SCIENCE CHINA Technological Sciences • RESEARCH PAPER •
November 2013 Vol.56 No.11: 2778–2786 doi: 10.1007/s11431-013-5326-y
Influence of volute distortion on the performance of turbocharger centrifugal compressor with vane diffuser ZHENG XinQian1*, JIN Lei1 & TAMAKI Hideaki2 1 2
State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing 100084, China; Turbo Machinery and Engine Technology Department, IHI Corporation, Yokohama 2358501, Japan Received May 2, 2013; accepted August 8, 2013; published online September 12, 2013
As the geometry of the volute of turbocharger compressor is non-axisymmetric, it causes a distortion at the outlet of the diffuser and influences the upstream components. A distortion model in which a pressure distortion was applied as outlet boundary condition was established to simulate the distortion induced by the volute. It turned out to be sufficient to impose a circumferentially asymmetric pressure distribution at the outlet of the diffuser to replace the volute. Based on the distortion model which was verified, the influence of the amplitude of the distortion on the performance of centrifugal compressor was studied in detail. The results show that the distortion severely harms aerodynamic stability of the investigated compressor. The larger the amplitude of the distortion, the worse the performance of the compressor. The distortion induced by asymmetric volute propagates to upstream components and causes local flow separation at part of diffuser and impeller, and then causes the compressor surge. When the amplitude of the volute distortion is 10%, the stable flow range of the centrifugal compressor decreases to near zero. To authors’ knowledge, the relationship between the compressor performance and distortion amplitude is first obtained quantitatively, which provides evidence to improve the performance of turbocharger compressor by decreasing the distortion induced by asymmetric volute. turbocharger, vane diffuser, centrifugal compressor, stability, distortion Citation:
Zheng X Q, Jin L, Tamaki H. Influence of volute distortion on the performance of turbocharger centrifugal compressor with vane diffuser. Sci China Tech Sci, 2013, 56: 27782786, doi: 10.1007/s11431-013-5326-y
Nomenclature A amplitude of distortion m
mass flow rate (kg s1)
N
rotating speed (r min1)
PR
pressure ratio
R2
radius of the impeller (mm)
SFR
stable flow range
efficiency
1 Introduction Turbocharging technology plays an important role for internal combustion engines nowadays. Turbocharging can improve engine power density and fuel economy, while decreasing CO2 emissions [1, 2]. With the increasing stringent emission regulation requirements, high rates of exhaust gas recirculation (EGR) are generally used to reduce the NOx emissions, for which high pressure ratio turbocharging technology is required [3–5]. In addition, high pressure ratio turbocharging technology is also the core technology to recover engine power in high altitudes conditions [6, 7]. Unfortunately, high pressure ratio always comes with the
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flow being transonic in the compressor which decreases the stable flow range and efficiency of the compressor. Thus, increasing the stable flow range and the efficiency is the main work for high pressure ratio compressor design and development [8]. A turbocharger centrifugal compressor includes three main parts, the impeller, diffuser and volute. While the former two are axisymmetric, the volute is asymmetric. The volute is usually designed as a spiral-shaped, overhung housing that collects air from diffuser and passes it to the pipe system. A number of authors have paid attention to the non-axisymmetric flow induced by the volute in centrifugal compressor. The volute is mostly designed in a way to shape a uniform circumferential static pressure distribution along the volute section at a design condition. However, the volute acts as a diffuser at lower flow rate than the design one and acts as a nozzle at higher flow rate than the design flow rate, respectively. This causes a rotationally nonaxisymmetric pressure distribution in the diffuser exit. This non-axisymmetric pressure distribution in the diffuser exit has a significant impact on the upstream components, including the diffuser and impeller [9, 10]. The experimental work of Hagelstein et al. [11] showed that the volute results in a very large pressure distortion in the diffuser at off-design condition which has considerable effect on the upstream components. The study of Xu et al. [12] also confirmed that the volute tongue caused the static pressure distortion at the volute inlet and this non-uniform pressure would impact the upstream flows. The measurements and simulations conducted by Zheng et al. [13] give evidence that the flow distortions in a high pressure ratio compressor impeller were much more severe, which implies that the non-axisymmetric flow induced by the volute has great influences on the performance of a high pressure-ratio compressor. The unsteady flow analysis in the impeller conducted by Fatsis et al. [14] indicated that the outlet static pressure