Abstract

Rack clogging can produce dramatic changes in channel hydraulics. Previous studies have investigated the hydraulics of trash racks for various parameters, but the methodology and the findings were not sufficiently refined. Free-surface depression has also been neglected so far. This study considers the rack blockages as impermeable and box-shaped accumulations (instead of considering their bar thicknesses or spacings) for the hydraulic conditions. Hence, flume experiments were performed to clarify the impact of the governing variables on the rack head loss and to examine the characteristics of free-surface depression (i.e. the length of free-surface depression and maximum depth of the depression) because of predefined blockage ratios. The results prove that the rack head loss and flow turbulence behind the rack mainly depend on the rack blockage and Froude number. However, the results for the blockage ratio ≤0.13 at the approach Froude number ≤0.12 has a minor effect on the resulting rack head loss; therefore, the effects are negligible. This study proposed design equations that determine the rack head loss, length of free-surface depression, and maximum depth of the depression behind the rack because of the box-shaped accumulation body that could be used by water engineers. Furthermore, the study improves upon the process understanding of rack blockages to avoid the potential hazards of open channel infrastructure.

Highlights

  • This study considers the rack blockages as impermeable and box-shaped accumulations for hydraulic conditions.

  • Flume experiments were performed to clarify the impact of governing variables on the rack head loss.

  • We propose design equations that determine the rack head loss, length of free-surface depression, and maximum depth of the depression behind the rack.

  • The study improves upon the process understanding of rack blockages to avoid potential hazards of open channel infrastructure.

NOTATION

     
  • Ab

    wetted area of the box-shaped plate

  •  
  • As

    wetted area of the bars and supports

  •  
  • At

    total wetted area of the rack field

  •  
  • B

    blockage ratio as presented in Equation (2)

  •  
  • d

    depth of box-plate blockage in the vertical direction

  •  
  • Eu

    energy at upstream

  •  
  • Fo

    approach flow Froude numbers

  •  
  • Fu

    upstream Froude numbers in case of rack blockage

  •  
  • g

    gravitational acceleration

  •  
  • hd

    downstream water depth

  •  
  • hm

    maximum depth of the depression

  •  
  • ho

    approach flow depth

  •  
  • hu

    upstream water depth

  •  
  • Ld

    length of the free-surface depression

  •  
  • Q

    flow discharge

  •  
  • Ro

    approach Reynolds number

  •  
  • Uo

    approach flow velocity

  •  
  • Uu

    upstream mean velocity

  •  
  • α

    rack angle

  •  
  • Δ Eud

    energy loss

  •  
  • Δh

    hydraulic head loss

  •  
  • ξ

    head loss coefficient

  •  
  • υ

    kinematic viscosity

INTRODUCTION

One main difficulty that confronts stream crossing structures is debris. This debris can accumulate at the openings and culverts of bridge structures, producing a damaging impact on the structure's operations (Chang & Shen 1979; Diehl 1997). The trash rack is one main countermeasure that is used to trap debris and stop it from entering open structures and causing undesirable outcomes (Bradley et al. 2005; EA 2009). However, debris racks face a major hazard with harmful consequences caused by rack clogging (EA 2009). Trash rack blockage can block the waterway openings and increase the backwater, thereby increasing the potential for flooding and destroying nearby infrastructure.

Many researchers have investigated the accumulation and impact of debris at river structures (Stockstill et al. 2009; Weitbrecht & Rüther 2009; Tamagni et al. 2010). In their field study, Ibrahim et al. (2015) investigated the debris accumulation upstream of the hydroelectric power station of New Naga Hammady Barrages in the Nile River. This research aimed to investigate the impact of debris accumulation at the trash racks of hydroelectric facilities and turbines, which negatively affected electricity production. In addition, the racks were designed for specific locations to counter transported debris from high-yield source areas before reaching the hydroelectric power station or turbine racks.

The backwater rise because of large wood accumulations has been investigated by certain researchers (Rimböck 2003; Elliot et al. 2012; Gems et al. 2012; Schmocker & Hager 2013; Schmocker &Weitbrecht 2013; Ruiz-Villanueva et al. 2014). Schalko et al. (2018) conducted flume experiments with a fixed bed to detect the effect of the hydraulic conditions; they also investigated large wood accumulation characteristics on the backwater rise Δh for two model scales. The organic fine material, accumulation compactness and length, and log diameter were used to identify the effect of large wood characteristics on Δh, as follows:
formula
(1)
where ho = approach flow depth, LWD = dimensionless large wood accumulation factor, Fo = approach Froude number, I = flow diversion factor = ratio between length of accumulation and mean log diameter, Fm = organic fine material, hereby described as leaves and branches in an accumulation, and added as a volume percentage of the solid large wood volume VS, and K = bulk factor = ratio between the loose large wood volume VL and VS. However, it is difficult to define the large wood characteristics to estimate Δh in natural cases, especially with different debris mixtures.

