Analysis of the Turbulent Flow of an External Gear Pump by ...ltces.dem.ist.utl.pt/lxlaser/lxlaser2008/papers/13.3_1.pdf · occurring in it. In addition, these results can help to

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

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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.


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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


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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


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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


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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)


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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 2000fps 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)


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(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.


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

ti ti+3

ti+6 ti+9

ti+12 ti+15


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

ti ti+3

ti+6 ti+9

ti+12 ti+15


- 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 [ m

m / s

]

y=1.8y=3.7

y=6.0

y=7.9

y=9.8

y=11.7y=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=1.8y=3.7

y=6.0

y=7.9

y=9.8

y=11.7y=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

[ m

m /

s ]

y=3.48y=5.4

y=7.5

y=9.2

y=10.8

y=12.9y=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=3.48y=5.4

y=7.5

y=9.2

y=10.8

y=12.9y=15.4

(b)


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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.

Hart DP (1998) The Elimination of Correlation Errors in PIV Processing, 9th

International

Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon.

Hart DP (1999) Super-Resolution PIV by Recursive Local-Correlation, Journal of Visualization

(10).

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.

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.

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.


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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.

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.

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Documents

Analysis of the Turbulent Flow of an External Gear Pump by ...ltces.dem.ist.utl.pt/lxlaser/lxlaser2008/papers/13.3_1.pdf · occurring in it. In addition, these results can help to