Experimental Study of the Flow in an External Gear Pump by Time Resolved Particle Image Velocimetry

Transcription

1 Experimental Stud of the Flow in an External Gear Pump b Time Resolved Particle Image Velocimetr b Nihal Ertürk Supervised b: Anton Vernet and Josep A. Ferré A Thesis Submitted to Graduate Programme in Chemical and Process Engineering Universit of Rovira I Virgili In the fulfillment of the Requirements for The Degree of Master of Science in Chemical and Process Engineering June, 28, Tarragona Spain

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3 Contents 1 Introduction 1 2 Objectives 3 3 Experimental Procedure Experimental set-up Flow Seeding Techniques for TRPIV Image Analsis Preliminar Image Processing Interrogation Area Triple Image Correlation Boundar Treatment Conditional Average Results and Discussion Velocit fields and streamlines Velocit profiles Conclusions 21 7 Future Work 22 References 23 Appendix 25

4 List of Figures 1.1 Scheme of an external gear pump 3.1 Schematic drawing of the test bench 3.2 Examples of the experimental image series of the external gear pump (a) suction chamber (b) impulse chamber 3.3 Rise velocities dependence on bubble radius 3.4 For several bubble diameters, the ratio of vertical deviation and test section length in function of mean horizontal velocit. The limit value, H/L.3 has been indicated as straight horizontal line. 4.1 Removing reflections b median estimator across the time series. (a) Original Image, (b) Image with Clean-Up Mask process 4.2 Cross-correlation procedure. 4.3 Triple Image Correlation scheme and example of correlation of peak improvement. Right and left correlation planes have been multiplied to obtain an enhanced peak 4.4 Representation of the selected image. (a) Original image. (b) Selected image 4.5 Correlation of the image frames to define a Specific Position of the Gear 5.1 Velocit fields results which are obtain in different frequenc rates (a) Inlet with 5fps (b) Inlet with 1fps (c) Inlet with 2fps (d) Outlet with 1fps 5.2 Streamlines results which are obtain in different frequenc rates (a) Inlet with 5fps (b) Inlet with 1fps (c) Inlet with 2fps (d) Outlet with 1fps 5.3 Velocit fields of suction chamber with 1fps for different positions of gear teeth 5.4 Streamlines of suction chamber with 1 fps for different positions of gear teeth 5.5 Inlet flow in the suction chamber at 1fps (a) Mean v (b) Mean u (c) Magnitude of mean v velocit contours (d) Magnitude of mean u velocit contours. 5.6 Outlet flow in the impulse chamber at 1fps (a) Mean v (b) Mean u (c) Magnitude of mean v velocit contours (d) Magnitude of mean u velocit contours. 5.7 Inlet flow in the suction chamber at 1fps rms of velocit (a) v component (b) u component. 5.8 Outlet flow in the impulse chamber at 1fps rms of velocit (a) v component (b) u component.

5 Acknowledgments I would like to thank m supervisors, Anton Vernet and Josep A. Ferre for their support and help. Thanks to Robert Castilla and Esteve Codina for their collaboration and support in the laborator experimentation in LABSON at UPC. Also, thanks to everbod at ECCoMFiT group at URV. This stud was financiall supported b the Spanish Ministr of Science and Education and FEDER under projects DPI and DPI

6 Abstract Time Resolved Particle Image Velocimetr (TRPIV) has been used to investigate the turbulent flow in an external gear pump. The fluid movement through the pump is maintained b the rotation of the gears that carries the fluid from the intake side to the discharge side of the sstem. Small air bubbles have been used as flow seeding to obtain the images. For the range of velocities used in this stud the buoanc effects have been found negligible. The time sequences of TRPIV recordings images have been processed using domestic PIV software. The software uses the Local Field Correction which is able to resolve the flow structures smaller than interrogation window. Processing the images is done b the usual cross-correlation PIV proceeding based on FFT algorithm. In order to improve the correlation peak detection, Triple Image Correlation is used in place of the usual cross-correlation. In addition, a method to improve the accurac of TRPIV image analsis near boundaries has been applied. A weighting function is used to the interrogation windows for the correction to estimate the actual placement of the velocit vector when the interrogation area overlaps the image boundar. All of these give to the technique advantages in terms of accurac and robustness. Instantaneous and average fluid motions in the suction and in the impulse chamber of the pump have been analzed. Conditional averages in the suction and impulse chamber around gears have been obtained using a correlation procedure to catch the flow field at a fixed position of the gears. Time evolution of the average motion shows that the direction of the velocit patterns changes as a function of the movement of the gearwheel. The results obtained can help to understand the effect of the flow field in the pump performance and its efficienc.

