Front. Energy Power Eng. China 2008, 2(4): 381–385 DOI 10.1007/s11708-008-0084-4
RESEARCH ARTICLE
Suping WEN, Xiaowen HU, Yong ZHANG, Jun WANG, Tingbin LI
Optimal r/b ratio of bend channel in centrifugal compressor E
Higher Education Press and Springer-Verlag 2008
Abstract A numerical investigation on the flow in a bend channel by coupling the impeller with the vaneless diffuser in a centrifugal compressor with different r/b ratios (bend radius r to bend channel width b) is presented. The jet-wake effect of the impeller outlet is considered and flow pattern in the bend channel and the performance of the centrifugal compressor stage are investigated. The results indicate that there is an optimal r/b ratio for increasing the stage efficiency to the highest for a specific compressor stage. The change in r/b ratio significantly affects the flow angle of the bend channel outlet. The prime reason for the total pressure loss in the bend channel is the wall friction in the bend channel. Keywords centrifugal compressor, bend channel, numerical calculation
1
Introduction
The bend channel is a basic element of multistage centrifugal compressors for guiding the swirling flow from the diffuser to the return channel. Different from the usual Uturn bend, the 180u annular bend channel of the centrifugal compressor presents extremely complex fluid dynamic characteristics due to the upstream influence of the jet/wake effect of the impeller outlet and the flow pattern in the diffuser. Most theoretical and experimental investigations focus on the understanding of the flow patterns in the bend channel and the return channel [1,2], but little attention has been paid to the design method for bend channels, especially for the bend channels of centrifugal compressors. The flow pattern in the bend channel is mainly influenced by the curvature and the pressure gradient between the inner and the outer wall of the bend channel. The Translated from Journal of Engineering Thermophysics, 2008, 29(2): 233–236 [译自: 工程热物理学报] Suping WEN (*), Xiaowen HU, Tingbin LI School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China E-mail:
[email protected] Yong ZHANG, Jun WANG Shenyang Blower Works, Shenyang 10022, China
understanding of the flow pattern in the bend channel is helpful for bend channel design. Akaike and Toyokura [3] experimentally studied the bend with five different shapes by varying the bend channel width and radius of the curvature. They came up with the conclusion that the flow in the bend channel has a tendency to become uniform at the outlet of the bend channel and that the flow is two dimensional. Therefore, two dimensional design theory could be applied in bend channel design. Oh and Engeda [4], Inoue and Koizumi [5] also reported the same tendency in their research. Lenke and Simon [6] investigated the influences of geometric design variables on separation behavior in the bend channel by numerical simulation. Their results show that when the ratio of bend channel width to mean streamline radius of curvature is less than 0.8, the separation behavior in the bend channel can be improved. Fister et al. [7] predicted the flow pattern in the bend channel with 5 different inlet shape lines. In this paper the bend channel is studied by coupling the impeller with the vanelesss diffuser, and the influence of impeller jet/wake effect on bend channel inlet flow pattern is fully considered, which is totally different from the method adopted in Ref. [4]. Meanwhile, the influence of different r/b ratios on the outlet flow angle in the bend channel and centrifugal compressor stage performance are investigated. It is found that different r/b ratios have significant influence on the centrifugal compressor stage performance, and that there is an optimal r/b ratio for increasing the stage efficiency to the highest; and, the prime reason for total pressure loss in the bend channel is the wall friction.
2 2.1
Numerical models Geometry model
The meridional view of the centrifugal compressor stage used in this research is shown in Fig. 1. The computational domain includes the impeller, the vaneless diffuser, the bend channel and the outlet extension. The major parameters of the stage are shown in Table 1. The design mass flow rate qm 5 0.5477 kg/s, the revolution speed n 5 12000 r/min, and the designed pressure ratio e 5 1.466.
