ORIGINAL PAPER

CFD and digital particle tracking to assess flow characteristicsin the labyrinth flow path of a drip irrigation emitter

Yunkai Li Æ Peiling Yang Æ Tingwu Xu Æ Shumei Ren ÆXiongcai Lin Æ Runjie Wei Æ Hongbing Xu

Received: 9 March 2007 / Accepted: 14 March 2008 / Published online: 26 March 2008

� Springer-Verlag 2008

Abstract It is necessary to have a comprehensive

understanding of the flow mechanisms within drip irriga-

tion emitters to design emitters that have a high anti-

clogging performance. The use of computational fluid

dynamics (CFD) to research the flow characteristics is

appropriate because the labyrinth flow path is narrow and

its boundary is complex. In this paper, a CFD for numeric

model was developed for numerical simulation of the

velocity distribution and turbulence intensity distributions

within labyrinth emitters. A two-dimensional digital par-

ticle-tracking velocimetry (2D-DPIV) visual display

system of the full flow fields was also constructed using

plain laser inducement fluorescence velocity measurement

technology, custom-made fluorescent particles and a plane

model of the emitters. The object lens of a microscope was

fitted to a conventional charge coupled device (CCD)

camera to overcome the contradiction problems between

the image viewing area and resolution power within the

flow path. The measured turbulence and velocity distribu-

tion characteristics within the labyrinth flow path were in

good agreement with the calculated CFD results. This

enabled the optimal emitter design patterns to be deter-

mined based on the hydraulic characteristics and clogging

resistance in the labyrinth flow path.

Introduction

Labyrinth emitters provide the highest performance of the

non-compensating drip irrigation emitters. However, the

flow paths are easily clogged by the pollutants in the water

because the width and depth of the labyrinth is often small,

ranging in size from 0.5 to 1.2 9 10-3 m. While the use of

filters and system scouring reduces emitter clogging to

some extent, the key design issue is to ensure a sound flow

regime in the flow path (Adin et al. 1991; Dasberg et al.

1999; Li et al. 2006). To design emitters with high anti-

clogging performance, it is necessary to have a compre-

hensive understanding of the flow regime within the flow

path. Hence, the main requirement of the flow path

designers is to conduct flow analyses to visualize the full-

flow fields and supply effective theoretical guidance on

optimal flow path design.

The labyrinth flow path in drip emitters is narrow and

complex and conventional drip tubes or belts are not

transparent. Hence, there are difficulties in taking con-

ventional measurements of flow fields for evaluating

prototype designs. An augmented model of the emitter flow

path and Laser-Doppler velocimetry has been used to

observe the internal flow movement (Zhang et al. 2007).

Communicated by S. Raine.

Y. Li � P. Yang (&) � S. Ren � X. Lin

Center for Agricultural Water Research in China,

China Agricultural University, Beijing 100083, China

e-mail: liyunkai@126.com

T. Xu

International College at Beijing, China Agricultural University,

Beijing 100083, China

R. Wei

Beijing Lifangtiandi Sci-Tech Development Limited Company,

Beijing 100081, China

H. Xu

R&D Center for Plastic Manufacturing,

Beijing Chemical Engineering Research Institute,

Beijing 100013, China

123

Irrig Sci (2008) 26:427–438

DOI 10.1007/s00271-008-0108-1

However, this system focused on a single point, and the

augmented model did not take into account the boundary

layer similar to the prototype.

There are currently no published reports showing full-

field measurement within the labyrinth flow paths. Inade-

quate design theory has led to a series of ad hoc design

modifications involving experimental testing. Thus the

period of design and development of new emitters is often

lengthy and expensive. However, with the rapid develop-

ment of computer technology, simulation technology for

complex fluid flow has developed rapidly.

Computational fluid dynamics (CFD) has unique

advantages for analyzing fluid flow. It provides the

opportunity to combine numerical simulation with both

experimental and theoretical research to better understand

the fluid movement. CFD studies method possessed the

function of internal movement prediction, numerical

experiment and movement diagnosis, etc. It could help the

designers to select the most rapid and economical approach

to conveniently optimize the various alternatives, thus

significantly reducing the need for physical experimental

work. It could also help to achieve the optimal design,

subject to various constraints, and is an indispensable

component of modern emitter design theory (Wang et al.

