CN106948319B - A kind of fluted non-horizontal bottom plate of band falls energy dissipater and the method for bank stiling basin - Google Patents

Abstract

The invention relates to an energy dissipator and method for a sill stilling pool with a non-horizontal floor with grooves, comprising: a sill arranged at the bottom of an inclined flood discharge ramp, and the sill and the upstream building pass through an arc or a straight line Smooth connection; grooves are set at the bottom of the sill, the upstream trough edge of the groove is flush with the sill, the downstream trough edge is inclined to connect with the facing water surface of the positive slope, the top of the positive slope is horizontal, and the backwater surface of the positive slope is in a straight line or curve with the downstream channel Smooth connection, the groove and the drop sill form a stilling pool, and the bottom of the stilling pool is horizontal. In the present invention, a groove-shaped bottom plate is arranged under the sill and before the water flow is reattached, so as to increase the flow space of the vortex under the sill, thereby increasing the pressure in the central point area of the vortex, preventing cavitation of the water flow, and avoiding impact on the side wall of the stilling pool cavitation damage. Since the amount of earthwork for the groove and the front slope is not large, only some engineering points of the original design need to be slightly modified, and the present invention can be used in new constructions, and can also be applied to existing underflow energy dissipation projects at a lower cost. transformation.

Description

A kind of energy dissipator and method for falling sill stilling pool with grooved non-horizontal floor

technical field

The invention relates to an energy dissipator and method for a non-horizontal bottom plate with a groove and a sill stilling pool, which is a hydraulic facility and method, and is a method for effectively reducing cavitation caused by low pressure on the side wall of the stilling pool Facilities and methods for cavitation damage and reduction of impact pressure in reattachment point areas.

Background technique

As one of the main energy dissipation methods for flood discharge, underflow energy dissipation can adapt to high, medium and low water heads, has stable flow pattern, good energy dissipation effect, strong adaptability to geological conditions and tail water level changes, and slight flood discharge atomization and other advantages. Especially under the concept of eco-environmental friendliness, underflow energy dissipation, an energy dissipation method with low environmental sensitivity, has been increasingly valued and applied in the construction of high dams. For the high dam of about 160m, due to the limitation of the environment and site conditions, the bottom current energy dissipator was selected. The discharge flow of these projects has the characteristics of high water head and large single-width flow. If the traditional bottom flow energy dissipation is adopted, the maximum bottom flow velocity will exceed 40m/s, and it is difficult to ensure the safe operation of the stilling basin. In order to solve the problem of excessive flow velocity at the bottom of these engineering stilling pools, some conventional bottom flow energy dissipaters adapted to high water head and large unit width flow have emerged one after another. There is a water flow reattachment area in the conventional drop sill bottom flow energy dissipator, where the impact pressure of the water flow is relatively high, which is not conducive to the stability of the bottom plate.

Contents of the invention

In order to overcome the problems of the prior art, the present invention proposes an energy dissipator and a design method for a non-horizontal bottom plate falling sill stilling pool with grooves. The energy dissipator and design method described above are optimized on the basis of the conventional energy dissipator of the bottom flow of the falling sill, and multiple control points are carefully prepared to reduce the range of the low-pressure area in the center of the vortex and avoid the impact of cavitation water flow on the side wall of the stilling pool. Cavitation damage, and effectively reduce the impact pressure of the water flow reattachment area.

The object of the present invention is achieved in the following way: an energy dissipator with a grooved non-horizontal bottom sill stilling pool, comprising: a sill arranged at the bottom of the inclined spillway ramp, the sill and the upstream The buildings are connected smoothly through arcs or straight lines; grooves are provided at the bottom of the falling sill, the upstream groove edge of the groove is flush with the falling sill, the downstream groove edge is inclined to connect with the facing surface of the positive slope, and the top of the positive slope is horizontal. The backwater surface of the positive slope is smoothly connected with the downstream channel by a straight line or a curve, the groove and the drop sill form a stilling pool, and the bottom surface of the stilling pool is horizontal.

