numerical investigation of the clogging mechanism in labyrinth channel of the emitter

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERINGInt. J. Numer. Meth. Engng 2007; 70:1598–1612Published online 28 November 2006 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/nme.1935

Numerical investigation of the clogging mechanismin labyrinth channel of the emitter

Zhang Jun, Zhao Wanhua∗,†, Tang Yiping, Wei Zhengying andLu Bingheng

State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong University,Xi’an 710049, People’s Republic of China

SUMMARY

Emitter clogging is a main factor affecting the performance of drip irrigation products. Considering thesmall size and intricacy of emitters, numerical methods are introduced to study the clogging mechanism oflabyrinth channel in the emitter. A three-dimensional numerical model of clogging analysis is addressed,where Reynolds stress model with wall function is used to simulate the fluid flow in the Eulerian frame,and stochastic trajectory model is adopted to track the motion of the particles in a Lagrangian co-ordinatesystem without taking into account the agglomerating behaviour of particles. The analytical results showthat in the labyrinth channel, low-velocity region is developed ahead of each sawtooth and large vortexis shaped just behind it. Small particles are apt to deposit in those regions due to their better followingbehaviours than those of large ones. The potential clogging regions predicted by simulation are reasonablyconsistent with the experimental results. Further, it is also found that the particles ranging from 30 to50 �m behave best when passing through the labyrinth channel, and particle densities have a remarkableeffect on the penetration only when their diameters are large than 50 �m. Copyright q 2006 John Wiley& Sons, Ltd.

Received 8 June 2006; Revised 30 September 2006; Accepted 9 October 2006

KEY WORDS: clogging; emitter; labyrinth channel; moving trajectory; two-phase flow

1. INTRODUCTION

Emitter clogging has been considered one of the most annoying problems inhibiting the popular-ization of drip irrigation, it can be caused by physical, chemical or biological contaminants [1].

∗Correspondence to: Zhao Wanhua, Institute of Advanced Manufacturing Technology, School of MechanicalEngineering, Xi’an Jiaotong University, Xi’an 710049, People’s Republic of China.

†E-mail: [email protected]

Contract/grant sponsor: Ministry of Science and Technology of China; contract/grant numbers: 2002AA2Z4081,2005AA2Z4040Contract/grant sponsor: National Natural Science Foundation of China; contract/grant number: 50275119

Copyright q 2006 John Wiley & Sons, Ltd.

NUMERICAL INVESTIGATION OF THE CLOGGING MECHANISM 1599

Physical clogging is attributed to the deposition of suspended particles in irrigation water such assand, clay and silt ranging in size from 1 to 300�m; chemical clogging is caused by dissolvedsolids when they interact with each other to form precipitates, e.g. calcium carbonate, with adiameter of 1–74�m; biological clogging is due to the fact that algae and bacteria ranging from3 to 50 �m breed and then build up in stagnation zones of emitters [2]. Consequently, it can beconcluded that any of the cloggings can be ascribed to the deposition of particles with differentdiameters (sand, indissolvable carbonate, bacteria) in emitters.

During the last few decades, wastewater has been applied to irrigate crops, forests and rangelandsin many countries in order to save fresh-water. In general, various physical [3, 4] and chemical [5, 6]measures to treat the wastewater are taken to prevent the clogging of emitters. In fact, some residualsolid particles and microbes can still enter the emitters although the irrigation water has beenfiltrated or treated by different methods, leading to the clogging if those particles cannot pass thelabyrinth channel [7], which is due to the small scale of the channel and curved boundaries. Adinand Sacks [2] conducted farmland experiments to study the problem of emitter clogging underwastewater irrigation, and found that the clogging was closely related to the channel structure ofemitters. Taylor et al. [8] experimentally investigated several factors causing emitter clogging andpointed out that emitter design was the most important factor determining the degree of clogging.Therefore, the particle trajectory inside the labyrinth channel is very important for us to studythe clogging mechanism as well as the anti-clogging performance evaluation of emitters, but littlework has been done in this research area. The micro-characteristics in the channel are difficultto examine by traditional experimental methods due to the small size and intricacy of emitters,so some researchers employed numerical simulation approaches to investigate the flow field inemitters with different labyrinth channels [9–11], whereas all of those analyses were focused onthe single phase flow which cannot reveal the kinematic behaviour of the particles inside labyrinthchannels.

