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Estimation of oil supply time during engine start-up at very low temperatures.

INTRODUCTION

Engine oils must provide lubrication of various critical engine parts (piston/rings/liner zone, bearings, etc.), and their properties are well-understood within a wide range of temperatures, with the general knowledge that the viscosity increases with decreasing temperature. However, under very cold conditions (-20 ... -40[degrees]C), the lubricating oils exhibit a complex rheological behavior, which is particular to each type of oil. The oil behavior becomes non-Newtonian, and it appears to gel to a quasi-solid state in the oil pan.

If the oil fails to flow and the pump absorbs only air, catastrophic engine damage is likely to occur. The difficulties in starting and cranking automotive engines at temperatures around -18[degrees]C due to formation of gel structures (caused by the polymers used as additives in multi-grade oils) have been long recognized [1]. The particular cold-temperature behavior is due to the fact that the engine oils, especially the multigrades, are formulated by mixing base (stock) oil with additives that are various types of polymers. Base oils are different (Fig.1), and for mineral base oil the exact composition may vary from one batch to another. The chemical structure and amount of added polymers that serve as viscosity-index (VI) improvers is quite diverse [2], and impacts the low-temperature lubricant properties. Among other roles, the viscosity modifiers reduce viscosity changes with temperature, and also help the engine ability to start at low temperature. Some of the most common polymers include olefin co-polymers (OCP) and poly-alkyl-methacrylates (PMA). The mechanism that enables polymers to perform the VI improver function is not completely understood [3]. Additionally, the properties of used oil differ from those of the fresh oil, because the presence of particulate contaminants and soot impacts the low-temperatures behavior [4].

In order to provide an assessment of motor oil operability at low temperatures, a number of standard testing methods are available (Fig.2). The standard ASTM D5293 concerns the ability of oil to permit a satisfactory cranking speed at start-up. It is thus assumed that oil is present in bearings, and its viscosity is small enough as to permit engine cranking. ASTM D5293 indicates viscosity limits for various types of oils. Since the bearings are working at a significant speed, this test implies higher shear rates ([10.sup.4] ... [10.sup.5] [s.sup.-1]). ASTM D4684 refers to the ability of the oil to start flowing and reach the oil pump at start-up, and measures the yield stress and viscosities for controlled cooling temperatures and cooling profiles. Since the oil is initially undisturbed, this test envisages low shear rates (0.4 ... 15 [s.sup.-1]). Maximum viscosity for the test is 400 Pa.s. Another standard is ASTM D5133, based on the Scanning Brookfield Technique (SBT) that can provide a viscosity curve from -5 to -40[degrees]C, and calculates the Gelation Index of the sample. SBT is a low-shear rate test (0.2 [s.sup.-1]). The Gelation Index reveals changes in viscosity when temperature is decreased, and is indicative of structures formation in the oil. It was observed that a low cooling rate (e.g., 1[degrees]C/h) helps develop solid structures [4], which further decreases oil operability. The ASTM standards specify the type of equipment to be used for the testing.

The tests mentioned above are useful in selecting a particular type of oil for a certain application at a given temperature, as well as for comparing different oils. However, the rheological behavior may depend on the manner the shear stress increases with time, but cannot be tested because of equipment limitations. Another aspect concerns the yield point, which is the pair (shear rate, shear stress) where the flow is initiated. Oils at low temperatures present a strongly non-Newtonian behavior [2]. The range of shear rates tested per ASTM standards is limited, such that the measurements do not necessarily identify the yield point. In order to characterize the general flow curve, a wider range is necessary (an experimental method that addresses this aspect will be presented later).

RHEOLOGICAL MODELING AND MEASUREMENTS AT LOW TEMPERATURES

A number of rheological models are available to predict the flow curve [5,6,7], each providing approximations for particular media. The models most commonly used to describe the rheological behavior of the engineering fluids are the Newtonian, Bingham, power-law, and Herschel-Bulkley models (Eq.1, a and b). The Bingham plastic fluid is similar to a Newtonian fluid, exhibiting a linear shear stress vs. shear-rate curve, after an initial shear stress threshold, [t.sub.0], ('yield stress') has been reached. The power-law model describes a fluid for which the stress is proportional to the shear rate raised to an exponent.

