Nozzle Flow and Cavitation Modeling with Coupled 1D-3D AVL Software Tools

Transcription

1 Nozzle Flow and Cavitation Modeling with Coupled 1D-3D AVL Software Tools Published 09/11/2011 Valdas Caika and Peter Sampl AVL LIST GmbH Copyright 2011 SAE International doi: / ABSTRACT The paper is devoted to the coupled 1D-3D modeling technology of injector flow and cavitation in diesel injections systems. The technology is based on the 1D simulation of the injector with the AVL software BOOST-HYDSIM and 3D modeling of the nozzle flow with AVL FIRE. The nozzle mesh with spray holes and certain part of the nozzle chamber is created with the FIRE preprocessor. The border between the 1D and 3D simulation regions can be chosen inside the nozzle chamber at any position along the needle shaft. Actual coupling version of both software tools considers only onedimensional (longitudinal) needle motion. Forthcoming version already includes the two-dimensional motion of the needle. Furthermore, special models for the needle tip contact with the nozzle seat and needle guide contact with the nozzle wall are developed in HYDSIM. The co-simulation technology is applied for different common rail injectors in several projects. It proved to be an efficient and user-friendly engineering tool. An example of piezoelectric common rail injector with a minisac nozzle is presented. Based on it, different numerical and technical aspects of the nozzle flow and cavitation modeling are discussed. INTRODUCTION Fuel flow in high pressure common rail injectors is characterized by short time scale, pressure wave propagation, narrow gap between needle tip and nozzle seat and strong cavitation effects. Some injector parts can be modeled with sufficient accuracy by 1D flow and multi-body dynamics, others (e.g. nozzle) require 3D CFD simulation. Modeling of nozzle flow requires accurate needle motion, appropriate turbulence model and adequate coverage of phase change between the liquid and the vapor phases. Flow modeling technique in this work is based on the 1D HYDSIM model of the complete injector coupled with 3D FIRE model of the nozzle. The co-simulation procedure is governed by BOOST- HYDSIM. Initially HYDSIM performs the 1D simulation standalone up to the time instant when the needle lift reaches the prescribed tolerance (usually from 1 to 5 µm). At this point the 1D-3D co-simulation between HYDSIM and FIRE multiphase kernels is started. It continues up to the needle closing instant (with the same tolerance by default). Alternatively, the co-simulation can be performed at userdefined time/angle intervals. Between these intervals (e.g. pilot and main, main and post injections), when the needle is closed, the CFD simulation can be carried out with a single time step. In this way the computational effort for the entire injection cycle calculation is minimized. During the cosimulation HYDSIM transmits to FIRE the displacement vector of the needle tip and fuel pressure and temperature at the interface. Based on these data, FIRE moves the computational mesh, adjusts boundary conditions, computes and sends back to HYDSIM the hydraulic force vector acting on the needle tip, mass flow rate through the needle seat and spray holes and spatially averaged pressure and temperature in the user-selected mesh areas (e.g. sac volume). HYDSIM counterpart nozzle model contains a two-dimensional representation of the needle tip contour geometry which corresponds to the respective FIRE mesh surface. Using this contour geometry and the flow rate from FIRE, HYDSIM is capable of estimating the minimal geometric flow area and discharge coefficients at the needle seat and holes. Numerical modeling and experimental investigation of cavitation in diesel nozzles has been carried out by Alajbegovic et al. [1], Arcoumanis et al. [2], Chen and Heister [6], Schmidt and Corradini [16], Sou and Kinugasa [17], Yuan and Schnerr [18] and others. Most cavitation models are based on the Eulerian or Lagrangian formulation or their combination. A good survey of the cavitation models

