Large-Eddy Simulation of Cavitating Turbulent Flows in Fuel Injection Systems
Theresa Trummler, Steffen Schmidt
Chair of Aerodynamics and Fluid Mechanics, Technische Universität München
Local Project ID:
HPC Platform used:
SuperMUC, Phase I and II
Recent developments in direct Diesel and gasoline injection systems aim at increasing the rail pressures, to more than 3000 bar and 1000 bar respectively, to enhance liquid break-up and mixing which in turn improves combustion and reduces emissions. Higher flow accelerations, however, imply thermo-hydrodynamic effects, such as cavitation, which occurs when the pressure locally drops below saturation conditions and the liquid vaporizes. The subsequent collapse of such vapor structures, when convected into regions of higher pressure, causes the emission of strong shock-waves. High-velocity liquid jets directed towards nearby wall surfaces are created. Structure loads induced by such phenomena lead to material erosion, but are also employed to clean injection nozzles from surface deposits, and can promote primary jet break-up. Furthermore, flow cavitation can lead to choked conditions in a nozzle and thus maintains a pressure-drop independent mass flow rate. Surface erosion due to cavitation may be so strong that injection performance degrades severely or devices may fail.
Typically, characteristic dimensions of fuel channels inside Diesel injectors lie in the range of tens to several hundred microns. This strongly restricts the instrumentation of an injection nozzle with diagnostic equipment, such as optical measurement methods or pressure sensors, for experimental flow characterization. In addition, the high operational pressures state another limiting factor. Short intrinsic timescales imposed by inherent flow dynamics, by functional components such as open or closing of the control valve or injector needle, or by multiple injections per engine cycle, make time-accurate measurements challenging. Therefore, experimental analysis assessing cavitation erosion can usually supply information about incubation time, position, and the progress of erosion damage, but does not necessarily reveal the underlying flow mechanism, which would be desirable for identification of possible countermeasures and optimization. Computational Fluid Dynamics (CFD), on the other hand, may be used to investigate real-size geometries and flow structures in a time-accurate manner. CFD thus have the potential to become an important tool in the design process.
Description of the Project
The present research project focuses on the prediction of cavitation erosion in fuel injection systems using a CFD approach. Wave dynamics, interaction of cavitation and turbulence as well as flow transients due to moving geometries have important effects on cavitation erosion and need to be accounted for. Moreover, the mutual interaction of cavitation and spray break-up are investigated.
(1): Mutual interaction between turbulence and cavitation
Objective (1) was investigated by performing LES of spatially developing cavitating turbulent mixing layers and wall-resolved LES of the flow through a generic throttle.
The results of this investigation have been published in “Physics of Fluids” (Large-eddy simulation of turbulent cavitating flow in a micro channel by Egerer et al. ). Fig. 1 visualizes the interaction between turbulence and cavitation in a micro-channel featuring two different cavitation regimes.
(2): Effect of cavitation on spray break up
To investigate the effect of cavitation inside injection nozzles and its influence on the subsequent primary jet breakup, we implemented a model for a gas-water-vapor mixture. The model is based on an additional transport equation for the free gas component in the flow solver. The mass fraction for the gas content is transported using a second-order scheme to maintain a low numerical diffusivity and a sharp interface but also to ensure good computational performance. Results of this investigation have been published in “Physics of Fluids” (Large-eddy simulation of cavitating nozzle flow and primary jet break-up by Örley et al. ) and in  as part of a book chapter. Moreover, they were presented at two international conferences [9,13]. Fig. 2 visualizes the effect of strong cavitation on the jet characteristics.
During the last project phase, we have implemented this thermodynamic multi-component model proposed by Örley et al. into the in-house code CATUM with an efficient implicit LES for compact stencils . Furthermore, we improved and validated the thermodynamic modeling by introducing a thermodynamically fully consistent reconstruction scheme and extending the sensor functionals. A detailed description of the model extensions and its validation can be found in .
We performed high resolution simulations of four operating points of a reference experiment. Using the flow field data available for this experiment, we could successfully validate our thermodynamical gas model and the LES approach. The simulation results were then used to investigate the cavitation dynamics in the nozzle, the interaction of cavitation, mass flux and spray characteristics and to further evaluate the effects of partial gas entrainment. Fig. 3 depicts a time series with partial gas entrainment into the nozzle for an operating point featuring stronger cavitation. Our simulation results reveal that partial gas entrainment into the nozzle is one of the driving mechanisms for fluctuations close to the nozzle outlet and the increase of the spray angle. Furthermore, gas entrainment can lead to a sudden drop in the mass flux at the nozzle outlet. In case of strong gas entrainment, the gas can affect the cavitation dynamics by suppressing vapor formation or damp the intensity of collapses.
