Proceedings of 2013 IAHR Congress 2013 Tsinghua University Press, Beijing

ABSTRACT: A positive surge results from a sudden change in flow that increases the depth. It is the unsteady flow analogy of the stationary hydraulic jump and a geophysical application is the tidal bore. Although a positive surge may be analysed using a quasi-steady flow analogy, its inception and development is commonly predicted using the method of characteristics and Saint-Venant equations. After formation, the flow properties immediately upstream and downstream of the surge front must satisfy the continuity and momentum principles. This paper presents the results of new experimental investigations conducted in a large rectangular channel. Several experiments were conducted five different initial discharges (Q=0.035, 0.045, 0.050, 0.060 and 0.070 m/s) to investigate a positive surge propagating upstream against the initially steady flow for the same downstream gate opening after closure. In each case, a breaking (weak) bore was observed and free-surface measurements were performed using non-intrusive acoustic displacement meters. Detailed unsteady velocity measurements were further carried out with high temporal resolution using acoustic Doppler velocimetry for Q=0.035 and 0.045 m/s. The analysis of free-surface profiles revealed the influence of the flow rate on the surge characteristics. Unsteady flow turbulence analysis highlighted some patterns in streamwise and transverse velocities due to the effect of the flow rate. KEY WORDS: Environmental hydraulics, turbulence, positive surge, surge front, instantaneous velocity field, Reynolds stress, physical modelling. 1 INTRODUCTION

A positive surge results from a sudden change in flow that increases the depth. It is the unsteady

flow analogy of the stationary hydraulic jump and a geophysical application is the tidal bore (Chanson, 2012). Positive surges are commonly observed in man-made and natural channels. In water supply canals for irrigation and water power purposes, a positive surge may be induced by a partial or complete closure of a control structure, e.g. a gate, resulting in a sudden change in flow that increases the water depth. In rivers and estuaries, a form of positive surge is the tidal bore which is a positive surge of tidal origin. Tsunami-induced bores were also observed. Although a positive surge may be analysed using a quasi-steady flow analogy, its inception and development is commonly predicted using the method of characteristics and Saint-Venant equations. After formation, the flow properties immediately upstream and downstream of the surge front must satisfy the continuity and momentum principles (Henderson, 1966, Chanson 2004). For a fully-developed positive surge, the surge is seen by an observer travelling at the surge speed U as a quasi-steady flow situation called a hydraulic jump in translation (Fig. 1). In a

Propagation of a positive surge against an initially steady flow: influence of the flow rate

Carlo Gualtieri Assistant Professor, Dept. of Civil, Construction and Environmental Engineering (DICEA), University of Napoli "Federico II", Napoli (Italy) Email: carlo.gualtieri@unina.it

Hubert Chanson Professor, School of Civil Engineering, The University of Queensland, Brisbane QLD 4072, (Australia) E-mail h.chanson@uq.edu.au

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rectangular, horizontal channel and neglecting friction loss, if the subscripts 0 and conj refer, respectively, to the initial flow conditions and conjugate flow conditions, i.e., immediately behind the positive surge front, the solution of the continuity and momentum equations applied to a control volume across the surge front yields:

1Fr 81

21

dd 2

0

conj (1)

232

23conj

1Fr 81

2Fr

Fr

(2)

where dconj and d0 are respectively the new and initial flow depths (Fig. 1), and the Froude numbers Fr and Frconj are the surge Froude numbers defined respectively as:

conj

conjconj

0

0

d g

UVFr

d gUVFr

(3)

where U is the surge velocity as seen by a stationary observer on the channel bank and positive in the upstream direction and V0 is the flow velocity (Fig. 1).

d0

x

V0

U

dconjVconj

Initial water level

Fig. 1 Definition sketch of a positive surge. Positive surge for an observer standing on the bank

Positive surges were studied by hydraulicians and applied mathematicians for many decades since Since Barr de Saint-Venant (1871), Boussinesq (1877). Classical experimental works on undular surges included and Favre (1935), Lemoine (1948), Benet and Cunge (1971) and Treske (1994). Most of previous experimental studies were limited to visual observations and sometimes free-surface measurements, but more recently, unsteady turbulence measurements were carried out using particle image velocimetry (PIV) and acoustic Doppler velocimetry (ADV) techniques (Hornung et al., 1995, Koch and Chanson, 2009, Gualtieri and Chanson 2011a, 2011b, 2012). Finally, numerical studies of a surge were recently presented (Soares Frazo and Zech, 2002, Furuyama and Chanson, 2008, Lubin et al., 2010). A very recent reviews about tidal bores were prepared by Chanson (2012a, b).