2 for diesel injection nozzles is provided by Giannadakis et al. [11]. Cavitating flow modeling in FIRE standalone using the standard multi-fluid method has been performed by Wang and Greif [14, 15]. One-dimensional modeling of the injector needle and its effect on the nozzle cavitation is studied by Čaika et al. [8], Payri et al. [12] and Sou [17]. The technology developed in this work can be coupled with spray simulation in FIRE. NUMERICAL MODELING MULTI-PHASE FLOW CALCULATION The model presented below is based on the Eulerian method. There the vapor phase and the liquid phase follow their respective conservation laws and the coupling between the phases is enforced through interfacial exchanges. The cavitation is characterized by the vaporization rate, or the mass transfer rate from liquid phase to the vapor phase. Assuming vapor phase is composed of countless number of bubbles of variable size, the phase change rate can be derived from the growth of individual bubbles and the dynamics of each bubble. Bubble growth is described by the Rayleigh- Plesset equation which is the starting point of quantifying the phase change rate. By integrating over the whole spectrum of bubbles, the complete phase change rate has been obtained by Alajbegovic et al [1]. As a further step in the cavitation modeling a moment-based approach for solving bubble distribution function has been developed by Wang et al [15]. It solves for two additional transport equations of bubble number density and interfacial area. Turbulence has always been an important issue in capturing the cavitation, particularly low Re turbulence often encountered in the narrow gap region between needle and its seat. In this work the k-ζ-f model developed by Basara [1] is used in conjunction with the cavitation model. Within the multi-phase flow, each phase is considered a continuum media and the conservation laws apply (Ishii [10]). An ensemble averaging is employed to remove the microscopic interfaces. This results in macroscopic conservation equations analogous to their single-phase counterparts. The difference from single phase is new variable (volume fraction) and new interfacial exchange terms. The averaged continuity and momentum equations follow from the work of Drew and Passman [9]: where α, ρ, v and p are respectively the averaged volume fraction, density, velocity and pressure, the subscript k is a (1) (2) phase indicator (k=l, k=v, or k=a), v int is the interfacial velocity, Γ k is the phase change rate and M k is the interfacial momentum transfer term. Key element in cavitation modeling is the vaporization rate, or the interfacial mass exchange Γ k. For linear cavitation model, it is governed by the Rayleigh equation for the dynamics of a single bubble: where r is the bubble radius and Δp is effective pressure difference. For non-linear cavitation model the Rayleigh equation of bubble dynamics is given by: For a population of bubbles with a distribution function f, defined as the number of bubbles within the radius span of (r,r+dr), the total mass transfer rate in (x,t) will be: For the mono-distribution system of bubbles, the mass changer rate of a population of bubbles id given by: where N is the bubble number density representing the number of bubbles per unit volume. Different solutions exist for the equations (5) and (6) to obtain the mass exchange rate, refer to Wang et al. [15]. Details of the implementation into FIRE can be found in Greif and Wang [14]. FIRE kernel solves the coupled Navier- Stokes-equations for all phases according to the Finite Volume Method and SIMPLE scheme [4]. The k-ζ-f model turbulence model has been used. UPWIND difference scheme is applied to transport equations except for the momentum balance, for which MINMOD scheme is used. 1D INJECTOR MODEL General Description Injector chosen for investigation is a piezo-controlled common rail injector from Bosch (CRI3). Basic features of the CRI3 injector are sharp injector rate, small pilot injection (3) (4) (5) (6)

3 quantity (0.5 mm 3 ), reduced tolerances for low emission standards, multiple injections (up to 5 events per cycle), reduced static and dynamic forces (wear), no leakage, failsafe-principle, low noise and compact design [5]. The injector is designed for the rail pressure up to 180 MPa (CRI3.1) and 200 MPa (CRI3.2), respectively. Schematic of the injector is shown in Figure 1. The main assembly components of the injector are the piezoelectric stack actuator, hydraulic amplifier (coupler), control valve, throttle plate and nozzle. The injection process is regulated via the energizing duration of the piezoelectric actuator. Figure 2. Function of control valve with inlet, outlet and bypass throttles Figure 1. Schematic of BOSCH CRI3 piezoelectric injector Function of the control valve is shown in Figure 2 [5]. At the starting position no voltage is applied on the actuator. Hence the control valve seat is closed and the high pressure area is separated from the low pressure as shown in Figure 2, 1. Pressure balance across the needle keeps the nozzle closed. Activation of the piezo actuator opens the control valve and at the same time closes the bypass throttle (refer to Figure 2, 2). Pressure in the control volume drops down and the needle starts opening. Opening velocity depends on the area ratio between the inlet and outlet throttle. Closing of the control valve results in the fast refilling of the control volume through the inlet and bypass throttles. The outlet throttle plays the role of the inlet throttle as illustrated in Figure 2, 3. Pressure in the control volume gradually increases and the needle starts closing. Schematic and model of the nozzle with throttle plate are shown in Figure 3. Piezoelectric Actuator The piezoelectric stack actuator is schematically shown in Figure 4. It consists of a dense pile of separately contacted layers (wafers) of electrically active ceramic material. The layers are assembled mechanically in a series and connected electrically in parallel. When input voltage is applied to the stack actuator, electric field across the ceramic layers induces a mechanical strain, which results in an elongation of the stack. More detailed description of the piezoelectric actuator and complete injector model can be found in [7]. The piezoelectric stack has a very precise motion but its maximal idle displacement is usually small (40-50 µm). Amplifiers are used to magnify the stack end motion and attain the required amplitude of the control valve. Hydraulic amplifier of CRI3 injector consists of the two pistons and a volume between them. Lower piston is connected to the control valve body. Its motion depends on the ratio of the cross-sectional areas of the pistons. To magnify the stack end lift, the lower piston has a smaller diameter than the upper piston. CRI3 injector operates much faster than the traditional solenoid-controlled injector. Therefore it can generate multiple pulses (pilot, pre-, main and post injection) and manage variable lift of the injector needle. In combination with the modern combustion processes, this allows to enhance engine performance, improve emission quality and reduce noise [5]. HYDSIM-FIRE COUPLING INTERFACE HYDSIM-FIRE interface is illustrated in Figure 5: left figure shows the centered needle (model with 1 degree-of-freedom and one force component) while right figure - eccentric needle (model with 3 degrees-of-freedom and 3 force components).