7 Chapter 1 Introduction Internal flow in sstems which consists of the rotating passages is exceedingl complex, involving rotation and turbulence effects. The flow is interesting from a fluid mechanical perspective as it is often influenced b rotor-stator interaction mechanisms. A variet of measurement techniques have been applied to several industrial machines in the struggle for accurate quantitative flow descriptions. This means that methods have provided much fundamental knowledge of the flow phenomena occurring in rotating machines [1,2,3]. However, the quest that maintains high efficiencies and performances at a broader range of operating conditions raises the need for a more detailed knowledge of the local and instantaneous features of the rotating passages flow. A gear pump is used for transferring and metering of liquids and power transfer in a process. In this stud, the flow phenomena of an external gear pump (Figure 1.1) have been investigated on the increase of its efficienc and performance. The fluid is transferred around the interior of the casing in the pockets b the meshing of two gears rotating against each other to pump the fluid from the suction side to the discharge (impulsion) side under pressure. As the gears rotate, the spaces between the gears teeth transport the fluid at constant amount of fluid per revolution. INFLOW Suction Chamber Impulse Chamber OUTFLOW Figure 1.1 Scheme of an external gear pump. External gear pumps are capable of working against high differential pressures. The pressure in the outlet side is higher than the inlet side. Accordingl, the fluid will tr to find the path of least resistance and slip-back through the pump. To prevent this phenomenon, a dnamic sealing must be implemented [4]. There 1

8 are clearances for the dnamic seal parts to move and these clearances permit fluid to slip-back through the pump and reduce its theoretical efficienc. The degree of internal slippage in a gear pump determines its volumetric efficienc [1] which is the relation between actual pumped fluid flow rate,q to the losses of flow, Q L due to the leakage or slip-back of the fluid around the gear and casing (eqn. 1.1). The mean flow rate of the pump is the result of the volumetric capacit, C v and the rotational velocit, ω (eqn 1.2). Q η v = (1.1) Q+ Q C v L ω Q= (1.2) 2π The volumetric efficienc has to be improved b minimizing the mechanical tolerances of manufacturing [4]. Gear pumps can produce a high frequenc pressure pulsation and thus increase of fluctuations of deliver flow flow rate ripples in suction and impulsion chambers, which tends to damage pressure gauges. To reduce the ripples, tooth profile, gear shape and pump bod plates are needed to be improved. Investigations show that it is not possible to get external gear pumps with no deliver fluctuation [5]. The efficienc of the pump is directl related with the relationship between the moving parts and clearances factors. In addition, the viscosit of the flow will effect for a thin fluid (such as water) or a moderatel viscous fluid (such as particular oil). Increasing the performance of an external gear pump can be achieved b reducing the size of the pump, increasing the pressure as well as the rotational velocit [6,7]. In the last decades, Digital Particle Image Velocimetr (DPIV) technique had been developed and applied to various flow fields. To allow the Time Resolved Particle Image Velocimetr (TRPIV) the images have to be captured using high speed digital cameras which make possible to increase the time resolution. DPIV needs tracing particles to follow the flow movement. In general these are small solid or liquid particles that reflect the laser light. In the case of the external gear pump analzed here, small air bubbles have been used efficientl as particle seeding since solid particles and water drops can seriousl damage the pump model. In order to show the potential of the TRPIV technique as an efficient analsis tool in the design of industrial gear pumps, the main objective of the present stud is to provide detailed instantaneous and mean data of the internal flow field. Chapter 2 describes the purpose and objectives of this stud. Chapter 3 explains the experimental procedure and PIV setup and Chapter 4 gives details on the methodolog for analzing the images b using TRPIV. Chapter 5 presents the results and discussion, including instantaneous ensembleaveraged PIV velocit data followed b conclusions in Chapter 6 and future work in Chapter 7. 2

9 Chapter 2 Objectives The purpose of this paper is to clarif the role of the suction and impulse chamber and analze the flow occurring in it. In addition, these results can help to decide modifications of the geometr of the pump in order to increase its performance. For this purpose, the Time Resolved Particle Image Velocimetr (TRPIV) has been applied to the analsis of the turbulent flow inside an external gear pump. The TRPIV is a non-invasive technique and is a powerful instrument for the analsis of complex instantaneous flow structures allowing the stud of fast changing sstems. In order to demonstrate the potential of the TRPIV technique as an efficient analsis tool in the design of industrial gear pumps, the main objectives of the present stud for the technique are, To provide detailed instantaneous data of the internal flow field in the rotating passages of a pump gear b using air bubbles as flow seeding, Implementation of local field correction to cross-correlation PIV proceeding based on FFT algorithm, Improving the analsis techniques to obtain more accurate results. 3

10 Chapter 3 Experimental Procedure 3.1 Experimental Set-up The pump sstem analzed is from the LABSON group of the Universitat Politecnica de Cataluna (UPC). The pump is an external gear pump (Figure 1.1) where each cogwheel has a diameter of 54 mm and a height of 36 mm. The number of teeth in each wheel is 11, the volumetric capacit of this model is 44 cm 3 /rev and the rotational velocit of the gear was 2 rpm. The cover of test pump has been completel made of methacrlate in order to allow the image acquisition. The test bench (Figure 3.1) is composed b two hdraulic circuits. The upper circuit is the primar or driven one, contains the test pump that takes the moving fluid from the tank and impulses it through pressure fall back to the tank again. The pump is driven b an oleohdraulic motor and it is a component of the secondar circuit which is placed under the pump sstem. The motor is in turn driven b a hdraulic power-pack. This scheme allows modifing ver easil the rotational velocit of the test pump acting on the flow rate of the driver circuit, but has the disadvantage that it is not possible to select a certain velocit with precision. Oil tank High velocit Digital camera Test pump Computer Oil tank and power Laser generator Laser sheet Figure 3.1 Schematic drawing of the test bench. 4

