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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 liuhoulin 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 d Q 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 ensured 1 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 pumps 4 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 machinery 7 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 227 models 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 Nilsson 11 con ducted the steady and unsteady computation of the flow in the H llerforsen 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 Li 13 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 method 14 The MRFSimpleFoam solver employs the finite volume technique to discretize the Navier Stokes equations in the rotating reference frame 0 R u 2 RRR uuur R p u where R u 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 fields 15 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 Jasak 18 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 thm 12 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 algorithm 19 has been inclu ded into the separating axis theorem algorithm 18 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 practice 20 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 1 up 20 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 s n is 3 4 3 65 s n Q n H Before the simulation studying the grid indepe ndency and selecting the turbulent model are nece ssary 21 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 s n 111 Suction chamber inlet diameter s D m 0 08 Impeller inlet diameter i D m 0 09 Blade inlet diameter 1 D m 0 0812 Impeller outlet diameter 2 D m 0 2 Impeller outlet width 2 b m 0 047 Blade inlet angle 1 o 18 3 Blade outlet angle 2 o 30 Volute base circle diameter 3 D m 0 212 Volute inlet width 3 b 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 d Q 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 worki