The application of a minimum specific energy concept for a fish ladder design

WARSAW UNIVERSITY OF TECHNOLOGY Index 351733 FACULTY OF CIVIL ENGINEERING COMMITTEE FOR CIVIL AND WATER ENGINEERING POLISH ACADEMY OF SCIENCES ISSN 1230-2945 DOI: 10.24425/ace.2022.140185 ARCHIVES OF CIVIL ENGINEERING Vol. LXVIII ISSUE 1 2022 ©2022. Michał Kubrak, Błażej Smoliński, Jaromír Riha, Apoloniusz Kodura, Paweł Popielski, Kamil Jabłoński. pp. 555 –568 This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License(CCBY-NC-ND4.0,https://creativecommons.org/licenses/by-nc-nd/4.0/), whichpermits use, distribution,andreproduction in any medium, provided that the Article is properly cited, the use is non-commercial, and no modifications or adaptations are made. Research paper The application of a minimum specific energy concept for a fish ladder design Michał Kubrak1, Błażej Smoliński2, Jaromír Riha3, Apoloniusz Kodura4, Paweł Popielski5, Kamil Jabłoński6 Abstract: Structural solutions in terms of fish ladders and the use of natural materials to construct them often raise concerns regarding the possibility of using the standard calculation methods. The fish ladder being designed on the Wisłok river consists of three pools, separated from each other by baffles made of rock boulders. The purpose of this study was to analyze water surface profiles for fish ladder at specific values of flow rates. The paper presents the results of hydraulic calculations under the conditions of constant flow rate based on the concept of a minimum specific energy. According to this method, water flow through boulders is critical. Thus, it does not take into account head losses, which are hard to estimate and which are the integral part of typical calculation methods, e.g. the use of equations to determine the flow rate of a weir. An additional advantage of this method is that there is no need to assume the flow pattern of one specific weir. Verification calculations of the water depths were conducted using the HEC–RAS software, under an assumption of an one-dimensional steady water flow. Water depths in the fish ladder, calculated using both methods, were similar, despite the adopted different calculation concepts, and can be used in ichthyologic analyses. Keywords: fish ladder, dam, specific energy, critical flow 1PhD., Eng., Warsaw University of Technology, Faculty of Building Services, Hydro and Environmental Engineering, ul. Nowowiejska 20, 00-653 Warsaw, Poland, e-mail: [email protected], ORCID: 0000-00018097-3803 2PhD., Eng., Warsaw University of Technology, Faculty of Building Services, Hydro and Environmental Engineering, ul. Nowowiejska 20, 00-653 Warsaw, Poland, e-mail: [email protected], ORCID: 0000-00033662-2007 3Prof., DSc., PhD, Eng., Brno University of Technology, Faculty of Civil Engineering, Veveří 331/95, 602 00 Brno, Czech Republic, e-mail: [email protected].cz, ORCID: 0000-0002-1362-5769 4DSc., PhD., Eng., Warsaw University of Technology, Faculty of Building Services, Hydro and Environmental Engineering, ul. Nowowiejska 20, 00-653 Warsaw, Poland, e-mail: [email protected], ORCID: 0000-0001-7040-1625 5DSc., PhD., Eng., Warsaw University of Technology, Faculty of Building Services, Hydro and Environmental Engineering, ul. Nowowiejska 20, 00-653 Warsaw, Poland, e-mail: [email protected], ORCID: 00000002-5425-5821 6M.Sc., Eng., Energoprojekt-Warszawa SA, Al. Niepodległości 58, 02-626 Warsaw, Poland, e-mail: kjablon- [email protected] 556 M. KUBRAK, B. SMOLIŃSKI, J. RIHA, A. KODURA, P. POPIELSKI, K. JABŁOŃSKI 1. Introduction Fish ladders enable the migration of fish and other aquatic organisms through structures partitioning a riverbed. Therefore, fish ladders are a key element in improving the ecological state of flowing waters [1]. Two fish ladder types can be distinguished – purely technological devices (pool and slot fish ladders, fish locks, fish lifts) and ones that imitate the natural environment (bypass channels, bed ramps). Regardless of the fish ladder type, it is crucial to check the values of hydraulic parameters (water depth and flow velocities) and refer them to the values that should correspond to an effective fish pass. Evaluating fish ladders in terms of satisfying appropriateichthyologicalrequirementsissignificantlychallenging,bothwhenengineering new ones and analysing already operating devices. [2] demonstrated that existing fish ladders often do not function correctly. Measuring