A design method of the above-mentioned energy dissipator, the steps of the method are as follows:

The steps of conventional sill design: determine the height d of the sill according to the hydraulic parameters of the incoming water flow, and the bottoming position of the hydraulic jump after the incoming water flow passes the sill, and determine the length L and hydraulic jump of the hydraulic jump according to the bottoming position of the hydraulic jump Angle α with the bottom plate;

Steps for determining the downstream edge of the groove: the length l from the sill to the downstream edge of the groove is: 0.7 to 0.9 times the hydraulic jump length, namely: l = (0.7 to 0.9) L;

The step of trial calculation of the groove depth: determine the trial length l ₁ of the bottom of the groove according to Δd , the trial length of the bottom of the groove is: l ₁ =1- Δd ; where Δd is the trial depth of the groove, the Trial calculation groove depth is either drawn up during preliminary design, or revised and determined according to the evaluation results;

Steps for calculating the pressure at the vortex center point: Calculate the vortex center pressure of the groove after falling the ridge according to the following formula:

In the formula: P ₀ —pressure at the center point of the eddy current, ρ—fluid density, g—gravitational acceleration, c—flow velocity attenuation coefficient, c= f (V ₁ , d, h ₀ ), V ₁ — is the flow velocity on the ridge, d — Height of drop ridge, h ₀ - water depth above ridge, b - short axis of elliptical vortex, b=d/2, k - ratio of major axis to short axis of elliptical vortex, k=a/b, a - elliptical vortex The major axis of the vortex, a = l ₁ /2, h ₂ - the downstream water depth above the bottom plate of the stilling basin;

Judgment and correction steps: Judging whether the trial calculation groove depth Δd is appropriate based on the pressure P ₀ of the vortex center point, if P ₀ >0, then reduce Δd , if P ₀ <0, then increase Δd , and return to " Steps for Trial Calculation of Groove Depth"; if P ₀ =0, enter the next step;

Steps to determine the shape of the back water surface of the front slope: determine the angle β between the back water surface of the front slope and the horizontal line and the length Lr of the back water surface of the front slope, β = (0.5~1.0) α , Lr=(1~2) h ₀ .

The beneficial effects produced by the present invention are: the present invention sets a bottom plate in the shape of a groove under the sill and before the water flow is reattached to increase the flow space of the vortex under the sill, thereby increasing the pressure in the center of the vortex and preventing cavitation of the water flow , to avoid cavitation damage to the side wall of the stilling pool. At the same time, a positive slope equal to the water inflow injection angle is set in the area before and after the water flow reattachment point to reduce the impact pressure in the water flow reattachment point area and avoid excessive impact pressure causing damage to the bottom plate of the stilling pool. Since the amount of earthwork for the groove and the front slope is not large, only some engineering points of the original design need to be slightly modified. Therefore, the present invention can be used in new construction projects, and can also be applied to existing bottom flow consumption at a lower cost. The transformation of energy dissipators is beneficial to improve the operational reliability and safety of underflow energy dissipators.

Description of drawings

The present invention will be further described below in conjunction with drawings and embodiments.

Fig. 1 is the elevation view of conventional drop sill type underflow energy dissipator;

Fig. 2 is the elevation view of the energy dissipator described in Embodiment 1 of the present invention;

Fig. 3 is a flow velocity distribution diagram of the swirling flow described in Embodiment 1 of the present invention;

Fig. 4 is a schematic diagram of the flow state of a conventional drop;

Figures 5-8 are schematic diagrams of the vortex streamlines behind the ridge in the four numerical simulation results;

Fig. 9 is a flow chart of the method described in Embodiment 2 of the present invention.

Detailed ways

Embodiment one:

The conventional drop sill type bottom flow energy dissipator, as shown in Figure 1, is to set a certain height drop sill 100 at the head of the stilling basin (see Figure 1), and connect it with the stilling basin on the horizontal floor. This kind of energy dissipator diverts the high-speed water flow entering the stilling tank away from the bottom area, thereby reducing the flow velocity at the bottom and protecting the bottom plate of the stilling tank. The characteristics of conventional sill bottom flow are: first, the effect of water flow through the sill, and there is a shearing effect between the water flow and the water flow on both sides of the high-speed jet; Under the conditions of high flow velocity in the pool or low downstream water level, even a negative pressure zone appears; third, the flow velocity at the bottom of the water flow is lower than that of the traditional bottom flow, but there is a water flow reattachment area, and the impact pressure of the water flow in this area is relatively high, which is not conducive to the stability of the bottom plate.