2006).

CFD has been used to conduct exploratory research into

the property of flow movement within the labyrinth flow

path of drip irrigation emitter. Palau et al. (2004) simulated

the relationship between pressure and discharge rates for an

in-line emitter labyrinth with the commercially available

CFD software, FLUENT. Li et al. (2005) also simulated the

flow characteristics within three types of column labyrinth

path emitters using FLUENT, enabling the velocity mag-

nitude, vorticity magnitude, and the turbulence intensity

distribution to be visualized. Wei et al. (2006) simulated the

flow characteristics in triangular, rectangular, and trape-

zoidal labyrinth flow paths and Zhang et al. (2007)

simulated the relationship between flow rate and pressure

head, as well as the flow field distribution in the small arc

labyrinth channels. However, there is some debate regard-

ing the selection of an appropriate numerical model for

simulating the flow characteristic in drip irrigation emitters.

The discharge of the labyrinth path emitters is generally

only about 0.2–8 L h-1 at pressures of 10–150 kPa, the

cross-sectional area is about 0.6–1.0 9 10-6 m2, the cross-

sectional average velocity tð Þ is 0.1–1.0 m s-1, and the

value of Reynolds number (Re, Re ¼ tR=m; m is the moving

viscous coefficient of fluid and R is the hydraulic diameter)

is about 70–1,000. Hence, some scholars (Palau et al. 2004;

Zhang et al. 2007) have used laminar models to conduct the

CFD numerical simulation. However, the majority of the

emitter discharge exponents are in the range of 0.50–0.65,

which indicates that the internal flow is turbulent (Dasberg

et al.1999). Hence, some scholars (Li et al. 2005; Wei et al.

2006; Zhang et al. 2007) have recently used a turbulent

model for CFD research into emitters.

Evaluations of the fractal flow path of emitters have been

identified as an effective approach to realizing the goal of

simultaneously improving the hydraulic properties and

clogging resistance in emitters (Li et al. 2007). In this paper,

a CFD numerical simulation was used to analyze the fluid

movement in labyrinth flow paths and a two dimensional

digital particle image velocimetry (2D-DPIV) visual display

system was developed to validate the veracity of the CFD

method. Numerical experimental research was also con-

ducted to identify the optimal designs for labyrinth flow

paths.

Model construction and its solution

Construction of the theoretical model

The fluid in the emitter is water, as a result, it is assumed to

be viscous, steady, and incompressible at room temperature

under pressures of 10–150 kPa. The fluid gravity and the

surface roughness of the channel wall are considered, while

ignoring the surface tension. The mathematical–physical

simulation model could be established with basic control-

ling equations and solution-determination conditions as

follows (Murray 1970).

Continuum equation

ou

oxþ ov

oyþ ow

oz¼ 0 ð1Þ

Navier-Stokes equation system

oðquÞotþr � ðquUÞ ¼ � op

oxþ lr2uþ qfx

oðqvÞotþr � ðqvUÞ ¼ � op

oyþ lr2vþ qfy

oðqwÞotþr � ðqwUÞ ¼ � op

ozþ lr2wþ qfz

ð2Þ

Standard k-e equation

o

otðqkÞ þ o

oxiðqkUÞ ¼ o

oxi½ðlþ lt

rk

ok

oxiÞ� þ Gk þ Gb � qe

� YM

ð3Þo

otðqeÞ þ o

oxiðqeUÞ ¼ o

oxi½ðlþ lt

re

oeoxiÞ� þ C1e

ekðGk

þ ClGbÞ � C2eqe2

kð4Þ

428 Irrig Sci (2008) 26:427–438

123

Gk ¼ l 2ou

ox

� �2

þ otoy

� �2

þ ow

oz

� �2" #

þ ou

oyþ ov

ox

� �2(

þ ou

ozþ ow

ox

� �2

þ ov

ozþ ow

oy

� �2)