and determining the aforementioned hydraulic parameters of fish ladders is the subject of numerous measurements, both in the field [3], [4], as well as on a laboratory scale [5,6]. Software use also plays an important role in analysing the hydraulic flow rate parameters in fish ladders. Such CFD software as FLOW 3D [7,8], DualSPHysics [9] and programmes for hydraulic computations in open channels (HEC–RAS) are used for this purpose [10]. The objective of this study was to calculate the water table elevations in the planned fish ladder on the Wisłok river at selected values of discharge. The depths, at known discharge in fish ladder pools were calculated based on an assumed minimum specific energy in the section with large-size boulders. The suggested method enabled to simply estimate water depths in the planned fish ladder which allows to calculate values of water flow velocity. Thus-calculated water depths were compared to the depths calculated using the HEC–RAS software for a one-dimensional steady flow. 2. Characteristics of the designed fish ladder The Wisłok riverbed, in the cross-section of the designed fish ladder, is horizontal and has a width of 35 m. Across the width of a river, a 1.30 m high fixed-crest dam is located. Water flowing over the top of the fixed-crest dam is passed into a reinforced concrete drop structure, in which hydraulic jump is formed, and then water flows with a subcritical flow. The designed fish ladder is to be located at 58.500 km of the Wisłok river. The fish ladder imitating natural habitat and hydraulic conditions characteristic of the Wisłok waters was designed in the form of a cascading rapids stretching along the entire riverbed width. The fish ladder was to consists of four rows of boulders, forming three pools located downstream of the weir. The pools were separated with baffles made of four rows of 1.0÷1.5 m high rock boulders. Each baffle was equipped with fish migration slots of varied width and spacing. The designed solution is shown in Figs. 1and 2. THE APPLICATION OF A MINIMUM SPECIFIC ENERGY CONCEPT. . . 557 Fig. 1. Diagram of the designed fish ladder – top view Fig. 2. Diagram of the designed fish ladder – longitudinal section along the axis Introducing boulders into the riverbed (Fig. 2) will cause damming up and change the water flow conditions. Rock heights, their number and slot widths for each boulder row are shown in Table 1. Table 1. Dimensions of boulders in individual rows Boulder row Boulder height 𝑝[m] Number of slots 𝑛[–] Slot width 𝐵[m] 1st 1.5 7 1.0 2nd 1.0 6 1.0 3rd 1.0 5 1.6 4th 1.0 6 2.2 According to the information in an ichthyological expertise [11] developed for the purposes of the fish ladder being designed, it should satisfy the following requirements regarding the minimum depths in individual pools, at a discharge of 𝑄=2.72 m3/s for individual fish species: 0.4 m for brown trout, 0.45 m for grayling, chub, roach and dace, 0.5 m for barbel, bream, perch, pike, salmon and sea trout and 0.8÷1.0m for sturgeon. 558 M. KUBRAK, B. SMOLIŃSKI, J. RIHA, A. KODURA, P. POPIELSKI, K. JABŁOŃSKI 3. Hydraulic calculations Water flow depths were calculated for two variants of different flow patterns. In the first variant, the discharge is so low that the water flows through the slots between the boulders. Whereas in the second case, at higher values of discharge, water flows through the slots and over the boulder crest. In the calculations, a rectangular shape of boulders and slots was assumed. It should be noted, that the exact shape of the boulders is not known. During the design process, only height of boulders was assumed. The calculations were conducted based on the concept of a minimum specific energy [12]. According to this method, water flows for given discharge through the slots, with a minimum energy (the flow is critical). Thus, it does not take into account head losses, which are hard to estimate and which are the integral part of typical calculation methods, e.g. the use of equations to determine the flow rate of a weir. The local losses, such as those in a flow over boulders, occur in short length of the channel. In such short lengths, the losses due to shear at the boundaries are very small and can be neglected. An additional advantage of this method is that there is no need to assume the flow pattern of one specific weir. The use of minimum specific energy concept provides conceptual simplicity, however this method has some limitations. It is not suitable if the flow through the slots or over the boulders is submerged. Thecalculationswere conductedfor5differentvaluesofdischarge(2.72m3/s,4.10m3/s, 10.70 m3/s, 16.86 m3/s and 32.80 m3/s), for which water depths at specific cross-sections were earlier measured in the riverbed without the boulders. Depth values calculated using the HEC–RAS software, under the assumption of 1D steady flow were used to verify calculated water depths in pools. 