Experimental Study of the Flow in an External Gear Pump by ... · PDF fileExperimental Study...

Experimental Study of the Flow in an

External Gear Pump by Time

Resolved Particle Image Velocimetry

by

Nihal Ertürk

Supervised by:

Anton Vernet and Josep A. Ferré

A Thesis Submitted to

Graduate Programme in Chemical and Process Engineering

University of Rovira I Virgili

In the fulfillment of the Requirements for

The Degree of Master of Science in Chemical and Process Engineering

June, 2008, Tarragona Spain

Contents

1 Introduction 1

2 Objectives 3

3 Experimental Procedure 4

3.1 Experimental set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3.2 Flow Seeding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

4 Techniques for TRPIV Image Analysis 8

4.1 Preliminary Image Processing . . . . . . . . . . . . . . . . . . . . . 8

4.2 Interrogation Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

4.3 Triple Image Correlation. . . . . . . . . . . . . . . . . . . . . . . . . 10

4.4 Boundary Treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4.5 Conditional Average . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

5 Results and Discussion 13

5.1 Velocity fields and streamlines . . . . . . . . . . . . . . . . . . . . 13

5.2 Velocity profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

6 Conclusions 21

7 Future Work 22

References 23

Appendix 25

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 velocity. The limit value, H/L ≈ 0.03 has been indicated as straight horizontal line.

4.1 Removing reflections by 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 Velocity fields results which are obtain in different frequency rates (a)

Inlet with 500fps (b) Inlet with 1000fps (c) Inlet with 2000fps (d) Outlet with 1000fps

5.2 Streamlines results which are obtain in different frequency rates (a) Inlet with 500fps (b) Inlet with 1000fps (c) Inlet with 2000fps (d) Outlet with 1000fps

5.3 Velocity fields of suction chamber with 1000fps for different positions of gear teeth

5.4 Streamlines of suction chamber with 1000 fps for different positions of gear teeth

5.5 Inlet flow in the suction chamber at 1000fps (a) Mean v (b) Mean u (c) Magnitude of mean v velocity contours (d) Magnitude of mean u velocity contours.

5.6 Outlet flow in the impulse chamber at 1000fps (a) Mean v (b) Mean u (c) Magnitude of mean v velocity contours (d) Magnitude of mean u velocity contours.

5.7 Inlet flow in the suction chamber at 1000fps rms of velocity (a) v component (b) u component.

5.8 Outlet flow in the impulse chamber at 1000fps rms of velocity (a) v component (b) u component.

Acknowledgments

I would like to thank my 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 laboratory experimentation in LABSON at UPC. Also, thanks to everybody at ECCoMFiT group at URV. This study was financially supported by the Spanish Ministry of Science and Education and FEDER under projects DPI2006-02477 and DPI2006-14476.

Abstract

Time Resolved Particle Image Velocimetry (TRPIV) has been used to investigate the turbulent flow in an external gear pump. The fluid movement through the pump is maintained by the rotation of the gears that carries the fluid from the intake side to the discharge side of the system. Small air bubbles have been used as flow seeding to obtain the images. For the range of velocities used in this study the buoyancy 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 by 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 accuracy of TRPIV image analysis near boundaries has been applied. A weighting function is used to the interrogation windows for the correction to estimate the actual placement of the velocity vector when the interrogation area overlaps the image boundary. All of these give to the technique advantages in terms of accuracy and robustness. Instantaneous and average fluid motions in the suction and in the impulse chamber of the pump have been analyzed. 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 velocity 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 efficiency.

1

Chapter 1

Introduction

Internal flow in systems which consists of the rotating passages is exceedingly complex, involving rotation and turbulence effects. The flow is interesting from a fluid mechanical perspective as it is often influenced by rotor-stator interaction mechanisms. A variety 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 study, the flow phenomena of an external gear pump (Figure 1.1) have been investigated on the increase of its efficiency and performance. The fluid is transferred around the interior of the casing in the pockets by 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.

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. Accordingly, the fluid will try to find the path of least resistance and slip-back through the pump. To prevent this phenomenon, a dynamic sealing must be implemented [4]. There

INFLOW OUTFLOW

Suction Chamber

Impulse Chamber

2

are clearances for the dynamic seal parts to move and these clearances permit fluid to slip-back through the pump and reduce its theoretical efficiency. The degree of internal slippage in a gear pump determines its volumetric efficiency [1] which is the relation between actual pumped fluid flow rate,Q to the losses

of flow, LQ 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

capacity, vC and the rotational velocity, ω (eqn 1.2).

L

vQQ

Q

+=η (1.1)

π

ω

2

vCQ = (1.2)

The volumetric efficiency has to be improved by minimizing the mechanical tolerances of manufacturing [4].

Gear pumps can produce a high frequency pressure pulsation and thus increase of fluctuations of delivery 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 body plates are needed to be improved. Investigations show that it is not possible to get external gear pumps with no delivery fluctuation [5]. The efficiency of the pump is directly related with the relationship between the moving parts and clearances factors. In addition, the viscosity of the flow will effect for a thin fluid (such as water) or a moderately viscous fluid (such as particular oil). Increasing the performance of an external gear pump can be achieved by reducing the size of the pump, increasing the pressure as well as the rotational velocity [6,7].

