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The Puddle Theory of Oil Consumption©David P. Hoult a & Byron T. Shaw II aa Sloan Automotive Laboratory , Massachusetts Institute of Technology , Cambridge,MassachusettsPublished online: 25 Mar 2008.

To cite this article: David P. Hoult & Byron T. Shaw II (1994) The Puddle Theory of Oil Consumption©, Tribology Transactions,37:1, 75-82, DOI: 10.1080/10402009408983268

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The Puddle Theory of Oil Consumption@ DAVID P. HOULT and BYRON T. SHAW I1

Sloan Automotive Laboratory Massachusetts Institute of Technology

Cambridge, Massachusetts

A theoretical model is developed to explain oil consumption in IC engines, based on the mechanism of oil being blown from a

puddle directly below the top ring gap through the top ring gap into the combustion chamber during top ring reversal. This phe- nomenon is widely reported i n the literature and is hereafter deemed

the puddle theory of oil consumption. The model developed is sup- ported by experiments conducted on a small, prodr~ction single- cylinder diesel engine at various speeds using two oils. The collected

data were used to construct semi-empirical, non-dimensional scaling laws to predict oil consumption. The formulas presented are capable

of predicting oil consumption within ten percent, the experimental

accunzcy.

INTRODUCTION

This paper presents a theory and supporting experiments for the following model of oil consumption: Suppose that

Presented at the 48th Annual Meeting in Calgary, Alberta, Canada

May 17-20,1993 Final manuscript approved February 3, 1993

oil consumption in a four stroke reciprocating engine occurs only during the five crankangle degrees when the gas flow- ing through tlhe top ring gap first reverses, and flows into the combustion chamber from the second land. This phe- nomenon is typically observed about 100" after top dead center on the expansion stroke (I). Suppose that the oil consumed comes from the second land. Then oil consump- tion would be expected to correlate with lubricant prop- erties at the temperature of the second land. This explains the correlation found by M. Smith (2). He found that oil consumption scaled with the low shear viscosity of the oil being used if the viscosity was evaluated at elevated tem- peratures, such as the temperature of the second land of the piston. HE: found that oil consumption decreased with increasing viscosity.

The oil is then carried by the gas stream directly into the combustion chamber; that is, the crown land remains dry. This was observed by Wong and Hoult (3). The crown land was shown to remain dry under various operating condi- tions with different oils. This suggests that the theory that oil is forced past the top ring and is later consumed may not be valid. If oil were forced around the top ring, one would expect an accumulation of oil on the crown land. Such an accumulation is not observed. This study also showed

AP Aref A* d

d2

DAS

g hi

hf hre~ Ah h*

LIF 12

= area of second land oil puddle beneath top ring gap = second land reference area = non-dimensionalized second land puddle area = distance between second land and cylinder liner = second land diameter = data acquisition system = ring gap width = second land oil film thickness before top ring reversal = second land oil film thickness after top ring reversal = second land oil film thickness for t < 0 = hi - hr = non-dimensionalized change in second land oil film

thickness = laser-induced-fluorescence = length of second land

P = oil dynamic viscosity = air dynamic viscosity

Y = oil kinematic viscosity O.C. = oil consumed P = presslure on surface of oil

Q = mass flow rate of blowby gas through top ring gap QmaX = maximum value of Q RPM = speed of engine, revlmin RI, R2 = radii of curvature of the oil surface ro = radius of puddle of oil consumed P = oil density S = oil surface u = oil surface tension Ta = Taylor number = pUlu

t,,, = time for Q to reach QMAX after top ring reversal u = oil velocity in the puddle U, = gasflow velocity over oil puddle

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an inconclusive correlation between measured oil con- sumption rates and oil consumption rates calculated from oil transported by the top ring face, based on the oil film thickness measurements under the top ring. No correlation was observed for the gas exchange stokes. It is important to note here that these measurements and calculations are for modern engines using modern lubricants, where the engine components and lubricant characteristics have been carefully tuned to minimize oil consumption. Observed oil consumption rates and oil film thicknesses may not be sim- ilar in older engines, upon which previous mechanisms of oil consumption are based.

If this mechanism is correct, then changing the timing of the top ring reversal and hence the reverse gas flow through the top ring gap would affect the oil consumption of an engine. This behavior has been observed (4). The actual spout of oil being blown through the top ring gap was ob- served in an experimental engine with a glass cylinder liner (5). A follow-up paper reported decreases in oil consump- tion when the top ring has a lap joint, thus obstructing the reverse flow of gas and oil (6).

