Effects of Reynolds number and blockage ratio on the turbulence characteristics of open channel flow passing through trash rack

Trash racks are extensively used to prevent debris from being transported to down-stream reaches of waterways. However, debris accumulation at the screens can significantly affect their hydraulic performance, resulting in negative economic and environmental consequences. Basic research related to the mechanism of these physical processes is still rather limited. In this experimental study, the flow fields, including the turbulence intensities, Reynolds stresses, and turbulent kinetic energy near a trash rack in a fixed-bed open channel for subcritical flow conditions are investigated for two Reynolds numbers and two blockage ratios. The experimental study investigates the important physical mechanisms relating to turbulence generation and possible sediment deposition induced by the vertical trash rack. Reynolds number effect on time mean streamwise velocity is predominant in the trash rack’s downstream free surface layer as a higher Reynolds number flow has higher normalized streamwise velocity in the free surface layer and lower in the inner layer. In both the Reynolds number effect case and the blockage ratio effect case peak normalized turbulent kinetic energy was observed immediately downstream of the trash rack and with the increment of longitudinal distance downstream of the trash rack, normalized Turbulent kinetic energy is decreased.


Introduction
Accumulation of debris within the intakes of hydraulic structures and watercourses poses a substantial issue of concern.Such accumulation often leads to suboptimal performance and has detrimental effects on the operation of the structure.Specifically, debris can amass and obstruct water passage through openings in bridges or culverts, leading to upstream flooding, increased local erosion, and potential structural damage [1,2].Hydropower intakes, navigation facilities, and flood control works are affected as a result of debris buildup [3].Various researchers e.g.[4,5,6] have documented potential consequences linked to the buildup of debris, illustrating its potential impacts.Hence, it is imperative to consider debris management in the design of hydraulic structures, and It must be established how to deal with this debris.Trash screens are commonly employed methods for managing debris in conveyance systems.Screens, composed of metallic bars, are installed at the entrance of various hydraulic structures like units, pumping stations, culverts, water intakes, irrigation canals, and other hydraulic structures.Their purpose is to prevent debris from entering and causing potential harm or operational complications.They are also placed to promote safe fish mobility and, as a result, to prevent species of fish from accessing the structure.A serious hazard develops when the blockage forms at a location that makes it difficult to remove the blockage [7].To ensure extendedterm upkeep, it is recommended to use trash screens to safeguard the culvert's entrance against debris and sediment.Furthermore, one of the major characteristics that should be thoroughly examined in trash screen design is hydraulic head loss [8,9,10] due to the potential danger of encountering significant issues as the head loss in the screen rises.Because intake circumstances may greatly impact both hydraulic performance and cost, the inclusion of the inlet screen design is a vital element within the overall structural design.
Open channel flows exhibit a free surface along with a near-bed flow characterized by a boundary layer-type behavior.These flows encompass intricate three-dimensional turbulent structures that impact the flow dynamics.Nonetheless, the majority of open channel flows exhibit non-uniform characteristics due to continually shifting boundary conditions resulting from alterations in flow rate, cross-sectional shape, bed roughness, and the presence of hydraulic structures, etc.When the boundary condition changes due to an imbalance of viscous, gravitational, and inertial forces, the flow becomes disrupted.Subsequently, the flow endeavors to attain a state of fully developed flow in the downstream direction.The developing turbulent flow in an open channel is an intricate three-dimensional phenomenon, regulated by factors such as the Reynolds number and blockage ratio.In order to evaluate the interaction between fluid and sediment, as well as sediment erosion in open channel flows, it is essential to understand the flow characteristics around any obstacles.These characteristics are closely linked to the hydrodynamic features, including the vertical distribution of time-averaged velocities, turbulence intensities, Reynolds stresses, and turbulent kinetic energy.
Although numerous researchers have examined the impact of Reynolds number and blockage ratio on head loss properties in open channel flow [10,11,12,13], the turbulence characteristics in the vicinity of trash racks in open channel flow have not yet been comprehensively explored.Hence, in order to fill this research gap, the present investigation aims to examine how the Reynolds number and blockage ratio influence turbulence attributes in the flow over vertical trash screens.