In this paper, an analytical model of emitter clogging is developed using the Euler–Lagrangianapproach. The liquid phase is treated by the Eulerian approach, i.e. the liquid parameters weredefined as functions of spatial co-ordinates. The solid phase is treated by the Lagrangian approach,which means the parameters of each particle are functions of time [12]. Precipitates in those threecategories of clogging are regarded as the solid phase, but their agglomerating behaviour is neglectedin this numerical model. The flow field distribution of the liquid phase and moving trajectoriesof the solid phase are obtained, and experiments are carried out to verify the effectiveness ofthe developed model. The results of this study may help understand the clogging mechanism andprovide theoretical foundation for the structural design and optimization of labyrinth channels.

2. MATHEMATICAL MODEL

2.1. Physical model and grids generation

In this study, the emitter with trapezoidal labyrinth channel is under consideration, as can be seenin Figure 1. After entering the emitter from the external pipe through filter grids, the water isgradually deprived of energy by the continuous trapezoidal channel units, then gathers in the trapand finally flows out of the emitter through a hole drilled on the external pipe wall. Emitters areassembled with external pipes on the arc surface in practical use, thus the open channel can beclosed so as to transport the irrigation water. Here, a three-dimensional physical model is built up,

Copyright q 2006 John Wiley & Sons, Ltd. Int. J. Numer. Meth. Engng 2007; 70:1598–1612DOI: 10.1002/nme

1600 Z. JUN ET AL.

Figure 1. CAD model of the emitter with trapezoidal labyrinth channel.

Figure 2. 2-D schematic diagram of physical model illustrating geometrical dimensions.

Figure 3. Computational grids of the channel unit: (a) longitudinal plane;and (b) transverse section II and III.

ignoring the two parts, i.e. filter grids and water trap. The arc surface between emitter and externalpipe is negligibly small, so the cross-section of the channel is simplified to rectangle. Both of theinlet and outlet are lengthened in order to develop a stable flow field. Figure 2 illustrates the 2-Dschematic diagram of the model.

Considering the sharp bends of the channel boundary, to get high quality grids, channel unitswere divided each other so as it can be meshed with structured hexahedron grids. The regionsnear the wall and corners were given a finer mesh to simulate the flow field with great velocitygradient. The cross-section was also meshed using non-uniform structured grids. Figure 3 showsviews of channel unit grids in the longitudinal plane and transverse section, respectively. The



computational domain employed in the computation contained 350 550 control volume cells. Froman investigation on the grid independence of the numerical solutions, little influence on the finalresults was found when using even finer grids.

2.2. Equations of fluid motion

The fluid in the emitter is water, as a result, it can be assumed to be viscous, steady, incompressibleand at room temperature. The fluid gravity and the surface roughness of the channel wall areconsidered. For this kind of labyrinth channel with rectangular cross-section, the critical Reynoldsnumber (Recr), which is difficult to calculate using existing hydromechanics theory, differs fromthat inside a straight channel with a circle cross-section and smooth wall when the flow is transitedto turbulence. Nishimura et al. [13] through experiments and simulations found that the Recris about 350 for the wavy channel used in their study, much lower than 2300. A few similarconclusions were also available in the literature [14, 15].

In this research, the Re is about 800 under the normal working conditions of the emitters, soa turbulence model was employed to simulate the continuous phase. There are several turbulencemodels that can be used, such as standard k–�, RNG k–�, Realizable k–�, but all of them onlycalculate the turbulent stress with isotropic turbulent viscosity, and the rotary flow and variation ofsurface curvature along the channel are not taken into account [16, 17]. Here, Reynolds stress model(RSM) [18] was adopted, which can account for the effects of streamline curvature, swirl, rotation,and rapid changes in strain rate in a more rigorous manner than one-equation and two-equationmodels.

