URANS and SAS analysis of flow dynamics in a GDI nozzle

Transcription

1 , 3rd Annual Conference on Liquid Atomization and Spray Systems, Brno, Czech Republic, September 010 J.-M. Shi*, K. Wenzlawski*, J. Helie, H. Nuglisch, J. Cousin * Continental Automotive GmbH Siemensstr. 1, Regensburg, Germany Continental Automotive SAS 1 av. Paul Ourliac BP 1149, Toulouse Cedex 1, France Coria INSA de Rouen, Campus du Madrillet - BP 8, Saint Etienne du Rouvray cedex, France Abstract URANS and SAS analysis of turbulent flow in a GDI nozzle was carried out. The vortex structures, velocity and pressure distributions predicted based on the two different approaches were compared both for instant and statistical values. FFT analysis was applied to the time series of mass flow rate, the velocity, pressure and turbulence quantities at monitoring points. Only one dominant frequency was predicted by the URANS approach using the SST turbulence model. A clear correlation was found among the frequency of the mass flow rate, pressure and velocity at monitor points. In contrast, SAS predicted multiple frequencies. Though no simple correlation was obtained, the frequency of big event in mass flow time series was found to be linked to the first dominant frequency of the pressure monitors. Introduction The quality of spray and mixture formation in engine can be very different from fuel injection nozzle A to nozzle B even under the same operating conditions. This indicates a strong effect of the in-nozzle flow on spray formation. This work is an effort in pursuing understanding about the link between nozzle internal flow and spray formation. For this purpose, high resolution zoomed spray visualization study in the proximity of the nozzle exit for a three-hole GDI injector were carried out at CORIA in cooperation with Continental Automotive. The liquid ligaments in the process of primary breakup are clearly recognizable under an injection pressure up to 0bar. The obtained shot-to-shot spray images indicate that there exist multiple frequencies in the primary breakup process. The simulation work reported here was to find the link between the in-nozzle flow and the primary breakup frequencies in order to obtain new understanding of atomization mechanism. The flow in a fuel injection nozzle is characterized by high shear strain rate, high flow acceleration and deceleration, and high pressure gradient linked with throttle geometries. Therefore, vortex generation and their dynamics in the nozzle is the key point to understand the flow dynamics. The simulation work was based on the commercial CFD solver ANSYS-CFX1.0. The URANS approach based on the k-omega SST model [1] and the Scale-Adaptive-Simulation (SAS) approach [] were applied. The latter is also a RANS modelling approach but with a DES-like capability, allowing to resolve the turbulence vortex structures in the region where the mesh size is below the local physical turbulence scale. In this paper, we present a case study for the injection pressure 10 bar. The experience we made in house and also in literature [4] is that simulation of turbulent cavitating flow in fuel injection nozzle is very sensitive to cavitation modelling. Here we restricted our study to deal with the single-phase flow without considering cavitation. Best practice study for the mesh size and time step dependence were carried out. Instant results and time average and RMS values of field variables and monitor quantities were compared for 3 different computational grids. FFT analysis was applied to the time series of mass flow rate, the velocity, pressure and turbulence quantities at monitoring points. Correlation or link between the mass flow rate, pressure monitors, and the vortex motion was examined. The spray visualization study is still on going in order to obtain a reliable statistics for the primary breakup frequencies. Here we mainly report the results from the numerical study. Simulation model and Numerical methods The nozzle is axis-symmetrical with three injection holes. A 10 -sector geometrical model was adopted in simulation and a cyclic period condition was applied at the sector boundaries (see Figure 1, left). Three monitoring points were defined (see Figure 1, right) in order to get time series of the local velocity, pressure, and turbulence variables. The fluid applied was n-heptane, with a density 680 kg/m 3 and a viscosity 3.885e-4 Pa s. Neglecting the cavitation model, a single phase turbulent flow problem of incompressible fluid was considered. The Corresponding author: Junmei.Shi@continental-corporation.com 1

