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Numerical multiphase simulation and validation of the flow in the piston ring pack of an internal combustion engine
Tribology International 101 (2016) 98–109
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Tribology International journal homepage: www.elsevier.com/locate/triboint
Numerical multiphase simulation and validation of the flow in the piston ring pack of an internal combustion engine A. Oliva, S. Held Institute of Internal Combustion Engines, Technische Universität München, Germany
art ic l e i nf o
a b s t r a c t
Article history: Received 11 January 2016 Received in revised form 18 March 2016 Accepted 3 April 2016 Available online 16 April 2016
The piston ring pack is important for the sealing of the combustion chamber of an internal combustion engine. It plays a major role in friction, wear and oil consumption considerations. Both experimental and theoretical studies in this area are difficult due to the complexity of this highly dynamic system. The paper deals with the numerical investigation by means of computational fluid dynamics of the gas and oil flow in the piston ring pack. Having been validated with experimental data, the simulation results show gas and oil transport mechanisms, which can be used to improve existing models of 0D/1Dsimulations. This leads to a better understanding of the processes in the piston ring pack and helps to further optimize the tribological system. & 2016 Elsevier Ltd. All rights reserved.
Keywords: Piston rings Numerical analysis Lubrication oil Fluid mechanics
1. Introduction The piston ring pack is still part of comprehensive research. Reduction of friction, blow-by losses, oil consumption, and wear are the key challenges of the piston assembly development. In order to achieve the optimum of all these targets, it is important to gain an understanding of the oil distribution and the oil transport processes in the ring pack. Numerical simulation of the ring pack flow can be a means to obtain further knowledge of the mechanisms involved. Using 0D/1D-simulations to calculate the piston ring pack, which are based on chamber-orifice models, is state of the art. These models have been under continuous investigation for the last decades and have been gradually improved by implementing increasing model depth. The majority of the 0D/1D-studies focus on the blow-by flow [3,7,10,23], ring/piston dynamics [10,19,20,23], friction and hydrodynamics [2,10,13,19,20] and oil transport/consumption [2,3,7,10,19,22,23] as well as corresponding experimental approaches [1,5,6,11,14,22,24]. However, it is difficult to obtain reliable discharge coefficients for the flow through the piston ring gaps or the flow between the rings and the related grooves. In addition, the oil flow is usually modeled with the Reynolds equation for thin films, which is generally not a good assumption for all parts of the computational domain (e.g. ring grooves). The CFDsimulation of the piston ring pack is able to give new insights and its results can help improving existing 0D/1D-models. Hronza et al. [8] introduced an improved approach using the 2D-Navier–Stokes equations instead of the Reynolds equation to model the oil phase. This approach considers partially flooded http://dx.doi.org/10.1016/j.triboint.2016.04.003 0301-679X/& 2016 Elsevier Ltd. All rights reserved.
areas and free surface determination of the oil film. However, the interaction between gas and oil phase is only accounted for in the form of a boundary condition. This, in turn, is not sufficient to calculate all occurring oil transport mechanisms in the piston ring pack. There have only been a few studies about CFD-simulation of the piston ring pack in the past. The authors of [25] introduced a 3Dmodel of the piston ring pack which considers oil and gas flow. A weakness of this simulation is the neglection of the ring movement, which is a key aspect of all transport processes in the piston ring pack. The authors of the aforementioned paper concluded that the circumferential positions of the ring end gaps only have an insignificant influence on the blow-by. Other studies deal with cavitation effects on the running surface of the compression ring, which have been validated with experimental data [16,17]. The computational domain of the models is limited to the area around the compression ring, but it shows that even very local effects are investigated in the ring pack. Latest studies presented a method to calculate the gas flow through the piston ring pack in a diesel engine with a twodimensional CFD-approach [12]. This method was applied to the ring pack of a gasoline engine and is further enhanced in the present work. Measured pressure and ring movement data allowed the validation of the simulation. The consideration of oil in the simulation allowed to capture a number of oil transport mechanisms in the results. The piston and ring pack of the examined engine is shown in Fig. 1.
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Nomenclature a cm f, fk h, hk M kl n p pcc p12 p23 q, qk t T u, uk v w
αk Γkl
acceleration mean piston speed body force field (of phase k) enthalpy (of phase k) interfacial momentum transfer term engine speed pressure combustion chamber pressure first ring land pressure second ring land pressure heat flux (of phase k) time temperature velocity field (of phase k) velocity volume based heat source volume fraction of phase k interfacial mass transfer term
2. Theoretical basics To calculate the multiphase flow in the ring pack, the following basic equations of numerical fluid mechanics are essential: mass, momentum and energy conservation. The mass conservation law defines the time dependent changes in mass to be equal with all mass flow changes in a control volume [4]. ∂ρ þ ∇ ρu ¼ 0 ∂t
ð1Þ
The momentum conservation is a vector equation. For all spatial directions, the time dependent change in momentum is equal to all applying forces on the control volume. The forces can either be surface or volume forces [4]. ∂ ρu þ ∇ ρuuT ¼ ∇ τ ∇p þ ρf ð2Þ ∂t In addition, consider temperature gradients in the piston ring flow, the energy conservation equation was solved. The time dependent change of energy is equal to the work performed on the control volume [4].
99
Λkl λ ρ, ρk τ, τk τ tk φ
interfacial thermal energy transfer term conrod ratio density (of phase k) viscous stress tensor (of phase k) turbulent stress tensor crank angle
ATS BB BDC CAD CFD ITDC IMEP TDC TS
anti-thrust side blow-by bottom dead center computer aided design computational fluid dynamics ignition top dead center indicated mean effective pressure top dead center thrust side
for multiphase flows can be stated as (cf. [9]) N X ∂ α k ρk þ ∇ α k ρk uk ¼ Γ kl ∂t l ¼ 1;l a k
The momentum conservation equation is also extended with the volume fraction α for multiphase calculations. Momentum exchange between the phases has been considered for the calculation of the ring pack. The exchange model takes into account the relative velocity of the phases and drag coefficients dependent on the Reynolds number. This approach allows for the modeling of the momentum exchange and captures the interaction of the different velocity fields. A general formulation of the multiphase momentum conservation equation is shown in Eq. (6) [9]. ∂ α k ρk uk þ ∇ αk ρk uk uTk ¼ ∇ ðαk τ k Þ ∂t ∇ α k pk þ α k ρk f k þ
N X
Mkl
l ¼ 1;l a k
∂ðρhÞ þ ∇ ðρuhÞ ¼ ∇ ðτ uÞ ∇ ðpuÞ þ ∂t þ ρf u ∇ q þ ρw
ð3Þ
Both oil and gas phase in the piston ring pack flow coexist with a significant volume fraction. For that reason, a multi-fluid approach was chosen to model the flow. With this approach, the entire set of conservation equations was solved for each single phase. Accordingly, the volume fractions of all phases must sum up to 1. N X
αk ¼ 1
ð4Þ
k¼1
The simple mass conservation equation is extended with the volume fraction α and a term to consider mass exchange between the phases. Flow phenomena such as evaporation or cavitation can be taken into account with this term. For the calculation of the piston ring pack flow, no mass exchange was modeled between the gas and the oil phase. The general mass conservation equation
ð5Þ
Fig. 1. Piston and ring pack of the examined engine.
ð6Þ
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Fig. 2. Model depths for the simulation of the piston ring pack [12].
Due to the extension for multiphase flows, several additional terms are included in the energy conservation equation, cf. Eq. (7) [9]. ∂ αk ρk hk ∂ðαk pk Þ ∇ ð α k pk uk Þ þ ∇ αk ρk hk uk ¼ ∇ ðαk τ k uk Þ þ ∂t ∂t þ αk ρk f k uk ∇ αk qk þ αk ρwk þ
N X
Λkl
ð7Þ
l ¼ 1;l a k
The energy exchange between the phases for the calculation of the ring pack flow was modeled with a Ranz–Marshall approach [15]. Therefore, not only the energy transfer between the walls and the fluids, but also between the phases was considered. After defining all equations for the calculation of the multiphase flow in the piston ring pack, the geometric model depth should also be discussed. Hence, it is important to know the potential flow paths in the ring pack [21]
through the ring end gaps, via the ring grooves in axial direction, through the gaps between the rings and liner, and circumferentially along the ring lands.
The possible geometric model approaches for the ring pack are shown in Fig. 2. A detailed discussion about the advantages and disadvantages of the different approaches was already investigated in [12]. The comparatively low calculation time and relatively easy implementation of ring movement (axial, radial, and twist), which is decisive for a correct calculation of the fluid flow, supports the choice of the 2D-cut model. Omitting the ring end gaps is a disadvantage of this particular method. However, this was compensated by minimal clearance gaps of the rings in axial and radial direction. Despite the simplifications in the present model, flow phenomena can be accurately captured in the simulation. Besides calculating the flow in the piston ring pack, the focus of this paper is the numerical simulation of the oil transport mechanisms. The most important transport mechanisms for oil in the ring pack are [18,21,22]
blow-by/reverse blow-by oil transport, pumping/squeezing of oil in the ring grooves, oil throw off caused by inertia forces, and oil scraping off the cylinder wall.
