Hysteresis in Oil Flow through a Rotating Tube with Twin Exit Branches

Oil enters a horizontal rotating tube through a radially-attached duct at one end. The tube 
with the other end closed is attached with radial twin exit branches permitting oil to exit into 
open air. Air begins to enter through one of the two branches into the tube when its rotational 
speed reaches certain critical values. An experimental study is performed to investigate this 
air-oil two-phase flow behavior. Both the tube and the branches are transparent to allow 
illumination and flow visualization during spin-up and spin-down processes. The branch-totube 
diameter ratio, rotational speed, and oil flow rate are varied. Changes in oil flow rates 
are measured as a function of rotational speed. A comparison is made between cases of a 
varying total oil flow rate due to rotation effects and a constant one under control. It is 
disclosed that cavitation in oil flow is induced by air entering the branches opposite to the 
ejecting oil flow. Subsequently air bubbles progress in the tube. The origin of this intrusion 
depends on the hydraulic head loss of the piping system. This study can be applied to oil 
lubrication analysis of rotating machinery, such as automotive transmission lines.


INTRODUCTION
Efficiency is one of the most important concerns in the design of rotating machinery.High-speed rotating machinery, including jet turbines, power generators and automotive transmission systems, need working fluids to protect key parts in the system and still fulfill the efficiency requirement.
To meet these challenges, the durability of such machines relies on an adequate supply of lubricant or coolant.For the automotive transmission in automobiles, an optimized flow rate of lubricating oil, which runs through the hollow shaft serving as a flow passage, can prevent wear and seizure, dissi- pate heat, reduce friction, and enhance efficiency.On the other hand, an over-supply of lubricating oil may cause agitation loss in the automotive transmission.The needed amount of lubricating oil is difficult to determine because of the structural complexity of the automotive transmission and Corresponding author.250 SUN-WEN CHENG AND WEN-JEI YANG   its operation under rotating conditions.Among various factors that can reduce the supply of oil, cavitation is perhaps the most important cause.
Cavitation is caused by either the physical properties of liquids or the special shapes of flow passages.There are two categories of cavitation: vaporous cavitation and gaseous cavitation.The origin and effects of cavitation, and variables affecting its development, were investigated by Backe and Riedel (1972)  and Riedel (1972).They found that cavitation in oil flow is susceptible to periodic changes in either pressure or flow rate.Cavitation may be triggered in hydraulic equip- ment by flow constrictors, such as orifices and valves.The consequence of flow constrictors on the unsteady characteristics of oil flow was studied by Ishihara et al. (1975).Because of its low vapor pressure and high air content, mineral oil used in hydraulic equipment tends to disclose gaseous cavitation.In the present study, cavitation is caused by the introduction of outside air into the rotating system with hysteresis of air-oil flow.
Hysteresis in air-oil flow is originated by the compressibility of gases which are brought into the system by cavitation and contribute a viscous damping effect to flow dynamics.Hysteresis of cavitation in an unsteady oil flow through sharpedged orifices was detected with the aid of scattered laser beams by Ishihara et al. (1979).They found hysteresis between the incipience and desinence of vaporous cavitation, following the disappearance of gaseous cavitation in oil flow initially with a high air content, related to pressure difference.They also observed gaseous cavitation in the annular stratified and dispersed flow regimes and vaporous cavitation in the bubbly or froth flow regime.However, little attention has been paid to hysteresis of air-oil two-phase flow in rotating ducts so far.
Hysteresis in air-oil flow is still obscure in com- prehensive pipelines, as in an automotive transmis- sion line, although cavitation can be predicted for a single flow part.The effect of cavitation on oil flow rate has been analyzed with theoretical modeling done by Backe (1973)  and Kojima et al. (1991).
Predictions of oil flow rate generally agree with ex- perimental data but significant deviations remain.
This paper presents an experimental study of the hysteresis in air-oil flow caused by cavitation in a horizontal rotating tube with a radial entrance and twin branches for oil exit, as shown in Fig. 1.Air cavitation and two-phase flow in both the tube and the branches were observed by flow visualization.Flow rates and inlet gauge pressure were also measured under the same operating conditions.

