NUMERICAL INVESTIGATION OF SPRAY FORMATION IN COAXIAL NOZZLES

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1 Paper ID ILASS8-4 ILASS8--15 ILASS 8 Sep. 8-1, 8, Como Lake, Italy NUMERICAL INVESTIGATION OF SPRAY FORMATION IN COAXIAL NOZZLES Mikhail Konstantinov*, Claus Wagner German Aerospace Center (DLR), Institute for Aeroynamics an Flow Technology, Bunsenstrasse 1, D-3773 Göttingen, Germany *mikhail.konstantinov@lr.e claus.wagner@lr.e ABSTRACT In this paper the results of numerical investigation of atomization process of liqui fuel (Diesel) in Laval an coaxial nozzles are presente. The calculations have been performe using CFD coes of STAR-CD. The epenences between the ifferent cases of pressure rop an spray formation have been analyse. For that purpose a moel to simulate unsteay two-phase atomization process has been employe. Results of transient flow through various 3D nozzle shapes an the resulting spray evelopment have to be iscusse. The three type of nozzle (Laval, converging an coaxial) are consiere. It was foun that for the nozzles uner consieration the finer atomization occurs for low initial mass flow rates. The atomization process in such nozzles occurs by fragmentation between high velocity gas jet an fuel volume. Further, the pressure conitions of gas flow are of great relevance for atomization process. INTRODUCTION The quality of liqui atomization is probably the most essential factor for reucing emissions in Diesel engines. The atomization process epens among other things on the velocity of the fuel exiting the injection nozzle an on the extent of cavitation within the nozzle. Exit velocity moulations strongly influence the break-up processes, the spray penetration an also the inter-roplet an wall-roplet interactions. The problem of fuel injection has always been in centre of new technological evelopments. The technical an economical requirements inclue reuction of the concentration of pollutants in emission an economical consumption as well as optimal reliability an performance. A great progress in this area has been obtaine with the introuction of the Common-Rail-Systems an pumpinjectors in past two ecaes. Both methos use the avantages of high injection pressures. One of the essential aspects of this type of injector is the occurrence of cavitation in each injection hole ue to the fall of the static pressure at the holes entrance. The cavitation process within the nozzles may play a major role in the spray break-up [1-4]. In aition to further progress in the evelopment of efficient an conventional injection methos, the atomization must be improve as well as the power consumption. Herewith a spray can play a leaing role in improvement an refinement of injection strategies. One possible approach to solve this problem is to use of Laval or coaxial nozzles. The atomization process in such nozzles occurs by fragmentation between high velocity gas jet an fuel volume. Coaxial nozzles are effectively use in Rocket Engines [5]. In this case the interaction between the high velocity of gas (fuel) an the low velocity of liqui (oxygen) occurs. A similar process of atomization in liqui/gas systems is observe in Laval nozzle. The Laval nozzles are employe in textile inustry for generation of nonwovens (so-calle Nanoval process) [7]. In this case the melt flow leaves the spinneret an seize by ajacent gas, which is accelerate accoring to gas ynamics rules in Laval nozzle. The gas flow may reach a sonic or even supersonic spee. At the same time the melt flow is splitting into a multitue of fine filaments about 1m iameter in size. In both coaxial an Laval nozzle the atomization might be reache by low volume flux of liqui. Therefore it is interesting to stuy an atomization process for liqui/gas systems when liqui is a fuel (in our case Diesel). A ispersion of particles will be employe as the control parameter for etermination the quality of the injection. NUMERICAL METHOD The calculations have been performe using the CFD coes of STAR-CD with the secon-orer ifferencing schemes MARS (monotone avection an reconstruction scheme) an CD (for ensity only). For the nozzle air flow simulations the supply pressure an chamber pressure were prescribe at the in- an outlet, respectively. The simulations were carrie out consiering turbulent flows. The Reynolsaverage Navier-Stokes equations were solve together with the k- RNG moel. For the spray computations, the break-up moel of Hsiang an Faeth [8], collisions moel of O Rourke [9], wall-interaction moel of Bai an Gosman [1] an 1

