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Modelling Approach on a Gerotor Pump Working in Cavitation Conditions
Available online at www.sciencedirect.com
ScienceDirect Energy Procedia 101 (2016) 701 – 709
71st Conference of the Italian Thermal Machines Engineering Association, ATI2016, 14-16 September 2016, Turin, Italy
Modelling approach on a Gerotor pump working in cavitation conditions Dario Buonoa, *, Fulvio Domenico Schiano di Colaa, , Adolfo Senatorea, , Emma Frosinaa,, Giorgio Buccilli b,, Jonathan Harrisonb, a
Department of Industrial Engineering, University of Naples Federico II, Via Claudio 21, Naples 80125, Italy b Gamma Technologies, 601 Oakmont Lane, Suite 220 Westmont, IL, 60559, USA
Abstract
Gerotor pumps are widely used on engine hydraulic circuits. The design of these pumps is mainly focused on the study of the leakages through the rotors. Modelling or experimental techniques can be adopted during the components design and optimization phases. The study presented in this paper shows results of a research study made on a gerotor pump. The study has been approached with modeling and experimental techniques. The pump has been tested on a hydraulic bench of the University of Naples “Federico II”. Tests have allowed the complete characterization of the pump including in worst conditions like cavitation. In fact, calibrated orifices have been installed on the suction and delivery side of the pump forcing the cavitation. This research is focused on the detection of the cavitation that, as well known, is induced by the low pressure at pump suction, by the presence of air in the pumped oil, by the sloshing of the oil inside the sump and by the recent reduction of sump capability (to reduce maintenance costs). The experimentation phase has been followed by modeling; an accurate model of the pump has been built using the commercial 1D software GT-SUITE. The code developers have added new applications to replicate, with the best accuracy, the experimental data especially in cavitating conditions. The model results have been compared with the experimental data showing a good agreement. The model is able to correctly predict the pump performance including delivery flow rate, total power loss, volumetric efficiency and temperature influence. by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license © 2016 2016Published The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Scientific Committee of ATI 2016.
* Corresponding author. Tel. +39-081-768-32-76, Fax. +39-081-239-41-65, E-mail address: [email protected]
1876-6102 © 2016 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Scientific Committee of ATI 2016. doi:10.1016/j.egypro.2016.11.089
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Dario Buono et al. / Energy Procedia 101 (2016) 701 – 709
Keywords: Cavitation, Experimentation and 1D Modeling Approches, Engine Lubrication Circuit, Gerotor Pump.
1. Introduction As well known, the demands of an increasing environmental control for the reduction of atmospheric gaseous emissions has led the automotive world to an ever tighter control of engine exhaust emissions. On one hand, great attention has been paid to obtain a greater efficiency in the "Top Part" of the engine (intake system, combustion, exhaust system, yet on the other hand recently greater attention is being paid to its "Bottom Part". In other words the reduction of losses from auxiliaries can assume an important role. In this sense, referring to the engine lubrication circuit, increased attention must be paid to the optimization of all the oil consumers such as bearings and of the oil pump. As a consequence, in the last years many studies on the pumps of the lubrication circuits have been addressed to the reduction of the absorbed power. Many of these are concerned with Gerotor pumps that are widely used for engine lubrication, although there are some examples of different solutions used, however, by much higher costs. Therefore, studies aimed to optimize the performance or to reduce problems of Gerotor pumps are really important. There are many research studies focused on the improvement of performance of the Gerotor pumps. Studies have been done with modeling and experimental techniques. Modeling techniques can adopt, depending on the objective and the modeled object, 3D or 1D solutions. Several authors have written about modeling of Gerotor pumps with 1D modeling techniques. For example, Neyrat et al [1], Fabiani et al [2], Senatore et al [3-5] have modeled the Gerotor pump with 1D method. Frosina et al [6] developed a Gerotor pump model with the same methodology well correlating the experimental pressure ripples. Also in this paper a Gerotor pump has been studied adopting an experimental-1D modeling techniques. The aim of the research is the study with a modeling approach of conditions in possible malfunctions caused by cavitation. In particular, low inlet pressure conditions coupled with the presence of air in the aspirate oil (typically around 7%) and with the sloshing of the oil in the sump due to dynamic of the vehicle are causes of Cavitation. Therefore, recently the manufacturers are reducing the sump capability to reduce maintenance costs. However, in addition to the above causes of cavitation, also the risk of a very small swing on the strainer of the pump must be added. During sudden accelerations of the engine or in high speed operating conditions some other cavitation causes can occur for, as an example, the presence of oil foam in the sump. As a consequence, cavitation is a phenomenon that can occur much more frequently than known or what can be supposed. There are not many studies available in literature, L. Ippoliti et al [7] and Yuan, YQ et al. [8]. This paper, therefore, is focused on the analysis of the cavitation on the Gerotor pumps. The investigated pump has 9 teeth on the inner rotor and 10 teeth on the outer. The study has been approached with both experimental and modeling techniques. A first experimental campaign has been done to validate the 1D simulation model built up with the commercial code GTSUITE [9], developed by Gamma Technologies. The research is a result of a close collaboration between the Hydraulic Power Research Group of the University of Naples “Federico II” and the engineers of Gamma Technologies. The pump has been tested on a hydraulic bench of the University of Naples, where it has been forced to cavitate by placing calibrated orifices on the suction and delivery side of the pump. Tests have given important information on the pump performance. Then, data have been used to validate the accurate 1D numerical model. The model has demonstrated a good agreement with the experimental data, it is able to replicate the real pump in cavitation conditions. 2. Test equipment and measuring method The pump has been tested in the hydraulic Lab of Industrial Engineering Department of University of Naples “Federico II”. The test bench layout is shown in Figure 1. The bench is able to drive the pump in the real operation condition reaching a shaft rotational speed of 8000RPM. The pump is powered by a hydraulic axial piston motor of 12 cm3/rev. The motor is connected to a power unit that consists of an oil tank with a nominal capacity of 100 L, an axial piston pump with theoretical displacement of 71 cm3/rev, a three phase electric motor with 4 poles, capable of
