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[2] 周誦明. 機(jī)械類專業(yè) 畢業(yè)設(shè)計(jì)指導(dǎo)書. 武漢：華中理工大學(xué)出社，1993. [3] 趙雪松,任小中, 于華. 機(jī)械制造裝備設(shè)計(jì).武漢:華中科技大學(xué)出版社， 2009. [4] 謝家瀛. 組合機(jī)床設(shè)計(jì)簡(jiǎn)明手冊(cè).北京：機(jī)械工業(yè)出版社，2002. 指導(dǎo)教師簽字： 系主任簽字： 年 月 日 226 2012,24(2):226-234 DOI: 10.1016/S1001-6058(11)60238-2 RESEARCH OF INNER FLOW IN A DOUBLE BLADES PUMP BASED ON OPENFOAM* LIU Hou-lin, REN Yun, WANG Kai, WU Deng-hao, RU Wei-min,TAN Ming-gao Research Center of Fluid Machinery Engineering and Technology, Jiangsu University, Zhengjiang 212013, China, E-mail: (Received September 24, 2011, Revised January 9, 2012) Abstract: The inner flow analysis of centrifugal pumps has gradually become an important issue for the hydraulic design and performance improvement. Nowadays, CFD simulation toolbox of pump inner flow mainly contains commercial tools and open source tools. There are some defects for commercial CFD software for the numerical simulation of 3-D turbulent internal flow in pump, especially in capturing the flow characteristics under the off-design operating conditions. Additionally, it is difficult for researchers to do further investigation because of the undeclared source. Therefore, an open source software like Open Field Operation and Manipulation (OpenFOAM) is increasingly popular with researchers from all over the world. In this paper, a new computational study was implemented based on the original solver and was used to directly simulate the steady-state inner flow in a double blades pump, with the specific speed is 111. In order to disclose the characteristics deeply, three research schemes were conducted. The ratios (/dQ Q) of the flow rate are 0.8, 1.0 and 1.2, respectively. The simulation results were verified with the Particle Imaging Velocimetry (PIV) experimental results, and the numerical calculation results agree well with the experimental data. Meanwhile, the phenomena of flow separation under the off-design operating conditions are well captured by OpenFOAM. The results indicate that OpenFOAM possesses obvious strong predominance in computing the internal flow field of pump. The analysis results can also be used as the basis for the further research and the improvement of centrifugal pump. Key words: numerical simulation, double blades pump, internal flow, Particle Imaging Velocimetry (PIV) Introduction Double blades pumps is a kind of centrifugal pump with two blades. There are two symmetrical curve impeller passages from its inlet to outlet and the impeller outlet is quite wide. Therefore, it usually becomes one of impeller shapes in solid-liquid two- phase centrifugal pump. However, due to the short development history and the imperfect design theory, its impellers are often designed with a combination of experience of the designers so far in practice, so that its performance and stability are not ensured1-3. Determining the pump performance is decided by * Project supported by the National Natural Science Funds for Distinguished Young Scholar (Grant No. 50825902), the National Natural Science Foundation of China (Grant Nos. 51079062, 51179075 and 51109095) and the Natural Science Foundation of Jiangsu Province (Grant Nos. BK2009006, BK2010346). Biography: LIU Hou-lin (1971-), Male, Ph. D., Professor examining its inner flow characteristics is undoubte- dly the best method to improve the performance of pumps4-6. Recently, with the rapid progress in CFD and computer technology, the internal flow simulation has gradually become the important foundation of optimization and design for turbo-machinery7-10. Now, the fluid machinery CFD simulation toolbox mainly contains commercial tools and open source tools. Over the years, the commercial software pack- ages are fashionable in the world by its abundant fun- ction and fine easy-use quality. On the other hand, as a CFD software, commercial tool is not very profe- ssional, the computational results for pumps are less than satisfactory, especially in capturing the flow cha- racteristics under the off-design operating conditions. Furthermore, its undeclared source brings a considera- ble inconvenience for the application of numerical simulation in fluid machineries. Although codes can be added to implementation through user-define-fun- ctions, it has a strong limitation. For example, when the SIMPLE algorithm and two-equation turbulence 227models have to be improved, one need to have a through understanding of the governing equations, discretization method, turbulence models and iteration algorithm. However, the core algorithm code and data processing method can not be acquired because of commercialization and only several options can be chosen. Therefore, many open source CFD software are becoming popular and a high quality open source CFD simulation platform like the Open Field Operation and Manipulation (OpenFOAM) is out- standing due to its powerful function, clear archite- cture, expand feature and unified format. The OpenFOAM CFD toolbox was released as an open source December 