11 The light source was a pulsed Monocrom Infrared laser with a wavelength of 8nm. A high velocit digital camera (Photron Ultima APX-RS) with resolution of pixel has been used. Digital images have been obtained with an acquisition frequenc of 5 fps, 1 fps and 2 fps. The buffer memor of the digital camera allows to record up to 248 images per experiment, equivalent to 4, 2 or.5 seconds depending of the sampling rate used. All the images obtained (Figure 3.2) were stored in a digital support for later processing. The data and post processing was done using a domestic PIV software developed b ECCoMFiT group of Universitat Rovira i Virgili (URV). (a) (b) Figure 3.2 Examples of the experimental image series of the external gear pump (a) suction chamber (b) impulse chamber 3.2 Flow seeding Most PIV experiments have been reported to use small solid particles for flow seeding. However, for this gear pump sstem, the use of solid materials can produce material erosion and damage the transparent surface of methacrlate and can also cause problems in the gear sstem because of metal-metal contact between the teeth. The use of water drops as particle seeding could be considered but it can produce problems of oxidation of the steel gears. Finall, small air bubbles have been used in spite of some disadvantages: (i) the size of the bubbles is not easil controllable and a large variabilit in the its size can make difficulties to estimate the velocit lag [8], (ii) the densit ratio is ver large and (iii) the presence of gas in a liquid can reduce the velocit of sound and hence it can make the flow becoming compressible at relativel low velocit [9]. In the present case, the size of the bubbles is controlled b using pressurized air flowing through a porous media that avoids the generation of large size bubbles, the control of the air flow also allow to control the densit of particles in the measurement area. Drag and buoanc forces associated with acceleration are the main forces that act on bubbles for their motion in fluid than the force of the fluid flowing. These forces can be optimized to allow bubbles to quickl relocate to a desired area [1]. B combining the drag force and the buoanc force, Stokes Law given in eqn 3.1 can be formed based on gravit acceleration (g), bubble radius (r) and kinematic fluid viscosit (ν) to estimate the bubble rise velocit ( v rise ). 5

12 v rise 2 2r g = (3.1) 9 ν From this equation, Figure 3.3 has been illustrated to show that the rise velocities have a strong dependence on the bubble radius for the mineral oil (oil; ρ = 885 kg/m 3, µ =.28 Pa.s) used in this stud..7.6 Rise velocit (v s ) [ m / s ] Bubble Radius (r) [ mm ] Figure 3.3 Rise velocities dependence on bubble radius. If the flow has a horizontal mean velocit ( v ) and when the particle reaches the end of the test section, it has gone out off its path with an amount (eqn 3.2) L H = v (3.2) rise v where the length of the test section is (L), Using equations (3.1) and (3.2), the ratio of vertical deviation and horizontal length of the test section can be defined as in equation 3.3 in order to find the ratio and keep the bubbles in the laser sheet. H L 2 2r g = (3.3) 9ν v In the experiments, the laser sheet has a 1 mm thickness and the test section has a length of 3 mm. In order to keep the bubbles in the laser sheet, H/L ratio needs to be approximatel.3. In Figure 3.4 the ratio of the vertical deviation and the horizontal length of the test section is plotted against mean velocit for 6

13 various bubble diameters for the characteristics of the mineral oil used. The mean velocit of the flow is function of the rotational speed of the pump. For 2 rpm, the mean velocit in the suction chamber has been obtained about.25 m/s and for this mean velocit the limit diameter size of the bubble is.7 mm. Then we can optimize the bubble size with a negligible value for the particles move in vertical direction. It has been found the optimum diameter size of the air bubbles.1 mm which is also supported b the analsis of Bolinder [11] D =.1 mm D =.2 mm D =.3 mm D =.4 mm D =.5 mm D =.7 mm H/L =.3 H/L ratio mean v [m/s] Figure 3.4 For several bubble diameters, the ratio of vertical deviation and test section length in function of mean horizontal velocit. The limit value, H/L.3 has been indicated as straight horizontal line. The effect of gas-liquid mixture on the sonic speed of the flow has also been considered. A sufficientl high volume fraction of air can reduce the sonic speed down to 2 m/s [9]. In the present case, the gas maintains its temperature constant and the pressure of the pump sstem is quite low. When the size of the interrogation area (64x64 pixel) and usual densit of particles (suggested around 1-15 particles per interrogation area [8] are used for low velocities, the flow shows reasonabl far awa from compressibilit characteristics. In the lest desirable situation which is the sonic speed is approximatel 2 m/s, the rotational speed of the pump should be around 1 rpm in order to have a Mach number. In the present configuration of the experimental setup, the rotational velocit of the gear was working at 2 rpm. 7

14 Chapter 4 Techniques for TRPIV Image Analsis Specific aspects of the time resolved PIV technique have been applied to analze the turbulent flow in the external gear pump. The aim is to take advantages for the use of time resolved PIV series of images to overcome some issues that can effect PIV measurements and to improve the performance and the accurac of the technique. 4.1 Preliminar Image Processing First consideration on the processing of time series of PIV images can be introduced apart from the characteristics of the flow that is being measured. Since the time histor of the illumination at each image location is available, statistical properties of the series can be analzed. Hence, a Clean-up Mask process has been applied to improve on the processing of time series of the experimental images. This procedure allows removing and/or reducing the spurious permanent reflections of the light from the illumination process of the laser. The median value across the image time series is estimated to clean these reflections from the original images. Figure 4.1a presents an outlet region of the field of view for a single instantaneous image, while Fig 4.1b displas the differences between the original image and the median image from a time series of 4 images. The median value of the illumination at each point provides information that affects the detection of the actual displacement of the particles [16] (a) (b) Figure 4.1 Removing reflections b median estimator across the time series. (a) Original Image, (b) Image with Clean-Up Mask process 8