In most previous studies, the hydraulic conditions or head losses of racks were, for example, by using the effect of bar thickness, spacing, or blockage ratio (e.g. Kirschmer 1926; Osborn 1968; Clark et al. 2010; Raynal et al.2013a, 2013b; Albayrak et al. 2018). However, examining different bar thicknesses or spacings as blockages without attaching debris does not adequately represent the natural blockage effect on the trash racks because of the differences in the blockage locations and distributions. Josiah et al. (2016) examined an inclined trash rack with circular bars; they used clear bar spacings of 5 and 10 mm and bar diameters of 2, 3, 6, 8, 10 mm to obtain different blockage ratios that varied from 0.17 to 0.68 during the study. Based on their results, they proposed the head loss equation by using all possible parameters that affected rack losses, such as the blockage ratio, unit discharge, and inclination angle with the channel bed. Böttcher et al. (2019) experimentally compared the trash rack with circular bars and fish protection systems (flexible fish fence made using horizontal cables instead of bars for different bar and cable spacings). The results showed that the head loss coefficient was independent of the tested Bar–Reynolds number. In addition, a design equation was proposed to estimate the head loss for both rack options. A few studies have been performed for flow through bar racks using numerical analyses (e.g. Hermann et al. 1998; Meusburger et al. 1999), as exemplified by Tsikata et al. (2014).

Several studies have been performed to understand the characteristics of turbulent flow around cylinders (Nakagawa et al. 1999; Dutta et al. 2003; Agelinchaab et al. 2008). Agelinchaab et al. (2009) exemplified how Knisely (1990) and Matsumoto (1999) presented excellent reviews of flows around rectangular cylinders. Agelinchaab et al. (2009) studied the turbulence characteristics of pairs of identical rectangular and streamlined cylinders in an open channel of varying cylinder inclinations using particle image velocimetry. They observed that a strong asymmetric flow pattern occurred when the cylinder inclination increased. In addition, the induced asymmetric hydrodynamic loads could lead to more vibration problems and eventually to structural failures.

Most studies on rack hydraulic conditions, in particular, on head loss due to blockages have focused on the bar spacing or the thickness. However, a knowledge gap exists on the hydraulic rack losses related to the blockages from debris clogging; these blockages have been simplified into a horizontal box shape in this study. Furthermore, to the best of our knowledge, no former study has addressed detailed descriptions about the characteristics of free-surface depression using designing equations because of predefined horizontal blockages. Therefore, this experimental study is aimed at clarifying the effects of various rack blockages arising from debris on the head loss and the length and maximum depth of the free-surface depression downstream of the rack for a vertical trash rack with a fixed bed.

EXPERIMENTAL SETUP

The flume experiments were conducted in a trapezoidal open channel at the Hydraulic Laboratory of Channel Maintenance Research Institute, National Water Research Center, Egypt. The channel was 16.22 m long, 0.42 m deep, and 0.6 m wide. The experimental equipment has been described in greater detail in Zayed et al. (2018a, 2018b).

To study the rack hydraulic behaviors, a rack was placed vertically and perpendicular to the channel within a fixed bed 8 m downstream of the intake. The rack always consists of vertical mild steel bars that are circular; they are 3 mm in diameter, 25 cm deep, and have a clear spacing of 20 mm. The welded rack bars were supported by outer bars and fixed to the flume side wall. The outer supporting structure was minimized, and consequently the rack itself (bars and outer supports) had hardly any influence on the head loss and approach flow conditions.