All of these oil transport mechanisms are illustrated in Fig. 3 and can be reproduced in the results of the simulation.
3. Experimental setup For validation purposes, it is essential to gather numerous measurement results. The experimental setup to obtain said measurements consists of three main parts – the engine itself, the measurement system, and a lever system. The gasoline engine used for the investigations presented in this paper is a naturally aspirated single cylinder four stroke research engine. Some of its basic geometrical specifications and the simulated operating point are listed in Table 1. The piston of the engine is equipped with sensors for pressure and temperature measurement. The pressure is measured inside the combustion chamber, the ring lands (i.e. the areas between two adjacent piston rings) and the crankcase. Temperature sensors are distributed over the height of the piston and the liner in an equidistant manner. In addition, relative axial movement of the piston rings in the respective piston grooves is detected via eddy current sensors attached to the groove flanks. The position of the sensors in the measurement piston can be found in Fig. 4, which shows the cross section through the piston exemplary at thrust side (the piston skirt is truncated in figure). The piston features one additional temperature sensor which is located in the center of the piston crown, which is not displayed. The combustion chamber pressure is indicated using a pressure sensor integrated into the cylinder head. To guide the cables of the sensors to the outside of the engine while minimizing potential damage of the fragile connecting wires due to buckling load and induced shear stress, a two-component lever system is installed. In general, the cables are attached to the lever while they are passed through the pivot axis at the pivot points in order to exert only torsional instead of buckling load on the lever [26]. Furthermore, a blow-by meter is attached to the crankcase in order to provide an estimate of the blow-by of the investigated engine.
4. Validation of the 1D-simulation As described in the introduction section, the first step in the simulation chain is a one-dimensional simulation. Therefore, the examined engine is modeled in the commercial tool AVL EXCITE, which features a detailed chamber-orifice model for the piston ring pack and a number of additional models, e.g. for the hydrodynamic contact of the rings and the liner. This simulation is conducted in order to obtain an entire crank angle-resolved set of motion data for each ring. Because of its huge impact on the ongoing mechanisms in the ring pack, a complete knowledge of the ring movement is essential for setting up the subsequent 2DCFD simulation.
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Typical input parameters for the 1D-model are:
geometrical data: e.g. detailed dimensions of piston, rings and liner,
mechanical data: e.g. material properties and surface characteristics,
thermodynamic data: e.g. combustion chamber pressure curve and temperature curve from a pressure analysis, and
fluid properties of the engine oil.
In addition to this basic data, settings for the hydrodynamic contact must be chosen and flow rate coefficients must be defined for calibration purposes in each of the narrow sections of the rings. This includes the contact areas between rings and liner and between rings and their corresponding upper and lower ring groove flank. Based on these inputs a simulation of the ring pack can be performed. As a result, the main variables are the mass flows as well as the associated enthalpy flows through the orifices, the pressure and the temperature in the chambers, resulting forces on the rings, and thus the velocity and the acceleration of the rings. By comparing simulated and measured data, an iterative adjustment of the flow rate coefficients is possible. The parameters which are taken into account in this calibration process are
pressure curves (combustion chamber pressure and ring land pressures),
integral blow-by value, and axial ring motion.
Fig. 3. Oil transport mechanisms. Table 1 Enginepoint data.
and
operating
Parameter
Value
Bore Stroke Conrod length Engine speed IMEP Engine oil
82.5 mm 92.8 mm 144 mm 1500 rpm 5 bar SAE 5W-30
Fig. 4. Position of the measurement points at the thrust side of the piston.
In addition to the measured data, the resulting axial ring lift of the calibrated simulation for all three rings is shown in Fig. 5. It can be noted that the curves for the first ring correlate very well. Both gradient and position of the contact position alteration are identical within the measurement's uncertainty limits. Moreover, the axial lift curves for all three rings are consistent with theoretical considerations done in recent studies [12]. The measurement signal of the axial lift sensors at the second and third ring is not of adequate signal quality to allow neither comparability to the simulation data nor reproducibility over several operation cycles. This behavior can be traced back to the fact that the first ring has the largest gap between the ring and the corresponding ring groove compared to the other two rings. As a result, this implicates a larger range of motion and therefore a better detectable signal amplitude generated by the eddy current sensor. In addition, the mounting position of the sensors in the present experimental setup cannot guarantee complete overlap due to relative radial movement between ring and piston. Current changes in the experimental setup aim at eliminating these limiting factors. l The measured integral blow-by value of 3:42 min can be reproduced accurately by means of the calibrated simulation model. The measured and simulated pressure curves at the two ring land measuring points also show good correlation (cf. Fig. 6). Position and height of the pressure peaks and the gradients on the positive and negative flanks correspond well with the first ring land pressure. The second ring land pressure amplitude is rather underestimated in the 1D-simulation due to simplifications made in the modeling process. For example, the piston skirt is neglected in the simulation tool and therefore crankcase pressure is applied below the third piston ring per definition. As a consequence, only pressure gradients with limited intensity can result over the third ring using the chamber-orifice model. Despite that, the simulated second ring land pressure curve is an acceptable approximation of the measured one.
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Fig. 7. Simulation volume (light blue). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 5. Relative axial lift of the three piston rings.
Fig. 6. Comparison of 1D-simulated and measured pressure curves.
5. Meshing methodology To generate a computation mesh of the piston ring pack, a detailed geometric model of the real piston assembly is required. Said models are generally built by means of a CAD-software. For the investigations presented in this paper, the geometric model was built in a parameterized way in order to optimize the required time for potential iterations. Starting from basic dimensions of the piston, rings and liner, the model is extended by consideration of
piston crowning and ovality data. In a subsequent step, the influence of thermal expansion due to the thermal load at the operating point is superimposed on the CAD-model. For simplification purposes, the piston skirt is truncated slightly below the third piston ring. On the one hand, the area below the third piston ring has a direct connection to the crankcase and therefore the assumption of neglecting most of the piston skirt is applicable. Averaged in circumferential direction, the connection is valid due to the decrease of the piston diameter in the piston pin area (cf. Fig. 1). On the other hand, this model assumption reduces the total number of cells of the mesh and hence the runtime of the simulation. In order to improve the numerical stability of the subsequent CFD-simulation performed on the mesh, additional inlet and outlet volumes are attached to the upper and lower end. The completed geometric model of the fluid area is visualized in Fig. 7 (cf. light blue section), where the gray part with the red-colored surface cut on the left represents the piston. In this image, the dark blue section on the right belongs to the boundary imposed by the liner and the three gray elements represent the piston rings. As discussed in the theoretical section, a 2D-cut is chosen for this simulation. To obtain a simulation mesh the cut is mapped with a two-dimensional mesh first and then extruded with one cell layer thickness. Due to the huge range of dimensions (e.g. from the mm-range in the reservoir areas behind the rings to the μm-range in the contact areas), a special meshing strategy had to be developed which has been discussed in detail in [12]. As a short insight into this method, the basic steps shall be summed up as follows:
subdivision of 2D-cut into better meshable parts (‘subgeometries’) in the CAD-software,
export of subgeometry elements and import in CFD-tool, manual meshing of subgeometries using structured meshes as far as possible, and
connection of the meshed parts and creation of required selections.
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Fig. 9. Piston velocity curve (λ ¼ 0:32, n ¼ 1500 rpm).
Fig. 10. Temperature boundary condition at the inlet.
Fig. 8. Simulation mesh (left) and computational domain (right).
