Hydrodynamic performance enhancement of a mixed-flow pump

Transcription

1 IOP Conference Series: Earth and Environmental Science Hydrodynamic performance enhancement of a mixed-flow pump To cite this article: J H Kim and K Y Kim 202 IOP Conf. Ser.: Earth Environ. Sci Related content - Parametric performance evaluation of a hydraulic centrifugal pump M W Heo, K Y Kim, S B Ma et al. - Numerical simulation of internal flow in mixed-flow waterjet propulsion T T Wu, Z Y Pan, Y Y Jia et al. - Application of PIV for the flow field measurement in a mixed-flow pump Y Inoue and T Nagahara View the article online for updates and enhancements. This content was downloaded from IP address on 24/09/208 at 02:56

2 Hydrodynamic performance enhancement of a mixed-flow pump J H Kim and K Y Kim 2 Department of Mechanical Engineering, Graduate School, Inha University, 253 Yonghyun-Dong, Nam-Gu, Incheon, , Rep. of Korea 2 Department of Mechanical Engineering, Inha University, 253 Yonghyun-Dong, Nam-Gu, Incheon, , Rep. of Korea kykim@inha.ac.kr Abstract. This paper presents an optimization procedure based on a radial basis neural network surrogate model for design of a vaned diffuser in a mixed-flow pump. Numerical analysis of fluid flow in a mixed-flow pump has been carried out by solving three-dimensional Reynolds-averaged Navier-Stokes equations with the shear stress transport turbulence model. The optimization processes have been performed twice to investigate the coupled effects of diverse variables. The first optimization process has been conducted with two design variables defining the straight vane length ratio and the diffusion area ratio, and the second one has been conducted with four design variables, i.e., the angle at the diffuser vane tip, the distance between the impeller blade trailing edge and the diffuser vane leading edge, and the two design variables used in the first optimization. The efficiency as a hydrodynamic performance parameter has been selected as the objective function for optimizations. The objective function values have been assessed through three-dimensional flow analysis at design points sampled by Latin hypercube sampling in the design space. The first and second optimizations with the coupled effects of diverse variables have yielded maximum increases in efficiency of 7.6% and 9.75%, respectively, compared to the reference shape. The off-design performance has been also improved in most of the optimum shapes except in the shut-off flow region.. Introduction With the recent development of optimization techniques associated with three-dimensional Reynoldsaveraged Navier-Stokes (RANS) analysis, high efficiency design of turbomachinery became possible. Among variety of optimization techniques, systematic optimization strategies using surrogate models have been widely applied to the design of turbomachinery to achieve high performance. Many studies have been carried out to optimize the performance of various turbomachines. Kim and Seo [] performed a blade shape optimization of a centrifugal fan having forward-curved blades using the response surface approximation (RSA) model [2] coupled with three-dimensional RANS analysis. Aerodynamic design optimization using the Kriging (KRG) meta-model [3] was suggested by Zhiheng et al. [4] for vaned diffusers in centrifugal compressors, and the application of the KRG model to the design optimization of a vaned diffuser validated the feasibility of the method for practical engineering design. The radial basis neural network (RBNN) model [5] for multi-criteria optimization of two-dimensional blade sections was applied by Huppertz et al. [6]. Kim et al. [7] optimized the design of the circumferential casing grooves to maximize both the stall margin and peak adiabatic efficiency of a transonic axial compressor by using a hybrid multi-objective evolutionary Published under licence by Ltd