In the last decades, Digital Particle Image Velocimetry (DPIV) technique had been developed and applied to various flow fields. To allow the Time Resolved Particle Image Velocimetry (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 analyzed here, small air bubbles have been used efficiently as particle seeding since solid particles and water drops can seriously damage the pump model. In order to show the potential of the TRPIV technique as an efficient analysis tool in the design of industrial gear pumps, the main objective of the present study is to provide detailed instantaneous and mean data of the internal flow field.

Chapter 2 describes the purpose and objectives of this study. Chapter 3 explains the experimental procedure and PIV setup and Chapter 4 gives details on the methodology for analyzing the images by using TRPIV. Chapter 5 presents the results and discussion, including instantaneous ensemble-averaged PIV velocity data followed by conclusions in Chapter 6 and future work in Chapter 7.

3

Chapter 2

Objectives

The purpose of this paper is to clarify the role of the suction and impulse chamber and analyze the flow occurring in it. In addition, these results can help to decide modifications of the geometry of the pump in order to increase its performance. For this purpose, the Time Resolved Particle Image Velocimetry (TRPIV) has been applied to the analysis of the turbulent flow inside an external gear pump. The TRPIV is a non-invasive technique and is a powerful instrument for the analysis of complex instantaneous flow structures allowing the study of fast changing systems.

In order to demonstrate the potential of the TRPIV technique as an efficient analysis tool in the design of industrial gear pumps, the main objectives of the present study for the technique are,

• To provide detailed instantaneous data of the internal flow field in the rotating passages of a pump gear by using air bubbles as flow seeding,

• Implementation of local field correction to cross-correlation PIV proceeding based on FFT algorithm,

• Improving the analysis techniques to obtain more accurate results.

4

Chapter 3

Experimental Procedure

3.1 Experimental Set-up

The pump system analyzed is from the LABSON group of the Universitat Politecnica de Catalunya (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 capacity of this model is 44 cm3 /rev and the rotational velocity of the gear was 200 rpm. The cover of test pump has been completely made of methacrylate in order to allow the image acquisition.

The test bench (Figure 3.1) is composed by two hydraulic circuits. The upper circuit is the primary 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 by an oleohydraulic motor and it is a component of the secondary circuit which is placed under the pump system. The motor is in turn driven by a hydraulic power-pack. This scheme allows modifying very easily the rotational velocity 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 velocity with precision.

Figure 3.1 Schematic drawing of the test bench.

Computer

Oil tank and power

Laser sheet Laser generator

Oil tank High velocity Digital camera

Test pump

5

The light source was a pulsed Monocrom Infrared laser with a wavelength of 800nm. A high velocity digital camera (Photron Ultima APX-RS) with resolution of 1024×1072 pixel has been used. Digital images have been obtained with an acquisition frequency of 500 fps, 1000 fps and 2000 fps. The buffer memory of the digital camera allows to record up to 2048 images per experiment, equivalent to 4, 2 or 0.5 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 by 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 system, the use of solid materials can produce material erosion and damage the transparent surface of methacrylate and can also cause problems in the gear system 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. Finally, small air bubbles have been used in spite of some disadvantages: (i) the size of the bubbles is not easily controllable and a large variability in the its size can make difficulties to estimate the velocity lag [8], (ii) the density ratio is very large and (iii) the presence of gas in a liquid can reduce the velocity of sound and hence it can make the flow becoming compressible at relatively low velocity [9].

In the present case, the size of the bubbles is controlled by 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 density of particles in the measurement area. Drag and buoyancy 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 quickly relocate to a desired area [10]. By combining the drag force and the buoyancy force, Stokes Law given in eqn 3.1 can be formed based on gravity acceleration

(g), bubble radius (r) and kinematic fluid viscosity (ν) to estimate the bubble rise

velocity ( risev ).

6

ν

grvrise

2

9

2= (3.1)

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/m3, µ = 0.028 Pa.s) used in this study.

Figure 3.3 Rise velocities dependence on bubble radius.

If the flow has a horizontal mean velocity ( yv ) and when the particle reaches the

end of the test section, it has gone out off its path with an amount (eqn 3.2)

y

risev

LvH = (3.2)

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.

yv

gr

L

H

ν

2

9

2= (3.3)

In the experiments, the laser sheet has a 1 mm thickness and the test section has a length of 30 mm. In order to keep the bubbles in the laser sheet, H/L ratio needs to be approximately 0.03. In Figure 3.4 the ratio of the vertical deviation and the horizontal length of the test section is plotted against mean velocity for

0 0.2 0.4 0.6 0.8 10

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Bubble Radius (r) [ mm ]

Ris

e v

elo

city (

v s)

[ m

/ s

]

7

various bubble diameters for the characteristics of the mineral oil used. The mean velocity of the flow is function of the rotational speed of the pump. For 200 rpm, the mean velocity in the suction chamber has been obtained about 0.25 m/s and for this mean velocity the limit diameter size of the bubble is 0.7 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 0.1 mm which is also supported by the analysis of Bolinder [11].