ð5Þ

where U denotes fluid velocity, U ¼ ui~þ vj~þ wk~ (m s-1),

u, v, w denote the projected values on axes of x, y, and z,

respectively; q (kg m-3) and l (Pa s) denote the water

density and dynamical viscidity coefficient, respectively; p

(Pa) is the fluid pressure; fx fy fz are projected values of

mass force (considering only gravity), fx = fy = 0,

fx = -g; lt denotes the viscidity coefficient of turbulent

flow; Gk and Gb denote the average velocity gradient and

the turbulent pulse kinetic energy caused by buoyancy,

Gb = 0; YM denotes the kinetic energy dissipation ratio

caused by the pulse dilation, YM = 0; The constants in the

model are: C1e = 1.44, C2e = 1.92, Cl = 0.09, rk = 1.0,

re = 1.3.

Finding the solution

Geometric model and computational domain

The emitter flow path consisted of the inlet, outlet and main

body. The local water head loss was the main energy-dis-

sipation pattern in the flow path of the emitter (Glaad et al.

1980), and about 98% of water head loss in dentation

labyrinth flow path occurred at the dentation structure

(Ozekici et al.1991). For the convenience of establishing

the computational domain model (Fig. 1) and for the pur-

pose of saving computational resources, the energy-

dissipating unit of the plastic prototype of the emitter was

simplified by neglecting the effects caused by the inlet and

outlet. Table 1 shows the geometric parameters of the flow

path.

Gridding

Grid selection is an important factor influencing the accu-

racy of the solution in numerical simulation methods

(Zhang et al. 2007). In order to obtain high quality grids,

each flow path unit was divided into five sections that were

meshed with structured hexahedron grids. GAMBIT was

used for gridding, and the length of the grid unit was

5 9 10-5 m. The finite volume method was solved using

Eqs. (1)–(5).

Boundary conditions

To perform the CFD analysis, the pressure inlet condition

was set at the emitter inlet boundary, while the pressure

outlet condition was set along the external zone boundary.

Except for the inlet and outlet of the flow path, the velocity

vectors on the other boundaries were set to zero. The wall

was assumed to behave under no-slip conditions, and a

standard log-law wall function was used for the near-wall

linear sub-layer.

Finding a solution to the model

The coupling implicit algorithm with definite constants was

used for the numerical calculation. The first-order conser-

vative upwind difference scheme was used for pressure

items. SIMPLEC was used for coupling between pressure

and velocity (Fluent Inc. 2003). The convergence accuracy

was chosen to be 1 9 10-4.

Construction of visual display system with 2D-DPIV

System integration and its key components

The 2D-DPIV system was used to display the internal flow

within the emitter and consisted of both hardware and

software components. The hardware included a dual-pulse

LASER, CCD camera, synchronic controller, image-col-

lection board, and a computer. The software required was

used for image-collection, display, velocity calculation,

and velocity field analysis.

Image collection and processing

The 2D-DPIV system of image collection and processing

consisted of a frame straddle CCD, wave-filtering slice,

image-collection board, and a computer. The digital cam-

era was a Kodak MEGAPLUS II [resolving power of

1,600 9 1,200 (2M)]. The dimension of emitter flow paths

is usually 0.5–1.2 9 10-3 m and dentation interval is

usually within 3.0–5.0 9 10-3 m. The large viewing area

associated with when using the conventional DPIV system

for measurement, resulted in low image quality and test

accuracy. In this application, the viewing area being

(0.5 9 10-3) m 9 (0.5 9 10-3) m, the system could not

WH

Inlet

Outlet

Fig. 1 Computational domain of the labyrinth flow path (M16)

Irrig Sci (2008) 26:427–438 429

123

display the flow movement characteristics around each

dentation, hence the CCD camera was modified by

installing a G10-2111 (Beijing Daheng Camera Company)

microscope object lens (fourfold) to obtain an appropriate

digital-image resolving power with a viewing area of

(4 9 10-3) m 9 (4 9 10-3) m.

Laser light source

Laser emitters have been used as the light source in the

DPIV measurement because they are high-energy mono-

chrome sources with high stability, directional control and

pulse control. The dual-pulse laser emitter used in this

DPIV system was a t Q Nd; YAG (LABEST Company).