EXPERIMENTAL APPARATUS AND PROCEDURE
A schematic of the experimental setup is shown in Fig. 2. It consists of a hydraulic system, an oil inlet assembly, a test section, and a driving system (Fig. and Table I)./in-A: 203.2 mm /Am: 203.2 mm The hydraulic system contains oil tanks, pumps, pipelines and bypasses, valves and a water-cooled heat exchanger.The last one is used to control the oil temperature within 31.0-33.0Cand to mini- mize viscosity effect on flow rates.The remaining pieces are used to maintain total oil flow rate into the oil inlet assembly and back to the base oil tank.
The oil inlet assembly consists of a stationary pressure chamber, a rotary shaft, lip seals, and double-sealed ball bearings.The rotary shaft is drilled hollow through one end without penetrating the other.Another circular duct is drilled perpendicular to the shaft so that oil flow runs toward the shaft centerline and turns 90 into the test section.
The test section is made of transparent, light- weight, thin acrylic tubes (3.175 mm thick) permit- ting flow visualization.It consists of two concentric tubes that rotate simultaneously.The inner tube is attached perpendicularly with the branches.Its upstream end is connected to the rotary shaft, and its downstream end to a spider flexible coupling connected to a drive shaft (explained later).The distance between the twin branches is fixed, but their inner diameters are varied.The outer tube is to lead oil flow into two stationary collectors that drain oil into a moveable tank, where a set of beakers may be used to measure the effluent flow rates.
The driving system has a drive shaft transferring power from a dynamometer, monitored by a digital tachometer, to both the test section and the oil inlet assembly.The rotational speed has practically no deviation below 1800rpm and within 1% up to 2500rpm.The maximum operating speed was restricted to protect the acrylic tubes.
Flow patterns in the branches including both front and side views were observed, together with the flow pattern in the inner tube.Flow patterns were recorded using a stroboscope and a camcorder with a high-speed shutter function.
The effluent flow rates were measured at inter- vals of 200rpm and up to 2500rpm.More data were measured at certain speeds of interest.Air bubbles inside the system were purged prior to each test run.The flow rates were also measured at the following critical rotational speeds: at the appear- ance and disappearance of air bubble(s), at the instant an air pocket was formed or vanished, and at the moment oil flow became annular with air in the core.The corresponding inlet gauge pressure was also recorded for reference.

RESULTS AND DISCUSSION
In the interest of brevity, only two cases of test Section #2 (specified in Table I) are presented to show the effects of the Coriolis force on both oil flow rate and air-oil flow pattern.Case has an approximately constant total oil flow rate Q: (Figs. 3-5), while Case 2 keeps valves unaltered so that Q: varies with rotational speed (Figs.6-8).
Figures 9 and 10 illustrate the oil flow rates and the inlet pressure versus the rotational speed at steady state, respectively.
When stationary, i.e. 0rpm, the branches were placed horizontally to measure the effluent flow rates through the upstream and downstream branches A and B. The ratio of QA to QB is not proportional to the ratio of their flow cross- sectional areas, but is nearly equal to the result estimated by the hydrodynamically developing flow model associated with hydraulic head losses.
The fully-developed laminar flow approach devi- ates less than 5% because of high oil viscosity and relatively long flow passages.
In the spin-up process, Qr of Case 2 initially grows slightly larger due to a reduced apparent friction factor for a single-phase flow.This fact is similar to the conclusions drawn by White (1964) and Shchukin (1967).The Qr gradually drops at higher rotational speeds W because the centrifugal force acts in the rotating entrance duct (Fig. 9(b)).
Prior to the first critical speed Wcl, no air bubble appears in the tube, but "air caves" reside on the leading sides of both branches (Fig. l(a)).As W approaches Wc, the air cave in Branch A reaches the tube, while that in Branch B vanishes.This phenomenon was illustrated by Cheng and Yang (1996).In both cases QB increases to the maximum which exceeds the corresponding QA.
At W-Wcl, air bubbles are formed at the downstream side of the Branch A root (Figs.3(a), 6(a) and 8(a)).The bubbly flow chokes flow passage and causes QB in both cases to reduce slightly, while QA rises (Fig. 9).Each time two or three bubbles pass the midway of the tube, more air bubbles are introduced into the tube.At a higher W, consecu- tive bubbles ranging from 1/8 to 5/16 inch in diameter fill the whole tube and begin to decrease Q in both cases (Figs.6(b) and 8(b)).
