带诱导轮离心泵流场数值模拟

1、Numerical Simulation of Flow Field in a Centrifugal Pump with InducerWei Chao1Zhong Weicong 2 Zhang Feng 2College of Astronautics, Northwestern Polytechnical University, Xian 710072, ChinaXian Aerospace Propulsion Institute, Xian 710100, ChinaAbstract: Based on the N-S Equation and the non-structure

2、d mesh technology, the 3D steady incompressible turbulent flow within a centrifugal pump with inducer was simulated. The internal static pressure distribution, velocity distribution and the delivery head were obtained. Moreover, cavitation was also analyzed. The numerical results show that cavitatio

3、n 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. It s found that cavitation is related with the assembly angle of the inducer and centrifugal wheel. The numerical result

4、s agree with the experimental data very well.Keywords: inducer; centrifugal pump; numerical simulation; cavitationIntroductionThe 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 usu

5、ally 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, its difficult to control the R&D duration and R&D cost. With the development of CFD t

6、echnology, 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

7、 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.ModelingGoverning equationsIn the paper, the 3D steady incompressible turbulent flow within the centrifugal pump was s

8、imulated with the standard k - turbulent model. The governing equations are as follows 1-3:Continuity equation里+Uu )=0d td xjjMomentum equation合(c )合(c)(Pu )+ Vu u/ =j/8 u日T8xk j 8 p 8+8x8xij，c 、8 u日T8 xk j(2)The turbulence kinetic energy, K , and its rate of dissipation, , are obtained from the fol

9、lowing transport equations:P8kd t+ p ui8k8=(p-8 x8 xjj+ pT b k8k ) 8xj8u+ pit 8xj8u(i 8xj8u+ j) - p 8xi(3)dpd t +p u8k 8 xk8p(P + 丁8 xb8)8xkc k8uPt 8 i(j8ui +8xj8 u 2富) 一 C 2 pKi(4)The turbulent viscosity, pt , is computed by combiningk and as follows:K 2p = p C The model constantsC ,C, C ,band b ha

10、ve the following default values: C = 1.44 , C = 1.44 ,C = 1.92 , b = 1.3 ,Discretization of the Governing equationsThe governing equations were discretized by second order upwind scheme. Pressure-velocity coupling was achieved by using SIMPLE algorithm. In the computation, under-relaxation was used

11、to control the update of computed variables at each iteration.Mesh generationThe geometry model of the centrifugal pump studied in the paper is shown in figure 1. A iming at the complex structure of pump, multi-block mesh generation technique was used to make mesh generation easier and improve mesh

12、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

13、 were still irregular, so unstructured mesh was adopted. The whole research domain contained 715517 mesh cells and 206303 mesh nodes.Fig.1 Geometry model of the centrifiigal pumpFig.2 Mesh superimposed on the computational domainBoundary ConditionsThe entrance face of the inducer was specified as ma

14、ss-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.Calculation casesThe flowing media of the centrifugal

15、 pump is N 2O4. Table.1 lists the calculation cases in the paper.Table.1 Calculation casesCalculation casesFlux (L/s)Rotational velocity (r/min)Case 111910000Case 212710000Case 313310000Case 414410000Results and Discussioninducer increases theFig.3 shows the static pressure contours of the whole com

16、putational domain in case 1. The entrance pressure of the centrifugal wheel, and improves the anti-cavitation capability of the centrifugal pump.LuOc+079.6i：i.U&9.30c*069.0u.i*u6S.70t+068.40c+068.10.i+06?.8i：i.i+i：i&?.5O.;*U6?.20.i+i：iF.6.如 6.60e+06&.3u.i*u66.00e+065.7D.1+U65.皿+口65.1UC+UF.4-.80i+064

17、.50c+064.2i：i.i*u.3.90c*063.60t+063.30c*063j：iuo+i：iF.70t+062.4UC+U&2.10-i+u6I.SOc+061.50c*06L池+口69.0u-i*u5.00c*053j：ii：io+u5Fig.3 Static pressure contours ofthe whole computational domain (Pa)8.17.1*03.00C+U6UM+Lla.80e+U6?.：J .i+Ua. 61 c+U&2.41C+U6F.4.5.;*O3.21 c+Lifea.oac+ue5.59c+Ll.sac* u&5.16C+I

18、J.62c+U6.42C+U6.a3e+U6.03 c+U&S.33C+U5：2；.44.i*U6.36C+U53.010+014.39e+05a.4ac+u5土 1R+LI4.51C+U41.52C+U5.29t+U-349.1*05ti.bU-i+OO-546.1+115i.：30.i*00-?4：Jt+U5IJJJU.i+IJU-y.4.Ll.;+O5O.i：ii：i.%+i：n：i(a) Static pressure contours (Pa) (b) Velocity contours (m/s)Fig.4 Contours of the inducerFig.4 shows th

19、e 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 di

20、fference between the cascadeis another low pressure area liable topressure surface and the suction one near the blade exit, the exit of the inducer suffer from cavitation.口如+口？9.45.i+068.36.1+067.8U+067.274+066.72.2+066.17.;*065.62.1*065J：i8.i+064.5：3M唱3.93t*063.445062.39-062.34t*061.80c+061.25t+061

21、.54e*05-3.93.05 VI 1.U-i*02 1.08.1*02 1.02-02 9.60.2+01 9.0i：i.i+01 840.1+01 法如+E T.ao.i+cn 6.60.1+01 6.00.1*01 5.4 如+E 4.80.1+01 4.20.1*01 3.60C+U1 3.00.2+01 240.1+01 1.8i：i.i+i：i1 I i.ao-i+oi6.00.1+00-9.40.1*05(a) Static pressure contours (Pa) (b) Velocity contours (m/s)Fig.5 Contours of the centr

22、ifugal 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

23、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 pressur

24、e, 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

25、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 whe

26、el.9.80 e+03 -3.77e+04-8.52 e+04 -1.33e+05 -1.S0e+05 -2.2Se+05 2.75 e+05 -3.23e+05 -3.70 e+05 -4. IE： e+05 -4.65 e+05 -5.13 e+05 -5.60 e+05 -B.07 e+05 -6.55 e+05 -7.02 e+05 -7.50 e+05-7.97 e+05I -S.45e+05(b) The centrifigal wheel(a) The inducerFig.6 Cavitation areas in the pump-S .92 e+05 * -g.ie+05

27、vrevnBFlux(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