A Detailed Analysis of the Cycle-To-Cycle Variations featured by RANS Engine Modeling

Transcription

1 A Detailed Analysis of the Cycle-To-Cycle Variations featured by RANS Engine Modeling Riccardo Scarcelli 1, Thomas Wallner 1, Keith Richards 2, Eric Pomraning 2, P. Kelly Senecal 2 1 Argonne National Laboratories, Lemont, IL, USA 2 Convergent Science Inc., Madison, WI, USA Introduction The accurate analysis of cycle-to-cycle variations (CCV) is instrumental in fully evaluating the performance of internal combustion engines (ICEs). However, dealing with cyclefluctuating numerical results is neither easy, nor desirable at times, with particular regard to the industrial engine design process. Reynolds Averaged Navier-Stokes (RANS) modeling is widely used in the automotive industry mostly due to relatively low computational requirements. RANS simulations benefit from the enhanced numerical stability provided by relatively large turbulent viscosity. In addition, RANS simulations are typically run on coarse meshes with upwinded numerical schemes that also enhance stability by adding more numerical viscosity. Large Eddy Simulations (LES) are used to directly calculate some of the turbulent scales and have been proposed for years to evaluate cyclic variability in engines [1, 2]. Several studies are available in literature that compare RANS and LES results, either in terms of engine flow characterization [3] or as a tool to evaluate cyclic variability and combustion stability [4]. It is well understood that LES are more suitable than RANS to describe the stochastic nature of cyclic variability in ICEs. However, RANS has recently shown the capability to capture a certain degree of CCV in engine simulations [5, 6, 7]. These recent findings have tried to shift a paradigm in the multi-dimensional engine modeling community according to which RANS must deliver an ensemble average solution. While for some applications this assumption can still hold true, there are also many turbulent flows for which RANS does not provide an ensemble average result. Therefore, it should not be taken for granted that multi-cycle RANS simulations will feature converging pressure traces after a certain number of consecutive cycles. An unsteady RANS (or URANS) simulation in many cases is not expected to deliver a time-average (or ensemble averaged) result. Furthermore, in a multi-cycle engine simulation, which represents a typical URANS case, each new cycle is naturally perturbed based on the outcome of the previous cycle. The only way multi-cycle RANS can deliver an ensemble-average converged solution is that the natural cyclic perturbation itself is dampened. This paper shows that this is possible if dissipative numerics are used. A gasoline direct injection (GDI) single-cylinder engine is simulated using multi-cycle RANS. It is shown that the degree of cyclic variability shown by RANS simulations depends on the specific operating conditions. The cyclic variability of the in-cylinder pressure traces is related to the variability of the flow properties from one cycle to the next. Such variability can be captured even in motored or cold flow (i.e. in absence of combustion) simulations. This paper shows how the degree of predicted cyclic variability changes as a function of numerical viscosity introduced by mesh size or numerical schemes. It also shows that the modeled and resolved fluctuations of the turbulent parameters can have the same order of magnitude for lowdissipative schemes. This means that regardless of the large turbulent viscosity introduced by RANS, the resolved scales can still show significant fluctuations. Lastly, a typical study on the convergence of statistics shows that RANS results lead to similar conclusions to LES, although the principles of the two formulations are different. The cyclic variability phenomenon in RANS simulations requires careful validation against engine data, which is often shown in terms of average quantities. While stable combustion cases are less likely to show significant CCV, there are combustion systems that operate at the edges of the combustion stability range. For those systems, large CCV might be delivered by RANS. Engine Setup The experimental activities discussed in this study were carried out at Argonne National Laboratory (ANL) on a singlecylinder research engine. The engine design is representative of a modern GDI engine used for automotive applications. Engine specifications are listed in Table 1. The engine has a 4-valve, 40 pent roof combustion chamber design with a central spark plug and injector. Two operating conditions were studied at 2000 RPM, 6 bar IMEP, consisting of one stoichiometric dilute case with 18% EGR (Case 1) and one stoichiometric non-dilute case (Case 2). Table 2 lists the main specification of the two cases examined in this paper. 1