3 algorithm combined with the KRG model. The RBNN model coupled with the response surface of a low-order polynomial has been reported for turbomachinery design by Rai and Madyavan [8]. Wang et al. [9] used the KRG model to perform the aerodynamic design optimization of a centrifugal compressor impeller. Arabnia and Ghaly [0] conducted a multi-objective optimization of an axial turbine stage with design variables related to blade geometry using a genetic algorithm combined with an artificial neural network. On the other hand, among various types of pump, a mixed-flow pump, which has an intermediate specific speed between axial and centrifugal pumps, is rapidly increasing the demand with its advantages across industry. Thus, experimental and numerical studies for mixed-flow pumps tend to increase gradually. Goto [] improved the hydrodynamic performance through the investigations on mixed-flow pump impellers with four different tip clearances. Ashihara and Goto [2] enhanced the hydrodynamic performance of mixed flow pump impellers by using an optimization algorithm. Efficiency enhancements by modification of vaned diffuser geometry in a mixed flow pump were studied by Kim et al. [3, 4]. Muggli et al. [5] carried out a numerical study to evaluate mixed flow pump characteristics from shutoff to maximum flow. Oh and Kim [6] applied an approximate onedimensional flow analysis method in a conceptual design optimization to enhance the efficiency of mixed flow pump impellers. Hao and Shuliang [7] also improved the efficiency of a mixed flow pump impeller by a combined approach using inverse design and a genetic algorithm. This work presents a numerical optimization procedure based on a RBNN surrogate model with three-dimensional RANS analysis for design of a vaned diffuser in a mixed-flow pump. The objectives of this work are: firstly, to investigate the coupled effects of diverse variables on the enhancement of hydrodynamic performance of a vaned diffuser design in a mixed-flow pump via the proposed design optimization method; secondly, to examine the differences in the internal flow field among the reference and two optimum shapes to understand the flow physics associated with the improved efficiency. 2. Mixed-Flow Pump Design The pump model investigated in this work is a mixed-flow pump used for irrigation and drainage. A commercial mixed flow pump that has been tested in various experiments [3] was selected in order to have access to reliable experimental data. The mixed-flow pump consists of an impeller with five blades and a diffuser with six vanes, with a specific speed of Ns=N Q 0.5 /H 0.75 =099. at the best efficiency point (BEP). The volumetric flow rate and the total head at the design point of the reference pump model are m 3 /min and 8.92 m, respectively, with an efficiency of 83.3%. Additional design specifications are listed in Table. 3. Numerical Approach Description The internal flow field of the mixed-flow pump is analyzed by solving three-dimensional steady incompressible RANS equations with the shear stress transport (SST) turbulence model through a finite-volume solver, the commercial code ANSYS-CFX.0 [8]. The computational domain for the numerical analysis which consists of the single passage of the mixed-flow pump impeller and the vaned diffuser is shown in Fig.. The flow field is analyzed by Table. Design specifications of the mixed-flow pump. Design volumetric flow rate, m 3 /min Tip clearance, mm.0 Rotational speed, r/min Number of main blades (vanes) 5 (6) Total head, m 8.92 Maximum diameter of impeller, mm

4 Figure. Computational domain and typical grids in the mixed-flow pump. assuming that the flow between two adjacent main blades (and vanes) is periodic in the direction of rotation. The total pressure and the designed mass flow rate are set at the inlet and outlet of the computational domain, respectively. Water is considered as the working fluid, and the solid surfaces in the computational domain are considered to be hydraulically smooth with no-slip and adiabatic conditions. The stage method is applied for the connection between the rotating impeller and the vaned diffuser stage. A structured grid system is constructed in the computational domain, with O-type grids near the main blade and vane surfaces and H/J/C/L-type grids in the other regions. The inlet and outlet blocks are constructed using approximately 30,000 and 70,000 grid points, respectively, while the main impeller (or vaned diffuser) passage is constructed using approximately 250,000 grid points. In the previous work [3], a grid-dependency test has been carried out with various numbers of grids, and the optimum number of grids was selected as approximately 600,000 grid points. Figure shows a typical example of the grid structure system used for the numerical analysis of the mixed-flow pump. In the numerical analysis, root mean square (RMS) residual values of the momentum and mass are set to fall below.0e-05 and the imbalances of mass and energy are kept below.0e-02 as part of the convergence criteria. The physical time scale is set to 0./ω, where ω is the angular velocity of the main blades. The converged solutions are obtained after approximately 600 iterations. The computations have been performed by a PC with an Intel Xeon CPU of a clock speed of 2.5 GHz. The computational time for one analysis is about 5-6 hours depending upon the geometry considered and the rate of convergence. 4. Objective Function and Design Variables The purpose of the current optimization is to maximize the efficiency (η) of a mixed-flow pump, which is defined as follows, ghq () P where, ρ, g, H, Q, and P indicate the density, acceleration of gravity, total head, volume flow rate, and power, respectively. In the previous work [3], through analyses of the internal flow field at the design point of the reference model, some losses due to flow separation were observed in the region of the vaned diffuser of a mixed flow pump. These losses have an adverse effect on the pump s overall performance. Thus, in order to reduce losses and enhance the pump efficiency, the optimal design of the vaned diffuser geometry is required. 3