2 atomization moel of Chaves an Obermeier [11-1] have been use. The Hsiang an Faeth moel covers all types of break-up that are of interest in Diesel engine spray applications. The characteristic break-up time is The liqui nozzle hole is. mm in iameter for all nozzle types. Further the Laval an converging nozzles have an equal contraction iameter of 4 mm. 1 5 D, (1) Oh / 7 u u where D is the instantaneous roplet iameter, u the roplet velocity an is roplet ensity Oh the Ohnesorge number Oh, () 1/ D where is surface tension an is roplet viscosity. The subscript enotes the roplet/isperse phase, nonsubscripte quantities are taken to refer to the continuous phase. The estimate stable roplet iameter is given by the equation Fig. 1. Scetch of the Laval nozzle. D s 1/ 4 6.D. (3) D u u Break-up takes place when the rop Weber number is greater the critical value of u u D We 6 (4) The roplet iameters change accoring to following rate equation D t D Ds. (5) The collision moel of O Rourke istinguishes between coalescence, separation an bouncing interactions. As bounary conitions the atomization moel propose by Chaves an Obermeier [11] has been use. In the moel, the liqui core is represente by a chain of primary roplets which leave the nozzle with the chamber velocity u ch an initial iameter equal to the nozzle iameter D. Seconary roplets are strippe off from the primary ones over the length of the liqui core L c. The moel assumes that the following two mechanisms are responsible for spray formation: Detachment of rops from the liqui jet core emerging from the nozzle by aeroynamic forces; the sizes of the rops prouce epen on the position along the liqui core where stripping occurs an on the ejection angle, whose maximum value must be prescribe. Collision between the primary rops in the liqui core cause by the time varying injection velocity. The time epenent process of atomization has been examine for 3 types of air/flui nozzles. The corresponing CFD moels for Laval, Converging an Coaxial nozzles with bounary conitions are presente in Fig Fig.. Scetch of the converging nozzle Fig. 3. Scetch of the coaxial nozzle The calculations have been carrie out for two variants of mass flow rate 8e-4 kg/s an 8e-5 kg/s an for pressure ratio of air P 1 /P = 1.5; ; 3; 4; an 6. For the converging an coaxial nozzles only one pressure ratio P 1 /P = has been use. The aim of investigations is to observe the flows with small quantity an very low initial velocity of the liqui phase. The employe parameters are summarize in Table 1.

3 Nozzle type Laval, Converging, Coaxial Hole iameter. mm Air pressure ratio P 1 /P 1.5; ; 3; 4; 6 Fuel Heptan Fuel mass flow 8.e-5; 8.e-4 kg/s Atomization moel Chaves an Obermeier (MPI-) [11-1] Break-up moel Hsiang an Fateh[8] Collision Moel O Rourke [9] Table 1. Numerical conitions NUMERICAL RESULTS The spray formations have been calculate transient with constant bounary conitions. The result analysis was performe at the time when spray characteristics have to reach a evelope state (approximately. s). At first the results for Laval nozzle are presente. A high quality atomization occurs even behin Laval cross-section. In Fig. 4 the proportional roplet istribution for fuel flow rate 8.e-4 kg/s an P 1 /P =4 is shown. In this case a very strong atomization of flui occurs an the roplets are almost invisible in the cyliner chamber because of their small size. For the same case another picture in Fig. 5 is shown. Here all roplets are plotte with the equal size. The colours correspon to the iameter of roplets. The roplet size in the cyliner chamber is changing between 6 an.6 m. Fig. 5. The same istribution as in Fig.4 with fixe plotte size of roplets [m]. Accoring gas velocities an Mach number for this case are presente in Figs. 6 an 7. Fig. 6. The Gas velocity [m/s] istribution for P 1 /P =4 an m = 8.e-4 kg/s Fig. 4. Spay formation in Laval nozzle by P 1 /P =4 an m = 8.e-4 kg/s. The roplet size [m] is proportionally presente. Fig. 7. Mach number istribution for P 1 /P =4 an m = 8.e-4 kg/s. The extreme value of gas velocities an high Mach numbers play a significant role for the spray formation. On the one han the flui particles are accelerate ue to the high 3