Dario Buono et al. / Energy Procedia 101 (2016) 701 – 709
delivering a maximum power of 18,5 kW and a heat exchanger air – oil. The axial piston pump is a variable displacement one. During the tests the shaft rotation speed of the tested pump can be varied through an electrohydraulic regulator handled by a dedicated card. This card manages the displacement of the axial piston pump of the Power Unit with respect to the input signal of a potentiometer. Several transducers are installed on the test bench to monitor and acquire all the operating parameters like the oil flow rate, the mean suction and delivery pressure and the instantaneous suction and delivery pressure. Looking at Figure 1c, the oil from a tank is pressurized by the tested pump. The thermostatic tank, with an oil volume capacity of 13 dm3, is enable to heat oil up to a temperature of 150°C. Four pressure transducers (P1, P2, P3, P4) are installed in the circuit. Transducers (P1) and (P2) are the mean pressure ones and they are located respectively at the inlet and outlet side of the pump. Both of them are type Burkert 8314 with a measuring range of 0 ÷ 10 bar. These sensors are based on ceramic technology measurement principle. Transducers (P3) and (P4) are both instantaneous pressure transducers and they are located inside two chambers close to the rotors. Both are type AVL LP11DA P4 with a measuring range of 0 ÷ 10 bar while P3 with a measuring range of 0 ÷ 30 bar. The frequency response of both sensors is > 50 kHz. These sensors are able to measure the pressure ripples in a pump shaft rotation thanks to the clock signal of an incremental optical encoder installed on the pump shaft. The delivery pressure has been regulated with the lamination valve (R3). This valve, as shown in Figure 1c, is located at the delivery port of the pump before the flow-meter. The flow-meter (called Q in Figure 1c) works with a functional principle based on the controlled generation of Coriolis forces and measures also the temperature and density of the oil. Cavitating conditions have been achieved reducing the diameter of the suction port with four calibrated orifices (R1). These orifices are shown in figure 1b, where the first one (15mm) corresponds to the regular diameter of the inlet port. The diameter has been varied from 15mm to 3mm to force the pump to cavitate. As it will be shown, the performance of the pump changes drastically with the reduction of the orifice diameter. The bench presents another orifice at the pump delivery port called (R2) with a diameter of 5mm. This orifice is necessary to dampen the pressure waves in the pressurized path. Different signals are acquired by the hardware system NI PCI16-E1-MIO (12-bit ADC converter resolution). All the signals are routed to the board NI PCI-MIO 16-E1 through a 68-pin shielded desktop connector block NI SCB-68. A finite - machine study, developed with National Instruments LabVIEW® 2015 software, thus to control, manage and capture data.
P1 = Mean Delivery Pressure Transducer P2 = Mean Suction Pressure Transducer P3 = Instantaneous Delivery Chamber Pressure Transducer P4 = Instantaneous Suction Chamber Pressure Transducer Q = Flow Meter R1 = Suction Calibrated Orifice R2 = Delivery Calibrated Orifice R3 = Delivery Throttle Valve
Figure 1: a) 9/10 Pump; b) Calibrated orifices – Suction port, c) Test bench layout
In this context it is possible to distinguish three acquisition methodologies: x Low sampling rate for main bench parameters (flow-rate, mean pressure, rpm); x External clock variable sampling rate (instantaneous suction and delivery pressure);
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x Time dependent sampling frequency (10 kHz) with a fixed time window (1 ÷ 10 s). The complete characterization of the pump has been done during the experimental campaign. Pressure, flowrate and temperature have been monitored. As shown in Figure 2, for a shaft rotational speed of 3000 RPM and oil temperature of 80°C, test results for suction pressure and the flow-rate have been diagrammed as a function of the delivery pressure. The delivery pressure is varied with the throttle valve (R4) in the range [1 ÷ 6] bar with steps of 1bar. The oil used during tests is a full synthetic 5W40 long life engine oil. The properties are listed in Table 1.
Full Synthetic 5W40 Long Life Engine Oil 80 cSt @ 40 °C / 13,7cSt @ Viscosity (ASTM D445) 100 °C Viscosity Index 176 Sulphated Ash (ASTM D874) 1,3 wt % Phosphorous 0,1 Flash Point (ASTM D92) 231 °C Density (ASTM D4052) 0,85 g/ml @15,6 °C Total Base Number (ASTM D2896) 11,8 MRV (ASTM D4684) 24,453 cP @ -35 °C HTHS Viscosity (ASTM D4683) 3,9 ή @ 150 °C Figure 2: Experimental data at 3000rpm and 80°C
Table 1: Oil properties
3. 1D Simulation Model The 1D pump flow model is discretized into many volumes comprised of pipes and flowsplits (volumes), and pipe passages are further discretized into subvolumes. The 1D Navier-Stokes equations, namely conservation of mass, momentum and energy are solved every timestep in every subvolume. Conservation of species is also considered to solve for species transport throughout the system. In Figure 3, the flow volumes used in the model are shown by alternating colors. Both the inlet and outlet ports are divided into three sections for more accurate wave propagation through the port in the interest of comparing pulsations to test. By dividing the ports into three sections, the expansion area in each section can be more accurately defined based on the real port dimensions from CAD, whereas a single section approach sometimes requires calibration of the expansion area of the inlet port to capture the drop in volumetric efficiency at high speed due to incomplete filling of the chambers.