Experimental Setup
The experiments are carried out using a vertical trash screen model within a glass-walled rectangular flume with fixed sand bed conditions.The flume measured 10 m in length, 0.6 m in width, and 0.65 m in depth, and was set up at the Hydraulic and Water Resources Engineering Laboratory located at the Indian Institute of Technology Kharagpur, India.The channel bed was inclined at a constant longitudinal slope of 0.3% along the entire length of the flume.The illustrative representation of the experimental arrangement is presented in Fig. 1.The incoming flow rate was regulated using a valve and quantified with a flow meter.The water depth within the flume was altered by adjusting the tailgate position located at the downstream extremity of the flume.Water depths are measured to the closest 1 mm using a movable point gauge.
A 3D Acoustic Doppler Velocimetry (3D ADV) apparatus was employed for measuring instantaneous flow velocities.In contrast to a three-receiver probe, the Vectrino Plus, a downlooking ADV probe with four receivers manufactured by Nortek, notably reduced the noise signal in the measurements.Utilizing a 10 MHz acoustic frequency, it captured instantaneous During data collection, it was ensured that the sampling volume did not come into contact with the flume bed.In order to establish statistical time-independence of time-averaged velocities, the sampling duration was fixed at 300 s.During the experiments, the signal-tonoise (SNR) ratio and correlation coefficient with the lowest values were retained as 20 and 74, respectively.The signal recorded by the Vectrino Plus in the proximity of the bed flow area encompasses spikes attributed to the interplay between an incident and reflected pulses.Consequently, the raw data underwent filtration utilizing a spike removal technique known as the phase-space threshold method, which was developed by Goring and Nikora [14].The specific details regarding the experimental conditions were outlined in Table 1.The channel bed is built of smooth-finished concrete and coated with uniform sand particles of median diameter d 50 = 2 mm to make it rough.The geometric mean size of the sand, calculated as the square root of the product of d 84.1 and d 15.9 , is 1.95, while the geometric standard deviation (σ g ) was assessed to be 1.24 using the formula σ g = d 84.1 /d 15.9 .The gradation coefficient G = 1 2 (d 84.1 /d 50 +d 50 /d 15.9 ) for the sand sample was 1.24 which falls below 1.4.This implies that the sand exhibits a uniform particle size distribution.In this context,d 84.1 and d 15.9 represent the sizes of sediment particles where 84.1% and 15.9% of the mixture, respectively, consist of finer particles.3 demonstrates the influence of Reynolds number and blockage ratio on the vertical profiles of time-averaged streamwise velocities (u/u ∞ ) along the central axes at both upstream and downstream positions of the trash rack.The turbulent flow characteristics are scaled using the free stream velocity (u ∞ ), while the vertical coordinate is scaled based on the flow depth(Z).Experiments Run1 and Run2 are exclusively focused on investigating the impact of Reynolds number on turbulence characteristics, while experiments Run2 and Run3 are employed to examine the effect of blockage ratio (Table 1).Measurements are taken at positions x=5.7 m, 5.9 m, 6.1 m, and 6.5 m.The velocity measurement at x=5.7 m pertains to an upstream region of the trash rack, while velocity profiles at x=5.9 m, 6.1 m, and x=6.5 m are in the downstream region.The graphs in the upper row of Fig. 3 are intended to assess the influence of the Reynolds number, while those in the lower row aim to evaluate the impact of the blockage ratio.Nezu and Nakagawa [15] distinguished the flow layers by examining the Turbulent Kinetic Energy (TKE) budget.Nezu and Nakagawa contended that the transfer of turbulent kinetic energy (TKE) in open-channel flow is compared to this cascade process through the spectral subranges.
Based on this comparison, the turbulent flow in the open channel can be categorized into three distinct layers.These layers are characterized as 1) Inner layer (z < 0.2h), 2) Intermediate layer (0.2h ≤ z ≤ 0.6h), and 3) Free surface layer (0.6h < z ≤ 1h) Due to the overlapping velocity distribution, the impact of the Reynolds number is less pronounced in z≤ 0.5h in the upstream area.Nevertheless, in the downstream section, the influence of the Reynolds number is observed across the entire flow depth, except at the 6.5 m location in the region z≤0.15h.In both the upstream and downstream regions, the effect of the Reynolds number is substantial within the free surface layer (z > 0.6h).At the downstream position, with the rise in Reynolds number, the percentage rise in maximum velocity is smaller compared to the percentage rise in time-averaged velocity near the free surface layer; Hence, in downstream areas, the normalized time-averaged streamwise velocities (u/u ∞ ) within the free surface layer are greater for flows with higher Reynolds numbers compared to those with lower Reynolds numbers.Conversely, in upstream locations, this trend is reversed.Therefore, the primary influence of the Reynolds number is observed in the free surface layer downstream of the trash rack.A flow with a higher Reynolds number exhibits a higher normalized streamwise velocity in the free surface layer and a lower velocity in the inner layer.Within the free surface layer, we can discern the presence of secondary current effects by observing the reversal of its magnitude in the downstream area.In the second row of Fig. 3, the effect of blockage ratio on time-averaged streamwise velocity is evident in the intermediate and free surface layers, but its influence diminishes in the inner layer.In the downstream region, a collapse of data is found, which shows time mean velocities for different blockage ratio flows are self-similar at far downstream locations.