The results of this investigation are published in Atomization and Sprays  and were presented at several international conferences [12, 14,15].
(3): Analysis of the shedding dynamics and shedding mechanisms in cavitating nozzle flows
In cavitating nozzle flows, such as the above mentioned investigations [1, 3, 6], clouds are shed periodically at the end of the vapor sheet. This shedding process is initiated either by the motion of a liquid re-entrant jet or a condensation shock. Cloud cavitation in nozzles interacts with the flow field in the nozzle, the mass flow and the spray break- up and can cause erosion damage. Using our highly resolved LES results, we study the process of cloud cavitation shedding, the re-entrant jet and the condensation shocks in a scaled-up generic step nozzle with injection into gas. The time-resolved three-dimensional LES results covering several shedding cycles provide deeper insight into the flow field, and the shedding matches experimentally derived cloud shedding models. We observe that at lower cavitation numbers, shedding is initiated by condensation shocks, which has not yet been reported for nozzle flows with a constant cross-section. Additionally, we analyze the upstream flow in and beneath the vapor sheet in detail and provide spatially and temporally resolved data on the velocity and height of this flow. The results of this analysis are published in the International Journal of Multiphase Flow .
(4): Numerical assessment of cavitation and cavitation erosion in realistic injector geometries including dynamic needle movement
In order to control the effects of cavitation inside a realistic Diesel injector and their influence on the jet and spray characteristics when injected into a gas phase, a detailed understanding of flow phenomena is necessary. Therefore, moving boundaries were implemented in the CFD code INCA  and enabled us to asses the effect of moving bodies on the flow during an injection cycle. Within this project, Örley et al. [5,10] have performed Large-eddy simulations of turbulent, cavitating fuel flow inside a 9-hole Diesel injector including needle movement. Fig. 4 shows coherent vortical structures of the main injection phase.
(5): Evaluation of the effect of full-thermodynamic modeling on the cavitating flow and the numerical erosion prediction for a realistic injector
In this numerical study the effects of the full-thermodynamic modeling on the cavitating dynamics and the erosion potential are investigated. Large-eddy simulations of one-eighth of a typical 8-hole Diesel injector using barotropic and full-thermodynamic pre-computed tables are performed. Therefore we use a thermodynamic database (REFPROP) to create precomputed 1-D barotropic and 2-D full-thermodynamic tables for pure liquid and pure vapor states and values of the corresponding pressure, temperature, density, and internal energy in the mixture region. The speed of sound, the viscosity, and the thermal conductivity in the mixture region are modeled.
Fig. 5 depicts results of the full-thermodynamic simulation. We found that the cavitation dynamics for the full-thermodynamic case are faster as the frequencies of the inflow and outflow mass flow rates are higher. Both cases do not predict erosive events close to the material surface – which is in agreement with the experimental findings of Delphi Technologies. However, the barotropic simulation shows higher pressure impacts on the walls. Finally, viscous heating is assessed in the case of the full-thermodynamic computation. Due to viscous forces in the fluid, it is heating up near the adiabatic walls. At the exit of the spray hole, where the heated vapor is mixed with liquid, the average temperature increase is about 30K.
The objective Full thermodynamic modeling was part of the EU-Project CaFE(Development and experimental validation of computational models for Cavitating Flows, surface Erosion damage and material loss, http://cafe-project.eu) Grant Agreement No 642536. Within this EU-project a strong collaboration with Delphi Technologies was held.