There are also more prominent problems in the conventional bottom flow. First, the vortex flow structure under the bottom flow is the inherent flow property caused by the sudden change in the size of the bottom flow in the conventional bottom flow. That is, the central area of the vortex is the flow field. In the obvious low-pressure area in the center, there may even be negative pressure; second, the impact pressure near the reattachment point of the water flow is relatively large, which is not conducive to the stability of the bottom plate of the stilling pool. How to avoid the risk of damage to the side wall of the stilling pool caused by cavitation and cavitation in the low-pressure area and reduce the impact pressure in the area where the water flow reattaches is a concern of hydraulic design and researchers.

This embodiment is an energy dissipator with a grooved non-horizontal bottom plate falling sill stilling pool, as shown in FIG. 2 . This embodiment includes: a sill arranged at the bottom of the inclined flood discharge ramp, and the sill is smoothly connected with the upstream building through an arc or a straight line; the bottom of the sill is provided with a groove, and the edge of the groove upstream It is flush with the falling sill, the slope of the downstream groove is connected to the water facing surface of the positive slope, the top of the positive slope is horizontal, the back surface of the positive slope is smoothly connected with the downstream channel in a straight line or a curve, and the groove and the falling sill form a stilling force pool, the bottom surface of the stilling pool is horizontal.

In this embodiment, on the basis of the conventional drop sill, grooves are added after the drop sill to form a stilling pool, as shown in Figure 2, the dotted line A-A section is the horizontal bottom plate of the conventional drop sill bottom flow energy dissipator. For the convenience of explanation, each key control point is indicated by numbers in Fig. 2. Wherein the control point 8 is the reattachment point of the jet flow on the ridge of the conventional falling ridge bottom flow.

In this embodiment, the transformation of the conventional drop sill is reflected in the optimization of each control point:

The arc or straight line formed by control points 1 and 2 is connected with the upstream building. Control points 1 to 2 are the connection between the sill and the upstream buildings. The above-mentioned upstream is generally an inclined diversion slope, and the water flows rapidly down from the top of the slope, which has a certain amount of energy. The flow channel before the sill should be smooth so that the water flows to the sill without resistance. The alignment of control points 1 and 2 depends on the slope angle of the upstream ramp.

At control point 2, set a vertical drop sill composed of control points 2, 3, and 4. This part of the control point is the backwater surface of the drop ridge, which can be perpendicular to the horizontal plane, or slightly inclined. It can be considered that the drop sill is composed of two parts, one part is the height of the conventional drop sill, and the second part is the depth of the groove.

A groove formed by control points 3-4-5-6 is set downstream of the sill. The upstream side wall of the groove merges with the back water surface of the sill to form a vertical surface, and the downstream side wall of the groove merges with the facing water surface of the front slope to form an inclined slope. The falling ridge and the groove are located below the water tongue, and the water flow forms a swirl around the horizontal axis behind the ridge. In order to avoid the destructiveness of this swirl, this embodiment increases the depth behind the ridge to form a groove. The purpose is to The space under the water tongue is increased, so that the pressure in the center of the vortex is increased, and the cavitation phenomenon does not occur in the water flow, so as to avoid cavitation damage to the side wall of the stilling pool. The theoretical principles and mathematical basis for achieving this effect are as follows:

According to the basis of fluid mechanics, the basic motion equation of incompressible two-dimensional water flow in the Cartesian coordinate system can be expressed as:

Continuity equation:

(1)

Motion equation:

(2)

In the formula: x , y - coordinate axes of the Cartesian coordinate system;

u , v - flow velocity in x direction and flow velocity in y direction;

F _x , F _y - mass force in x direction and mass force in y direction;

ρ—fluid density; μ—molecular viscosity coefficient.

Due to the vortex flow under the falling ridge, its streamline is a group of ring-shaped closed curves centered on the central singularity. Here we assume that this group of ring-shaped curves is elliptical. Then the streamline cluster equation of the vortex under the falling ridge can be written as:

(3)

In the formula: a and b are constants, which are the semi-major axis and semi-minor axis of the ellipse respectively, a = kb , k is the ratio of the semi-major axis to the semi-minor axis of the ellipse; m is a value between [0, 1] Numerical values representing different streamlines.