Many of these steps can be performed with specifically developed macro-assistance, thus enabling the creation of a functional mesh in a reasonable time. The completed quasi-2D mesh is shown in Fig. 8 on the left. The application of the presented meshing process allows the use of significantly differing cell sizes over the computational domain. In Fig. 8 the variation in cell sizes is visualized by different tones of gray. This procedure has to be repeated for every ring separately in the lower and the upper contact position. The six meshed parts can then be combined to eight complete meshes. These are necessary to model the movement of the ring, including axial, radial, and twisting movement of the three rings. In combination with switching between the meshes, a specifically developed mesh deformation algorithm can map to every state between the contact positions. A typical cell count of a single mesh is at approximately 200,000 cells. 6. Comparison of 1D-simulation and 2D-CFD simulation The next step in the simulation chain is to implement a singlephase 2D-CFD simulation performed on the presented mesh with the
commercial tool AVL FIRE, covering a complete working cycle. This helps to manage and gradually increase the degree of complexity. Moreover, a detailed insight into the blow-by gas flow can be achieved. The required boundary conditions can be classified in an analog manner to the ones of the 1D-investigations (cf. Section 4). The geometrical data has already been considered in the meshing process. In addition, it can be used to calculate the piston velocity over the time – the corresponding data is shown in Fig. 9. For the simulation a coordinate system fixed to the piston is applied. Thus a transformation from the inertial system, which in itself is fixed to the observer, is required. Therefore, the inverse piston velocity is imprinted on the liner side of the mesh as a boundary condition. The used fluid (air) is initialized in three selections with the respective initial pressure. This is a necessary step to meet the pressure gradient at the beginning of the working cycle. Said pressure gradient is induced by the negative pressure of the naturally aspirated engine during the suction phase. Hence, the convergence of the simulation can be enhanced in the beginning and helps to optimize the calculation time. The required thermodynamic data includes pressure and temperature curves at the inlet of the computational domain, which is equivalent to the averaged quantities in the combustion chamber. The combustion chamber pressure was already shown in Fig. 6, the temperature boundary condition is illustrated in Fig. 10 . The latter can be derived from a pressure analysis of the former quantity. As a result of taking into account these boundary conditions, the 2D-CFD simulation can be performed. The obtained results can be classified in two categories – vectorial and scalar results. In the following, the vectorial results will be used to provide a qualitative overview over the flow paths and phenomena. The scalar results (e.g. pressure curves) enable quantitative evaluation, calibration and validation. In Fig. 11, the velocity field of the calibrated final simulation is displayed at selected crank angles in order to illustrate the basic behavior of the blow-by flow. It is obvious that the blow-by gas flow, induced during the high pressure phase, gradually penetrates into the piston ring pack. In total it takes about 80 °CA for the blow-by to pass the ring pack. Two basic flow paths can be identified – the first through the gaps between the rings and their
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Fig. 11. Velocity field of the gas flow simulation at selected crank angles.
Fig. 12. Comparison of simulated and measured pressure curves.
corresponding ring grooves as well as over the reservoir areas behind the rings, and the second between the rings and the liner. The latter mechanism can most likely be attributed to circumferential effects in the real engine. On the one hand, a perfect shapeadaption capacity cannot be guaranteed over the circumference, i.e. there will always be residual gaps between rings and liner. On the other hand, the resulting space from the combined surface roughness adds to the residual gap. Due to deflection and redirection of the flow, both stable and dynamic vortices and their respective recirculation regimes respectively emerge. Especially in the reservoir areas and in the area below the second ring's nose, a vortex formation can be observed. The pressure curve results, evaluated in the ring land areas, can be used for validation purposes – they are shown in Fig. 12, in combination with the 1D-simulated and the measured data. The peaks, including their position and amplitude, show a good
correlation with the measured data, especially for the first ring land pressure (p12). The gradients of the pressure curves match just as well. It can also be noted that the 2D-CFD simulation shows a distinct peak of the second ring land pressure (p23), which is in contrast to the 1D-simulation. Smaller differences in the second ring land pressure curve and the delayed drop of pressure can be associated with model assumptions and the respective errors. In particular, the influence of the ring end gap cannot be completely compensated in the 2D-model. Using the minimal clearance model, the reduction of the pressure, built up during the high pressure period, is delayed. This is a result of the compensation of the pressure gradients during the low pressure period and intake stroke, which can only take place via the (constant) minimal gaps, while the influence of the ring end gaps increases in the real engine throughout these phases.
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Another means of validation possibility is the integral blow-by l matches the measured value. The CFD-simulated value of 3:45 min value within a deviation of less than one percent. The blow-by curve cannot be measured directly but can be compared with the 1D-simulated data (cf. Fig. 13). The CFD- and 1D-simulated curves correlate very well regarding the general behavior (peaks, amplitude, and gradients). The CFD-simulation shows a stronger influence of the ring contact position alteration (e.g. 15° CA and 210° CA in Fig. 13), as this effect can be resolved better in 2D-CFD. The delay of the ascending flank of the CFD-blow-by curve, compared to the one provided by the 1D-simulation, can be explained in a equivalent way as the delay of the ring land pressure drop. The flow through the ring end gaps can accelerate the first penetration of the blow-by flow. It is noteworthy that both integral value and blow-by curves are alike between the cycles when performing a multi-working cycle CFD-simulation with the presented setup.
7. Multiphase simulation constraints After achieving good results for the calculation of the gas flow in the piston ring pack, an oil phase was added to the model for further improvement of the simulation and adaption to the reality. Therefore, several extensions of the simulation model were necessary. Due to calculation time restrictions, it was not possible to calculate multiple cycles of the engine, so the oil was initialized at the start of the simulation. The initialization of oil in the oil reservoirs of the ring grooves is shown in Fig. 14. Empirical findings from the literature [21,27] and the fact that the oil supply rises from the combustion chamber to the crankcase, the oil filling ratios behind the rings were initialized in a gradual manner. The first piston ring was initialized with 5%, the second ring with 10%, and a ratio of 15% was chosen behind the third ring.
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Initializing the oil at the bottom of the reservoirs is valid due to the starting point of the simulation at BDC. The remaining flow area was initialized with air. Because the oil filling ratios behind the rings require an estimation, they were varied in a study to investigate the influences of the oil filling ratio on the oil distribution in the piston ring pack. To enable oil supply in the system, in every down stroke of the piston, oil was introduced to the simulation pressureless beneath the third ring (oil ring) in an additional study. The modeling concept assumes that there is always enough oil beneath the oil ring during the down stroke of the piston. The acceleration of the piston is responsible for inertia forces on the fluid in the piston ring pack. Because of the comparatively small accelerated masses, this force is not taken into account for a large number of gas flow calculations. However, this assumption is invalid for multiphase flows with oil. The piston acceleration curve for 1500 rpm can be seen in Fig. 15 and was included in the multiphase simulation as a volume force in the momentum equation (cf. Eq. (6)). The liquid phase is highly influenced by the acceleration forces as the acceleration due to the piston is several magnitudes above the influence of gravity. As mentioned in the theoretical section of this paper, exchange models can be considered between the single phases. A mass exchange between gas and oil phase was not modeled in the simulation as it would have required the introduction of a third phase, namely gaseous oil. In wide parts of the piston ring pack, the temperatures are moderate, hence evaporation of oil was neglected. Momentum exchange between the gaseous and liquid phase was calculated with a model based on interfacial area density, drag coefficient, and relative velocity between the phases. The drag coefficient is a function of the disperse phase's Reynolds number. Energy exchange between the phases was modeled with a Ranz–Marshall approach [15]. The heat transfer is calculated with a Nusselt number correlation. The exchange of turbulence between the phases could not be modeled with the software used for the investigations shown in this paper. Thus, the turbulence fields of both phases have been assumed to be homogeneous. The remaining constraints (piston speed, pressure, temperature, and ring movement) are identical to the simulation of the gas flow.
8. Multiphase simulation results
Fig. 13. Comparison of the simulated blow-by curves.
In this section, the results of the oil distribution in the piston ring pack at selected crank angles are introduced and discussed. The focus is on the oil transport phenomena known from the literature and experimental studies. Furthermore, results from the piston ring study with an oil supply (model extension) and the variation of oil filling ratios are shown. To simplify the interpretation of the oil distribution, arrows are added to each figure. They show the current normalized vector of the liner velocity and the piston acceleration at the specific crank angle.
Fig. 14. Oil initialization.
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Fig. 16 shows the oil distribution in the ring pack at various selected crank angles. The initialization of the oil behind the single rings can be seen at 179° CA. During the intake stroke, pressures below atmospheric pressure are possible as the research engine used for this investigations is naturally aspired. Therefore, the effect of reverse blow-by on oil can be observed at 152° CA. Caused by the gas flow, the oil behind the first and second ring is pushed back by a small amount. Behind the third ring, however, a gas bubble can be observed, because a bigger amount of oil is initialized in the third ring reservoir. The beginning of the first out of four oil alterations in the ring grooves during a full combustion cycle is shown at 42° CA. The alteration is completed at 20° CA, whereby the interaction between the gas and oil flow can especially be observed in the second and third ring groove. A possible cause for this are the high velocities in the ring pack at this point of time. Right before BDC (154° CA), the oil is again in the lower position of the oil reservoirs and an oil leakage to the crankcase is observable. At the end of the simulation (540° CA), the oil is almost in the same position as was the case at the initialization. However, small amounts of oil was lost to the crankcase and the combustion chamber.