4 gas velocity. On the other han in the gas flow behin the nozzle the flui particles ten to collapse which improves the process of atomization. The quality of atomization has been stuie analysing the mean roplet size D 5 in the chamber. This parameter can be etermine by integrating the roplet size istribution. In Fig. 8 the resulting istributions for Heptan mass flow rate of 8.e- 5 kg/s are presente. It is shown, that higher pressure ratios P 1 /P lea of a finer atomization process. Furthermore, the ifference between the cases P 1 /P = 3 an P 1 /P = 4 is small. P 1 /P mot=8.e-5 kg/s mot=8.e-4 kg/s Integrate Size Distribution, % Particles Diameter, m Fig. 8. Integrate particle size istribution for kg/s P1/P=1.5 P/P1= P1/P=3 P1/P=4 m = 8.e , m Fig. 1. Depenence between mean particles iameter an air pressure ratio. From Fig. 1 we conclue that for a fix pressure ratio better atomization is obtaine for lower mass flow rate. In Fig. 11 the change of 5 in epenence from mass flow ratio m Gas / m for Laval nozzle is presente. Fig. 1 an Fig. 11 reflect the phenomena that the possibility of even finer atomization for m =8e.-5 kg/s is almost exhauste for the case P1/P = 4. The results reflect that atomization improves with smaller mass flow rates It was expecte, that for higher mass flux an higher initial velocity of liqui the atomization will be yet finer. But the results presente in Fig.9 reflect, that the particles size for m =8.e-4 kg/s is coarser than for m =8.e-5 kg/s. Aitionally, a more intensive evaporation takes place for higher mass flow rates. mot gas /mot flui mot=8.e-5 kg/s mot=8.e-4 kg/s Integrate Size Distribution, % Particles Diameter, m Fig. 9. Integrate particle size istribution for kg/s P1/P=; mot P1/P=3; mot P1/P=4; mot P1/P=6; mot m = 8.e-4 A comparison of results obtaine for two ifferent mass flows in the Laval nozzle can be presente as epenence between mean particles size 5 an gas pressure ratio. The results presente in Fig. 1 reflect that consierably particles size changes occur in omain of P 1 /P = 4 for m =8.e-5 kg/s. For a further increase of P1/P the atomization will be insignificantly change. For obtain a similar atomization for higher flui mass flow a higher air pressure ratio is neee , m Fig. 11. Depenence between mean particles iameter an mass flow ratio m /. Gas m The calculation of a spray formation for the converging nozzle reflects a similar effect as for the Laval nozzle. Namely finer roplets size has been observe for smaller m for the same ratio of P1/P. A irect comparison of the particle sizes obtaine in the Laval an the converging nozzle is shown in Fig. 1. The corresponing probability ensity istributions for these cases are presente in Fig. 13. Integrate Size Distribution, % Particles Diameter, m P/P1=: Laval nozzle P1/P=, converging nozzle Fig. 1. Particles size istribution behin Laval an converging nozzle by m =8.e-5 kg/s an P1/P =. 4