In this paper the authors present the results from new experimental works conducted in a large rectangular in which the positive surge propagated upstream against an initially steady flow. All experiments were performed with the same downstream gate opening after closure and five different initial discharges (Q=0.035, 0.045, 0.050, 0.060 and 0.070 m/s). For each case, free-surface

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measurements were performed using non-intrusive acoustic displacement meters, and detailed unsteady velocity measurements were carried out with high temporal resolution using Doppler velocimetry for Q=0.035 and 0.045 m/s. Overall this study was aimed at revealing the influence of the flow rate on the hydrodynamics characteristics of a positive surge. 2 EXPERIMENTAL SETUP. CHANNEL AND INSTRUMENTATION. SURGE GENERATION 2.1 Experimental setup

The experiments were performed in a large tilting flume at the University of Queensland previously used by Chanson and co-workers (Koch and Chanson, 2009, Chanson, 2010, Gualtieri and Chanson 2011a, 2011b, 2012). The channel was 0.5 m wide, 12 m long and it was horizontal. The flume was made of smooth PVC bed and glass walls, and waters were supplied by a constant head tank. The water discharge was measured with orifice meters with an accuracy of less than 2%. A tainter gate was located next to the downstream end, at x=11.15 m from the channel intake, where x is the distance from the channel upstream end. Its controlled and rapid closure induced a positive surge propagating upstream.

The study was carried out with the same gate opening after closure (hg = 15 mm) and five different initial discharges (Q=0.035, 0.045, 0.050, 0.060 and 0.070 m/s). Unsteady free-surface measurements were performed using seven non-intrusive acoustic displacement meters Microsonic Mic + 25/IU/TC with an accuracy of 0.18 mm and a response time of less than 50 ms. The acoustic displacement meters were located at x=1.985 m, 2.995 m, 4 m, 5 m, 6 m, 9 m and 10.9 m, where x is the downstream distance from the channel intake. For Q=0.035 and 0.045 m/s detailed unsteady velocity measurements were carried out with high temporal resolution using an acoustic Doppler velocimeter (ADV) Sontek 16MHz micro-ADV equipped with a two-dimensional side-looking head acoustic Doppler velocimetry. The velocity range was 1.0 m/s, the sampling rate was 50 Hz and the data accuracy was 1% of the velocity range. The translation of the ADV probe in the vertical direction was controlled by a fine adjustment travelling mechanism connected to a Mitutoyo digimatic scale unit. The error on the vertical position of the probe was z

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Steady gradually-varied flow conditions were established for at least 5 min prior to measurements and the flow measurements data acquisition was started about 1.5 min prior to gate closure. A positive surge was generated by the rapid partial closure of the downstream gate. The gate closure time was less than 0.2 s (Koch and Chanson, 2009, Gualtieri and Chanson 2011a,2011b,2012). After closure the surge propagated upstream and each experiment was stopped when the bore front reached the intake structure.

One gate opening after closure was considered (Table 1). In Table 1, hg is the gate opening and the surge front celerity U was calculated using the displacement meters data between x=6 m and 4 m; also, d0 was measured at x=5 m and dconj was derived using Eq. (1). In Table 1 the data for Run 35-4 and Run 45-4 refer to the average of 23 runs with the same gate opening but different vertical elevation z for the ADV system sampling volume.

All the measurements were performed on the channel centreline. The earlier work of Koch and Chanson (2009) showed little transverse differences but close to the sidewall where the ADV system was further adversely affected by the sidewall proximity. Note that, if the structure of flow in positive surges is generally 3D, previous studies showed a quasi-two-dimensional free-surface in breaking, weak surges (Koch and Chanson, 2009, Gualtieri and Chanson 2011a, 2011b, 2012).