2 Table 1 Specifications of the single cylinder GDI engine at ANL Displacement L Bore mm Stroke mm Compression Ratio 12.1 : 1 Intake Valve MOP 100 CA ATDC Exhaust Valve MOP 255 CA ATDC GDI Injector 6 hole, solenoid Injection Pressure 150 bar Spark system Coil-based, 0.7 mm gap Fuel EPA Tier II EEE Table 2 Specifications of the examined test cases Test Case 1 2 Engine Speed [RPM] IMEP [bar] 6 6 EGR [%] 18 0 Relative air fuel ratio, λ 1 1 Start of Injection (SOI) [ CA ATDC] Fuel mass injected [mg] Spark Advance (SA) [ CA ATDC] Experimental COV IMEP [%] model is used as baseline for our combustion cases, although similar results in terms of CCV were recently shown using the G-equation combustion model [7]. In order to speed up the detailed chemistry solutions, the multi-zone model [9] is used during the combustion event. The computational cells are grouped into zones based on temperature and equivalence ratio in the multi-zone approach. Gasoline direct injection and spark-ignition are simulated using state-of-the-art sub-models, well documented in previous publications [6, 7]. Results and Discussion Cycle-to-cycle variations for combustion cases Figure 1 and Figure 2 show the cyclic variability of the numerical in-cylinder pressure traces for both the GDI cases examined in this study. The numerical dataset includes 21 consecutive cycles for both cases. CFD Setup The CFD code CONVERGE, version 2.1 [8], was used for all simulations performed in this work. Despite the use of a rather coarse base mesh, local mesh embedding and adaptive mesh refinement (AMR) were used to place additional grid resolution where it is needed. Unless otherwise specified, in the cases simulated in this paper the central difference numerical scheme (2 nd order accuracy) is used and base grid is set to 4 mm and additional mesh refinements deliver a local grid size in the order of 0.5 mm (3 levels of refinement) during the gasexchange and combustion phases, and mm (5 levels of refinement) at the spark plug location during the ignition event. AMR and embedding allow achieving such a high mesh resolution with a maximum cell count of less than 2 million cells. As a result, a full engine cycle was simulated in hours on processors. The SAGE detailed chemistry solver [8] is used to simulate gasoline combustion, together with a mechanism for iso-octane consisting of 110 species and 488 reactions and extensively validated for several operating conditions including GDI, port fuel injection (PFI), as well as lean and EGR dilute operation. While the use of direct chemistry to simulate flame propagation in SI engines is non-conventional, recent studies showed that this can be successfully achieved when using fine meshes, as this significantly reduces sub-grid effects [10]. The SAGE Figure 1 Cyclic variability of the pressure traces for Case 1 Figure 2 Cyclic variability of the pressure traces for Case 2 Case 1 is characterized by large CCV and this qualitatively matches the experimental COV IMEP value ( 8%, as listed in 2

3 Table 2). One important thing to notice in Figure 1 is that there is clearly no convergence pattern of the numerical traces. Some typical high-low sequences can be detected and even a severe partial burn (cycle #6) is delivered by simulations. Recent studies show that each of the single cycles fit within the experimental dataset and that the numerical average pressure cycle lies close to the experimental average pressure cycle [7]. Case 2 is characterized by a significantly lower CCV (which qualitatively matches the COV IMEP = 1.4%, as listed in Table 2), and a small fluctuation of the experimental pressure traces around the average value, that matches the experimental counterpart [7]. When an in-depth analysis is carried out to understand the causes of such large variability for Case 1, a great similarity between the in-cylinder pressure traces and the flow properties (in-cylinder tumble and near-spark velocity magnitude) at the time of the spark can be observed, as shown in Figure 3. In particular, the flow properties near the spark plug significantly affect the peak pressure calculations. This analysis leads to the same conclusions of the previously cited LES studies, i.e. cyclic variability is mainly due to the variability of the in-cylinder flow properties. In particular, the flow configuration in the near-spark region is important as this significantly affects the early flame development and the entire combustion duration. While this is somewhat known, the interesting part is that these conclusions were derived using RANS, which is a non-conventional approach to study cyclic variability. the result of the previous cycle. Combustion