The rack blockage was modeled and mounted on the trash rack at the water-level height as a plate in the shape of an impermeable box. Actually, the wetted rack components (bars and outer supports) represented the blockage ratio of B = 0.08 (Figure 1). Instead of changing the bar diameter and spacing, plates of various sizes with depths of d = 2.3, 2.9, 3.6, 6.0, 7.5, 9.6, and 12.0 cm in the vertical direction were attached to the rack to obtain the blockage ratios of B = 0.13, 0.25, 0.32, 0.45, 0.50, 0.64, and 0.69, respectively. In fact, the predefined debris plate blockage (impermeable and regular shape) was comparable with the debris blockage proposed by Melville & Dongol (1992). The rack blockage simulation study concerns the rack accumulation caused by the floating debris. Because of the additional accumulation, the debris is dragged to the bottom of the rack, and the accumulation is extended vertically downward (see Schmocker & Hager 2013; Schalko et al. 2019a, 2019b). Furthermore, Hartlieb (2015) illustrated that the accumulation body was considerably less permeable because of the additional organic fine material (e.g. leaves and small branches). Actually, the initial debris accumulation has a major effect on the backwater rise; the debris properties and the mixture have a negligible effect (Schmocker & Hager 2013). From the field observation experiences, the different accumulation layers at the back of the initially trapped rack accumulations can create an impermeable accumulating body. Accordingly, the proposed debris blockage can efficiently simulate natural observations. The blockage ratio B is calculated using the following expression:
formula
(2)
where Ab is the wetted area of the box-shaped plate; As is the wetted area of the bars and supports; and At is the total wetted area of the rack field.
Figure 1

Rack model in the channel (a) side view and (b) upstream view.

Figure 1

Rack model in the channel (a) side view and (b) upstream view.

In all the experiments and flow rates, the approach flow depth of ho = 25 cm was maintained by the predefined tail gate openings. Given the approach flow conditions (subscript o) measured without the rack blockage, a defined flow discharge Q = 20, 25, 30, 35, and 40 L/s resulted in the approach flow Froude numbers Fo = (Uo/[gho]0.5) ≈ 0.06, 0.07, 0.08, 0.01, and 0.12, respectively; these numbers were based on the approach flow velocity Uo, approach flow depth ho, and gravitational acceleration g. The corresponding Reynolds number (Ro = Uoho/υ) varied from 21625 to 46088 based on the approach flow velocity, flow depth, and kinematic viscosity υ. Therefore, all the experiments were performed with the turbulent and subcritical approach flow regimes. The Reynolds number based on the approach flow velocity and rack blockage depth (Rd = Uod/υ) varied from 2165 to 22588 (Table 1). To identify the water surface elevations for the rack with different configurations, the upstream and downstream water surfaces were measured by a point gauge at mid span along the channel at x intervals of 10 cm. However, because of the disturbed flow, the measurements of the downstream water surface were taken at several locations to obtain the average value. The characteristics of free-surface depression were detected from these data. To calculate the hydraulic head loss Δh, the upstream and downstream water depths (hu and hd, respectively) were measured carefully at x = −1.5 m and at x = 4.5 m, respectively to avoid the turbulence zone; we took x = 0 m at the rack foot. The head loss coefficient ξ is determined as follows:
formula
(3)
where Uu is the upstream mean velocity, and g is the gravitational acceleration.
Table 1

Parameter range and test conditions

ParametersRange
Q 20–40 L/s 
B 0.08–0.69 
Fo 0.06–0.12 
Ro 21,625–46,088 
ho 25 cm 
Uu2/2 g 0.05–0.14 cm 
ParametersRange
Q 20–40 L/s 
B 0.08–0.69 
Fo 0.06–0.12 
Ro 21,625–46,088 
ho 25 cm 
Uu2/2 g 0.05–0.14 cm 

OBSERVATIONS AND RESULTS

Rack head loss

The effect of Fo and B on ξ was examined in the range of Fo = 0.06–0.12 and B = 0.08, 0.13, 0.25, 0.32, 0.45, 0.50, 0.64, and 0.69. In Figure 2, ξ is plotted as a function of B for various Fo. As shown by Zayed et al. (2018a, 2018b, 2020), the head loss coefficient increases strongly with B. This is because the increasing blockage ratio decreases the rack surface area, which results in an increased ξ value. Regarding the blockage ratio effect, the rack with B = 0.25, 0.32, 0.45, 0.50, 0.64, and 0.69 increases ξ by approximately 1.6, 5, 12, 20, 31, and 45.5 times, respectively, as compared with the rack with B = 0.08 (Figure 2). This means that the blockage ratios significantly affect the rack head loss coefficients and should not be larger than 25% for additional safety. In addition, large uncertainties are observed for Fo < 0.12, which correspond to the measurements of B< 0.32 based on the head loss coefficients, in which the head losses are so low that they cannot be accurately measured; this results in high relative uncertainties. It further proves that the development of head loss as a function of the blockage ratio is not linear.