distortion could propagate upstream and had an impact on the incidence of the blade leading edges as well as other parameters. Gu et al. [15, 16] analyzed the effect of the slope of circumferential static pressure variation at the impeller exit on compressor performance at off-design conditions, the results show that circumferentially increasing pressure in the rotating direction at the impeller exit lowered down the efficiency of the impeller. As for computation method, the work of Dickmann et al. [17] showed that it was possible to compute the entire compressor stage flow field that is typical for a configuration with a volute by imposing a circumferentially asymmetric pressure distribution at the exit of the vaned diffuser. Qualitative results about the impact of volute’s asymmetry on the performance also have been investigated. Zheng et al. [18] conducted the first work that gave quantitative estimations. The performances of a compressor with and without the volute were compared using three-dimen-
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sional viscous CFD. The relative constriction in stable flow range was up to 42% at the design speed, which indicated that the volute had great influences on the stable flow range of a high pressure-ratio centrifugal compressor. Lin et al. [19] used experimental method to evaluate the impact of the volute’s asymmetry on compressor performance. The result showed that the volute constricted the stable flow range by up to 47% and maximum efficiency decreases by 4.8% at design speed. Many researches are conducted on how the distortion induced by volute affects the performance of compressor. However, to the authors’ knowledge, little work showed the relationship between the amplitude of the distortion and the change of compressor performance. In order to improve the compressor performance by decreasing the distortion, it is very important to understand how performance changes with the change of the distortion amplitude. In this work, a distortion model to simulate the distortion induced by the volute was established using three-dimensional viscous CFD. The influence of the amplitude of the distortion on the performance of the compressor and the propagation of the distortion in the compressor are presented and analyzed.
2 Simulation method 2.1
Flow model
The Reynolds-average Navier-Stokes equations were solved based on a three-dimensional steady compressible assumption and finite volume scheme. Spatial discretization was done with a central scheme [20]. A fourth-order RungeKutta scheme was applied to temporal discretization [21]. Spalart-Allmaras (S-A) one-equation model was chosen for turbulence closure. The CFL number was chosen as 3 and a multi-grid procedure was applied to accelerate convergence. The rotor-stator was modeled as frozen rotor which means the rotating system is calculated in relative coordinates and the flow quantities are transferred over the interface without varying the relative position of impeller and diffuser. And the position of rotor-stator is set at 1.08R2 (R2 is the radius of impeller at the outlet). 2.2
Meshing
The main parameters of the centrifugal compressor used in this paper are shown in Table 1. A multi-block structured grid was used to mesh the impeller. In the simulation, a constant tip clearance of 0.5 mm was assumed. The wall distance of the first layer of the near-wall grid was set to be 0.003 mm at vane diffuser, 0.002 mm at impeller and 0.001 at blades to meet the requirement of a boundary layer resolution sufficiently fine for the S-A model (y+10). For the detailed flow analysis, a fine grid with a higher
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grid number was set up to attain a higher resolution of flow quantities. In this paper, the whole compressor grid including 9 impeller passages and 16 diffuser vanes has 274 blocks and 10 million of cells. The minimum orthogonality of the mesh is 15.1 and the maximum aspect ratio is less than 5000, the maximum expansion ratio is less than 10. All the mesh quality can meet the requirement of simulation. Figure 1 shows the mesh of impeller and diffuser in one flow passage.
or is 40°, and thus the rotor was moved from angle to +13.33° and +26.66°, respectively, as shown in Figure 3 (left). Then three different relative positions of impeller and diffuser were created. The maximum efficiency point with uniform outlet condition was chosen as evaluation point. The performance results for the three different conditions are shown in Figure 3 (right). The relative difference are 0.006% for mass flow rate, 0.032% for total-total pressure ratio, and 0.066% for efficiency, which means that neglecting the influence of the rotor position for the calculation of performance quantities is reasonable. In the work of Zheng [18], S-A model and k-ε model were compared. And the simulation result which used the same simulation method with this paper was compared with the test result. The result shows that S-A model is more suitable in this simulation and the simulation method can be used to discuss the performance and stability of the compressor used in this paper.