Figure 3: Discretization of flow passages in the 1D model.
Figure 4: 1D flow model of the gerotor pump.
Figure 4 shows the 1D flow model of the gerotor pump. Since the pump has 10 outer teeth, there are 10 chamber volumes, and one cycle of the pump is represented as one revolution of the outer gear. The flow path from the oil pan to the chamber volumes is highlighted blue, while the flow path from the chambers to the outlet is highlighted
Dario Buono et al. / Energy Procedia 101 (2016) 701 – 709
red. There are three different leakage paths highlighted in green, pink, and orange. The dominant leakage path highlighted in green represents leakage between chambers. The other two minor leakage paths include leakage between the outer gear outer radius and housing highlighted in orange, and leakage in the rounded edge of the outer gear highlighted in pink. These leakage paths are shown visually in Figure 5. Though there is a small gap between the gear sides and housing, this leakage path is much smaller than the dominant leakage path between the gears, and thus is ignored in the model. The "InletEnv" part on the map represents the ambient condition in the oil pan from the test. The changing volume in each "Vol1", Vol2", etc… part pulls the oil from the pan into each chamber as its volume expands. Then when the volume in each chamber compresses, the oil is forced to the outlet side of the pump. The "Orifice_control" part uses a calibrated orifice diameter to meet the test target pressure.
Figure 5: Three internal leakage paths are used in the model. The dominant path is highlighted green (leakage between teeth), the two minor paths are highlighted orange and pink.
The 1D model was built directly from the CAD model of the pump using the GEM3D pre-processor of GTSUITE, allowing the model to be built very quickly. Included in the flow model are the automatically generated volume and port area profiles from GEM3D as shown in Figure 6. There are three distinct sections for both the inlet and outlet ports, to represent the flow area between the pumping chambers and these port sections.
Figure 6: Chamber volume and area profiles used in the 1D model. The three inlet and outlet port area profiles represent communication with the ports that have been divided into three sections.
The model has 133 total flow volumes, 110 of which are pipe subvolumes. Though the number of pipe subvolumes could be reduced dramatically, the higher number of subvolumes in the model provides the most accurate prediction of wave dynamics in the system. No sensitivity study was done on the number of subvolumes though, the discretization length, DX, in all pipes was simply set to 5mm (i.e. a 100mm pipe with 5mm DX will have 20 sub-volumes). The average timestep is 1.6e-6 seconds. Most cases converge in 4 to 5 pump cycles, requiring less than a few minutes of wall clock time to run on a modern PC. Certain assumptions were made in the model, including the air content in the oil, which was set to 1.3e-4 by mass fraction at the entry to the suction tube (free + dissolved gas), which equates to ~0.3% free air by volume at 1 bar and 80⁰C with dissolved gas at the saturated condition. Since the air content is unknown from the test, this value is a good assumption, as it is close to the equivalent amount of gas dissolved in oil sitting in a tank at equilibrium at STP. It should be noted the gas content was simulated between zero and 10% free air, and the 1.3e-4 by mass fraction value gave the best prediction compared to test. The clearance gap between the inner gear and outer gear (total play) measured 0.101mm. This same gap was used in the model for the dominant leakage path between the pumping chambers, highlighted in green
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in Figure 4 and 5. Though this clearance gap will change as the pump rotates due to contact between the gears, the contact between the gears is not modelled and this gap is assumed constant. The radial clearance between the outer gear and housing measured 0.1015mm. This clearance was used for the minor leakage path highlighted in orange in Figure 4 and 5. These conditions were used to generate all results shown below. 4. Results The model was compared to test at 80⁰C for several different suction tube restriction orifice sizes, ranging from 3mm to 15mm. In Figure 7 the mass flow is compared between model and experiment for a suction tube orifice diameter of 15mm, with good agreement. At the highest speed of 6000 RPM, the flow increases in both the model and test between 1 and 2 bar outlet pressure because the speed in the test at 2 bar is 6120 RPM, which is a little higher than the 6000 RPM condition at 1 bar. Moreover, the flow has the largest deviation at high speed and high outlet pressure. This is most likely due to 3D effects at the inlet port causing incomplete filling in the test that cannot be captured in the 1D model without extra calibration of the inlet port expansion area in the model.
Figure 7: Comparison at 80⁰C, 15mm suction tube orifice diameter, vs outlet pressure (P1 location).
The suction tube orifice diameter was varied at 80⁰C, and the comparison between model and test for this condition is shown in Figure 8. Good agreement is made between model and test where the mass flow decreases with decreasing inlet orifice diameter, which causes a drop in the suction pressure, to the point where at 3mm orifice diameter the flow is nearly constant over all pump speeds. It is also shown in Figure 8 the gas content increases as the inlet orifice diameter decreases, exhibiting cavitation conditions. The gas content represents the free gas by volume at the local pressure in the inlet port, which is in vacuum. There is also dissolved gas in this inlet port volume, but dissolved gas occupies no volume and thus is not considered in this plot. 8b
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Figure 8: Comparison with different suction tube orifice diameters, while holding outlet pressure at 3 bar and 80⁰C: a) Mass flow-rate, b) Suction pressure, c) Inlet gas volume fraction at local pressure
Pressure pulsations were also compared between model and test at 3000 RPM and 80⁰C, as shown in Figure 9, for suction tube orifice diameters of 15mm and 5mm, with good agreement in pressure amplitude, and primary frequency content.