The motion of the fluid is described by the continuity and Navier–Stokes equations, can bewritten as follows:

��xi

(�ui ) = 0 (Continuity) (1)

��xi

(�uiu j ) = − �p�x j

+ ��xi

(�

�ui�x j

− �u′i u

′j

)(Navier–Stokes) (2)

where u is the velocity vector, � is the fluid molecular viscosity, and u′i u

′j is the Reynolds stress

tensor. The differential equation (Equation (3)) for each component of the Reynolds stress isdeveloped to provide each stress component, allowing for anisotropy in turbulent stress terms.

��xk

(�uk�uiu j ) = Pi j + �i j + ��xk

(�t�k

�u′i u

′j

�xk+ �

�u′i u

′j

�xk

)− 2

3��i j (3)

Here Pi j the exact production term, is given by

P = −�

(u′i u

′k

�u j

�xk+ u′

j u′k

�ui�xk

)(4)


1602 Z. JUN ET AL.

�i j is the pressure–strain term, and is decomposed into two components that are given as

�i j,1 = −C1��

k

(u′i u

′j − 2

3k�i j

)(5)

�i j,2 = −C2

(Pi j − 2

3Pk�i j

)(6)

where the constants C1 and C2 are 1.8 and 0.6, respectively, �t is the turbulent viscosity, linkedto the turbulent kinetic energy k and dissipation rate � via the relation

�t = �C�k2

�(7)

The values for k and � come directly from the differential transport equations

�(�kui )

�xi= �

�x j

[(� + �t

�k

)�k�x j

]+ 1

2Pi j − �� (8)

�(��ui )

�xi= �

�x j

[(� + �t

��

)��

�x j

]+ 1

2C1�Pi j − C2��

�2

k(9)

where the constants are

C� = 0.09, C1� = 1.44, C2� = 1.92, �k = 0.82 and �� = 1.0

The governing equations which have been described above were discretized by the controlvolume numerical technique, and then the SIMPLE pressure–velocity coupling technique witha second-order upwind scheme for the convection terms was employed in order to solve thediscretized equations over the computational domain. The CFD program Fluent6.2® was used forthe calculations.

2.3. Equations of particles motion

According to the international standard of clogging test methods for emitters [19], a sand with aphysical density of 2500 kg/m3 was used as the clogging material in this test instead of aluminiumoxide. The volume fraction of the sand ranges from 0.01 to 0.08% in all phases of the test, theparticulate loading � is from 2.5× 10−4 to 2.0× 10−3. Using these parameters, it is possible toestimate the average distance between individual particles of the particulate phase. An estimate ofthis distance has been given by Crowe et al. [20]:

L

dp=(

�

6

1 + �/

�/

)1/3

(10)

where L/dp is the interparticle space, is the material density ratio �p/�, �p and � are the densitiesof the particle and fluid, respectively. L/dp obtained is about 17.36–8.68, the particles can thereforebe treated as isolated, and the motion of particles does not have a significant effect on the fluidflow in the region where the particles are in a fully separated condition. A common approach usedin simulating this kind of two-phase flow is by employing the Lagrangian discrete phase model to



compute the particle trajectory. The trajectory calculation is performed by means of Equation (11)which expresses an balance between inertia force, drag force and gravity, while the effects of thevirtual mass, Basset force, the force due to pressure drop and the accumulation term are small [21]and thus they were neglected without causing significant errors.

mpdupdt

= FD + FM (11)

where mp is the mass of the particle, mp = �p�d3p/6, dp is the particle diameter, up is the particle

velocity. FD is the drag force acting on the particle given by

FD = ��dp8

CDRep(u − up) (12)

where CD is the drag coefficient and it is usually expressed as a function of the particle Reynoldsnumber Rep, and can be shown as follows:

CD = a1 + a2Rep

+ a3Re2p

(13)

Rep = �pdp|up − u|�

(14)

where the constants a1, a2, a3 are given in Table I for the present ranges of Rep [22].FM is the difference of gravity and buoyancy of particle, defined as follows:

FM = �(�p − �)gd3p6

(15)

It should be noted that the particle trajectories calculated above adopt a deterministic trackmodel, but the fluctuating velocity of the fluid due to turbulence cannot be ignored, for it alsoaffects the motion of the particles. Therefore, the instantaneous fluid velocity can be expressed asfollows:

u = u + u′ (16)

where u is the mean fluid phase velocity, u′ is the fluctuating fluid phase velocity given by

u′ = √u′u′, v′ =

√v′v′, w′ =

√w′w′ (17)

Table I. Constants for drag coefficient CD.