Turbulence Intensities
Fig. 4 depicts the vertical distributions of normalized turbulence intensity in the streamwise direction, denoted as σ u /u ∞ .An increasing Reynolds number amplifies the intensity of smallscale movements, namely, turbulence intensities [16].Reynolds number effect on normalized streamwise turbulence intensity (σ u /u ∞ ) is seen in inner and intermediate layers, that is σ u /u ∞ of flow with low Reynolds number is higher than the high Reynolds number flow in an upstream location of trash rack for given blockage ratio.Whereas in the downstream location x=6.1m high Reynolds number flow has a high magnitude in the region z < 0.4h and at the location, x= 6.5m diminishes throughout the depth.The lower row of Fig. 4 illustrates the influence of the blockage ratio on the normalized turbulence intensity in the streamwise direction.The effect of the blockage ratio on σ u /u ∞ is observed in both the inner and intermediate layers, i.e., σ u /u ∞ of flow with low blockage ratio surpasses that of the high blockage ratio flow in the upstream location of trash rack.The effect of the blockage ratio is evident in turbulence intensities along the streamwise direction, particularly pronounced in the free surface layer at downstream positions.

Reynolds Stresses 3.3.1. Reynolds Normal Stresses:
The Reynolds normal stresses (RNSs) quantify the strength of turbulence and provide insight into the fluctuating velocity components.The RNSs are influenced by various factors such as velocity, roughness size, roughness orientation, etc. Streamwise Reynolds normal stresses denoted as σ uu .They are normalized using the free stream velocity of the approaching flow, denoted as u 2 ∞ .Fig. 5 depicts the effect of Reynolds number and blockage ratio on the vertical distribution of normalized streamwise (σ uu /u 2 ∞ ) Reynolds normal stresses (RNSs) in upstream and downstream of the trash rack.In this Fig. 5 top row demonstrates that for a given blockage ratio with increasing in Reynolds number σ uu /u 2 effect is diminished (x=6.5m).Bottom row in Fig. 5 shows variation of σ uu /u 2 ∞ for given Reynolds number.With the increasing blockage ratio σ uu /u 2 ∞ shows a higher magnitude in the downstream.) is influenced by changes in Reynolds number and blockage ratio, both upstream and downstream of the trash rack.In Fig. 6 top row peak value is noticed in the inner layer (z < 0.2h) and decreases with increasing depth.In the upstream region lower Reynolds number flow has a higher magnitude up to the intermediate layer and collapses in a single curve, whereas in the downstream it shows a negative magnitude in the free surface layer demonstrating secondary currents.In Fig. 6 bottom row for given Reynolds number with increasing in blockage ratio shows lower magnitude τ uw /u 2 ∞ in the upstream region and collapses in the single curve in the free surface layer.In downstream lower blockage ratio (Br=25%) is invariant with the streamwise direction whereas blockage ratio Br=65% has a positive peak in the inner layer and negative magnitudes in the free surface layer.This demonstrates higher blockage ratio develops secondary currents downstream of the trash rack.∞ ) along the central axes at both upstream and downstream of the trash rack.