Figure 3.4 For several bubble diameters, the ratio of vertical deviation and test section length in function of mean horizontal velocity. The limit value, H/L ≈ 0.03 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 sufficiently high volume fraction of air can reduce the sonic speed down to 20 m/s [9]. In the present case, the gas maintains its temperature constant and the pressure of the pump system is quite low. When the size of the interrogation area (64x64 pixel) and usual density of particles (suggested around 10-15 particles per interrogation area [8] are used for low velocities, the flow shows reasonably far away from compressibility characteristics. In the lest desirable situation which is the sonic speed is approximately 20 m/s, the rotational speed of the pump should be around 1000 rpm in order to have a Mach number. In the present configuration of the experimental setup, the rotational velocity of the gear was working at 200 rpm.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 110

-4

10-3

10-2

10-1

100

mean vy [m/s]

H/L

ra

tio

D = 0.1 mm

D = 0.2 mm

D = 0.3 mm

D = 0.4 mm

D = 0.5 mm

D = 0.7 mm

H/L = 0.03

8

Chapter 4

Techniques for TRPIV Image Analysis

Specific aspects of the time resolved PIV technique have been applied to analyze 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 accuracy of the technique.

4.1 Preliminary 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 history of the illumination at each image location is available, statistical properties of the series can be analyzed.

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 displays the differences between the original image and the median image from a time series of 400 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 by median estimator across the time series. (a) Original Image, (b) Image with Clean-Up Mask process

100 200 300 400 500 600 700

50

100

150

200

250

300

100 200 300 400 500 600 700

50

100

150

200

250

300

9

4.2 Interrogation Area

Instantaneous images have been analyzed using local field correction (LFC) [12] and TRPIV. LFC is a correlation PIV method able to accurately resolve flow structures smaller than interrogation window [13]. The technique used here is a cross-correlation method that provides a remarkable capability for accurately resolving small scale structures in the flow. Typical 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 10 to 15 particles in an interrogation area have to be present [8]. In the present work, 64x64 pixels interrogation area has been used by considering the adequate particles intensity 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].

( ) ( ) ( )yjxiIjiIyxRL

Lj

K

Ki

II ++= ∑∑−=−=

,',, (4.1)

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.

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 analysis led to the application of a FFT in PIV image processing, which significantly decreased the time required for the necessary operations to produce a velocity measurement [13].

t

t+∆t

cross-correlation peak search

v

Image 1

Image 2

I

I′

10

4.3 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 strategy by multiplying both correlation planes in order to improve the peak detection [16]. This leads to the reduction of the spurious correlation peaks appearing in only 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 (ti-1, ti) and (ti, ti+1) for the image corresponding to time ti. 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 only 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 by this algorithm. The peak obtained from the triple image correlation is more obvious than the corresponding peaks on the standard cross correlation planes.

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.

10 20 30 40 50 60

10

20

30

40

50

60

10 20 30 40 50 60

10

20

30

40

50

60

10 20 30 40 50 60

10

20

30

40

50

60

ti+1 ti ti-1

11

4.4 Boundary Treatment

Since, iterative standard algorithms introduce significant errors when the interrogation location is closer to the image boundary, a special treatment of the interrogation area near the image boundaries has been introduced to obtain the same level of accuracy available at inner locations [16]. The boundary treatment is applied to the images with weighting function which is responsible computing the corrected position of the velocity displacement relative to the boundary. A weighting function is needed to avoid instabilities in the iterative process of compensation of the particle pattern or changing the frequency response of a moving average [17]. The use distorts the grey level of the original images, introducing error. The LFC-TRPIV method works accurately even if it has this error built in, but with “double weighting”, which consists of averaging the result that calculated by its symmetrical 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 continuously rotating in a specific time interval. Analyzing this specific area, we have introduced a conditional average function which provides the gears a stable position in a specific time interval with velocity 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 velocity vectors are averaged to obtain a conditional velocity field representing the characteristic flow structure at this gear position (Figure 4.4).

Figure 4.4 Representation of the selected image. (a) Original image. (b) Selected image.

20 40 60 80 100 120 140 160 180

20

40

60

80

100

120

140

160

180

50 100 150 200 250 300 350 400 450 500 550

100

200

300

400

500

600

(a)

(b)

12

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 they have been used for the analyzing 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 system has been investigated by the conditional average function with a reliable velocity field and accurate results.

Figure 4.5 Correlation of the image frames to define a Specific Position of the Gear.

13

Chapter 5

Results and Discussion

5.1 Velocity 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 500 fps, 1000 fps and 2000fps respectively) and for the outlet chamber (Figures 5.1d-5.2d) at 1000 fps. All the inlet measurements were taken in a horizontal (x-y) plane at vertical location coincident with the flow entrance, while the outlet measurements were taken only 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 symmetrically 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.