2 commercial flow solver ANSYS-CFX1.0 was applied to the investigation. Both URANS simulation based on the k-ω SST two-equation model [1] and Scale-Resolved simulation based on the SST-SAS modelling [] were carried out. The SAS model is also based on the RANS two-equation modelling approach, but with a DES-like capability. A detailed description of the CFX SST-SAS model could be found in [3]. This model differs from the SST-RANS model by an additional SAS source term Q SAS in the transport equation for the turbulence eddy frequency ω, Q SAS L k k C max,,0 max S (1) L vk k Where S is the shear strain rate, k is the turbulence kinetic energy, 1 modelled turbulence and vk max S / U, CS L k / C 1/ 4 is the length scale of the L is the von Karman length scale corresponding to a three 1 S dimensional generalisation of the classic boundary layer thickness definition U ( y) / U ( y). Here the coefficient C times the local mesh size is introduced as the lower limiter for L vk to control damping of the finest resolved turbulent fluctuations as in LES. This limiter was derived from the consideration of preventing the SAS SAS eddy viscosity ( C L ) S from decreasing below the LES Smagorinsky subgrid-scale eddy viscos- LES t vk ity t ( C S ) S. The CFX SAS implementation adopts a second order upwind scheme in RANS regions and a second order central scheme in the LES region. Three meshes with about 0.9 M, 1.6 M and 3.0 M hexa cells (Figure ) were prepared for the analysis. Best Practice study for mesh size and time step were carried out. Vortex structure, velocity and pressure distribution from the two approaches were compared each other in terms of instant, time averaged values and the standard deviations. FFT analysis was applied to get frequencies of mass flow rate, velocity, pressure and turbulence quantities at various monitoring points as displayed in Figure 1. Correlation or link between the mass flow rate, pressure monitors, and the vortex motion was examined. total pressure 11 bar Sac center Injection hole entrance center cyclic cyclic opening static pressure 1 bar Outlet center Figure 1. Computational domain, boundary conditions (left) & monitoring points (right) Figure. Computational meshes at injection hole outlet, the total mesh size is from left to right 0.9M, 1.6M, 3.0M cells, respectively

3 Results and Discussion Vortex visualization Vortex structures and their dynamics are the key points to capture the flow dynamics. The instant vortex cores in the nozzle from the SAS analysis using the 0.9M mesh are visualized in Figure 3 by applying the nd Q V V invariant of the velocity gradient tensor,. Three counter-rotating vortex pairs, which enter the injection hole from the sac-volume, can be observed. The ring vortices mainly linked to the flow separation due to the sudden expansion of the geometry in the sac. The sac vortex pairs are caused by flow acceleration when the fluid is entering the injection hole from the sac volume. Strong vortices separating from the needle surface in the region direct over the injection hole entrance were also predicted. Needle shear vortices needle separation vortices linked to injection hole Ring vortex separated from needle Ring vortex at sac wall Ring vortex separated from needle sac vortex due to flow acceleration sac bottom vortex due to flow acceleration sac vortex due to flow acceleration Figure 3. Vortex core visualization in the nozzle, Q=.5e11 [s - ], SST 0.9M mesh. Figure 4 compares the instant vortices in sac volume for the SST and the SAS results of various meshes, where the iso-surfaces are coloured by the pressure values from 0 to 10 bar. For the coarse mesh of 0.9 M cells the SAS approach and the SST model predicted similar sac vortex structures to each other, with some smaller vortices in the region direct over the injection hole entrance observed in the SAS results (Figure 4 a-b). With increasing mesh refinement (Figure 4 c-d) the SAS approach predicted many fine-scale vortices instead of the big ring vortices in the corresponding region as observed in Figure 3 or in Figure 4 a-b). The flow is relatively inactive in the sac centre. Hence similar vortex structures were obtained for all cases. A comparison of instant vortices in injection hole is presented in Figure 5, where the Q iso-surfaces are coloured by the pressure in the range from - bar (blue) to bar (red). Negative pressure is predicted in the vortex cores in injection hole, which is a consequence of neglecting cavitation in the present simulation model and can be considered as an indication of cavitation occurrence. The results indicate strong vortex cavitation in the injection hole. With reference to these vortex structures it can be expected that the SAS and the URANS-SST approach are to predict very different vortex structures and thus different vortex cavitation behaviour and different flow dynamics. Also, the results displayed in Figure 6 for the instant pressure distribution at the symmetrical plane of the injection hole indicate that the vortex cavitation prediction is sensitive to the mesh resolution. a) SST, 0.9M mesh Q=0.81e1 [s - ] b) SAS, 0.9M mesh Q=1.44e1 [s - ] c) SAS, 1.6M mesh Q=1.44e1 [s - ] Figure 4. Vortices in sac-volume coloured by pressure in the range 0-10 bar d) SAS, 3.0M mesh Q=1.44e1 [s - ] 3