10, 2004, which is based on C+ routine and contains many C+ modules which can be freely combined with some other modules such as tensor, vector, turbulence models, numerical algori- thm, discretion modules, automatic control modules and so on. Therefore, it is convenient to employ its solvers in simulating complex physical models in che- mical reaction, turbulent flow and heat conduction, etc. A variety of work on the internal flow in fluid machinery via OpenFOAM was done. Nilsson11 con- ducted the steady and unsteady computation of the flow in the Hllerforsen turbine runner and draft tube, and compared the results obtained by the OpenFOAM with those by the CFX-5 and in experiments. Eve- ntually, the applicability and reliability of the OpenFOAM in a Kaplan water turbine runner and draft tube was verified. Petit et al.12 validated an im- plementation of the General Grid Interface (GGI) in the OpenFOAM by using the frozen rotor steady app- roach and the sliding grid unsteady approach. How- ever, all the simulations were performed for a simpli- fied 2-D model of a centrifugal pump. Li13 simulated boundary layer in wind tunnel by OpenFOAM, which revealed that it was suitable for using OpenFOAM to conduct a Computational Wind Engineering (CWE) research. Currently, there is not much work regarding the study of the inner flow of pumps through compa- rison between the OpenFOAM simulation and experi- ments, and the related reports are seldom found. As an open source code, the OpenFOAM provi- des direct access to models and solver implementation details. However, there are some defects for the OpenFOAM in the numerical simulation of 3-D turbu- lent internal flow in hydroturbines. For the CFD simu- lation of hydroturbines, separate 3-D mesh passages or full geometry are generally connected together in order to simulate the flow of water through a succe- ssion of complex geometries like pumps where the stationary suction and volute are located, along with the rotating impeller. The requirement to fit all the meshes with conformal matching interfaces is often very difficult or leads to geometric compromises that would affect the numerical quality of the simulation results. Therefore, there is a need for a treatment of rotor-stator interfaces, which is necessary for the simulation of the whole hydroturbines inner flow. Although the capability has existed in the OpenFOAM, there is no definition in the case directory. There is also a need for a set of boundary conditions that makes it easy to capture basic features in a similar way as it can be done in some other CFD solvers. Furthermore, relaxation factors which control under- relaxation, have an important influence on improving stability of a computation. However, there is no gui- ding principle about those factors. Therefore, the paper focuses on centrifugal pump with the conside- ration of these factors. The numerical simulation of pump by using the OpenFOAM is achieved and the computational results are verified by Particle Imaging Velocimetry (PIV) experiments. The research also provides the foundation for achieving higher computa- tion accuracy of pump inner flow by improving the CFD method with self-compiling program in the OpenFOAM. In this paper, in order to compute the intera- ctions between rotating and fixed components in pumps, a Multiple Reference Frames (MRF) solver is used. At the same time, the simulation results are also validated by PIV test. The operating system used is SUSE Linux 10.3, and the version number used for the present computations is OpenFOAM 1.5-dev. 1. Numerical method and model 1.1 Governing equations The OpenFOAM toolbox already provides a solver called MRFSimpleFoam for solving the steady- state Reynolds-Averaged Navier-Stokes equations with turbulence models, such as the standard k model. The coupling between velocity and pressure is treated using the SIMPLE method14. The MRFSimpleFoam solver employs the finite-volume technique to discretize the Navier-Stokes equations in the rotating reference frame: =0Ru +2+=RRR uuur +Rp u where Ru is flow velocity in rotating frame, rotating frame speed, r position vector, p fluid pressure, fluid density, and the kinematic vis- cosity. 1.2 General Grid Interface (GGI) Due to the interaction between stator and rotor, 228 how to cope with the grids and information tran- smission of the coupling parts in the computational domain is a key issue to simulate precisely the flow fields15-17. The frozen rotor method in MRFSimpleFOAM solver is a steady-state formula- tion where the relative positions in rotor and stator are fixed. In the same time frame, the rotor and the stator parts will be meshed separately. For non-stationary turbo-machinery simulations, the relative rotation of mesh parts will necessarily produce non-conformal in- terfaces between the fixed and moving sections. A connection between these meshes is needed in order to simplify the mesh complexity in various turbo-machi- nery simulations and hence reduce the computer time cost. The GGI, developed by Beaudoin