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Q contains contributions of coriolis and centrifugal forces. The energy, temperature and velocity components are density weighted averages defined as: rq L ~ ~q~ , qi ~ðkzkt Þ T. r Lxi Reynolds stress wj 2 L~ wi L~ tij ~ðmzmt Þ z { (+w)dij , Lxj Lxi 3 2 ~ ez1w k, E~~ ~iw ~ i zk, P ~pz r 3 2 where k represents turbulence kinetic energy. 2.3
Fig. 1
Table 1
Meridional sketch map of computing model
Main structure parameters of stage
outlet set angle of impeller/(u)
D2/mm
D4/mm
b2/mm
16
450
640
12
2.2
Governing equation
The general Reynolds averaged Navier-Stokes governing equations can be written in Cartesian coordinate form as follows: LU z+F i z+F v ~Q, ð1Þ Lt where Fi,Fv are the vector of the conservative variables and the inviscid and viscous flux vectors, respectively; Q contains the source terms. The resulting time averaged Navier-Stokes equations for relative velocities in the rotating frame of reference become 2
r
3
2
r~ wi
Numerical method
The Spalart-Allmaras turbulence model is used for calculating the turbulence viscosity. The total temperature and total pressure are specified at the inlet boundary; the inlet velocity direction is axial. In the outlet boundary condition for which the mass flow is imposed with pressure adaptation, the initial outlet pressure is assumed, because this pressure has no effect on the computing results. The structured grid, as shown in Fig. 2, is used for computational domain. Because of the axisymmetric structure of the computational domain, only one passage is used for a computational domain which has 7 6 105 cells, and the first cell y+ away from the wall is controlled bellow 5. The same template is used for mesh generation when the r/b ratio is changed. The steady state is performed. The flow solver is based on a cell-centred finite volume approach associated with a central spatial discretization scheme and with an explicit 4th order Runge-Kutta time integration method. Jameson type dissipation with 2nd and 4th order derivatives of conservative variables is used in the spatial discretization scheme, while the implicit residual smoothing and the local time stepping are used in combination with Runge-Kutta method to speed up the convergence.
3
6 7 6 7 6 P d1i zr~ 6 r~ 7 ~1 7 wi w 6 7 6 w1 7 6 7 6 7 6 6 7 ~2 7 wi w U~6 r~ w2 7, F ii ~6 P d2i zr~ 7, 6 7 6 7 6 P d3i zr~ 6 r~ 7 ~3 7 wi w 4 5 4 w3 5 ~ ~ ~i rEzP w rE 2 3 0 6 7 2 3 6 ti1 7 0 6 7 6 6 7 7 7, Q~6 ({r)½2v|wz(v|(v|r)) 7, F vi ~{6 4 6 ti2 7 5 6 7 2 2 6 ti3 7 rw+ 0:5v r 4 5 qi z~ wj tij
Fig. 2
Computing grid
3 Results and discussion 3.1
Analysis of stage performance
Figure 3 shows the influence of r/b ratio on the polytrophic efficiency gpol of the centrifugal compressor stage.
Optimal r/b ratio of bend channel in centrifugal compressor
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simulations with different r/b ratios show that there does not appear to be any separation and backflow in the bend channel. So it can be concluded that wall friction is the main reason for the total pressure loss. If the r/b ratio is too large, friction loss will increase, but if it is too small, separation loss will increase. So, if there is no special restriction to axial size, an r/b ratio of around 1.0 should be the best choice. 3.2
Fig. 3 stage
Influence of r/b ratio on polytrophic efficiency of
It can be seen that there is a peak value of polytrophic efficiency gpol when the r/b ratio reaches 1.0. When the r/b ratio is less than 1.0, the efficiency decreases quickly with decreasing r/b ratio. When the r/b ratio is very small, flow separation appears at the outlet of the bend channel and leads to flow loss increase. The numerical investigation of Lenke et al. [6] indicates that the separation behavior in the bend channel can be improved when the ratio of bend channel width to mean streamline radius of curvature is less than 0.8, and that too large a ratio will cause an increase in streamline length and axial size of the centrifugal compressor. This tendency can also be seen in Fig. 3. When the r/b ratio is larger than 1.0, the stage efficiency decreases with increasing r/b ratio. Figure 4 shows the influence of r/b ratio on total pressure loss. TheÐ weight average total pressure Ptot can be Ptot rVr dA . The result shows that the total calculated by Ð rVr dA pressure loss increases linearly with the increase in r/b ratio, and that the larger the r/b ratio is, the longer the flow path in the bend channel becomes. Numerical
Flow pattern in bend channel