9a
9b
Figure 9: Pressure pulsation comparison at 3000 RPM and 80⁰C with different suction tube orifice diameters: a) 15mm, b) 5mm
Cavitation conditions can be formed during cold temperature with suction tubes that are inadequately sized for the pump. This scenario was studied by extrapolating the cavitation performance of the baseline model to different oil types ranging from 5W40, 5W30, 5W20, 0W30, and 0W20. In this scenario, both cold (20⁰C) and hot oil (80⁰C) were examined at a common engine operating condition of 3000 RPM and 3 bar gauge outlet pressure at full flow condition using a fixed outlet restriction orifice size of 3.2mm, with the suction tube diameter varying between 3mm and 14mm. As shown in Figure 10, the oil type has an influence on the oil flow through the pump at a given suction tube diameter, and there is clearly a minimum tube diameter that must be used to prevent the onset of cavitation. Though the hot oil condition shows little variation in the mass flow between the different oil types, the cold temperature condition shows the lower viscosity oil grade causes less friction related pressure drop in the suction tube and will allow smaller suction tube diameters to be used. The air content was fixed at 1.3e-4 by mass fraction in the sump for all conditions in Figure 10.
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10a
10b
Figure 10: Influence of oil type and suction tube diameter on pump mass flow at: a) Toil = 20⁰C, b) Toil = 80⁰C 5. Conclusions A numerical and experimental investigation on the cavitation in a gerotor oil pump has been done in this paper. A pump has been studied with both methodologies to investigate the performance under different operating conditions. In particular the pump has been forced to cavitate varying the suction and the delivery pressure. The research is focused on the study of the pump when the pressure of the fluid volume goes under the oil saturation pressure with a high impact on the overall performance. Gerotor pumps are particularly subject to cavitate under particular operating conditions of the engine. The vehicle dynamics and the recent tendency to reduce the mass of oil in the sump can also affect cavitation. Therefore, the research to avoid cavitation is crucial nowadays. An experimental investigation has been performed by the University of Naples “Federico II” on a hydraulic test bench. The pump, driven by a hydraulic motor, has been forced to cavitate reducing the inlet diameter of the sump with calibrated orifices. The Pump performance in no-cavitating and cavitating conditions has been measured; these data have been used to compare to a 1D simulation model. The model has been built up with GT-SUITE, a mono-dimensional code developed by Gamma Technologies. The comparison between the model results and experimental data has shown a good accuracy, where the (p, Q) curves have a maximum difference of 7%. The model has demonstrated to correctly predict cavitation, in fact it is able to evaluate the delivery flow-rate reduction due to the reduction of the orifice at the suction side of the pump. As consequence, the model correctly evaluates the suction pressure reduction. An important output of the model is the vapor fraction variation with the pump inlet diameter. The vapor fraction is constant and close to zero with no restriction and increases dramatically with the inlet diameter reduction, thereby confirming cavitation. References [1] Neyrat, S., Orand, N., and Jonquet, D., (2005), “Modeling and Analysis of an Automatic Transmission Internal Gear Oil Pump with Cavitation”, SAE Technical Paper 05NVC-150, [2] Fabiani, M., Mancò, S., Nervegna, N., Rundo, M. et al., (1999)“Modelling and Simulation of Gerotor Gearing in Lubricating Oil Pumps”, SAE Technical Paper 99P-464, 1999, [3] A. Senatore, D. Buono, E. Frosina, L. Santato (2013), “Analysis and Simulation of an Oil Lubrication Pump for the Internal Combustion Engine”. In: Fluids Engineering Systems and Technologies. San Diego, 15-21 November 2013ASME, Proceedings (IMECE) vol. 7B, ISBN/ISSN: 9780791856321, doi: 10.1115/IMECE2013-63468, [4] A. Senatore, D. Buono, E. Frosina, L. Arnone, L. Santato, F. Monterosso, M. Olivetti (2013), “A tridimensional CFD analysis of the lubrication circuit of a non-road application Diesel engine”. 11th International Conference on Engines and Vehicles, ICE 2013; Capri, Naples; Italy, September 15-19 2013, [5] A. Senatore, D. Buono, E. Frosina, A. De Vizio, P. Gaudino, A. Iorio (2014), “A Simulated Analysis of the Lubrication Circuit of an In-Line Twin Automotive Engine”. SAE 2014 World Congress and Exhibition; Detroit, MI; United States,
Dario Buono et al. / Energy Procedia 101 (2016) 701 – 709 [6] E. Frosina, A. Senatore, D. Buono, L. Santato, “Analysis and Simulation of an Oil Lubrication Pump for Internal Combustion Engines”, ASME J. of Fluids Eng., 2015, Vol. 137, Issue 5, [7] Lppoliti, L, Hendrick, P., (2013), “INFLUENCE OF THE SUPPLY CIRCUIT ON OIL PUMP PERFORMANCE IN AN AIRCRAFT ENGINE LUBRICATION SYSTEM”, PROCEEDINGS OF THE ASME TURBO EXPO: TURBINE TECHNICAL CONFERENCE AND EXPOSITION, Vol. 2. [8] Yuan, Y.Q., Tao, W., Liu, E.A., Barber, GC., Zou, Q., Guessous, L., Du, Z.X., (2007), “Engine lubrication system analysis by considering aeration and cavitation within the rotating oil supply passage” : TRIBOLOGY TRANSACTIONS 50(1), page 3949, [9] Harrison, J., Aihara, R., Eisele, F., (2016),“Modeling Gerotor Oil Pumps in 1D to Predict Performance with known Operating Clearances”, SAE 2016World Congress and Exhibition; Detroit, MI; United States,
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ScienceDirect Energy Procedia 101 (2016) 701 – 709
71st Conference of the Italian Thermal Machines Engineering Association, ATI2016, 14-16 September 2016, Turin, Italy
Modelling approach on a Gerotor pump working in cavitation conditions Dario Buonoa, *, Fulvio Domenico Schiano di Colaa, , Adolfo Senatorea, , Emma Frosinaa,, Giorgio Buccilli b,, Jonathan Harrisonb, a
Department of Industrial Engineering, University of Naples Federico II, Via Claudio 21, Naples 80125, Italy b Gamma Technologies, 601 Oakmont Lane, Suite 220 Westmont, IL, 60559, USA
Abstract