2.3
2.4
Table 1
Main parameters of the centrifugal compressor Parameter Design rotating speed Design mass flow rate Blade number of impeller Blade number of diffuser Impeller outlet diameter Diffuser outlet diameter Diffuser width
Value 111,700 (r min1) 0.48 (kg s1) 9/9 main/splitter blades 16 diffuser vanes 100 (mm) 154.6 (mm) 4.0 (mm)
Validation of simulation method
2.3.1 Grid independence analysis Simulations were done with one single flow passage of a centrifugal compressor. The turbulence model, boundary conditions, mesh topology, wall distance of the first layer of the near-wall grid and other factors of the cases were all kept the same. Figure 2 shows the relationship between total pressure ratio and non-dimensional efficiency with the grid number. It can be seen that the predicted pressure ratio and efficiency maintained substantially constant when the grid number is more than 350000. 2.3.2 Rotor-stator interaction The interaction between rotor and stator is one of the key issues in this work. The simulated compressor has 9+9 impeller blades and 16 diffuser vanes. Because the rotor-stator is modeled as frozen rotor, the angular position of impeller and diffuser may have influences on simulation results. The impact of the relative position of impeller and diffuser on performance has to be evaluated. The periodicity of the rot-
Figure 1
Created mesh of the compressor.
Establishing distortion model
2.4.1 Distortion model In order to study how the volute influences the upstream components, a distortion model was established to simulate the distortion caused by the volute. A centrifugal compressor includes three main components: impeller, diffuser and volute. If the simulation domain includes impeller, diffuser and volute, it is called original model in this paper, as shown in Figure 4(a). In order to change the amplitude of the distortion induced by the volute, the volute was removed and a circumferentially non-uniform pressure distribution was applied as outlet boundary condition to replace the volute, as shown in Figure 4(b), which was called distortion model. Based on this distortion model, it is convenient to change the amplitude of the distortion and research how performance changes with the change of the distortion amplitude. 2.4.2 Model verification A vaneless diffuser compressor was chosen to verify this
Figure 2
The independence of grid with single passage.
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Figure 3
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Figure 5
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Different rotor positions φ for independence test (left) and influence of rotor position on performance quantities (right).
model. A pressure distribution at the diffuser outlet was obtained by calculating the whole compressor with volute (original model). This pressure distribution was set as outlet boundary condition of the distortion model, as shown in Figure 5. Two sections were chosen to compare the flow parameters distributions in the diffuser using original model and distortion model, as shown in Figure 6. From Figure 6, it can be seen that the flow parameters distributions with original model and distortion model are consistent. So, the
Figure 4
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Original model and distortion model.
CFD domain and principle of the outlet boundary condition.
conclusion that the distortion model can be used to simulate the distortion induced by the volute can be made. A similar model was used by Dickmann et al. [17] to compute the flow field of vane diffuser compressor. 2.5
Simulation procedure
Distortion model was used in this simulation and the simulation focused on the influence of the amplitude of the volute distortion on the performance of centrifugal compressor. This simulation can be divided into three steps. 1) First step. The performance lines with uniform outlet boundary condition were simulated. Total pressure, temperature, and velocity components were imposed at the inlet as inlet boundary condition. As for outlet boundary condition, an average static pressure was imposed near choke and self-adaptive mass flow rate at other operating conditions. Both impeller and diffuser were set as adiabatic non-slip boundaries. 2) Second step. The volute distortions P() acting as outlet condition of the distortion were obtained, as shown in eq. (1). is the circumferential angle, P is the circumferential area-average pressure. From the first step simulation, the static pressure at diffuser outlet of each simulation case with uniform outlet boundary condition can be obtained. P is the series of static pressure obtained from the first step simulation. In order to isolate the amplitude influence on compressor performance, the shape of distortion outlet boundary condition was set as sine curve. The amplitude of volute distortion was defined in eq. (2).
