Ported wall extension hydraulics

Fei-dong Zheng ,Ping-yi Wang ,Jian-feng An ,Yun Li ,

a College of River and Ocean Engineering,Chongqing Jiaotong University,Chongqing 400074,China

b National Engineering Technology Research Center for Inland Waterway Regulation,Chongqing 400074,China

c State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering,Nanjing 210029,China

Abstract Ported wall extensions are important hydraulic structures used to reduce crosscurrents in upper approaches to locks.The effect of such extensions located upstream of a solid guard wall on flow characteristics depends on many factors,including geometric and hydraulic parameters.In this study,the hydraulic performance of ported wall extensions was experimentally investigated in terms of the permeability coefficient,expanding angle,extension length,and flow depth.The results demonstrate that the dimensionless maximum transverse velocity is closely related to the permeability coefficient,expanding angle,and flow depth.By contrast,the dimensionless eddy length mainly depends on the permeability coefficient,expanding angle,and extension length.Furthermore,the optimum permeability coefficient increases with the expanding angle or flow depth,and it is approximately constant for different extension lengths.These results have the potential to provide direct guidance for the design of effective ported wall extensions in upper approaches to locks.? 2021 Hohai University.Production and hosting by Elsevier B.V.This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

Keywords:Ported wall extension;Permeability coefficient;Transverse velocity;Eddy length;Navigation safety

1.Introduction

Flow conditions within the upper approach to a lock can affect the safety of tows that approach or leave the lock and the time required for tows to transit the lock(McCartney et al.,1998;Li et al.,2020).Due to the geometrical restriction of a solid guard wall,flow in the upper approach is characterized by significant crosscurrents upstream of the solid guard wall and the formation of eddy currents between the guard wall and riverbank(Stockstill et al.,2004).Downbound tows have to reduce speed as they approach the guard wall for a rest,thereby losing steerageway and the ability to overcome the effects of these currents(Franco and Pokrefke,1983;Gambucci,2010;Wang and Zou,2014;Wooley,1997,1998).Ported wall extensions,located upstream of a solid guard wall,are commonly used in lock extension projects to promote the flow conditions in the upper approach(Lynch,2001;Wang et al.,2016).A ported wall extension consists of a series of port openings spaced at a certain distance.This allows part of flow that enters the upper approach to pass under the extension and thereby helps reduce the strong crosscurrents near the end of the wall.

The hydraulics of ported wall extensions are related to many factors,including geometric and hydraulic parameters.Past investigations have mainly focused on the crosscurrents in the upper approach.In the hydraulic studies conducted by Hu et al.(2019),Wang and Lu(2013),and Zhang et al.(2019),the hydraulics of ported wall extensions were investigated in relation to the maximum transverse velocity in upper approaches as they can drastically impact the ease with which a downbound tow can drift into the approaches.Li et al.(2007)studied the flow velocity distribution in the upper approach for six types of ported wall extensions,and the performance of these walls was assessed at different permeability coefficients and flow depths.In fact,eddy currents tended to rotate a downbound tow,thereby remarkably increasing the difficulties for the tow in approaching the solid guard wall(Franco and Pokrefke,1983;McCartney et al.,1998;Wooley,1998).The effect is even more pronounced when the eddy length is close to the length scale of the tow.Therefore,two goals should be required in adequate design of a ported wall extension:a significant reduction of crosscurrents and an eddy length compatible with the tow length.As a matter of fact,the flow region between a ported wall extension or a solid guard wall and the riverbank is typically a dead water zone.Many studies have been conducted to investigate the fundamental properties of recirculating flows in dead zones attached to the side wall of an open channel(Constantinescu et al.,2009;Kimura and Hosoda,1997;Liu,1995;Sanjou and Nezu,2017;Savvidis et al.,2017;Shen et al.,2003;Yue,1986).However,these studies have not detailed the flow structure in a dead zone when its centerline is parallel to the incoming main flow.Furthermore,the effect of a ported wall on eddy characteristics in the zone has not been sufficiently studied.

The objective of this study was to detail the hydraulic characteristics in the upper approach with ported wall extensions.Physical model experiments were systematically performed with a particular emphasis on the effects of the permeability coefficient,expanding angle,extension length,and flow depth.The findings of this study may provide direct guidance for the hydraulic design of ported wall extensions in upper approaches to locks.

2.Methodology

2.1.Presentation

Fig.1 shows a typical ported wall extension in the upper approach along with the coordinate system(xOy).The ported wall extension with a length(l)is located upstream of the solid guard wall,forming an angle(β)with the guard wall in the plan and an intercepted flow width(lint)with the riverbank.The permeability coefficient of the ported wall extension(ω)is defined as the ratio of the ported area(Ap)to the intercepted flow area(Aint).The approach flow velocity(Vin)and the flow depth(h)correspond to the values at the approach entrance,where the flow has a horizontal surface with no crosscurrents.