It is known that gas-driven flows of viscous lubricants depend on both surface tension and viscosity. The ratio of viscous to surface tension forces being Ta = ~ U l u , called the Taylor number in recognition of G. I. Taylor's original work on such flows (7), enters prominently in the theory.

In the first section, the theory of this model is developed. Explicit scaling laws for oil consunlption and its dependence on lubricant properties, engine micro-geometry, and engine operating conditions are developed.

The next section describes the experiments, which were done on a small ID1 single-cylinder diesel engine. The au- thors used the self-calibrating laser-induced-fluorescence method (LIF), see (8) for a recent description of the tech- nique, to measure the oil film thickness on the second land, the tritium method (9) to measure oil consumption, pres- sure transducers to measure the piston land pressure and the combustion pressure, and a wet test meter to measure the cycle average blowby. With these measurements, the gas flow through the top ring gap, the amount of oil in the puddle, and the oil consumed were independently deter- mined. Typical data are shown in (10).

The third section shows that the scaling predicted by the theory, both for the size of the puddle, and the thickness of the oil removed, is consistent with all of the data taken.

The last section gives recommended formulas for esti- mating the oil consumption in a four stroke reciprocating engine, and cautions the reader that, in poorly built or old engines, there may be additional sources of oil consumption, such as valve stem leakage (11). The authors believe that the puddle theory describes the most important oil con- sumption mechanism in most well-built modern engines.

THEORY

Figure 1 shows a side view of a piston, with a sketch of the location of the puddle with a radius ro. The mass flow through the top ring gap of width g is Q (kglsec). This causes an average gas flow over the oil on the second land of U,.

For the scaling laws derived in this section, a crude model of the gas and oil flow suffices. An axi-symmetric flow of gas and oil is defined as follows: Consider two parallel plates, spaced approximately a distance d = (cylinder bore diam- eter -d2)/2 apart, where d2 is the diameter of the second land of the piston. Let the upper plate be the cylinder liner and the lower plate the second land; d is the clearance be- tween the second land and the liner, at the time, t = 0, when Q becomes positive on the expansion stroke. The for- mula for d given above is approximate because there is a correction when the piston centerline does not coincide with the liner centerline. Clearly, a planar geometry is suitable, as d << bore diameterl2.

For t < 0, there is an oil film on the surface of thickness href << d. The ring gap is approximated as a hole in the second land at r = 0, of radius gl2. At 1 = 0 + , the gas flow into the hole starts. The time t,,, at which the maximum value of Q is attained results in the maximum U,. Polar coordinates will be used with r pointing upwards from the second land. The region corresponding to the upper half plane comprises the model of the flow.

Let the oil surface S be:

On S , the pressure is given by:

where the radii of curvature are shown to be:

where:

Now the air flowing over the oil exerts a shear stress on the oil. If u is the oil velocity, this stress balance is approximately:

where p, = air viscosity and p, = oil viscosity. The air viscosity is taken at the average of the liner and second land temperatures, and the oil viscosity is taken at the second land temperature. This gives an estimate for 14:

Now consider the oil flow: The horizontal gradients are on the order of 10 mm, the distance between the top and

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T h e Puddle Theory of Oil Consumption 77

Skirt 3 Fig. 1-Side view of piston, showing dimensions relevant to oll

consumption.

second ring o n the piston; whereas the gradients in z are o n the o r d e r o f 10 microns, the thickness of the oil film o n the second land. Hence a lubrication type flow which is nearly parallel to the second land is expected, where the pressure gradient normal to the second land is zero to first approximation:

T h u s the horizontal pressure gradient, using Eqs. [2] and [3], is related to the shape of the free surface:

With this result the horizontal gradient of pressure is:

where ro = the radius of the puddle. This unsteady capillary-viscous flow has a radial momen-

tum equation of the form:

T h e inertial a n d viscous terms a r e assunied to describe the diffusion of the vorticity, d u e to the viscous shear stress applied to the oil f ree surface S downward into the oil. T h u s these terms a r e taken to be the same order of magnitude. If the vorticity has diffused throughout the oil film, then:

where tmax is the time for the gas flow 4 to reach its max- imum value, (Lax.

T h e balance of the acceleration term with the pressure gradient yields a n estimate of ro. Consider:

which yields:

T h e estimate for the change in height of the oil film begins with the requirement that there is n o flow through the free surface:

For the presenlt problem, this results in the following equation:

where w is the velocity in the z direction a t the surface. Continuity requires that the last two terms in [14] are the same size. Balancing the first two terms gives:

This gives the estimate for the change in height of the free surface as:

where hi is thr: initial height o f the oil film, a n d hf is the final height of the oil film.

For purposes of correlating the data, the authors used averaged (over the second land) film thicknesses for h; and Iy. In addition, hrCr is taken to be equal to (h; + hJ)/2.