Among these models, the most complex is Herschel-Bulkley fluid (Fig.3), which incorporates the elements of Newtonian, power-law, and Bingham fluid models. The parameters of the Herschel-Bulkley equation are usually determined by fitting experimental points.

When the vehicle remains stationary for a sufficiently long time, the oil may flow back to the pan, such that the oil pump is not primed.

Prior to the engine start-up, the lubricant is at rest, such that the shear rate is zero, and will increase during the engine cranking. The flow in the engine sump is driven by the weak suction created by the oil pump (entraining air), and the values of the shear rate, [gamma], in the oil are very low. Thus, in order to realistically simulate the pumping at start-up, accurate test data are needed for low values of the shear rate. A testing procedure was developed, and is presented below.

The equipment used for oil testing was a parallel-plate design, controlled-stress rheometer (TA Instruments) with an environmental test chamber that permits the accurate control of the temperature, as well as of the lubricant soaking time at a given temperature. For this work, generic 10W30 oil was chosen, formulated to perform at API SN level. The oil was submitted to a temperature of -40[degrees]C. This value represents an extreme case of cold start-up, when the oil is in gelled state. The pumpability of oil is difficult, and it may cause engine damage during start-up.

Since at a very low temperature the oil is (when at rest) in a quasisolid state, a 'yield point' can be intuitively defined as the pair (shear rate, shear stress)=([[gamma].sub.0], [[tau].sub.0]) where the lubricant starts to flow, such that after the yield point (i.e., for [gamma] > [[gamma].sub.0]) it behaves as a fluid. The Herschel-Bulkley model may be used:

[tau] = [[tau].sup.(e).sub.0] + k[[gamma].sup.n.sub.0] = [[tau].sub.0] + k([[gamma].sup.n] - [[gamma].sup.n.sub.0]), if [gamma] > [[gamma].sub.0] (1a)

where k is a consistency parameter, and n is a power-law index, and [[tau].sup.(e).sub.0] is the extrapolation of the power-law curve on the stress axis.

Measurements with a 10W30 engine oil showed that cold lubricant is a viscoelastic medium that exhibits both a storage (elastic) modulus and a loss (viscous) modulus when submitted to a small oscillatory shear rate. Thus, in the context of CFD the region [gamma] < [[gamma].sup.0], may be modeled as either a Hookean or a viscous (Newtonian) medium. For applications such as the pumping during engine start-up, it is more convenient to model this region as a lower Newtonian medium [5] using the Herschel-Bulkley fluid model:

[tau] = const x [gamma] = [[mu].sub.0] [gamma], if [gamma] < [[gamma].sub.0] (1b)

where is the "zero-shear" viscosity. This modeling describes a medium that exhibits two different, discontinuous fluid-behavior regions. From a practical standpoint, the yield point is difficult to determine from measurement results. Also, the presence of this discontinuity means that the Herschel-Bulkley might not provide a satisfactory approximation for cold oil behavior for numerical simulations.

Two types of measurement were performed using the rheometer in order to characterize the initial lubricant behavior: oscillatory shear rate amplitude sweep, and linear shear-stress ramp. For the measurements presented below, the oil sample was initially exposed to -40[degrees]C for a period of four hours.

In the oscillatory shear-rate amplitude sweep test, the motion is applied as an oscillatory (sinusoidal) rotation of the shaft with an angular frequency of 10 rad/s, such that the shear strain increases linearly with time from [10.sup.-4] to 10 [s.sup.-1]. The oscillation amplitude is small, in order to avoid the destruction of the gel structures. The results are shown in Fig.4. The viscoelastic characteristics of the cold oil are characterized by the complex shear modulus,

[G.sup.*] = [G.sup.'] + iG" (2)

where G' is the storage (elastic) modulus that represents the ability of the material to store energy, while G" is the loss (viscous) modulus that represents the ability of the material to dissipate energy. At low shear rates, the storage (G') and loss (G") moduli are constant, but they start decreasing as shear rate increases. The yield point for the oscillatory tests is defined as the 5% drop in the value of the storage modulus. It can be seen that during the oscillatory motion for low shear rates, the lubricant exhibits a significant elastic behavior, with the phase angle [delta]=23[degrees] (since 5=0[degrees] for a purely elastic response, and [delta] = 90[degrees] for a purely viscous (Newtonian) behavior).

