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Chinese Journal of Mechanical Engineering Volume 27 Issue 1 2014 [Doi 10.3901%2FCJME.2014.01.171] Tan, Lei; Zhu, Baoshan; Cao, Shuliang; Bing, Hao; Wang, Yuming -- Influence of Blade Wrap Angle on Centrifugal Pum

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   CHINESE JOURNAL OF MECHANICAL ENGINEERING Vol. 27, No. 1, 2014 · 171 ·   DOI: 10.3901/CJME.2014.01.171, available online at www.springerlink.com; www.cjmenet.com; www.cjmenet.com.cn Influence of Blade Wrap Angle on Centrifugal Pump Performance by Numerical and Experimental Study TAN Lei 1 , ZHU Baoshan 1, * , CAO Shuliang 1 , BING Hao 1 , and WANG Yuming 2   1  State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, China 2  State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, China Received March 9, 2013; revised September 6, 2013; accepted November 12, 2013 Abstract:  The existing research on improving the hydraulic performance of centrifugal pumps mainly focuses on the design method and the parameter optimization. The traditional design method for centrifugal impellers relies more on experience of engineers that typically only satisfies the continuity equation of the fluid. In this study, on the basis of the direct and inverse iteration design method which simultaneously solves the continuity and motion equations of the fluid and shapes the blade geometry by controlling the wrap angle, three centrifugal pump impellers are designed by altering blade wrap angles while keeping other parameters constant. The three-dimensional flow fields in three centrifugal pumps are numerically simulated, and the simulation results illustrate that the blade with larger wrap angle has more powerful control ability on the flow pattern in impeller. The three pumps have nearly the same pressure distributions at the small flow rate, but the pressure gradient increase in the pump with the largest wrap angle is smoother than the other two pumps at the design and large flow rates. The pump head and efficiency are also influenced by the blade wrap angle. The highest head and efficiency are also observed for the largest angle. An experiment rig is designed and built to test the performance of the pump with the largest wrap angle. The test results show that the wide space of its efficiency area and the stability of its operation ensure the excellent performance of the design method and verify the numerical analysis. The analysis on influence of the blade wrap angle for centrifugal pump performance in this paper can be beneficial to the optimization design of the centrifugal pump. Keywords:  blade wrap angle, centrifugal pump, performance, numerical simulation, experiment 1 Introduction ∗   The centrifugal pump is of wide application in industrial and agricultural productions, consuming a large amount of electric power with great potential in energy saving. Among all components in the centrifugal pump, the impeller is the most important flow passage because it is the only part that does work  [1] . Therefore, new or modified design methods for the impeller have been proposed continually to improve its comprehensive performance especially the efficiency. WANG [2]  and LU, et al [3]  provided a design method for centrifugal pump impeller based on S  2  stream surface considering the slip factor on the blade. ZANGENEH [4]  and GOTO, et al [5]  designed the centrifugal pump impeller by governing the circulation distributions along streamlines. TAN, et al [6] , proposed a direct and inverse iteration design method for centrifugal pump impeller. On the other hand, * Corresponding author. E-mail: bszhu@mail.tsinghua.edu.cn This project is supported by National Natural Science Foundation of China (Grant Nos. 51176088, 51179090), National Basic Research Program of China (973 Program, Grant No. 2009CB724304), General Financial Grant from the China Postdoctoral Science Foundation (Grant  No. 2011M500315), and Open Research Fund Program of State Key Laboratory of Hydroscience and Engineering of China (Grant No. sklhse-2012-E-02) © Chinese Mechanical Engineering Society and Springer-Verlag Berlin Heidelberg 2014   some researchers paid attention to the influences of design  parameters on pump characteristics. CAO, et al [7]  and BING, et al [8]  considered the effect of velocity torque distribution on the pump efficiency. BONAIUTI, et al [9–10] , analyzed the influence of several parameters, especially the blade loading, on the impeller performance. The blade wrap angle is defined as the one between the tangent lines at leading and trailing edges of the blade. An increase in blade wrap angle would lead to a longer flow  passage between the blades and thus a significant rise in friction loss. On the contrary, a small blade angle will generate a short flow passage but result in a poor control on the flow in impeller arousing separation loss probably. Therefore, the blade wrap angle is a key parameter for  blade shape, flow pattern in impeller and performance of  pump. For the same impeller diameter, YANG, et al [11] , used a cubic curve to form blade shape and compared the efficiencies of those impellers with different blade wrap angles. CAO, et al [12] , numerically simulated five impellers with different blade wrap angles and showed that the angle had great effect on the internal flow and hydraulic  performance of pumps. ZHANG, et al [13] , numerically analyzed the relationship between the blade wrap angle and the centrifugal pump performance. In this paper, three centrifugal pump impellers were designed with different blade wrap angles using the direct    TAN Lei, et al: Influence of Blade Wrap Angle on Centrifugal Pump Performance by Numerical and Experimental Study  · 172 ·   and inverse iteration design method. The influence of the  blade wrap angle on the centrifugal pump performance was investigated both numerically and experimentally. 