9 research outputs found

    Eulerian CFD modeling of nozzle geometry effects on ECN Sprays A and D: assessment and analysis

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    This is the author's version of a work that was accepted for publication in International Journal of Engine Research. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published as https://doi.org/10.1177/1468087419882500.[EN] Diesel spray modeling is a multi-scale problem with complex interactions between different flow regions, that is, internal nozzle flow, near-nozzle region and developed spray, including evaporation and combustion. There are several modeling approaches that have proven particularly useful for some spray regions although they have struggled at other areas, while Eulerian modeling has shown promise in dealing with all characteristics at a reasonable computational effort for engineering calculations. In this work, the sigma -Y single-fluid diffuse-interface model, based on scale separation assumptions at high Reynolds and Weber numbers, is used to simulate the engine combustion network Sprays A and D within a Reynolds-averaged Navier-Stokes turbulence modeling approach. The study is divided into two parts. First of all, the larger diameter Spray D is modeled from the nozzle flow till evaporative spray conditions, obtaining successful prediction of numerous spray metrics, paying special attention to the near-nozzle region where spray dispersion and interfacial surface area can be validated against measurements conducted at the Advanced Photon Source at Argonne National Laboratory, including both the ultra-small-angle X-ray scattering and the X-ray radiography. Afterwards, an analysis of the modeling predictions is made in comparison with previous results obtained for Spray A, considering the nozzle geometry effects in the modeling behavior.The authors thank the freely shared X-ray radiography and ultra-small-angle X-ray scattering measurements performed at Argonne National Laboratory by the following authors: Daniel J. Duke, Jan Ilavsky, Katarzyna E. Matusik., Brandon A. Sforzo., Alan L. Kastengren and Christopher F. Powell. They also thankfully acknowledge the computer resources at Picasso and the technical support provided by Universidad de Malaga (UMA; RES-FI-2018-1-0039).Pandal, A.; García-Oliver, JM.; Pastor Enguídanos, JM. (2020). Eulerian CFD modeling of nozzle geometry effects on ECN Sprays A and D: assessment and analysis. International Journal of Engine Research. 21(1):73-88. https://doi.org/10.1177/1468087419882500S7388211PAYRI, R., GARCIA, J., SALVADOR, F., & GIMENO, J. (2005). Using spray momentum flux measurements to understand the influence of diesel nozzle geometry on spray characteristics. Fuel, 84(5), 551-561. doi:10.1016/j.fuel.2004.10.009Payri, R., Salvador, F. J., Gimeno, J., & Zapata, L. D. (2008). Diesel nozzle geometry influence on spray liquid-phase fuel penetration in evaporative conditions. Fuel, 87(7), 1165-1176. doi:10.1016/j.fuel.2007.05.058Payri, R., Salvador, F. J., Gimeno, J., & de la Morena, J. (2009). Effects of nozzle geometry on direct injection diesel engine combustion process. Applied Thermal Engineering, 29(10), 2051-2060. doi:10.1016/j.applthermaleng.2008.10.009Payri, F., Payri, R., Salvador, F. J., & Martínez-López, J. (2012). A contribution to the understanding of cavitation effects in Diesel injector nozzles through a combined experimental and computational investigation. Computers & Fluids, 58, 88-101. doi:10.1016/j.compfluid.2012.01.005Kastengren, A. L., Powell, C. F., Wang, Y., Im, K.