5 PDF P/P1=: Laval nozzle P1/P=: converging nozzle Behin the simplifie coaxial nozzle the qualitatively ifferent roplets behaviour has been observe. The gas flow also improve the spray formation process, but we can see in Fig. 16 that the value of m =8.e-5 kg/s is too small for this simplifie geometry. The velocity istribution with spray formation for the case of m =8.e-4 kg/s in Fig. 17 is presente Particles Diameter, m Fig. 13. Probability ensity istribution behin Laval an converging nozzle by m =8.e-5 kg/s an P1/P =. Despite of similar shapes of the nozzles geometries the obtaine results are ifferent. It is shown that the iverging part of the Laval nozzle in combination with its converging part plays a important role. In this region very strong atomization of flui occurs. In Figs 14 an 15 the gas velocity behaviour an spray formations in both nozzles are shown. For the case of the Laval nozzle the break-up of roplets is more pronounce than as for the converging nozzle. Fig. 16. Coaxial nozzle: Distribution of gas velocity [m/s] an spray formation for m =8.e-5 kg/s an P1/P =. Fig.14. Laval nozzle: Distribution of gas velocity [m/s] an spray formation for m =8.e-5 kg/s an P1/P =. Fig. 17. Coaxial nozzle: Distribution of gas velocity [m/s] an spray formation for m =8.e-4 kg/s an P1/P =. Aitionally the flow simulations with m =3.e-4 kg/s have been performe. The results of these simulations confirm the observation obtaine in Fig. 1 except for lowest mass flow rate in this simplifie geometry (see Fig. 18). Fig.15. Converging nozzle: Distribution of gas velocity [m/s] an spray formation for m =8.e-5 kg/s an P1/P =. 5

6 Integrate Size Distribution, % P1/P=; mot=8.e-5 kg/s P1/P=; mot=8.e-4 kg/s P1/P=; mot=3.e-4 kg/s Particles Diameter, m Fig.18. Particles size istribution behin coaxial nozzle. CONCLUSIONS The presente numerical approach which inclues the simulation of a compressible flow an spray formation makes possible to preict the grae of atomization behin air/flui nozzles. It was foun that for the consiere nozzles the finer atomization occurs for slow initial velocities of fuel, i.e. for higher values of m Gas / m. Further, it was shown, that a higher gas pressure ratio P1/P improves the whole atomization process. With the presente approach qualitative characteristics of nozzle flow an spray structures have been accurately preicte. The results are restricte to the selecte nozzles geometries an the consiere analysis of particles ispersion. It must be note that effects like evaporation an penetration length are not consiere in this paper. ACKNOWLEDGMENT The authors woul like to thanks Dr. L. Gerking for interesting ieas an iscussions. NOMENCLATURE Symbol Quantity SI Unit P 1 Supply pressure Pa P Chamber pressure Pa m Mass flow kg/s Characteristic s break-up time u Velocity m/s Density kg/m³ Viscosity kg/m s Surface tension N/m D Droplet iameter m We We number [-] Oh Ohnesorge number [-] REFERENCES [1] R. Marcer, P. Le Cottier, H. Chaves, B. Arguerolles, C. Habchi & B. Barbeau, A Valiate numerical simulation of Diesel injector flow using a VOF Metho, SAE Paper No -1-93,. [] E. Giannaakis, D. Papoulias, M Gavaises, C. Arcoumanis, C. Soteriou an W. Tang, Evaluation of the preictive capability of Diesel nozzle cavitation moels, SAE Paper No , 7. [3] J. Murphy, D. Schmit, S. P. Wang, M. L.Corraini, Multi-imensional moelling of multiphase flow physics: high-spee nozzle an jet flows a case stuy, Nuclear Engineering an Design, 4, pp ,. [4] M. Konstantinov, C. Wagner, Numerical simulation of unsteay nozzle flow an spray formation uner Diesel engine conitions, Proc. of the 1 th ILASS Europe Meeting, 7. [5] J. J. Smith, G. Schneier, D. Suslov, M. Oschwal, O. Hain, Steay-state high pressure LOx/H rocket engine combustion, Aerospace an Technology, 11, pp , 7.. [7] L. Gerking, Nanoval Process for Spunbone Nonwovens, Chemical Fibers International, vol. 5, Dec.. [8] G. M. Faeth, L. P. Hsiang, P.-K. Wu, Structure an breakup properties of sprays, Int. Journal Multiphase Flow 1, [9] P. O Rourke, Collective rop effects on vaporising liqui sprays, PhD Thesis, University of Princeton, [1] B. C. Bai, A. D. Gosman, Development of methoology for spray impinging simulation, SAE Paper No 9583, [11] F. Obermeier, H. Chaves, Stuy of pressure fluctuations flows, separation an cavitation in the nozzle an their influence on spray formation, Proc. of the 6 th Workshop of the IDEA Project, 199. [1] F. Obermeier, Experimental an theoretical stuy of the influence of unsteay high frequency flow conitions on flow separation an cavitation within a nozzle an spray formation of fuel injectors uner Diesel enginen conitions, IDEA Project, Subprogram FM.1,