Energy 75 (2014) 534e548
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Numerical investigation of impeller trimming effect on performance of an axial flow fan Chunxi Li*, Xinying Li, Pengmin Li, Xuemin Ye School of Energy Power and Mechanical Engineering, North China Electric Power University, Baoding 071003, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 19 February 2014 Received in revised form 20 July 2014 Accepted 4 August 2014 Available online 29 August 2014
To study the performance variations of an axial fan after impeller trimming, numerical simulations are executed under the following conditions: trimming quantity of 5%, 10%, and 15% of blade height, with tip clearance changed and unchanged. The effects of trimming quantity and tip clearance on flow field and performance of the axial fan are investigated, and formulae are presented for total pressure rise and flow rate ratio versus impeller diameter ratio and for operating points before and after impeller trimming. The simulated results show that the performance curves after impeller trimming tend to decline. Near the design flow rate, the performance of the fan with unchanged tip clearance is aerodynamically superior to that with changed tip clearance; the former deteriorates at a large flow rate. The margin of parameters provided by design units exceeding the actual operation requires the fan to normally operate to the left of the rated load, therefore, axial fans with tip clearance unchanged after impeller trimming have been found to maintain better performance. The equations, denoting total pressure rise ratio and flow rate ratio versus impeller diameter ratio are available to determine the trimming quantity according to actual requirements of operating points after impeller trimming. © 2014 Elsevier Ltd. All rights reserved.
Keywords: Axial fan Impeller trimming Numerical investigation Performance Operation points
1. Introduction With the increase of installed capacity in thermal power units, the variable pitch axial flow fan, with its numerous advantages of high efficiency, large flow rate, low noise, lower startup torque, and excellent regulating characteristics, becomes a popular choice for forced draft fans, induced draft fans, and primary air fans in modern large-scale power plants. For safety reasons, the flow rate and total pressure rise of these fans are required to have margins of 20% ~ 30% during the design stage of the combustion system in fossil fuel power plants in China [1]. Owing to the restrictions on fan type, the actual flow rate margins of axial fans can be as high as 60% in particular applications [1]. Therefore, it is extremely necessary to regulate flow rate to meet actual requirements and improve fan performance at low cost. Many approaches have been proposed to adjust flow rate and improve turbo-machinery performance. He et al. [2] investigated the influence of the blade installation angle on the performance of
* Corresponding author. Postal address: P O Box 29, Yonghuabei Street 619, Baoding 071003, China. Tel.: þ86 312 7522924; fax: þ86 312 5012520. E-mail addresses:
[email protected],
[email protected] (C. Li),
[email protected] (X. Li),
[email protected] (P. Li), yexuemin@163. com (X. Ye). http://dx.doi.org/10.1016/j.energy.2014.08.015 0360-5442/© 2014 Elsevier Ltd. All rights reserved.
windward axial fans in an air-cooled power plant and initiated a new performance by modifying the blade installation angle of the axial fans. Gao et al. [3] presented measures to improve the aerothermal performance of unshrouded turbines through the management of tip leakage and injection flows. Numerical simulations were conducted on both flat and cavity tips to investigate the effects of tip injection on aero-thermal performance of the tip leakage flow. Mohamed and Shaaban [4] proposed two different airfoil geometries to improve the aerodynamic efficiency of turbines by optimizing the blade pitch angle. Wu et al. [5] proposed a new method of changing the chord length distribution to adapt low stream velocity and increase startup torque, and improved the total performance of the turbine with a new hydrofoil. Alternatively, moderate impeller trimming is a simple and effective method for reducing the excessive flow rate margin of axial fans in practical operations. Presently, the trimming theories and investigations for centrifugal fans [6] and pumps [7e8] are well developed and widely used in engineering practice. Owing to the intrinsic structure difference between axial flow fans and centrifugal fans, the direct applications of the theory and formulae of centrifugal to axial fans may lead to errors in results. Thus these investigations should be conducted on the impacts of impeller or blade trimming on axial fan performance. However certain investigations have reported the effect of impeller trimming on axial
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Nomenclature d D h k pp pt1 pt2 Dp qv r u
D d h r jrt
hub diameter, mm impeller diameter, mm total blade height, mm the coefficient related to pipeline resistance pressure head in a pipeline system, Pa total pressure at the inlet of the impeller, Pa total pressure at the outlet of the impeller, Pa total pressure rise across the fan, Pa flow rate of fan, m3/s local blade height, mm the circumferential velocity of the impeller, m/s relative trimming quantity, % the changed tip clearance after blade trimming, mm fan efficiency fluid density, kg/m3 the total pressure rise coefficient
Subscript c d o u
changed tip clearance design value value of the original fan unchanged tip clearance