15 4.2 Interrogation Area Instantaneous images have been analzed using local field correction (LFC) [12] and TRPIV. LFC is a correlation PIV method able to accuratel resolve flow structures smaller than interrogation window [13]. The technique used here is a cross-correlation method that provides a remarkable capabilit for accuratel resolving small scale structures in the flow. Tpical dimensions of an interrogation area are given in the literature for PIV between 16x16 to 128x128 pixels. In order to obtain a reliable estimator of the particle image displacement, about 1 to 15 particles in an interrogation area have to be present [8]. In the present work, 64x64 pixels interrogation area has been used b considering the adequate particles intensit in each interrogation area. In order to get an estimated displacement, the usual cross-correlation PIV processing is performed for each interrogation area. Figure 4.2 illustrates the digital PIV process. The cross-correlation shifts the second window across the first and sums the matching values (eqn 4.1) [8]. R K L ( x ) I( i, j) I' ( i+ x, j ), = (4.1) II + i= K j= L At the point where images match best, the correlation is at its peak value. This peak is located and provides the best estimate for the displacement of the particles in the window. Image 1 I cross-correlation t peak search I t+ t v Image 2 Figure 4.2 Cross-correlation procedure. To calculate the cross-correlation between two corresponding interrogation windows from successive images, fast-fourier transforms (FFT s) are used. Digital recording and computer analsis led to the application of a FFT in PIV image processing, which significantl decreased the time required for the necessar operations to produce a velocit measurement [13]. 9

16 Triple Image Correlation An image can be paired with the next or previous image in the time series. Thus, a correlation algorithm involving the three images should prove more robust to out of plane motion than the usual single pair correlation algorithm. A similar approach was proposed in another background [14,15]. The algorithm used here implements this strateg b multipling both correlation planes in order to improve the peak detection [16]. This leads to the reduction of the spurious correlation peaks appearing in onl one of the correlation planes. Triple Image Correlation scheme is illustrated in Figure 4.3 on behalf of an example. The interrogation area has been selected from the time series where the gear movement is appearing. The interrogation area is coordinated as 345 pixel horizontal and 81 pixel vertical of the images. Two correlation planes are obtained from the image pairs (t i-1, t i ) and (t i, t i+1 ) for the image corresponding to time t i. After that, these correlation planes are combined into the correlation plane and this plane verifies an enhanced correlation peak for the case of appearing one tooth one of the interrogation windows. The spurious peaks that appear in onl one of the two correlation peaks can lead to the erroneous estimation of the displacement of the particles. But as shown in the Figure 4.3, those spurious peaks have been cancelled b this algorithm. The peak obtained from the triple image correlation is more obvious than the corresponding peaks on the standard cross correlation planes. t i+1 t i t i-1 Figure 4.3 Triple Image Correlation scheme and example of correlation of peak improvement. Right and left correlation planes have been multiplied to obtain an enhanced peak. 1

17 Boundar Treatment Since, iterative standard algorithms introduce significant errors when the interrogation location is closer to the image boundar, a special treatment of the interrogation area near the image boundaries has been introduced to obtain the same level of accurac available at inner locations [16]. The boundar treatment is applied to the images with weighting function which is responsible computing the corrected position of the velocit displacement relative to the boundar. A weighting function is needed to avoid instabilities in the iterative process of compensation of the particle pattern or changing the frequenc response of a moving average [17]. The use distorts the gre level of the original images, introducing error. The LFC-TRPIV method works accuratel even if it has this error built in, but with double weighting, which consists of averaging the result that calculated b its smmetrical counterpart, the error can be reduced [18]. 4.5 Conditional Average The flow structure in the inlet/outlet chamber depends on the position of the gear. Thus, a full time mean will give non real flow structures in these chambers. A conditional mean based on the location of the gear is obtained. The gears are continuousl rotating in a specific time interval. Analzing this specific area, we have introduced a conditional average function which provides the gears a stable position in a specific time interval with velocit field of the flow at this time. The image series in time are correlated with a selected image (Figure 4.4b) which consists of one tooth of the gear to define the specific position of the gear. This allows locating the instantaneous fields that has the gear in the selected position. Those instantaneous velocit vectors are averaged to obtain a conditional velocit field representing the characteristic flow structure at this gear position (Figure 4.4) (b) (a) Figure 4.4 Representation of the selected image. (a) Original image. (b) Selected image. 11

18 72 images with the same position which has been shown in the Figure 4.5 as the peaks of crossing lines of the correlation plane have been found for the suction chamber and the have been used for the analzing of the rotating parts. The same process has been applied to the suction chamber. The conclusion that can be drawn is that the turbulence effect of the rotating gears to the sstem has been investigated b the conditional average function with a reliable velocit field and accurate results. Figure 4.5 Correlation of the image frames to define a Specific Position of the Gear. 12

19 Chapter 5 Results and Discussion 5.1 Velocit fields and streamlines Figures 5.1 and 5.2 show the conditional averages obtained for the inlet chamber at different sampling rate (Figures 5.1a-5.2a, 5.1b-5.2b and 5.1c-5.2c at 5 fps, 1 fps and 2fps respectivel) and for the outlet chamber (Figures 5.1d-5.2d) at 1 fps. All the inlet measurements were taken in a horizontal (x-) plane at vertical location coincident with the flow entrance, while the outlet measurements were taken onl in a horizontal plane in the upper plane of the chamber. Hence, it is not possible to see in Figure 5.1d that the vectors are leaving from the chamber. For the suction chamber, it could be seen that the fluid flows through the gears from the two sides of the chamber smmetricall and produces two vortices on the right and left side of the chamber. The small vortices also appear in the end points of gear teeth. For the impulse chamber is clearer to observe the flow with two vortices which are closer to the center side of the pipe and small vortices are not obtained in the end points of gear teeth. It is clear that the flow in the inlet chamber is more complex that the flow at the outlet. 13

