Numerical Simulation of Flow__ Field in a Centrifugal Pump with Inducer(带诱导轮离心泵流场仿真)

Numerical Simulation of Flow Field in a Centrifugal Pump with InducerWei Chao 1 Zhong Weicong 2 Zhang Feng 21. College of Astronautics, Northwestern Polytechnical University, Xi’an 710072, China2. Xi’an Aerospace Propulsion Institute, Xi’an 710100, ChinaAbstract: Based on the N-S Equation and the non-structured mesh technology, the 3D steadyincompressible turbulent flow within a centrifugal pump with inducer was simulated. The internalstatic pressure distribution, velocity distribution and the delivery head were obtained. Moreover,cavitation was also analyzed. The numerical results show that cavitation mainly happens at the outeredges of the entrance blades and the roots of the exit blades in the inducer, the hub entrance and theroots of part blades in the centrifugal wheel. It’s found that cavitation is related with the assemblyangle of the inducer and centrifugal wheel. The numerical results agree with the experimental data verywell.Keywords: inducer; centrifugal pump; numerical simulation; cavitation1 IntroductionThe delivery head, mass flux, efficiency and cavitation performance of pump are important for the design of turbopump-fed liquid rocket engine. The prepositive inducer is usually used to improve the cavitation performance of centrifugal pump. In the conventional R&D mode of pump, the relationships of performance parameters and structure are estimated by empirical formulae. As a result, it’s difficult to control the R&D duration and R&D cost. With the development of CFD technology, the parameters, such as velocity, pressure and cavitation degree, can be obtained by numerical simulation method. The method is proved valid and becomes more and more important in the R&D process of pump. The paper simulated the 3D steady incompressible turbulent flow within a centrifugal pump with inducer using CFD method. The internal static pressure distribution, velocity distribution and the delivery head were obtained. Moreover, the cavitation was also analyzed.2 Modeling2.1 Governing equationsIn the paper, the 3D steady incompressible turbulent flow within the centrifugal pump was simulated with the standard ε−k turbulent model. The governing equations are as follows [1-3]: 2.1.1 Continuity equation()0=∂∂+∂∂j ju x t ρρ (1) 2.1.2 Momentum equation()()i i j i i i i j i j i j i j j i F g x u x x u x x p x u x u u x u t −+⎟⎟⎠⎞⎜⎜⎝⎛∂∂∂∂−⎟⎟⎠⎞⎜⎜⎝⎛∂∂∂∂+∂∂+⎟⎟⎠⎞⎜⎜⎝⎛∂∂∂∂=∂∂+∂∂ρμμμρρ32 (2)The turbulence kinetic energy,κ, and its rate of dissipation, ε, are obtained from the following transport equations:ρμκσμμκρκρ−∂∂+∂∂∂∂+∂∂+∂∂=∂∂+∂∂)(])[(ij j i j i t j k t j j i x u x u x u x x x u t (3) κερμεεσμμερερε221)(])[(c x u x u x u k c x x x u ti j j i j i t k t k k k −∂∂+∂∂∂∂+∂∂+∂∂=∂∂+∂∂ (4) The turbulent viscosity,t μ, is computed by combining κand εas follows:εκρμμ2C t = (5) The model constants ,,,μC 1C 2C εσ and εσ have the following default values: ，，，44.1=μC 44.11=C 92.12=C 3.1=εσ，0.1=κσ。

2.2 Discretization of the Governing equationsThe governing equations were discretized by second order upwind scheme. Pressure-velocity coupling wasachieved by using SIMPLE algorithm. In the computation, under-relaxation was used to control the update of computed variables at each iteration.2.3 Mesh generationThe geometry model of the centrifugal pump studied in the paper is shown in figure 1. Aiming at the complex structure of pump, multi-block mesh generation technique was used to make mesh generation easier and improve mesh quality. The basis idea is dividing the complex computational domain into some less irregular subdomains, meshing them separately and then connecting them together. Based on this idea, the pump was divided into three subdomains: inducer, centrifugal wheel and turbine housing. However, the subdomains were still irregular, so unstructured mesh wasadopted. The whole research domain contained 715517 mesh cells and 206303 mesh nodes.Fig.1 Geometry model of the centrifugal pump Fig.2 Mesh superimposed on the computational domain2.4 Boundary ConditionsThe entrance face of the inducer was specified as mass-flow-inlet boundary. The exit of turbine housing was specified as outflow