Calculation of capacity of spillway № 2 Boguchanskoye HPP with free water overflow

. The article considers a variant with the operation of spillway No. 2 of the Boguchanskaya HPP as the main spillway structure for the period of temporary operation of the hydroelectric complex. In the process of developing options for skipping construction costs, a calculation was made of the throughput with a free overflow through a flat threshold at the level of 167.0m at the FSL=175m and forcing the UVB to the level of 185.0 m with the damping of the flow energy in the water well. The task of the calculations is to obtain the discharge characteristics of the considered spillway option with the calculated flood hydrograph with a probability of 0.2%. At the same time, based on the throughput capacity of the spillway No. 1, the dependence of the turbine flow rate and the water depth in the downstream, as well as the transformation of the flood of a given probability, the estimated flow rate is 5500 m3/s, the maximum head H=18 m (determining) at a minimum threshold level of 167.0 m. Weir refers to weirs with a wide threshold. The throughput capacity of the spillway No. 2, operating in the free overflow mode, was determined. The change in the lateral compression coefficient depending on the head for the middle and outer working spans is considered. The outlines of free-falling jets behind the culverts operating in the free overflow mode are obtained, which makes it possible to refine the outlines of the side walls of the spillway.


Introduction
In developing options for skipping construction costs during the temporary operation of the structures of the Boguchanskaya HPP, a variant with the operation of spillway No. 2 as the main spillway structure was considered.
In this variant, the capacity of the spillway No. 2 was calculated with a free overflow through a flat threshold at the level of 167.0m at NHL=175 m and forcing the UPL to the level of 185.0m.It was considered, among other things, the damping of the energy of the flow in the water well.
These calculations aim to obtain the consumption characteristics of the considered option for the period of temporary operation of the hydroelectric complex.
-Throughput capacity of the spillway No. 1 Q1=f(upstream level), presented in graphical form in fig. 3.
-Taking into account fluctuations in water levels in the downstream with a change in the level of the upstream and the number of operating culverts of spillways No. 1 and No. 2 and HPP units, the flow rate of one turbine can be described by the equation: -Dependence of the water depth in the downstream pool h DSL on the flow rate: -The maximum discharge of the hydroelectric complex is Qр=0.2%=11700m3/s, taking into account the transformation of the flood with the probability of Р=0.2%, at which 5500 m3/s is supposed to pass through spillway No. 2.

Calculation of the capacity of spillway № 2 with free overflow of water
The operation of spillway No. 2 during the period of temporary operation provides for a rise in the level of the upper pool of the reservoir to provide the possibility of partial transformation of the flood.According to the layout of the culverts of spillway No. 2, the maximum head is H = 18 m with a minimum threshold of 167.0 m.This head is decisive for the capacity of spillway No. 2 and assessing the safety of its operation in the downstream.
In various variants of the culvert layout, the minimum length of the horizontal threshold is C min =38.0 m, which corresponds to its relative length C min /H=38/18=2.11.When the ratio C/H>2 according to [1 -5], the weir belongs to the weirs with a wide threshold.
The flow through the weir with a wide threshold is determined by the formula: Following [1 -3] with the headwater area F>4bH, the effective head is assumed to be equal to the geometric head.For the case under consideration, when spillway No. 2 operates with the entire front, for the central hole, we have even for the maximum head F / (b*H) = 15 * (185-136) / (10 * 18) = 4.08> 4, where the channel mark in front of the pressure face spillway No. 2 is taken equal to 136.0 m.
Consequently, in the entire range of possible modes of operation of spillway No. 2 during the period of temporary operation, when determining the throughput, one can neglect the velocity head of the flow in the upstream.
The spillway lateral compression coefficient, according to [1], is determined by the following relationship: where: is estimated width of the headwater; is coefficient taking into account planned flow compression; is coefficient taking into account the protrusion of the upstream side of the dividing bulls; The estimated width of the headwater Bc depends on the number and combination of working spans.Depending on the order of opening the gates, the same working span may have a different throughput.To eliminate this uncertainty, in further calculations, we take as a priority the opening of the middle span and then the successive connection of the work of the spans located on the right and left.Thus, the gate opening formula will look like this: 3-4-2-5-1, where the count of spans starts from the power plant building.
When the spillway operates with the entire front, for middle spans Bc = b+0.5(t 1 +t 2 )=10+0.5(6+4)=15m.For the outer working spans, it becomes a sufficiently large value at which the ratio b/ Bc <0.2, which is taken as the minimum value in calculations.
Following the accepted values, we have b/ Bc =10/15=0.67for the average working Finally, taking into account the accepted values of the parameters, we have: -for medium working spans: On fig. 4 shows the change in the lateral compression ratio depending on the head.Taking into account (10)  When the spillway operates with the entire front, the capacity of 2 ... 4 spans will be determined by dependence (12), and the 1st and 5th spans by dependence (13).
On fig. 5 shows the dependence of the capacity of the spillway No. 2 when working with the entire front under pressure.In the same place, curves of the throughput of the spillway are plotted, depending on the combination of the opening of spans.The shutter opening sequence is as follows: 3-4-2-5-1.As seen from fig. 5, the maximum consumption of the construction period is 5500 cubic meters.m/s can be passed at a head of 17.5 m, which corresponds to the level of the threshold of the culvert at 167.5 m at UPL =185.0mcorresponds to the mark of the threshold of the culvert 167.5 m.