20 INFLOW v velocit - direction u velocit x - direction Suction Chamber Impulse Chamber OUTFLOW x [mm] x [mm] [pixel] [mm] [píxel] [mm] x [pixel] (a) x [píxel] (b) x [mm] x [mm] [pixel] [pixel] [mm] [mm] x [pixel] x [pixel] (c) (d) Figure 5.1 Velocit fields results which are obtain in different frequenc rates (a) Inlet with 5fps (b) Inlet with 1fps (c) Inlet with 2fps (d) Outlet with 1fps 14

21 x [mm] x [mm] [pixel] [mm] [píxel] [mm] x [pixel] (a) x [píxel] (b) x [mm] x [mm] [píxel] [pixel] [mm] [mm] x [pixel] x [pixel] (c) (d) Figure 5.2 Streamlines results which are obtain in different frequenc rates (a) Inlet with 5fps (b) Inlet with 1fps (c) Inlet with 2fps (d) Outlet with 1fps It has been shown that the sampling rate do not have an important effect on the flow structure obtained, at least at the rotation frequenc used here. To find the flow evolution inside the suction chamber the instantaneous data obtained for a sampling rate of 1 fps has been used since it gives a rather better resolution the other two cases (5 fps and 2 fps). Figure 5.3 and Figure 5.4 show the velocit vectors and streamlines at six consecutive times which corresponds to different position of the gear teeth. It can be observed that the centre of the large vortices do not change their position with the rotation of gear, while the small vortices could appear, disappear or join to large ones. 15

22 t i t i+3 t i+6 t i+9 t i+12 t i+15 Figure 5.3 Velocit fields of suction chamber with 1fps for different positions of gear teeth. 16

23 t i t i+3 t i+6 t i+9 t i+12 t i+15 Figure 5.4 Streamlines of suction chamber with 1 fps for different positions of gear teeth. 17

24 5.2 Velocit profiles The suction chamber velocit profiles (Figure 5.5) show that the v velocit component is considerabl increasing when the fluid is flowing through the gear teeth and the maximum negative velocit of mean v has been found in the center of the inlet side of the gear pump. The mean u velocit component reaches its maximum on the right middle and on the left middle side of the gear pump. Figure 5.5 shows that the profiles become less smmetric as the move awa from the inlet section. This lack of smmetr could be generated b the model performance and needs a more detailed analsis with a different rotation velocit and image acquisition at more than one horizontal plane Mean v vs x =3.48 =5.4 =7.5 =9.2 =1.8 =12.9 = Mean u vs x =3.48 =5.4 =7.5 =9.2 =1.8 =12.9 =15.4 v [ mm / s ] u [ mm / s ] x [ mm ] (a) x [ mm ] (b) Magnitude of mean v velocit [ mm / s ] Magnitude of mean u velocit [ mm / s ] [ mm ] [ mm ] x [ mm ] (c) x [ mm ] (d) Figure 5.5 Inlet flow in the suction chamber at 1fps (a) Mean v (b) Mean u (c) Magnitude of mean v velocit contours (d) Magnitude of mean u velocit contours. 18

25 1 5 Mean v vs x =1.8 =3.7 =6. =7.9 =9.8 =11.7 = Mean u vs x =1.8 =3.7 =6. =7.9 =9.8 =11.7 =13.7 v [ mm / s ] -5-1 u [ mm / s ] x [ mm ] (a) x [ mm ] (b) Magnitude of mean v velocit [ mm / s ] Magnitude of mean u velocit [ mm / s ] [ mm ] [ mm ] x [ mm ] x [ mm ] -6 (c) (d) Figure 5.6 Outlet flow in the impulse chamber at 1fps (a) Mean v (b) Mean u (c) Magnitude of mean v velocit contours (d) Magnitude of mean u velocit contours. Velocit profiles at the impulse chamber (Figure 5.6), shows that the v velocit component is increasing when the fluid is passing through the gear teeth and the maximum negative velocit of mean v has been found in the center of the outlet side of the gear pump. The mean u velocit component reaches to maximum on the right middle and on the left middle side of the gear pump. Results show that the flow in the suction chamber is much more complex than the flow in the impulse chamber. Therefore the inlet chamber is the one that needs more detailed an extended stud. Figures 5.7 and 5.8 show the results of rms of velocities (u and v components) of the flow at suction and impulse chamber of the external gear pump sstem. It is essentiall to observe that rms value is increasing when the fluid is close to the rotating gears and rms value reaches its maximum at the gear zone. 19

26 rms of v [ mm / s ] rms of velocit (v component) versus x =3.48 =5.4 =7.5 =9.2 =1.8 =12.9 =15.4 rms of u [ mm / s ] rms of velocit (u component) versus x =3.48 =5.4 =7.5 =9.2 =1.8 =12.9 = x [ mm ] x [ mm ] Figure 5.7 Inlet flow in the suction chamber at 1fps rms of velocit (a) v component (b) u component. rms of v [ mm / s ] rms of velocit (v component) versus x =1.8 =3.7 =6. =7.9 =9.8 =11.7 =13.7 rms of u [ mm / s ] rms of velocit (u component) versus x =1.8 =3.7 =6. =7.9 =9.8 =11.7 = x [ mm ] x [ mm ] Figure 5.8 Outlet flow in the impulse chamber at 1fps rms of velocit (a) v component (b) u component. 2