fans. Ye and Zhu [9] deduced the relationship between performance parameters and trimming quantity by integration. However, this method originates from the additional premise that the twisted pattern of the axial fan blade should be known, so the accuracy of its conclusions should be further validated. Taking advantage of the same mould to produce a series of impellers and reduce the cost of blade manufacturing, Lv et al. [10] presented the performance curves of pressure ratioeflow rate and efficiencyeflow rate for impeller trimming quantities of 15%, 30%, 45%, and 57% of blade height, using numerical simulation under the condition of constant vortices. Owing to the excessive impeller trimming quantity and lacking the relation of performance parameters before and after impeller trimming, these results are still limited for practical applications. After blade trimming, the tip clearance is changed accordingly, which results in increments of both fan losses and noise level. €ger [11] investigated the effects of different tip Venter and Kro clearances on the performance of an axial flow fan, and evaluated the variations of static pressure, volumetric flow rate, and efficiency; the results indicated that the effect of tip clearance depends on the type and size of the rotor, as well as the type of installation. Fukano and Jang [12] analysed the noise of axial flow fans by using two hot-wire probes rotating with the blades. PIV (Particle image velocimetry) was employed by Zhu et al. [13] for exploring the transient flow field of the blade tip region in a low-speed axial fan with different tip clearance heights under design conditions. The results indicated that with increased tip clearance, the tip leakage vortex clearly changes; the intensity and scope of tip leakage vortex expand, and the vortex location simultaneously moves closer to the pressure side chord-wise and thus, the flow instability is enhanced. In addition, they introduced a PDA (phase doppler anemometer) system and a CFX-Tascflow software platform [13] to investigate the effect of tip leakage flow structure on rotor tip and to reveal the characteristics and formation process of the leakage vortex. Jin et al. [14e15] presented the internal mechanism of tip leakage losses at the blade tips of radial forward-skewed, and backward-skewed blades in a low-pressure axial fan, accomplished by PIV and CFD
535
(computational fluid dynamics) software. According to experimental and numerical results, the forward-skewed blade demonstrates increasing leakage losses and an expanding stable operating range with appropriate skew angles compared to the radial blade, and a backward-skewed blade weakens the tip leakage flow. Taghavi-Zenouz and Eslami [16] numerically studied different operating conditions and tip clearances to determine the effects of an isolated axial compressor rotor blade row on tip flow characteristics. Their work focused on the detection of unsteady behaviour of tip leakage flows using LES (large eddy simulation) and RANS (Reynolds-averaged NaviereStokes) methods. The results showed that increasing the tip gap size increases the vortex intensity at each flow coefficient and decreases its fluctuating frequency at near stall conditions. Corsini et al. [17] applied a blade tip endplate to reduce fan noise by changing the tip leakage flow behaviour based on experimental and numerical investigations. Similar geometries appeared in the research work of Sitaramand and Sivakumar, who studied the effects of a rotor partial shroud on a low aspect ratio axial flow fan [18]. Thompson et al. [19] tested the effects of stepped-tip gaps and clearance levels on the performance of a transonic axial-flow compressor rotor. The results showed that for small and intermediate clearances, stepped tip gaps improve the pressure ratio, efficiency, and flow rate range for most operating conditions. Ramakrishma and Govardhan [20] numerically simulated the aerodynamic performance of low-speed axial flow compressor rotors with different tip clearance levels and combined rotor sweep configurations, and presented performance curves, including energy coefficient versus flow rate coefficient and spanwise variation of total pressure rise coefficient versus clearance. As mentioned above, the published studies on impeller trimming mostly focus on centrifugal fans and pumps, while few on axial fans. Consequently, extensive in-depth research on tip clearance and axial fan performance still needs to be conducted for direct engineering applications, particularly for establishing the formulae between tip clearance and fan performance parameters. Recently, the rapid development of CFD technology has improved simulation accuracy for fan performance and ensured a relative error within 5% compared with experimental results [21]; this provides an economical and efficient tool to predict axial fan performance after impeller trimming. In the present paper, three relative impeller trimming quantities of 5%, 10%, and 15% of blade height are simulated with Fluent for an OB-84 type axial fan. The performance of the fan is investigated with regard to leakage losses before and after impeller trimming under both changed and unchanged tip clearances. Additionally, performance curves before and after impeller trimming, are compared. Finally, equations are proposed for flow rate and full pressure rise versus impeller diameter ratio before and after blade trimming under operating conditions, which predict impeller diameters according to the actual requirements and provide an important reference for impeller trimming in practical applications of axial fans. 2. Computational model 2.1. Physical model A variable-pitch OB-84 type axial fan with rear guide vanes, as shown in Fig. 1, is selected for examining the effect of impeller trimming on fan performance. The fan consists of 15 guide vanes and 14 rotor blades. The base profile of the rotor blade in the axial fan adopts an asymmetrical airfoil of NACA 3506, as shown in Fig. 2. The diameter of the original fan is D ¼ 1500 mm and the installation angle of the rotor blades is 32 . The fan is driven at constant rotational speed of 1200 rpm; the flow rate and total pressure rise are 37.12 m3/s and 2254 Pa, respectively, at design operating point.
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Fig. 1. Schematic diagram for the OB-84 type axial fan.