14

u velocity

x - direction 0

v velocity

y - direction

Figure 5.1 Velocity fields results which are obtain in different frequency rates (a) Inlet with 500fps (b) Inlet with 1000fps (c) Inlet with 2000fps (d) Outlet with 1000fps

Suction

Chamber

Impulse

Chamber

INFLOW

OUTFLOW

Suction

Chamber

Impulse

Chamber

INFLOW

OUTFLOW

(a)

x [mm]

x [pixel]

y [pixel]

y [mm]

(b)

x [mm]

x [píxel]

y [mm]

y [píxel]

(c)

x [mm]

x [pixel]

y

[mm]

y

[pixel]

x [pixel]

y [pixel]

y [mm]

x [mm]

(d)

15

Figure 5.2 Streamlines results which are obtain in different frequency rates (a) Inlet with 500fps (b) Inlet with 1000fps (c) Inlet with 2000fps (d) Outlet with 1000fps

It has been shown that the sampling rate do not have an important effect on the flow structure obtained, at least at the rotation frequency used here. To find the flow evolution inside the suction chamber the instantaneous data obtained for a sampling rate of 1000 fps has been used since it gives a rather better resolution the other two cases (500 fps and 2000 fps). Figure 5.3 and Figure 5.4 show the velocity 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.

(b)

y [mm]

x [mm]

x [píxel]

y [píxel]

x [mm]

y

[mm]

x [pixel]

y

[pixel]

(a)

(c)

x [pixel]

y

[mm]

x [mm]

y

[píxel]

y

[pixel]

x [pixel]

y

[mm]

x [mm]

(d)

16

Figure 5.3 Velocity fields of suction chamber with 1000fps for different positions of gear teeth.

ti ti+3

ti+6 ti+9

ti+12 ti+15

17

Figure 5.4 Streamlines of suction chamber with 1000 fps for different positions of gear teeth.

ti ti+3

ti+6 ti+9

ti+12 ti+15

18

5.2 Velocity profiles

The suction chamber velocity profiles (Figure 5.5) show that the v velocity component is considerably increasing when the fluid is flowing through the gear teeth and the maximum negative velocity of mean v has been found in the center of the inlet side of the gear pump. The mean u velocity 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 symmetric as they move away from the inlet section. This lack of symmetry could be generated by the model performance and needs a more detailed analysis with a different rotation velocity and image acquisition at more than one horizontal plane.

Figure 5.5 Inlet flow in the suction chamber at 1000fps (a) Mean v (b) Mean u (c) Magnitude of mean v velocity contours (d) Magnitude of mean u velocity contours.

0 5 10 15 20 25 30-350

-300

-250

-200

-150

-100

-50

0

50

100Mean v vs x

x [ mm ]

v

[ m

m /

s ]

y=3.48

y=5.4

y=7.5

y=9.2

y=10.8

y=12.9

y=15.4

(a)

0 5 10 15 20 25 30-200

-100

0

100

200

300

400Mean u vs x

x [ mm ]

u

[ m

m /

s ]

y=3.48

y=5.4

y=7.5

y=9.2

y=10.8

y=12.9

y=15.4

(b)

0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

x [ mm ]

y

[ m

m ]

Magnitude of mean v velocity [ mm / s ]

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-50

0

50

(c)

0 5 10 15 20 25 300

2

4

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16

x [ mm ]

y

[ m

m ]

Magnitude of mean u velocity [ mm / s ]

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-100

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300

(d)

19

Figure 5.6 Outlet flow in the impulse chamber at 1000fps (a) Mean v (b) Mean u (c) Magnitude of mean v velocity contours (d) Magnitude of mean u velocity contours.

Velocity profiles at the impulse chamber (Figure 5.6), shows that the v velocity component is increasing when the fluid is passing through the gear teeth and the maximum negative velocity of mean v has been found in the center of the outlet side of the gear pump. The mean u velocity 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 study.

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 system. It is essentially 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.

0 5 10 15 20 25 300

5

10

15

x [ mm ]

y

[ m

m ]

Magnitude of mean v velocity [ mm / s ]

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-150

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-50

0

50

(c)

0 5 10 15 20 25 300

5

10

15

x [ mm ]

y

[ m

m ]

Magnitude of mean u velocity [ mm / s ]

-60

-40

-20

0

20

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80

(d)

0 5 10 15 20 25 30-250

-200

-150

-100

-50

0

50

100Mean v vs x

x [ mm ]

v

[ m

m /

s ]

y=1.8

y=3.7

y=6.0

y=7.9

y=9.8

y=11.7

y=13.7

(a)

0 5 10 15 20 25 30-80

-60

-40

-20

0

20

40

60

80

100Mean u vs x

x [ mm ]

u

[ m

m /

s ]

y=1.8

y=3.7

y=6.0

y=7.9

y=9.8

y=11.7

y=13.7

(b)

20

Figure 5.7 Inlet flow in the suction chamber at 1000fps rms of velocity (a) v component (b) u

component.

Figure 5.8 Outlet flow in the impulse chamber at 1000fps rms of velocity (a) v component (b) u

component.