Figure 2

Head loss coefficient ξ versus blockage ratio B for various Fo.

Figure 2

Head loss coefficient ξ versus blockage ratio B for various Fo.

The effect of the approach Froude number on Δh was investigated for various B values. Figure 3 shows Δh as a function of Fo in the range of B = 0.08–0.69. The head loss increases with Fo for each blockage ratio. Moreover, Δh appears clearly with the blockage ratio (Figure 3). For Fo = 0.12, Δh resulted in 0.39 cm for B = 0.32 as compared with Δh = 1.45 cm for B = 0.50. This is because a higher blockage ratio represents a greater flow resistance, which leads to greater head loss. For Fo < 0.12 with B< 0.13, the Δh values can be neglected; this is because of low velocity with low flow resistance, which reduces the drag force. Figure 4 shows the relationship between the upstream Froude number in the case of blockage ratio and approach Froude number. For a lower B (B < 0.13), the curve shows that the impact of Fo on Fu is not significant in the range of Fo < 0.12 because of low backwater rise. In general, the Fu values decrease with increasing B based on the results. For Fo = 0.12, Fu resulted in 0.118 for B = 0.25 compared with Fu = 0.098 for B = 0.69. Due to the higher blockage ratio, the upstream backwater rise increases, which results in a lower Fu. Actually, the introduction of Fu simplifies the rack loss assessment in the field measurements because Fo is associated with uncertainties resulting from unexpected blockage ratios. Therefore, the upstream Froude number due to the blockage can be described by a relationship with the approach Froude number Fo = 0.06–0.12 (R2 = 0.95).
formula
(4)
Figure 3

Head loss Δh versus approach Froude number Fo for various B.

Figure 3

Head loss Δh versus approach Froude number Fo for various B.

Figure 4

Upstream Froude number Fu versus approach Froude number Fo for different blockage ratios.

Figure 4

Upstream Froude number Fu versus approach Froude number Fo for different blockage ratios.

Design equation for rack head loss

An attempt was made to estimate the rack head loss, and the regression model was applied to the proposed Equation (5) using the experimental data. Based on Fo, Fu can be defined as Equation (4) for practical applications.
formula
(5)

Clearly, Equation (5) has been developed for the classical screen (perpendicular and vertical to the flow direction) with box-shaped plates, which is a concept different from the bar diameters and spacings. In particular, the proposed equation is valid for 0.06 ≤ Fo ≤ 0.12, 0.08 ≤ B ≤ 0.69 and circular bars. As presented in Equation (5), the largest effective factor on ξ is the blockage ratio with an exponent of 1.84. The fit of Equation (5) has a high adjusted R2 value of 0.93, which indicates a good fit to the experimental data. Moreover, the standard errors of the independent coefficients are 0.07 and 0.21, whereas the highest value represents the approach Froude number Fo and the lowest value the blockage ratio. Actually, the high standard error for Fo is due to the low velocity, which results in a low drag force; therefore, the uncertainties for Fo increase in the experimental tests. Figure 5 shows a comparison between the measured and predicted head loss by Equation (5). In Figure 5, the coefficient of determination R2 and the standard error are 0.95 and 0.13, respectively. Figure 5 shows that the uncertainty zone or overestimation of Δh (highlighted in red) for the measured Δh < 0.5 cm. These points refer to Δh recorded at B < 0.25 for Fo < 0.12. Actually, this zone is consistent with the results in Figures 2 and 3 because of the low drag force (as discussed previously). Besides the uncertainty zone, 88% of the data falls within the 25% predicted range, which implies that the results are within the acceptable band. Therefore, it is recommended to apply Equation (5) for Δh > 0.5 cm.

Figure 5

Comparison between the measured head loss and the predicted by Equation (5), and ±25% prediction range.

Figure 5

Comparison between the measured head loss and the predicted by Equation (5), and ±25% prediction range.

Characteristics of free-surface depression

The investigations of (1) length of the free-surface depression Ld and (2) maximum depth of the depression hm downstream of the rack were analyzed for various blockage ratios and approach Froude numbers.

