Micro-PIV characterization of the flow in a milli-labyrinth-channel used in drip irrigation

Abstract

The baffle-fitted labyrinth-channel is largely used in drip irrigation systems. The existing baffles, which play an important role for generating head losses and ensure the flow regulation on the irrigation network, produce vorticity regions where the velocity is low or equal to zero. These vortices are likely to favor the deposition of particles or biochemical development causing dripper clogging which drastically reduces its performance. Flow topology in the dripper labyrinth-channel must be described to analyze dripper clogging sensibility and the effect on irrigation efficiency. Also, a question remains about the regime of this low Reynolds number flow. In the present study, the flow is characterized experimentally by micro-particle image velocimetry (micro-PIV) technique on ten-pattern repeating baffles used in drip irrigation dripper. Square cross-section is of about 1.4 mm$^2$. Studied inlet Reynolds number varies from 345 to 690, which is equivalent to 1.4–2.8 l h$^{-1}$. The mean velocity distribution and turbulence quantities within the labyrinth-channel flow are presented and discussed in this paper. The results underline that flow regime is turbulent and non-isotropic.

Graphical abstract

Appendices

Appendix 1: Uncertainly analysis

1.1 Peak locking

The peak-locking effect is due to the sensor geometry in digital cameras. This phenomenon occurs when particle images are much smaller than the pixel size, so that the displacement tends to be biased towards discrete pixel values (Westerweel 2000). Peak-locking significantly reduces the accuracy of micro-PIV measurements although the effects on the mean velocities may be within acceptable limits. Indeed, the mean velocities are the only statistics that are insensitive to peak locking as it was found by Christensen (2004). The peak-locking effect can lead to awkward results for instantaneous spatial derivative data such as velocity gradient and also for turbulent velocity fluctuations. The easiest way to analyze this phenomenon is to plot an histogram of the fractional part of velocity components (displacements) which is between $-\,0.5$ and $+\,0.5$ pixel units. In the present study, the pixel size, due to the magnification, is equivalent to 1.074 $\upmu$m, which is close to the particles diameter. The histograms of displacements are presented in Fig. 20. The degree of peak locking can be quantified as:

$$\begin{aligned} C=1-\frac{N_{\text {min}}}{N_{\text {max}}}, \end{aligned}$$

(A.1)

where $N_{\text {min}}$ (minimum of $\%$) and $N_{\text {max}}$ (maximum of $\%$) are the lowest and highest percent of counts in the fractional histogram. Hence, if $C=0$, this indicates the absence of peak-locking, whereas $C=1$ indicates very strong peak locking. Four levels of peak-locking can be distinguished (Overmars et al. 2010):

• $C<0.2$, virtually no peak-locking occurs,

• $0.2<C<0.4$ mild peak-locking occurs,

• $0.4<C<0.6$ strong peak-locking occurs,

• $C>0.6$ severe peak-locking.

1.2 Signal-to-noise ratio (SNR)

The choice of the optimal diameter for seeding particles is a compromise between an adequate tracer response of the particles in the fluid, which requires small diameters, and a high signal-to-noise ratio (SNR) of the scattered light signal, which requires large diameters. The cross-correlation SNR is based on the measure of the primary peak ratio (PPR), namely the ratio between the highest correlation peak and the second tallest peak (Kumar and Hassebrook 1990). The optical properties may be deteriorated when choosing 1 $\upmu$m diameter, even though there is no peak-locking effect which could induce erroneous estimates for mean velocities and fluctuating velocity second-order moments. In practice, for 1 $\upmu$m diameter, the SNR from the fourth baffle is less than 4, which is the threshold value for correct detection. Therefore, it is not possible to use the 1 $\upmu$m particles to conduct the micro-PIV experiments for baffles farther than the third one. The labyrinth-channel prototype is illuminated by the right side where $x> 0$ (Fig. 1c). As a consequence, the laser light-sheet is more diffused by the 1-$\upmu$m particles and even more when the laser light-sheet moves deeper into the labyrinth-channel.

Fig. 20

The subpixel analysis in the third baffle, $Re=345$ (a, b), $Re=690$ (c, d). a u subpixel. b v subpixel. c u subpixel. d v subpixel

Appendix 2: Data processing

Fig. 21

Chart of micro-PIV data processing

See Fig. 21.