0 5 10 15 20 25 300

0.5

1

1.5

2

2.5

3

3.5

4rms of velocity (v component) versus x

x [ mm ]

rms o

f v

[ m

m /

s ]

y=3.48

y=5.4

y=7.5

y=9.2

y=10.8

y=12.9

y=15.4

0 5 10 15 20 25 300

0.5

1

1.5

2

2.5

3

3.5

4rms of velocity (u component) versus x

x [ mm ]

rms o

f u

[

mm

/ s

]

y=3.48

y=5.4

y=7.5

y=9.2

y=10.8

y=12.9

y=15.4

0 5 10 15 20 25 300

0.2

0.4

0.6

0.8

1

1.2

1.4rms of velocity (v component) versus x

x [ mm ]

rms o

f v

[ m

m /

s ]

y=1.8

y=3.7

y=6.0

y=7.9

y=9.8

y=11.7

y=13.7

0 5 10 15 20 25 300

0.1

0.2

0.3

0.4

0.5

0.6

0.7rms of velocity (u component) versus x

x [ mm ]

rms o

f u

[

mm

/ s

]

y=1.8

y=3.7

y=6.0

y=7.9

y=9.8

y=11.7

y=13.7

21

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 study of the flow structures in the suction and impulse chamber of an external gear pump. Results show the possibility that the analysis technique presented can be used to obtain detailed information of the instantaneous velocity fields, in systems with moving elements, which are not part of the fluid flow. The ability to separate particles from the reflection and to clean/remove the spots allows improving the peak detection for the direction of the velocity. A simple triple image correlation algorithm can improve the peak correlation in rather moving parts appear in the image. The technique for boundary treatment developed by Usera et.al [15] has been applied with the use of weighting function to obtain the same level of accuracy available at inner locations of the system. Corrected positions of the velocity displacement relative to the boundary have been computed. A conditional average velocity 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 analysis of the suction chamber is needed for a better understanding of the dynamic behavior of the flow. The results of this study will be presented in 14th International Symposium on Applications of Laser Techniques to Fluid Mechanics in Portugal, July, 2008 and will be published in the proceedings of the conference (see Appendix).

22

Chapter 7

Future Work

The aim of the work that has been presented here was the possibility 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 study with different rotational velocities of the gear to increase the efficiency and performance of the system.

In addition to this, experimental study of cavity flow analysis in channel will be investigated by simultaneously measuring the velocity, the temperature and concentration fields with a combined Time-Resolved Particle Image Velocimetry (TRPIV) and Planar Laser-Induced Fluorescence (PLIF) system. 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 cavity channel. In addition, PLIF system can be also used to obtain whole-field concentration data for mixing performance in this channel.

23

References

[1] Wernet M. P., (2000) Application of DPIV to study both steady state and transient turbomachinery flows, Optics & Laser Technology 32, 497-525.

[2] Pedersen N., Larsen P.S., Jacobsen C. B., (2003) 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: 61-72.

[3] Day S.W., McDaniel J.C., (2005) PIV Measurements of Flow in a Centrifugal Blood Pump: Steady Flow Journal of Biomechanical Engineering, Volume 127, Issue 2, pp. 244-253.

[4] Dearn R, B.Sc.(Hons), (June 2001) European Marketing Manager, The fine art of gear pump selection and operation, World pumps, Volume 2001, Issue 417, pp 38-40.

[5] Iyoi H and Ishimura S (1983) χ-Theory in gear geometry, Transaction of ASME Journal of Mechanisms, Transmissions, and Automation in Design 105, pp 286–290.

[6] Codina E, Kamashta M, (1999) ECOPUMP project, Enhanced design of high pressure gear pumps using environmentally acceptable hydraulic fluids, BRITE Contract n BRPRCt95-0094, Tech. rep., LABSON-UPC.

[7] Castilla R, Gamez-Montero P, Huguet D, Codina E, (2007) Turbulence in Internal Flows in Minihydraulic Components, CIMNE, pp 241-251.

[8] Raffel M, Willert C, Kompenhans J (1998) Particle Image Velocimetry: A Practical guide, Springer.

[9] Brennen C E (2005) Fundamentals of Multiphase Flow, Cambridge University Press.

[10] Moore J (2007) Dry sump pump bubble elimination for hydraulic hybrid vehicle systems, Master thesis in the department of Mechanical engineering, The University of Michigan.

[11] Bolinder J (1999) On the accuracy of a digital particle image velocimetry system, Tech. rep., Lund Institute of Technology.

[12] Usera G, Vernet A, Ferré JA (2004) Consideration and Improvements of the Analysis Algorithms Used for Time Resolved PIV of Wall bounded Flows, 12th International Symposium on Applications of Laser Techniques to Fluid

24

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), 1493-501.

[14] Willert CE and Gharib M, (1991) Digital particle image velocimetry, Exp. Fluids (10), 181-193.

[15] Hart DP (1998) The Elimination of Correlation Errors in PIV Processing, 9th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon.

[16] Hart DP (1999) Super-Resolution PIV by Recursive Local-Correlation, Journal of Visualization (10).

[17] Nogueria J, Lecuona A, and Rodriguez PA (2001) Local field correction PIV, implemented by means of simple algorithms, and multigrid versions, Meas. Sci. Technol, 12, 1911-1921.

[18] Nogueria J, Lecuona A and Rodriguez PA (2002) Accuracy and time performance of different schemes of the local field correction PIV technique, (33), 743-751.