-S., & Wang, J. (2009). X-RAY RADIOGRAPHY MEASUREMENTS OF DIESEL SPRAY STRUCTURE AT ENGINE-LIKE AMBIENT DENSITY. Atomization and Sprays, 19(11), 1031-1044. doi:10.1615/atomizspr.v19.i11.30Pickett, L. M., Manin, J., Kastengren, A., & Powell, C. (2014). Comparison of Near-Field Structure and Growth of a Diesel Spray Using Light-Based Optical Microscopy and X-Ray Radiography. SAE International Journal of Engines, 7(2), 1044-1053. doi:10.4271/2014-01-1412Dahms, R. N., Manin, J., Pickett, L. M., & Oefelein, J. C. (2013). Understanding high-pressure gas-liquid interface phenomena in Diesel engines. Proceedings of the Combustion Institute, 34(1), 1667-1675. doi:10.1016/j.proci.2012.06.169Arienti, M., & Sussman, M. (2017). A numerical study of the thermal transient in high-pressure diesel injection. International Journal of Multiphase Flow, 88, 205-221. doi:10.1016/j.ijmultiphaseflow.2016.09.017Vallet, A., Burluka, A. A., & Borghi, R. (2001). DEVELOPMENT OF A EULERIAN MODEL FOR THE «ATOMIZATION» OF A LIQUID JET. Atomization and Sprays, 11(6), 24. doi:10.1615/atomizspr.v11.i6.20Siebers, D. L. (2008). Recent Developments on Diesel Fuel Jets Under Quiescent Conditions. Flow and Combustion in Reciprocating Engines, 257-308. doi:10.1007/978-3-540-68901-0_5Oefelein, J., Dahms, R., & Lacaze, G. (2012). Detailed Modeling and Simulation of High-Pressure Fuel Injection Processes in Diesel Engines. SAE International Journal of Engines, 5(3), 1410-1419. doi:10.4271/2012-01-1258Demoulin, F.-X., Reveillon, J., Duret, B., Bouali, Z., Desjonqueres, P., & Menard, T. (2013). TOWARD USING DIRECT NUMERICAL SIMULATION TO IMPROVE PRIMARY BREAK-UP MODELING. Atomization and Sprays, 23(11), 957-980. doi:10.1615/atomizspr.2013007439Desantes, J. M., Garcia-Oliver, J. M., Pastor, J. M., & Pandal, A. (2016). A COMPARISON OF DIESEL SPRAYS CFD MODELING APPROACHES: DDM VERSUS E-Y EULERIAN ATOMIZATION MODEL. Atomization and Sprays, 26(7), 713-737. doi:10.1615/atomizspr.2015013285Desantes, J. M., García-Oliver, J. M., Pastor, J. M., Pandal, A., Baldwin, E., & Schmidt, D. P. (2016). Coupled/decoupled spray simulation comparison of the ECN spray a condition with the -Y Eulerian atomization model. International Journal of Multiphase Flow, 80, 89-99. doi:10.1016/j.ijmultiphaseflow.2015.12.002Garcia-Oliver, J. M., Pastor, J. M., Pandal, A., Trask, N., Baldwin, E., & Schmidt, D. P. (2013). DIESEL SPRAY CFD SIMULATIONS BASED ON THE Σ-Υ EULERIAN ATOMIZATION MODEL. Atomization and Sprays, 23(1), 71-95. doi:10.1615/atomizspr.2013007198Navarro-Martinez, S. (2014). Large eddy simulation of spray atomization with a probability density function method. International Journal of Multiphase Flow, 63, 11-22. doi:10.1016/j.ijmultiphaseflow.2014.02.013Pandal, A., Pastor, J. M., García-Oliver, J. M., Baldwin, E., & Schmidt, D. P. (2016). A consistent, scalable model for Eulerian spray modeling. International Journal of Multiphase Flow, 83, 162-171. doi:10.1016/j.ijmultiphaseflow.2016.04.003Pandal, A., Payri, R., García-Oliver, J. M., & Pastor, J. M. (2017). Optimization of spray break-up CFD simulations by combining Σ-Y Eulerian atomization model with a response surface methodology under diesel engine-like conditions (ECN Spray A). Computers & Fluids, 156, 9-20. doi:10.1016/j.compfluid.2017.06.022Pandal, A., García-Oliver, J. M., Novella, R., & Pastor, J. M. (2018). A computational analysis of local flow for reacting Diesel sprays by means of an Eulerian CFD model. International Journal of Multiphase Flow, 99, 257-272. doi:10.1016/j.ijmultiphaseflow.2017.10.010Payri, R., Ruiz, S., Gimeno, J., & Martí-Aldaraví, P. (2015). Verification of a new CFD compressible segregated and multi-phase solver with different flux updates-equations sequences. Applied Mathematical Modelling, 39(2), 851-861. doi:10.1016/j.apm.2014.07.011Salvador, F. J., Gimeno, J., Pastor, J. M., & Martí-Aldaraví, P. (2014). Effect of turbulence model and inlet boundary condition on the Diesel spray behavior simulated by an Eulerian Spray Atomization (ESA) model. International Journal of Multiphase Flow, 65, 108-116. doi:10.1016/j.ijmultiphaseflow.2014.06.003Demoulin, F.-X., Beau, P.