In the shear-stress linear ramp test, the stress is linearly increased with time from [10.sup.1] Pa to [10.sup.4] Pa (equipment limitations preclude testing at higher stress values). The experimental results (Fig.5) show that the viscosity initially increases slightly up to a maximum value, [[mu].sub.max], after which it starts decreasing. The shear rate initially increases quasi-linearly, but changes slope at almost the same value of stress that corresponds to the maximum viscosity. The yield point is taken as the location of the maximum viscosity.

The values of yield stress and yield strain rate differ significantly for the two methods. The ratio of yield stresses, [R.sub.[tau]] = [[tau].sub.0,osc]/[[tau].sub.0], is 0.5, while the ratio of shear rates, [R.sub.[tau]] = [[gamma].sub.0,osc]/[[gamma].sub.0], is about 18. This indicates that in oscillatory conditions, when the gel structures are not destroyed, the solid character of the oil is preserved up to larger values of shear rate. For the problem of oil pumping at start-up, characterized by a slow continuous motion, the results from the linear stress ramp method are more appropriate, since the continuous motion with increasing stress is expected to destroy the gel structures.

The Herschel-Bulkley approximation can be used to model the oil behavior (Fig.6). A curve-fitting technique was used to calculate the parameters (k and n). It can be observed that both [tau] and [mu] predicted by Herschel-Bulkley do not provide a satisfactory approximation of the experimental values, mainly in the low shear-rate region prior to the yield point. The viscosity in Herschel-Bulkley is approximated as a constant value before the yield point (while the actual viscosity is much lower), and its slope is discontinuous. For the computational simulations, the large value of the initial constant viscosity may cause numerical instabilities. Since the stability and accuracy of CFD simulations at start-up are strongly dependent on the shear stress vs. shear rate curve, the tabular implementation of the experimental data is considered a better alternative to using the Herschel-Bulkley approximation.

COMPUTATIONAL METHOD

The CFD software PumpLinx (Simerics Inc.) was used for the numerical simulations. The rheological properties of oil can be implemented either by using the Herschel-Bulkley model (Eq.1a, b), or by defining the stress-vs.-shear rate dependence. In the present work, a look-up table was used for specifying the shear stress as a function of shear rate. The multiphase model uses the Volume of Fluid approach. For any arbitrary phase, a, the conservation equation is implemented in the form

[[partial derivative]/[partial derivative]t] [[integral].sub.V] [[rho].sub.[alpha]] [f.sub.[alpha]] dV + [[??].sub.S] [[rho].sub.[alpha]][f.sub.[alpha]] (u - [u.sub.g]) x dS = 0 (3)

where [rho] is the density, [u.sub.g] is the grid velocity, V is the control volume, and S is its enclosed surface. The summation of the phase volume fractions must satisfy the following relations:

[summation][f.sub.[alpha]] = 1

[summation][[rho].sub.[alpha]][f.sub.[alpha]] = [rho] (4)

The governing equations for the mass and momentum conservation for the system of phases may be expressed in the integral form:

[[partial derivative]/[partial derivative]t] [[integral].sub.V] [rho]dV + [[??].sub.S][rho] (u - [u.sub.g]) x dS = 0 (5)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

The terms on the right side of the momentum equation represent, respectively, the molecular and turbulent shear force, the pressure force and the body force. The shear stress is given by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

where [[mu].sub.t] is the turbulent viscosity, and k is turbulent kinetic energy. For turbulence, the standard k-e model is used. When the look-up table is supplied to the code, the shear stress is calculated based on the shear rate as

[[tau].sub.ij] = func ([[gamma].sub.ij]), [[gamma].sub.ij] = [partial derivative][u.sub.i]/[partial derivative][x.sub.j] (8)

The equations are implemented in a symmetric form such that an arbitrary number of phases can be included in the simulation. The interface between the various phases is maintained using a higher order interface capturing scheme [8].

Simulation Process for Estimation of the Oil Pump Priming Time

The danger of engine failure during the cold start-up increases with the time that the lubricating requires to reach the oil pump (i.e., pump priming time), since it affects the oil supply to various critical engine components (bearings, piston ring-pack, etc.). In principle, this time can be measured by direct testing in a cold environmental chamber. However, the testing poses numerous challenges, and is consequently costly and time consuming. The numerical simulations, performed with CFD codes with non-Newtonian and multi-phase modeling capabilities, and using rheological data acquired for particular engine oils, have the potential to estimate the priming time faster and more economically than direct testing.