and Jasak18 can be used for that purpose in OpenFOAM. It is a new coupling interface for OpenFOAM, joining multi- ple non-conformal regions where the patches nodes on each side of the interface do not match. This interface uses weighted interpolation to eva- luate and transmit flow values across a pair of confor- mal or non-conformal coupled patches. The basic GGI interface is similar to a case of “static” sliding inter- faces with the advantage that no remeshing is required for the neighboring cells of the interface. The GGI uses the Sutherland-Hodgman algori- thm12 for computing the master and shadow face in- tersection area. Some quick rejection algorithms based on an axis aligned bounding box have been impleme- nted to speed up the search for potential face neigh- bors. Then, in order to rapidly handle the final non- overlapping filtering test, an efficient Hormann- Agathos point-in-polygon algorithm19 has been inclu- ded into the separating axis theorem algorithm18. Finally, discretization effects are taken into account in order to properly scale the GGI weighting factors to handle the possible presence of non-overlapping faces and hence keep the GGI interface conservative. 1.3 Boundary and initial conditions While the Partial Differential Equation (PDE) is solved with the finite volume method, a suitable inter- polation scheme of values typically from cell centres to face centres has a great effect on the numerical results, especially for the convection term. The conve- ction scheme of the existing solver is specified as default by limited linear differencing, which is a Total Variation Diminishing (TVD) scheme. Although it offers a second-order accurate discretization scheme for the convection term, it creates an unconditionally unstable discretisation practice20. In order to achieve stability, a fist-order accurate upwind differencing scheme has been introduced and the simulation results show that the TVD scheme can result more easily in iteration divergence and computation failure than the upwind differencing scheme in simulating the pump inner flow. Therefore, TVD scheme is not applicable to simulate the pump inner flow in the OpenFOAM. In this paper, Guassian up-wind scheme is used and can get the satisfactory results in numerical tests. In addition to appropriate discretization schemes, under-relaxation is another important technique used for improving the stability of a computation, particu- larly in solving steady-state problems. Under-relaxa- tion works by limiting the amount, in which a variable changes from one iteration to the next, either by limi- ting the solution matrix and source prior to solving for a field or by modifying the field directly. An under- relaxation factor , 01 specifies the amount of under-relaxation, ranging from none at all for =1 and increasing in strength as 0. There- fore, selecting an appropriate relaxation factor has great influence on the efficiency of computation. If the relaxation factor is too large, it will lead to divergence of computation easily. If it is too small, the result will converge slowly. Besides, an appropriate relaxation factor depends on the specific problem itself. Thus, there is no instruction about relaxation factor in simu- lating pump inner flow. At the same time, if the rela- xation factors are used by default in the OpenFOAM to examine the pump inner flow, the result will be un- stable. In this paper, the relaxation factors are suitable for simulating the pump inner flow according to +=1up20. At last, the relaxation factors are determined after many tests and the under-relaxation factors of relevant variables (i.e., pressure, momentum, turbulence kinetic energy and turbulence dissipation rate) are 0.3, 0.7, 0.3 and 0.3, respectively. In order to simulate the flow field in and the whole pump, the GGI method is needed to transmit the information between rotor and stator. 1.4 Model A 3-D model of double-blade pump for simula- tion is generated by Pro/E. The suction chamber is designed by semi-spiral method, while the volute is designed by equal velocity moment method and the cross section is rectangular, and type line is the loga- rithmic spiral. The design parameters of the double blades pump are shown in Table 1. Herein the calculation formulas of sn is 3/43.65=sn QnH Before the simulation, studying the grid indepe- ndency and selecting the turbulent model are nece- ssary21,22. The geometry is meshed in hybrid grid by GAMBIT and the OpenFOAM is used to simulate the inner flow in the double-blade pump. The data for stu- dying grid independency are shown in Table 2. If the head difference is smaller than 0.2%, the grid number is acceptable. According to the computation, Scheme 2 meets the need. So Scheme 2 of grid is adopted. The grids are show in Fig.1. 