-A., Blokkeel, G., Mura, A., & Borghi, R. (2007). A NEW MODEL FOR TURBULENT FLOWS WITH LARGE DENSITY FLUCTUATIONS: APPLICATION TO LIQUID ATOMIZATION. Atomization and Sprays, 17(4), 315-345. doi:10.1615/atomizspr.v17.i4.20Pandal, A., Pastor, J. M., Payri, R., Kastengren, A., Duke, D., Matusik, K., … Schmidt, D. (2017). Computational and Experimental Investigation of Interfacial Area in Near-Field Diesel Spray Simulation. SAE International Journal of Fuels and Lubricants, 10(2), 423-431. doi:10.4271/2017-01-0859Weller, H. G., Tabor, G., Jasak, H., & Fureby, C. (1998). A tensorial approach to computational continuum mechanics using object-oriented techniques. Computers in Physics, 12(6), 620. doi:10.1063/1.168744Faeth, G. M. (1983). Evaporation and combustion of sprays. Progress in Energy and Combustion Science, 9(1-2), 1-76. doi:10.1016/0360-1285(83)90005-9Pitzer, K. S., Lippmann, D. Z., Curl, R. F., Huggins, C. M., & Petersen, D. E. (1955). The Volumetric and Thermodynamic Properties of Fluids. II. Compressibility Factor, Vapor Pressure and Entropy of Vaporization1. Journal of the American Chemical Society, 77(13), 3433-3440. doi:10.1021/ja01618a002Lebas, R., Menard, T., Beau, P. A., Berlemont, A., & Demoulin, F. X. (2009). Numerical simulation of primary break-up and atomization: DNS and modelling study. International Journal of Multiphase Flow, 35(3), 247-260. doi:10.1016/j.ijmultiphaseflow.2008.11.005Duret, B., Reveillon, J., Menard, T., & Demoulin, F. X. (2013). Improving primary atomization modeling through DNS of two-phase flows. International Journal of Multiphase Flow, 55, 130-137. doi:10.1016/j.ijmultiphaseflow.2013.05.004Gimeno, J., Bracho, G., Martí-Aldaraví, P., & Peraza, J. E. (2016). Experimental study of the injection conditions influence over n-dodecane and diesel sprays with two ECN single-hole nozzles. Part I: Inert atmosphere. Energy Conversion and Management, 126, 1146-1156. doi:10.1016/j.enconman.2016.07.077Kastengren, A., Ilavsky, J., Viera, J. P., Payri, R., Duke, D. J., Swantek, A., … Powell, C. F. (2017). Measurements of droplet size in shear-driven atomization using ultra-small angle x-ray scattering. International Journal of Multiphase Flow, 92, 131-139. doi:10.1016/j.ijmultiphaseflow.2017.03.005Kastengren, A. L., Tilocco, F. Z., Powell, C. F., Manin, J., Pickett, L. M., Payri, R., & Bazyn, T. (2012). ENGINE COMBUSTION NETWORK (ECN): MEASUREMENTS OF NOZZLE GEOMETRY AND HYDRAULIC BEHAVIOR. Atomization and Sprays, 22(12), 1011-1052. doi:10.1615/atomizspr.2013006309Matusik, K. E., Duke, D. J., Kastengren, A. L., Sovis, N., Swantek, A. B., & Powell, C. F. (2017). High-resolution X-ray tomography of Engine Combustion Network diesel injectors. International Journal of Engine Research, 19(9), 963-976. doi:10.1177/1468087417736985Payri, R., Gimeno, J., Cuisano, J., & Arco, J. (2016). Hydraulic characterization of diesel engine single-hole injectors. Fuel, 180, 357-366. doi:10.1016/j.fuel.2016.03.083Naber, J., & Siebers, D. L. (1996). Effects of Gas Density and Vaporization on Penetration and Dispersion of Diesel Sprays. SAE Technical Paper Series. doi:10.4271/960034Pope, S. B. (1978). An explanation of the turbulent round-jet/plane-jet anomaly. AIAA Journal, 16(3), 279-281. doi:10.2514/3.7521Battistoni, M., Magnotti, G. M., Genzale, C. L., Arienti, M., Matusik, K. E., Duke, D. J., … Marti-Aldaravi, P. (2018). Experimental and Computational Investigation of Subcritical Near-Nozzle Spray Structure and Primary Atomization in the Engine Combustion Network Spray D. SAE International Journal of Fuels and Lubricants, 11(4), 337-352. doi:10.4271/2018-01-0277Chesnel, J., Reveillon, J., Menard, T., & Demoulin, F.-X. (2011). LARGE EDDY SIMULATION OF LIQUID JET ATOMIZATION. Atomization and Sprays, 21(9), 711-736. doi:10.1615/atomizspr.2012003740Devassy, B. M., Habchi, C., & Daniel, E. (2015). ATOMIZATION MODELLING OF LIQUID JETS USING A TWO-SURFACE-DENSITY APPROACH. Atomization and Sprays, 25(1), 47-80. doi:10.1615/atomizspr.2014011350García-Oliver, J. M., Malbec, L.-M., Toda, H. B., & Bruneaux, G. (2017). A study on the interaction between local flow and flame structure for mixing-controlled Diesel sprays. Combustion and Flame, 179, 157-171. doi:10.1016/j.combustflame.2017.01.023Han, D., & Mungal, M. . (2001). Direct measurement of entrainment in reacting/nonreacting turbulent jets. Combustion and Flame, 124(3), 370-386. doi:10.1016/s0010-2180(00)00211-xHill, B. J. (1972). Measurement of local entrainment rate in the initial region of axisymmetric turbulent air jets. Journal of Fluid Mechanics, 51(4), 773-779. doi:10.1017/s0022112072001351Post, S., Iyer, V., & Abraham, J. (1999). A Study of Near-Field Entrainment in Gas Jets and Sprays Under Diesel Conditions. Journal of Fluids Engineering, 122(2), 385-395. doi:10.1115/1.48326