The flowchart of the proposed approach is summarized in Fig.7. For an actual engine case, where the type of oil and operating conditions are known, rheological testing is capable to provide accurate oil data that can be used by the numerical simulations. The validation of the numerical approach is achieved by performing reference experiments on simple geometries (see the next section). Once the validation is completed, numerical simulations are performed using the actual engine geometry.

Validation of the Numerical Approach

In order to verify the validity of the numerical approach, the results of the numerical simulations were compared against the experimental data obtained with a test device that mimics the cold lubricant suction through the oil pick-up tube during the engine start-up. The test also verifies the assumption that the oil properties, determined using a linear stress ramp, are applicable for oil suction from an undisturbed state.

The experimental device (Fig.8) consists of an oil pan and a suction tube connected to a vacuum pump. At its simplest, the suction tube has a square cross-section (21 mm in size), and the time-changing oil level in the tube is monitored by a computer-controlled digital camera with frame rate of 60 fps. For this test, the oil pan is a transparent vessel containing 800 [cm.sup.3] of oil. The square tube (made of polycarbonate) is located at 25 mm above the pan bottom, while the initial oil level was set at 50 mm above the bottom. The device is maintained at a controlled temperature (-40[degrees]) inside an environmental chamber, and the observation and image recording are done through an observation window. The temperature is monitored by thermocouples installed in the chamber, and in the oil pan. For all the experiments described in the section, the oil pump provides a suction pressure of 60 kPa. The vacuum pump and the camera are synchronized, such that they can be triggered together to obtain an accurate timing of the images.

The cooling time and profile is known to have a significant influence on the cold oil properties, because it impacts the formation of the gel structures. ASTM D4684 specifies a cooling profile (at controlled rates) from 80[degrees]C to temperatures between -20 and -40[degrees]C over a period of over 45 h. However, in order to expedite the testing procedure for validation purposes, the environmental chamber was set to a constant temperature of -40[degrees]C, such that the entire experimental device was cooled from the ambient temperature (22[degrees]C) to the target temperature. The experiments were performed after a chosen soaking time (4, 20 or 48 h), which was counted after the oil pan temperature reached the target temperature. As the actual experiments required a short amount of time (of the order of 10 s) and were performed without opening the chamber, the oil temperature change during the experiments is negligible. The data in Fig.9 show that the rise of the oil in the suction tube is slower for longer exposure times.

The CFD validation simulations were performed for the case of 4 h of soaking. The computational domain was discretized using about one million hexahedral cells. The simulations were performed using the explicit method for the multi-phase module, with a time step [DELTA]t = 0.3 ms. The maximum Courant number over the simulation was 0.34. Different mesh densities and time steps were tested, such that a good accuracy was achieved at a reasonable computational cost. The boundary conditions are shown in Fig.10, where [f.sub.oil] is oil the volume fraction, and [DELTA]p is the suction pressure (60 kPa).

The comparison between simulation results and experimental data shows a good agreement in terms of the motion of the oil/air interface inside the pick-up tube (Fig.11). In an actual engine geometry, the CFD simulation permits to estimate the time necessary for the oil to reach the oil pump, and subsequently to fill the oil passages. There are a number of factors that impact the accuracy of the predictions.

For instance, the stress-vs-shear rate curve has to be measured in conditions similar of actual cool-down process (i.e., similar soaking time and cooling rates). Also, at low temperatures the shape of oil/air interface, surface tension and the contact angle at low temperatures may be different than at the usual engine temperatures. Figure 12 shows the observed shape of oil/air interface at -40[degrees]C during the experiment in the polycarbonate tube, for the two soaking times (a) 4 h, and (b) 20 h. The shape of the interface for 4 h is quasihemispherical, and the value of the contact angle is about 165[degrees], while the simulation predicts a flatter interface. For the 20 h soaking time, the apparent contact angle is about 178[degrees], and an air gap can be observed between the wall and the oil/air interface. The contact angles may differ if a different material (aluminum or steel) is chosen for the pick-up tube.