(a) Wc 1=970 RPM (c) Wc2 1050 RPM, +0.500 sec (d) Wc2=1050 RPM, 4.000 sec 200 P.PM +11,000 sec (g)W=1200 RPM, +12,967 sec FIGURE 6 Flow patterns inside tube in spin-up process (Case 2) (Din =a", ds 1/2", dA---'t, dB gl";Q < QT-ini 0.3 GPM).At W= Wc2 (around 1050 rpm), bubbles quickly accumulate to form several air pockets in the tube (Figs.3(b)-(c) and 6(c)-(d)).Beyond the moment when the pockets shrink and the first bubble reaches the Branch B root, no more bubbles are introduced until the last one enters Branch B. For both cases Q falls lower with a rise in QA (Fig. 9).An air cavity occupies almost the entire flow pas- sage of Branch A (Fig. 5), and the size of the oil stream on the trailing side varies with the forma- tion of air bubbles.Meanwhile, a moving air pocket exits through Branch B with little change in the size of the oil stream.
At Wc3, air-oil flow becomes annular through- out the whole tube.Air is induced into the core and is carried downstreamwise due to interfacial fric- tion.The oil stream on the trailing side shrinks to a rivulet with scattered oil droplets inside Branch B.
For Case 1, Wc3 is at 1400rpm (Fig. 3(e)).QA decreases while QB increases because some of the oil flow is blocked with the air core to enter Branch A. Beyond We3, QA has a trend to approach QT (Fig. 9(a)).For Case 2, We3 is lower at 1320rpm (Fig. 6(h)).QA, Q and QT all decrease as W increases (Fig. 9(b)).The oil layer in the tube becomes thinner, and eventually becomes invisible to measure QB (Fig. 3(f)).
In the spin-down process, the air-oil annular flow in the tube can be sustained at Ws lower than Wc2 (Figs. 4 and 7).QA and Q vary slightly prior to another critical speed (Fig. 9).For both cases, the air core between the branches is flushed out, while the remaining air in the upstream tube in front of Branch A gradually breaks into bubbles.
The difference is that Case 2 has a mc4 (around 970 rpm) when the air core still remains at a certain distance downstream of the Branch A root, causing air bubbles to congregate into pockets in the downstream tube (Fig. 7(b)).It results in a bubbly flow at Wcs=950rpm (Fig. 7(c)) and a single- phase oil flow at mc6=920rpm (Fig. 7(d)).In Case 1, however, transitions from annular to bubbly-slug flow and to single-phase flow are hard to distinguish at about Wc6 970 rpm (Figs. 4(b)- (d)).These phenomena are accompanied by abrupt changes in QA and Q (Fig. 9).Below mc6 the flow rates are about the same as those measured in the spin-up process.
In summary, bubbly and annular types of oil flow are observed in the horizontal rotating tube.Cavitation is induced by outside air entering through Branch A into the tube.This is in contrast to the cavitation of Ishihara (1985) which is generated by flow through a constriction inside a stationary hydraulic system due to pressure drop.Furthermore, hysteresis between spin-up and spin- down processes prevails in both cases with or without constant total oil flow rate.The study has disclosed that rotation causes the number of flow patterns to reduce from four (in stationary case) to two, i.e., bubbly and annular flow.This situation is equivalent to flow regimes in the high mass velocity region in Baker's plot (Wallis, 1969) flow-regime correlation in adiabatic horizontal two-phase flow.
The experimental results are consistent with two parameters: the rotational Reynolds number and the Rossby number.The former is defined as the ratio of the Coriolis force to the viscous force, and the latter as the ratio of the Coriolis force in the rotational direction to the inertia force in the flow direction.The rotational Reynolds number explains why a higher rotational speed is required to over- come oil viscosity and separate oil flow from the leading side of each branch.The Rossby number justifies the cause of lean oil flow when an air cavity appears inside the branches: once the Coriolis force dominates, oil flow is forced to the trailing side which corresponds to the high pressure side in single-phase flow.CONCLUSIONS 1.In general, Q: decreases with an increase in W if operating conditions are unvaried.
2. Pin increases quadratically with an increase in W because of the centrifugal force in the radially rotating entrance branch.