For plane potential flow, the streamline differential equation is:

udy — vdx = 0 (4)

The solution to the potential flow problem can be attributed to solving the Laplace equation. On the basis of determining the streamline equation, through solving, we can obtain the following definite solution that can satisfy the above equation.

(5)

Where: P ₀ is the pressure at the center of the vortex.

The velocity distribution of the elliptical vortex is shown in Fig. 2. Points A and B are located on the same streamline, so it can be seen from the flow field definite solution (5) that the flow velocity at point A is V _A =v _A =- α ·a, and the flow velocity at point B is V _B =u _A = αk ² b , where k≠1.

Equation (5) gives the pressure distribution of the vortex, but the pressure P ₀ at the center of the vortex is still unknown and needs to be solved. As shown in Figure 3, the ellipse can be divided into left and right parts along the y- axis, and P ₀ can be obtained by applying the momentum theorem to the left half.

Firstly, it is assumed that the pressure on the periphery of the vortex is the same as that on the façade of the slump, and the average pressure on the façade of the slump is defined as P _m .

The momentum Δk on the cut is:

(6)

Put formula (5) into formula (6) to get

(7)

The corresponding impulse F _t can be expressed as the following formula:

(8)

Momentum and impulse are equal to get:

(9)

Substituting equation (9) into the pressure solution in equation (5), we can get:

(10)

Formula (10) is merged and arranged as follows:

(11)

From the hydraulic characteristics of the vortex flow under the sill, it can be seen that determining the major axis a and the minor axis b of the outermost vortex flow line is the key to determining its hydraulic characteristics. It can be seen from Figure 4 that the short axis b is half of the height of the sill, and its value is controlled by the shape of the sill; the long axis a is half of the length of the reattachment of the water flow, and its length is related to the height of the sill and the depth of water above the sill. The specific calculation formula for:

(12)

However, it is difficult to calculate the hydraulic characteristics only by determining the major and minor axes of the outermost streamline. Since the vortex under the falling ridge is formed by the strong shear between the high-speed jet on the ridge and the surrounding water body, it is a forced vortex, so the hydraulic characteristics of the vortex are determined A connection between the vortex and the high velocity jet must also be established to determine the parameters in the equation. The parameters of the equations are given by the establishment of the kinematic connection conditions below.

Movement connection conditions:

The vortex under the falling ridge is a forced vortex driven by the high-speed jet on the ridge. The flow velocity of the outermost streamline of the vortex is related to the shear diffusion of the jet on the ridge. Therefore, we assume that the outermost streamline is located at the flow velocity of point B , substituting into formula (5) has:

(13)

The coefficient c in the formula is the velocity attenuation coefficient, , is the flow velocity over the ridge, is the drop height, For the depth of the water on the ridge.

Figure 5-8 shows the streamlines of the vortex under the sill in the numerical simulation results, from which it can be seen that the streamline of the vortex under the sill is deformed to a certain extent on the outermost side due to the influence of the solid wall and the external mainstream, and most of the flow The lines are similar ellipse, which shows that the assumption that the flow line of the central vortex under the falling ridge is ellipse is correct.

For engineering, the minimum pressure of the vortex under the ridge is the most concerned index in design. The minimum pressure of the vortex appears at the center of the elliptical streamline, so the minimum pressure of the vortex can be obtained by substituting Equation (13) into Equation (10). Its expression is:

(14)

Due to the existence of the vortex under the falling sill, the elevation of the falling sill is not the hydrostatic pressure distribution, the specific distribution is:

,

The average pressure on the elevation of the sill can be obtained by integrating along the elevation of the sill:

(15)

Substituting formula (19) into formula (18) can get:

(16)

In the formula _, h2 is the downstream water depth above the bottom plate of the stilling basin.

Select several working conditions of the numerical simulation, and compare the minimum pressure result of the vortex under the numerical simulation with the calculation result of formula (16). The comparison results are shown in Table 1. The velocity attenuation coefficient c in the table is obtained from the numerical simulation results. The calculation results of the data in the table are smaller than the numerical simulation results, and the relative error is within 10%, but this is relatively safe for engineering.

Table 1 Comparison of numerical simulation results and calculation results of vortex minimum pressure

The vortex under a specific engineering ridge can be changed from negative pressure to positive pressure by setting the groove. See Table 2 for details.