The flow pattern in the bend channel is affected significantly by the inflow fluid from the impeller. The jet/wake effect of the impeller outlet makes the radial velocity and tangential velocity extremely uneven from the hub to the shroud side. Although it will be mixed to some extent when the fluid passes through the vaneless diffuser, the fluid velocity distribution at the inlet of the bend channel is not uniform at all. Separation will occur at the shroud side of the outlet of the vaneless diffuser with a large D4/D3 ratio. The distribution of radial velocity and tangential velocity of the inlet section in the bend channel is shown in Fig. 5(a), where the r/b ratio is equal to 1.0. It can be seen that, affected by the upstream flow of the impeller and the vaneless diffuser, the radial velocity and tangential velocity around the shroud side are lower than those around the hub side, and backflow can also be found around the shroud side. The radial velocity and tangential velocity distribution at the outlet section of the bend channel are shown in Fig. 5 (b), where the r/b ratio is equal to 1.0. It can be seen that the flow tends to be uniform at the outlet of the bend channel, with radial velocity and tangential velocity at the outlet being more uniform than those at the inlet section of the bend channel. In addition, the backflow around the shroud side disappears. Different from the inlet section, the radial velocity around the shroud side is higher than those around the hub side. Although this result is similar to the experimental result of Akaike and those of the numerical investigations in Refs. [4–6], it is more practical because it considers the influence of the impeller and the vaneless diffuser on the bend channel. 3.3 Influence of r/b ratio on flow pattern in the bend channel
Fig. 4
Influence of r/b ratio on total pressure loss
Figure 6 shows the influence of r/b ratio on circumference average radial velocity Vr and circumference average tangential velocity Vt of the bend channel outlet section. For the centrifugal compressor stage investigated, it can be seen that the changes in r/b ratio have little effect on the change in radial velocity. Radial velocity distribution stays almost unchanged with increases in r/b ratio, and the radial velocity Vr around the shroud side is higher than that around the hub side. However, the changes in
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Fig. 5
Fig. 6
Distribution of velocity of inlet and outlet of bend channel (a) Inlet of bend channel; (b) outlet of bend channel
Influence of r/b ratio on outlet velocity of bend channel (a) Distribution of Vr; (b) distribution of Vt
r/b ratio have significant influence on tangential velocity. Vt decreases with the increase in r/b ratio, and the tangential velocity Vt spanwise distribution becomes more uniform. Figure 7 shows the influence of r/b ratio on flow angle a at the outlet section of the bend channel. It can be seen that the flow angle a of the outlet section of the bend channel increases with an increase in r/b. The main reason for this is that the flow path becomes longer with increasing r/b ratio, and that the effect of wall friction on flow angle is greater. When r/b ratio is changed from 0.75 to 1.5, the flow angle a will change around 2 degrees. The suitable increase of the flow angle makes the return channel at the back of the bend channel short, and lessens the loss. But if the r/b ratio is too large, it will increase the wall friction loss in the bend channel and the axial size of the centrifugal compressor.
Fig. 7 Influence of r/b ratio on outlet flow angle of bend channel
Optimal r/b ratio of bend channel in centrifugal compressor
4
Conclusions
By presenting a numerical study of the bend channel with different r/b ratios, several conclusions are reached: 1) The centrifugal compressor stage investigated in this research has the highest efficiency when the r/b ratio reaches 1.0. So it can be concluded that the optimal r/b ratio is around 1.0. 2) The circumference average angle of the bend channel outlet increases with the increase in r/b ratio. This increase in r/b ratio is good for the decrease of flow loss in the return channel, but it also causes the incidence angle of the return channel blade to increase and makes the flow in the return channel worse, which should be taken into account when designing the bend channel. 3) Wall friction is the main reason for the total pressure loss in the bend channel. Acknowledgements
This work was supported by the Hi-Tech Research and Development Program of China (No. 2006AA05Z220) and the National Natural Science Foundation of China (Grant No. 50476055).
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References 1. Aungler R. Aerodynamic design and analysis of vaneless diffusers and return channels. ASME Paper No. 93-GT-101, New York, 1993 2. Davis W R. Three-dimensional boundary layer computation on the stationary end-walls of centrifugal turbomachinery. T ASME J Fluid Eng, 1976, 98: 431–442 3. Akaike S, Toyokura T. Flow in interstage return bend of centrifugal turbomachinery. In: Kisbocskoi L, Szabo A, eds. Proceedings of the 6th Conference on Fluid Machinery. Budapest, Hungary, 1979, 11–20 4. Oh J M, Engeda A. A numerical study of the U-turn bend in return channel systems for multistage centrifugal compressors. J Mechanical Engineering Science, 2005, 219(8): 749–756 5. Inoue Y, Koizumi T. Experimental study on flow patterns and losses in return passages for centrifugal compressor. ASME Fluid Eng Div, 1983, 3: 13–21 6. Lenke L J, Simon H. Numerical simulation of the flow through the return channel of multistage centrifugal compressors. In: 43rd IGTI-ASME Conference. Stockholm, Sweden, 1998, 10–19 7. Fister W, Zahn G, Tasche J. Theoretical and experimental investigations about vaneless return channels of multi-stage radial flow turbomachines. ASME paper 82-GT-209, 1982