27 Chapter 6 Conclusions The use of air bubbles as tracing particles for PIV has been proved as a fine alternative to the use of solid or liquid particles. TRPIV has been applied to the stud of the flow structures in the suction and impulse chamber of an external gear pump. Results show the possibilit that the analsis technique presented can be used to obtain detailed information of the instantaneous velocit fields, in sstems with moving elements, which are not part of the fluid flow. The abilit to separate particles from the reflection and to clean/remove the spots allows improving the peak detection for the direction of the velocit. A simple triple image correlation algorithm can improve the peak correlation in rather moving parts appear in the image. The technique for boundar treatment developed b Usera et.al [15] has been applied with the use of weighting function to obtain the same level of accurac available at inner locations of the sstem. Corrected positions of the velocit displacement relative to the boundar have been computed. A conditional average velocit field has been obtained for specific gear position allowing an average time evolution of the flow structures in the suction chamber. The results obtained show that a detailed analsis of the suction chamber is needed for a better understanding of the dnamic behavior of the flow. The results of this stud will be presented in 14 th International Smposium on Applications of Laser Techniques to Fluid Mechanics in Portugal, Jul, 28 and will be published in the proceedings of the conference (see Appendix). 21

28 Chapter 7 Future Work The aim of the work that has been presented here was the possibilit of using air bubbles to investigate with TRPIV the flow inside the suction chamber and impulse chamber of an external gear pump. For future work, it is been decided to stud with different rotational velocities of the gear to increase the efficienc and performance of the sstem. In addition to this, experimental stud of cavit flow analsis in channel will be investigated b simultaneousl measuring the velocit, the temperature and concentration fields with a combined Time-Resolved Particle Image Velocimetr (TRPIV) and Planar Laser-Induced Fluorescence (PLIF) sstem. PLIF technique is an optical measurement tool which will provide to have quantitative information that can be obtained on heat transfer phenomena and temperature distribution of the fluid in the cavit channel. In addition, PLIF sstem can be also used to obtain whole-field concentration data for mixing performance in this channel. 22

29 References [1] Wernet M. P., (2) Application of DPIV to stud both stead state and transient turbomachiner flows, Optics & Laser Technolog 32, [2] Pedersen N., Larsen P.S., Jacobsen C. B., (23) Flow in a Centrifugal Pump Impeller at Design and Off-design Conditions. Part 1: PIV and LDV measurements, Journal of Fluids Engineering, vol: 125, pages: [3] Da S.W., McDaniel J.C., (25) PIV Measurements of Flow in a Centrifugal Blood Pump: Stead Flow Journal of Biomechanical Engineering, Volume 127, Issue 2, pp [4] Dearn R, B.Sc.(Hons), (June 21) European Marketing Manager, The fine art of gear pump selection and operation, World pumps, Volume 21, Issue 417, pp [5] Ioi H and Ishimura S (1983) χ-theor in gear geometr, Transaction of ASME Journal of Mechanisms, Transmissions, and Automation in Design 15, pp [6] Codina E, Kamashta M, (1999) ECOPUMP project, Enhanced design of high pressure gear pumps using environmentall acceptable hdraulic fluids, BRITE Contract n BRPRCt95-94, Tech. rep., LABSON-UPC. [7] Castilla R, Gamez-Montero P, Huguet D, Codina E, (27) Turbulence in Internal Flows in Minihdraulic Components, CIMNE, pp [8] Raffel M, Willert C, Kompenhans J (1998) Particle Image Velocimetr: A Practical guide, Springer. [9] Brennen C E (25) Fundamentals of Multiphase Flow, Cambridge Universit Press. [1] Moore J (27) Dr sump pump bubble elimination for hdraulic hbrid vehicle sstems, Master thesis in the department of Mechanical engineering, The Universit of Michigan. [11] Bolinder J (1999) On the accurac of a digital particle image velocimetr sstem, Tech. rep., Lund Institute of Technolog. [12] Usera G, Vernet A, Ferré JA (24) Consideration and Improvements of the Analsis Algorithms Used for Time Resolved PIV of Wall bounded Flows, 12 th International Smposium on Applications of Laser Techniques to Fluid 23

30 Mechanics, Lisbon. [13] Nogueria J, Lecuona A, and Rodriguez PA, (1997) Data validation, false vectors correction and derived magnitudes calculations on PIV data, Meas. Sci. Technol. (8), [14] Willert CE and Gharib M, (1991) Digital particle image velocimetr, Exp. Fluids (1), [15] Hart DP (1998) The Elimination of Correlation Errors in PIV Processing, 9 th International Smposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon. [16] Hart DP (1999) Super-Resolution PIV b Recursive Local-Correlation, Journal of Visualization (1). [17] Nogueria J, Lecuona A, and Rodriguez PA (21) Local field correction PIV, implemented b means of simple algorithms, and multigrid versions, Meas. Sci. Technol, 12, [18] Nogueria J, Lecuona A and Rodriguez PA (22) Accurac and time performance of different schemes of the local field correction PIV technique, (33),