25

APPENDIX

14th Int Symp on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 07-10 July, 2008

1037

- 1 -

Analysis of the Turbulent Flow of an External Gear Pump by Time Resolved

Particle Image Velocimetry

Nihal Ertürk1, Anton Vernet

1, Josep A. Ferré

1, Robert Castilla

2, Esteve Codina

2

1: Department of Mechanical Engineering, University of Rovira I Virgili, Tarragona, Spain, [email protected],

[email protected], [email protected]

2: Department of Fluid Mechanics, Technical University of Catalonia, Terassa, Spain,

[email protected], [email protected]

Abstract

Time Resolved Particle Image Velocimetry (TRPIV) has been used to investigate the turbulent flow in an external gear pump. The fluid movement through the pump is maintained by the rotation of the gears that carries the fluid from the intake side to the discharge side of the system. Small air bubbles have been used as flow seeding to obtain the images. For the range of velocities used in this study the buoyancy 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 by 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 accuracy of TRPIV image analysis near boundaries has been applied. A weighting function is used to the interrogation windows for the correction to estimate the actual placement of the velocity vector when the interrogation area overlaps the image boundary. All of these give to the technique advantages in terms of accuracy and robustness. Instantaneous and average fluid motions in the suction and in the impulse chamber of the pump have been analyzed. 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 velocity 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 efficiency.

1. Introduction

The internal flow that develops in a system which consists of the rotating passages is exceedingly

complex, involving streamline curvature, rotation and turbulence effects. The flow is interesting

from a fluid mechanical perspective as it is often influenced by rotor-stator interaction mechanisms.

A variety 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 study, the flow phenomena of an external gear pump (Fig 1) have been investigated

on the increase of its efficiency and performance. The fluid is transferred around the interior of the

casing in the pockets by 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.

mailto:[email protected]






1037

- 2 -

Fig 1. Scheme of an external gear pump.

The mean flow rate of the pump is the result of the volumetric capacity and the rotational velocity.

The volumetric efficiency has to be improved by minimizing the mechanical tolerances of

manufacturing (Dearn 2001). Gear pumps can produce a high frequency pressure pulsation and thus

increase of fluctuations of delivery 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

body plates are needed to be improved. Investigations show that it is not possible to get external

gear pumps with no delivery fluctuation (Iyoi and Ishimura, 1983). The efficiency of the pump is

directly related with the relationship between the moving parts and clearances factors. Increasing

the performance of an external gear pump can be achieved by reducing the size of the pump,

increasing the pressure as well as the rotational velocity (Codina and Kamashata, 1999, and Castilla

et al, 2007).

The purpose of this paper is to clarify the role of the suction chamber and analyze the flow

occurring in it. In addition, these results can help to decide modifications of the geometry of the

pump in order to increase its performance. For this purpose, the use of a Time Resolved Particle

Image Velocimetry (TRPIV) has been applied into the analysis of the turbulent flow inside an

external gear pump. The TRPIV is a non-invasive technique and is a powerful instrument for the

analysis of complex instantaneous flow structures allowing the study of fast changing systems.

In the last decades, Digital Particle Image Velocimetry (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 analyzed here, small air bubbles have been used

efficiently as particle seeding since solid particles and water drops can seriously damage the pump

model. In order to show the potential of the TRPIV technique as an efficient analysis tool in the

design of industrial gear pumps, the main objective of the present study is to provide detailed

instantaneous and mean data of the internal flow field.

2. Experimental Procedure

The pump system analyzed is from the LABSON group of the Universitat Politecnica de Catalunya

(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 capacity of this model is 44cm3/rev and the rotational velocity of

the gear was 200 rpm. The cover of test pump has been completely made of methacrylate in order to

allow the image acquisition. The test bench (Fig 2) is composed by two hydraulic circuits. The

upper circuit is the primary or driven one, contains the test pump that takes the moving fluid (oil;

ρ=885 kg/m3, µ=0.028 Pa.s) from the tank and impulses it through pressure fall back to the tank

again. The pump is driven by an oleohydraulic motor, which is a component of the secondary

circuit which is placed under the pump system.

INFLOW OUTFLOW

Suction Chamber

Impulse Chamber

v velocity y - direction

0

u velocity x - direction


1037

- 3 -

Computer

Oil tank and power pack Laser sheet

Laser generator

Oil tank High velocity Digital camera

Test

Fig 2. Schematic drawing of the test bench.

The light source was a pulsed Monocrom Infrared laser (800nm). A high velocity digital camera

(Photron Ultima APX-RS) with resolution of 1024×1024 pixel has been used. Digital images have

been obtained with an acquisition frequency of 500 fps, 1000 fps and 2000 fps. The buffer memory

of the digital camera allows to record up to 2048 images per experiment, equivalent to 4, 2 or 0.5

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 by 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 system, the use of solid materials can produce material erosion and damage the

transparent surface of methacrylate and also problems in the gear system 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. Finally, small air bubbles have been used in spite

of some disadvantages: (i) the size of the bubbles is not easily controllable and a large variability in

the its size can make difficulties to estimate the velocity lag (Raffel et al, 1998), (ii) the density ratio

is very large and (iii) the presence of gas in a liquid can reduce the velocity of sound and hence it

can make the flow becoming compressible at relatively low velocity (Brennen, 2005). In the present

case, the size of the bubbles is controlled by 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

density of particles in the measurement area. Drag and buoyancy 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 quickly relocate to a desired area (Moore, 2007).