The plots of shear rate, y, are represented in Fig.13. It can be observed that the values of the shear rate in the bulk of the oil are very small (<10-2 [s.sup.-1]) immediately after start-up. From the point of view of the CFD simulations, this shows the importance of availability of the oil stress-vs.-shear rate curve, because it has a significant influence on the estimation of lubricant initial motion within the oil passages, when the corresponding viscosity is of the order of 105 Pa.s. One can notice that small approximation differences (as is the case with Herschel-Bulkley curve) amount to large estimation differences in terms of viscosity especially prior to the yield point.

SUMMARY

The present work proposes an approach to estimate the time necessary at start-up for cold oil to flow in the engine, such that lubrication can be provided for critical engine components. The rheological properties of oil at very low temperatures (-40[degrees]C) are radically different from those at common temperature, and depend on the particular chemical composition of the oil. In the current approach, it is recognized that an accurate knowledge of low-temperature oil properties can be achieved by measurements using a rheometer. The time needed by the cold oil to reach the oil pump (and subsequently various engine components), could be, in principle, measured by direct testing in a cold environmental chamber.

However, this method is costly and time consuming. The proposed approach consists in using CFD software with non-Newtonian capabilities that implements the measured rheological data, as well as robust, high-resolution multi-phase models. This approach was validated against experimental data (obtained for generic 10W30 oil at -40[degrees]C) for the simple case of a straight, square cross-section tube that mimics the pick-up of an actual engine. The numerical results are in good agreement with experimental data, which shows that a realistic estimation of oil feed time in an actual engine can be achieved by CFD simulations.

Bogdan R. Kucinschi and Teng-Hua Shieh

TEMA

REFERENCES

[1.] Horowitz, H. and Vick, G., "Low Temperature Cranking and Flow Properties of Waxy, Polymer-Thickened Motor Oils," SAE Technical Paper 620529, 1962, doi:10.4271/620529.

[2.] Tanveer, S., Sharma, U.C, and Prasad, R., "Rheology of multigrade engine oil," Indian J. of Chem.Tech., 13: 180-184, 2006, ISSN: 0971457X.

[3.] Covitch, M.J and Trickett, K. J., "How Polymers Behave as Viscosity Index Improvers in Lubricating Oils," Adv. in Chem.Eng. andSci., 5:134-151, 2015, dx.doi.org/10.4236/aces.2015.52015

[4.] Miiller, G.C., "Low-Temperature Rheological Response of Fresh Versus Used Oils Using the Scanning Brookfield Technique," Viscosity and Rheology of In-Service Fluids as They Pertain to Condition Monitoring, STP 1564, Rishell Amy, Ed., pp. 119-130, 2013, doi:10.1520/STP156420120090

[5.] Barnes, H.A., Hutton, J.F., Walters, K., "An introduction to Rheology", 1989, ISBN : 0444874690.

[6.] Macosko, C.W., "Rheology: principles, measurements, and applications", 1994, ISBN: 0471185752.

[7.] Khonsari, M.M. and Booser, E.R., "Applied Tribology: Bearing Design and Lubrication," 2nd ed., 2008, ISBN: 978-0470057117

[8.] Ubbink, O. and Issa, R.I., "Method for capturing sharp fluid interfaces on arbitrary meshes", J. Comput. Phys., 153: 26-50, 1999, dx.doi.org/10.1006/icph.1999.6276

CONTACT INFORMATION

Bogdan R. Kucinschi

Toyota Motor Engineering & Manufacturing North America, Inc.

Toyota Technical Center

1555 Woodridge Ave., Ann Arbor, MI 48105

(734) 995-6336

bogdan.kucinschi@tovota.com

Tom Shieh

Toyota Motor Engineering & Manufacturing North America, Inc.

Toyota Technical Center

1555 Woodridge Ave., Ann Arbor, MI 48105

(734) 995-3119

tom.shieh@tovota.com

ACKNOWLEDGMENTS

The authors would like to thank Dr. Sujan Dhar (Simerics Inc.) for the support with the rheological modeling in the CFD software PumpLinx, and Dr. Lexie Niemoller (TA Instruments) for the useful discussions on low-temperature rheological measurements.
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Author:Kucinschi, Bogdan R.; Shieh, Teng-Hua
Publication:SAE International Journal of Fuels and Lubricants
Article Type:Technical report
Date:Jun 1, 2016
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