T h e r e a r e two assumptions in the model which a re likely to be wrong it1 detail: T h e inward flow is likely to be un- stable, and hence not axi-symmetric, a n d the initial film thickness distribution is not quite flat, on the scale of mi- crons. Neither of these difficulties change the scaling laws, Eq. [I21 and [16].

EXPERIMENT!;

T h e engine ~ t s e d was a 4.5 kw ID1 diesel. T w o lubricants

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were used, a 15W40 a n d a SAE3O oil. Table 1 gives the engine specifications.

T h e acquired data consist of LIF measurements of the piston land oil film thickness, cylinder and liner pressures using piezoelectric transducers, blowby measurements us- ing a wet-test meter, a n d oil consumption by the tritium method. Figure 2 shows a schematic of the instrumentation used to collect these data.

Figures 3 a n d 4 show the locations of the L l F a n d pressure probes. T h e data were collected with a PC-based data ac- quisition system. T h e DAS sampled the data a t 5 points per crank angle, with 12-bit accuracy, a n d is clocked by a shaft encoder with 2000 pulses/rev.

Details of the nieasurements a re given in (8) a n d (10). Because the oil consumed comes only from the puddle

directly below the top r ing gap, the rings had to be pinned, to lix the azimuthal location of the puddle directly in front of the LIF probe.

NOT TO S C A I E

Preliminary observations showed substantial variations in blowby when the piston rings are to rotate. -l-his Fig. %Axial locations of LIF probe and pressure transducer, side view.

-'-y pe No. Cylinders Bore and Stroke Connecting Roc1

Compression Ratio Cooling System Lubrication System Rated I'ower Maximum Torque Typical Application

Horizont;~l, 4 Stroke, ID1 Diesel 1 75 x 70 mni (2.95 x 2.76 in) 1 10.1 nlni (4.33 in) 0.309 liter (18.86 cu. in.) 23: 1 Water-cooled1Natural Convection Trochoiclal I'unlp/No Oil Filter 4.5 kw @ 3000 rpni (6 bhp) 15.2 Nm Remote Power Generation

SHAFT INDEX P C )

OIL FILM THICKNESS -

AIR TEMP

PRESSURE

TORQUE

LINER COOLANT AND OIL SUMP TEMPERP;IIJRES

Fig. 2-Schematic of englne lnstrumentatlon.

EXHAUST I

Optic Fiber

Optical Access-

h e r 9lindef-I

Ifansducer

Third Ring Gap C

Fig. 4--Circumferential location of LIF probe and pressure transducer, cross-sectional view.

was traced (12) to the fact that the area fo r flow through the piston ring gap varies by nearly a factor o f two de- pending o n whether the g a p is o n the thrust o r antithrust side of the piston. This study (12) was completed by using pinned rings a n d adjusting the blowby theory to match land pressure a n d blowby simultaneously.

T h e authors adjusted the blowby theory (I) to match the piston land pressure. Figure 5 shows the typical agreement, which was within five percent (experimental) accuracy for pressure. T h e e r ror in blowby was about ten percent, again near the accuracy of the measurement.

From such agreement, the axial position of the LIF probe was fixed in the middle of the second land, a t the point in time when the oil puddle is blown through the top ring gap.

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The Puddle Theory of Oil Consumption 79

I ..... Measured , \ Cylinder Pressure ,I ;

I I

Measured Land : ; Pressures . ,

a I - Calculated 2nd : 1 Land Pressure / ;

, 8

I I

. 8

Crankangle Degrees

Fig. 5--Experimental and calculated cylinder and piston land pressures.

The axial location of the LIF probe in the center of the speed range is within l o crankangle of the center of the puddle. Clearly, such accuracy is necessary since the whole oil consumption phenomenon occurs within a time period of less than 5" crankangle!

Figure 6 shows a typical pressure and oil film data set of all four channels. Figure 7 shows the oil consumption data over the 1500-3000 rpm speed range tested. Although there is no clear trend of oil consumption with speed when the rings are free for the reasons mentioned, when the rings are pinned, the oil consumption increases roughly linearly with speed, as one expects if the volume of the puddle does not change greatly with operating conditions.

From the fitted blowby theory, the flow through the top ring gap can be found. Figure 8 shows the flow -Q as a function of crankangle degrees, with the time interval t,,,, labeled. Note that the positive Y-axis corresponds to flow downward through the top ring gap, toward the crankcase. Knowing Q,,,, it is easy to determine the maximum average air flow U , over the oil film on the second land.