Turbulent Kinetic Energy
Turbulent kinetic energy (TKE) is a vital parameter in quantifying turbulence.Therefore, TKE profiles were examined to evaluate the impacts of Reynolds numbers and blockage ratios, as depicted in Fig. 7.A significantly elevated level of normalized turbulent kinetic energy, expressed as k/u 2 ∞ is observed in the close vicinity downstream of the trash rack, particularly where the wake effect is most pronounced.Further downstream higher normalized TKE was noticed near the bed as well as towards the free surface for a high blockage ratio for both Reynolds number flows.In both the Reynolds number effect case and the blockage ratio effect case peak normalized TKE was observed immediate downstream of the trash rack and with the increment of longitudinal distance downstream of the trash rack, normalized TKE magnitudes follow a decreasing trend.

Conclusions
This study examined how turbulence characteristics in the upstream and downstream regions of vertical trash screens are influenced by variations in Reynolds number and blockage ratio, considering a fixed continuous rough bed.The study's key findings are listed below.
• Reynolds number effect on time-averaged streamwise velocity is predominant in the trash rack's downstream free surface layer, With increased Reynolds numbers, the flow demonstrates increased normalized streamwise velocity in the free surface layer while registering a decrease in the inner layer.• The effect of blockage ratio on the average streamwise velocity is noticeable in the intermediate and free surface layers but diminishes in the inner layer.• The effect of blockage ratio is noticed in both upstream and downstream for streamwise turbulence intensity and this effect is severe in downstream's free surface layer.• With the increasing blockage ratio Streamwise Reynolds normal stress shows a higher magnitude in the downstream.• In the upstream region lower Reynolds number flow effect on Reynolds shear stresses has a higher magnitude up to the intermediate layer and collapses in a single curve, whereas in the downstream it shows a negative magnitude in the free surface layer demonstrating secondary currents.
• In the downstream region lower blockage ratio flow(Br=25%) for Reynolds shear stresses is invariant with the streamwise direction whereas higher blockage ratio flow(Br=65%) has a positive peak in the inner layer and negative magnitudes in the free surface layer.This demonstrates higher blockage ratio develops secondary currents downstream of trash rack.• For both the Reynolds number and blockage ratio scenarios, the peak observed normalized Turbulent Kinetic Energy(TKE) occurred immediately downstream of the trash rack, and with the increment of longitudinal distance downstream of the trash rack, it follows a decreasing trend.

Figure 1 .
Figure 1.Flume's definition sketch with vertical screen

Figure 2 .
Figure 2. Plan view for ADV measurement locations upstream and downstream of vertical screen

Figure 3 .
Figure 3.Effect of Re and Br on the vertical profiles of normalized time-averaged streamwise velocity(u/u ∞ ) along the central axes at both upstream and downstream of the trash rack.

Figure 4 .
Figure 4. Effect of Re and Br on the vertical profiles of normalized streamwise turbulence intensity(σ u /u ∞ ) along the central axes at both upstream and downstream of the trash rack.

Figure 5 .
Figure 5.Effect of Re and Br on the vertical profiles of normalized streamwise Reynold normal stress(σ uu /u 2 ∞ ) along the central axes at both upstream and downstream of the trash rack.

Figure 6 .
Figure 6.Effect of Re and Br on the vertical profiles of normalized Reynold shear stress(τ uw /u 2 ∞ ) along the central axes at both upstream and downstream of the trash rack.

Figure 7 .
Figure 7. Effect of Re and Br on the vertical profiles of normalized Turbulent kinetic energy(k/u 2 ∞ ) along the central axes at both upstream and downstream of the trash rack.

Table 1 .
The hydraulic and physical characteristics of all conducted experiments.