Fig.1.Sketch of an upper approach with a ported wall extension.

As stated above,the maximum transverse velocity(Vme)and the eddy length(le),defined as the length between the upper and lower eddy ends(Ramos et al.,2019),are two key indices or criteria used to determine the hydraulic behavior of a ported wall extension.Hydraulic considerations indicate that these parameters should mainly depend on the following variables(Chanson,2004):

wheregis the gravitational acceleration.Straightforward dimensional analysis is conducted to transform Eq.(1)into its dimensionless version as following:

Eq.(2)evidently demonstrates that the values ofVme/Vinandle/lintprimarily depend on the geometrical characteristics of the ported wall extension and a Froude number-based dynamic parameter regarding the approach flow velocity and the intercepted flow width.

2.2.Experimental setup and methodology

Fig.2 schematically shows the experimental design.The facility basically consisted of an upstream reservoir,a rectangular notch weir,and a concrete flume with a length of 15.4 m and a rectangular section of 2.5 m×0.2 m.The channel invert was horizontal.A solid guard wall and its ported wall extension made of PVC sheets(1-cm thickness)were arranged on the riverside of the approach in the flume.The extension consisted of a series of rectangular cells spaced at 0.142 8 m between their centers and connected with beams.Draft curtains were attached to the beams between the cells,and their bottoms were set at the same elevation in each experimental run.The tailgate at the lower flume end was used to attain the necessary boundary conditions for the approach flow depth at the entrance section of the approach channel.The approach width between the solid guard wall and the bank was 0.57 m,and the scale of the Froudian model was 1:70,assuming a standard approach width of 40 m(Henderson,1966).

Water was circulated in the flume through a pump,and the discharge was measured with a rectangular sharp-crested weir(Montes,1998).The approach flow depth at the entrance section of the approach was controlled by a point gauge with an accuracy limit of 0.1 mm.The eddy lengths were measured using a scale ruler with a resolution of 1 mm.The velocity in the approach was obtained with an acoustic Doppler velocimeter(ADV)Nortek?Vectrino+(serial no.VCN9235),with a side-looking head equipped with four receivers(Leng and Chanson,2015).The ADV velocity range was set to be±0.3 m/s,with a data accuracy limit of 1% of the velocity range.The velocity measurements were performed in planes parallel to the flume bed as close as possible to the water surface.As shown in Fig.2(c),data points on each plane were distributed on grids of 0.20 m(y-direction)×0.07 m(x-direction)in the critical zones,and the grid resolution was reduced to 0.40 m×0.07 m in the zones near the approach entrance.For the ease of result analyses in this paper,the geometric and hydraulic parameters in the following discussions are provided in full-scale values unless otherwise stated.

Fig.2.Experimental design.

Based on the results of dimensional analysis,seven experiment series were designed(Table 1).In each series,a wide range ofωwas tested with aVinvalue of 1.5 m/s to investigate the effects ofωonVmeandle.Series A,B,and C were designed with the samelandhvalues to investigate the effects of differentβvalues.In Series B,D,and E,the effects of differentlvalues were studied with the sameβandhvalues.Series B,F,and G keptβandlvalues constant to investigate the influences of differenthvalues.The investigated inflow Froude number(Fr)ranged from 0.20 to 0.26.

Table 1Experimental series.

3.Results and discussion

3.1.Overall flow structure in upper approach

For each experimental run,extensive velocity measurements were obtained near the water surface on thex-yplane parallel to the flume bottom.Fig.3 shows the typical velocity distribution and the velocity contour ofV/Vin,whereVis the plan velocity at any point.This figure demonstrates that two different flow regions were formed in the upper approach.One was a large recirculating flow region located between the wall and adjacent bank,and it was characterized by low velocity and reversed flows.The other was a crosscurrent flow region where the upstream main flow traveled toward the extension wall at a high speed.Part of this flow went to the outlet through the port openings,and the remaining flow impinged on the wall.Coherent vortices existed in the mixing layer between the main and recirculating flows(Wang et al.,2019).Clearly,velocity decayed rapidly in the interfacial region.