 Christian P. Egerer, Stefan Hickel, Steffen J. Schmidt, and Nikolaus A. Adams, 2014. Large-eddy simulation of turbulent cavitating flow in a micro channel, Physics of Fluids 26, 085102 (2014); https://doi.org/10.1063/1.4891325
 Felix Örley, Vito Pasquariello, Stefan Hickel, S., Nikolaus A. Adams, 2015. Cut-element based immersed boundary method for moving geometries in compressible liquid flows with cavitation. Journal of Computational Physics, 283, 1-22. https://doi.org/10.1016/j.jcp.2014.11.028
 Felix Örley, Theresa Trummler, Stefan Hickel, Michael S. Mihatsch, Steffen J. Schmidt, and Nikolaus A. Adams, 2015. Large-eddy simulation of cavitating nozzle flow and primary jet break-up. Physics of Fluids 27, 086101. http://dx.doi.org/10.1063/1.4928701
 Christian P. Egerer, Steffen J. Schmidt, Stefan Hickel, and Nikolaus A. Adams, 2016. Efficient implicit LES method for the simulation of turbulent cavitating flows. Journal of Computational Physics, 316, 453–469. http://doi.org/10.1016/j.jcp.2016.04.021
 Felix Örley, Stefan Hickel, Steffen J. Schmidt, and Nikolaus A. Adams, 2016. Large-Eddy Simulation of turbulent, cavitating fuel flow inside a 9-hole Diesel injector including needle movement. International Journal of Engine Research, 1–17. http://doi.org/10.1177/1468087416643901
 Theresa Trummler, Daniel Rahn, Steffen J. Schmidt, and Nikolaus A. Adams, 2018. Large-eddy simulations of cavitating flow in a step nozzle with injection into gas. Atomization and Sprays, 28(10), 931–955. http://doi.org/10.1615/AtomizSpr.2018027386
 Theresa Trummler, Steffen J. Schmidt, and Nikolaus A. Adams, 2020. Investigation of condensation shocks and re-entrant jet dynamics in a cavitating nozzle flow by Large-Eddy Simulation. International Journal of Multiphase Flow. doi.org/10.1016/j.ijmultiphaseflow.2020.103215
 Polina Gorkh, Steffen J. Schmidt, and Nikolaus A. Adams, 2019. Full thermodynamic simulation of a realistic diesel injector. Cafe-Project. Cavitating Flows, surface Erosion damage and material loss.
 Felix Örley, Theresa Trummler, Stefan Hickel, Michael S. Mihatsch, Steffen J. Schmidt, and Nikolaus A. Adams, 2015. Large-eddy simulation of cavitating nozzle and jet flows. Journal of Physics: Conference Series (656(1), 012096), 2015. http://doi:10.1088/1742-6596/656/1/012096
 Felix Örley, Stefan Hickel, Steffen J. Schmidt, and Nikolaus A. Adams, 2015.LES of cavitating flow inside a Diesel injector including dynamic needle movement. Journal of Physics: Conference Series 656, 012097–5. http://doi.org/10.1088/1742-6596/656/1/012097
 Felix Örley, Theresa Trummler, Michael S. Mihatsch, Steffen J. Schmidt, and Stefan Hickel, 2018. LES of cavitating nozzle and jet flows. In: ERCOFTAC Series. Springer Netherland, 2018, pp- 133-139. https://doi.org/10.1007/978-3-319-63212-4_16
 Theresa Trummler, Daniel Rahn, Steffen J. Schmidt, and Nikolaus A. Adams, 2018. Large-eddy simulation of cavitating nozzle flows and primary jet break-up with gas-entrainment into the nozzle. Proceedings of the 10th International Symposium on Cavitation (CAV2018). http://doi.org/10.1115/1.861851_ch126
 Felix Örley, Theresa Trummler, Stefan Hickel, Michael S. Mihatsch, Steffen J. Schmidt, and Nikolaus A. Adams, 2015. LES of Cavitating Nozzle and Jet Flows. Direct and Large-Eddy Simulation. X, ERCOFTAC Workshop DLES 10, 2015
 Theresa Trummler, Philipp Söntgerath, Steffen J. Schmidt, and Nikolaus A. Adams, 2016. Numerical simulation of cavitating nozzle and jet flows. Colloquium Cavitation and Cavitation-Erosion, Duisburg, Germany, 2016.
 Theresa Trummler, Steffen J. Schmidt, and Nikolaus A. Adams, 2018. Numerical Simulations of Multiphase Flows in Injection Systems and Generic Nozzles. Invited Speaker: PRACE High Performance Computing Summit Week, Ljubljana, Slovenia, 2018. https://events.prace-ri.eu/event/622/images/87-M1774A_PD18_Progr_280518_WEB.pdf
Theresa Trummler, M.Sc.
Lehrstuhl für Aerodynamik und Strömungsmechanik
Technische Universität München
Boltzmannstr. 15, D-85748 Garching bei München (Germany)
e-mail: theresa.trummler [@] tum.de
LRZ project ID: pr86ta