In this study, the performances of an original fan and a fan with three relative impeller trimming quantities are examined. Considering the enlarged tip clearance after impeller trimming, which will lead to serious leakage losses, the fan geometry with unchanged tip clearance under the same trimming condition is also simulated for comparison. Keeping the tip clearance unchanged is realised by installing a conical cylinder to the inner surface of the axial fan, as shown in Fig. 3a. The conical cylinder is installed at both the straight section of the bell-mouth and the entrance section of the guide vane to achieve smooth transition in practical application. To simulate the fan model, the structure of both the bell-mouth and guide vane regions is simplified as Fig. 3b with the unchanged tip clearance of 4.5 mm. The fan structure with unchanged tip clearance in Fig. 3b is obtained by removing the black region from the original structure in Fig. 3a. Structural parameters of the original fan and the fan after impeller trimming are listed in Table 1, where the subscripts 0 and 1 denote the parameters before and after impeller trimming respectively, and d refers to the hub diameter. Relative trimming quantity, D, in Table 1 is expressed as
D¼
D0 D1 D0 d
(1)
where D0 and D1 denote impeller diameter before and after impeller trimming. When the relative impeller trimming quantities are 5%, 10%, and 15% of blade height, the impeller diameter after trimming can be determined by using Eq. (1).
Fig. 2. Base profile of rotor blade adopting NACA airfoil.
Fig. 3. Diagram of axial fan with unchanged tip clearance after impeller trimming.
The changed tip clearance, d, after blade trimming is given as
d¼
D0 D1 þ 4:5 2
(2)
The clearance ratio is the ratio of tip clearance to impeller diameter, e.g. d/D0 for the original impeller and d/D1 for the trimmed impeller. 2.2. Mesh generation According to a multi-block topology meshing strategy and the characteristics of the OB-84 type axial fan, the computational domain is divided into bell-mouth, impeller, guide vane, and diffuser, as shown in Fig. 1. The partitioning of the fan structure requires the mesh of four component parts to be generated individually. To restrict the mesh number and achieve the optimal allocation of computational resources, the total meshes of the fan are created by referring to the impeller's meshes, and the other parts are subsequently meshed. The mesh was generated by using T-Grid type and Tet/Hybrid elements in the Gambit 2.4.6 pre-processing module. The mesh diagram is showed in Fig. 4, including the mesh of the fan in Fig. 4a, the enlarged view around the impeller in Fig. 4b, the meshes of the impeller in Fig. 4c and of the blade tip in Fig. 4d. In the present modelling, a size function was employed to densify the mesh in the blade tip clearance when meshing the impeller region, as shown in Fig. 4b and d. This was achieved by first meshing the blade surface, then meshing the impeller volume. The specific parameters of the size function used are listed as follows: the type is meshed, the source and attachment entities are the surfaces of all blades and impeller volume, the growth rate is 1.2, and the maximum size is
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Table 1 Structural parameters of original fan and fan after impeller trimming. Original parameters
Trimmed 1 2 3
Clearance Clearance Clearance Clearance Clearance Clearance
unchanged changed unchanged changed unchanged changed
Impeller diameter D0, mm
Hub diameter d, mm
Hub ratio d/D0
Tip clearance d, mm
Clearance ratio d/D0, %
1500
900
0.6
4.5
0.3
Impeller diameter D1, mm
Relative trimming quantity D ¼ D0 D1 =D0 d
Hub ratio d/D1
Tip clearance d, mm
Clearance ratio d/D1, %
1470 1470 1440 1440 1410 1410
5% 5% 10% 10% 15% 15%
0.612 0.612 0.625 0.625 0.638 0.638
4.5 19.5 4.5 34.5 4.5 49.5
0.306 1.327 0.313 2.396 0.319 3.511
Fig. 4. The mesh diagram of the fan.
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15. Compared with the mesh in the impeller, the meshes in the bellmouth, guide vane, and diffuser are sparser. Inspection of the mesh indicates that the skewness ratio value of all elements is less than 0.97 and the maximum values of skewness ratio are 0.771, 0.785, 0.749 and 0.750 from the bell-mouth to the diffuser, respectively. Thus, the high quality of the mesh is guaranteed in the present work. Next, the mesh independence test is executed on a computational domain with 10 groups of different mesh numbers. Fig. 5 shows that when the mesh number exceeds 2.26 million, the variations of full pressure rise and efficiency are very slight. Hence the mesh number of 2.26 million is selected for present numerical studies.
