Non-intrusive measurements of shallow water discharge

https://doi.org/10.1016/j.flowmeasinst.2017.05.007Get rights and content

Highlights

  • Open flows with depth from 2.5 to 8 cm were investigated using visualization method.

  • Surface velocities increasingly differ from main flow velocities as depth decreases.

  • Measurement of shallow flow discharge requires no complex or expensive equipment.

Abstract

Waste-water channels or physical hydraulic models often convey shallow water flows with depths around 5 cm. Such free surface flows can in principle be measured using standard measuring flumes or thin-plate weirs, but proper employment of these is often practically impossible, e.g. due to limited space. To avoid this, various flow meters with contact probes (i.e. »area-velocity« probes) are employed instead, but in reality this often results in inaccurate measured values of discharge. This paper presents an effective way to determine discharge of very shallow flow without intruding the flow. Our approach is based on computer aided visualization, namely on the quantification of the field of vectors representing local velocities on the water surface of the flow. In contrast to other studies, this method does not require complex measuring equipment, special lights or special devices for the seeding of particles. Experiments were conducted in 0.5 m and 1.06 m wide rectangular channels, made of glass and concrete, respectively, and they show that this method could be employed both in hydraulic laboratories and in the field. Measurements showed that velocity on the surface of the shallow water flow differs from theoretical average mean flow velocity in the observed cross section, and further that this difference increases with the decrease of water depth. This suggests that the assumption, which states that in shallow water flows the surface velocity is similar enough to the mean flow velocity, is not necessarily correct.

Introduction

Free surface shallow flows with depths of 3–10 cm are not very common in general hydraulics practice, but can occur quite frequently in physical hydraulic models (where demands of the model similarity dictate water depths of at least several centimeters, thus: »As a matter of experience, a lower limit of about three centimeters is conventionally used« [1]), and also in waste-water channels. Discharges of such shallow flows are usually measured using contact probes (e.g. area-velocity flowmeters in pipes calculate discharge Q as a product of measured average velocity U and cross-section area A), or measuring structures, such as standard flumes or thin-plate weirs (placed in properly designed approach channels). These solutions can be quite problematic when the measuring equipment interferes with the observed flow too much (typically when the flow is too shallow for the proper use of a certain instrument) or when the space at measuring site is simply too limited. Surface-area flowmeters, for example, have another weakness, which lies in the fact that in shallow flows even a small error at determination of flow velocity can lead to considerable relative error of the calculated discharge. An overview of the problems associated with shallow flow measurement is given in [2].

To avoid interruption of the observed flow, the method of particle image velocimetry (PIV) can be used, as has been very convincingly demonstrated by [3], [4], [5].

In paper [3] two-dimensional flow at groin field was observed in a physical model, consisting of a 1.82 m wide flume. The water depth was h = 0.046 m, the mean flow velocity in the main channel was U = 0.16 m/s, bulk Reynolds number was about 7500. Flow dynamics at the surface of shallow water flow was measured with a proposed variant of the LSPIV method. A specially designed particle dispenser was used. No laser light sheet was needed. Authors conclude: »Shallow flows are dominated by two-dimensional flow structures, which means that the overall behaviour of the flow can be analyzed using surface velocities.«.

Paper [4] presented experiments performed in a physical model consisting of 0.91 m wide flume. Velocities at water surface were measured on the basis of visualization of the controlled surface waves – thus authors named this method CSWIV. They used food color to dye the water and a set of numerous halogen lights to provide required illumination. Research showed that CSWIV could be used in laboratory conditions, but not yet in the field.

Paper [5] presented modelling of a shallow reservoir, performed in a 4 m wide physical model and also with a numerical simulation. Velocities at the surface of the flow were measured using a proposed variant of the LSPIV, that enabled authors to measure velocities from 0 to 0.06 m/s. Researchers concluded: »LSPIV efficiency as a surface velocity measurement tool reveals capable in low velocity shallow water that presents numerous difficulties and challenges to the existing instruments.«

The above mentioned papers [3], [4], [5] focused on velocity field at the surface of a shallow flow, without determining the discharge. The same can be said about a study of two-dimensional coherent structures in shallow flows [6], somewhat older research on unsteady surface-velocity field measurement using particle tracking velocimetry [7], and a recent paper on shallow-flow visualization analysis by proper orthogonal decomposition [8].

When it comes to measuring of small discharges, for example in cases of shallow water in sewer channels, one has to bear in mind that flow properties in narrow sewer channels should be distinguished from flow properties in wide river channels where surface velocity u is similar enough to mean flow velocity U (calculated as U = Q/A). Our research shows that, for shallow flows, the above mentioned assumption of u being very similar to U is not necessarily correct. In very shallow water flows surface velocities u can differ from values U considerably, even up to 40%, depending on the flow depth, and this relation has to be taken into account at performing discharge measurements, as described in the following sections of this paper.

The aim of the study is to show that shallow water subcritical flow discharges can be measured accurately without interrupting the flow (in contrast to contact probes), without complex and expensive equipment (in contrast to variants of PIV and similar methods), using illumination that can be provided in the field (i.e. without laser light sheet, for example), using non-expensive particles and without special particle-seeding device. This was demonstrated in two rectangular channels for velocities ranging from 0.2 to 0.7 m/s, water depths from 0.025 to 0.080 m, and discharges from 3.5 to 26 l/s. The method described in this paper is accurate enough for laboratory application and also robust enough for field research – all this at a lower cost compared to solutions of similar accuracy.

Section snippets

Experimental set-up

A total of 22 experiments were performed in two rectangular channels. The first was horizontal (slope I = 0) glass-walled flume with dark glass bottom, B = 0.5 wide, 0.5 m high and 6 m long. The second was almost horizontal (I = 0.001) concrete channel, B = 1.06 m wide, 0.6 m high and 20 m long. Employment of two different channels allowed observation of potential scale effects and effects related to channel roughness. Scheme of the experimental set-up is shown in Fig. 1.

All observed flows were

Results

Experiments were performed in a glass flume representing typical laboratory conditions and in a concrete channel representing conditions similar to ones in the field. All the main parameters and results of the experiments are listed in Table 1.

Measurement of the discharge was based on a non-intrusive determination of surface velocities. Typical results are shown in Fig. 2 and Fig. 3.

The visualization method, employed in the present study, allows determination of velocity vectors within user

Conclusions

The following two conclusions can be derived on the basis of presented experiments:

  • 1)

    Discharges of shallow water flows (with depths from 26 to 80 mm) can be measured accurately (measured values differ from flowmeter results by 7% or less), non-intrusively and without complex equipment. This can be achieved by employing presented visualization method, which is useful both in laboratory conditions and in ones that are similar to field applications.

  • 2)

    Commonly used assumption that velocity at the

References (13)

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