    Comparison of different techniques for characterizing the diesel injector internal dimensions

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    [EN] The geometry of certain parts of diesel injectors is key to the injection, atomization and fuel-air mixing phenomena. Small variations on the geometrical parameters may have a strong influence on the aforementioned processes. Thus, OEMs need to assess their manufacturing tolerances, whereas researchers in the field (both experimentalists and modelers) rely on the accuracy of a certain metrology technique for their studies. In the current paper, an investigation of the capability of different experimental techniques to determine the geometry of a modern diesel fuel injector has been performed. For this purpose, three main elements of the injector have been evaluated: the control volume inlet and outlet orifices, together with the nozzle orifices. While the direct observation of the samples through an optical microscope is only possible for the simplest pieces, both Computed Tomography Scanning and the visualization of silicone molds technique have proven their ability to characterize the most complex internal shapes corresponding to the internal injector elements. Indeed, results indicate that the differences observed among these methodologies for the determination of the control volume inlet orifice diameter and the nozzle orifice dimensions are smaller than the uncertainties related to the experimental techniques, showing that they are both equally accurate. This implies that the choice of a given technique for the particular application of determining the geometry of diesel injectors can be done on the basis of availability, intrusion and costs, rather than on its accuracy.This work was partly sponsored by "Ministerio de Economia y Competitividad", of the Spanish Government, in the frame of the Project "Estudio de la interaccion chorro-pared en condiciones realistas de motor", Reference TRA2015-67679-c2-1-R.Salvador, FJ.; Gimeno, J.; De La Morena, J.; Carreres, M. (2018). Comparison of different techniques for characterizing the diesel injector internal dimensions. Experimental Techniques. 42(5):467-472. https://doi.org/10.1007/s40799-018-0246-1S467472425Mobasheri R, Peng Z, Mostafa S (2012) Analysis the effect of advanced injection strategies on engine performance and pollutant emissions in a heavy duty DI-diesel engine by CFD modeling. Int J Heat Fluid Flow 33(1):59–69Dhar A, Agarwal AK (2015) Experimental investigations of the effect of pilot injection on performance, emissions and combustion characteristics of Karanja biodiesel fuelled CRDI engine. Energy Convers Manag 93:357–366Mohan B, Yang W, Chou SK (2013) Fuel injection strategies for performance improvement and emissions reduction in compression ignition engines—a review. Renew Sust Energ Rev 28(x):664–676Petrovic V, Bracanovic Z, Grozdanic B, Petrovic S, Sazhin S, Knezevic D (2015) The design of a full flow dilution tunnel with a critical flow venturi for the measurement of diesel engine particulate emission. FME Trans 43(2):99–106Ilić Z, Rasuo B, Jovanović M, Janković D (2013) Impact of changing quality of air/fuel mixture during flight of a piston engine aircraft with respect to vibration low frequency spectrum. FME Trans 41(1):25–32Luján JM, Tormos B, Salvador FJ, Galgar K (2009) Comparative analysis of a DI diesel engine fuelled with biodiesel blends during the European MVEG-A cycle: Preliminaru study I. Biomass & Bioenergy 33(6–7):941–947Postrioti L, Mariani F, Battistoni M (2012) Experimental and numerical momentum flux evaluation of high pressure diesel spray. Fuel 98:149–163Payri R, Salvador FJ, Gimeno J, Venegas O (2016) A technique to match the