Analysis of the cavitation in Diesel Injectors F. Echouchene (*), H. Belmabrouk (*), L. Le Penven (**), M. Buffat (**) * Laboratoire d électronique et de microélectronique, Département de Physique, Faculté des Sciences de Monastir, 5000 Tunisie. ** LMFA UMR CNRS 5509, laboratoire de l'ucb Lyon I, ECL INSA. E-mail : frchouchene@yahoo.fr, Hafedh.Belmabrouk@fsm.rnu.tn Abstract The injection system in Diesel engine has an important effect on the fuel consumption, the combustion process and the pollution emission. The cavitation influences the nature of the fuel spray and the efficiency of the combustion process in Diesel engines. In this study, we investigated numerically the cavitating flow inside a Diesel injector. The mixture model is adopted and the commercial Fluent software is used to solve numerically the transport equations. The discharge coefficient is computed for several cavitation number and wall roughness heights. The profile of the density mixture, the vapor volume fraction, the mean velocity and the turbulent kinetic energy are reported. The effect of injector pressure on the fuel spray atomization is analyzed. Keywords: cavitating flow, wall roughness, mixture model, Diesel injector 1. Introduction Throughout the world, automobiles consume an important fraction of energy. Therefore, it is advantageous to reduce this energy consumption by optimizing the flow, the combustion process and the injection of fuel. The injection system in Diesel engine has an important effect on the fuel consumption, the combustion process and the pollution emission. The cavitation phenomenon occurs when the local pressure of the fluid is lesser than vapor pressure at the temperate of the fluid. Vapor bubbles are then formed convected by the flow and may collapse. This may cause mechanical damage on turbo-machinery and hydraulic systems. On the contrary, we can take advantage of cavitation in some industrial and medical 91
applications. Indeed, cavitation may enhance spray breakup and it has an important effect on the performance of Diesel injector systems and efficiency of the combustion process [1-3]. Several models have been developed in the last years to simulate the cavitating flow inside Diesel injectors [4 9]. They are based on a single-fluid or multi-fluid frame-work, Eulerian- Eulerian or Eulerian-Lagrangian approaches. The previous studies consider a smooth wall. However, wall roughness leads to higher shear stresses in the liquid near the wall and produces additional disturbance of the velocity and pressure. In the present paper we analyze several features of the turbulent cavitating flow inside a Diesel injector. 2.Theoretical formulation and geometry configuration A single fluid approach is used to simulate the multiphase flow. The mixture can be considered as a single phase with its physical properties varying according to the local concentration of liquid and vapor. fraction α according to: The mixture density ρ is related to the vapor volume + (1 α)ρ,where ρ v and ρ l are the vapor density and liquid density respectively. The motion of the fluid is governed by the following equations (Palau-Salvador et al. [10]) - mass conservation equation - momentum conservation equation - transport equation of the vapor mass fraction - transport equation of the turbulent kinetic energy k and the dissipation rate ε. The transport equations are solved using the commercial software package Fluent 6.3. The numerical model is based on the finite-volume-method. The transport equations are discretized using first upwind schemes. Computational domain is discretized using the GAMBIT preprocessor [13] and approximately 3525 cells. An axisymmetric geometry is used to simulate the flow in a typical Diesel injector as shown in figure 1. The inlet radius R 1 =11.52mm, the orifice radius R 2 =4.032mm, the inlet pipe length L 1 =16mm and the orifice length L 2 =32mm. At the inlet and outlet sections, static pressures are adopted as boundary conditions. The upstream pressure varies, as Nurick s experiments, [4] between 1.9bar to 1000bar and the exit pressure was fixed at 0.95bar. The wall roughness is involved in the wall law. 3.Results and discussions The coefficient of discharge C d and the cavitation number K are two important parameters for describing the performance of nozzles. The coefficient of discharge is the ratio of the 92
effective mass flow rate through the nozzle to the theoretical maximum mass flow rate : = The cavitation number is defined by: K = Figure 2 shows the discharge coefficient C d versus the cavitation number K for several values of the roughness height Ks. It appears that C d is about 0.60 to 0.75. This order of magnitude is in good agreement with the experimental data reported by Nurick [4]. Figure 2 proves also that the coefficient of discharge C d increase slightly with the cavitation number K. Figure 3 exhibits the axial evolution of mixture density in wall vicinity for several values of the roughness and for two values of the injection pressure ( K=1.45 or K=1). It shows that upstream the nozzle, the fluid is at liquid state. For a small injection pressure, when the fluid penetrates in the orifice, an important depression takes place, cavitation appears and the density has very small values. Then, the fluid is formed by a mixture of liquid and vapor. For large pressure injection, the wall roughness has a very small effect on the mixture density. The cavitation zone is very extended and the cavitation tends to an hydraulic-flip. Figure 4 shows the vapor volume fraction distribution for a rough wall (K s =100µm and P in =10bar). It appears clearly that the cavitation takes place near the sharp edge and it elongates downstream. The vapor bubbles migrate toward the axis. It results that the density is greater near the wall. The atomization of the spray is enhanced is the central region. Figure 5 shows the velocity field of the mixture for a rough wall (K s =100µm