Gerotor pumps are widely used on engine hydraulic circuits. The design of these pumps is mainly focused on the study of the leakages through the rotors. Modelling or experimental techniques can be adopted during the components design and optimization phases. The study presented in this paper shows results of a research study made on a gerotor pump. The study has been approached with modeling and experimental techniques. The pump has been tested on a hydraulic bench of the University of Naples “Federico II”. Tests have allowed the complete characterization of the pump including in worst conditions like cavitation. In fact, calibrated orifices have been installed on the suction and delivery side of the pump forcing the cavitation. This research is focused on the detection of the cavitation that, as well known, is induced by the low pressure at pump suction, by the presence of air in the pumped oil, by the sloshing of the oil inside the sump and by the recent reduction of sump capability (to reduce maintenance costs). The experimentation phase has been followed by modeling; an accurate model of the pump has been built using the commercial 1D software GT-SUITE. The code developers have added new applications to replicate, with the best accuracy, the experimental data especially in cavitating conditions. The model results have been compared with the experimental data showing a good agreement. The model is able to correctly predict the pump performance including delivery flow rate, total power loss, volumetric efficiency and temperature influence. by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license © 2016 2016Published The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Scientific Committee of ATI 2016.
* Corresponding author. Tel. +39-081-768-32-76, Fax. +39-081-239-41-65, E-mail address: [email protected]
1876-6102 © 2016 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Scientific Committee of ATI 2016. doi:10.1016/j.egypro.2016.11.089
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Dario Buono et al. / Energy Procedia 101 (2016) 701 – 709
Keywords: Cavitation, Experimentation and 1D Modeling Approches, Engine Lubrication Circuit, Gerotor Pump.
1. Introduction As well known, the demands of an increasing environmental control for the reduction of atmospheric gaseous emissions has led the automotive world to an ever tighter control of engine exhaust emissions. On one hand, great attention has been paid to obtain a greater efficiency in the "Top Part" of the engine (intake system, combustion, exhaust system, yet on the other hand recently greater attention is being paid to its "Bottom Part". In other words the reduction of losses from auxiliaries can assume an important role. In this sense, referring to the engine lubrication circuit, increased attention must be paid to the optimization of all the oil consumers such as bearings and of the oil pump. As a consequence, in the last years many studies on the pumps of the lubrication circuits have been addressed to the reduction of the absorbed power. Many of these are concerned with Gerotor pumps that are widely used for engine lubrication, although there are some examples of different solutions used, however, by much higher costs. Therefore, studies aimed to optimize the performance or to reduce problems of Gerotor pumps are really important. There are many research studies focused on the improvement of performance of the Gerotor pumps. Studies have been done with modeling and experimental techniques. Modeling techniques can adopt, depending on the objective and the modeled object, 3D or 1D solutions. Several authors have written about modeling of Gerotor pumps with 1D modeling techniques. For example, Neyrat et al [1], Fabiani et al [2], Senatore et al [3-5] have modeled the Gerotor pump with 1D method. Frosina et al [6] developed a Gerotor pump model with the same methodology well correlating the experimental pressure ripples. Also in this paper a Gerotor pump has been studied adopting an experimental-1D modeling techniques. The aim of the research is the study with a modeling approach of conditions in possible malfunctions caused by cavitation. In particular, low inlet pressure conditions coupled with the presence of air in the aspirate oil (typically around 7%) and with the sloshing of the oil in the sump due to dynamic of the vehicle are causes of Cavitation. Therefore, recently the manufacturers are reducing the sump capability to reduce maintenance costs. However, in addition to the above causes of cavitation, also the risk of a very small swing on the strainer of the pump must be added. During sudden accelerations of the engine or in high speed operating conditions some other cavitation causes can occur for, as an example, the presence of oil foam in the sump. As a consequence, cavitation is a phenomenon that can occur much more frequently than known or what can be supposed. There are not many studies available in literature, L. Ippoliti et al [7] and Yuan, YQ et al. [8]. This paper, therefore, is focused on the analysis of the cavitation on the Gerotor pumps. The investigated pump has 9 teeth on the inner rotor and 10 teeth on the outer. The study has been approached with both experimental and modeling techniques. A first experimental campaign has been done to validate the 1D simulation model built up with the commercial code GTSUITE [9], developed by Gamma Technologies. The research is a result of a close collaboration between the Hydraulic Power Research Group of the University of Naples “Federico II” and the engineers of Gamma Technologies. The pump has been tested on a hydraulic bench of the University of Naples, where it has been forced to cavitate by placing calibrated orifices on the suction and delivery side of the pump. Tests have given important information on the pump performance. Then, data have been used to validate the accurate 1D numerical model. The model has demonstrated a good agreement with the experimental data, it is able to replicate the real pump in cavitation conditions. 2. Test equipment and measuring method The pump has been tested in the hydraulic Lab of Industrial Engineering Department of University of Naples “Federico II”. The test bench layout is shown in Figure 1. The bench is able to drive the pump in the real operation condition reaching a shaft rotational speed of 8000RPM. The pump is powered by a hydraulic axial piston motor of 12 cm3/rev. The motor is connected to a power unit that consists of an oil tank with a nominal capacity of 100 L, an axial piston pump with theoretical displacement of 71 cm3/rev, a three phase electric motor with 4 poles, capable of