Table 1 Experimental flow conditions

Run Q m/s d0 m hg m Type U m/s dconj m Fr Remarks 35-4 0.035 0.1036 0.015 Weak 0.673 0.151 1.338 ADV & surface measurements 45-4 0.045 0.1214 0.015 Weak 0.835 0.195 1.445 ADV & surface measurements 50-4 0.050 0.1200 0.015 Weak 0.839 0.208 1.541 Free-surface measurements 60-4 0.060 0.1399 0.015 Weak 0.830 0.230 1.441 Free-surface measurements 70-4 0.070 0.1545 0.015 Weak 0.964 0.264 1.519 Free-surface measurements

Fig. 2 Weak surge, Run 35-4. Lateral view (left) and looking downstream at the incoming wave crest

(right)

3 BASIC FLOW PATTERNS

Previous studies (Koch and Chanson, 2009, Gualtieri and Chanson 2011a, 2011b, 2012)

demonstrated that at low inflow Froude numbers, e.g. Fr

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flow structure (Koch and Chanson 2008, Gualtieri and Chanson 2011a, 2011b, 2012). The breaking bore front was associated with some air entrainment in the roller (Figs. 2 and 3). For the entire range of investigations, the bore celerity ranged from 0.67 to 0.96 m/s (Table 1, column 6). Overall the flow patterns were consistent with earlier studies (Koch and Chanson, 2009, Chanson, 2010, Gualtieri and Chanson 2011a, 2011b, 2012).

Typical instantaneous free-surface profiles are presented in Figs. 4 and 5. Each curve shows the instantaneous dimensionless flow depth d/d0 as a function of the dimensionless time from gate closure t(g/d0)0.5. Note that the zero dimensionless time corresponded to 10.0 seconds prior to the wave crest passage at the sampling location. Fig. 4 shows some data for the weak surges for Q = 45 and 60 L/s (Runs 45-4 and 60-4) at x=5 m. The roller passage was associated with a marked discontinuity of the free-surface, although the free-surface elevation rose slowly immediately prior to the roller, with the free-surface curving upwards ahead of the roller toe (Koch and Chanson, 2009, Gualtieri and Chanson 2011b, 2012). The maximum water depth was higher for the surge with the larger flow rate, i.e. Q=60 L/s. The free-surface profiles at x=5 m were not significantly affected by the presence of the ADV system.

Fig. 3 Weak surge, Run 60-4. Lateral view looking upstream (left) and from above (right)

Fig. 4 Runs 45-4 and 60-4. Dimensionless instantaneous water depth d/d0 at x = 5 m.

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Fig. 5 Runs 35-4, 45-4, 50-4, 60-4 and 70-4. Dimensionless instantaneous water depth d/d0 at x = 5 m.

Fig. 5 shows the instantaneous dimensionless flow depth d/d0 at x = 5 m as a function of the dimensionless time from gate closure t(g/d0)0.5 for all five experiments. The maximum water depths were lower for the surges with the smaller flow rates, i.e. Q=35 and 45 L/s. The comparison indicated that, for the larger flow rate, the increase in the water depth to the steady-state conditions due to the passage of the surge was larger, as expected for the higher Froude number. In a fully-developed surge, the ratio of conjugate depths (dconj/d0) must satisfy the continuity and momentum equations (Eq. (1)). Present experimental results were generally close to those predicted by the momentum principle.

4 UNSTEADY FLOW FIELD IN THE SURGES. RESULTS AND DISCUSSION

For two flow rates, i.e. Q=35 and 45 L/s, detailed velocity measurements were carried out beneath

the bore front using the ADV system located at x=5 m (Table 1). Each experiment was repeated to obtain the vertical distribution of the velocity component time series at several vertical elevations, z. Figs. 6 and 7 illustrate the unsteady turbulent velocity field at two vertical elevations for the two surges, i.e. Run 35-4 and Run 45-4. Each graph presents the dimensionless velocities Vx/V0 and Vy/V0 and water depth d/d0, where V0 is the flow velocity (Fig. 1 and Table 1), against the dimensionless time t(g/d0)0.5. Herein Vx is the longitudinal velocity component positive downstream, and Vy is the horizontal transverse velocity component positive towards the left wall. The zero dimensionless time corresponded to 10.0 seconds prior to the first wave crest passage at the sampling location.