A detailed consideration of the results also shows various oil transport mechanisms in the ring pack. At the second ring, the oil transport due to blow-by/reverse blow-by can be seen (cf. Fig. 17). The ring is in the lower position of the groove and there is oil between the groove and the ring at 320° CA. The oil is pushed in the direction of the second ring land due to leveling of the pressure difference. When the ring starts to alternate, the blow-by is intensified. The higher velocities enable entrainment of oil from the gap between ring and groove. A single droplet is teared out of the film and is transported by the blow-by flow (331° CA). The droplet impinges on the cylinder wall and deposits as an oil film (342° CA), before the oil interacts with one of the rings again. An example for pumping and squeezing of oil in the ring pack can be observed at the first ring, which is in the lower position in the groove at 338° CA in Fig. 18. Oil is visible between top ring and the
Fig. 15. Piston acceleration curve (λ ¼ 0:32, n ¼ 1500 rpm).
Fig. 17. Oil transport mechanism: blow-by/reverse blow-by oil transport.
Fig. 16. Oil distribution (volume fraction of oil) in the piston ring pack at selected crank angles.
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Fig. 18. Oil transport mechanism: pumping/squeezing of oil in the ring grooves.
Fig. 19. Oil transport mechanism: oil throw off caused by inertia forces.
upper ring flank. Due to the inertia forces driven alteration of the top ring at gas exchange TDC, oil is pushed in the direction of the groove as well as to the top land. At 348° CA, the top ring can be seen in the upper position in the ring groove (cf. Fig. 18). Pumping and squeezing of oil is an oil transport mechanism which occurs in almost every ring alteration. Oil throw off in the direction of the combustion chamber caused by inertia forces is an important issue for the combustion process development of supercharged gasoline engines. Even single oil droplets can be responsible for unintended ignitions in the combustion chamber during the compression stroke, which can lead to knocking in the engine. An example for an oil droplet moving towards the top land to the combustion chamber is shown in Fig. 19. Before the gas exchange TDC, an oil droplet is forming above the top ring (cf. 313° CA). The oil forming the droplet emerges from the reservoir behind the first ring. Although the piston slows down close to TDC, the acceleration still increases. Due to inertia forces, the oil droplet is moving along the top land in the direction of the combustion chamber. If the oil droplet is large enough, the potential for its intrusion into the combustion chamber is significant. A similar behavior is also possible at ITDC. Scraping oil off the cylinder wall and therefore controlling of the oil supply are tasks of the second and the oil ring. This process
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Fig. 20. Oil transport mechanism: oil scraping off the cylinder wall.
is illustrated in Fig. 20. The scraping process and the redirection of the oil at the edge of the napier ring can be observed well in this figure. Furthermore, the oil is set into a rotational motion in the second ring land between the second and the oil ring. The scraping process at the oil ring takes place in a similar way. The first simulation showed the oil distribution and even some oil transport mechanisms could be calculated. Fig. 16 illustrates that the oil supply of the ring pack decreases after one working cycle. Calculating multiple cycles with the first model would lead to a dry piston ring pack. In reality, the ring pack is permanently supplied with oil. The oil in the crankcase from the piston cooling jet and the plain bearings deposits on the liner underneath the piston and therefore supplies the ring pack with oil. During the down stroke of the piston, the assumption of full oil filling below the oil ring is valid (cf. [23]). This fact has been used for the model extension of the simulation with the oil supply. The results of the extended model are depicted in Fig. 22. The results for the oil distribution during the upstroke of the piston – before oil is introduced into the computational domain – are identical to the results without oil supply. As soon as the piston is moving downwards, the oil supply leads to two inlet oil transport paths. Because the movement of the oil ring strongly depends on the inertia and friction forces of the ring, the oil ring usually remains in the upper position in the groove during the downward stroke of the piston. Thus, the oil can enter the ring pack below the oil ring to the oil reservoir. The second identified transport path feeds the oil film in the radial gap between the rings and the liner. The oil film is partially scraped off of each of the rings. As a consequence, the oil finds its way to the respective reservoir of the rings (cf. 300° CA). At the second ring, the oil is scraped off in a stronger fashion compared to the other rings and the oil remains longer in the ring land, before it flows to the reservoir of the oil ring. The oil reservoir of the second ring is filled again from above, due to blow-by flow. At the end of this paper, the effect of different oil filling ratios in the oil ring reservoir should be discussed. Fig. 21 shows the oil alteration at ITDC for three varying initial oil filling ratios (15%, 20% and 25%). The basic behavior of all three variants is equivalent. The starting location for the oil alteration at the oil ring reservoir is strongly dependent on the reverse blow-by for this particular case. The bubble of the reverse blow-by breaks up the oil and therefore defines the spot for the beginning of the alteration. Similar oil distributions of the calculation have been taken into account for comparison purposes, to show the time shift due to the different initial oil filling ratios. The acceleration vector is pointing upwards for all variations and time steps shown in Fig. 21. The main finding of this study is that the higher the oil filling ratio, the earlier the oil
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Fig. 21. Comparison of different oil filling ratios (5/10/15, 10/15/20, and 15/20/25 from top to oil ring in percent) exemplary displayed for the oil ring.
The 1D-results were validated with experimental data for the
piston ring motions, ring land pressures, and integral blow-by. The 2D-results were validated with experimental data for ring land pressures and integral blow-by. Additionally, 1D- and 2Dsimulated blow-by curves were in good agreement to one another. The correlation between simulated and experimental data was very good, even in the case of multiple working cycles. After successfully investigating the gas flow in the ring pack, the model was extended to a multiphase simulation, considering gas and oil flow. The multiphase results showed the general behavior of oil during a working cycle (e.g. oil alteration in the ring grooves as well as gas interaction with the oil). Oil transport mechanisms could be observed in the results of the simulation model: blow-by/reverse blow-by oil transport, pumping/squeezing of oil in the ring grooves, oil throw off caused by inertia forces, and oil scraping off the cylinder wall. The model was extended with an oil supply below the oil ring. The study of the varying initial oil filling ratios in the oil reservoirs showed the importance of the amount of oil in the ring pack. The model is able to describe the oil transport in the piston ring pack. The insights of the CFD-results can help to improve 1Dmodels for the piston ring pack.
Acknowledgements
Fig. 22. Oil distribution in the piston ring pack (with additional oil inlet) at selected crank angles.
alternates in the reservoir. This fact emphasizes the effect of oil filling ratios on the oil supply of the complete piston ring pack .
9. Conclusion
A CFD-model was developed for the calculation of the gas and
oil flow in the piston ring pack of an internal combustion engine and optimized with regard to calculation time. A 1D-model for the calculation of the ring motion was developed simultaneously. An existing meshing methodology was applied successfully and extended for the current case.
The authors would like to thank C. Kirner and B. Uhlig from the institute of internal combustion engines of the Technische Universität München. They provided experimental data (piston ring movement, ring land pressures and integral blow-by) to validate the simulations.
References [1] Avan EY, Mills R, Dwyer-Joyce R. Ultrasonic imaging of the piston ring oil film during operation in a motored engine. SAE technical paper 2010-01-2179; 2010. [2] Chen H. Modeling the lubrication of the piston ring pack in internal combustion engines using the deterministic method [Ph.D. thesis]. MIT; 2011. [3] Cho Y, Tian T. Modeling engine oil vaporization and transport of the oil vapor in the piston ring pack. SAE technical paper 2004-01-2912; 2004. [4] Ferziger JH, Perić M. Computational methods for fluid dynamics. Berlin: Springer; 2002. [5] Furuhama S, Hiruma M, Tsuzita M. Piston ring motion and its influence on engine tribology. SAE technical paper 790860; 1979.
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[6] Furuhama S, Sasaki S. New device for the measurement of piston frictional forces in small engines. SAE technical paper 831284;1983. [7] Gamble RJ, Priest M, Taylor CM. Detailed analysis of oil transport in the piston assembly of an gasoline engine. Tribol Lett 2002;14(2002):147–56. [8] Hronza J, Bell D. A lubrication and oil transport model for piston rings using a navier-stokes equation with surface tension. SAE technical paper 2007-011053; 2007. [9] Ishii M, Hibiki T. Thermo-fluid dynamics of two-phase flow. New York: Springer; 2011. [10] Liu L. Modeling the performance of the piston ring-pack with consideration of non-axisymmetric characteristics of the power cylinder system in internal combustion engines [Ph.D. thesis]. MIT; 2005. [11] Nakayama K, Seki T, Takiguchi M, Someya T, Shochi F. The effect of oil ring geometry on oil film thickness in the circumferential direction of the cylinder. SAE technical paper 982578; 1998. [12] Oliva A, Held S, Herdt A, Wachtmeister G. Numerical simulation of the gas flow in the piston ring pack of an internal combustion engine. SAE technical paper 2015-01-1302; 2015. [13] Priest M, Dowson D, Taylor CM. Theoretical modelling of cavitation in piston ring lubrication. J Mech Eng Sci 2000;214(2000):435–47. [14] Przesmitzki S, Vokac A, Tian T. An experimental study of oil transport between the piston ring pack and cylinder liner. SAE technical paper 2005-01-3823; 2005. [15] Ranz WE, Marshall WR. Evaporation from drops. Chem Eng Progr 1952;48:141–6. [16] Shahmohamadi H, Mohammadpour M, et al. On the boundary conditions in multi-phase flow through the piston ring-cylinder liner conjunction. Tribol Int 2015;90(2015):164–74. [17] Shahmohamadi H, Rahmani R, Homer R, Paul K, Olin G. Cavitating flow in engine piston ring-cylinder liner conjunction. ASME IMECE; 2013.