itself introduces a significant perturbation to the engine cycle, especially for the engine platform analyzed in this paper. Gasoline is injected relatively early, which means that the injection-induced flow does not dominate the flow field at the beginning of the combustion process, as happens for different engine applications such as diesel engines or stratified GDI combustion. Therefore, any small flow perturbation will have a significant effect on combustion and this will introduce a significant perturbation for the next cycle. To decouple the role of combustion and gas-exchange in terms of cyclic variability, the analysis of the evolution of the cold flow is carried out by eliminating the combustion event. Figure 4 shows the results of the cold-flow analysis for Case 1 in terms of in-cylinder tumble. The first of 17 consecutive cycles is indicated in red and from now on every first cycle will be thrown away as it is significantly affected by the initial conditions. It can be seen that the cyclic variability for the cold flow case simulation is very similar to the fired case shown in Figure 3, with tumble ratio values between 0.5 and 0.8. Therefore, the cyclic variability of the in-cylinder flow is an intrinsic property of internal combustion engines and can be shown by using RANS even for a non-fired case. If combustion is re-activated, the variations in the flow configuration from cycle-to-cycle observed in Figure 4 would certainly lead to changes in flame propagation and combustion progress, thus delivering larger pressure fluctuations discussed earlier for Case 1 (Figure 1). Figure 3 Cyclic variability of the flow properties for Case 1 at the time of the spark (40ºCA BTDC) Analysis of flow cyclic variability In a typical URANS simulation, as occurs for an actual engine cycle, the solution keeps changing due to the several perturbations to the flow coming from specific events (moving piston and valves, gas-exchange, injection, combustion). As discussed earlier, the initial condition for one specific cycle is Figure 4 Cyclic variability of the flow properties for Case 1, at the time of the spark, by simulating gas-exchange and injection only Recent studies show that the cold flow CCV for Case 1 and Case 2 are very similar [7]. Clearly, the effect on combustion is quite different, as can be seen comparing Figure 1 and Figure 2. The key to understand this result is not considering only the cyclic variability of the flow, but also how this affects the flame speed. For stoichiometric non-dilute combustion, the flame 3

4 speed is relatively high and the effect of flow cyclic fluctuations on flame speed is minor. For dilute combustion, the flame speed is lower. Therefore, the cyclic variability of the flow properties can significantly affect flame propagation. Effect of numerical viscosity on CCV The numerical results shown in this paper demonstrate that RANS is capable of calculating the flow variability to some extent. While LES are expected to deliver a more accurate characterization of the flow scales and introduce the stochastic component of the flow, multi-cycle RANS should not always be expected to deliver converging pressure traces, and in some cases (such as Case 1 of this paper) can capture large CCV. It is the authors opinion that a common reason why RANS modeling in some cases suppresses cyclic variability, and delivers a converging ensemble average result, lies in the high numerical viscosity that characterizes many RANS simulations. To clarify and validate this statement, the analysis of the cold-flow case is carried out for Case 1 while progressively increasing numerical viscosity by modifying specific numerical settings such as grid resolution and amount of upwinding. A total of 11 consecutive cycles (the first one is thrown away and not included in this analysis) for Case 1 (suppressing combustion) are simulated using: The standard mesh used in this paper to simulate the combustion cases and defined in the CFD Methodology chapter, here referred to as Fine A coarser mesh (same level of embedding and AMR) with bigger base grid (8 mm), here referred to as Coarse A coarser mesh (same level of embedding and AMR) with bigger base grid (16 mm), here referred to as Ultra- Coarse The standard Fine mesh with a 1 st order upwinded scheme, here referred to as Upwind Table 3 summarizes the grid size and numerical settings used for the four cases shown in this section. Figure 5 shows the crank-resolved tumble for 10 consecutive cycles for the 4 cases tested. It should be mentioned that upwinded schemes are very dissipative and using upwinding is similar in effect to significantly increasing the cell size (i.e., both coarse meshes and upwinded numerics increase numerical viscosity). The