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Figure 6
Pmax Pmin 2P
,
(1) (2)
where Pmax is the maximum value of the static pressure circumferentially, Pmin is the minimum value of the static pressure circumferentially. 3) Third step. The performance lines with distortion outlet boundary condition were simulated. In the third step simulation, total pressure, temperature, and velocity components were imposed at the inlet as inlet boundary condition. The distortion outlet boundary conditions were imposed at the outlet as outlet boundary condition. The results of simulation cases with uniform outlet boundary condition were used as initial solution. Both impeller and diffuser were set as adiabatic non-slip boundaries. The simulation was considered to be converged if all the flow variables did not vary more than 0.1% over 1000 consecutive iterations. In order to obtain relatively accurate surge point, the average static pressure gap between two near simulation points is 0.5 kPa at near surge conditions.
3 Results and discussion In order to evaluate the influence of the volute distortion on compressor performance in high pressure ratio status, the rotating speed of 111700 r min1 was chosen. 3.1
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Compression of distortion model and original model about flow parameters distribution.
P ( ) P (1 A sin ),
A
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Propagation of volute distortion
Figure 7(b) shows the amplitude of the static pressure dis-
tortion in the compressor at near surge condition. At every radial position, the static pressure distribution was obtained by averaging the values on the corresponding cross-flow section, and the amplitude of static pressure distribution was calculated by eq. (2). It is found that the volute distortion can propagate from the diffuser outlet to impeller inlet. In the diffuser, the amplitude of the pressure distortion increases as it propagates upstream from the diffuser outlet to vane throat, and then decreases from vane throat to diffuser inlet. In the impeller, the amplitude of the pressure distortion has a downward trend from the impeller outlet to impeller inlet. The magnification of pressure distortion from diffuser outlet to vane throat is similar to the result of pressure distortion propagation in vaneless diffuser [13, 22]. According to the acoustic wave theory, the energy density of pressure distortion (I) can be defined as I ∆P 2 / Z ,
(3)
Z is the acoustic impedance. According to the law of energy conservation, the distortion energy is constant in any flow area (A), which means: I A constant.
(4)
The flow area at vane throat is smaller than other sections. So the energy density at vane throat will be larger and therefore P is larger. So the amplitude of pressure distortion at vane throat is the largest. It is worth to point out that flow separation can affect the effective flow area (A) and the interaction between the impeller and the diffuser also attributes to the propagation of volute distortion.
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Figure 7 Amplitude of pressure distortion in the compressor near surge. (a) Locations in the compressor; (b) amplitude of pressure distortion in the compressor at near surge condition; (c) amplitude of pressure distortion in the compressor at near surge, peak efficiency and near choke conditions with 3% volute distortion; (d) pressure distortion propagation in vane diffuser at near surge and peak efficiency condition (schematic diagram); (e) pressure distortion propagation in vane diffuser at near choke condition (schematic diagram).
Figure 7(c) shows the amplitude of the static pressure distortion in the compressor at three typical conditions with 3% volute distortion. The pressure distortion propagation at peak efficiency condition is similar to that at near surge condition, and the schematic diagram of pressure distortion propagation in vane diffuser is shown in Figure 7(d). While, at near choke condition, the amplitude of pressure distortion decrease to near zero when the distortion passes through the vane diffuser. At near choke condition, choking occurs at the throat of the diffuser vane, the flow at vane throat section is supersonic and shock wave appears at this section. The flow upstream of the vane throat is not affected by the pressure distribution downstream of the vane throat because the pressure information from downstream of the throat cannot travel upstream. So the amplitude of pressure distor-
tion decreases to near zero when the pressure distortion passes through the vane throat as shown in Figure 7(e). Figure 7(c) also shows that the maximum amplitude of pressure distortion at near choke condition is smaller than that at other two conditions. The reason is that the cut section to analyze the pressure distortion crosses the shock wave as shown in Figure 7(e), which means pressure distortion exists at part of cut section and at other part of cut section the pressure distortion is uniform. 3.2
Influence on compressor performance
The influence of the volute distortion on compressor performance is displayed in the performance lines for total-total pressure ratio in Figure 8(a), and for efficiency in
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Figure 8 Influence of the volute distortion on compressor performance. (a) Compressor total pressure ratio with different amplitude of volute distortion; (b) compressor efficiency with different amplitude of volute distortion.