4 Figure 3. Injector nozzle with needle and throttle plate (sketch and model) As shown in Figure 5, on each data exchange step FIRE transfers to HYDSIM the following variables: F N - force vector acting on needle tip q seat - flow rate through needle seat q holes - flow rate through spray holes (outlet) p topv - boundary pressure below interface line T topv - boundary temperature below interface line p sac - average pressure in sac volume T sac - average temperature in sac volume p gas - boundary pressure in spray chamber T gas - boundary temperature in spray chamber In return at the end of the exchange time step HYDSIM transfers to FIRE the following data: X d - displacement vector of needle tip p nozv - boundary pressure above interface line T nozv - boundary temperature above interface line Our injector example is limited to the centered needle model with 1 degree-of-freedom (longitudinal motion). The needle lift tolerance for co-simulation start is set to 2 µm (small value is required for the convergence of FIRE multi-phase solver). HYDSIM calculation step is 10 7 s, exchange step with FIRE is 10 6 s. This step is applied only for the intervals where needle lift exceeds the tolerance (i.e. during injection). Between the injection events the 5 times larger time step is used ( s). FIRE COMPUTATIONAL GRID Computational grid used in the CFD simulation is shown in Figure 6. The whole domain consists of the hollow cylinder around the needle shaft, needle seat area with nozzle sac and eight cylindrical holes. For the sake of reduction of the computational effort, only one of the eight periodic 45- degree-segments is modeled. The refined mesh consists of hexahedral cells with 35 cell layers in the circumferential direction so that one layer corresponds to degrees. Cell size in the narrowest needle seat gap is µm. The outlet bore is meshed separately and connected to the sac-volume by arbitraryinterfaces. The nozzle gap itself contains 50 cell rows in the radial direction (which is the main flow direction) and 11 rows in vertical direction (normal to the main flow direction). This mesh topology is chosen according to the AVL experience with the 3D nozzle flow simulation [4]. The needle movement is accomplished by the mesh-deformation at solver runtime. Only one mesh is created in a reference position. The mesh-deformation-function shifts the needle surface at each time step according to the needle displacement received from HYDSIM. After that, the position of the internal nodes is updated by the Laplace

5 Figure 4. Piezoelectric actuator and hydraulic amplifier (sketch and model) Figure 5. FIRE calculation domain with exchange variables (left - centered needle, right - shifted needle) interpolation scheme. To prevent collapsing cells at zero or very small needle lift, a minimal gap size (2 µm in the actual case) is maintained in the mesh. The needle movement below this minimal gap is simulated by cell-blocking, i.e. assigning a high flow resistance to all those cells that are actually located within the solid needle. RESULT ANALYSIS NEEDLE MOTION AND INJECTION RATE Investigation is carried out for 4 load cases with the conventional diesel fuel (EN 590). Selected calculation and measurement results are shown in Figure 7 and Figure 8. For convenience, the results are plotted in the crank angle domain. Injection rate measurements in Bosch tube are performed in AVL injection lab. First case C1 (Figure 7, left)

6 Figure 6. FIRE mesh of nozzle segment (left - low needle lift, right - maximum lift) Figure 7. Needle lift and injection rate for load cases 1 (left) and 2(right)