Table 2 Prediction of minimum pressure of vortex in actual engineering

At the starting position near the upstream of the reattachment point 8, the slope-changing bottom plate of the control point 7-9-10 is set. The slope-changing bottom plate is the front slope, and the reattachment point is the contact point between the water tongue and the slope-changing bottom plate. The reattachment point is located on the back water surface of the front slope, and the inclination angle of the back water surface of the front slope is equal to the water inflow angle. Avoid excessive impact pressure to damage the bottom plate of the stilling basin. The theoretical principles and mathematical basis for achieving this effect are as follows:

When the bottom plate of the stilling tank is horizontal, the impact pressure on the bottom plate is proportional to the flow rate head on the ridge, which can be expressed as:

,

Among them: the coefficient c is the function of the height d of the sill, the depth of the water on the sill h ₀ , the reattachment length L, and the incident angle α between the water flow and the bottom plate of the stilling tank: .

If a reverse slope is set with a slope of β, the formula for calculating the impact pressure is:

,

If the β angle is increased, the impact pressure will also decrease. Taking the drop height d=2m, the water depth h0=2m above the ridge, and the flow velocity V0=40m/s above the ridge as an example, in the case of a horizontal floor, the incident angle α=37.4, and the attached length L=6.2m. Table 3 shows the changes of pool impact pressure and reverse slope β.

Table 3: Changes in stilling pool impact pressure and reverse slope β

Embodiment two:

This embodiment is a design method for the energy dissipator described in Embodiment 1. The steps of the method are as follows, and the process is shown in Figure 9:

(1) The steps of conventional sill design: determine the height d of the sill according to the hydraulic parameters of the incoming water flow, and the bottoming position of the hydraulic jump after the incoming water flow passes the sill, and determine the length L of the hydraulic jump according to the bottoming position of the hydraulic jump and the angle α between the hydraulic jump and the bottom plate.

If it is a new design, first carry out the design of the conventional drop sill, if it is the modification of the existing design, skip this step and use the existing drop sill data.

According to the hydraulic parameters such as the incoming water head and downstream water depth, the height d of the sill is determined, and then the point position 8 is attached, and the length L, the angle α between the water flow and the bottom plate, etc. are attached, as shown in Figure 2.

(2) Steps for determining the downstream edge of the groove: the length l from the sill to the downstream edge of the groove is: 0.7 to 0.9 times the hydraulic jump length, namely: l = (0.7 to 0.9) L.

After determining the additional length L, the angle α between the water flow and the bottom plate, etc., determine the control point 6. After the incoming flow conditions and d are determined, the value of L is fixed, so the length l of the position of the control point 6 can be determined according to (0.7～ 0.9) L OK.

(3) Steps for trial calculation of groove depth: determine the trial length l ₁ of the bottom of the groove according to Δd , the trial length of the bottom of the groove is: l ₁ =1- Δd ; where Δd is the trial depth of the groove, Said trial groove depth is either drawn up during the preliminary design, or revised and determined according to the evaluation results.

To determine the height of control point 3-4, it needs to be obtained through trial calculation. First increase the height of the drop ridge by a trial calculation, that is, the depth Δd of the groove, then the length of the control point 4-5 is l- Δd . Then enter the next step, by calculating and judging whether the pressure P ₀ at the center of the vortex is zero, if it is not zero, you need to change Δd , through continuous trial calculation and modification, until P ₀ is zero. The Δd here is a trial calculation value. If the purpose of P ₀ is zero, then Δd can be used as formal groove data. If the purpose of P ₀ is not achieved, it is still a temporary data. For convenience, Here and in the subsequent calculations, there is no difference between the symbols of the temporary data and the official data, and Δd is used uniformly.

(4) Steps for calculating the pressure at the center point of the vortex: calculate the center pressure of the vortex in the groove after the sill falls according to the following formula:

,

In the formula: P ₀ —pressure at the center point of the eddy current, ρ—fluid density, g—gravitational acceleration, c—flow velocity attenuation coefficient, c= f (V ₁ , d, h ₀ ), V ₁ — is the flow velocity on the ridge, d — Height of drop ridge, h ₀ - water depth above ridge, b - short axis of elliptical vortex, b=d/2, k - ratio of major axis to short axis of elliptical vortex, k=a/b, a - elliptical vortex The major axis of the vortex, a = l ₁ /2, h ₂ - the downstream water depth above the stilling basin floor.