By combining the drag force and the buoyancy force, Stokes Law given in Equation 1 can be

formed based on gravity acceleration (g), bubble radius (r) and kinematic fluid viscosity (ν) to

estimate the bubble rise velocity ( risev ).

ν

grvrise

2

9

2= (1)

If the flow has a horizontal mean velocity ( yv) and when the particle reaches the end of the test

section, it has gone out off its path with an amount

y

risev

LvH = (2)

where the length of the test section is ( L ), Using equations (1) and (2), the ratio of vertical


1037

- 4 -

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.

yv

gr

L

H

ν

2

9

2= (3)

In the experiments, the laser sheet has a 1 mm thickness and the test section has a length of 30 mm.

In order to keep the bubbles in the laser sheet, H/L ratio needs to be 0.025. The mean velocity 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 100 µm which is also supported by the analysis of Bolinder 1999.

The effect of gas-liquid mixture on the sonic speed of the flow has also been considered. A

sufficiently high volume fraction of air can reduce the sonic speed down to 20 m/s (Brennen 2005).

In the present case, the gas maintains its temperature constant and the pressure of the pump system

is quite low. When the size of the interrogation area (64x64 pixel) and usual density of particles

(suggested around 10-15 particles per interrogation area (Raffel et al, 1998) are used for low

velocities, the flow shows reasonably far away from compressibility characteristics. In the lest

desirable situation which is the sonic speed is approximately 20 m/s, the rotational speed of the

pump should be around 1000 rpm in order to have a Mach number. In the present configuration of

the experimental setup, the rotational velocity of the gear was working at 200 rpm.

3. Techniques For TRPIV Image Analysis

Instantaneous images were analyzed using local field correction (LFC) (Nogueria et al, 1997) and

TRPIV. LFC is a correlation PIV method able to accurately resolve flow structures smaller than

interrogation window (Willert and Gharib, 1991). The technique used here is a cross-correlation

method that provides a remarkable capability for accurately resolving small scale structures in the

flow. Typical 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

10 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 by considering the adequate particles

intensity in each interrogation area.

100 200 300 400 500 600 700

50

100

150

200

250

300

100 200 300 400 500 600 700

50

100

150

200

250

300

(a) (b)

Fig 3. Removing reflections by 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 Clean-

up 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 displays the differences between the original image


1037

- 5 -

and the median image from a time series of 400 images. The median value of the illumination at

each point provides information that adversely affects the detection of the actual displacement of

the particles; they tend to lock the correlation to null displacement.

In order to get an estimated displacement, the usual cross-correlation PIV processing is performed

for each interrogation area. To calculate the cross-correlation between two corresponding

interrogation windows from successive images, fast-Fourier transforms (FFT’s) are used. Digital

recording and computer analysis led to the application of a FFT in PIV image processing, which

significantly decreased the time required for the necessary operations to produce a velocity

measurement (Willert and Gharib, 1991). An image can be paired in principle 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 (Hart 1998 and Hart 1999). The algorithm used here

implements this strategy by multiplying both correlation planes in order to improve the peak

detection (Usera et al, 2004). This leads to the reduction of the spurious correlation peaks appearing

in only one of the correlation planes. Since, iterative standard algorithms introduce significant

errors when the interrogation location is closer to the image boundary, a special treatment of the

interrogation area near the image boundaries has been introduced to obtain the same level of

accuracy available at inner locations (Usera et al, 2004). The boundary treatment is applied to the

images with weighting function which is responsible computing the corrected position of the

velocity displacement relative to the boundary. A weighting function is needed to avoid instabilities

in the iterative process of compensation of the particle pattern or changing the frequency response

of a moving average (Nogueria et al, 2001 and Nogueria et al, 2002).

4. Results

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 continuously rotating in a specific time interval.

Analyzing this specific area, we have introduced a conditional average function which provides the

gears a stable position in a specific time interval with velocity field of the flow at this time. The

image series in time are correlated with a selected image (Fig 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 velocity vectors are averaged to obtain a

conditional velocity field representing the characteristic flow structure at this gear position (Fig 4).

Fig 4. Representation of the selected image. (a) Original image. (b) Selected image.

20 40 60 80 100 120 140 160 180

20

40

60

80

100

120

140

160

180

50 100 150 200 250 300 350 400 450 500 550

100

200

300

400

500

600

(a)

(b)


1037

- 6 -

Fig 5 and 6 show the conditional averages obtained for the inlet chamber at different sampling rate

(Fig 5a-6a, 5b-6b and 5c-6c at 500 fps, 1000 fps and 2000 fps respectively) and for the outlet

chamber (Fig 5d-6d) at 1000 fps. All the inlet measurements were taken in a horizontal (x-y) plane

at vertical location coincident with the flow entrance, while the outlet measurements were taken

only in a horizontal plane in the upper plane of the chamber. Hence, it is not possible to see in Fig

5d 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 symmetrically 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.