31 APPENDIX 25

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33 14th Int Smp on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 7-1 Jul, Analsis of the Turbulent Flow of an External Gear Pump b Time Resolved Particle Image Velocimetr Nihal Ertürk 1, Anton Vernet 1, Josep A. Ferré 1, Robert Castilla 2, Esteve Codina 2 1: Department of Mechanical Engineering, Universit of Rovira I Virgili, Tarragona, Spain, nihal.erturk@urv.cat, anton.vernet@urv.cat, josep.a.ferre@urv.cat 2: Department of Fluid Mechanics, Technical Universit of Catalonia, Terassa, Spain, castilla@mf.upc.edu, ecodina@mf.upc.edu Abstract Time Resolved Particle Image Velocimetr (TRPIV) has been used to investigate the turbulent flow in an external gear pump. The fluid movement through the pump is maintained b the rotation of the gears that carries the fluid from the intake side to the discharge side of the sstem. Small air bubbles have been used as flow seeding to obtain the images. For the range of velocities used in this stud the buoanc effects have been found negligible. The time sequences of TRPIV recordings images have been processed using domestic PIV software. The software uses the Local Field Correction which is able to resolve the flow structures smaller than interrogation window. Processing the images is done b the usual cross-correlation PIV proceeding based on FFT algorithm. In order to improve the correlation peak detection, Triple Image Correlation is used in place of the usual cross-correlation. In addition, a method to improve the accurac of TRPIV image analsis near boundaries has been applied. A weighting function is used to the interrogation windows for the correction to estimate the actual placement of the velocit vector when the interrogation area overlaps the image boundar. All of these give to the technique advantages in terms of accurac and robustness. Instantaneous and average fluid motions in the suction and in the impulse chamber of the pump have been analzed. Conditional averages in the suction and impulse chamber around gears have been obtained using a correlation procedure to catch the flow field at a fixed position of the gears. Time evolution of the average motion shows that the direction of the velocit patterns changes as a function of the movement of the gearwheel. The results obtained can help to understand the effect of the flow field in the pump performance and its efficienc. 1. Introduction The internal flow that develops in a sstem which consists of the rotating passages is exceedingl complex, involving streamline curvature, rotation and turbulence effects. The flow is interesting from a fluid mechanical perspective as it is often influenced b rotor-stator interaction mechanisms. A variet of measurement techniques have been applied to several industrial machines in the struggle for accurate quantitative flow descriptions which mean that methods have provided much fundamental knowledge of the flow phenomena occurring in rotating machines. However, the quest that maintains high efficiencies and performances at a broader range of operating conditions raises the need for a more detailed knowledge of the local and instantaneous features of the rotating passages flow. A gear pump is used for transferring and metering of liquids and power transfer in a process. In this stud, the flow phenomena of an external gear pump (Fig 1) have been investigated on the increase of its efficienc and performance. The fluid is transferred around the interior of the casing in the pockets b the meshing of two gears rotating against each other to pump the fluid from the suction side to the discharge (impulsion) side under pressure. As the gears rotate, the spaces between the gears teeth transport the fluid at constant amount of fluid per revolution

34 14th Int Smp on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 7-1 Jul, u velocit x - direction v velocit - direction INFLOW Suction Chamber Impulse Chamber OUTFLOW Fig 1. Scheme of an external gear pump. The mean flow rate of the pump is the result of the volumetric capacit and the rotational velocit. The volumetric efficienc has to be improved b minimizing the mechanical tolerances of manufacturing (Dearn 21). Gear pumps can produce a high frequenc pressure pulsation and thus increase of fluctuations of deliver flow flow rate ripples in suction and impulsion chambers, which tends to damage pressure gauges. To reduce the ripples, tooth profile, gear shape and pump bod plates are needed to be improved. Investigations show that it is not possible to get external gear pumps with no deliver fluctuation (Ioi and Ishimura, 1983). The efficienc of the pump is directl related with the relationship between the moving parts and clearances factors. Increasing the performance of an external gear pump can be achieved b reducing the size of the pump, increasing the pressure as well as the rotational velocit (Codina and Kamashata, 1999, and Castilla et al, 27). The purpose of this paper is to clarif the role of the suction chamber and analze the flow occurring in it. In addition, these results can help to decide modifications of the geometr of the pump in order to increase its performance. For this purpose, the use of a Time Resolved Particle Image Velocimetr (TRPIV) has been applied into the analsis of the turbulent flow inside an external gear pump. The TRPIV is a non-invasive technique and is a powerful instrument for the analsis of complex instantaneous flow structures allowing the stud of fast changing sstems. In the last decades, Digital Particle Image Velocimetr (DPIV) technique had been developed and applied to various flow fields. To allow the TRPIV the images have to be captured using high speed digital cameras which make possible to increase the time resolution. DPIV needs tracing particles to follow the flow movement. In general these are small solid or liquid particles that reflect the laser light. In the case of the external gear pump analzed here, small air bubbles have been used efficientl as particle seeding since solid particles and water drops can seriousl damage the pump model. In order to show the potential of the TRPIV technique as an efficient analsis tool in the design of industrial gear pumps, the main objective of the present stud is to provide detailed instantaneous and mean data of the internal flow field. 2. Experimental Procedure The pump sstem analzed is from the LABSON group of the Universitat Politecnica de Cataluna (UPC). Each cogwheel has a diameter of 54 mm and a height of 36 mm. The number of teeth in each wheel is 11, the volumetric capacit of this model is 44cm 3 /rev and the rotational velocit of the gear was 2 rpm. The cover of test pump has been completel made of methacrlate in order to allow the image acquisition. The test bench (Fig 2) is composed b two hdraulic circuits. The upper circuit is the primar or driven one, contains the test pump that takes the moving fluid (oil; ρ=885 kg/m 3, µ=.28 Pa.s) from the tank and impulses it through pressure fall back to the tank again. The pump is driven b an oleohdraulic motor, which is a component of the secondar circuit which is placed under the pump sstem

