For corresponding camber line geometry see Figure3, where circle arc camber line is added for comparison.
Transcript
Papiernička’2006
Kosprdová Jindra, Vlček Petr 1
THE INFLUENCE OF RADIAL IMPELLER BLADE GEOMETRY ON ITS COMPRESSION AND BLADE LOADING
KOSPRDOVÁ Jindra, Ing., ČKD NOVÉ ENERGO, a.s., Klečákova 1947, 192 02 Praha 9 Czech Republic Department 12107, Faculty of Mechanical Engineering, CTU in Prague, Czech Republic [email protected]ČEK Petr, Ing., ČKD NOVÉ ENERGO, a.s., Klečákova 1947, 192 02 Praha 9 Czech Republic [email protected]
Abstract:
This paper is concerned with the influence of 2D radial blade geometry on its compression, static pressure and relative velocity distributions along the blade. The other basic geometric parameters are held constant. The change of the blade geometry was carried out through the selection of the camber line angle as a function of the radius, i.e. b = f(R). The influence of the blade geometry change on the observed values was determined from numerical solution of the flow in the impeller with help of the CFX software. The numerical solution was performed for original impeller geometry from the series of stages produced by ČKD NOVÉ ENERGO, a. s. and for designed variants.
1. Introduction
Gas static pressure increase flowing through the impeller is determined by the quantity Astat for which the following equation is valid:
lossdynstat A-A-AA , whereAstat represents work required for static pressure increase in the impellerA represents total amount of work delivered to the gas in the impeller
dynA represents work required for absolute kinetic energy increase in the impeller lossA represents work lost due to viscous friction in the impeller
On the basis of these quantities we can define: RA
A-A dyn as a degree of reaction and
A
A-A loss as
impeller efficiency. Framework in which these quantities range comes from „1D“ design. With the help of this „1D“ design fundamental impeller geometry (D1, D2, b1, b2, 1b , 2b ) and impeller revolutions are determined
for prescribed static pressure increase (in the stage), mass flow rate and inlet conditions. However actual values of A , R , depend on the impeller meridional cross section geometry and on the impeller blade geometry
(determined by the functions Rfb and t = f(R) = const. in this case). Thus after „1D“ design is done it only
remains to determine the best meridional cross section and impeller blade geometry. Here we are concerned only with the impeller blade geometry while meridional cross section remains the same (see Figure1). Four variants of
Rfb were proposed and are depicted in Figure2 along with the original distribution. Variants that lie
below the curve „original“ result in longer blades than those that lie above. Thus when t = const. variants 2 and 3 have smaller flow area than variants 1 and 4. For corresponding camber line geometry see Figure3, where circle arc camber line is added for comparison.
The Influence of Radial Impeller Blade Geometry on its Compression and Blade Loading
Kosprdová Jindra, Vlček Petr 2
Subscript t means total state Figure1 Table 1
B la d e C a m b e r L in e A n g le a s a F u n c t io n o f R a d iu s
Figure 3 Blade camber lines shapes for the original impeller and for designed variants
The Influence of Radial Impeller Blade Geometry on its Compression and Blade Loading
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Blade Camber Line Coordinates
0,04
0,06
0,08
0,1
0,12
0,14
0,16
0,18
0,2
0,22
0,24
-0,12 -0,08 -0,04 0 0,04 0,08 0,12
x [m]
y[m
]
original
variant1
variant2
variant3
variant4
circle arc
radius center
originalvar4
circle arc
var1
var2 var3
2. Numerical Solution of the Fluid Flow in the Impeller
The fluid flow in the impeller was solved for the original blade and for all designed variants with the help of the CFX software. Boundary conditions for these calculations were the same for all cases. These conditions were taken from the specification for the original impeller. The calculations were solved only for one point of the impeller characteristic. Only one segment of the whole impeller was used for the CFD analysis. This segment belongs to one blade of the impeller. Computational grids were qualitatively and quantitatively similar for all calculations.
3. Results and Discussion
Static pressure increase is linked to relative velocity drop, which is the reason to be especially concerned with these two quantities. On the basis of the calculations results we analysed the influence of the made changes on relative velocity at the outlet and its changes along the flow passage, outlet pressure, static pressure and relative velocity distributions along the blade. The following figures show observed quantities for designed variants in comparison with values calculated for original blade shape.