3. QA and QB are affected by the Coriolis force acting on the radially rotating exit branches.
4. In the spin-up process, air bubbles are intro- duced at Wcl from open air, through either exit branch against the ejecting oil flow, and into the horizontal rotating tube.The intruding air may block the flow passage and reduce QB.At Wc2, the air can accumulate to form air pockets as a bubbly-slug flow in the tube, and Q increases.
Beyond We3, an annular flow with air in the core of the tube is observed, and Q decreases with an increase in W.
5. In the spin-down process, both QA and Q vary slightly as an annular flow exists in the tube.At We4, which may be lower than Wc2, the air core breaks and air in the tube is flushed down- streamwise.However, there may exist an insig- nificant difference between Wc4 and Wcs, where a bubbly flow appears.For a constant Q3: case, mc6 comes slightly below We5 and the flow pattern resumes single-phase type.But for a varying QT case, mc6 can be far below 6.Pin in the spin-down process is higher than that in the spin-up process between We3 and mc6 because the air core built by the annular flow blocks the incoming oil flow through the entrance branch in the tube.

FIGURE 7
FIGURE 7 Flow patterns inside tube in spin-down process (Case 2).

FIGURE 8
FIGURE 8 Flow patterns around Branch A in spin-up process (Case 2).
state (0 rpm) transition from single-phase flow to bubbly flow transition from bubbly flow to bubbly-slug flow transition from bubbly-slug flow to annular flow transition from annular flow to bubbly-slug flow transition from bubbly-slug flow to bubbly flow transition from bubbly flow to single-phase flow entrance branch horizontal rotating tubeE EN NE ER RG GY Y M MA AT TE ER RI IA AL LS S Materials Science & Engineering for Energy SystemsEconomic and environmental factors are creating ever greater pressures for the efficient generation, transmission and use of energy.Materials developments are crucial to progress in all these areas: to innovation in design; to extending lifetime and maintenance intervals; and to successful operation in more demanding environments.Drawing together the broad community with interests in these areas, Energy Materials addresses materials needs in future energy generation, transmission, utilisation, conservation and storage.The journal covers thermal generation and gas turbines; renewable power (wind, wave, tidal, hydro, solar and geothermal); fuel cells (low and high temperature); materials issues relevant to biomass and biotechnology; nuclear power generation (fission and fusion); hydrogen generation and storage in the context of the 'hydrogen economy'; and the transmission and storage of the energy produced.As well as publishing high-quality peer-reviewed research, Energy Materials promotes discussion of issues common to all sectors, through commissioned reviews and commentaries.The journal includes coverage of energy economics and policy, and broader social issues, since the political and legislative context influence research and investment decisions.S SU UB BS SC CR RI IP PT TI IO ON N I IN NF FO OR RM MA AT TI IO ON N Volume 1 (2006), 4 issues per yearPrint ISSN: 1748-9237 Online ISSN: 1748-9245 Individual rate: £76.00/US$141.00Institutional rate: £235.00/US$435.00Online-only institutional rate: £199.00/US$367.00For special IOM 3 member rates please email s su ub bs sc cr ri ip pt ti io on ns s@ @m ma an ne ey y. .cco o. .uuk k E ED DI IT TO OR RS S D Dr r F Fu uj ji io o A Ab be e NIMS, Japan D Dr r J Jo oh hn n H Ha al ld d, IPL-MPT, Technical University of Denmark, Denmark D Dr r R R V Vi is sw wa an na at th ha an n, EPRI, USA F Fo or r f fu ur rt th he er r i in nf fo or rm ma at ti io on n p pl le ea as se e c co on nt ta ac ct t: : Maney Publishing UK Tel: +44 (0)113 249 7481 Fax: +44 (0)113 248 6983 Email: subscriptions@maney.co.uk or Maney Publishing North America Tel (toll free): 866 297 5154 Fax: 617 354 6875 Email: maney@maneyusa.comFor further information or to subscribe online please visit w ww ww w. .mma an ne ey y. .cco o. .uuk k C CA AL LL L F FO OR R P PA AP PE ER RS S Contributions to the journal should be submitted online at http://ema.edmgr.comTo view the Notes for Contributors please visit: www.maney.co.uk/journals/notes/emaUpon publication in 2006, this journal will be available via the Ingenta Connect journals service.To view free sample content online visit: w ww ww w. .i in ng ge en nt ta ac co on nn ne ec ct t. .cco om m/ /c co on nt te en nt t/ /m ma an ne ey y