Figure 8(b). It can be seen that the main trends of the performance lines remain similar, and the pressure ratio and efficiency remain nearly unchanged as the amplitude of volute distortion increases. While, as the amplitude of volute distortion increases, the stable flow range decreases obviously. As stable flow range is the most influencing factor on turbocharger centrifugal compressor, the influence of amplitude of volute distortion on compressor stability needs detailed study. 3.3
Influence on compressor stability
3.3.1 Influence on compressor stable flow range The stable flow range is defined as m choke m surge SFR 100%, m choke N const
(5)
where m choke is the mass flow rate at choke condition, m surge is the mass flow rate at surge condition.
The influence of the volute distortion on compressor stability is displayed in Figure 9 which is obtained from Figure 8. From the results, it can be seen that the stable flow range
Figure 9
Influence of the volute distortion on compressor stability.
decreases as the amplitude of volute distortion increases. When the amplitude of volute distortion is 5%, compared to 0% volute distortion, the relative drop of stable flow range is 55.3%. When the amplitude of volute distortion is 10%, the stable flow range decreases to near zero and the relative drop of stable flow range is near 100%, which means the compressor cannot work. 3.3.2 Mechanism on compressor stability The flow near the shroud has much lower momentum than that near the hub and the middle span, so the flow separation may first appear near the shroud [23]. Based on this, in this paper, just the flow fields at 90% span (near shroud) are analyzed. Figures 10 and 11 show the Mach number distribution at 90% span of diffuser and impeller with 3% and 5% amplitude, respectively. The two analysis points are shown in Figure 8(a). From Figure 10, it can be seen that the flow field of 3% and 5% volute distortion is non-axisymmetric, and at part of flow passage in diffuser flow separation appears. From Figure 11, it can be seen that the flow field of 3% and 5% volute distortion is non-axisymmetric. The low momentum fluid gathered at the top of the blade, and flow separation appears at these sections. Also, backflow can be seen at vaneless space of impeller outlet to diffuser vane inlet. From the results, flow separation appears at some flow passages of diffuser and impeller. Also the flow at vaneless part of diffuser degenerates. All these flow phenomena can contribute to the initiation of stall at some flow passages and then cause the whole compressor surge. For uniform volute distortion, the flow field in the compressor is axisymmetric which means all the flow passages are the same. So, the compressor surge appears when all the flow passages reach the critical condition that can cause stall. For non-uniform volute distortion, the flow field is non-axisymmetric which means the flow passages are different from each other. So it is easier to reach the critical condition at part of flow passages, and cause stall at part of flow passages when the mass flow rate of compressor is
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Figure 10 Absolute Mach number distribution at 90% span of diffuser (near shroud).
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propagates from diffuser outlet to vane throat. The propagation of volute distortion is different with or without shock wave at vane throat. Without shock wave at vane throat, the volute distortion can propagate from diffuser outlet to impeller inlet; with shock wave at vane throat, the volute distortion can only propagate to vane throat for the pressure information from downstream cannot travel through shock wave. 2) The volute distortion of the distortion model was set as sine curve and different amplitude of volute distortion was set to study the influence of volute distortion amplitude on compressor performance. The results show that pressure ratio and efficiency nearly unchanged as the amplitude of volute distortion increases. 3) Compared to uniform outlet condition, distortion outlet conditions are easy to reach stall condition at some flow passage. The higher the amplitude of volute distortion, the easier for some passages to reach the stall condition. So, the stable flow range of compressor decreases as the amplitude of volute distortion increases. When the amplitude of volute distortion is 10%, the stable flow range decreases to near zero. The results provide evidence that the performance of turbocharger compressor can be improved if the distortion induced by asymmetric volute is decreased or eliminated. This work was supported by the National Natural Science Foundation of China (Grant No. 51176087). 1
Figure 11 Relative Mach number distribution at 90% span of impeller (near shroud).
relatively high. And the higher the amplitude of volute distortion, the easier for some passages to reach the stall condition. Stall at part of flow passages can cause the whole compressor surge. So, the stable flow range decreases as the amplitude of volute distortion increases.
4 Conclusions Turbocharging is very important for the power density, economy and emission of internal combustion engine. The distortion induced by volute has great effect on the performance of turbocharger compressors. In order to reveal the relationship between the compressor performance and the distortion, a distortion model to simulate the distortion induced by the volute was established. The influence of the amplitude of the volute distortion on the performance of the compressor is fist obtained quantitatively. The main conclusions are drawn below. 1) The amplitude of volute distortion increases as it
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