MRF model is selected for the coupling between the impeller and the casing in the present work. The exchange of moving and stationary wall parameters is achieved by using the interface. When the difference in volumetric flow rate between inlet and outlet is less than 105, and the residuals of speed parameters in all directions and k, ε are simultaneously less than 104, it is reasonable to presume that the current calculation is converged. 3. Results and discussion 3.1. Comparison of fan performance
A commercial CFD scheme of Fluent 6.3.26 is used to simulate the internal flow field and performance of the axial fan. The realizable keε turbulence model is widely used for solving complex flows, including swirling flow, boundary layer separation and secondary flow under highly adverse pressure gradient; the numerical results correspond well with experimental results [6,22e23]. Thus, the realizable keε turbulence model is selected to solve the 3D steady Reynolds-averaged equations in the present work. The implicit segregated method is considered. Non-slip wall conditions are applied to the boundaries, while standard wall functions are utilised in the near wall region. For turbulent flows or complex flows, the ‘SIMPLEC’ algorithm can improve the convergence in computing. Therefore in the present study, the ‘SIMPLEC’ algorithm is used to couple the pressure and velocity fields. For the discretisation of convective terms, diffusive terms, and turbulent viscosity coefficient, a second-order upwinding procedure is applied. The effects of gravitation and wall roughness on the flow field are negligible. The computational domain uses the inlet cross section of the bell-mouth as the inlet and the outlet cross section of the diffuser as the outlet. The inlet is established as the velocity entrance and the outlet is set as free outflow. The fan model is divided into stationary and moving regions; that is, the impeller is the moving region and the others are stationary regions. The MRF (multiple reference frame) model, considering the interference at the interface between the moving and stationary zones, is widely used for fluid machinery and turbo-machinery applications; it is an efficient way to simulate steady flows in a short computation time. The flow field in axial fans is generally considered to be a steady process exclusive of surge and stall phenomena. Considering the complexity of data processing and the time required for the computation of unsteady calculation, the
Before simulating the trimmed fan model, the numerical simulation results of the original fan are compared with experimental performance curves reported in the reference [24]. Under the mesh number of 2.26 million, a comparison of numerical and experimental results is presented in Fig. 6, with average relative errors of 1.6% for full pressure rise and 5.8% for efficiency when flow rate ranges from 33.29 m3/s to 46.61 m3/s. Consequently, the numerical results agree with experimental results, indicating a reliable and effective method for predicting the performance of an axial fan after impeller trimming. For a clear comparison of fan performance before and after impeller trimming, the detailed results of total pressure rise (Dp) and efficiency (h) are presented in Tables 2 and 3, and variations in performance curves are illustrated in Figs. 7 and 8. Results shown in Table 2 and Fig. 7 clarify that Dp values for the trimmed fan decline variously with respect to those of the original fan. For the fan with changed tip clearance, Dpc drops dramatically at low flow rate and minimally at high flow rate; for the fan with unchanged tip clearance, Dpu decreases weakly at low flow rate and notably at high flow rate. Additionally, with increasing impeller trimming quantity, the reduction of Dp significantly advances as the flow rate increases for unchanged tip clearance. Compared with the original fan at qvd of 37.12 m3/s, Dpc declines by 22.29%, 34.30%, and 45.42% for three trimming cases with tip clearance increased from d ¼ 4.5 mme19.5 mm, 34.5 mm, and 49.5 mm; Dpu only drops by 9.59%, 18.85%, and 31.01%, which are obviously lower than the former. This clearly demonstrates that impeller trimming has an extremely significant effect on fan performance. Table 3 and Fig. 8 show that the maximum value of hc tends to move towards low flow rate when the impeller trimming quantities are 10% and 15%. For the cases of unchanged tip clearance, compared with the efficiency of the original fan, Dhu increases with flow rate and even increases over that of the original fan in particular conditions (e. g. when the impeller trimming quantity is
Fig. 5. Independent verification of mesh number.
Fig. 6. Comparison of experimental and numerical performance curves.
2.3. Computational method and boundary conditions
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Table 2 Total pressure rise of original fan and fan after impeller trimming. Parameters
P/Pa
Relative trimming quantity D ¼ D0 D1 =D0 d
0% 5% 10% 15%
Tip clearance d, mm
qv/(m3 s1) 33.29
34.96
37.12
39.95
41.61
43.28
44.94
46.61
4.5 19.5 4.5 34.5 4.5 49.5 4.5
2454 1826 2291 1603 2154 1523 1944
2375 1792 2211 1657 2030 1454 1784
2254 1752 2038 1613 1829 1337 1555
2037 1562 1772 1441 1538 1170 1225
1890 1412 1599 1318 1352 1073 1017
1740 1264 1420 1196 1158 974 788
1579 1121 1229 1072 952 876 544
1419 987 1036 954 737 780 293
Tip clearance d, mm
qv/(m3 s1) 33.29
34.96
37.12
39.95
41.61
43.28
44.94
46.61
4.5 19.5 4.5 34.5 4.5 49.5 4.5
0.797 0.690 0.804 0.607 0.804 0.583 0.785
0.809 0.711 0.817 0.634 0.803 0.584 0.771
0.817 0.724 0.809 0.648 0.786 0.577 0.739
0.811 0.734 0.781 0.637 0.745 0.559 0.669
0.799 0.708 0.756 0.621 0.708 0.545 0.608
0.783 0.681 0.723 0.599 0.660 0.524 0.520
0.760 0.650 0.678 0.571 0.593 0.499 0.400
0.733 0.617 0.622 0.540 0.505 0.471 0.244
Table 3 Efficiency of original fan and fan after impeller trimming. Parameters
h
Relative trimming quantity D ¼ D0 D1 =D0 d
0% 5% 10% 15%
5% and qv < 37.12 m3/s). In most flow rate domains (at an impeller trimming quantity of 5%, it is the total flow rate domain; for the 10% case, the domain is qv 44.94; for the 15% case, the domain is qv < 43.28 m3/s), the efficiency (hu) with unchanged tip clearance is
higher than that (hc) of the changed tip clearance. The comparison with original fan at design flow rate illustrates that fan efficiency for three trimming quantities reduces by 13.67%, 21.91%, and 30.09% when the tip clearance is changed, yet decreases by 0.96%,
Fig. 7. Total pressure riseeflow rate curves of the axial fan.