4 a) SST, 0.9M mesh Q=0.81e1 [s - ] b) SAS, 0.9M mesh c) SAS, 1.6M mesh Q=.5e1 [s - ] Q=.5e1 [s - ] Figure 5. Vortices in injection hole coloured by pressure in the range - bar to bar d) SAS, 3.0M mesh Q=.5e1 [s - ] a) SST, 0.9M mesh b) SAS, 0.9M mesh c) SAS, 1.6M mesh d) SAS, 3.0M mesh Figure 6. Instant pressure at symmetrical plane coloured by pressure values in the range - bar to bar The corresponding time averaged vortex structures are displayed in Figure 8, coloured according to the pressure fluctuation. The time averaged vortex structures in the sac volume are alike to each other and the ring vortices as observed in Figure 3 are again recognizable in the statistics sense of the SAS results (Figure 7, top). In contrast, the time statistical vortex structures in injection hole are less similar between the SAS and SST results. The time mean vortex cores in SST simulation are similar to the instant vortices in Figure 5, with long and smooth Q iso-surfaces. Due to multiple scale vortices with higher fluctuations were resolved in SAS, the time average of the vortex cores are much shorter and more irregular than in SST (Figure 7, bottom). This difference is also reflected in the time averaged pressure distribution over the symmetrical plane of the injection hole presented in Figure 8. However, these averaged pressure distributions show very similar pattern in all cases, and are similar to the instant SST results presented in Figure 6. That suggests, URANS simulation is sufficient to capture the mean flow features in the statistical sense. a) SST, 0.9M mesh b) SAS, 0.9M mesh c) SAS, 1.6M mesh d) SAS, 3.0M mesh Figure 7. Time averaged vortex structures in sac-volume (top, coloured by standard pressure deviation bar) and in injection hole (bottom, coloured by standard pressure deviation 0-4 bar), Q=0.81e1 [s - ] In comparison, the colour of the iso-surfaces in Figure 7 indicate that the SAS approach predicted much higher fluctuations than the SST model both in the sac volume and in injection hole. The standard deviation of pressure and velocity over the symmetrical plane, displayed in Figure 9 and Figure 10, also confirm this conclusion. With a reference to Figure 5, Figure 7, Figure 8, Figure 9 and Figure 10 together, it can be concluded that 4