The laser emitter had a work frequency of 10 Hz, wave

length of 5.32 9 10-7 m, laser energy of 0.05 J, pulse

width of (6–8) 9 10-9 s, radiating angle of 0.6 mrads,

super Gauss facula mode and a dual-pulse time interval of

less than 1 9 10-6 s.

Analysis software

The system analysis software used was MicroVec Version

2.0 developed by Wei Yunjie. Tecplot 9.0 was used for

displaying the whorl fields.

Tracing fluorescence particles of 2D-DPIV

An important factor in the operation of the DPIV system is

the tracing particle. Tracing particles have been developed

in some countries. However, during the process of manu-

facturing plain model, the existence of nick caused noise in

the shooting images and reduced the accuracy of velocity

measurement (Fig. 2). Hence this paper introduced plane

laser inducement fluorescence technology and used wave-

filtering slice to eliminate the noise beyond the fluores-

cence. Custom-made fluorescence particles that could be

suspended in water with a micro-disturbance were con-

structed from polystyrene (density of 1.02 kg m-3), with

an average diameter of (1–1.5) 9 10-5 m. The particles

produced an adequate dispersion response to the laser

(fluorescence wave band of 6.20 9 10-7 m) and a wave-

filtering slice was used to eliminate all noises in the plane

model.

The concentration of the tracing particles affects the

ability of the DPIV system to accurately identify the flows.

High concentrations of the particles affected the velocity

field and could cause 2-phase flow. However, low con-

centrations of tracing particles could affect the

measurement accuracy. Preliminary experiments showed

that 1–2% was an appropriate concentration of fluores-

cence particles for the DPIV system.

Characteristics of fluid flow in the fractal flow

path of emitters

Characteristics of velocity distribution

A digital camera was used to obtain photos of the flow

fields. The characteristic parameter distribution (e.g.,

velocity) on a profile was achieved by correlation analysis

between the two adjacent frames of particle images. Fig-

ure 3 shows images of the particle flow fields in the flow

path and Fig. 4 shows the resulting velocity distribution

under 10, 50, 100 and 150 kPa. Some whorls were

observed in the labyrinth flow path. However, the velocity

distributions were similar under the four different pressure

levels. The velocity distribution could be divided into

regions experiencing mainstream velocity and secondary

flow velocity regions. The mainstream swayed on both

sides of the flow path. The mainstream continuously mixed

into the secondary flow and energy exchange continuously

occurred to dissipate the pressured energy. From this, it is

concluded that the flow within the labyrinth flow paths

were turbulent at these pressures and that there was no

transition from laminar to turbulent flow within this

Table 1 Geometric parameters of the labyrinth flow path (M16)

Width of path W/10-3 m Depth of path D/10-3 m Length of path L/10-3 m Dentation height H/10-3 m Dentation number N

0.90 0.89 128 1.30 22

L denotes the central length of the fluid flow in the path

Fig. 2 Visual display for the flow fields in flow path unit. 1. 2: nick

430 Irrig Sci (2008) 26:427–438

123

pressure range. Hence, the turbulent model should be used

in CFD numerical simulation for pressures, in the range of

10–150 kPa.

The velocity in the mainstream was high, while the

velocity in the secondary flow region was low (Fig. 4). The

regions of low velocity included A, B, C and D (Fig. 4a).

Small particles tend to subside in regions of low velocity

and may eventually block the emitters. Hence, while

designing the rational flow paths, the design should elim-

inate regions of low velocity by creating smooth arc

connections in these regions. This will also enhance the

self-cleaning capacity by optimization of the flow path

boundaries. With increasing pressure, the region of low

velocity gradually diminished and the velocity adjacent to

the boundary increased. Hence, the optimal arc radius will

be different for emitters designed to operate at different

pressures.

Figure 5 shows the CFD analysis of velocity distribution

under different pressures. Comparison of Fig. 4 and Fig. 5

suggests that the CFD calculated results are in good

agreement with the physical testing, confirming the

appropriateness of using CFD analysis to evaluate emitter

performance in the 10–150 kPa pressure range.