3.1. I Variant of flow pattern – flow in the slots At low values of discharge, water in the fish ladder will overcome rows of boulders flowing through the slots between such rows. The discharge for one slot is equal to: (3.1) 𝑄= 𝑄𝑡 𝑛 where: 𝑄– discharge in a single slot, 𝑄𝑡– total discharge, 𝑛– number of slots for a given row of boulders. It was assumed, that the water flows through the slots with a minimum specific energy. The general equation for critical flow is [13]: (3.2) 𝐴3 𝐵 = 𝛼𝑄2 𝑔 where: 𝐴– cross-sectional area of the water stream for critical flow conditions, 𝐵– slot width, 𝛼– Saint–Venant coefficient (it was assumed that 𝛼=1). Water depth in a single slot was calculated using the critical flow equation (3.2) – Fig. 3. Therefore, water depth in a single slot is a critical depth – Fig. 4. The critical depth location presented in Fig. 4requires additional comment. In order to keep critical depth across the boulder slots, the boulder’s crest should be of sufficient length THE APPLICATION OF A MINIMUM SPECIFIC ENERGY CONCEPT. . . 559 Fig. 3. Scheme of I variant of flow pattern – top view Fig. 4. Scheme of I variant of flow pattern (𝑣0) – cross-section (as in broad-crested weirs). In fact, the exact location of the critical depth is unknown and can’t be determined analytically. However, in the presented method, the unsubmerged water flow is assumed and the location of the critical depth does not influence the value of water depth 𝐻. In a cross-sectional bed, the critical depth ℎ𝑐is calculated from the equation (3.2) rearranged into: (3.3) ℎ𝑐=3 √︄𝛼𝑄2 𝑔𝐵2 At critical flow, the depth is equal to twice the kinetic energy head and therefore twothirds of the critical specific energy. Neglecting the velocity head (𝑣≈0), it can be assumed that water depth upstream of a given row of boulders 𝐻is approximately equal to: (3.4) 𝐻= 3 2ℎ𝑐 The aforementioned method was used to estimate water depth upstream of each row of boulders. The critical depth, previously calculated from relationship (3.3) is the water depth in the slot, at known water flow rate. 560 M. KUBRAK, B. SMOLIŃSKI, J. RIHA, A. KODURA, P. POPIELSKI, K. JABŁOŃSKI 3.2. II Variant of flow pattern – flow between the slots and over the boulders When the water depth upstream of the boulders, calculated from the equation (3.4) is higher than the boulder height, water flows not only through the slots but also over the boulder crest. A scheme of water flow in the II variant is presented in Fig. 5. Fig. 5. Scheme of II variant of flow pattern – top view Total discharge through the fish ladder is the sum of discharge in 𝑛+1rows of boulders 𝑄1and in 𝑛slots 𝑄2: (3.5) 𝑄𝑡=(𝑛+1)𝑄1+𝑛𝑄2 Critical water flow occurs in the slots and over the boulders – Fig. 6. Fig. 6. Scheme of II variant of flow pattern (𝑣≈0) – cross-section As in the case of variant I, assuming that the flow is unsubmerged, the exact location of the critical depth is unknown and it does not affect the calculated value of 𝐻1. By transforming the critical flow equation (3.2) to calculate 𝑄1and 𝑄2, one obtains: (3.6) 𝑄1=√︄𝑔 𝛼 𝐴3 1 𝐵1 where: 𝐴1– cross-sectional area of the water stream flowing over boulders in 𝑛+1sections, 𝐵1– water table width for the stream of water flowing over the boulders and: (3.7) 𝑄2=√︄𝑔 𝛼 𝐴3 2 𝐵2 THE APPLICATION OF A MINIMUM SPECIFIC ENERGY CONCEPT. . . 561 where: 𝐴2– cross-sectional area of the water stream flowing between 𝑛slots, 𝐵2– water table width for the stream of water flowing between the slots. 𝐴1=ℎ𝑐1𝐵1 (3.8) 𝐴2=ℎ𝑐2𝐵2 (3.9) Depth 𝐻1is related to boulder crests, while 𝐻2to pool bottom: 𝐻1= 3 2ℎ𝑐1 (3.10) 𝐻2= 3 2ℎ𝑐2 (3.11) i.e.: (3.12) 𝐻2=𝑝+𝐻1 where: 𝑝– boulder height. Then, the total discharge through the fish ladder is equal to: (3.13) 𝑄𝑡=(𝑛+1)v u u u u t𝑔 𝛼2 3(𝐻2−𝑝)𝐵13 𝐵1 +𝑛v u u u u t𝑔 𝛼2 3𝐻2𝐵23 𝐵2 The calculations, due to the implicit form of equation (3.13) were conducted using the method of successive approximations. Water depth upstream of the boulders 𝐻2was calculated for a known value of discharge 𝑄𝑡using equation (3.13), followed by calculating water depth in the slot based on equation (3.11). 