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delivering a maximum power of 18,5 kW and a heat exchanger air – oil. The axial piston pump is a variable displacement one. During the tests the shaft rotation speed of the tested pump can be varied through an electrohydraulic regulator handled by a dedicated card. This card manages the displacement of the axial piston pump of the Power Unit with respect to the input signal of a potentiometer. Several transducers are installed on the test bench to monitor and acquire all the operating parameters like the oil flow rate, the mean suction and delivery pressure and the instantaneous suction and delivery pressure. Looking at Figure 1c, the oil from a tank is pressurized by the tested pump. The thermostatic tank, with an oil volume capacity of 13 dm3, is enable to heat oil up to a temperature of 150°C. Four pressure transducers (P1, P2, P3, P4) are installed in the circuit. Transducers (P1) and (P2) are the mean pressure ones and they are located respectively at the inlet and outlet side of the pump. Both of them are type Burkert 8314 with a measuring range of 0 ÷ 10 bar. These sensors are based on ceramic technology measurement principle. Transducers (P3) and (P4) are both instantaneous pressure transducers and they are located inside two chambers close to the rotors. Both are type AVL LP11DA P4 with a measuring range of 0 ÷ 10 bar while P3 with a measuring range of 0 ÷ 30 bar. The frequency response of both sensors is > 50 kHz. These sensors are able to measure the pressure ripples in a pump shaft rotation thanks to the clock signal of an incremental optical encoder installed on the pump shaft. The delivery pressure has been regulated with the lamination valve (R3). This valve, as shown in Figure 1c, is located at the delivery port of the pump before the flow-meter. The flow-meter (called Q in Figure 1c) works with a functional principle based on the controlled generation of Coriolis forces and measures also the temperature and density of the oil. Cavitating conditions have been achieved reducing the diameter of the suction port with four calibrated orifices (R1). These orifices are shown in figure 1b, where the first one (15mm) corresponds to the regular diameter of the inlet port. The diameter has been varied from 15mm to 3mm to force the pump to cavitate. As it will be shown, the performance of the pump changes drastically with the reduction of the orifice diameter. The bench presents another orifice at the pump delivery port called (R2) with a diameter of 5mm. This orifice is necessary to dampen the pressure waves in the pressurized path. Different signals are acquired by the hardware system NI PCI16-E1-MIO (12-bit ADC converter resolution). All the signals are routed to the board NI PCI-MIO 16-E1 through a 68-pin shielded desktop connector block NI SCB-68. A finite - machine study, developed with National Instruments LabVIEW® 2015 software, thus to control, manage and capture data.
P1 = Mean Delivery Pressure Transducer P2 = Mean Suction Pressure Transducer P3 = Instantaneous Delivery Chamber Pressure Transducer P4 = Instantaneous Suction Chamber Pressure Transducer Q = Flow Meter R1 = Suction Calibrated Orifice R2 = Delivery Calibrated Orifice R3 = Delivery Throttle Valve
Figure 1: a) 9/10 Pump; b) Calibrated orifices – Suction port, c) Test bench layout
In this context it is possible to distinguish three acquisition methodologies: x Low sampling rate for main bench parameters (flow-rate, mean pressure, rpm); x External clock variable sampling rate (instantaneous suction and delivery pressure);
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x Time dependent sampling frequency (10 kHz) with a fixed time window (1 ÷ 10 s). The complete characterization of the pump has been done during the experimental campaign. Pressure, flowrate and temperature have been monitored. As shown in Figure 2, for a shaft rotational speed of 3000 RPM and oil temperature of 80°C, test results for suction pressure and the flow-rate have been diagrammed as a function of the delivery pressure. The delivery pressure is varied with the throttle valve (R4) in the range [1 ÷ 6] bar with steps of 1bar. The oil used during tests is a full synthetic 5W40 long life engine oil. The properties are listed in Table 1.
Full Synthetic 5W40 Long Life Engine Oil 80 cSt @ 40 °C / 13,7cSt @ Viscosity (ASTM D445) 100 °C Viscosity Index 176 Sulphated Ash (ASTM D874) 1,3 wt % Phosphorous 0,1 Flash Point (ASTM D92) 231 °C Density (ASTM D4052) 0,85 g/ml @15,6 °C Total Base Number (ASTM D2896) 11,8 MRV (ASTM D4684) 24,453 cP @ -35 °C HTHS Viscosity (ASTM D4683) 3,9 ή @ 150 °C Figure 2: Experimental data at 3000rpm and 80°C
Table 1: Oil properties
3. 1D Simulation Model The 1D pump flow model is discretized into many volumes comprised of pipes and flowsplits (volumes), and pipe passages are further discretized into subvolumes. The 1D Navier-Stokes equations, namely conservation of mass, momentum and energy are solved every timestep in every subvolume. Conservation of species is also considered to solve for species transport throughout the system. In Figure 3, the flow volumes used in the model are shown by alternating colors. Both the inlet and outlet ports are divided into three sections for more accurate wave propagation through the port in the interest of comparing pulsations to test. By dividing the ports into three sections, the expansion area in each section can be more accurately defined based on the real port dimensions from CAD, whereas a single section approach sometimes requires calibration of the expansion area of the inlet port to capture the drop in volumetric efficiency at high speed due to incomplete filling of the chambers.