and P in =10bar). Near the sharp edge, the radial component is important. This confirms the migration of the bubbles toward the central region rather than their convection along the wall. Hence, the zone of low pressure gives rise to the formation of bubbles and not to a recirculation zone. The velocity profile is almost flat in the central region. This is expected since the flow is turbulent. Moreover, the flow becomes almost fully developed is approximately when z/d 1. Indeed, the turbulent velocity components enhance the transfer of momentum between adjacent fluid layers and tend to reduce the mean velocity gradient. Near the wall, velocity profiles exhibit step gradient. Velocity profiles indicate that the roughness does not influences the velocity in the central region and its affect is confined in the wall vicinity. Figure 6 exhibits t radial profiles of the turbulent kinetic energy k for different values of z/d. In the central region k=3m 2 /s 2. The production of kinetic energy is important near the wall and especially in the vicinity of the sharp edge. The formation of vapor induces an important 93
gradient of momentum and this yields a significant increase of k. This figure indicates also that the wall roughness effects the turbulent kinetic energy in the region close the wall. The profile of the dissipation rate ε are intimately correlated with the profile of k. the dissipation rate is almost constant and very small in the central region and it exhibits an important increase near the wall (ε~10 6 m 2 /s 3 ). 4. Conclusion In this study we investigated numerically the cavitating flow inside an axisymmetric Diesel injector. The main results are the following: The injection pressure has an important effect on the cavitation and its characteristics. The cavitation is initiated near the sharp edge and then it elongates downstream. The vapor bubbles migrate toward the axis. Thus, the atomization of the spray is enhanced in the central region. The cavitation induces an important increase of the turbulent kinetic energy k and its dissipation rate ε. The cavitation enhances the spray atomization and fuel-air homogenization. Hence, it affects the performance of the engine and soot emissions. In the near future, we intend to examine the effect of geometrical characteristics of the Diesel injector on the cavitation. 94
5. References [1] N. Dumont, O. Simonin, and C. Habchi. Cavitating flows in diesel injectors : a bibliographical review. In Eight International Conference on Liquid Atomization and Spray systems ICLASS2000, Pasadena, CA, USA, 2000. [2] C. Vortmann, G.H. Schnerr, and S. Seelecke. Thermodynamic modeling and simulation of cavitating nozzle flow. International Journal of Heat and Fluid Flow 24 (2003) 774-783. [3] S. Martynov. Numerical Simulation of the Cavitation Process in Diesel Fuel Injectors. Doctoral Thesis, University of Brighton, 2005. [4] M. von Dirke, A. Krautter, J. Ostertag, M. Mennicken and C. Badock. Simulation of cavitating flow in Diesel injectors. Oil & Gas Science and Technology-Rev. IFP, Vol.54 (1999), No.2, pp. 223-226. [5] N. DUMONT, O. SIMONIN and C. HABCHI. Numerical simulation of cavitating flows in Diesel injectors by a homogeneous equilibrium modeling approach. : Fourth International Symposium on Cavitation CAV2001. California Institute of Technology. Pasadena, CA, USA, 2001. 22, 54, 87, 90, 91. [6] E. Giannadakis, M. Gavaises, H. Roth, and C. Arcoumanis. Cavitation Modeling in Single-Hole Diesel Injector Based on Eulerian-Lagrangian Approach. in Proc. THIESEL International Conference on Thermo- and Fluid Dynamic Processes in Diesel Engines. Valencia, Spain. 2004. [7] M. Gavaises and E. Giannadakis. Modeling of cavitation in large scale Diesel injector nozzles. 19 th Annual Meeting of the Institute for Liquid Atomization and Spray Systems (Europe) Nottingham, 6-8 September 2004. [8] W. Lei, L. Chuan-jing, L. Jie and C. Xin. Numerical simulations of 2D periodic unsteady cavitating flows. Journal of Hydrodynamics. Ser.B,2006,18(3):341-344. [9] S. B. Martynov, D. J. Mason, and M. R. Heikal. Numerical simulation of cavitation flows based on their hydrodynamic similarity. Int. J. Engine Res. (2006) Vol. 7. [10] G. Palau-Salvador, P. González-Altazano and J. Arviza-Valverd Numerical modeling of cavitating flows for simple geometries using FLUENT V.6.1. Spanish Journal of Agricultural Research (2007) 5(4), 460-469 ISSN: 1695-971-X. [11] W. Pattanapol, S. J. Wakes, M. J. Hilton and K. J. M. Dickinson. Modeling of surface Roughness for flow over a complex vegetated Surface. International Journal of mathematical, Physical and Engineering Sciences 2;1 www.waset.org Winter 2008. [12] B. Blocken, T. Stathopoulos, and J. Carmeliet. CFD simulation of the atmospheric boundary layer: wall function problems. Atmospheric Environment 41 (2007) 238-252. [13] Fluent Inc., 2006. Fluent 6.2 User s Guide. Fluent Inc., Lebanon. 95
Figure captions Figure 1 : The geometry of the planar nozzle. Flow is from left to right. Figure 2: Discharge coefficient C d as function of cavitation number for different roughness height K s. Figure 3: Density of mixture on the wall for different roughness height K s. Figure 4: Distribution of vapor volume fraction for rough wall (Ks=100µm, P in =10bar). Figure 5: Velocity vectors (m/s) for roughness wall (K s =100µm, P in =10bar). Figure 6: Turbulent Kinetic Energy for smooth wall and roughness wall (K s =100µm, P in =10bar). 96
Figure 1 Figure 2 1,0 0,9 Discharge coefficient C D 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 K s = 0 K s = 20µm K s = 100µm Nurick, 1976 0,0 1,0 1,2 1,4 1,6 1,8 2,0 Cavitation number K 97
Figure 1000 Density of mixture [kg/m 3 ] 800 600 400 200 K = 1.45 smooth K s =100µm 0 K = 1-2 -1 0 z/d 1 2 3 4 2 Figure 4 98
Figure 5 Figure 6 4 0 T u rb u le n t K in e tic E n e rg (m y 2 k /s 2 ) 3 5 3 0 2 5 2 0 1 5 1 0 5 z /D = 1 z /D = 2 z /D = 3 0,0 0 0 0,0 0 1 0,0 0 2 0,0 0 3 0,0 0 4 r (m) 99