Characteristics of turbulence intensity distribution

The turbulence intensity is one physical variable

describing the turbulence strength of the flow and it can

be used as one of the indices for describing the energy

dissipation properties of emitters. By experimental

research, Murray (1970) showed that the reduction in

particle sedimentation rate increased with respect to

increasing flow turbulence intensity. This indicated that

the pollutant carrying capacity of turbulent flow increased

with turbulence intensity. Hence, the turbulence intensity

could be used as one of the indices for describing the

clogging resistance of emitters.

Figure 6 shows the turbulence intensity distributions in

conventional labyrinth flow path and fractal flow path

under the pressure of 100 kPa. The figure also indicates

that the turbulence intensity in the fractal flow path was

higher than that in the labyrinth path. The turbulence

intensity along the whole mainstream was similar, which

could explain why the index of flow regime in the fractal

flow path was smaller than that in the conventional flow

path. Figure 6a, b indicates that the turbulence intensity in

the unit length of two labyrinth flow paths increases along

the flow direction (Li et al. 2005). The turbulence intensity

in the whole flow path displayed a cyclical repetition from

weak to strong but the straight-line portion of the flow path

weakened the turbulence intensity. Hence to increase the

turbulence intensity, the length of straight line in the flow

path should be reduced. Where there are more energy

dissipation nodes in the fractal flow path, the turbulence

intensity along the whole path is maintained at a relatively

high level.

Optimal designs for fractal flow path

There were some low velocity regions in the flow path

(Fig. 4). Because energy was dissipated in the low velocity

regions, pollutants could be deposited causing path clog-

ging (Shi et al. 1995). Based on the requirement for

emitters to enhance clogging resistance, the flow path

should be designed in order to avoid or limit the existence

of low velocity regions.

Numerical experimental design

Velocity in region D (Fig. 4) was relatively high, where the

arc connection had a radius of 0.5 W (W denotes the path

width). The same arc connection treatment was applied in

regions A and C where the secondary flow area was

Fig. 3 DPIV images of the

particle distribution flow fields

in flow path unit. a Former

frame. b Latter frame

Irrig Sci (2008) 26:427–438 431

123

Fig. 4 The velocity distribution under different pressure with DPIV test (m s-1). a 10 kPa, b 50 kPa, c 100 kPa, d 150 kPa

432 Irrig Sci (2008) 26:427–438

123

Fig. 5 The velocity distribution

under different pressure with

CFD analysis (m s-1).

a 10 kPa, b 50 kPa, c 100 kPa,

d 150 kPa

Irrig Sci (2008) 26:427–438 433

123

Fig. 6 Turbulence intensity

distribution in unit length of the

fractal flow path (%).

a Common labyrinth flow path.

b Common labyrinth flow path-

II. c Fractal flow path

Table 2 Numerical experimental treatment for optimal deign of labyrinth flow path

Tr Region B (W) Region C (W) Gridding Tr. Region B (W) Region C (W) Gridding

1 0.5 0.5 a 6 1.0 0.5 f

2 0.8 0.8 b 7 0.5 1.0 g

3 1.0 1.0 c 8 0.8 0.5 h

4 0.5 0.8 d 9 1.0 0.8 i

5 0.8 1.0 e

Gridding: refer to Fig. 8 for details

Fig. 7 Numerical experiment

design for optional designs and

gridding

434 Irrig Sci (2008) 26:427–438

123

similar. Refer to Table 2 for details, and Fig. 7 shows the

gridding.

Effect on hydraulic characteristics of different designs

Table 3 shows the numerically simulated free discharges of

the prototype and optimized emitters modeled under dif-

ferent pressures. The results indicate that the discharge of

various optimized models were all smaller than that of the

prototype emitter with a discrepancy of less than 10.0%.

There was no significant difference in the free discharges

of the optimized emitters with various arc treatments. This

also reflected that the reduction in cross-section could

increase the friction-resistance and enhance the hydraulic

characteristics of the flow path.

Table 3 shows the results of the indices of flow regime

(x) and the discharge coefficient (Kd) by the regression

equation q = Kdhx (q is the free discharge and h is the

work pressure). The results indicate that the indices of flow

regime for various optimized emitters were all smaller than

that of the prototype emitter with a discrepancy of less than

6.0%. This also shows that the optimization treatment had

little effect on the hydraulic characteristics of the flow path.