results show that switching from fine mesh (red curve) to coarse (blue) and ultra-coarse (green) mesh results in the tumble being progressively under-estimated. The numerical results for the upwinded scheme (black curve) are similar to those from the ultra-coarse mesh, which demonstrates that upwinding introduces a large numerical dissipation. Not only coarse mesh and upwinded scheme both reduce the calculated tumble - which consequently would have a weaker effect on flame propagation and CCV but the cyclic variability of the calculated tumble is progressively suppressed, as can be observed in detail in Figure 6. Figure 5 Crank-resolved tumble ratio for 10 simulated cycles of Case 1 (cold-flow analysis) and using several numerical settings Table 3 Numerical settings used to highlight the effect of numerical viscosity on CCV Fine Coarse Ultra-Coarse Upwind Scheme Central Central Central Upwind Base Mesh 4 mm 8 mm 16 mm 4 mm Embedding Cylinder Level Embedding Valves Level Embedding Injector Level AMR Level Minimum Mesh 0.5 mm 1 mm 2 mm 0.5 mm Figure 6 Crank-resolved tumble ratio for 10 simulated cycles of Case 1 (cold-flow analysis) at the end of the compression stroke 4

5 If these highly dissipative simulations include combustion, the cyclic variability would be largely reduced and RANS results would deliver more conventional, although less accurate, converging-like results. Recent results using the G-equation combustion model have exhibited the same trend of increased repeatability with coarser grids and more upwinding. The G-equation approach to combustion, however, can be easily tuned to compensate for the dissipative error [7]. As such, numerical viscosity adds stability/repeatability with a cost in terms of accuracy. This was also recently shown for simple non-ice applications, such as the simulation of a cylinder in a cross flow [5]. However, when high accuracy in predicting the flow properties is requested, RANS simulations have to deal with non-converging flow properties and, in some cases, large CCV of the pressure traces. Modeled TKE and Resolved TKE In a turbulent flow, each physical quantity u can be decomposed in an ensemble average component, u and a turbulent fluctuating component, u as follows: u = u + u (1) In URANS, the modeled ensemble average component varies with time. It is important to understand that in a URANS (or RANS) simulation, the true ensemble average may not be predicted [11]. Therefore, u should be decomposed to include a simulated true ensemble averaged part, u and a resolved fluctuation, u : u = u + u = u + u + u (2) Therefore, URANS takes into account for both resolved and modeled fluctuations. Due to the cyclic behavior of ICEs, in engine simulations the time average is replaced by the ensemble-average concept. When RANS modeling is used, turbulent viscosity is used to remove the small flow scales and model all the turbulent fluctuating velocities. Yet, the larger flow scales are not destroyed and time- or cycle-resolved fluctuations can still exist in the flow. Figure 7 shows the modeled and resolved TKE distributions on a vertical plane through the intake and exhaust valves, during the gas-exchange process (270ºCA BTDC), for all the cold-flow cases simulated in this paper. The modeled TKE is obtained as ensemble average value on consecutive cycles (the first cycle is not considered here), while the resolved TKE is calculated using the velocity fluctuations, u, v, and w, as follows: RRRRRRRR TTT = 1 2 (u 2 + v 2 +w 2 ) (3) Note that u is calculated by subtracting the simulated true ensemble mean velocity (post-processed by averaging individual flow-field snapshots of consecutive cycles at the same crank angle) from the instantaneous velocity, u : u = u u (4) It can be seen that, for the finest mesh used in this paper, the resolved TKE has the same order of magnitude of the modeled TKE. This results shows that for this engine case the turbulent viscosity introduced by RANS is not capable of suppressing the cycle-resolved fluctuations of the larger flow scales and therefore does not result in a true ensemble average. By progressively coarsening the mesh or using lower order schemes, the modeled TKE is reduced, which is consistent with the observation of decreased flow intensity in Figure 5. However, the reduction of the resolved TKE is much more significant, which is consistent with the observation of suppressed CCV in Figure 6. Convergence of statistics It has been shown in this paper that RANS does not deliver an ensemble average result for the examined case and is therefore able to capture CCV in engine simulations. However, the convergence of statistics after a certain number of cycles needs to be assessed. This analysis was performed for the cold