refractive index of different diesel fuels with the refractive index of transparent materials to improve the experimental visualization. Exp Tech 40(1):261–269Duran SP, Porter JM, Parker TE (2015) Ballistic imaging of diesel sprays using a picosecond laser: characterization and demonstration. Appl Opt 54(7):1743Payri R, Salvador FJ, Gimeno J et al (2011) Flow regime effects on non-cavitating injection nozzles over spray behavior. Int J Heat Fluid Flow 32(1):273–284Koukouvinis P, Gavaises M, Li J, Wang L (2016) Large Eddy simulation of diesel injector including cavitation effects and correlation to erosion damage. Fuel 175:26–39Som S, Aggarwal SK (2010) Effects of primary breakup modeling on spray and combustion characteristics of compression ignition engines. Combust Flame 157(6):1179–1193Salvador FJ, De la Morena J, Martínez-López J, Jaramillo D (2017) Assessment of compressibility effects on internal nozzle flow in diesel injectors at very high injection pressures. Energy Convers Manag 132:221–230Salvador FJ, Gimeno J, de la Morena J, Martí-Aldaraví P (2012) Using one-dimensional modelling to analyze the influence of the use of biodiesels on the dynamic behaviour of solenoid-operated injectors in common rail systems: Results of the simulation and discussion. Energy Convers Manag 54(1):122–132Taghavifar H, Khalilarya S, Jafarmadar S, Baghery F (2016) 3-D numerical consideration of nozzle structure on combustion and emission characteristics of DI diesel injector. Appl Math Model 40(19–20):8630–8646Edelbauer W (2017) Numerical simulation of cavitating injector flow and liquid spray break-up by combination of Eulerian–Eulerian and volume-of-fluid methods. Comput Fluids 144:19–33Salvador FJ, Carreres M, Jaramillo D, Martínez-López J (2015) Comparison of microsac and VCO diesel injector nozzles in terms of internal nozzle flow characteristics. Energy Convers Manag 103:284–299Salvador FJ, Martínez-López J, Romero JV, Roselló MD (2013) Study of the influence of the needle eccentricity on the internal flow in diesel injector nozzles by computational fluid dynamics calculations. Int J Comput Math 91, no. June:24–31Payri R, Salvador FJ, Carreres M, De la Morena J (Apr. 2016) Fuel temperature influence on the performance of a last generation common-rail diesel ballistic injector. Part II: 1D model development, validation and analysis. Energy Convers Manag 114:376–391Salvador FJ, Hoyas S, Novella R, Martinez-López J (2011) Numerical simulation and extended validation of two-phase compressible flow in diesel injector nozzles. Proc Inst Mech Eng Part-D-J Automob Eng 225(D4):545–563Satkoski C, Shaver G (2011) Piezoelectric fuel injection: pulse-to-pulse coupling and flow rate estimation. IEEE/ASME Trans Mechatron 16(4):627–642Ferrari A, Mittica A (2016) Response of different injector typologies to dwell time variations and a hydraulic analysis of closely-coupled and continuous rate shaping injection schedules. Appl Energy 169:899–911Payri R, Salvador FJ, Gimeno J, De la Morena J (2011) Analysis of diesel spray atomization by means of a near-nozzle field visualization technique. At Sprays 21(9):753–774Li T, Moon S, Sato K, Yokohata H (Feb. 2017) A comprehensive study on the factors affecting near-nozzle spray dynamics of multi-hole GDI injectors. Fuel 190:292–302Yu W, Yang W, Zhao F (2017) Investigation of internal nozzle flow, spray and combustion characteristics fueled with diesel, gasoline and wide distillation fuel (WDF) based on a piezoelectric injector and a direct injection compression ignition engine. Appl Therm Eng 114:905–920Salvador FJ, Carreres M, Crialesi-Esposito M, Plazas AH (2017) Determination of critical operating and geometrical parameters in diesel injectors through one dimensional modelling, design of experiments and an analysis of variance. Proc Inst Mech Eng Part D J Automob EngMacian V, Bermúdez V, Payri R, Gimeno J (2003) New technique for determination of internal geometry of a diesel nozzle with the use of silicone methodology. Exp Tech 27, no April:39–43Piano A, Millo F, Postrioti L, Biscontini