Hence, the clogging resistance property should be consid-

ered in optimal design of emitter flow paths and the self-

cleaning capacity could be enhanced by increasing the

velocity of flow near the boundary wall of the path.

Effect on clogging resistance characteristics by

different optimization treatments

Changing the structure of the flow path is one approach to

enhancing the clogging resistance of the flow path. From

the perspective of the flow path, there are two main reasons

for clogging. One reason is that the flow path is narrow and

large suspended particles cannot pass easily. The other

reason is that the low-flow velocity causes some suspended

particles to deposit and reduce the cross-section of the flow.

The latter phenomenon is not apparent initially but the

effect worsens over time. Tong et al. (1998) showed that

the number of suspended particles deposited in the low

velocity region increased gradually. However, increasing

the velocity near the boundary wall of flow path could

prevent or alleviate clogging in the path.

Figure 8 shows the numerical experiment results of the

velocity distribution in the typical unit of the flow path with

treatments 1–9 at 100 kPa. These data show that the sec-

ondary flow developed in regions A and C with treatments

1–9 operating at 100 kPa. Howver, the velocity near the

boundary wall increased as the arc radius was reduced. For

region B, secondary flow was difficult to develop and the

velocity of secondary flows under various treatments were

not significantly different. Hence, in this region the sec-

ondary flow should be eliminated. Treatment 6 was

selected as the best combination of the arc radii and Fig. 9

shows the velocity in the typical unit length of the path.

Discussion

Direct particle imaging

This paper has reported on the development of a full-field

non-disturbance test for evaluating the flow path of emit-

ters. However, some problems with the system should be

noted:

(1) The experiment applied the plane model of labyrinth

flow path of cylindrical emitters and ignored the

Table 3 Free discharges and discharge–pressure relationships under various optimization treatments

No. of Tr. Free discharge q L-1/h Discharge–pressure relationship

Work pressure h/kPa Discharge

coefficient

Kd

Index of flow

regime xR2

10 30 50 70 90 100 110 130 150

0 0.87 1.38 1.81 2.12 2.42 2.59 2.74 2.91 3.19 0.84 0.49 0.99

1 0.79 1.32 1.68 1.97 2.25 2.33 2.48 2.69 2.89 0.78 0.48 0.99

2 0.80 1.37 1.75 2.06 2.29 2.37 2.48 2.69 2.89 0.81 0.47 0.99

3 0.82 1.36 1.74 2.05 2.31 2.42 2.55 2.76 2.97 0.81 0.48 0.99

4 0.80 1.34 1.70 1.99 2.24 2.36 2.55 2.68 2.87 0.80 0.47 0.99

5 0.82 1.36 1.74 2.04 2.37 2.42 2.54 2.83 3.06 0.81 0.48 0.99

6 0.79 1.35 1.69 2.01 2.27 2.35 2.52 2.71 2.91 0.79 0.48 0.99

7 0.82 1.39 1.76 2.07 2.32 2.42 2.53 2.81 2.93 0.82 0.47 0.99

8 0.79 1.34 1.72 2.05 2.34 2.44 2.50 2.71 2.89 0.79 0.48 0.99

9 0.81 1.35 1.73 2.07 2.30 2.38 2.58 2.76 3.02 0.80 0.48 0.99

Treatment 0 denoted the measured practical discharge of emitter prior to optimization

Irrig Sci (2008) 26:427–438 435

123

roughness of the model and the circumfluent issues.

From the geometric perspective, there is some

roughness on the path wall except for specially

processed fine surfaces. In engineering practice, the

roughness of the solid surface is usually 1.0–

25.0 9 10-6 m. For single-phase flow, considering

the path wall as geometrically smooth surface does

not cause irrational results in practice. However for 2-

phase flow, the particle dimension and path surface

roughness are on the same scale. In this case, if the

path wall is considered as geometrically smooth, then

the vertical velocity of the particle would approach

zero resulting in an inappropriate increase in colli-

sions between path wall and the particles. The DPIV

test showed that relatively large errors occur where

the particle concentration is high and there are

differences in manufacturing workmanship between

the plane model and the plastic model. In addition, the

boundary of labyrinth flow path and the collision

mechanism between particles and path wall are both

complex. Hence there is a need to conduct prototype

research using plastic emitters.