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[18] Tian T. Modeling the performance of the piston ring-pack in internal combustion engines [Ph.D. thesis]. MIT; 1997. [19] Tian T, Wong VW, Heywood JB. A piston ring-pack film thickness and friction model for multigrade oils and rough surfaces. SAE technical paper 962032; 1996. [20] Tian T, Wong VW, Heywood JB. Modeling the dynamics and lubrication of three piece oil control rings in internal combustion engines. SAE technical paper 982657; 1998. [21] Thirouard B. Characterization and modeling of the fundamental aspects of oil transport in the piston ring pack of internal combustion engines [Ph.D. thesis]. MIT; 2001. [22] Thirouard B, Tian T. Oil transport in the piston ring pack (Part I): identification and characterization of the main oil transport routes and mechanisms. SAE technical paper 2003-01-1952; 2003. [23] Thirouard B, Tian T. Oil transport in the piston ring pack (Part II): zone analysis and macro oil transport model. SAE technical paper 2003-01-1953; 2003. [24] Thirouard B, Tian T, Hart DP. Investigation of oil transport mechanisms in the piston ring pack of a single cylinder diesel engine. SAE technical paper 982658; 1998. [25] Veettil M, Fanghui S. CFD analysis of oil/gas flow in piston ring-pack. SAE technical paper 2011-01-1406; 2011. [26] Weimar HJ. Entwicklung eines laseroptischen Messsystems zur kurbelwinkelaufgelösten Bestimmung der Ölfilmdicke [Ph.D. thesis]. TH Karlsruhe; 2002. [27] Yilmaz E. Sources and Charateristics of oil consumption in a spark-ignition engine [Ph.D. thesis]. MIT; 2003.
Contents lists available at ScienceDirect
Tribology International journal homepage: www.elsevier.com/locate/triboint
Numerical multiphase simulation and validation of the flow in the piston ring pack of an internal combustion engine A. Oliva, S. Held Institute of Internal Combustion Engines, Technische Universität München, Germany
art ic l e i nf o
a b s t r a c t
Article history: Received 11 January 2016 Received in revised form 18 March 2016 Accepted 3 April 2016 Available online 16 April 2016
The piston ring pack is important for the sealing of the combustion chamber of an internal combustion engine. It plays a major role in friction, wear and oil consumption considerations. Both experimental and theoretical studies in this area are difficult due to the complexity of this highly dynamic system. The paper deals with the numerical investigation by means of computational fluid dynamics of the gas and oil flow in the piston ring pack. Having been validated with experimental data, the simulation results show gas and oil transport mechanisms, which can be used to improve existing models of 0D/1Dsimulations. This leads to a better understanding of the processes in the piston ring pack and helps to further optimize the tribological system. & 2016 Elsevier Ltd. All rights reserved.
Keywords: Piston rings Numerical analysis Lubrication oil Fluid mechanics
1. Introduction The piston ring pack is still part of comprehensive research. Reduction of friction, blow-by losses, oil consumption, and wear are the key challenges of the piston assembly development. In order to achieve the optimum of all these targets, it is important to gain an understanding of the oil distribution and the oil transport processes in the ring pack. Numerical simulation of the ring pack flow can be a means to obtain further knowledge of the mechanisms involved. Using 0D/1D-simulations to calculate the piston ring pack, which are based on chamber-orifice models, is state of the art. These models have been under continuous investigation for the last decades and have been gradually improved by implementing increasing model depth. The majority of the 0D/1D-studies focus on the blow-by flow [3,7,10,23], ring/piston dynamics [10,19,20,23], friction and hydrodynamics [2,10,13,19,20] and oil transport/consumption [2,3,7,10,19,22,23] as well as corresponding experimental approaches [1,5,6,11,14,22,24]. However, it is difficult to obtain reliable discharge coefficients for the flow through the piston ring gaps or the flow between the rings and the related grooves. In addition, the oil flow is usually modeled with the Reynolds equation for thin films, which is generally not a good assumption for all parts of the computational domain (e.g. ring grooves). The CFDsimulation of the piston ring pack is able to give new insights and its results can help improving existing 0D/1D-models. Hronza et al. [8] introduced an improved approach using the 2D-Navier–Stokes equations instead of the Reynolds equation to model the oil phase. This approach considers partially flooded http://dx.doi.org/10.1016/j.triboint.2016.04.003 0301-679X/& 2016 Elsevier Ltd. All rights reserved.
areas and free surface determination of the oil film. However, the interaction between gas and oil phase is only accounted for in the form of a boundary condition. This, in turn, is not sufficient to calculate all occurring oil transport mechanisms in the piston ring pack. There have only been a few studies about CFD-simulation of the piston ring pack in the past. The authors of [25] introduced a 3Dmodel of the piston ring pack which considers oil and gas flow. A weakness of this simulation is the neglection of the ring movement, which is a key aspect of all transport processes in the piston ring pack. The authors of the aforementioned paper concluded that the circumferential positions of the ring end gaps only have an insignificant influence on the blow-by. Other studies deal with cavitation effects on the running surface of the compression ring, which have been validated with experimental data [16,17]. The computational domain of the models is limited to the area around the compression ring, but it shows that even very local effects are investigated in the ring pack. Latest studies presented a method to calculate the gas flow through the piston ring pack in a diesel engine with a twodimensional CFD-approach [12]. This method was applied to the ring pack of a gasoline engine and is further enhanced in the present work. Measured pressure and ring movement data allowed the validation of the simulation. The consideration of oil in the simulation allowed to capture a number of oil transport mechanisms in the results. The piston and ring pack of the examined engine is shown in Fig. 1.
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Nomenclature a cm f, fk h, hk M kl n p pcc p12 p23 q, qk t T u, uk v w
αk Γkl
acceleration mean piston speed body force field (of phase k) enthalpy (of phase k) interfacial momentum transfer term engine speed pressure combustion chamber pressure first ring land pressure second ring land pressure heat flux (of phase k) time temperature velocity field (of phase k) velocity volume based heat source volume fraction of phase k interfacial mass transfer term
2. Theoretical basics To calculate the multiphase flow in the ring pack, the following basic equations of numerical fluid mechanics are essential: mass, momentum and energy conservation. The mass conservation law defines the time dependent changes in mass to be equal with all mass flow changes in a control volume [4]. ∂ρ þ ∇ ρu ¼ 0 ∂t
ð1Þ
The momentum conservation is a vector equation. For all spatial directions, the time dependent change in momentum is equal to all applying forces on the control volume. The forces can either be surface or volume forces [4]. ∂ ρu þ ∇ ρuuT ¼ ∇ τ ∇p þ ρf ð2Þ ∂t In addition, consider temperature gradients in the piston ring flow, the energy conservation equation was solved. The time dependent change of energy is equal to the work performed on the control volume [4].
99
Λkl λ ρ, ρk τ, τk τ tk φ
interfacial thermal energy transfer term conrod ratio density (of phase k) viscous stress tensor (of phase k) turbulent stress tensor crank angle
ATS BB BDC CAD CFD ITDC IMEP TDC TS
anti-thrust side blow-by bottom dead center computer aided design computational fluid dynamics ignition top dead center indicated mean effective pressure top dead center thrust side
for multiphase flows can be stated as (cf. [9]) N X ∂ α k ρk þ ∇ α k ρk uk ¼ Γ kl ∂t l ¼ 1;l a k
The momentum conservation equation is also extended with the volume fraction α for multiphase calculations. Momentum exchange between the phases has been considered for the calculation of the ring pack. The exchange model takes into account the relative velocity of the phases and drag coefficients dependent on the Reynolds number. This approach allows for the modeling of the momentum exchange and captures the interaction of the different velocity fields. A general formulation of the multiphase momentum conservation equation is shown in Eq. (6) [9]. ∂ α k ρk uk þ ∇ αk ρk uk uTk ¼ ∇ ðαk τ k Þ ∂t ∇ α k pk þ α k ρk f k þ
N X
Mkl
l ¼ 1;l a k
∂ðρhÞ þ ∇ ðρuhÞ ¼ ∇ ðτ uÞ ∇ ðpuÞ þ ∂t þ ρf u ∇ q þ ρw
ð3Þ
Both oil and gas phase in the piston ring pack flow coexist with a significant volume fraction. For that reason, a multi-fluid approach was chosen to model the flow. With this approach, the entire set of conservation equations was solved for each single phase. Accordingly, the volume fractions of all phases must sum up to 1. N X
αk ¼ 1
ð4Þ
k¼1
The simple mass conservation equation is extended with the volume fraction α and a term to consider mass exchange between the phases. Flow phenomena such as evaporation or cavitation can be taken into account with this term. For the calculation of the piston ring pack flow, no mass exchange was modeled between the gas and the oil phase. The general mass conservation equation
ð5Þ
Fig. 1. Piston and ring pack of the examined engine.