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Fig. 8. Efficiencyeflow rate curve of the axial fan.
3.80%, and 9.49% when the tip clearance is unchanged. The present investigation exhibits a linear relationship between impeller trimming quantity and reductions of total pressure rise and efficiency when the results of the fan with unchanged tip clearance are compared with the original fan. That is, as impeller trimming quantity increases per centimeter, total pressure rise and efficiency will drop by approximately 25 Pa and 0.68 percentage points, respectively, at the identical flow rates. Figs. 7 and 8 indicate that the overall performance of the fan with unchanged tip clearance is better than that with changed tip clearance under most conditions; however, it is worse at an extremely large flow rate (e. g. the impeller trimming quantity is 10% and qv > 44.94 m3/s; the impeller trimming quantity is 15% and qv 43.28 m3/s). To explore the above variations and possible reasons, the effects of structure parameters of the trimmed axial fan on flowing losses will be presented in the following sections. 3.2. Variations in flowing losses In general, the aerodynamic losses occurring in blade passages can be grouped into the following categories [25]: annulus losses, tip leakage losses, vortex losses, and profile losses. The tip leakage losses and vortex losses occupy a large proportion of total aerodynamic losses. Therefore, the effects of impeller trimming on tip leakage, and vortex losses will be analysed in detail. 3.2.1. Variations in tip leakage losses The tip clearance between the blade tip and casing, allows some fluid to cross the blade tip from the pressure side of the blade to the
suction side owing to the pressure difference between the pressure and suction sides, which results in tip leakage losses. The total pressure distribution near the blade tip under different impeller trimming quantities at design flow rate is presented in Fig. 9. Fig. 9a shows that, for the original fan, the leakage vortex is at the position of 30% chord-wise length and adjacent to the suction surface with minimum pressure. Fig. 9b and c reveal that with increase of impeller trimming quantity, the formation position of the tip leakage vortex, namely, the minimum pressure on the blade tip, gradually moves downstream, and is accompanied by an expanded region of influence and intensity of the vortex core, which is subject to a positive pressure gradient on the suction surface. Additionally, the trajectory of the tip leakage vortex deviates from the suction side to the pressure side along the mainstream. Thus the developing direction of the tip leakage vortex is opposite the rotating direction of the impeller, which is consistent with the phenomenon reported in the literature [13e14,26e27]. A comparison of the performance for the trimmed fan with unchanged and changed tip clearance shows that the position of the tip leakage vortex core of the former significantly deviates upstream and that the scale of the leakage vortex changes slightly with respect to the latter. Nevertheless, the tip leakage vortex core still has a tendency to move downstream compared with the original. These phenomena can be explained as follows: as airflow passes the tip clearance, the presence of a boundary layer formed on the casing wall acts as a blockage to the tip leakage flow. The principle of minimum potential energy [28] asserts that for the flow passing the tip clearance, airflow shifts to the direction of minimised total potential energy, so parts of the airflow wrap around the gap
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Fig. 9. Total pressure distribution near the blade tip at design flow rate.
passage and flow along the blade surface instead. When the tip clearance increases to 49.5 mm, although the airflow speed affected by the boundary layer tends to reduce to some extent, the scale of the tip clearance is far larger than the boundary layer thickness; therefore, part of the airflow directly passes through the tip clearance and weakens the work capacity of the impeller. On the other hand, the flow passing blade passages is destructed by the relative motion between the casing and the impeller, resulting in the separation of airflow and the generation of turbulence [29] in the tip clearance, as well as the massive dissipation of energy during these processes, finally reducing the total pressure rise and efficiency of the axial fan. When the tip clearance is unchanged after impeller trimming, the boundary layer on the blade tip and casing plays an appreciable role in reducing the radial space of the tip clearance. Therefore, a large percentage of airflow wraps around the blade surface, which retards the amount of tip leakage flow, increases the work capacity of the impeller, and decreases the loss of total pressure rise. Consequently, the deflection degree of the tip leakage vortex core downstream slightly declines.