35 14th Int Smp on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 7-1 Jul, Oil tank High velocit Digital camera Test Computer Oil tank and power pack Laser sheet Laser generator Fig 2. Schematic drawing of the test bench. The light source was a pulsed Monocrom Infrared laser (8nm). A high velocit digital camera (Photron Ultima APX-RS) with resolution of pixel has been used. Digital images have been obtained with an acquisition frequenc of 5 fps, 1 fps and 2 fps. The buffer memor of the digital camera allows to record up to 248 images per experiment, equivalent to 4, 2 or.5 seconds depending of the sampling rate used. All the images obtained were stored in a digital support for later processing. The data and post processing was done using a domestic PIV software developed b ECCoMFiT group of Universitat Rovira i Virgili (URV). Most PIV experiments have been reported to use small solid particles for flow seeding. However, for this gear pump sstem, the use of solid materials can produce material erosion and damage the transparent surface of methacrlate and also problems in the gear sstem because of metal-metal contact between the teeth. The use of water drops as particle seeding could be considered but it can produce problems of oxidation of the steel gears. Finall, small air bubbles have been used in spite of some disadvantages: (i) the size of the bubbles is not easil controllable and a large variabilit in the its size can make difficulties to estimate the velocit lag (Raffel et al, 1998), (ii) the densit ratio is ver large and (iii) the presence of gas in a liquid can reduce the velocit of sound and hence it can make the flow becoming compressible at relativel low velocit (Brennen, 25). In the present case, the size of the bubbles is controlled b using pressurized air flowing through a porous media that avoids the generation of large size bubble, the control of the air flow also allow to control the densit of particles in the measurement area. Drag and buoanc forces associated with acceleration are the main forces that act on bubbles for their motion in fluid than the force of the fluid flowing. These forces can be optimized to allow bubbles to quickl relocate to a desired area (Moore, 27). B combining the drag force and the buoanc force, Stokes Law given in Equation 1 can be formed based on gravit acceleration (g), bubble radius (r) and kinematic fluid viscosit (ν) to estimate the bubble rise velocit ( v rise ). 2 2 r g v rise = (1) 9 ν v If the flow has a horizontal mean velocit ( ) and when the particle reaches the end of the test section, it has gone out off its path with an amount L H = v (2) rise v where the length of the test section is ( L ), Using equations (1) and (2), the ratio of vertical - 3 -

36 14th Int Smp on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 7-1 Jul, deviation and horizontal length of the test section can be defined as in equation 3 in order to find the ratio and keep the bubbles in the laser sheet. H L 2 2 r g = (3) 9ν v In the experiments, the laser sheet has a 1 mm thickness and the test section has a length of 3 mm. In order to keep the bubbles in the laser sheet, H/L ratio needs to be.25. The mean velocit of the flow is function of the rotational speed of the pump. Then we can optimize the bubble size with a negligible value for the particles move in vertical direction. It has been found the optimum diameter size of the air bubbles 1 µm which is also supported b the analsis of Bolinder The effect of gas-liquid mixture on the sonic speed of the flow has also been considered. A sufficientl high volume fraction of air can reduce the sonic speed down to 2 m/s (Brennen 25). In the present case, the gas maintains its temperature constant and the pressure of the pump sstem is quite low. When the size of the interrogation area (64x64 pixel) and usual densit of particles (suggested around 1-15 particles per interrogation area (Raffel et al, 1998) are used for low velocities, the flow shows reasonabl far awa from compressibilit characteristics. In the lest desirable situation which is the sonic speed is approximatel 2 m/s, the rotational speed of the pump should be around 1 rpm in order to have a Mach number. In the present configuration of the experimental setup, the rotational velocit of the gear was working at 2 rpm. 3. Techniques For TRPIV Image Analsis Instantaneous images were analzed using local field correction (LFC) (Nogueria et al, 1997) and TRPIV. LFC is a correlation PIV method able to accuratel resolve flow structures smaller than interrogation window (Willert and Gharib, 1991). The technique used here is a cross-correlation method that provides a remarkable capabilit for accuratel resolving small scale structures in the flow. Tpical dimensions of an interrogation area are given in the literature for PIV between 16x16 to 128x128 pixels. In order to obtain a reliable estimator of the particle image displacement, about 1 to 15 particles in an interrogation area have to be present (Raffel et al, 1998). In the present work, we have used 64x64 pixels for the interrogation area b considering the adequate particles intensit in each interrogation area (a) (b) Fig 3. Removing reflections b median estimator across the time series. (a) Original Image, (b) Image with Clean-Up Mask process An improvement on the processing of time series of the experimental images is the use of a Cleanup Mask process to remove and/or reduce the spurious permanent reflections of the light from the illumination process of the laser. The median value across the image time series is estimated to clean these reflections from the original images. Fig 3a presents an outlet region of the field of view for a single instantaneous image, while Fig 3b displas the differences between the original image - 4 -