7 Figure 8. Needle lift and injection rate for load cases 3(left) and 4(right) Figure 9. Phase distribution in 1st pilot injection for case 1 (left, middle - surface plots, right - mid-plane cut)

8 Figure 10. Phase distribution in 2nd pilot injection for case 1 (left, middle - surface plots, right - mid-plane cut) Figure 11. Phase distribution in main injection for case 1 (top - surface plots, bottom - mid-plane cuts)

9 is a full load condition with the speed 1000 rpm and rail pressure 78 MPa. It consists of the two pilot injections and main injection. The maximum needle lift at the pilot injections is very small (0.06 mm) and the injection quantity is about 2 mm 3 per stroke. At the main injection the needle lift reaches 0.55 mm for HYDSIM-FIRE co-simulation model and 0.50 mm for HYDSIM calculation standalone. The measured injection rate matches well enough the calculated flow with both models. The main injection quantity is 45 mm 3 per stroke. Note that HYDSIM standalone calculations are performed with needle seat and spray holes discharge coefficients estimated from the standard nozzle flow test. Second case C2 (Figure 7, right) is a part load condition with the speed 2000 rpm and rail pressure 100 MPa. It also consists of the two pilot injections and main injection. At the main injection the needle lift in HYDSIM-FIRE cosimulation is again a bit higher than in HYDSIM calculation standalone (0.29 mm against 0.26 mm). The measured injection rate matches better the calculated flow rate of HYDSIM-FIRE model. The injected fuel quantity for both pilot injections is 2.8 mm 3 and for main injection - 24 mm 3. Third case C3 (Figure 8, left) is a full load condition containing one pilot and main injection. Engine speed is 3000 rpm and rail pressure 160 MPa. The needle lift and injection rate are nearly same for the HYDSIM-FIRE and HYDSIM standalone models. In the main injection the measured injection rate is somewhat higher than calculated because of the bias in the measurement set-up. The pilot injection quantity is 2.4 mm 3 and main injection quantity mm 3. Fourth case C4 (Figure 8, right) is a full load condition with the maximum speed 4000 rpm and rail pressure 160 MPa. It contains the main injection only. The maximum needle lift for the HYDSIM-FIRE model is 0.74 mm, for the HYDSIM model mm. Measured injection rate agrees well the calculated flow rate for both 1D and 1D/3D models. Main injection quantity is 71.5 mm 3. In all cases the needle motion has an almost triangular shape with nearly linear opening and closing sides. This enables the linear fuel quantity control by the energizing time. Note that the needle lift is limited to 0.90 mm. At real operation this value can never be reached because the needle always exhibits ballistic motion. CAVITATION AT SEAT AND HOLES For cavitation analysis the load cases 1 and 3 are chosen. For visualization, the volume fraction is plotted on outer surface and in the mid-plane. The results for case 1 are the volume fraction of diesel vapor at selected time instants of two pilot and the main injections. Vapor phase distribution during the 1 st pilot injection is shown in Figure 9. There blue color represents 100% diesel liquid, red color - 100% diesel vapor. Needle reaches the prescribed tolerance of 2 µm at HYDSIM angle 2.83 deg (corresponds to FIRE angle 0 deg). At very opening, as soon as the needle lift reaches 2.5 µm (FIRE angle deg) light vaporization area is visible at needle seat (refer to left graph) which vanishes within the next few steps. From this point till full lift of 63 µm cavitation does occur neither at seat nor in the hole. The needle seat starts cavitating when the lift drops to 25 µm (FIRE angle 1.44 deg). From this instant till needle closing (FIRE angle 1.61 deg) the cavitation region widely spreads across the seat and inside the hole. Large vapor area develops in the mid-plane on the upper side of the hole (refer to right graph). It propagates through the entire hole from inlet to outlet. Phase distribution in 2 nd pilot injection is shown Figure 10. It is quite similar to that in the 1 st pilot injection, only the cavitation at needle seat is stronger. Vapor phase distribution during the main injection is depicted in Figure 11. The two-phase flow behavior at opening (left graphs) resembles that of the pilot injections: light vapor area can be traced back at seat at FIRE angle deg corresponding to needle lift 4.5 µm. From this point till maximum lift of 550 µm and beyond it no vaporization areas are visible neither at seat nor in the hole (refer to middle graphs). Analogously to pilot injections, seat starts cavitating when needle lift drops down to 25 µm (FIRE angle 23.1 deg). This position corresponds to the seat flow area mm 2. For comparison, total geometric area of the holes is mm 2. Cavitation at seat and in the hole occurs almost simultaneously. It develops rapidly the seat upwards and the hole outwards till complete needle closing (FIRE angle 23.3 deg). One can also observe a distinct vapor cloud in the nozzle sac near the wall surface. Generally vapor distribution in pilot and main injections is fairly similar. Hence, for the specific injection pressure cavitation behavior is mostly determined by the needle lift characteristic which is triangular for this injector type. Another important parameter is the hole inlet radius, but it is very difficult to control. Liquid velocity for selected time instants of 1 st pilot and main injections is shown in Figure 12. Highest velocity at pilot injection is around 280 m/s. It is almost uniform at seat and in the hole. At maximum lift of main injection (550 µm) the highest fluid flow takes place at the hole inlet (refer to middle graph). Liquid velocity there reaches 360 m/s. Calculation results for case 3 are the volume fraction of diesel vapor and liquid velocity at selected time instants for the pilot and main injections. Vapor phase distribution during the pilot injection is shown in Figure 13. Again blue color represents 100% diesel liquid, red color - 100% diesel vapor. Needle reaches the prescribed tolerance of 2 µm at HYDSIM angle 5.56 deg (corresponds to FIRE angle 0 deg). From the very opening entire needle seat gets strongly covered with diesel vapor (refer to top left graph) which gradually reduces with the increasing needle lift. Partial vapor regions are clearly visible inside the nozzle sac and at the hole inlet (left and middle graphs). At maximum needle lift of 42 µm (FIRE angle deg) vapor region contracts to the narrowest seat area as shown in top middle graph. At needle closing the cavitation area spreads the seat upwards and penetrates