The LIF results are easily summarized: When the LIF probe is located on the second land during the transition to reverse gasflow through the top ring gap, Fig. 9, a sharp transition is observed in the oil film thickness on the second land, if and only if the LIF probe is located in the puddle during transition. Figure 9 also shows second land oil film traces for two operatifig conditions, one where the transition is observed and a second where the transition is not ob- served. Due to the occurrence of the ring transition in an extremely short period of time and its timing dependence on speed and load, it is impossible to locate the LIF probe in a position to observe the transition for all speeds and loads. The probe location was chosen to observe the tran- sition for the maximum number of operating conditions, based on preliminary calculations.

In Fig. 9, 2000 rpm, the initial oil film thickness on the second land is the same as that on the preceding (conlpres-

-- TDC Shafl index

-- Oil Film Thickness :\

..... I I

Cylinder Pressure : i , , - - 8 .

Liner Pressure : :

180 270 360 450 540

Crankangle Degrees

Fig. GTyplcal data set, showing TDC Index, oil film thickness, cylinder and land pressure data.

I 15W-40 - Pinned Rings

1 0 SAE30 - Pinned Rings

1500 2000 2500 3000

Speed (RPM)

Fig. 7-Measured oil consumptlon rate for two olls, pinned and unpinned rlngs.

sion) stroke. The final film thickness is observed on the expansion stroke in the region of the ring transition. These thicknesses are shown in Figs. 10(a)-(d) for one oil. From a practical point of view, the compression stroke, combined with the expansion stroke, allows a longer time period in which to collect the second land oil film thickness data. Thus, the average values of hi and ty can be easily defined from the data on the compression and expansion strokes, respectively. Without this approximation, the pre-transition oil film thickness could not be determined for the cases where the transition is unobservable.

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. . . . . . . Net Biowby Gas Flow - Top Ring Gap Gas Flow

120 1 1

180 270 360 450 540

CA Degrees

Fig. 8-Calculated net blowby and blowby through top ring gap showing relevant parameters.

initial thickness

Final thickness

7 1 I I

11.5 12.5 13.5 14.5 15.5

t Distance Along Piston (mm) Bonom of top ring

t Top of second ring

Flg. 9-Second land oil film thlckness during top ring transltlon on ex- pansion stroke.

P >

1 he next step is a comparison of the estimated oil con- sumption, using the results of the theory section, with the actual oil consumption, as shown in Fig. 7.

ANALYSIS

The oil consumed (O.C.) according to the puddle theory is:

O.C. (per cycle) = pAhAp [171

where p is the density of the oil at the second land tem-

- Compression

- - - - Expansion

. . ---.. 1 - - - - - -. . -. . = - - , - - - - - -

11.5 12.5 13.5 14.5 15.5

Distance along piston (mm)

Fig. lO(a)-Second land oll film thickness comparison, 1500 rpm.

- Compression

Expansion

0 I I I

11.5 12.5 13.5 14.5 15.5

Distance along piston (mm)

Fig. lO(b)--Second land oil film thlckness comparison, 2000 rpm.

perature, Ah is the change in second land film thickness (= hi - hf), and Ap is the area of the puddle. A convenient reference area Aref is:

where h is the length of the second land. The non-dimensional puddle area can be defined as:

2 O.C. A * = 4 = - - Aref 7 ~ p ~ h l %

4

In [19] it is helpful to use the measured values of hi and

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The Puddle Theory of Oil Consumpt.ion 8 1

- Compression

- - - - Expansion

All Data

. .

Distance along piston (mm) 1 rTa

Fig. lO(c)--Second land oil film thickness comparison, 2500 rpm. Flg. 11-Taylor number dependence of non-dlmensional puddle area, A*.

- Compression

--.- Expansion

. - . I _ . I - .. - - - -. . . - 1 11. - - 1 - I. .

1.5 12.5 13.5 14.5 15.5

Distance along piston (mm)

. All Data

0.9 - -- y = x

0.8 -

0.7 -

0.5 0.6 0.7 0.8 0.9 1

1 .O[Ua tMAX (Tap113 (muAlmu)] + 0.6 Fig. 10(d)-Second land 011 film thickness comparison, 3000 rpm. Fig. 12-Theoreticel correlation for non-dlmensional change In 011 film

thickness,, h*.

hf and the measured oil consumption. Thus A* becomes an experimentally determined variable,

which may be compared with theory. Figure 1 1 shows the result, which verifies that A* varies as ( ~ a ) - " ~ , as predicted by Eq. [12].

A further check can be performed on the theory as it predicts that the quantity h* = (hi - hf)lh; varies linearly with [(Ua~,,,lro) (p,Ip)], Eq. [16]. The result is shown in Fig. 12, and again the scaling is as predicted.