5 angle [deg] 26th IAHR Symposium on Hydraulic Machinery and Systems In this work, four variables related to the geometry of a vaned diffuser in a mixed-flow pump are applied to the optimization to investigate their coupled effects on the pump s efficiency. As shown in Fig. 2, these variables are the straight vane length ratio (SVLR = L 2 /L ), the diffusion area ratio (DAR = A 2 /A ), the angle ( = 2 / ) at the diffuser vane tip, and the distance ratio ( = 2 / ) between the impeller blade trailing edge (TE) and the diffuser vane leading edge (LE). Here, L and A are the straight vane length and diffusion area, respectively, and subscripts and 2 indicate the reference and varied shapes, respectively. In Fig. 2(a), the SVLR is represented as the ratio of the length of the newly modified straight vane section (b-c`) to the length of the reference straight vane section (b-c). The DAR determined by the hub and casing is defined as the ratio of A to the area of discharge. Thus, the DAR is varied with the changes of the casing shape of the reference, whereas the hub is fixed by the shaft, as shown in Fig. 2(a). Angle β is defined as the angle between the axis of rotation and a tangent of the camber line at the vane tip. The entire β distribution is changed equally along a vane tip having fixed meridional geometry, as shown in Fig. 2(b). Here, when the β distribution at vane tip is changed uniformly, the vane profiles at other locations are interpolated using a B-spline curve from hub to tip. Lastly, the distance ratio is defined as the ratio of modified distance 2 to the reference distance. The distance between impeller blade TE and diffuser vane LE is not changed in spanwise direction from hub to tip, as shown in Fig. 2(a). The impeller blade TE is fixed to limit the size of the impeller, and only diffuser vane LE is varied to change the distance. 5. Optimization Techniques In each optimization process, two or four design variables are selected to investigate their coupled effects on the pump s efficiency. Namely, the first optimization process is conducted with two design variables, the SVLR and DAR, and the second is conducted with four design variables,,, and the (a) Meridional view defining the SVLR, DAR and. Changed distribution Reference distribution LE Meridional location (b) β distribution at vane tip. Figure 2. Definition of design variables. + - TE 4