2 Centrifugal Pump Impeller Design 2.1 Design method The direct and inverse iteration design method for centrifugal pump impeller is based on the continuity and motion equations of the fluid with the effects of the blade shape on the flow being considered. This method is applied  by a set of computer code written with FORTRAN language. The initial parameters at the beginning of the design program are as follows: (1) flow rate, head and rotation speed of centrifugal pump and the fluid properties; (2) shape of hub and shroud, leading and trailing edges of the meridional flow passage; (3) blade thickness distribution, blade number and blade wrap angle. 2.1.1 Process of design Fig. 1 shows the process of the direct and inverse iteration design method. Fig. 1. Process of direct and inverse iteration design method First, according to the given design parameters of the centrifugal pump, the traditional design method is adopted to design the initial impeller configuration. Second, based on the continuity and motion equations of the fluid, the meridional velocity distribution is obtained by the iteration  between the S  1  and S  2  stream surfaces. Third, with the obtained meridional flow field, the blade shape is generated using point-by-point integrations. Through this step, a new impeller is obtained. Fourth, the iteration of the S  1  and S  2  stream surfaces is operated again for the new designed impeller to get an update meridional velocity distribution. The third and fourth steps should be repeated until the differences of the meridional transversals of two successive designed impellers are within a prescribed tolerance. For the present impeller design, the tolerance is set to be 0.000 1. 2.1.2 Blade drawing The relation between blade wrap angles and meridional streamlines can be described by the bone line integration equation as follows. 0 0 1d ,tan l e l r  ϕ  β  = ∫   (1) where ϕ   is the blade wrap angle, e  β  is the blade angle, r   is the calculation point radius, and 0 l   is the total length of the meridional streamline. The three-dimensional blade  bone lines can be determined by integrating the Eq. (1) along the meridional streamlines from blade leading edge to trailing edge. In Eq. (1), parameters r  , 0 l   and d l   are determined from coordinates of the flow net by meridional flow calculation using two surfaces iteration, therefore the  blade bone lines can be integrated if the blade angle distributions are given. The blade angle distributions along meridional streamlines can be described as a quadratic function, which can be expressed as 2 e  al bl c  β   = + + , (2) where a , b  and c  are coefficients. At the blade leading edge l   0, e  β   is 1  , e e  β β  =  (3) where 1 e  β   is the blade angle at the blade leading. At the  blade trailing edge l   l  0 , e  β   is 2  , e e  β β  =  (4) where 2 e  β   is the blade angle at the blade trailing. By eliminating the coefficients b  and c , the quadratic function can be written as 2 11 00 ( )( ) e ee e l al l l l   β β  β β   −= + + − , (5) where the parameter a  is the only unknown variable, which can be given by the designer to determine the blade angle distribution. The blade wrap angle is a key parameter for impeller designing as it is directly related to the ability of doing   CHINESE JOURNAL OF MECHANICAL ENGINEERING   · 173 ·   work, the flow pattern, the friction loss, the separation loss and so on. So the value of the blade wrap angle should be easily controlled in impeller design process [13] . In previous  blade drawing method [14] , the blade angle distribution was given by the parameter a , and then the blade shape was structured according to Eq. (1). It is easy to determine the distribution of the blade angle but hard to make the blade wrap angle equal to a constant in this method. Most designers pay more attention on the value of the blade wrap angle rather than the distribution of the blade angle especially in the industry companies. To make the blade wrap angle satisfy the given value, a blade drawing method by controlling the blade wrap angle is given as shown in Fig. 2. Fig. 2. Process of blade drawing method The main steps of this blade drawing method are given as follows: (1) setting the value of the blade wrap angle by designers; (2) generating a value of parameter a  to form a  blade angle distribution along the meridional streamline; (3) integrating the Eq. (1) to draw the blade shape and calculate the blade wrap angle; (4) thickening and smoothing the blade. Steps (2) and (3) are repeated until the  blade wrap angle meets the given value. 