10 Figure 12. Liquid velocity for case 1 (left- 1st pilot, max. lift, middle - main injection, max. lift, right - main injection end) Figure 13. Phase distribution in pilot injection for case 3 (top - surface plots, bottom - mid-plane cuts)

11 strongly into the nozzle hole. Shortly before closing (FIRE angle 2.92 deg) the vapor area stretches in the mid-plane on the upper side of the hole till the outlet (refer to bottom right graph). Nozzle sac gets almost completely filled with the liquid phase. Vapor phase distribution during the main injection is depicted in Figure 14. The cavitation behavior at opening is similar to the pilot injection, only it ceases somewhat faster. Cavitation areas at needle seat and in the holes vanish at FIRE angle 25.3 deg which corresponds to the needle lift of 32 µm. From this point till maximum lift of 770 µm (FIRE angle 36.7 deg) and beyond it no vaporization areas are visible neither at seat nor in the hole (refer to middle and right graphs). Analogously to the previous case, seat starts cavitating again when needle lift drops down to 34 µm (at FIRE angle 48.1 deg). Vapor distribution pattern at seat and in the hole for cases 1 and 3 is somewhat similar. Liquid velocity for selected time instants of the pilot and main injections is shown in Figure 15. Highest velocity at pilot injection is around 350 m/s (in the narrowest seat area). In the main injection, at maximum lift of 770 µm the highest fluid flow is concentrated at the hole inlet (refer to right graph). Liquid velocity there reaches 450 m/s. Figure 14. Phase distribution in main injection for case 3 (left, middle - surface plots, right - mid-plane cut) Figure 15. Liquid velocity in main injection for case 3 (left- pilot closing, middle - main opening, right - main, max. lift)