G, Cavicchi A, and Pesce FC, (2016) “Numerical and experimental assessment of a solenoid common-rail injector operation with advanced injection strategies,” SAE Int J Engines 9(1)Mitroglou N, Lorenzi M, Santini M, Gavaises M (2016) Application of X-ray micro-computed tomography on high-speed cavitating diesel fuel flows. Exp Fluids 57(11):1–14Kastengren AL, Tilocco FZ, Powell CF, Manin J, Pickett LM, Payri R, Bazyn T (2012) Engine combustion network (ECN): measurements of nozzle geometry and hydraulic behavior. At Sprays 22(12):1011–1052Otsu N (1979) A threshold selection method from gray-level histograms. IEEE Trans Syst Man Cybern 9(1):62–6

    Gaseous jet through an outward opening injector: Details of mixing characteristic and turbulence scales

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    Direct injection (DI) strategy of natural gas (NG) into internal combustion engines (ICE) has led to higher thermal efficiency and lower exhaust emissions. In order to thoroughly understand the most relevant phenomena affecting the performances of such engines, computational fluid dynamics (CFD) plays a key role as an accurate description of the jet evolution and interaction within the combustion chamber is required to that aim. Accurate description of high-pressure gaseous jets is rather challenging at high Mach numbers, as the injected gas is strongly under-expanded once in the ambient, giving room to shocks due to compressibility effects. Also the interaction between shock waves and mixing layers needs to be carefully represented with a multi-dimensional model, calling for substantial computational resources requirements. In this paper a numerical investigation of the behavior of a gaseous jet (Argon) through an outward opening injector has been carried out. A Large Eddy Simulation (LES) approach has been used in order to track the structures derived by the interaction of the injected fuel with the surrounding ambient. Although already good results were obtained using a Reynolds Averaged Navier-Stokes (RANS) approach, the adoption of LES is required to characterize more accurately the jet properties in terms of vortex structures and mixing effectiveness. The effect of the Nozzle Pressure Ratio (NPR) on the jet evolution has been highlighted in the paper, showing how a higher NPR would give a faster injection process, compromising however the homogeneity of the mixture

    An experimental investigation of gas fuel injection with X-ray radiography

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    In this work, an outward-opening compressed natural gas, direct injection fuel injector has been studied with single-shot X-ray radiography. Three dimensional simulations have also been performed to compliment the X-ray data. Argon was used as a surrogate gas for experimental and safety reasons. This technique allows the acquisition of a quantitative mapping of the ensemble-average and standard deviation of the projected density throughout the injection event. Two dimensional, ensemble average and standard deviation data are presented to investigate the quasi-steady-state behavior of the jet. Upstream of the stagnation zone, minimal shot-to-shot variation is observed. Downstream of the stagnation zone, bulk mixing is observed as the jet transitions to a subsonic turbulent jet. From the time averaged data, individual slices at all downstream locations are extracted and an Abel inversion was performed to compute the radial density distribution, which was interpolated to create three dimensional visualizations. The Abel reconstructions reveal that upstream of the stagnation zone, the gas forms an annulus with high argon density and large density gradients. Inside this annulus, a recirculation region with low argon density exists. Downstream, the jet transitions to a fully turbulent jet with Gaussian argon density distributions. This experimental data is intended to serve as a quantitative benchmark for simulations. (C) 2017 Elsevier Inc. All rights reserved
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