In the breaking surges, an initial gentle rise of the free surface was linked to a rapid decrease of the longitudinal velocity component at all vertical elevations (Koch and Chanson, 2009). Immediately after, the passage of the roller was marked by a sharp rise in free-surface elevation corresponding to a discontinuity in terms of the water depth. The sudden increase in water depth corresponded to a rapid deceleration to yield a slower flow motion to satisfy the conservation of mass (Figs. 6 and 7). The velocity records showed some marked difference depending upon the vertical elevation z (Figs. 6 and 7). At the larger depth, i.e. z/d0 > 0.3, the streamwise velocity component decreased rapidly at the surge front but remained positive beneath the roller toe (Fig. 6, right and Fig.7, right). In contrast, for z/d0 < 0.3, a difference could be noted between Q=35 L/s and Q=45 L/s. For Run 35-4 some negative Vx values were observed although for a short duration, for a dimensionless time t(g/d0)0.5 from 97 to 104 (Fig. 6, left). The existence a sudden longitudinal flow reversal indicated unsteady flow separation beneath the surge front. The longitudinal flow deceleration yielded negative streamwise Vx velocities with (Vx/V0)min=0.088. This flow feature was first reported for different flow rates by Koch and Chanson (2009), confirmed by Chanson (2010) and Gualtieri and Chanson (2011b), and obtained numerically by

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Furuyama and Chanson (2008). It should be also noted that these negative values of the streamwise velocity may contribute to sediment inception in movable beds as the transient recirculation motion next to the bed yields to a drag force acting in the upstream direction (Khezri and Chanson, 2012a, b). For Run 45-4, the streamwise Vx velocities remained always positive, but close to the zero (Fig.7, left).

Furthermore, close to the bed, i.e. z/d0=0.085 and 0.073, lower streamwise velocities Vx corresponded to larger values of the transverse velocities Vy (Figs. 6, left, and 7, left). This trend was already observed in earlier experimental studies (Koch and Chanson, 2009, Gualtieri and Chanson, 2011).

Overall, for both the flow rates, the turbulent velocity data showed some large fluctuations of all velocity components beneath the surge and in the flow field behind the surge. Large time variations of the longitudinal and transverse velocity components were seen at all vertical elevations.

Fig. 6 Run 35-4. Dimensionless instantaneous water depth d/d0 and velocity components Vx/V0 and

Vy/V0 at z/d0=0.085 (left) and z/d0=0.742 (right)

Fig. 7 Run 45-4. Dimensionless instantaneous water depth d/d0 and velocity components Vx/V0 and

Vy/V0 at z/d0=0.073 (left) and z/d0=0.709 (right)

5 CONCLUSION

This study presented some physical measurements in positive surges conducted under controlled

flow conditions in a large channel. Detailed turbulence measurements were performed with a

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high-temporal resolution (50 Hz) using side-looking acoustic Doppler velocimetry and non-intrusive free surface measurement devices. The dependant variable was the flow rate. In all the cases, breaking surges were observed.

The effect of the flow rate was related to increase of the water depth at the passage of the surge respect to the steady-state conditions. Detailed instantaneous velocity measurements were carried out for only two flow rates, i.e. Q=35 L/s and Q=45 L/s. These measurements showed a marked effect of the surge passage. In the breaking surge, the gentle rise of the free surface corresponded to a rapid flow deceleration at all vertical elevations, and at the lower flow rate, i.e. Q=35 L/s, some flow reversal were measured next to the bed, whereas at highest sampling points Vx/V0 remained positive. These negative values of the streamwise velocity are expected to contribute to sediment inception in movable beds. At the larger flow rate, i.e. Q=45 L/s, the streamwise velocities were always positive, independently from the vertical elevation. Furthermore, close to the bed, low streamwise velocities Vx corresponded to large values of the transverse velocities Vy. Finally, for both the flow rates, the turbulent velocity data showed some large time variations of the longitudinal and transverse velocity components beneath the surge and in the flow field behind the surge at all vertical elevations.

Overall, the results here presented mostly confirmed and extended the main findings of previous experimental works with the analysis of the influence of the flow rate on the surge characteristics.

ACKNOWLEDGEMENT The first author acknowledges that the paper was prepared as a part of MIUR PRIN 2010-2011 Research Project Hydroelectric energy by osmosis in coastal areas (HYDROCAR).

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