In addition, Fig. 9 indicates that the total pressure within the passage declines significantly with increase of impeller trimming. When impeller trimming quantities are 5% and 15% of blade height, the maximal total pressure distributed near the blade tip at design flow rate are 2500 Pa and 2200 Pa, for cases in which tip clearance is changed; the peak value decreases to 2625 Pa and 2500 Pa for cases in which tip clearance is unchanged. Particularly for an impeller trimming quantity of 15% of blade height, the maximal total pressure is obviously enhanced for cases with unchanged tip clearance. Thus, the relatively small tip gap for cases with unchanged tip clearance forces the major airflow to move along the blade surface and improve the total pressure rise in blade passages. Therefore, in this case, the reduced values of total pressure rise and fan efficiency are lower than those when the tip clearance is changed after impeller trimming. To reflect the effect of leakage flow intuitively, the surface of 33% axial chord length cross section is selected as the characteristic surface, and the streamline distribution around the blade tip with both changed and unchanged tip clearance corresponding to Fig. 9
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is illustrated in Fig. 10. As shown in Fig. 10b and c, the streamline distribution of leakage flow changes significantly after blade trimming with changed tip clearance compared with the original impeller (as shown in Fig. 10a). However, the streamline distribution under unchanged tip clearance shown in Fig. 10d and e exhibits relatively small variation. The complexity of leakage flow distribution can directly reflect the tip leakage losses, which finally manifests as variations of the total pressure rise and efficiency of the axial fan. 3.2.2. Variations in vortex losses When airflow passes the blade passage, a transverse pressure gradient is generated between two adjacent blades (Fig. 9), which expands from the pressure side of one blade to the suction side of another, because the total pressure of pressure side is higher than that of the suction side. As airflow moves along the blade airfoils, a centrifugal force protrudes on the suction side, which is in balance with the transverse pressure at the midsection of the blade. However, there is a dramatic difference in the flow characteristics of blade tip and root; the internal pressure in the boundary layer on the endwall surface is identical to the external pressure, and the internal velocity gradually decreases and tends toward zero on casing wall surface. Thus, the transverse pressure gradient in the boundary layer cannot be balanced, which drives the airflow in the boundary layer to moving from the pressure side to the suction side. All results mentioned above improve the pressure distribution on the suction side of adjacent blades, so a vortex is formed and carried away by the mainstream, converted into thermal energy during flowing processes, and gradually dissipated at the trailing edge of the blades, thus generating vortex losses [30]. With increased impeller trimming quantity at the design flow rate (shown in Fig. 11aed), the leakage vortex core gradually moves
towards the hub and its proportion in the rotor blade passage progressively expands, which may enhance the profound blockage effect on the passage between adjacent blades. Considering the influence of leakage vortex, the vortex losses in the impeller increases and the uniformity of airflow behind the impeller is disturbed; this has a negative effect on the guide vanes, resulting in the degradation of total pressure rise and efficiency. For the fan with unchanged tip clearance (Fig. 11e and g), the leakage vortex core is substantially maintained in the vicinity of the blade tip and the proportion of leakage vortex occupying the following passage is smaller than that with the changed tip clearance, thus, a smallscale mixing phenomenon emerges, generated by mixing leakage vortex and mainstream. Accordingly, at design flow rate, the total pressure rise of the fan with unchanged tip clearance is superior to that with changed tip clearance. When the tip clearance is changed, the vorticity distribution on the meridional plane of the blade passage is presented in Fig. 12aed. At high flow rate, the influenced areas of the vorticity in the radial direction, namely, from blade tip to hub surface, are higher than those at the design flow rate. The average vorticities on the meridional plane of blade passages at high flow rate are 445.54 s1, 448.62 s1, and 446.14 s1 for the impeller trimming quantities of 5%, 10%, and 15% of blade height, respectively; this represents minute variations between different trimming quantities. Therefore a slight change in total pressure rise is yielded with the increment of trimming quantity at high flow rate. Fig. 12eeg clearly show that the vorticity distribution on the meridional plane of the blade passage is extended from the casing surface to the hub surface and improves with increase of trimming quantity. The intensity of the vortex core increases by approximately 500 s1 compared with that at the design flow rate; the average vortex intensities on the meridional plane are 447.18 s1,
Fig. 10. Streamline distribution in the tip clearance at design flow rate.
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Fig. 11. Vorticity distribution on meridional plane of the blade passage at design flow rate.
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Fig. 12. Vorticity distribution on meridional plane of the blade passage at high flow rate.