5 the strongest vortices in the injection hole and the strongest flow fluctuation as well occur in the centre region of the injection hole. a) SST, 0.9M mesh b) SAS, 0.9M mesh c) SAS, 1.6M mesh d) SAS, 3.0M mesh Figure 8. Time averaged pressure at symmetrical plane a) SST, 0.9M mesh b) SAS, 0.9M mesh c) SAS, 1.6M mesh d) SAS, 3.0M mesh Figure 9. Standard deviation of pressure over symmetrical plane, 0-4bar a) SST, 0.9M mesh b) SAS, 0.9M mesh c) SAS, 1.6M mesh d) SAS, 3.0M mesh Figure 10. Standard deviation of velocity over symmetrical plane, 0-30 m/s Time series of monitors Time series were recorded for the local velocity, pressure, turbulence quantities at the monitor points (refer to Figure 1) and for the mass flow rate weighted average of turbulence kinetic energy, eddy viscosity, and turbulence length scale at the injection hole exit. As an example, a section of results for the mass flow rate and sac centre pressure are demonstrated in Figure 11. The SST time series are quite regular and seem to correlate each other. In comparison the SAS results are very irregular, show multiple frequencies. No simple correlation between the mass flow rate and the sac centre pressure can be observed in SAS. Mass flow rate Mass flow rate Sac center pressure Sac center pressure 140 Time step a) SST, 0.9M mesh b) SAS, 1.6M mesh Figure 11. Time series of monitored quantities Time step 5

6 The arithmetic mean value of the monitoring quantities and the corresponding relative fluctuations based on the standard deviations are summarized in Table 1. The mean values from SAS show a convergence trend with increasing mesh refinement. Especially, the average values of the modelled turbulence quantities at the nozzle outlet in SAS 1.6M mesh and in SAS 3.0M mesh are almost identical. This indicates a sufficient grid resolution. The standard deviation values also show the similar trend except for the value of pressure monitor at the injection hole entrance centre. Considering that turbulence eddies larger than the mesh size is direct resolved in SAS, the predicted (modelled) turbulence kinetic energy in SAS is much lower than the corresponding SST results. The eddy viscosity in the SST simulation is two orders higher than the molecular viscosity. The modelled eddy viscosity in SAS is about one order lower than the value from SST. The average length scale of the modelled turbulence is about 10 μm in SAS, which is about one fourth of the corresponding SST result. In addition, the standard deviations are much higher in the SAS results, indicating higher fluctuations predicted by the SAS approach. That is consistent with those results shown in Figure 7, Figure 9 and Figure 10. Parameter Table 1. Mean and standard deviation values of the monitors SST 0.9M Time mean value SAS 0.9M SAS 1.6M SAS 3.0M Standard deviation / Time mean * 100% SST SAS SAS SAS 0.9M 0.9M 1.6M 3.0M Mass flow rate [g/s] Average modelled turbulence length [mm] Average modelled turbulence kinetic [J/kg] Average modelled eddy [Pa s] 4.e- 1.e- 9.76e e e- 4.e-3 3.3e-3 3.3e Sac-center [bar] injection hole entrance center [bar] Velocity center [m/s] Velocity center [m/s] FFT analysis of monitor time series FFT analysis was applied to the time series of the monitor quantities. First, statistical convergence of the power spectrum was examined. An example is demonstrated in Figure 1 for the time series of the mass flow rate from the SST simulation. Here a main frequency of 1.6 khz was obtained, corresponding to a time period of 4.6e-5 [s]. The power spectrum can be considered as converged when the time reaches 5.55e-4 [s], corresponding to 1 time period. Therefore, a time interval larger than 10 time periods is necessary in order to get a converged FFT analysis result. P o w e r Time = 0 to 3.33e-4 [s] Time = 0 to 4.44e-4 [s] S p e c t r u m Frequency [khz] Figure 1. Convergence examination for FFT analysis of the mass flow rate time series from SST simulation using 0.9M mesh. The results indicate that 10 periods of time is needed to get a converged power spectrum 6 Time = 0 to 5.55e-4 [s] Time = 0 to 8.33e-4 [s] Time = 0 to 11.11e-4 [s]