2.2 Design parameters and results 2.2.1 Design parameters Some design parameters for centrifugal pump impeller are summarized in Table 1. Three blade wrap angles are selected according to the specific speed to analyze the influence of the blade wrap angle on the centrifugal pump  performance. The blade wrap angles are 100°, 110°, 120° for impellers A, B, C with all other parameters remaining the same. Table 1. Centrifugal pump design parameters   Parameter Value   Flow rate  Q  (m 3   ã  h  –1 ) 200 Head  H   m 32 Rotation speed  n  (r ã  min  –1 ) 1 480 Specific speed  n  s   95 Blade number   Z 6 Impeller inlet diameter  D 0  mm 148 Impeller outlet diameter   D 2  mm 322 Blade angle at exit  β  2 e  (°) 25 Blade width at exit  b 2  mm 22 2.2.2 Design results Fig. 3 shows the blade angle distributions along the meridional streamlines for the impeller C with the blade wrap angle of 120°, where  K   1 denotes the streamline at the impeller hub and  K   14 denotes the streamline at the impeller shroud. Each distribution curve denotes a quadratic function corresponding to a different value of  parameter a  in Eq. (5). They are parabolic curves near the hub and linear lines near the shroud. Compared to the blade angle distribution of the traditional design method [14]  on the assumption of one-dimensional or two-dimensional flow theory, the results of the direct and inverse iteration design method are three-dimensional. The blade angle distributions obviously change from hub to shroud corresponding to the twisty blade shape, because the fluid flow in the direct and inverse iteration design method is three-dimensional flow. Fig. 3. Blade angle distributions Three impellers with blade wrap angles of 100°, 110° and 120° are all designed by the direct and inverse iteration design method. Fig. 4 shows their 3D models. As can be seen in the figure, the curved surfaces are very smooth with a circular arc shape forming the blade head in order to improve the flow pattern at the impeller inlet. The blade length and the flow passage geometry vary as the blade wrap angles increase. Generally, the flow passage is larger with the larger blade wrap angles. 3 Numerical Simulation and Analysis 3.1 Computation domain and grid The computation domain and grid of the centrifugal  pump are shown in Fig. 5. Local refinement of the grid is applied near the blade surface and the volute tongue to guarantee the precision of the numerical simulation. The comparisons of the computational results using different grid distributions and different strategies for grid refinement indicate that the meshes in the present research are all fine enough to obtain the grid-independent computational results. When the number of the grid of the    TAN Lei, et al: Influence of Blade Wrap Angle on Centrifugal Pump Performance by Numerical and Experimental Study  · 174 ·   whole computation domain reaches 1 350 000, the value of  y + is between 30 and 300. (a) Impeller A (b) Impeller B (c) Impeller C Fig. 4. Three dimensional models of impellers (a) Impeller (b) Volute Fig. 5. Computation domain and grid of the centrifugal pump 3.2 Governing equations and computation method The continuity and motion equation of the fluid for three-dimensional viscous flow in pump are as follows: 0,  j j u x ∂=∂  (6) 2 ( ), i ji i i j i j i j j j uuu u u pu F t x x x x x  ρ  ρ ρ ρ µ  ′ ′∂ −∂ ∂ ∂∂+ = − + +∂ ∂ ∂ ∂ ∂ ∂   (7) 2,3  ji ii j t t ij j i i uu uuu k  x x x  ρ δ   ρ µ µ   ∂  ∂ ∂′ ′− + − +    ∂ ∂ ∂   =  where  F  i is the body   force, and δ ij  the kronecker    delta. The turbulent kinetic energy k   and turbulent dissipation rate ε  of the RNG k  - ε  model [15]  which are widely used in the hydraulic machinery are as follows: eff   2  , k t ij j i j j  Dk S  Dt x uk  x x  ρ α µ µ   ρε   ∂= +  ∂  ∂∂−∂ ∂  (8) eff  21 2 2 , t ij j j i j  DS R Dt x x uC C k x k  ε   ε ε  ε ε  ρ α µ µ ρ  ε ε   ∂ ∂+ −  ∂ ∂  ∂= −∂  (9) where / / , ij i j j i S u x u x = ∂ ∂ + ∂ ∂  eff   , t  µ µ µ  + = and 2 / . t   C k  µ  µ ε  =  The additional term  R  is 32 03  , (1 / )1  Rk  C  µ   ρ  ε  η η η  βη  −=+   (10) where / Sk  η ε  = , 2 ijij SSS  = , 0 4.38, η   =  0.084 5, C  µ   =   0.012,  β   = 1 1.42, C  ε   = 2  1.68, C  ε   = 1.0, k  a  = and0.769. a ε   =  In this study, the commercial CFD code Fluent is used to solve the above governing equations. The boundary conditions are set as follows: a constant flow velocity is set at the inlet; the pressure outlet option is set at the outlet, the standard wall functions are imposed over the impeller blades and sidewalls, the volute casing and the inlet and outlet pipe walls. The multiple rotating reference frame (MRF) is applied to couple the rotation and station domains. 3.3 Relative velocity distributions in impellers The relative velocity distributions in three impellers are shown in Fig. 6. As can be seen, the relative velocity at the impeller inlet is small and then increases gradually in the impeller with the maximum value at the impeller outlet. The relative velocity gradient is comparatively large near the blade surface. As the wrap blade angle becomes larger, the control ability of the blades on the flows in the impeller
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