(2) This work has shown the presence of two-dimen-

sional flow within the labyrinth path of emitters.

Fig. 8 Effect on velocity

distribution in typical unit of

labyrinth flow path by various

optimization radii (work

pressure 100 kPa) (m/s)

Fig. 9 Velocity distribution in

typical unit length of labyrinth

flow path after the optimization

(Tr. 6) (work pressure100 kPa)

(m/s)

436 Irrig Sci (2008) 26:427–438

123

However, the properties of flow, adjacent to the path

wall and the possible existence of secondary flow on

the cross-section needs further research.

CFD analysis

Using CFD for analyzing the flow fields of irrigation

emitters is a relatively new research application and the

stable-status theory and the macro-dimension model are all

approximating approaches. Hence, there are three types of

problems for this area of research:

(1) Stable-status treatment. Treating the flow in the path

as a continuous stable-status flow cannot describe the

response of drips from the emitter outlet to the flow

process. Under high pressure, the stable-status treat-

ment could be appropriate but large errors may occur

under low pressures when a non-stable status treat-

ment should be implemented.

(2) Boundary wall treatment. Using a boundary wall

function to treat the flow near the boundary wall can

cause errors because the boundary wall function is

applicable only for parallel walls within a certain

range. The complex structure of emitters, complex

bending of the flow and different thickness of

boundary layers can all produce errors.

(3) Single-phase flow. This research on clogging resis-

tance was based on the assumption that the flow was

single-phase. Further research should focus on using

multi-phase flow assumptions for analyzing the flow

locus of microorganisms, viscous particles and sus-

pended sands. The critical non-depositing velocity of

the particles as well as the interactive effect between

particle concentration, particle sizes and the flow

should be further studied.

Conclusions

This paper used CFD analysis and direct particle imaging

to study the flow charateristics in labyrinth flow paths.

Custom-made fluorescence particles were developed and

used with DPIV measurement technology to measure the

flow fields of emitters and conduct two-dimensional non-

disturbance tests within the flow path of emitters. An object

lens-modified microscope fitted to a conventional CCD

camera was used to display the flow fields and successfully

solved the contradiction between viewing region and

imaging resolving power within the critical scale of the

flow path. Based on this research, the following findings

can be made:

(1) Velocity distribution differences were used to divide

the flow into mainstream and secondary flows. The

mainstream continuously mixed into the secondary

flow and energy exchange continuously occurred in

the flow path. The mainstream flow was turbulent at

pressures between 10 and 150 kPa and there was no

transition process from laminar to turbulent flow

observed with increasing pressure. Hence, the turbu-

lent model could be used for CFD numerical

simulation in this pressure range. The simulated

velocity distribution for the central cross-section of

the emitter flow path was similar to the measured

velocity distribution by the 2D-DPIV test. Hence, the

established numerical simulation model for flow in

the labyrinth flow path relatively described the flow

process accurately.

(2) Designing of rational flow paths should involve

eliminating the regions of low velocity by creating

smooth arc connections in these regions and enhanc-

ing the self-cleaning capacity by optimization of flow

path boundaries. Evaluations of nine optimization

treatments for labyrinth flow paths had little effect on

the hydraulic characteristics of the flow path. Hence,

the clogging resistance property should be given

consideration in optimal design of flow path of

emitter and the self-cleaning capacity should be

enhanced by increasing the velocity of flow near the

boundary wall of the path. This work suggests that the

value of 0.5 W arc radius should be used in regions A

and C, while the value of 1.0 W arc radius should be

used in region B.

Acknowledgments We are grateful for financial support from the

National Natural Science Fund of China (NSFC) (No. 50379053,

No.50609029) and support by the Program for Changjiang Scholars

and Innovative Research Team in University (PCSIRT)

(No.IRT0657) and the Initiating Research Fund from China Agri-

cultural University (No.2005065).

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