Range of Rep a1 a2 a3

Rep�0.1 0 24 00.1<Rep�1 3.69 22.73 0.09031<Rep�10 1.222 29.1667 3.888910<Rep�100 0.6167 46.5 116.67100<Rep�1000 0.3644 98.33 2778


1604 Z. JUN ET AL.

where is a normally distributed random number. Substituting Equation (16) into Equation (11),a stochastic tracking model of the particles can be obtained

dupdt

= 1

�p(u + u′ − up)

dvpdt

= 1

�p(v + v′ − vp)

dwp

dt= 1

�p(w + w′ − wp) +

(1 − �

�p

)g

(18)

where �p is the relaxation time of the particle, �p = 4�pd2p/(3�CDRep).

For solving the equations of particle motion, a semi-analytical approach was employed. Thewhole time interval during which the particle was traced was divided into a number of subintervalsand length scale was used to set the subinterval for integration within each control volume. Itwas assumed that those forces do not vary during each subinterval. In addition, the parameter ofmaximum number of steps was adopted to abort trajectory calculations when the particle neverexits the flow domain.

2.4. Boundary conditions

At the inlet of the channel, a uniform fluid velocity may be specified as a boundary conditionfor the momentum equations according to the fluid flow rate through the emitter under normalworking conditions, which is obtained by the hydraulic performance experiment of emitters. Theparticle velocity at the inlet was assumed to be equal to the value of the fluid velocity becauseof the developing segment near the inlet. The outlet was treated as standard atmosphere for thefluid and escape for the particles. Turbulence intensity and hydraulic diameter were used to definethe turbulence parameters both in the inlet and outlet plane. On the wall surface, a restitutioncoefficient equal to 0.545 [23] in the water was used for the particles which was assumed to bespherical in the simulation. The fluid velocity was constrained to be zero (non-slip condition),and the standard log-law wall function was used in this paper to bridge the near-wall linearsublayer [24], where acute changes in the fluid velocity are expected, and this may be defined asfollows:

u∗

u�= 1

�ln(Ey+) (19)

in which u∗ is the averaged tangential velocity, the constants � and E are 0.42 and 9.79, u� andy+ are the wall friction velocity and the friction length, respectively, which are given by

u� =√�w/� (20)

y+ = �u�y/� (21)



where �w is the wall shear stress and y is the distance from the wall. The Reynolds stresses u′i u

′j

can be explicitly specified in terms of wall-shear stress using a local co-ordinate system

u ′2�

u2�= 5.1,

u ′2

u2�= 1.0,

u′2�

u2�= 2.3, −u′

�u′

u2�= 1.0 (22)

where � is the tangential co-ordinate, is the normal co-ordinate, and � is the binormal co-ordinate.

3. RESULTS AND DISCUSSION

3.1. Flow field distribution of the continuous phase

Figure 4 shows the numerically obtained fluid pressure distribution in the symmetry plane, wherethe pressure values are all relative values to the standard atmosphere. The whole pressure dropfrom inlet to outlet is reflected in the major and minor losses because no energy exchange withexternal environment occurs. Along the flow direction, the static pressure decreases gradually,and the pressure drop in each channel unit is almost equal. Figure 5 shows the fluid velocitydistribution in the symmetry plane. It can be seen from the whole tendency that the velocitydistribution of each channel unit is very similar except for the linking section of the channel. TheReynolds number reaches a value of 800, in such a circumstance, a phase shift appears betweenmainstream and channel boundary. The fluid mainly flows along the inside of each unit cornerwith an instantaneous speed ranging from 1.4 to 3.2m/s, as shown in the partial enlargement ofFigure 5, while the velocity in the corners marked A and in the regions behind the sawtooth is

Figure 4. Contour of pressure in longitudinal symmetry plane.