7 The results for the URANS simulation based SST model are presented in Figure 13. A dominant frequency of 1.6 khz is predicted for all the monitor quantities. This result is to expect in the RANS modelling, which can only resolve one scale. The interesting thing is the clear correlation among all these monitors of different locations. A mono frequency for all the monitors as predicted by the SST model was not predicted in SAS. It was found that the frequencies of the mass flow rate fluctuation are well correlated to the monitors located in the sac centre, as is displayed in Figure 14. Here two main frequencies, 1.5 khz and 5 khz, were predicted. In order to capture the main frequency of the flow, we evaluated the big events in pressure fluctuation at the sac centre (shown in Figure 15). The results are shown in Figure 16. It was found that the frequency 5 khz is the dominant frequency in the pressure fluctuation and in the relatively stronger vortex shedding from the needle. In addition, the vortex structures in the injection hole predicted by SAS are shown in Figure 17. More fine scale vortices can generally be observed in the injection hole at the time points of low mass flow rate. It needs to point out that the above work was restricted to single phase flow model. The flow frequencies in mass flow rate can be very different if the cavitation model is included. In addition, the spray visualization work is still on going at Continental Automotive. A comparison between simulation and measurement is planned. Conclusion The present URANS and SAS analysis has revealed the vortex structures in a GDI nozzle. The results allow draw the following conclusions: The URANS approach based on the SST model can only resolve one scale, while the SAS model can resolve multiple scales using mesh refinement. The SST and SAS model predicted very different instant vortex structures in the nozzle. Thus it is to expect, both model will produce very different results for vortex induced cavitation in injection hole. The both models were found to produce similar time averaged vortex structures in the sac-volume, but the SAS model predicted much higher fluctuations than the SST model. A mono flow frequency and a clear correlation between the mass flow rate and all the monitors were predicted by the SST model. In comparison, multiple frequencies were obtained in SAS. The overall correlation predicted by the SST model was not observed in SAS. Acknowledgement The authors would like to thank the internship students Mr. Ivan Krotow and Mr. Madhukar Kulkarni for the assistance with the post-processing and FFT analysis. The simulations were performed on the High Performance Computers at RRZE in the framework of cooperation with Prof. Dr.-Ing. Michael Wensing at University of Erlangen, which together with the support of Dr.- Ing. Thomas Zeiser at RRZE and is gratefully acknowledged. References [1] Menter, F.R., Zonal two equation k-ω turbulence models for aerodynamic flows, AIAA Paper (1993). [] Menter, F.R., and Egorov, Y., A scale adaptive simulation model using two-equation models, AIAA Paper (006). [3] Menter, F.R., and Egorov, Y., Development and application of SST-SAS turbulence model in the DESIDER Project, Second Symposium on Hybrid RANS-LES Methods, 17/18 June 007, Corfu, Greece. [4] Giannadakis E., Papoulias D., Gavaises M., Arcoumanis C., Soteriou C. and Tang W., Evaluation of the predictive capability of Diesel nozzle cavitation models, SAE

8 Outlet mass flow rate 1.6 khz Sac-center total pressure Inj. hole entrance center total pressure Inj. hole entrance center velocity U Inj. hole entrance center velocity V Inj. hole entrance center velocity W Inj. hole entrance center turbulence kinetic energy Inj. hole entrance center eddy viscosity Outlet center total pressure Outlet center velocity U Outlet center velocity V Outlet center velocity W Outlet center turbulence kinetic energy Outlet center eddy viscosity Frequency [khz] Figure 13. FFT analysis results for the time series of monitors: SST 0.9M mesh 8

9 P o w e r S p e c t r u m 1.5 khz 5 khz Mass flow rate Turbulence kinetic energy Eddy viscosity Turbulence length scale Frequency [khz] Figure 14. Correlation between the frequency of mass flow rate and the monitor quantities at sac centre [ms] Figure 15. Big events evaluation for the sac centre pressure fluctuation 1 [khz] [khz] Figure 16. Big events frequency distribution in sac centre pressure (left) and mass flow rate (right) 9

10 a) low mass flow rate b) high mass flow rate Figure 17. Vortex structures at low and high mass flow rate time points, indicating more fine scales in the injection hole at low mass flow rate 10