Fig.4(a)displays the velocity distributions at different sections of the recirculating flow.Clearly,the flow was not perpendicular to the cross-sections in the recirculation region.Fig.4(b)demonstrates the velocity distributions at different sections in a dimensionless form.The dimensionless velocity was calculated by dividing the absolute velocity magnitude(|V|)by the maximum value(|V|m)at that section.The velocity profiles for the cross-sections near the nose of the extension wall(e.g.,yfrom 28 m to 56 m)demonstrated some similarity,and the velocity at each cross-section near the extension wall was significantly higher than that further from the wall.It was also found that the velocity profiles near the intersection of the guard and extension walls(e.g.,yfrom 14 m to－28 m)exhibited a high degree of similarity and were nearly symmetric to the approach centerline.

Fig.3.Plan velocity field in upper approach and contour of V/Vin for l=70 m,β=0°,h=6.0 m,andω=0.14.

Fig.4.Velocity distributions of recirculating flow for l=70 m,β=0°,h=6.0 m,andω=0.14.

3.2.Effect of permeability coefficient

Fig.5 shows the typical contour lines of transverse velocity(Vx)in thex-yplane in a dimensionless form forl=70 m,β=0°,andh=6.0 m.The flow structures for differentωvalues presented some similarity.As the permeability coefficientω increased,the velocity region enclosed by a givenVx/Vinvalue moved downstream.To obtain a general understanding of the overall distribution of the transverse velocity,velocity measurements were used to determine the area(Ax)enclosed by a velocity contour of a particularVx/Vinvalue in terms of the intercepted flow area.As shown in Fig.6,the profiles ofAx/Aintfor differentωvalues were similar,andAx/Aintchanged at a much higher rate for a smallVx/Vinvalue.In addition,the curves ofAx/AintversusVx/Vinwere much steeper at smallVx/Vinvalues with largeωvalues.

Fig.5.Contours of normalized transverse velocity Vx/Vin for l=70 m,β=0°,and h=6.0 m.

Fig.6.Ax/Aint versus Vx/Vin for differentωvalues for l=70 m,h=6.0 m,andβ=0°.

Fig.7.Variations of Vmu/Vin,Vmd/Vin,and Vme/Vin withωfor l=70 m,h=6.0 m,andβ=0°.

Based on the distribution ofVx,two flow zones,namely,the extension and entrance zones,are specified in Fig.5.Fig.7 demonstrates the variations of the dimensionless maximum transverse velocity withωfor two flow zones.The maximum transverse velocities in the entrance zone(Vmu)and in the extension zone(Vmd)were respectively divided byVinto obtain the corresponding dimensionless transverse velocity.With the rise ofω,the values ofVmu/VinandVmd/Vintended to linearly decrease and linearly increase,respectively.This indicated that the maximum transverse velocity(Vme)in the approach reached the minimum at the permeability coefficient ω0(Fig.7).Hence,ω0was designated as the optimum permeability for the extension.

Fig.8 shows the variation of dimensionless eddy length(le/lint)forl=70 m,β=0°,andh=6.0 m.This figure demonstrates that the variation ofle/lintwithωfollowed an upward convex curve.With the rise ofω,thele/lintvalue first increased untilωreached 0.29 and then decreased.Yue(1986)investigated the characteristics of eddy flows in a dead zone.According to the findings of Yue(1986),the eddy length may be estimated as follows:

wherebis the mean width of the dead zone,andαis the angle between the main flow and the longitudinal centerline of recirculating flow(e.g.,α=0°in this study).This relationship indicates that the maximum eddy length is 2.5 times the width.Fig.8 evidently demonstrates that the measuredle/lintvalue forω=0 was significantly larger than the maximum dimensionless eddy length estimated by Eq.(3).It should be noted that the prediction model(Eq.(3))was developed within the experimental range of 45°<α<135°.Thus,it may be inferred that the characteristics of recirculating flows in this study were completely different from those in dead zones attached to the side wall of an open channel.

3.3.Effect of expanding angle

Fig.9 displays the plots ofVmu/VinandVmd/Vinversusω with differentβvalues forl=70 m andh=6.0 m.The comparison of the trend lines for differentβvalues indicated thatVmu/Vinwas systematically higher for a largerβfor any givenωvalue,whereas the difference became negligible for a largeω.However,no detectable effect ofβonVmd/Vinwas observed.Consequently,the minimumVme/Vinvalue increased with the rise ofβ,andω0increased gradually from 0.53 to 0.60 asβincreased from 0°to 10°.

Fig.10 shows the dependence ofle/lintonωaccording to the experimental measurements.Apparently,thele/lintprofile for a smallβvalue was essentially higher than that for a large β.The dimensionless eddy length had a maximum value of 3.85 atω=0.29 forβ=0°,3.34 atω=0.25 forβ=5°,and 2.95 atω=0.22 forβ=10°.It should be noted that the increase inβled to the rise of the mixing length between the main and recirculating flows,thereby contributing to the mass and momentum exchanges in the mixing layer.On the other hand,this increase made it considerably more difficult for the portion of main flow to enter the recirculation region along a ported wall extension.Further complexity arose when the current was allowed to flow through the extension.Therefore,the change of eddy length involved complicated mechanisms.