Fig 5. Velocity fields results which are obtain in different frequency rates (a) Inlet with 500fps (b)

Inlet with 1000fps (c) Inlet with 2000fps (d) Outlet with 1000fps

(a)

x [mm]

x [pixel]

y [pixel]

y

[mm]

(b)

x [mm]

x [píxel]

y

[mm]

y [píxel]

(c)

x [mm]

x [pixel]

y

[mm]

y

[pixel]

x [pixel]

y

[pixel]

y

[mm]

x [mm]

(d)


1037

- 7 -

(b)

y [mm]

x [mm]

x [píxel]

y [píxel]

x [mm]

y

[mm]

x [pixel]

y [pixel]

(a)

(c)

x [pixel]

y

[mm]

x [mm]

y

[píxel]

y

[pixel]

x [pixel]

y

[mm]

x [mm]

(d) Fig 6. Streamlines results which are obtain in different frequency rates (a) Inlet with 500fps (b) Inlet

with 1000fps (c) Inlet with 2000fps (d) Outlet with 1000fps

It has been shown that the sampling rate do not have an important effect on the flow structure

obtained, at least at the rotation frequency used here. To find the flow evolution inside the suction

chamber the instantaneous data obtained for a sampling rate of 1000 fps has been used since it

gives a rather better resolution the other two cases (500 fps and 2000 fps). Fig 7 and Fig 8 show the

velocity 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.


1037

- 8 -

Fig 7. Velocity fields of suction chamber with 1000 fps for different positions of gear teeth.

ti ti+3

ti+6 ti+9

ti+12 ti+15


1037

- 9 -

Fig 8. Streamlines of suction chamber with 1000 fps for different positions of gear teeth.

ti ti+3

ti+6 ti+9

ti+12 ti+15


1037

- 10 -

The suction chamber velocity profiles (Fig 9) show that the v velocity component is considerably

increasing when the fluid is flowing through the gear teeth and the maximum negative velocity of

mean v has been found in the center of the inlet side of the gear pump. The mean u velocity

component reaches its maximum on the right middle and on the left middle side of the gear pump.

Fig 9 shows that the profiles become less symmetric as they move away from the inlet section. This

lack of symmetry could be generated by the model performance and needs a more detailed analysis

with a different rotation velocity and image acquisition at more than one horizontal plane.

Fig 9. Inlet flow in the suction chamber at 1000fps (a) Mean v (b) Mean u

Fig 10. Outlet flow in the impulse chamber at 1000fps (a) Mean v (b) Mean u

Velocity profiles at the impulse chamber (Fig 10), shows that the v velocity component is

increasing when the fluid is passing through the gear teeth and the maximum negative velocity of

mean v has been found in the center of the outlet side of the gear pump. The mean u velocity

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

study.

0 5 10 15 20 25 30-250

-200

-150

-100

-50

0

50

100Mean v vs x

x [ mm ]

v [ mm / s ]

y=1.8

y=3.7

y=6.0

y=7.9

y=9.8

y=11.7

y=13.7

(a)

0 5 10 15 20 25 30-80

-60

-40

-20

0

20

40

60

80

100Mean u vs x

x [ mm ]

u [ mm / s ]

y=1.8

y=3.7

y=6.0

y=7.9

y=9.8

y=11.7

y=13.7

(b)

0 5 10 15 20 25 30-350

-300

-250

-200

-150

-100

-50

0

50

100Mean v vs x

x [ mm ]

v [ mm / s ]

y=3.48

y=5.4

y=7.5

y=9.2

y=10.8

y=12.9

y=15.4

(a)

0 5 10 15 20 25 30-200

-100

0

100

200

300

400Mean u vs x

x [ mm ]

u [ mm / s ]

y=3.48

y=5.4

y=7.5

y=9.2

y=10.8

y=12.9y=15.4

(b)


1037

- 11 -

5. Conclusion

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 study of the flow structures in the suction

and impulse chamber of an external gear pump. Results show the possibility that the analysis

technique presented can be used to obtain detailed information of the instantaneous velocity fields,

in systems with moving elements, which are not part of the fluid flow. The technique for boundary

treatment developed by Usera et al. (2004) has been applied with the use of weighting function to

obtain the same level of accuracy available at inner locations of the system. Corrected positions of

the velocity displacement relative to the boundary have been computed. A conditional average

velocity 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 analysis of the

suction chamber is needed for a better understanding of the dynamic behavior of the flow.

Acknowledgments

This study was financially supported by the Spanish Ministry of Science and Education and FEDER

under projects DPI2006-02477 and DPI2006-14476.

References

Brennen C E (2005) Fundamentals of Multiphase Flow, Cambridge University Press.

Bolinder J (1999) On the accuracy of a digital particle image velocimetry system, Tech. rep., Lund

Institute of Technology.

Castilla R, Gamez-Montero P, Huguet D, Codina E, (2007) Turbulence in Internal Flows in

Minihydraulic Components, CIMNE, pp 241-251.

Codina E, Kamashta M, (1999) ECOPUMP project, Enhanced design of high pressure gear pumps

using environmentally acceptable hydraulic fluids, BRITE Contract n BRPRCt95-0094, Tech. rep.,

LABSON-UPC.

Dearn R, B.Sc.(Hons), (June 2001) European Marketing Manager, The fine art of gear pump

selection and operation, World pumps, Volume 2001, Issue 417, pp 38-40.

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