Figure 3: Discretization of flow passages in the 1D model.
Figure 4: 1D flow model of the gerotor pump.
Figure 4 shows the 1D flow model of the gerotor pump. Since the pump has 10 outer teeth, there are 10 chamber volumes, and one cycle of the pump is represented as one revolution of the outer gear. The flow path from the oil pan to the chamber volumes is highlighted blue, while the flow path from the chambers to the outlet is highlighted
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red. There are three different leakage paths highlighted in green, pink, and orange. The dominant leakage path highlighted in green represents leakage between chambers. The other two minor leakage paths include leakage between the outer gear outer radius and housing highlighted in orange, and leakage in the rounded edge of the outer gear highlighted in pink. These leakage paths are shown visually in Figure 5. Though there is a small gap between the gear sides and housing, this leakage path is much smaller than the dominant leakage path between the gears, and thus is ignored in the model. The "InletEnv" part on the map represents the ambient condition in the oil pan from the test. The changing volume in each "Vol1", Vol2", etc… part pulls the oil from the pan into each chamber as its volume expands. Then when the volume in each chamber compresses, the oil is forced to the outlet side of the pump. The "Orifice_control" part uses a calibrated orifice diameter to meet the test target pressure.
Figure 5: Three internal leakage paths are used in the model. The dominant path is highlighted green (leakage between teeth), the two minor paths are highlighted orange and pink.
The 1D model was built directly from the CAD model of the pump using the GEM3D pre-processor of GTSUITE, allowing the model to be built very quickly. Included in the flow model are the automatically generated volume and port area profiles from GEM3D as shown in Figure 6. There are three distinct sections for both the inlet and outlet ports, to represent the flow area between the pumping chambers and these port sections.
Figure 6: Chamber volume and area profiles used in the 1D model. The three inlet and outlet port area profiles represent communication with the ports that have been divided into three sections.
The model has 133 total flow volumes, 110 of which are pipe subvolumes. Though the number of pipe subvolumes could be reduced dramatically, the higher number of subvolumes in the model provides the most accurate prediction of wave dynamics in the system. No sensitivity study was done on the number of subvolumes though, the discretization length, DX, in all pipes was simply set to 5mm (i.e. a 100mm pipe with 5mm DX will have 20 sub-volumes). The average timestep is 1.6e-6 seconds. Most cases converge in 4 to 5 pump cycles, requiring less than a few minutes of wall clock time to run on a modern PC. Certain assumptions were made in the model, including the air content in the oil, which was set to 1.3e-4 by mass fraction at the entry to the suction tube (free + dissolved gas), which equates to ~0.3% free air by volume at 1 bar and 80⁰C with dissolved gas at the saturated condition. Since the air content is unknown from the test, this value is a good assumption, as it is close to the equivalent amount of gas dissolved in oil sitting in a tank at equilibrium at STP. It should be noted the gas content was simulated between zero and 10% free air, and the 1.3e-4 by mass fraction value gave the best prediction compared to test. The clearance gap between the inner gear and outer gear (total play) measured 0.101mm. This same gap was used in the model for the dominant leakage path between the pumping chambers, highlighted in green
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in Figure 4 and 5. Though this clearance gap will change as the pump rotates due to contact between the gears, the contact between the gears is not modelled and this gap is assumed constant. The radial clearance between the outer gear and housing measured 0.1015mm. This clearance was used for the minor leakage path highlighted in orange in Figure 4 and 5. These conditions were used to generate all results shown below. 4. Results The model was compared to test at 80⁰C for several different suction tube restriction orifice sizes, ranging from 3mm to 15mm. In Figure 7 the mass flow is compared between model and experiment for a suction tube orifice diameter of 15mm, with good agreement. At the highest speed of 6000 RPM, the flow increases in both the model and test between 1 and 2 bar outlet pressure because the speed in the test at 2 bar is 6120 RPM, which is a little higher than the 6000 RPM condition at 1 bar. Moreover, the flow has the largest deviation at high speed and high outlet pressure. This is most likely due to 3D effects at the inlet port causing incomplete filling in the test that cannot be captured in the 1D model without extra calibration of the inlet port expansion area in the model.
Figure 7: Comparison at 80⁰C, 15mm suction tube orifice diameter, vs outlet pressure (P1 location).
The suction tube orifice diameter was varied at 80⁰C, and the comparison between model and test for this condition is shown in Figure 8. Good agreement is made between model and test where the mass flow decreases with decreasing inlet orifice diameter, which causes a drop in the suction pressure, to the point where at 3mm orifice diameter the flow is nearly constant over all pump speeds. It is also shown in Figure 8 the gas content increases as the inlet orifice diameter decreases, exhibiting cavitation conditions. The gas content represents the free gas by volume at the local pressure in the inlet port, which is in vacuum. There is also dissolved gas in this inlet port volume, but dissolved gas occupies no volume and thus is not considered in this plot. 8b
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Figure 8: Comparison with different suction tube orifice diameters, while holding outlet pressure at 3 bar and 80⁰C: a) Mass flow-rate, b) Suction pressure, c) Inlet gas volume fraction at local pressure
Pressure pulsations were also compared between model and test at 3000 RPM and 80⁰C, as shown in Figure 9, for suction tube orifice diameters of 15mm and 5mm, with good agreement in pressure amplitude, and primary frequency content.