ð6Þ
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Fig. 2. Model depths for the simulation of the piston ring pack [12].
Due to the extension for multiphase flows, several additional terms are included in the energy conservation equation, cf. Eq. (7) [9]. ∂ αk ρk hk ∂ðαk pk Þ ∇ ð α k pk uk Þ þ ∇ αk ρk hk uk ¼ ∇ ðαk τ k uk Þ þ ∂t ∂t þ αk ρk f k uk ∇ αk qk þ αk ρwk þ
N X
Λkl
ð7Þ
l ¼ 1;l a k
The energy exchange between the phases for the calculation of the ring pack flow was modeled with a Ranz–Marshall approach [15]. Therefore, not only the energy transfer between the walls and the fluids, but also between the phases was considered. After defining all equations for the calculation of the multiphase flow in the piston ring pack, the geometric model depth should also be discussed. Hence, it is important to know the potential flow paths in the ring pack [21]
through the ring end gaps, via the ring grooves in axial direction, through the gaps between the rings and liner, and circumferentially along the ring lands.
The possible geometric model approaches for the ring pack are shown in Fig. 2. A detailed discussion about the advantages and disadvantages of the different approaches was already investigated in [12]. The comparatively low calculation time and relatively easy implementation of ring movement (axial, radial, and twist), which is decisive for a correct calculation of the fluid flow, supports the choice of the 2D-cut model. Omitting the ring end gaps is a disadvantage of this particular method. However, this was compensated by minimal clearance gaps of the rings in axial and radial direction. Despite the simplifications in the present model, flow phenomena can be accurately captured in the simulation. Besides calculating the flow in the piston ring pack, the focus of this paper is the numerical simulation of the oil transport mechanisms. The most important transport mechanisms for oil in the ring pack are [18,21,22]
blow-by/reverse blow-by oil transport, pumping/squeezing of oil in the ring grooves, oil throw off caused by inertia forces, and oil scraping off the cylinder wall.
All of these oil transport mechanisms are illustrated in Fig. 3 and can be reproduced in the results of the simulation.
3. Experimental setup For validation purposes, it is essential to gather numerous measurement results. The experimental setup to obtain said measurements consists of three main parts – the engine itself, the measurement system, and a lever system. The gasoline engine used for the investigations presented in this paper is a naturally aspirated single cylinder four stroke research engine. Some of its basic geometrical specifications and the simulated operating point are listed in Table 1. The piston of the engine is equipped with sensors for pressure and temperature measurement. The pressure is measured inside the combustion chamber, the ring lands (i.e. the areas between two adjacent piston rings) and the crankcase. Temperature sensors are distributed over the height of the piston and the liner in an equidistant manner. In addition, relative axial movement of the piston rings in the respective piston grooves is detected via eddy current sensors attached to the groove flanks. The position of the sensors in the measurement piston can be found in Fig. 4, which shows the cross section through the piston exemplary at thrust side (the piston skirt is truncated in figure). The piston features one additional temperature sensor which is located in the center of the piston crown, which is not displayed. The combustion chamber pressure is indicated using a pressure sensor integrated into the cylinder head. To guide the cables of the sensors to the outside of the engine while minimizing potential damage of the fragile connecting wires due to buckling load and induced shear stress, a two-component lever system is installed. In general, the cables are attached to the lever while they are passed through the pivot axis at the pivot points in order to exert only torsional instead of buckling load on the lever [26]. Furthermore, a blow-by meter is attached to the crankcase in order to provide an estimate of the blow-by of the investigated engine.
4. Validation of the 1D-simulation As described in the introduction section, the first step in the simulation chain is a one-dimensional simulation. Therefore, the examined engine is modeled in the commercial tool AVL EXCITE, which features a detailed chamber-orifice model for the piston ring pack and a number of additional models, e.g. for the hydrodynamic contact of the rings and the liner. This simulation is conducted in order to obtain an entire crank angle-resolved set of motion data for each ring. Because of its huge impact on the ongoing mechanisms in the ring pack, a complete knowledge of the ring movement is essential for setting up the subsequent 2DCFD simulation.
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Typical input parameters for the 1D-model are:
geometrical data: e.g. detailed dimensions of piston, rings and liner,
mechanical data: e.g. material properties and surface characteristics,
thermodynamic data: e.g. combustion chamber pressure curve and temperature curve from a pressure analysis, and
fluid properties of the engine oil.
In addition to this basic data, settings for the hydrodynamic contact must be chosen and flow rate coefficients must be defined for calibration purposes in each of the narrow sections of the rings. This includes the contact areas between rings and liner and between rings and their corresponding upper and lower ring groove flank. Based on these inputs a simulation of the ring pack can be performed. As a result, the main variables are the mass flows as well as the associated enthalpy flows through the orifices, the pressure and the temperature in the chambers, resulting forces on the rings, and thus the velocity and the acceleration of the rings. By comparing simulated and measured data, an iterative adjustment of the flow rate coefficients is possible. The parameters which are taken into account in this calibration process are
pressure curves (combustion chamber pressure and ring land pressures),
integral blow-by value, and axial ring motion.
Fig. 3. Oil transport mechanisms. Table 1 Enginepoint data.
and
operating
Parameter
Value
Bore Stroke Conrod length Engine speed IMEP Engine oil
82.5 mm 92.8 mm 144 mm 1500 rpm 5 bar SAE 5W-30
Fig. 4. Position of the measurement points at the thrust side of the piston.
In addition to the measured data, the resulting axial ring lift of the calibrated simulation for all three rings is shown in Fig. 5. It can be noted that the curves for the first ring correlate very well. Both gradient and position of the contact position alteration are identical within the measurement's uncertainty limits. Moreover, the axial lift curves for all three rings are consistent with theoretical considerations done in recent studies [12]. The measurement signal of the axial lift sensors at the second and third ring is not of adequate signal quality to allow neither comparability to the simulation data nor reproducibility over several operation cycles. This behavior can be traced back to the fact that the first ring has the largest gap between the ring and the corresponding ring groove compared to the other two rings. As a result, this implicates a larger range of motion and therefore a better detectable signal amplitude generated by the eddy current sensor. In addition, the mounting position of the sensors in the present experimental setup cannot guarantee complete overlap due to relative radial movement between ring and piston. Current changes in the experimental setup aim at eliminating these limiting factors. l The measured integral blow-by value of 3:42 min can be reproduced accurately by means of the calibrated simulation model. The measured and simulated pressure curves at the two ring land measuring points also show good correlation (cf. Fig. 6). Position and height of the pressure peaks and the gradients on the positive and negative flanks correspond well with the first ring land pressure. The second ring land pressure amplitude is rather underestimated in the 1D-simulation due to simplifications made in the modeling process. For example, the piston skirt is neglected in the simulation tool and therefore crankcase pressure is applied below the third piston ring per definition. As a consequence, only pressure gradients with limited intensity can result over the third ring using the chamber-orifice model. Despite that, the simulated second ring land pressure curve is an acceptable approximation of the measured one.
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Fig. 7. Simulation volume (light blue). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 5. Relative axial lift of the three piston rings.
Fig. 6. Comparison of 1D-simulated and measured pressure curves.
5. Meshing methodology To generate a computation mesh of the piston ring pack, a detailed geometric model of the real piston assembly is required. Said models are generally built by means of a CAD-software. For the investigations presented in this paper, the geometric model was built in a parameterized way in order to optimize the required time for potential iterations. Starting from basic dimensions of the piston, rings and liner, the model is extended by consideration of
piston crowning and ovality data. In a subsequent step, the influence of thermal expansion due to the thermal load at the operating point is superimposed on the CAD-model. For simplification purposes, the piston skirt is truncated slightly below the third piston ring. On the one hand, the area below the third piston ring has a direct connection to the crankcase and therefore the assumption of neglecting most of the piston skirt is applicable. Averaged in circumferential direction, the connection is valid due to the decrease of the piston diameter in the piston pin area (cf. Fig. 1). On the other hand, this model assumption reduces the total number of cells of the mesh and hence the runtime of the simulation. In order to improve the numerical stability of the subsequent CFD-simulation performed on the mesh, additional inlet and outlet volumes are attached to the upper and lower end. The completed geometric model of the fluid area is visualized in Fig. 7 (cf. light blue section), where the gray part with the red-colored surface cut on the left represents the piston. In this image, the dark blue section on the right belongs to the boundary imposed by the liner and the three gray elements represent the piston rings. As discussed in the theoretical section, a 2D-cut is chosen for this simulation. To obtain a simulation mesh the cut is mapped with a two-dimensional mesh first and then extruded with one cell layer thickness. Due to the huge range of dimensions (e.g. from the mm-range in the reservoir areas behind the rings to the μm-range in the contact areas), a special meshing strategy had to be developed which has been discussed in detail in [12]. As a short insight into this method, the basic steps shall be summed up as follows:
subdivision of 2D-cut into better meshable parts (‘subgeometries’) in the CAD-software,
export of subgeometry elements and import in CFD-tool, manual meshing of subgeometries using structured meshes as far as possible, and
connection of the meshed parts and creation of required selections.