Figure 5 Static pressure profile at the outlet of the impeller rem. Values of the pressures are presented as over-pressures in relation to the inlet pressure (101300Pa)
theta
The Influence of Radial Impeller Blade Geometry on its Compression and Blade Loading
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-50000
-40000
-30000
-20000
-10000
0
10000
20000
30000
40000
50000
-0,2 0 0,2 0,4 0,6 0,8 1 1,2
0-1 streamwise
stat
ic p
ress
ure
original variant 1 variant 2 variant 3 variant 4
Fig .6 Static pressure distribution along the blade
-30
20
70
120
170
220
270
-0,2 0 0,2 0,4 0,6 0,8 1 1,2
0-1 streamwise
rela
tive
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oci
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original variant 1 variant 2 variant 3 variant 4
Figure 7 Relative velocity distribution along the blade
The Influence of Radial Impeller Blade Geometry on its Compression and Blade Loading
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Relative velocity increase at the impeller outlet for variants 2 and 3 in comparison with original blade shape can be seen in the figure 4. On the other hand for variants 1 and 4 we can see relative velocity drop in the part of the domain near blade suction side and in the case of variant 4 there also occurred relative velocity drop in the part of the domain near blade pressure side. In the case of static pressure at the impeller outlet (figure 5) for variants 1 and 4, where relative velocity drop occurred, static pressure increased and for variants 2 and 3, where relative velocity increase occurred, static pressure at the impeller outlet decreased. Regarding static pressure distribution along the blade (Figure 6) for variants 1and 4 we can see increase both at the pressure and suction sides. We can also see certain smoothing of this static pressure distribution in comparison with original blade shape (streamwise 0.4). Static pressure drop can be seen for variants 2 and 3 in accordance with expectations along the whole blade length. The values at the pressure side for variant 3 and the values at the suction side for variants 1 and 4 came out nearly the same. Improvement of relative velocity distribution occurred for variants 1 and 4 (see Figure 7) and worse results of this distribution can be seen for variants 2 and 3. Average values comparison of the outlet pressure (static and total), delivered work, polytrophic efficiency, ratios F2/F1 (F1 = area at the leading edge, F2 = area at the trailing edge), w1/w2 and the degree of reaction for all solved variants can be seen in the Table 2. From these values it is also evident that for variants 2 and 3 all these parameters changed downwards. According to expectations for variants 1 and 4 the observed parameters changed upwards. Relative velocity inlet to outlet ratio can be seen in this Table as well. These values range from 0,97 (acceleration of the flow toward the outlet) to 1,2(deceleration of the flow toward the outlet). When comparing values (w1/w2) and „etaT-T_pol“ better efficiency occurred for higher ratio w1/w2 (for higher deceleration of the flow toward the outlet). The degree of reaction decreases with higher deceleration. In the column cu1*u1 should theoretically be zero – the flow came into the computational domain in the radial direction. Non-zero values of this parameter are caused by the influence of the leading edge on upstream flow, i.e. the work delivered to the gas correspond to the value cu2*u2 from which the part cu1*u1 is consumed for the change of flow direction before the leading edge. The following figures are concerned with the comparison of some results for original blade shape and for the best variant 4. Relative velocity contours can be seen at three radiuses 0.13, 0.17 and 0.21 m.
original variant 4
Figure 8 Relative velocity contours – radius 0.13 m
The Influence of Radial Impeller Blade Geometry on its Compression and Blade Loading
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Figure 9 Details of relative velocity contours – radius 0.13 m – pressure side
Figure 10 Details of relative velocity contours – radius 0.13 m – suction side
Figure 11 Relative velocity contours – radius 0.17 m
The Influence of Radial Impeller Blade Geometry on its Compression and Blade Loading
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Figure 12 Details of relative velocity contours – radius 0.17 m – pressure side
Figure 13 Details of relative velocity contours – radius 0.13 m – suction side
Figure 14 Relative velocity contours – radius 0.21 m
Relative velocity contours at the area with constant radius 0.13 m can be seen in the figures 8, 9 and 10. Linear character of the relative velocity increase from the pressure side to the suction side can be seen in the part of the distance between pressure and suction sides. This linear character for original blade shape stopped in the
The Influence of Radial Impeller Blade Geometry on its Compression and Blade Loading
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middle of the distance between pressure and suction sides. Bigger regions with constant relative velocity occur from this place. On the other hand for variant 4 linear character stays up to 75% of the distance between pressure and suction sides. Further, for original blade the values of relative velocity are higher which is seen from relative velocity distribution along the blade. Maximal value of the relative velocity in both cases is around 200m/s, but the region of this value is larger for the original blade. Relative velocity contours at the area with constant radius 0.17 m can be seen in the figures 11, 12 and 13. Relative velocity is for original blade in comparison with variant 4 is larger n the whole area. The character of the relative velocity increase is the same for both cases. The same for contours at the area with constant radius 0.21 m can be seen in figure 14.
4. Conclusions
From the above-mentioned we can see that with the change of blade camber line angle changes in all observed quantities occurred. If we compare only the values in Table 2 it can be claimed that total pressure increase at the impeller outlet occurred for variant 1, namely by 1.5%, and for variant 4 by 3.1%. Static pressure increase for variant 1 was 1% and for variant 4 2%. On the other hand for variants 2 and 3 the total and static pressure decreased. For variant 2 it was 3% of total pressure and 2% of static pressure. For variant 3 this decrease was sharper actually 10.6% of the total pressure and 7.8% of the static pressure. It is similar in the case of work delivered to the gas. This work increased for variant 4 by 6.3% in comparison with the original blade shape. The highest decrease of this work is for variant 3 namely 17.2%. The last observed quantity was polytrophic efficiency. This efficiency was the highest for the best variant 4 95.05% and for the worst variant 3 it was 84.58%. It can be seen that for constant basic geometric parameters of the impeller the decrease of efficiency may be up to 10% only on bad design of the blade shape. Here it is necessary to think of the computational errors. We know the value of static pressure at the impeller outlet for original blade. This value was taken from design software used in ČKD NOVÉ ENERGO, a. s. and this value differs by 3% from the calculated one. It has to be remarked that this value is a re-count from experimental measurements. It is possible to say that the calculated values are realistic and the trend of changes (increase/drop) in observed quantities for similar computational grid, the same boundary conditions and the same numerical scheme, should be the same. Further, it is necessary to check the influence of these blade shape changes on the flow in other parts of compressor. It means that the next step is to solve the impeller-diffuser interaction.This contribution was prepared in ČKD NOVE ENERGO, a.s. within the scope of project “Research and development of flow part of centrifugal compressor”, that was realized under financial support of state resources through Czech Ministry of Industry and Trade.