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Figure 9: Pressure pulsation comparison at 3000 RPM and 80⁰C with different suction tube orifice diameters: a) 15mm, b) 5mm
Cavitation conditions can be formed during cold temperature with suction tubes that are inadequately sized for the pump. This scenario was studied by extrapolating the cavitation performance of the baseline model to different oil types ranging from 5W40, 5W30, 5W20, 0W30, and 0W20. In this scenario, both cold (20⁰C) and hot oil (80⁰C) were examined at a common engine operating condition of 3000 RPM and 3 bar gauge outlet pressure at full flow condition using a fixed outlet restriction orifice size of 3.2mm, with the suction tube diameter varying between 3mm and 14mm. As shown in Figure 10, the oil type has an influence on the oil flow through the pump at a given suction tube diameter, and there is clearly a minimum tube diameter that must be used to prevent the onset of cavitation. Though the hot oil condition shows little variation in the mass flow between the different oil types, the cold temperature condition shows the lower viscosity oil grade causes less friction related pressure drop in the suction tube and will allow smaller suction tube diameters to be used. The air content was fixed at 1.3e-4 by mass fraction in the sump for all conditions in Figure 10.
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Figure 10: Influence of oil type and suction tube diameter on pump mass flow at: a) Toil = 20⁰C, b) Toil = 80⁰C 5. Conclusions A numerical and experimental investigation on the cavitation in a gerotor oil pump has been done in this paper. A pump has been studied with both methodologies to investigate the performance under different operating conditions. In particular the pump has been forced to cavitate varying the suction and the delivery pressure. The research is focused on the study of the pump when the pressure of the fluid volume goes under the oil saturation pressure with a high impact on the overall performance. Gerotor pumps are particularly subject to cavitate under particular operating conditions of the engine. The vehicle dynamics and the recent tendency to reduce the mass of oil in the sump can also affect cavitation. Therefore, the research to avoid cavitation is crucial nowadays. An experimental investigation has been performed by the University of Naples “Federico II” on a hydraulic test bench. The pump, driven by a hydraulic motor, has been forced to cavitate reducing the inlet diameter of the sump with calibrated orifices. The Pump performance in no-cavitating and cavitating conditions has been measured; these data have been used to compare to a 1D simulation model. The model has been built up with GT-SUITE, a mono-dimensional code developed by Gamma Technologies. The comparison between the model results and experimental data has shown a good accuracy, where the (p, Q) curves have a maximum difference of 7%. The model has demonstrated to correctly predict cavitation, in fact it is able to evaluate the delivery flow-rate reduction due to the reduction of the orifice at the suction side of the pump. As consequence, the model correctly evaluates the suction pressure reduction. An important output of the model is the vapor fraction variation with the pump inlet diameter. The vapor fraction is constant and close to zero with no restriction and increases dramatically with the inlet diameter reduction, thereby confirming cavitation. References [1] Neyrat, S., Orand, N., and Jonquet, D., (2005), “Modeling and Analysis of an Automatic Transmission Internal Gear Oil Pump with Cavitation”, SAE Technical Paper 05NVC-150, [2] Fabiani, M., Mancò, S., Nervegna, N., Rundo, M. et al., (1999)“Modelling and Simulation of Gerotor Gearing in Lubricating Oil Pumps”, SAE Technical Paper 99P-464, 1999, [3] A. Senatore, D. Buono, E. Frosina, L. Santato (2013), “Analysis and Simulation of an Oil Lubrication Pump for the Internal Combustion Engine”. In: Fluids Engineering Systems and Technologies. San Diego, 15-21 November 2013ASME, Proceedings (IMECE) vol. 7B, ISBN/ISSN: 9780791856321, doi: 10.1115/IMECE2013-63468, [4] A. Senatore, D. Buono, E. Frosina, L. Arnone, L. Santato, F. Monterosso, M. Olivetti (2013), “A tridimensional CFD analysis of the lubrication circuit of a non-road application Diesel engine”. 11th International Conference on Engines and Vehicles, ICE 2013; Capri, Naples; Italy, September 15-19 2013, [5] A. Senatore, D. Buono, E. Frosina, A. De Vizio, P. Gaudino, A. Iorio (2014), “A Simulated Analysis of the Lubrication Circuit of an In-Line Twin Automotive Engine”. SAE 2014 World Congress and Exhibition; Detroit, MI; United States,
Dario Buono et al. / Energy Procedia 101 (2016) 701 – 709 [6] E. Frosina, A. Senatore, D. Buono, L. Santato, “Analysis and Simulation of an Oil Lubrication Pump for Internal Combustion Engines”, ASME J. of Fluids Eng., 2015, Vol. 137, Issue 5, [7] Lppoliti, L, Hendrick, P., (2013), “INFLUENCE OF THE SUPPLY CIRCUIT ON OIL PUMP PERFORMANCE IN AN AIRCRAFT ENGINE LUBRICATION SYSTEM”, PROCEEDINGS OF THE ASME TURBO EXPO: TURBINE TECHNICAL CONFERENCE AND EXPOSITION, Vol. 2. [8] Yuan, Y.Q., Tao, W., Liu, E.A., Barber, GC., Zou, Q., Guessous, L., Du, Z.X., (2007), “Engine lubrication system analysis by considering aeration and cavitation within the rotating oil supply passage” : TRIBOLOGY TRANSACTIONS 50(1), page 3949, [9] Harrison, J., Aihara, R., Eisele, F., (2016),“Modeling Gerotor Oil Pumps in 1D to Predict Performance with known Operating Clearances”, SAE 2016World Congress and Exhibition; Detroit, MI; United States,
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