flow simulation characterized by the largest degree of CCV, i.e. fine mesh and central scheme. Results shown in Figure 8 indicate that the convergence of both the mean flow field and the root mean square (RMS) of the velocity vectors takes place after consecutive cycles. Conclusions In this paper, the ability of RANS simulations to predict CCV in engine multi-cycle simulations to some extent has been demonstrated. On one hand, this has been validated with against a large set of engine data for several operating conditions. On the other hand, there still exists reluctance in the engine modeling community to accept that RANS can provide something other than an ensemble average solution. An in-depth analysis of CCV from RANS, with particular regard to cold-flow simulations, shows similar conclusions to those provided by LES studies. More detailed analysis of the turbulent kinetic energy shows that the energy associated with the resolved scales in an internal combustion engine can be as high as that associated with the modeled scales. In other words, the variability of the large flow scales from one cycle to the next is preserved, provided that low-dissipative numerics are used. It is shown that the non-converging behavior of the cyclic numerical results still meets the convergence of the flow statistics. More in general, it is shown that it makes sense to expect CCV from running RANS multi-cycle simulations. Recognizing this is critical for engine development and production, since this process in industry widely relies on RANS calculations. 5

6 Figure 7 Modeled TKE and resolved TKE during gas-exchange (270ºCA BTDC) for all the cold-flow cases simulated in this paper Figure 8 Mean and RMS velocity maps, at 270ºCA BTDC, for the Fine case after different number of consecutive cycles 6

7 Acknowledgments The submitted manuscript has been created by UChicago Argonne, LLC, Operator of Argonne National Laboratory ( Argonne ). Argonne, a U.S. Department of Energy Office of Science laboratory, is operated under Contract No. DE-AC02-06CH The U.S. Government retains for itself, and others acting on its behalf, a paid-up nonexclusive, irrevocable worldwide license in said article to reproduce, prepare derivative works, distribute copies to the public, and perform publicly and display publicly, by or on behalf of the Government. This research is funded by DOE's Vehicle Technologies Program, Office of Energy Efficiency and Renewable Energy. The authors would like to express their gratitude to Gurpreet Singh and Leo Breton, program managers at DOE, for their support. The research engine used to run these experiments was provided by Ford Motor Company. Special thanks to Brad Boyer and Steven Wooldridge and their team from Ford Motor Company for their guidance and support. References 1. Enaux B., Granet V., Vermorel O., Lacour C., Pera C., Angelberger C., et al., LES study of cycle-to-cycle variations in a spark ignition engine, Proceedings of the Combustion Institute, Vol. 33, pp , Granet V., Vermorel O., Lacour C., Enaux B., Dugue V., Poinsot T., Large-Eddy Simulation and experimental study of cycle-to-cycle variations of stable and unstable operating points in a spark ignition engine, Combust. Flame 159, 4, , Yang, X., Gupta, S., Kuo, T. and Gopalakrishnan, V., RANS and LES of IC Engine Flows A Comparative Study, Proceedings of the ASME 2013 Internal Combustion Engine Division Fall Technical Conference, ICEF , Dearborn, Michigan, Fontanesi, S., Paltrinieri, S., d Adamo, A., Duranti, S., Investigation of boundary condition and field distribution effects on the cycleto-cycle variability of a turbocharged GDI engine using LES, Oil & Gas Sci. Tech., doi: /ogst/ , Richards, K.J., Probst, D., Pomraning, E., Senecal, P.K., Scarcelli, R., The Observation of Cyclic Variation in Engine Simulations when using RANS Turbulence Modeling, ASME Paper ICEF , Scarcelli, R., Wallner, T., Sevik, J., Richards, K., Pomraning, E., Senecal, P.K., Capturing Cyclic Variability in EGR Dilute SI Combustion using Multi-Cycle RANS, ASME Paper ICEF , Scarcelli, R., Richards, K., Pomraning, E., Senecal, P.K., Wallner, T., Sevik, J., Cycle-to-Cycle Variations in Multi-Cycle Engine RANS Simulations, SAE Technical Paper , Richards, K.J., Senecal, P.K., Pomraning, E., CONVERGE Theory Manual, Convergent Science Inc., Madison, WI, Raju, M., Wang, M., Dai, M., Piggott, W., and Flowers, D., Acceleration of Detailed Chemical Kinetics Using Multi-zone Modeling for CFD in Internal Combustion Engine Simulations, SAE , Pomraning, E., Richards, K., and Senecal, P., "Modeling Turbulent Combustion Using a RANS Model, Detailed Chemistry, and Adaptive Mesh Refinement", SAE Technical Paper , Davidson, L., Fluid mechanics, turbulent flow and turbulence modeling,