3.3. Water depth calculation results The water depths calculated using the described method are presented in Table 2. 𝐻denotes water depths upstream of a given row of boulders, while ℎ– water depths in the slot. Table 2. Calculated values of water depths 𝑄[m3/s] 1st boulder row 2nd boulder row 3rd boulder row 4th boulder row 𝐻[m] ℎ[m] 𝐻[m] ℎ[m] 𝐻[m] ℎ[m] 𝐻[m] ℎ[m] 2.72 0.37 0.25 0.41 0.28 0.34 0.23 0.24 0.16 4.10 0.49 0.33 0.54 0.36 0.45 0.30 0.32 0.21 10.70 0.93 0.62 1.02 0.68 0.85 0.57 0.61 0.41 16.86 1.26 0.84 1.17 0.78 1.09 0.72 0.82 0.55 32.80 1.71 1.14 1.42 0.95 1.35 0.90 1.19 0.79 562 M. KUBRAK, B. SMOLIŃSKI, J. RIHA, A. KODURA, P. POPIELSKI, K. JABŁOŃSKI Table 2underlines depth values for which water depth upstream of the first row of boulders, calculated using the described method, was lower than the depth upstream of the second row. Such calculation results show that for flow rates of: 2.72 m3/s, 4.10 m3/s and 10.70 m3/s, the assumption on the critical water flow in slots within the first boulder row was incorrect and leads to non-physical results. The first row of boulders has a decisive influence on water damming for greater flow rates (16.86 m3/s and 32.80 m3/s). The fact that the first row of boulders is higher than the other ones is of additional significance. 3.4. Hydraulic jump downstream the weir Hydraulic jump may be formed in a fish ladder pool downstream of a fixed-crest dam. For this reason, basic hydraulic jump parameters were calculated, i.e., its conjugate depths and length. The conjugate depth upstream of hydraulic jump ℎ1was calculated using the energy equation: (3.14) ℎ3 1−𝐸0ℎ2 1+𝛼𝑣2 1 2𝑔 =0 where: ℎ1– conjugate depth upstream of the hydraulic jump, 𝐸0– energy upstream of the weir, 𝑣1– water flow velocity within the section of the conjugate depth upstream of the hydraulic jump. The conjugate depth downstream of the hydraulic jump ℎ2was calculated from: (3.15) ℎ2=−ℎ1 2+√︄ℎ2 1 4+2𝑣2 1ℎ1 𝑔 Hydraulic jump length 𝐿was estimated using the Wójcicki empirical formula [14]: (3.16) 𝐿=8−0.05ℎ2 ℎ1(ℎ2−ℎ1) The calculations were conducted for discharges at known water depth upstream of the fixed-crest dam, i.e., for: 16.86 m3/s and 32.8 m3/s. For a discharge of 2.72 m3/s, the hydraulic jump does not form in the first pool. In each of the cases, the conjugate depth downstream of the hydraulic jump calculated for the aforementioned values of discharge was significantly lower than the water depth upstream of the boulders calculated previously. The length of hydraulic jump was shorter than the distance of the first boulder row from the fixed-crest dam. This means that the hydraulic jump will not affect the water depth in individual fish ladder pools. 4. HEC–RAS software computations The verification computations were conducted using the HEC–RAS software [15]. It enables calculating a steady, 1D water flow and is widely used in engineering practice. THE APPLICATION OF A MINIMUM SPECIFIC ENERGY CONCEPT. . . 563 The first stage of HEC–RAS computations involved modelling the current riverbed condition, i.e., taking into account measured bathymetric sections with their locations and the existing fixed-crest dam (58.500 km) with a crest elevation of 190.50 m a.s.l. The fixedcrest dam was modelled as an “Inline Structure”, which is an element dedicated to such applications. This model did not include boulders in the river bed (Fig. 7). Fig. 7. Computational model of existing river bed generated in HEC–RAS Calibration of computational model was done by adjusting values of the roughness coefficient, in order to obtain the result of calculation that match the results of hydrological measurements. The calibration was conducted for a measured discharge of 𝑄=32.80 m3/s and corresponding measured water table elevations. The differences between measured water table elevations and the HEC–RAS computation results do not exceed 0.07 m. A comparison of the calculated and measured water table profile in the riverbed without the fish pass is shown in Fig. 8. Fig. 8. Calculated and measured water surface profile The second stage of the calculations included the new elevation of the fixed-crest dam (190.60 m a.s.l.) and the fish ladder structure with resulting bed geometry and boulder arrangement (Fig. 9).