6 26th IAHR Symposium on Hydraulic Machinery and Systems aforementioned two design variables. Their design ranges determined by the sensitivity tests are shown in Table 2. Nine and thirty-five design points for two optimizations are generated within the design space with the help of Latin hypercube sampling [9], respectively, as design of experiments. In this work, the RBNN surrogate model is applied to obtain the optimum shape of the vaned diffuser in the mixed-flow pump. The basic concept of the RBNN is to simulate human functions of learning from experience, and to make predictions using existing data. The main advantage of this model is the ability to reduce computational cost due to the linear nature of the radial basis functions. The RBNN model uses a linear combination of j radially-symmetric functions y i (x) for the response function as follows, F RBNN j ( x) w y ( x) (2) i where, w i are coefficients of the linear combination, y i are radial basis functions (typically Gaussian), and ε i are errors with equal variance σ 2. After constructing the RBNN model, the optimum point is sought using the sequential quadratic programming (SQP) [20]. The SQP is a gradient-based optimization technique and is a generalization of Newton s method. 6. Results and Discussion The validity of the numerical results was verified by comparison with experimental data in the previous work [3]. The mixed flow pump model used for this validation is considered as the reference shape. Figure 3 shows the validation results in relation to the performance test for the head coefficient (ψ = Q/ND 3 ) and efficiency on the entire flow coefficients ( = gh/n 2 D 2 ). Here, N and D indicate the rotating speed and the diameter, respectively. As shown in Fig. 3, the numerical head and efficiency values are in reasonable agreement with the experimental data from the shut-off to run-out flow coefficients. Therefore, it is assured that the numerical analysis of this work is valid and reliable. The optimum design variables for the vaned diffusers of mixed flow pump predicted by the RBNN surrogate model in each optimization are listed with the reference values in Table 3(a). In Table 2. Ranges of design variables. Variables SVLR DAR Lower Upper i i i x EXP -RANS -EXP -RANS x st OPT -2 nd OPT -REF - st OPT -2 nd OPT -REF Design Figure 3. Validation of the numerical results [3] Figure 4. Performance curves. 5

7 Table 3. Results of the design optimizations. (a) Design variables. Designs SVLR DAR Reference shape st optimum shape nd optimum shape (a) Design optimizations. Designs Prediction (%) RANS (%) Error (%) Increment (%) Reference shape st optimum shape nd optimum shape each optimizations, SVLR is optimized to be a longer shape, and DAR is optimized to be a narrower shape, in comparison with the reference shape. In the second optimization, is moved forward, whereas β remains almost same. The efficiency value of the reference shape obtained through the RANS calculation is 80.79%, as shown in Table 3(b). The efficiency values for the optimum shapes are predicted to be 88.27% and 90.73%, respectively, based on surrogate models constructed, and are calculated to be 87.95% and 90.54%, respectively, by the RANS analyses. The optimization results indicate that the RBNN surrogate model produces good predictions of optimum objective functions with the relative errors of 0.36% and 0.2%, respectively. Consequently, the efficiencies of two optimum shapes represent as 7.6% and 9.75% improvements, respectively, compared to the reference shape at the design flow coefficient. Figure 4 shows the head and efficiency performance curves for the reference and two optimum shapes. Considerable improvements in the efficiency curves of two optimum shapes are observed for flow coefficients higher than about 0.5, whereas the efficiency values for the reference and two optimum shapes are almost same in the region of the shut-off flow coefficients. And, the optimum shape by the second optimization shows the highest value in the run-out flow region, compared to the others. On the other hand, the reference and two optimum shapes have similar values for the head coefficient throughout the overall range of the flow coefficient. Therefore, by the present optimizations, the efficiency curves are significantly improved in the near run-out flow region without a reduction in head. Figure 5 shows the velocity contours on the meridional plane of the vaned diffuser for the reference and two optimum shapes. The velocity values are area-averaged in circumferential direction. As shown in Fig. 5(a), a large flow separation is observed in most of the hub region beyond the vane TE in the diffuser passage of the reference shape. However, this flow separation disappears in two optimum shapes, as shown in Figs. 5(b) and (c). Thus, the optimum shapes produce mostly stable flows in the diffuser passage. The velocity vectors at 0% span in the flow passage for the reference and two optimum shapes are plotted in Fig. 6. An extensive flow separation zone is occurred on the suction surface of the reference diffuser vane. The blockage line that formed as a result of the extensive flow separation in the reference vaned diffuser is shifted to the TE of vane. This extensive flow separation has an adverse effect on the entire system performance of the reference pump model. On the other hand, this flow separation zone is reduced in the optimum shape by the first optimization and is clearly suppressed in the optimum shape by the second optimization. These results obviously illustrate the enhancement of the mixed-flow pump s efficiency with the coupled effects of diverse variables as results of the optimization. 6