229 Table 1 The design parameters Parameter Sign Value Flow rate Q (m3/h) 25.86 Head H (m) 2.53 Rotation speed n (r/min) 750 Specific speed sn 111 Suction chamber inlet diametersD (m) 0.08 Impeller inlet diameter iD (m) 0.09 Blade inlet diameter 1D (m) 0.0812 Impeller outlet diameter 2D (m) 0.2 Impeller outlet width 2b(m) 0.047 Blade inlet angle 1(o) 18.3 Blade outlet angle 2 (o) 30 Volute base circle diameter 3D (m) 0.212 Volute inlet width 3b (m) 0.077 Table 2 Data for studying grid independency Grid number No. Impeller Volute Suction Total Head, H (m)1 618 738 220 175 300 103 1 139 016 2.46034 2 577 913 179 340 255 937 1 013 190 2.45974 3 505 999 143 450 202 830 852 279 2.43180 4 378 565 151 341 99 619 629 525 2.40151 Fig.1 Grids Table 3 Comparison of turbulence models Turbulent model Head, H (m) Standard k 2.45974 RNG k 2.44706 Omega SST 2.42225 The standard k, RNG k and Omega SST turbulence models have been used to simulate the inner flow in centrifugal pumps. With the same grid, the comparison among the three turbulence models was made and the results are shown in Table 3. It is found that compared with the experimental data, the head obtained by standard k model is the most accurate. Therefore, the standard k turbulence model is used to perform the simulation in this paper. For the test region, the impeller passage near the volute tongue is selected. In order to analyze the inner flow better, 7 pieces of plane curve are set in the im- peller mid-height, equidistant from the impeller inlet to the impeller outlet, and 12 points are distributed equidistantly on each curve. All the analyses of post processing in this paper are based on those monito- ring points as shown in Fig.2. Fig.2 Sample points In order to disclose the characteristics effectively, three research schemes are presented. The ratios (/dQ Q) of the flow rate are 0.8, 1.0 and 1.2, respe- ctively. 2. Results and analysis 2.1 Relative velocity distribution The relative velocity distributions are illustrated in Fig.3. It can be seen that from inlet to outlet under the same working condition, there is a low-speed zone near the middle of the pressure side at the inlet, along the direction of speed changed, which can be found in the top view of Fig.3. Then, a back flow vortex appears, with a remarkable jet-wake flow model. Furthermore, the velocities of all points in the low speed zone go upward with the increase of radius and the jet-wake flow feature becomes unnoticeable, fina- lly disappears. On the circle of impeller inlet, the rela- tive velocities decline gradually at first, from the suction side nearby to the pressure side nearby, and then, when it comes close to the pressure side, the velocity goes up again, peaking at the pressure side. With the increase of radius, the variations of velocity near the suction side are less regular than that near the pressure side. However, when starting from the middle of impeller passage, the velocity near the suction side rises gradually with the increase of radius. But the velocity near the pressure side always rise with the increase of radius. Moreover, the velocity gradient near the pressure side is larger than that near 230 the suction side. On the outlet circle, the velocity goes up gradually from the suction side. The flow in impeller passages is asymmetric due to the effect of volute. Particularly, the relative velocity of points near the volute tongue rise fastest, peaking at the patch slightly below the volute tongue. After that, they decline. In short, the values of velocity of points near the volute tongue are greater than that far from the tongue. Fig.3 relative velocity distribution in impeller passage and its local top view Under the same working condition, at the edge of the passage on the inlet circle, the velocity near the pressure side is much greater than that near the suction side. Besides, on the same circle near the inlet, the velocity near the suction side are greater than that near the pressure side. With the increase of radius, the gaps between the pressure side and suction side are narrow- wing and the velocities on those two sides tend to equal at the middle passage, and thus an equal speed area is formed. Then, the velocity near the pressure side is far greater than that near the suction side. Fig.4 Static pressure distribution in impeller passage Under different working conditions, the jet-wake model at the same position still holds. But with the increase of flow, the velocity of points in the back- ward flow vortex area also increase, while the scope reduces, and the feature with jet-wake model becomes less and less significant. The whole passage with the low flow conditions, the velocity reaches its minimum at the middle of the pressure side near the inlet, while peaking at the patch slightly below the volute tongue. Meanwhile, with the increase of flow, the greatest velocity in the whole passage decreases, the equal speed area enlarges, and gradually approaches impe- ller outlet. 231 Fig.5 Total pressure distribution in impeller passage 2.2 Static pressure and total pressure distribution The static pressure distribution and total pressure distribution of each point under different working con- ditions are illustrated in Fig.4 and Fig.5 respectively. It can be seen from Fig.4 that under the sa