With a best fit with A* via Eq. [12], and a best fit for h* via Eq. [16], the overall accuracy of the model is finally assessed by using predicted model values to compute oil consumption in Eq. [17], and comparing them with obser-

vation. This re:jult is shown in Fig. 13. It can be seen that the overall accu.racy of the model is better than 90 percent.

The final section discusses reasons for the errors and recommends specific equations for estimating oil consump- tion in reciprocating engines.

CONCLUSION!; '

It has been shown that the puddle theory of oil con- sumption broadly agrees with oil film thickness measure- ments on the s~-cond land of a reciprocating engine. The theory account:; for variations of oil consumption due to

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Normalized Data

In using these equations readers are reminded that this model is not yet tuned for best predictions. I n particular it has been shown that piston ring rotation plays a major role in determining Q,,, and hence U,, and hence oil consumption.

These are topics for a future paper.

ACKNOWLEDGMENT

This work is sponsored by the MIT Research Consortium on Lubrication in 1.C. Engines. Current participants include Ford Motor Co., Peugeot and Renault, Pennzoil Products Co., Sealed Power Technologies, and the U.S. Department of Energy. 'The authors are grateful to the sponsors.

The extremely long and complicated experimental pro- cedure could not have been completed without the diligence and dedication of Timothy A. Cherry, a previous graduate student.

0 0.2 0.4 0.6 0.8 1

Measured 0 C (glhr) REFERENCES

Fig. 13-Normalized comparison of measured to predicted oil consumption.

engine speed, load, lubricant properties, and engine rnicrogeometry.

The accuracy of the model is ninety percent because the oil film thickness measurements are accurate to about ten percent, the pressure measurements to five percent, the oil c011~~1mption measurements to five percent, and it is im- possible to correctly position the LIF probe for all speeds and loads. 'The theory contains coefficients of order one, even as the overall scaling is obeyed. T h e puddle theory is on very firm ground with these experimental results, even if not completely precise. -. I hus, to calculate oil consumption the authors recom- mend the Ibllowing equations:

over an axi-symmetric semi-circular puddle. Also,

(I ) Namazian, M. and Heywood, J., "Flow in the Piston-Cylinder-King Crevices of a Spark-Ignition Engine: Effect on Hydrocarbon Emissions, Efficiency and Power," SAE Paper No. 820088 (1982).

(2) Smith Jr., M.. Tunkel, N., Bachman, 1-1. and Fernandez, Mr., "A New Look at Multigraded Diesel Engine Oils,"SAE Paper No. 760558 (1976).

(3) Wong, V. W. and Hoult, D. P., "Experimental Survey of Lubricant Film Characteristics and Oil Consumption in a Small Diesel Engine," SAE Paper No. 910741 (1991).

(4) Essig. G., Kamp. H. and Wacker, E., "Diesel Engine Emissions Keduc- tion-The Benefits of Low Oil Consumption Design," SAE Paper No. 900591 (1 990).

(5) Saito, K . , Igashira, T. and Nakarla. M., "Analysis of Oil Consumption by Observing Oil BehaviorAround Piston King Using a Glass Cylinder Engine," SAE Paper No. 892107 (1989).

(6) Inoue,T.. Maeda, Y., Takeda. M. and Nakada, hl.. "Study of*l'ransient Oil Consumption of Automoti\re Engine:' SAE Paper No. 8921 10 (1989).

(7) Taylor, G. I., "Deposition of a Viscous Fluid on the Wall of a Tube:' Jour. of FI. Mech., 10, pp 161-165 (1961).

(8) Shaw 11. B., Hoult. D. and Wong. V., "Development of Engine Lubri- cant Film Thickness Diagnostics Using Fiber Optics and Laser Fluo- rescence," SAE Paper No. 920651 (1992).

(9) Warrick. F. and Dykehouse, R., "An Advanced Ratliotracer 71-echnique for Assessing and Plotting Oil Consunlption in Diesel and Gasoline Engines," SAE Paper No. 700052 (1970).

(10) Shaw I I . B. T., "Direct Obser\,ation of the Oil Consumption hlechanism of a Production Single-Cylinder Diesel Engine," hl. S. Thesis, h l lT, Cambridge, MA (1992).

(11) Hill, S. and Sytsma, S., "A System Approach to Oil Consumption," SAE Paper No. 910743 (1991).

(12) Cherry. T., "Gasfiow Computer Code Calibration Using :I Single Cyl- inder Diesel Engine," hf. S. Thesis, hll'l', Cambridge. hlA (1990).

and

Oil Consumption = 3 X 1 O4 RPM phih*ArefA*

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