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479.74 s1, and 523.11 s1 at high flow rate. A comparison of average vorticity values for the fan under two tip clearance conditions reveals that when the impeller trimming quantity is 5% of blade height, the average vorticities are basically identical, so the performance curves of total pressure rise change slightly for smaller impeller trimming. Nevertheless, when impeller trimming quantities are 10% and 15%, the average vorticities are significantly enhanced by 31.12 s1 and 77 s1 compared with changed tip clearance. Hence, it can be concluded that, at high flow rate, the overall performance of the fan with unchanged tip clearance is inferior to that with changed tip clearance at a large trimming quantity. 3.2.3. Variations in total pressure rise coefficient The total pressure rise coefficient is defined as: jrt ¼ (p2t p1t)/ 0.5ru2. Fig. 13 shows that for the fan with unchanged tip clearance and impeller trimming quantity at 5% of blade height (shown in Fig. 13a), the total pressure rise coefficient, jrtu, at design flow rate is always higher than that with changed tip clearance, jrtc; this is consistent with the variations in total pressure rise shown in Fig. 7. Under r/h < 0.75, jrtu and jrtc are slightly different; once r/h > 0.75, jrtc decreases significantly. This indicates that the tip leakage losses in the gap passage are the main reasons for deteriorating fan performance when the tip clearance is changed; it also leads to a lower total pressure rise coefficient. When the impeller trimming quantity is 10% (shown in Fig. 13b), jrt tends to vary by r/h ¼ 0.73 in two parts. When r/h is in the range of 0e0.73, the jrt curves of two cases at low flow rate are subtly different and even coincide at some points. However, when r/h covers the range of 0.73e1.1, the curves for changed tip clearance reduce dramatically, with an even larger
545
disparity at the tip clearance. When the impeller trimming quantity is 15% (shown in Fig. 13c), the variation of total pressure rise coefficient takes r/h ¼ 0.8 as a demarcation point, the upper values of jrtc are higher than those of jrtu, but the lower parts present an opposite tendency. Considering the excellent performance with total pressure rise curve at the design flow rate for the fan with unchanged tip clearance, the conclusion can be drawn that the tip leakage losses play a dominant role in blade passage losses. Under the case of high flow rate, the fan performance with impeller trimming quantity of 5% is examined in Fig. 13a. When r/ h < 0.9, jrtu are less than jrtc, whereas at r/h > 0.9, the curves display reverse variations, which exhibit similar behaviour to the fan with impeller trimming quantities of 10% and 15% at the design flow rate (shown in Fig. 13b and c). Thus, the tip leakage losses dominate a large proportion of the flowing losses, including the conditions of a fan with different impeller trimming quantities at the design flow rate and of a fan with small impeller trimming at large flow rate. Therefore, the fan with unchanged tip clearance presents superior performance. For the fan with impeller trimming quantity at 15% of blade height and at large flow rate (shown in Fig. 13c), jrtu is always smaller than jrtc from hub to rim, and the rise coefficient in tip clearance is negative. The above analysis states that both tip leakage and vortex losses play important roles in increasing flowing losses under changed tip clearance, so the overall performance tends to deteriorate. Comparing performance curves and flowing losses for the fan with changed and unchanged tip clearance, and considering that axial fans usually operate at the left of the rated load owing to the excessive margin, the conclusions suggest that when it is necessary
Fig. 13. Total pressure rise coefficients under different impeller trimming quantities.
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to regulate total pressure rise and flow rate to meet actual requirements, the impeller trimming quantity should be selected appropriately and the tip clearance should be maintained unchanged. In this way, the reductions of total pressure rise and efficiency are profoundly constrained. 3.3. Relation of operating points before and after impeller trimming The relation of operating point parameters before and after impeller trimming is a core issue, which attracts extensive attention regarding the actual operation of axial fans. Considering the effects of different pipeline characteristic curves, the relation of operating point parameters before and after impeller trimming is investigated by numerical simulation on the basis of fan performance. The pipeline characteristic curve of a ventilation system is usually a parabola passing the origin; namely, it is contented with pp ¼ kq2v, so several pipeline characteristic curves representing different flow losses can be generated by varying the resistance efficient, k, as shown in Fig. 14. The operating point is the intersection point of the pipeline characteristic curve and total pressure rise curve, and then the parameters of an operating point can be determined by examining the intersection point. The pipeline characteristic curve is maintained unchanged when the measurement of impeller trimming is adopted. Therefore the parameters of operating points after impeller trimming are determined by examining the corresponding intersection points under different trimming quantities (including changed and unchanged tip clearance cases), as shown in Fig. 14. Table 4 summarizes the parameters of operating points corresponding to five pipeline characteristic curves. The formulae of the axial fan after impeller trimming are similar to the affinity law of a centrifugal fan, and are established by comparing the flow rate and total pressure rise of operating points after impeller trimming, which is benchmarked against the original fan. Taking operating parameters qvo, and Dpo of the original fan as benchmarks, the relations of the flow rate ratio and total pressure rise ratio versus impeller diameter ratio after impeller trimming are given for the cases of changed and unchanged tip clearances. Figs. 15 and 16 depict that, under the condition of identically trimmed impellers and various pipeline curves, the curves of ln(qvo/ qv1) are close to linearly parallel, as are the ln(Dpo/Dp1) curves. The slopes are approximately equal when tip clearance is changed (shown in Fig. 15). The slope refers to the corresponding indices of flow rate ratio and total pressure rise ratio with Do/D1. The average slopes are m1 ¼ 2.83 for ln(qvo/qv1) curves and m2 ¼ 5.63 for ln(Dpo/ Dp1) curves. When the tip clearance is unchanged (shown in Fig. 16), the curves of ln(qvo/qv1) and ln(Dpo/Dp1) exhibiting a similar tendency in Fig. 13, are also approximately parallel for each pipeline curve. The slopes correspond to the indices of flow rate ratio and total pressure rise ratio with the parameter of a, and the average slopes are n1 ¼ 1 for ln(qvo/qv1) curves and n2 ¼ 2 for ln(Dpo/Dp1) curves. The formulae of flow rate and total pressure rise versus impeller diameter after axial fan impeller trimming are presented in Eqs. (3) and (4), which resemble the affinity law of a centrifugal fan. For the fan with changed tip clearance, the relations of flow rate ratio and total pressure rise ratio with Do/D1 are as follows:
qvo ¼ qv1
Do D1
2:83 ;
Dpo ¼ Dp1
Do D1
5:63 (3)
For the fan with unchanged tip clearance, the relations of flow rate ratio and total pressure rise ratio with a are formulated as follows:
Fig. 14. Determination of operating point parameters.