Studying the parameters of free-falling flow jets
The main purpose of studying the flow parameters at the waterhole is to determine the depth and speed of the outlet flow, which ultimately determine the degree of channel deformation in the downstream and its danger to the stability of the end of the spillway.
Further calculations are made for the conditions of skipping the maximum construction flow of 5500 cubic meters m/s.
The flow parameters in the compressed section in the area where the jet falls on the spillway surface of the spillway determine the nature of the conjugation of flows and the hydraulic situation in the downstream of the spillway No. 2. In the design variant of the spillway with a water well, a hydraulic jump will occur, the state of which will be determined by the ratio of the value of the second conjugate depth and the depth of the water well.In the variant of the spillway design with a jet discharge, a backwater curve will be formed at the water break, which will determine the distance of the jet discharge to the downstream.

Mode with free overflow of water through the threshold
The depth of the flow at the outlet of a culvert with a free overflow of water operating according to the weir scheme with a wide threshold can be determined from the graph in Fig. 6 [1], depending on the flow coefficient.Within the threshold relative length C/H=2….4,the discharge coefficient 34 .0 | m , which corresponds to the relative depth h/H=0.495.However, in [1], an impersonal depth is given without considering the real picture of the outflow.
In reality, the depth of the outlet flow depends on the relative length of the C/H threshold (or the relative head H/C).This depth is affected by the position of the tailwater level since it determines the shape of the longitudinal section of the jet emerging from the span.At a high level of the tailwater in the end section of the spillway, the flow is backed up, which acquires a downward curvature.The resulting centrifugal pressure reduces the speed of the flow, and its depth grows.With a low position of the downstream level (DSL), the flow in the outlet section of the spillway takes the form of a waterfall with a free fall of the jet, in which centrifugal forces are directed against gravity, which leads to an increase in flow velocities and a decrease in depth.
On fig.6 shows the data of modeling studies on a scale of 1:40 of the surface spillway of the Nizhnekamskaya HPP operating according to the spillway scheme with a wide threshold in the range of relative pressures Н/С=0.014…0.289.At an average flow velocity Vo in the end section of the threshold of the culvert, the jet trajectory is described by the equation: where ‫ݔ‬ is the horizontal distance from the outlet section of the culvert; ‫ݖ‬ is the vertical distance from the flow axis in the outlet section of the culvert to the axis of the considered flow section.
With such a system for describing the center of mass of the jet descending from the threshold of the culvert, in the coordinates of the reference X from the Considered Axis of Section (CAS) and the absolute marks Z of the vertical coordinate system, the equations for the shape of the upper surface of the incident jet will take the form: and the lower surface of the jet: where ℎ is the thickness of the jet in the normal section; zc is the tangent of the inclination angle to the tangent's horizon to the jet axis at the point with coordinates x, z.
The jet thickness h is determined from the continuity equation, in which the velocity is calculated taking into account the height of the fall: Value zc determined from the equation (6.4): Equations ( 16)…(19) were used to construct the longitudinal profiles of the jet at the culvert of spillway No. 2.
On fig.7 shows the profile of the jet at spillway No. 2 for the construction period with a water well with a free overflow of water over the threshold.

Results and Discussion
Calculating the parameters of free-falling jets allows you to set the height of the side walls of the spillway.
In the variant with a water well, the jet falls onto the drain surface at a distance of 77 m from the CAS.
In the variant with jet ejection, the jet falls onto the drain surface at a distance of 70 m from the CAS for the free overflow mode.
As can be seen from Figures 7 and 8, in the variant of spillway No. 2 with a free overflow, there is a need to increase the height of the side walls by 6…7 m in the range of elevations of 179.0…154.5 m [4][5][6][7][8][9][10]. 2. The outlines of free-falling jets behind the culverts operating in the free overflow mode are obtained, which make it possible to refine the outlines of the side walls of the spillway.The height of the side walls along the normal to the spillway surface of the spillway must be at least 15.0 m.

Fig. 1 .Fig. 2 . 2022 Fig. 3 .
Fig. 1.Longitudinal section of spillway No. 2 with combined options structures for the period of temporary operation of the hydroelectric complex

K
are coefficients taking into account the rounding of the vertical edges of the separating bulls; с в =167.0-136.0=31.0m -the height of the threshold from the upper pool.

K
spans and b/ Bc =0.2 for the extreme working spans.The coefficient is determined by the dependence: of Conferences 365, 03023 (2023) https://doi.org/10.1051/e3sconf/202336503023CONMECHYDRO -2022Thus, for the average working spans, we get the first approximation can be determined by the dependence: are coefficients that take into account the rounding of the vertical edges of the dividing bulls are determined by the dependence: the radius r=1.0m of the rounding of the vertical edges of the separating bulls, we obtain

2022 Fig. 4 .
Fig. 4. Dependence of the lateral compression ratio on pressure at the threshold of spillway No. 2

Fig. 5 .
Fig. 5.The dependence of the capacity of the spillway No. 2 from pressure and combination of working spans

Fig. 6 .
Fig. 6.Dependence of the relative depth h/H at the end of the weir sill on the relative head H/C

Fig. 7 .
Fig. 7. Longitudinal profile of spillway No. 2 for the construction period with a water well with free overflow of water over the threshold On fig. 8 shows the profile of the jet at spillway No. 2 during the construction period with jet discharge with free overflow of water over the threshold.

Fig. 8 .
Fig. 8. Longitudinal profile of the spillway No. 2 during the construction period with jet throw with free overflow of water over the threshold

E3S 2022 Conclusions 1 .
Web of Conferences 365, 03023 (2023) https://doi.org/10.1051/e3sconf/202336503023CONMECHYDRO -The throughput capacity of the spillway No. 2 operating in the free overflow mode has been determined.The capacity depending on the head can be determined by expression (12) for medium spans and (13) for extreme spans from fig. 5.