Figure 5. Contour of velocity in longitudinal symmetry plane.


1606 Z. JUN ET AL.

Figure 6. Velocity streamlines in the channel unit.

Figure 7. Velocity isolines in cross-section I.

only 0.5m/s, and two large vortices marked B are developed, as can be seen clearly in Figure 6,which may be attributed to the offset from the mainstream, leading to the formation of enclosedflow regions. In Figure 7 the calculation result shows the velocity isolines in cross-section I (referFigure 2), the velocity reaches a maximum in the position of 1

3 height and then falls down towardtop and bottom walls of the cross-section. It is easy to observe that the velocity represents an arcsymmetrical distribution about Y axis, which indicates that the Z velocity is very small and thefluid gravity can be ignored in the computation.



Figure 8. Numerically obtained particle trajectories in the trapezoidal labyrinth channel: (a) particle witha diameter of 5 �m; (b) particle with a diameter of 50 �m; and (c) particle with a diameter of 300 �m.

3.2. Moving trajectories of the dispersed phase

Particles were injected from the inlet plane of the channel and it was supposed that the initialvelocity of the particles was the same as that of the fluid. Stochastic tracking model was employedto predict the dispersion of particles due to turbulence in the fluid phase. In the flow field, drag forceis always directly proportional to the projected area of the particle to the direction of incomingflow, while inertia force is directly proportional to the volume of the particle. Therefore, the dragforce is much greater than the inertia force when the particle is small (e.g. dp = 5 �m); contrarily,the inertia force is dominant for large particle (e.g. dp = 300 �m).

Figure 8 shows the trajectories of particles with different diameters from the inlet to outlet.When the particle diameter is 5 �m, the trajectories follow the streamlines of the fluid very well atthe corner of each channel unit due to larger drag force, as can be seen in Figure 8(a). The particleseldom collides with the top and bottom walls, but it is prone to be dragged into the vorticesonce it passes by, and if the fluctuating velocity of the particle is equal to that of the vortices, theparticle always failed to escape from the vortices, then it is quite possible for the particle to swirlor deposit in the vortices, thereby, serious clogging may appear in those regions when the emittersare in use chronically. When the particle diameter increases to 50 �m, the drag force may increasenearly 100 times, while the inertia force increases nearly 1000 times, so both of the two forces areof the same order of magnitude. The trajectories of the particles alternated between following themain stream and colliding with top and bottom walls, see Figure 8(b). As the diameter increasesfurther, as shown in Figure 8(c), the particle possessing a larger inertia is driven by the centrifugalacceleration to drift toward the top and bottom walls when passing each corner, so the energy lossdue to frequent collisions with channel wall increases, while the possibility of being trapped inthe vortices decreases.

In Figure 9, the four regions obtained by numerical simulation where deposition occurred, canbe shown. The flow field in the regions marked A are nearly stagnant to the direction of incomingflow so that the passing particles are apt to deposit, while the deposition in the regions markedB are due to the vortices of the fluid. Figure 10 displays the distribution of the sediment at the


1608 Z. JUN ET AL.

Figure 9. Deposit regions of particles obtained by numerical simulation.

Figure 10. Deposit regions of particles at the initial stage in clogging experiment.

initial stage in clogging experiment, which was arranged by the international standard [19]. Thedeposition started in low-velocity regions and vortices, experimental results validate the reliabilityof numerical analysis.

Figure 11 shows the X velocity of particles with diameters of 5, 50 and 300�m along their pathlength, which indicates the particle capability of going forward. As shown in the figure, the Xvelocity decreases as the particle diameter increases. The maximum velocities of the three kinds ofparticles are 3.75, 2.70 and 1.93m/s, respectively. The particles of smaller size experience widerrange in velocity fluctuation than larger ones do. The horizontal line in each figure is a criticalmarker which can distinguish the sign of the velocity. It can be observed obviously from the twosides of the horizontal lines that the variation frequency of smaller particles is higher than thatof larger particles. From the above analyses, it is suggested that smaller particles are prone tobe influenced by the flow field of continuous phase. Furthermore, the path lengths of different



Figure 11. X velocity of single particle with different diameters along their path length: (a) particle witha diameter of 5 �m; (b) particle with a diameter of 50 �m; and (c) particle with a diameter of 300 �m.