8 LE TE (a) Reference shape. (b) st optimum shape. (c) 2 nd optimum shape. Figure 5. Velocity contours on the meridional plane. Diffuser vane LE Blockage line Main blade TE LE (a) Reference shape. Flow separation zone TE Flow separation zone (b) st optimum shape. (c) 2 nd optimum shape. Figure 6. Velocity vectors at 0% span in the flow passage. 7

9 7. Conclusion Optimizations of a vaned diffuser design in a mixed flow pump have been performed by using the RBNN surrogate model through three-dimensional RANS analysis. The optimization processes are conducted twice to investigate the coupled effects of diverse variables associated with the enhanced hydrodynamic performances. The first optimization process is conducted with two design variables defining the straight vane length ratio and the diffusion area ratio, and the second is conducted with four design variables defining the angle at the diffuser vane tip and the distance ratio between the impeller blade trailing edge and the diffuser vane leading edge including the aforementioned two design variables. The results of the design optimizations show that the efficiencies for two optimum shapes are improved by 7.6% and 9.75%, respectively, and the efficiency curves are significantly improved in the run-out flow region without a reduction in head, as compared to the reference shape. Through the analyses of the internal flow field in the reference shape, an extensive separation zone is observed in most of the hub region of the vaned diffuser. However, the efficiencies in two optimum shapes are mainly improved by reducing and removing an extensive separation zone from the passage. It means that the optimum shapes produce mostly stable flows in the diffuser passage. Acknowledgment This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MEST) (No ). References [] Kim K Y and Seo S J 2004 ASME J. Fluids Eng [2] Myers R H and Montgomery D C 995 Response Surface Methodology-Process and Product Optimization Using Designed Experiments (New York: John Wiley & Sons) [3] Martin J D and Simpson T W 2005 AIAA J [4] Wang Z H, Xi G and Wang X F 2006 Aerodynamic Design Optimization of Vaned Diffusers for Centrifugal Compressors Using Kriging Model Conference on Aerospace Propulsion AJCPP Paper [5] Orr M J L 996 Introduction to radial basis neural networks Center for cognitive science Edinburgh University Scotland UK [6] Huppertz A Flassig P M Flassig R J and Swoboda M 2007 Knowledge-based 2D blade design using multi-objective aerodynamic optimization and a neural network Proc. ASME Turbo Expo GT [7] Kim J H Choi K J Husain A and Kim K Y 20 AIAA J. of Prop. and Power [8] Rai M M and Madyavan N K 2000 AIAA J [9] Wang X F Xi G and Wang Z H 2006 Inst. Mach. Eng., Part A: J. Power and Energy [0] Arabnia M and Ghaly W 200 On the use of Blades Stagger and Stacking in Turbine Stage Optimization Proc. ASME Turbo Expo GT [] Goto A 992 ASME J. Turbomach [2] Ashihara K and Goto A 200 Turbomachinery blade design using 3-D inverse design method, CFD and optimization algorithm ASME Turbo Expo 200-GT-0358 [3] Kim J H Ahn H J and Kim K Y 200 Sci. China: Tech. Sci [4] Kim J H and Kim K Y 20 Int. J. Fluid Mach. and Syst [5] Muggli F A Holbein P and Dupont P 2002 ASME J. Fluids Eng [6] Oh H W and Kim K Y 200 Inst. Mach. Eng., Part A: J. Power and Energy [7] Bing H and Cao S L 20 Optimal design of mixed-flow pump impeller based on direct inverse problem iteration and genetic algorithm ASME-JSME-KSME Joint Fluids Eng. Conf. AJK [8] ANSYS CFX ANSYS CFX-Solver Theory Guide ANSYS Inc [9] McKay M D, Beckman R J and Conover W J 2000 Technometrics [20] MATLAB 2004 The Language of Technical Computing The Math Work Inc. 8