This step uses the turbine center pressure formula derived in Embodiment 1. For convenience, this formula can be expressed as:

.

(5) Judgment and correction steps: Judging whether the trial calculation groove depth Δd is appropriate based on the pressure P ₀ of the vortex center point, if P ₀ >0, then reduce Δd , if P ₀ <0, then increase Δd , after correction Return to "Procedure for Trial Groove Depth". If P ₀ =0, go to the next step.

The results of the trial calculation are compared to determine the final groove depth, which is the key data.

(6) Steps to determine the shape of the back water surface of the front slope: determine the angle β between the back water surface of the front slope and the horizontal line and the length Lr of the back water surface of the front slope, β = (0.5~1.0) α , Lr=(1~2) h ₀ .

In this step, after determining the groove depth, determine the angle β and Lr between the straight line 7-9 and the horizontal line, β = (0.5~1.0) α , Lr=(1~2) h ₀ , and finally determine the groove and positive slope other relevant data.

Finally, it should be noted that the above is only used to illustrate the technical solution of the present invention and not to limit it. Although the present invention has been described in detail with reference to the preferred arrangement, those skilled in the art should understand that the technical solutions of the present invention (such as The form of the falling ridge, the form of the positive slope, the application of various formulas, the sequence of steps, etc.) are modified or equivalently replaced without departing from the spirit and scope of the technical solution of the present invention.

Claims (1)

1. a kind of fluted non-horizontal bottom plate of band falls the design method of the energy dissipater of bank stiling basin, the energy dissipater includes：Set The bank that falls in inclined flood discharge ramp bottom, the bank that falls are linked up smoothly with upstream building by camber line or straight line；It is described Fall bank bottom set groove, groove upstream trough rim is concordant with falling bank, downstream trough rim inclination be connected with positive slope upstream face, it is described just Slope top of the slope is horizontal, and the back side on the positive slope is linked up smoothly with straight line or curve with Channel of Downstream, and groove forms the power that disappears with falling bank Pond, the stiling basin bottom surface is horizontal,

It is characterized in that, the step of the method, is as follows：

Routine falls the step of bank design：Determine step height d, and incoming flow by falling bank according to the hydraulic parameters of incoming flow Hydraulic jump afterwards bottoms out position, and the length L and the angle of hydraulic jump and bottom plate of location determination hydraulic jump are bottomed out according to hydraulic jumpα；

The step of determining groove downstream edge：Fall bank to the length of groove downstream edgelFor：0.7~0.9 times of hydraulic jump length, I.e.：l=（0.7~0.9）L；

The step of tentative calculation depth of groove：According toΔdDetermine the tentative calculation length of bottom portion of groovel ₁, the tentative calculation length of bottom portion of groove is：l ₁ =1-Δd, whereinΔdFor tentative calculation depth of groove, when tentative calculation depth of groove or Preliminary design, drafts, or according to judge Modified result determines；

The step of calculating vortex centers point pressure：The vortex centers pressure for falling bank rearward recess is calculated according to equation below：

In formula：P₀- vortex centers point pressure, ρ-fluid density, g- acceleration of gravity, c- flow rate attenuation coefficients, c=f（V₁, D, h₀）, V₁- for flow velocity on bank, d-step height, h₀- bank headwater depth, the short axle of b- ellipse vortex, b=d/2, k- are ellipse The major axis of circular vortex and the ratio of short axle, the major axis of k=a/b, a- ellipse vortex, a= l ₁/ 2, h₂- force reduction pool bottom it On downstream water depth；

The step of judging and correcting：By to swirl center point pressure P₀Judge tentative calculation depth of grooveΔdIt is whether suitable, if P₀> 0, then reduceΔdIf P₀<0, then increaseΔd, returned to after amendment " the step of tentative calculation depth of groove "；If P₀=0, then enter Next step；

The step of determining positive slope back side shape：Determine positive slope back side and horizontal angleβWith positive slope back side length Lr,β=（0.5~1.0）α, Lr=（1~2）h₀。