Figure 6 depicts the depression (dip) in the free-surface through the vertical rack (α = 90°, Fo = 0.06–0.12, B = 0.08–0.69) at selected streamwise locations x/ho between −4.8 and +15.4. The upstream flow of the rack is generally streamwise, but it is not exactly uniform. Actually, slight bends occur upward near the rack because of the flow deceleration caused by the rack obstruction. Figure 6 shows the variations in depression (dip) in the free surface immediately behind the rack for different blockage ratios and reference values (no rack). The presence of the rack substantially creates flow disturbances behind the rack because of the associated flow contraction, and the degree of this disturbance or free-surface depression depends on both the blockage ratios and approach Froude numbers. As the blockage ratio and Froude number increase, the downstream flow is severely disturbed, and the depression increases as well (Figure 7 and Table 2). Then, in a region far downstream the rack, the flow converts into a uniform condition. Regarding the bed stability and level measurements, it is recommended to consider the depression characteristics in the construction processes.

Table 2

Sample of experimental results

Blockage ratioFohm (cm)Ld (cm)
0.08 0.06 0.01 
0.08 0.12 0.02 10 
0.13 0.06 0.05 10 
0.13 0.12 0.15 35 
0.25 0.06 0.07 10 
0.25 0.12 0.31 85 
0.32 0.06 0.1 18 
0.32 0.12 0.35 140 
0.45 0.06 0.12 30 
0.45 0.12 0.78 235 
0.5 0.06 0.23 85 
0.5 0.12 0.88 285 
0.64 0.06 0.28 100 
0.64 0.12 1.14 335 
0.69 0.06 0.3 135 
0.69 0.12 1.3 385 
Blockage ratioFohm (cm)Ld (cm)
0.08 0.06 0.01 
0.08 0.12 0.02 10 
0.13 0.06 0.05 10 
0.13 0.12 0.15 35 
0.25 0.06 0.07 10 
0.25 0.12 0.31 85 
0.32 0.06 0.1 18 
0.32 0.12 0.35 140 
0.45 0.06 0.12 30 
0.45 0.12 0.78 235 
0.5 0.06 0.23 85 
0.5 0.12 0.88 285 
0.64 0.06 0.28 100 
0.64 0.12 1.14 335 
0.69 0.06 0.3 135 
0.69 0.12 1.3 385 
Figure 6

Variation of dip for the different blockage ratios at approach Froude number of Fo = 0.06, 0.07, 0.08, 0.10, and 0.12.

Figure 6

Variation of dip for the different blockage ratios at approach Froude number of Fo = 0.06, 0.07, 0.08, 0.10, and 0.12.

Figure 7

Flow turbulence for (a) B = 0.64 at Fo = 0.10, and (b) B = 0.25 at Fo = 0.06.

Figure 7

Flow turbulence for (a) B = 0.64 at Fo = 0.10, and (b) B = 0.25 at Fo = 0.06.

Length of free-surface depression

The effect of Fo and B on the relative length of the free-surface depression Ld/hu was examined in the tested range conditions. In Figure 8, Ld/hu was plotted as the function Fo for various B values. For B = 0.69, Ld/hu was 5.21 for Fo = 0.06 as compared with 13.8 for Fo = 0.12. Obviously, for the same blockage ratio, Ld/hu increases with increasing Fo, and it becomes stronger for higher blockage ratios. This fact results from the increase of the approach flow velocity with increasing Fo and a corresponding increase in the vibration amplitudes. Besides the Froude number, Ld/hu is also affected by B; Ld/hu increases with the increasing blockage ratio. For Fo = 0.12, Ld/hu resulted in 10.77 for B = 0.50 as compared with Ld/hu = 12.36 for B = 0.64. In particular, a high blockage ratio induced a high flow disturbance, which increased the Ld/hu value for each Fo (see Naudascher & Rockwell 2012; Tsikata et al. 2014; Böttcher et al. 2019). In other words, for a certain rack configuration, the free-surface depressions extend over a longer distance as the blockage ratio and Froude number increase (see Tsikata et al. 2009). Note that the flow disturbance induces an undesirable outcome for the rack circular bars and turbine components because of the flow vibration, thereby increasing their stiffness, which should be considered in the optimization processes (Figure 9). To simplify the findings, Equation (6) reflects the relationship between the relative length of the depression, its independent parameters blockage ratio, and the approach Froude number, which can be replaced by the upstream Froude number, as shown in Equation (4).
formula
(6)
Figure 8

Ld/hu versus Fo for various blockage ratios.

Figure 8

Ld/hu versus Fo for various blockage ratios.

Figure 9

Bar distortions resulting from flow disturbance and vibration.