qvo Dpo ¼ a; ¼ a2 qv1 Dp1
(4)
where a ¼ ½ðD2o d2 Þ=ðD21 d2 Þ0:5 . Eqs. (3) and (4) show that the variation in tip clearance has a significant effect on the operating point after impeller trimming. When the tip clearance is changed, ln(qvo/qv1) is 2.83 times as much as ln(Do/D1), and ln(Dpo/Dp1) is 5.63 times as much as ln(Do/D1)
C. Li et al. / Energy 75 (2014) 534e548
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Table 4 Operating point parameters when the tip clearance is changed and unchanged. Pipeline 1
D ¼ 0%, d ¼ 4.5 mm D ¼ 5%, d ¼ 19.5 mm D ¼ 5%, d ¼ 4.5 mm D ¼ 10%, d ¼ 34.5 mm D ¼ 10%, d ¼ 4.5 mm D ¼ 15%, d ¼ 49.5 mm D ¼ 15%, d ¼ 4.5 mm
Pipeline 2
Pipeline 3
Pipeline 4
Pipeline 5
qv/m3/s
Dp/Pa
qv/m3/s
Dp/Pa
qv/m3/s
Dp/Pa
Dp/m3/s
Dp/Pa
qv/m3/s
Dp/Pa
39.95 37.18 38.71 35.27 37.57 33.55 36.17
2020 1749.8 1894.1 1574.4 1785.9 1425.3 1656.5
41.61 38.98 40.2 37.09 38.97 35.23 37.48
1871 1642.5 1746.2 1487.1 1641.7 1341.1 1517.3
43.28 40.65 41.76 38.86 40.43 36.99 38.80
1701 1500.4 1583.7 1371.2 1484.7 1242.2 1367.2
44.94 42.20 43.22 40.50 41.78 38.24 39.98
1542 1359.6 1426.2 1255.5 1332.8 1146.1 1220.6
46.61 43.79 44.62 42.29 43.09 40.55 41.15
1382 1219.8 1266.4 1137.7 1181.1 1045.3 1076.8
before and after impeller trimming. For the fan with unchanged tip clearance, the flow rate ratio appears to be a linear correlation with a, whereas the total pressure rise ratio is quadratic. The above formulae are typically targeted at operating points before and after impeller trimming, instead of corresponding points with no modification of flow rate. Hence, Eqs. (3) and (4) given in the present study are available to predict the impeller diameters according to the actual demands of axial fans, which expand the applicability of these fans, and provide an insightful analysis for the impeller trimming in the practical transformation of axial fans.
4. Conclusions Compared with the original fan, the performance curves including total pressure rise and efficiency exhibit different reduction after impeller trimming, and the magnitude of this reduction is enlarged with increase of trimming quantity. At low flow rate, total pressure rise across the fan declines slightly when the tip clearance is unchanged, but is higher than that with changed tip clearance; however, efficiency curves are not exactly similar but are very close to those of the original fan. With increase of flow rate, total pressure rise and efficiency curves decrease dramatically and the overall performance simultaneously deteriorates. Considering that axial fans usually operating at the left of the rated load owing to their excessive margins provided by the original design, impeller trimming is an efficient way to regulate the fan output for meeting practical requirements. The tip clearance should be kept unchanged to constrain the reductions of total pressure rise and efficiency. When the tip clearance is changed, ln(qvo/qv1) is 2.83 times as much as ln(Do/D1), and ln(Dpo/Dp1) is 5.63 times as much as ln(Do/ D1) before and after impeller trimming. When the tip clearance is unchanged, the flow rate ratio and total pressure rise ratio appear to vary linearly and quadratically, respectively, with a. The equations obtained in this study are available to predict the impeller diameters according to the actual requirements and provide important references for impeller trimming in practical applications of axial fans. Acknowledgements
Fig. 15. Relations of flow rate ratio and total pressure ratio versus ln(Do/D1) with changed tip clearance.
This work has been supported by Natural Science Foundation of Hebei Province in China (Grant No. E2012502016) and Fundamental Research Funds for the Central Universities of Ministry of Education of China (Grant No. 13MS98). References
Fig. 16. Relations of flow rate ratio and total pressure ratio versus lna with unchanged tip clearance.
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