boundary. The wall function method was applied to model the near-wall region. The flow in the inducer and the centrifugal wheel was modeled in the Moving Reference Frame.2.5 Calculation casesT he flowing media of the centrifugal pump is N2O4. Table.1 lists the calculation cases in the paper.Table.1 Calculation casesCalculation cases Flux（L/s）Rotational velocity (r/min) Case 1 119 10000Case 2 127 10000Case 3 133 10000Case 4 144 100003 Results and DiscussionFig.3 shows the static pressure contours of the whole computational domain in case 1. The inducer increases the entrance pressure of the centrifugal wheel, and improves the anti-cavitation capability of the centrifugal pump.Fig.3 Static pressure contours of the whole computational domain (Pa)(a) Static pressure contours (Pa) (b) Velocity contours (m/s)Fig.4 Contours of the inducerFig.4 shows the static pressure and the velocity contours of the inducer in case 1. Obviously, the maximum velocity is located at the outer edges of the entrance blades, where the static pressure is very low. As a result, thelocation is liable to suffer from cavitation. Moreover，for the effect of the pressure difference between the cascade pressure surface and the suction one near the blade exit, the exit of the inducer is another low pressure area liable to suffer from cavitation.(a) Static pressure contours (Pa) (b) Velocity contours (m/s)Fig.5 Contours of the centrifugal wheelFig.5 shows the static pressure and the velocity contours of the centrifugal wheel in case 1.It can be seen that without stator blades, the static pressure distribution of each blade is different from another. The low pressure areas in the centrifugal wheel are mainly located at the hub entrance and the roots of part blades. The former is related to the low pressure area at the exit of the inducer, while the latter is caused by the pressure difference between the cascade pressure surface and the suction surface.In general, when the pressure is lower than the local saturated pressure, cavitation will happen[4]. The areas where the pressure is lower than the local saturated pressure are shown in Fig.6. It is shown that cavitation mainly happens at the following areas: the blade outer edge at the inducer entrance and the blade root at the exit of the inducer, the hub entrance and part blade roots of the centrifugal wheel. It can be seen that the cavitation area in the centrifugal wheel is corresponding to that in the exit part of the inducer in the circumferential direction, which indicates that cavitation is related with the assembly angle of the inducer and centrifugal wheel.(a) The inducer (b) The centrifugal wheelFig.6 Cavitation areas in the pumpD e l i v e r y h e a d (M P a )Flux(L/s)Fig.7 Comparison of the computational delivery heads and the experimental onesThe Fig.7 contrasts the computational and the experimental delivery heads under different cases. As shown in the figure, the delivery head decreases appreciably along with the increase of the flux. Furthermore, the computational delivery head is 10% larger than the experimental one. The main reason is that in the numerical simulation, the motion and fragmentation of the bubbles produced by cavitation as well as the volume loss are neglected, which magnifies the pressurizing capability factitiously.4 Conclusions(1) Cavitation mainly happens at the outer edges of the entrance blades and the roots of the exit blades in the inducer, the hub entrance and the roots of part blades in the centrifugal wheel.(2) The delivery head decreases appreciably along with the increase of the flux. For the motion and fragmentation of the bubbles produced by cavitation as well as the volume loss are neglected in the simulation, the computational delivery head is 10% larger than the experimental one.References1. B.E. Launder and D.B. Spalding. Lectures in Mathematical Models of Turbulence [M]. Academic Press, London, England, 19722. Tao Wenquan. Numerical Heat Transfer [M]. Xi’an Jiaotong University Press, Jun.20013. Wang Fujun. Analysis of Computational Fluid Dynamics [M].Beijing: Tsinghua University Press, 20044. Liu Guoqiu. Theory of Liquid-propellant Rocket Engine [M]. Astronautics Press of China, Jun.1993。