Figure 9

Bar distortions resulting from flow disturbance and vibration.

For a given blockage ratio, the resulting length of the free-surface depression [see Equation (6)] can be estimated for various approach flow conditions. This equation reveals that both the governing parameters have an exponential value of 1.87 for B, which is quite close to 2.05 for Fo at 95% probability limit; this shows that there is a significant impact on Ld/hu. The adjusted coefficient of determination of the best fit is R2 = 0.95, and the standard error is 0.14. Particularly, the standard errors of the governing parameter coefficients are 0.075 and 0.2; the highest value represents Fo, and the lowest value represents B. The measured relative length of the free-surface depression Ld /hu is plotted against the relative predicted length of the free-surface depression using Equation (6) and ±30% prediction range in Figure 10. A majority of the data points fall within ±30%; therefore, Equation (6) can be applied to estimate the length of the free-surface depression downstream of a vertical rack due to blockage. Based on Equation (6), as B increases from 0.08 to 0.25 and 0.32, the equation yields an increase of approximately 7.4 and 12.4 times in Ld/hu, respectively, for the average Fo.

Figure 10

Comparison between the measured Ld/hu and the predicted by Equation (6), and ±30% prediction range.

Figure 10

Comparison between the measured Ld/hu and the predicted by Equation (6), and ±30% prediction range.

Maximum depth of the depression

The relative maximum depth of the depression hm/hu was investigated for various Fo and B values. Figure 11 shows hm/hu versus the approach Froude number for different blockage ratios. Actually, hm/hu values for B ≤ 0.08 at Fo ≤ 0.12 can be neglected. The gap between the data for Fo = 0.06 is less than that for Fo = 0.12 within the range of B values, which means that the effect of the maximum depth of the depression appears gradually with Fo (Figure 11). For B = 0.69, hm/hu resulted in 0.011 for Fo = 0.06 compared with hm/hu = 0.046 for Fo = 0.12. Concerning the blockage impact, increasing B usually results in increasing the rack resistance and the relative maximum depth of depression, especially when considering B > 0.08 in the tested range of flow conditions. For Fo = 0.12, hm/hu resulted in 0.033 for B = 0.50 compared with hm/hu = 0.042 for B = 0.64. Again, these results arise from the flow disturbances at a high flow velocity with rack resistance. For both independent parameters, the maximum depth of depression increases with increasing Fo, and it evidently becomes stronger as the blockage increases, which reveals the profound impact of B and Fo on hm/hu. The relationship between the dimensionless term hm/hu and 0.06 ≤ Fo ≤ 0.12 and 0.08 ≤ B ≤ 0.69 based on the regression analysis is as follows:
formula
(7)
Figure 11

hm/hu versus Fo for various blockage ratios.

Figure 11

hm/hu versus Fo for various blockage ratios.

From Equation (7), both B and Fo have an exponent value of 1.68 at 95% probability limit, which reveals significant predictive factors. The standard error of Equation (7) is 0.14, and the adjusted coefficient of determination of the best fit is R2 = 0.94, which signifies a reliable fit of the experimental data. The standard errors of the B and Fo coefficients are 0.07 and 0.2, respectively, whereas the highest value represents Fo, and the lowest value represents B. Figure 12 shows the measured relative maximum depth of the depression hm/hu versus the relative predicted maximum depth of the depression using Equation (7) and ±20% prediction range. Actually, a majority of the data points are clustered in the prediction range, which presents a good fit to Equation (7) for describing the maximum depth of the depression for various blockages. For the average Fo, B increases from 0.08 to 0.25, whereas Equation (7) yields an increase of approximately 5.6 times in hm/hu. A further increase to B = 0.32, increases hm/hu by 9.2 times.

Figure 12

Comparison between the measured hm/hu and that predicted by Equation (7), and ±20% prediction range.

Figure 12

Comparison between the measured hm/hu and that predicted by Equation (7), and ±20% prediction range.