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Fig. 9. Piston velocity curve (λ ¼ 0:32, n ¼ 1500 rpm).
Fig. 10. Temperature boundary condition at the inlet.
Fig. 8. Simulation mesh (left) and computational domain (right).
Many of these steps can be performed with specifically developed macro-assistance, thus enabling the creation of a functional mesh in a reasonable time. The completed quasi-2D mesh is shown in Fig. 8 on the left. The application of the presented meshing process allows the use of significantly differing cell sizes over the computational domain. In Fig. 8 the variation in cell sizes is visualized by different tones of gray. This procedure has to be repeated for every ring separately in the lower and the upper contact position. The six meshed parts can then be combined to eight complete meshes. These are necessary to model the movement of the ring, including axial, radial, and twisting movement of the three rings. In combination with switching between the meshes, a specifically developed mesh deformation algorithm can map to every state between the contact positions. A typical cell count of a single mesh is at approximately 200,000 cells. 6. Comparison of 1D-simulation and 2D-CFD simulation The next step in the simulation chain is to implement a singlephase 2D-CFD simulation performed on the presented mesh with the
commercial tool AVL FIRE, covering a complete working cycle. This helps to manage and gradually increase the degree of complexity. Moreover, a detailed insight into the blow-by gas flow can be achieved. The required boundary conditions can be classified in an analog manner to the ones of the 1D-investigations (cf. Section 4). The geometrical data has already been considered in the meshing process. In addition, it can be used to calculate the piston velocity over the time – the corresponding data is shown in Fig. 9. For the simulation a coordinate system fixed to the piston is applied. Thus a transformation from the inertial system, which in itself is fixed to the observer, is required. Therefore, the inverse piston velocity is imprinted on the liner side of the mesh as a boundary condition. The used fluid (air) is initialized in three selections with the respective initial pressure. This is a necessary step to meet the pressure gradient at the beginning of the working cycle. Said pressure gradient is induced by the negative pressure of the naturally aspirated engine during the suction phase. Hence, the convergence of the simulation can be enhanced in the beginning and helps to optimize the calculation time. The required thermodynamic data includes pressure and temperature curves at the inlet of the computational domain, which is equivalent to the averaged quantities in the combustion chamber. The combustion chamber pressure was already shown in Fig. 6, the temperature boundary condition is illustrated in Fig. 10 . The latter can be derived from a pressure analysis of the former quantity. As a result of taking into account these boundary conditions, the 2D-CFD simulation can be performed. The obtained results can be classified in two categories – vectorial and scalar results. In the following, the vectorial results will be used to provide a qualitative overview over the flow paths and phenomena. The scalar results (e.g. pressure curves) enable quantitative evaluation, calibration and validation. In Fig. 11, the velocity field of the calibrated final simulation is displayed at selected crank angles in order to illustrate the basic behavior of the blow-by flow. It is obvious that the blow-by gas flow, induced during the high pressure phase, gradually penetrates into the piston ring pack. In total it takes about 80 °CA for the blow-by to pass the ring pack. Two basic flow paths can be identified – the first through the gaps between the rings and their
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Fig. 11. Velocity field of the gas flow simulation at selected crank angles.
Fig. 12. Comparison of simulated and measured pressure curves.
corresponding ring grooves as well as over the reservoir areas behind the rings, and the second between the rings and the liner. The latter mechanism can most likely be attributed to circumferential effects in the real engine. On the one hand, a perfect shapeadaption capacity cannot be guaranteed over the circumference, i.e. there will always be residual gaps between rings and liner. On the other hand, the resulting space from the combined surface roughness adds to the residual gap. Due to deflection and redirection of the flow, both stable and dynamic vortices and their respective recirculation regimes respectively emerge. Especially in the reservoir areas and in the area below the second ring's nose, a vortex formation can be observed. The pressure curve results, evaluated in the ring land areas, can be used for validation purposes – they are shown in Fig. 12, in combination with the 1D-simulated and the measured data. The peaks, including their position and amplitude, show a good
correlation with the measured data, especially for the first ring land pressure (p12). The gradients of the pressure curves match just as well. It can also be noted that the 2D-CFD simulation shows a distinct peak of the second ring land pressure (p23), which is in contrast to the 1D-simulation. Smaller differences in the second ring land pressure curve and the delayed drop of pressure can be associated with model assumptions and the respective errors. In particular, the influence of the ring end gap cannot be completely compensated in the 2D-model. Using the minimal clearance model, the reduction of the pressure, built up during the high pressure period, is delayed. This is a result of the compensation of the pressure gradients during the low pressure period and intake stroke, which can only take place via the (constant) minimal gaps, while the influence of the ring end gaps increases in the real engine throughout these phases.
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Another means of validation possibility is the integral blow-by l matches the measured value. The CFD-simulated value of 3:45 min value within a deviation of less than one percent. The blow-by curve cannot be measured directly but can be compared with the 1D-simulated data (cf. Fig. 13). The CFD- and 1D-simulated curves correlate very well regarding the general behavior (peaks, amplitude, and gradients). The CFD-simulation shows a stronger influence of the ring contact position alteration (e.g. 15° CA and 210° CA in Fig. 13), as this effect can be resolved better in 2D-CFD. The delay of the ascending flank of the CFD-blow-by curve, compared to the one provided by the 1D-simulation, can be explained in a equivalent way as the delay of the ring land pressure drop. The flow through the ring end gaps can accelerate the first penetration of the blow-by flow. It is noteworthy that both integral value and blow-by curves are alike between the cycles when performing a multi-working cycle CFD-simulation with the presented setup.
7. Multiphase simulation constraints After achieving good results for the calculation of the gas flow in the piston ring pack, an oil phase was added to the model for further improvement of the simulation and adaption to the reality. Therefore, several extensions of the simulation model were necessary. Due to calculation time restrictions, it was not possible to calculate multiple cycles of the engine, so the oil was initialized at the start of the simulation. The initialization of oil in the oil reservoirs of the ring grooves is shown in Fig. 14. Empirical findings from the literature [21,27] and the fact that the oil supply rises from the combustion chamber to the crankcase, the oil filling ratios behind the rings were initialized in a gradual manner. The first piston ring was initialized with 5%, the second ring with 10%, and a ratio of 15% was chosen behind the third ring.
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Initializing the oil at the bottom of the reservoirs is valid due to the starting point of the simulation at BDC. The remaining flow area was initialized with air. Because the oil filling ratios behind the rings require an estimation, they were varied in a study to investigate the influences of the oil filling ratio on the oil distribution in the piston ring pack. To enable oil supply in the system, in every down stroke of the piston, oil was introduced to the simulation pressureless beneath the third ring (oil ring) in an additional study. The modeling concept assumes that there is always enough oil beneath the oil ring during the down stroke of the piston. The acceleration of the piston is responsible for inertia forces on the fluid in the piston ring pack. Because of the comparatively small accelerated masses, this force is not taken into account for a large number of gas flow calculations. However, this assumption is invalid for multiphase flows with oil. The piston acceleration curve for 1500 rpm can be seen in Fig. 15 and was included in the multiphase simulation as a volume force in the momentum equation (cf. Eq. (6)). The liquid phase is highly influenced by the acceleration forces as the acceleration due to the piston is several magnitudes above the influence of gravity. As mentioned in the theoretical section of this paper, exchange models can be considered between the single phases. A mass exchange between gas and oil phase was not modeled in the simulation as it would have required the introduction of a third phase, namely gaseous oil. In wide parts of the piston ring pack, the temperatures are moderate, hence evaporation of oil was neglected. Momentum exchange between the gaseous and liquid phase was calculated with a model based on interfacial area density, drag coefficient, and relative velocity between the phases. The drag coefficient is a function of the disperse phase's Reynolds number. Energy exchange between the phases was modeled with a Ranz–Marshall approach [15]. The heat transfer is calculated with a Nusselt number correlation. The exchange of turbulence between the phases could not be modeled with the software used for the investigations shown in this paper. Thus, the turbulence fields of both phases have been assumed to be homogeneous. The remaining constraints (piston speed, pressure, temperature, and ring movement) are identical to the simulation of the gas flow.