3.4.Effect of extension length

Figs.11 and 12 demonstrate the effect of extension length forh=6.0 m andβ=5°.No significant influence of extension length(l)onVmu/VinorVmd/Vinwas detected.Therefore,the minimumVme/Vinvalue andω0remained essentially constant.For anyωvalue,le/lintwas systematically high for a largel,and had maximum values of 3.34 at ω=0.25 forl=70 m,3.65 atω=0.28 forl=80 m,and 3.80 atω=0.31 forl=90 m.For a given non-zeroβ,the increase inlsignificantly contributed to the mass and momentum exchanges in the mixing layer between the main and recirculating flows,thereby resulting in a largelevalue for ω=0.

3.5.Effect of flow depth

Fig.13 displays the variations ofVmu/VinandVmd/Vinwith ωfor differenthvalues forl=70 m andβ=5°.It was found that for any givenωvalue,theVmu/Vinvalues were essentially independent of flow depth,with a weak functional relationship betweenVmd/Vinandh.Additionally,a clear decrease in the minimumVme/Vinvalue and an increase inω0occurred with the rise ofh,andω0increased from 0.48 to 0.58 whenhincreased from 3.5 m to 6.0 m.

Fig.8.Variation of le/lint withωfor l=70 m,h=6.0 m,andβ=0°.

Fig.9.Variations of Vmu/Vin,Vmd/Vin,and Vme/Vin withωfor differentβvalues for l=70 m and h=6.0 m.

Fig.10.Variations of le/lint withωfor differentβvalues for l=70 m and h=6.0 m.

Fig.11.Variations of Vmu/Vin,Vmd/Vin,and Vme/Vin withωfor different l values for h=6.0 m andβ=5°.

Fig.12.Variations of le/lint withωfor different l values for h=6.0 m andβ=5°.

Fig.13.Variations of Vmu/Vin,Vmd/Vin,and Vme/Vin withωfor different h values for l=70 m andβ=5°.

Fig.14 clearly demonstrates the relationship betweenhandle/lintwith differentωvalues.For a givenωvalue,no detectable effect ofhonle/lintwas found.This indicates that the recirculating flow inside the dead zone was insensitive to the water depth.It may be partially explained by the fact that the depth-averaged mixing intensity remains almost constant for different water depths.This finding is consistent with previous studies(Liu,1995;Shen et al.,2003;Yue,1986),although previous researchers reported observations on recirculation flows in dead water zones attached to the side wall of an open channel.

In general,unsafe navigation conditions in the upper approach to a lock are strongly linked to significant crosscurrents and recirculating flows.The performance of a ported wall extension with respect to its navigability is primarily dependent on a significant reduction of crosscurrents and the eddy length compatible with the concerned tow length.A properly designed ported wall extension results from a relative balance of these two conditions.However,the present results clearly indicated that the permeability coefficient corresponding to the maximum eddy length was significantly smaller than its optimum value with respect to the reduction of crosscurrents.Therefore,only the major factor affecting tow manoeuvrability can be considered when the permeability coefficient of a port wall extension is estimated.

Fig.14.Variations of le/lint withωfor different h values for l=70 m andβ=5°.

Overall,this study has the potential to provide direct guidance for the hydraulic design of ported wall extensions in upper approaches to locks.Moreover,the present results demonstrate the unique features of recirculating flows in an upper approach.

4.Conclusions

In this study,the hydraulic behavior of ported wall extensions in an upper approach was investigated under different experimental conditions,including variations in the permeability coefficient,expanding angle,extension length,and flow depth.The main findings regarding the free-surface velocity fields and the eddy length properties can be summarized as follows:

(1)The dimensionless maximum transverse velocity and the dimensionless eddy length primarily depend on the geometrical characteristics of the ported wall extension and a Froude number-based dynamic parameter expressed in terms of approach flow velocity and intercepted flow width.

(2)A smaller expanding angle and a larger flow depth are effective in reducing the minimum value of the dimensionless maximum transverse velocity for different permeability coefficients.By contrast,the extension length has no detectable effect.

(3)For a given permeability coefficient,a larger expanding angle and a smaller extension length contribute to the reduction of dimensionless eddy length,which is considered independent of flow depth.

(4)The optimum permeability coefficient increases with the expanding angle or flow depth,whereas it is approximately constant for different extension lengths.

Declaration of competing interest

The authors declare no conflicts of interest.