Relative energy loss

In a subcritical flow regime, the energy loss through the rack was investigated to scrutinize the impact of rack operations for various blockage ratios on the flow behavior. During the experiments, the energy loss (Δ Eud) between the upstream and downstream ends of the vertical rack was obtained at x = −1.5 m and at x = 4.5 m, respectively (x = 0 m at the rack foot). The relative energy loss with regard to the upstream end (ΔEud/Eu) is calculated using the following expression:
formula
(8)
where hu and hd are the flow depths at the upstream and downstream ends of the rack, respectively. Also, Uu and Ud represent the average flow velocities at the upstream and downstream ends of the the rack, respectively; these velocities are obtained by dividing the flow discharge by the cross-sectional area. In Figure 13, ΔEud/Eu is plotted as a function of Fu for different B = 0.08–0.69. Figure 13 shows that by increasing the subcritical Fu, the relative energy loss increases. The relative energy loss ΔEud/Eu for B = 0.50 increases from ΔEud/Eu = 1.56% for Fu ≈ 0.06 to ΔEud/Eu = 5.36% for Fu ≈ 0.11. In addition, a large B value represents a high flow turbulence and resistance, which results in a high loss of relative energy. For Fu ≈ 0.11, ΔEud/Eu = 1.5% for B = 0.32, whereas ΔEud/Eu = 3.39% for B = 0.45.
Figure 13

Relative energy loss ΔEud/Eu versus Fu for various blockage ratios.

Figure 13

Relative energy loss ΔEud/Eu versus Fu for various blockage ratios.

Comparison with previous studies

A majority of the previous reviews dealt with the rack blockage by changing the bar spacing or thickness and deduced the head loss equations based on this concept (Kirschmer 1926; Raynal et al. 2013a; Josiah et al. 2016). However, this concept did not consider three main critical issues. First, the independent variable in natural observation is the accumulated body of debris, which continuously changed over time at the bars rack; whereas, the bars spacing or thickness remained constant. Second, the location of the blockage can affect the rack backwater rise (Abt et al. 1992); therefore, the distribution of blockage using bar spacing or thickness differs from the natural blockage observations. Third, from practical application, the rack designer designs the bar rack for a minimum bar blockage to obtain negligible head loss; therefore, the bar shape (except for stiffness and fish-friendliness racks that require narrow bar spacing) will have limited benefits on the rack loss. The bar shape effect appears with the bar blockage ratio for bar configurations in the flow direction. In other words, the design of the high bar blockage is not useful for practical applications because the natural blockage arises from the accumulated body of debris. Hence, this study focused on the blockage resulting from the accumulation of debris at the bar racks for the different configurations to simulate natural performances.

Previous studies on backwater rise arising from large wood accumulations (Schalko et al. 2019a, 2019b) concentrated on the accumulation of volume characteristics (accumulation length, large wood diameter, compactness, and the organic fine material) at the racks. The introduction of clogging as an area of the accumulation body in this study simplifies the assessment of the blockage ratio because the evaluation of the effective debris volume or characteristics is associated with high uncertainties and estimation difficulties.

CONCLUSIONS

The experiments investigated the rack head loss and the characteristics of free-surface depression behind a vertical rack because of blockage by debris clogging; a horizontal box-shaped accumulation body was used. The experiments were conducted with varying blockage ratios and different approach flow conditions. The results can be summarized as follows:

  • The main governing parameters to estimate ξ and the flow turbulence are B and Fo. As ξ increases with B and Fo, the relationship between ξ and B is not linear. The head loss coefficient ξ increases approximately 1.6, 5, 12, 20, 31, and 45.5 times at B = 0.25, 0.32, 0.45, 0.50, 0.64, and 0.69, respectively, compared with the rack with B = 0.08. However, at the examined range of B 0.13 at Fo 0.12, the rack head loss can be neglected because of the low rack blockage. Therefore, it is recommended to keep the rack with B< 25% at the range of Fo < 0.12 for additional safety.

  • A design equation was deduced to estimate ξ [Equation (5)], and the application of this equation is recommended for a rack with horizontal box-shaped blockage as the clogging debris for Δh > 0.5 cm.

  • The degree of flow disturbance behind the rack depends on both B and Fo. When the flow is severely disturbed, and the depression increases with increasing B and Fo. This may lead to vibration problems and consequently rack failures; therefore, increasing the rack stiffness should be considered in the design process.

  • Based on the dimensionless terms, the design Equations (6,7) were deduced to estimate the length Ld and the maximum depth of the depression hm downstream of the rack for the examined range of B and Fo; this simplified the practical applications.

ACKNOWLEDGEMENTS

This study was carried out at the Hydraulics Laboratory of Channel Maintenance Research Institute (CMRI), National Water Research Center. The authors would like to acknowledge CMRI for the technical support and cooperation.

DATA AVAILABILITY STATEMENT

All relevant data are included in the paper or its Supplementary Information.

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