8. Multiphase simulation results
Fig. 13. Comparison of the simulated blow-by curves.
In this section, the results of the oil distribution in the piston ring pack at selected crank angles are introduced and discussed. The focus is on the oil transport phenomena known from the literature and experimental studies. Furthermore, results from the piston ring study with an oil supply (model extension) and the variation of oil filling ratios are shown. To simplify the interpretation of the oil distribution, arrows are added to each figure. They show the current normalized vector of the liner velocity and the piston acceleration at the specific crank angle.
Fig. 14. Oil initialization.
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Fig. 16 shows the oil distribution in the ring pack at various selected crank angles. The initialization of the oil behind the single rings can be seen at 179° CA. During the intake stroke, pressures below atmospheric pressure are possible as the research engine used for this investigations is naturally aspired. Therefore, the effect of reverse blow-by on oil can be observed at 152° CA. Caused by the gas flow, the oil behind the first and second ring is pushed back by a small amount. Behind the third ring, however, a gas bubble can be observed, because a bigger amount of oil is initialized in the third ring reservoir. The beginning of the first out of four oil alterations in the ring grooves during a full combustion cycle is shown at 42° CA. The alteration is completed at 20° CA, whereby the interaction between the gas and oil flow can especially be observed in the second and third ring groove. A possible cause for this are the high velocities in the ring pack at this point of time. Right before BDC (154° CA), the oil is again in the lower position of the oil reservoirs and an oil leakage to the crankcase is observable. At the end of the simulation (540° CA), the oil is almost in the same position as was the case at the initialization. However, small amounts of oil was lost to the crankcase and the combustion chamber.
A detailed consideration of the results also shows various oil transport mechanisms in the ring pack. At the second ring, the oil transport due to blow-by/reverse blow-by can be seen (cf. Fig. 17). The ring is in the lower position of the groove and there is oil between the groove and the ring at 320° CA. The oil is pushed in the direction of the second ring land due to leveling of the pressure difference. When the ring starts to alternate, the blow-by is intensified. The higher velocities enable entrainment of oil from the gap between ring and groove. A single droplet is teared out of the film and is transported by the blow-by flow (331° CA). The droplet impinges on the cylinder wall and deposits as an oil film (342° CA), before the oil interacts with one of the rings again. An example for pumping and squeezing of oil in the ring pack can be observed at the first ring, which is in the lower position in the groove at 338° CA in Fig. 18. Oil is visible between top ring and the
Fig. 15. Piston acceleration curve (λ ¼ 0:32, n ¼ 1500 rpm).
Fig. 17. Oil transport mechanism: blow-by/reverse blow-by oil transport.
Fig. 16. Oil distribution (volume fraction of oil) in the piston ring pack at selected crank angles.
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Fig. 18. Oil transport mechanism: pumping/squeezing of oil in the ring grooves.
Fig. 19. Oil transport mechanism: oil throw off caused by inertia forces.
upper ring flank. Due to the inertia forces driven alteration of the top ring at gas exchange TDC, oil is pushed in the direction of the groove as well as to the top land. At 348° CA, the top ring can be seen in the upper position in the ring groove (cf. Fig. 18). Pumping and squeezing of oil is an oil transport mechanism which occurs in almost every ring alteration. Oil throw off in the direction of the combustion chamber caused by inertia forces is an important issue for the combustion process development of supercharged gasoline engines. Even single oil droplets can be responsible for unintended ignitions in the combustion chamber during the compression stroke, which can lead to knocking in the engine. An example for an oil droplet moving towards the top land to the combustion chamber is shown in Fig. 19. Before the gas exchange TDC, an oil droplet is forming above the top ring (cf. 313° CA). The oil forming the droplet emerges from the reservoir behind the first ring. Although the piston slows down close to TDC, the acceleration still increases. Due to inertia forces, the oil droplet is moving along the top land in the direction of the combustion chamber. If the oil droplet is large enough, the potential for its intrusion into the combustion chamber is significant. A similar behavior is also possible at ITDC. Scraping oil off the cylinder wall and therefore controlling of the oil supply are tasks of the second and the oil ring. This process
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Fig. 20. Oil transport mechanism: oil scraping off the cylinder wall.
is illustrated in Fig. 20. The scraping process and the redirection of the oil at the edge of the napier ring can be observed well in this figure. Furthermore, the oil is set into a rotational motion in the second ring land between the second and the oil ring. The scraping process at the oil ring takes place in a similar way. The first simulation showed the oil distribution and even some oil transport mechanisms could be calculated. Fig. 16 illustrates that the oil supply of the ring pack decreases after one working cycle. Calculating multiple cycles with the first model would lead to a dry piston ring pack. In reality, the ring pack is permanently supplied with oil. The oil in the crankcase from the piston cooling jet and the plain bearings deposits on the liner underneath the piston and therefore supplies the ring pack with oil. During the down stroke of the piston, the assumption of full oil filling below the oil ring is valid (cf. [23]). This fact has been used for the model extension of the simulation with the oil supply. The results of the extended model are depicted in Fig. 22. The results for the oil distribution during the upstroke of the piston – before oil is introduced into the computational domain – are identical to the results without oil supply. As soon as the piston is moving downwards, the oil supply leads to two inlet oil transport paths. Because the movement of the oil ring strongly depends on the inertia and friction forces of the ring, the oil ring usually remains in the upper position in the groove during the downward stroke of the piston. Thus, the oil can enter the ring pack below the oil ring to the oil reservoir. The second identified transport path feeds the oil film in the radial gap between the rings and the liner. The oil film is partially scraped off of each of the rings. As a consequence, the oil finds its way to the respective reservoir of the rings (cf. 300° CA). At the second ring, the oil is scraped off in a stronger fashion compared to the other rings and the oil remains longer in the ring land, before it flows to the reservoir of the oil ring. The oil reservoir of the second ring is filled again from above, due to blow-by flow. At the end of this paper, the effect of different oil filling ratios in the oil ring reservoir should be discussed. Fig. 21 shows the oil alteration at ITDC for three varying initial oil filling ratios (15%, 20% and 25%). The basic behavior of all three variants is equivalent. The starting location for the oil alteration at the oil ring reservoir is strongly dependent on the reverse blow-by for this particular case. The bubble of the reverse blow-by breaks up the oil and therefore defines the spot for the beginning of the alteration. Similar oil distributions of the calculation have been taken into account for comparison purposes, to show the time shift due to the different initial oil filling ratios. The acceleration vector is pointing upwards for all variations and time steps shown in Fig. 21. The main finding of this study is that the higher the oil filling ratio, the earlier the oil
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Fig. 21. Comparison of different oil filling ratios (5/10/15, 10/15/20, and 15/20/25 from top to oil ring in percent) exemplary displayed for the oil ring.
The 1D-results were validated with experimental data for the
piston ring motions, ring land pressures, and integral blow-by. The 2D-results were validated with experimental data for ring land pressures and integral blow-by. Additionally, 1D- and 2Dsimulated blow-by curves were in good agreement to one another. The correlation between simulated and experimental data was very good, even in the case of multiple working cycles. After successfully investigating the gas flow in the ring pack, the model was extended to a multiphase simulation, considering gas and oil flow. The multiphase results showed the general behavior of oil during a working cycle (e.g. oil alteration in the ring grooves as well as gas interaction with the oil). Oil transport mechanisms could be observed in the results of the simulation model: blow-by/reverse blow-by oil transport, pumping/squeezing of oil in the ring grooves, oil throw off caused by inertia forces, and oil scraping off the cylinder wall. The model was extended with an oil supply below the oil ring. The study of the varying initial oil filling ratios in the oil reservoirs showed the importance of the amount of oil in the ring pack. The model is able to describe the oil transport in the piston ring pack. The insights of the CFD-results can help to improve 1Dmodels for the piston ring pack.
Acknowledgements
Fig. 22. Oil distribution in the piston ring pack (with additional oil inlet) at selected crank angles.
alternates in the reservoir. This fact emphasizes the effect of oil filling ratios on the oil supply of the complete piston ring pack .
9. Conclusion
A CFD-model was developed for the calculation of the gas and
oil flow in the piston ring pack of an internal combustion engine and optimized with regard to calculation time. A 1D-model for the calculation of the ring motion was developed simultaneously. An existing meshing methodology was applied successfully and extended for the current case.
The authors would like to thank C. Kirner and B. Uhlig from the institute of internal combustion engines of the Technische Universität München. They provided experimental data (piston ring movement, ring land pressures and integral blow-by) to validate the simulations.
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