1610 Z. JUN ET AL.

Figure 12. Particle penetration through the trapezoidal labyrinth channel.

particles in the labyrinth channel can also be observed from the figures. The end points of velocityin the figures reveal that the particles have escaped from the channel, so the corresponding valueof abscissa (La, Lb, Lc) is the total path lengths of each particle, and it is obvious that smallerparticles travel longer than larger ones due to La>Lb>Lc, which also indicates that the motionof smaller particles is more turbulent.

Figure 12 shows the numerically obtained particle penetration curve for small trapezoidal channelunder the same calculation conditions. The particles released were uniformly ranged in a 5× 5 dotmatrix in the inlet plane and the number of tries in stochastic tracking technique was set to 10 inorder to ensure the statistical representation of the spread of the particle stream due to turbulence.As shown in the figure, the particle penetration is almost 100% when the particle diameters rangefrom 30 to 50 �m, regardless of their densities.

For those particles small than 30 �m, their penetration dramatically falls with a decrease indiameter. This is probably due to the fact that the diameter and hence the inertia of a particle issufficiently small, then the particle is capable of responding to the fluctuations of the turbulenceand thus turbulent diffusion will play an important role in the motion of the particle.

On the other hand, as also can be seen from Figure 12, an increase in diameter large than50 �m gives rise to the inertia force, then the energy loss due to the frequent collisions with topand bottom walls also increases, leading to a low particle penetration. The lower is the particledensity, the greater the descending rate of the penetration will be. However, the penetration of�p = 800 kg/m3 rebounds at the diameter of 300 �m, which is probably due to the fact that thedensity of the particles is smaller than that of the fluid and thus the ‘virtual mass’ force requiredto accelerate the fluid surrounding the particle is important, whereas it is neglected in this case.

4. CONCLUSIONS

In this study, a numerical simulation technique is employed to analyse the clogging mechanismin labyrinth channel of the emitter in order to provide an alternative to the usual approach of



using costly real-life experimental investigations. The RSM with wall function has been used forthe simulation of the highly rotational turbulent fluid flow occurring in the labyrinth channel, andstochastic tracking model has been adopted to follow the tracks of the particles neglecting theagglomerating behaviour of particles. A number of useful conclusions can be drawn from thecalculation results.

(1) A phase shift appears between mainstream and channel boundary when the flow field isstable, which result in the formation of stagnation zone ahead and behind each sawtoothof the labyrinth channel. The velocity magnitude in these regions is much lower than thatof the mainstream. In the cross-section of the channel, velocity was found to be nearlysymmetrical about Y axis, so the fluid gravity has no obvious effect on the fluid phase.

(2) Compared with larger particles, smaller particles have a better following behaviour to thefluid and a less probability of collision with top and bottom walls of the channel, but theyare apt to be dragged into the stagnation zones in the flow field, and it is extremely possiblefor these particles to swirl in those regions and deposit owing to the gravity. An increase inparticle diameter leads to a decrease in X velocity, which indicates that the smaller particlesare more turbulent.

(3) The particle penetration reaches a highest value at the diameter of 30–50 �m. When thediameters are small than 30 �m, the penetration dramatically falls with a decrease inthe diameter, regardless of the particle density; while the diameter is large than 50 �m,the descending rate of the penetration increases slowly as the density decreases.

ACKNOWLEDGEMENTS

It is gratefully acknowledged that the work presented in this paper is supported by the NationalHigh Technology Research and Development Program of China (‘863’ Program, No. 2002AA2Z4081,2005AA2Z4040) and the National Natural Science Foundation of China (No. 50275119).

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numerical investigation of the clogging mechanism in labyrinth channel of the emitter

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