12 SUMMARY 1D-3D simulation technology for nozzle flow and cavitation modeling is presented. It is based on the 3D multi-fluid method in the commercial CFD tool AVL FIRE and 1D fluid flow and multi-body dynamics approach in BOOST- HYDSIM software. The co-simulation procedure is controlled by HYDSIM. The coupling version v2010 (available on the market) is limited to the longitudinal needle motion. New version v2011 already includes the twodimensional motion of the needle. Using the developed technology, the cavitation regions at needle seat and nozzle holes can be more accurately predicted than with a standard 3D simulation which uses prescribed needle lift and nozzle pressure as boundary conditions. Developed co-simulation method has a significant advantage over the injector flow modeling with a standalone CFD code. A single computational grid created in the pre-processing stage for the closed needle position is usually sufficient. During co-simulation this grid is continuously corrected according to the needle position computed by HYDSIM. Needle opening/closing phases can be handled by the low needle lift treatment technique in FIRE (several options are available for this). In this way a single co-simulation run can easily cover multiple injection events within any user-defined time/angle range. A co-simulation example with the piezoelectric common rail injector is presented. It includes a sophisticated HYDSIM model with numerous hydraulic, mechanical and electrical components (e.g. piezoelectric stack actuator). For coupled simulation, 1D nozzle model is substituted by a refined 3D multi-phase model covered by FIRE domain. The injector model is validated by comparing the measured and calculated injection rates for different load cases. For two characteristic cases with multiple injection events the cavitation occurrence at needle seat and in the nozzle hole has been analyzed. REFERENCES 1. Alajbegovic, A., Greif, D., Basara, B. and Iben, U., Cavitation Calculation with the Two-fluid Model, 3 rd European-Japanese Two-phase Flow Group Meeting, Certosa di Pontignano, Italy, September Arcoumanis, C., Flora, H., Gavaises, M., and Badami, M., Cavitation in Real-Size Multi-Hole Diesel Injector Nozzles, SAE Trans. J. of Engines, 109,2000, doi: / AVL BOOST HYDSIM, User's Guide, Graz AVL FIRE, Eulerian Multiphase, Graz Boecking, F. et al., Passenger Car Common Rail Systems for Future Emissions Standards, MTZ 7-8/2005, Vol. 66, Chen, Y. and Heister, S.D., Modeling Cavitating Flows in Diesel injectors. Atomization and Sprays, 1996, Volume 6, Čaika, V., Kammerdiener, T., and Dörr, N., Operation of Piezoelectric Common Rail Injector with Diesel and FT- Kerosene, SAE Technical Paper , 2007, doi: / Čaika, V., Sampl, P., Tatschl, R., Krammer, J. et al., Coupled 1D-3D Simulation of Common Rail Injector Flow Using AVL HYDSIM and FIRE, SAE Technical Paper , 2009, doi: / Drew, D.A. and Passman, S.L. Theory of Multicomponent Fluids, Springer, New York, Ishii, M. Thermo Fluid Dynamic Theory of Two-Phase Flow, Eyrolles, Paris, Giannadakis, E., Gavaises, M. and Arcoumanis, C., Modeling of Cavitation in Diesel injector Nozzles, J. Fluid Mechanics, 2008, 616, Payri, F., Margot, X., Patouna, S., Ravet, F. et al., A CFD Study of the Effect of the Needle Movement on the Cavitation Pattern of Diesel Injectors, SAE Technical Paper , 2009, doi: / Sun, X., Kim, S., Ishii, M. and Beus, S. Modeling of Bubble Coalescence and Disintegration in Confined Upward Two-phase Flow, Nuclear Engineering and Design, 230, 3-26, Wang, D.M. and Greif, D., Progress in Modeling Injector Cavitating Flows with a Multi-fluid Method. FEDSM , ASME Forum on Cavitation and Multiphase Flow, Miami, FL, USA, July Wang, D.M. et al., Interfacial Area and Number Density Transport Equations For Modeling Multiphase Flows with Cavitation, Proc. ASME 9th Int. Symposium on Gas-Liquid Two-Phase Flow, FEDSM'05, Houston, Texas, USA, June Schmidt, D.P. and Corradini, M.L., The Internal Flow of Diesel Fuel injector Nozzles. Int. J. Engine Research, 2001, 2, Sou, A., Kinugasa, T., Numerical Simulation of Developing Cavitating Flow in a Nozzle of Pressure Atomizer, THIESEL 2010 Conference on Thermo- and Fluid Dynamic Processes in Diesel Engines, Valencia, Spain, September Yuan, W. and Schnerr, G.H., Cavitation in Injection Nozzles: Effect of Injection Pressure Fluctuations, Proc. 4 th Int. Symposium on Cavitation, Pasadena, CA, USA, 2001.

13 CONTACT INFORMATION Dr. Valdas Čaika AVL List GmbH Hans-List-Platz 1, A-8020 Graz, Austria The Engineering Meetings Board has approved this paper for publication. It has successfully completed SAE's peer review process under the supervision of the session organizer. This process requires a minimum of three (3) reviews by industry experts. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of SAE. ISSN Positions and opinions advanced in this paper are those of the author(s) and not necessarily those of SAE. The author is solely responsible for the content of the paper. SAE Customer Service: Tel: (inside USA and Canada) Tel: (outside USA) Fax: CustomerService@sae.org SAE Web Address: Printed in USA