Method for calculating critical submerged depth of side-inlet based on CSSS method

Abstract

The application discloses a method for calculating critical submerged water depth of a side-type water inlet based on a CSSS method. A point sink spherical critical surface model is constructed, and a conservation relationship between an effective working area and a radial flow velocity is established based on a continuity equation. For complex boundary working conditions, a dimensionless criterion is introduced to determine the effectiveness of the spherical assumption, and when the spherical assumption is invalid, an anisotropic ellipsoid correction is started, and a coordinate stretching equivalent method is used to calculate a limited effective area. A physical correction coefficient is constructed by using a potential flow geometric component and a dynamic loss component to replace pure statistical regression. A dynamic safety margin is calculated in combination with a vortex evolution time scale. The application solves the problem of prediction distortion of the critical water depth under a complex flow field, and improves the physical precision and operation safety of engineering design.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of hydraulic engineering, and particularly relates to a method for calculating a critical submerged water depth of a side-type intake based on a CSSS method. BACKGROUND

[0002] As a key water intake structure in water conservancy and hydropower engineering, the operation safety of the side-type intake is directly related to the benefit and stability of the entire hub. If the submerged water depth is insufficient, a through suction vortex will be formed in front of the intake, leading to air intake of the water conveying system, causing unit vibration, output swing, and even cavitation damage. Therefore, accurately calculating the critical submerged water depth to ensure that the intake can avoid the generation of harmful vortexes under various working conditions is a crucial link in water conservancy engineering design.

[0003] At present, in the design and calculation of the critical submerged water depth of the side-type intake, Gordon's empirical formula or a point sink model based on simple geometric assumptions are generally used at home and abroad. These existing technologies mainly rely on statistical regression of specific model test data, usually assuming uniform flow convergence and simplifying the boundary conditions to regular geometric cutting. In engineering practice, designers often directly apply these semi-empirical formulas to determine the design elevation by looking up charts or simple algebraic operations.

[0004] However, the existing technologies have limitations in dealing with complex engineering environments and cannot meet the high-precision design requirements. Specifically, the following problems exist: most existing models are based on isotropic spherical convergence assumptions, ignoring the extrusion or stretching effect of the flow field by the extremely close side wall or strong vortex centrifugal force, resulting in serious distortion of the calculation results in asymmetric or restricted spaces; the correction coefficient is usually treated as a black box parameter lacking physical meaning, and it is difficult to reflect the essential influence of dynamic factors such as strong shear and high turbulence on the critical condition through statistical fitting, and the generalization ability is poor; the traditional method only provides a static critical value and fails to consider the evolution time scale and transient fluctuation risk of the vortex from generation to penetration, lacking an evaluation mechanism for dynamic safety margin. SUMMARY

[0005] The application aims to provide a method for calculating the critical submerged water depth of a side-type intake based on a CSSS method, in order to solve the above-mentioned problems of the prior art.

[0006] The technical scheme provides a method for calculating the critical submerged water depth of a side-type intake based on a CSSS method, which comprises the following steps:

[0007] Taking the center of the side-type intake as the origin and the to-be-sought critical submerged water depth as the characteristic radius, a point sink critical surface model describing the flow convergence characteristics is constructed;

[0008] Based on the fluid continuity principle, a continuity balance equation relating the effective working area of the point sink critical surface model, the radial flow velocity, and the intake flow rate is established.

[0009] A radial flow velocity coefficient is introduced to construct a flow velocity mapping expression of the radial flow velocity and the far-field uniform inflow velocity;

[0010] Geometric boundary parameters of the side-type intake are obtained, the spatial topological relationship between the geometric boundary parameters and the characteristic radius is analyzed, and an effective working area expression under boundary constraints is derived;

[0011] According to the hydraulic and boundary conditions of the side-type intake, the numerical representation of the radial flow velocity coefficient is calculated;

[0012] The continuity balance equation, the flow velocity mapping expression, the effective working area expression, and the numerical representation of the radial flow velocity coefficient are solved simultaneously to obtain the critical submerged water depth of the side-type intake.

[0013] The beneficial effects are that the present application solves the problem of distorted critical water depth prediction under a complex flow field, and improves the physical precision and operation safety of engineering design. BRIEF DESCRIPTION OF DRAWINGS

[0014] Figure 1 A step flowchart of a basic framework for calculating the critical submerged water depth of a side-type intake based on the CSSS method in the embodiments of the present application.

[0015] Figure 2 A step flowchart of determining the effective working area of the CSSS sphere and the relationship between the radial flow velocity of the CSSS sphere based on the continuity equation in the embodiments of the present application.

[0016] Figure 3 A step flowchart of defining four groups of dimensionless criteria in the embodiments of the present application.

[0017] Figure 4 A step flowchart of calculating the effective area of an ellipsoid in the embodiments of the present application. DETAILED DESCRIPTION

[0018] The present application will be further described in detail below in combination with specific embodiments. The embodiments are implemented on the premise of the technical solutions of the present application, and detailed implementation modes and specific operation processes are given, but the protection scope of the present application is not limited to the following embodiments.

[0019] Embodiment 1: The present embodiment details a basic framework for calculating the critical submerged water depth of a side-type intake based on the CSSS method. As shown in the figure, the present embodiment is applicable to water conservancy engineering design under conventional boundary conditions, and realizes rapid solution of the critical submerged water depth by constructing an idealized spherical critical surface model and combining geometric boundary determination. The core technical problem solved by the present embodiment is how to convert a complex three-dimensional hydraulic problem into a geometric and algebraic problem for solution. Figure 1 ​

[0020] Step 101, with the center of the side inlet as the origin and the critical submerged water depth to be solved as the radius, a point sink spherical critical surface (CSSS) sphere is constructed.

[0021] In this embodiment, the center of the side inlet generally refers to the geometric center of the inlet section, which is taken as the coordinate origin (0, 0, 0) to establish a Cartesian coordinate system. The critical submerged water depth S c is defined as the vertical distance from the free water surface to the center of the inlet, at which depth the water flow is just in a critical state of generating a penetrating suction vortex. The constructed point sink spherical critical surface (CSSS) is a virtual physical control surface, and its radius is S c . The sphere represents the equipotential surface of the water flow converging to the inlet. Under the assumption of ideal point sink flow, the radial velocity distribution of the fluid through the sphere is uniform. This step utilizes the spherical symmetry to simplify the flow field analysis, converting the complex free surface flow problem into a flux problem on a closed surface.

[0022] Step 102, based on the principle of fluid continuity, a continuity conservation relationship between the effective working area of the CSSS sphere and the radial flow velocity of the CSSS sphere is established.

[0023] Specifically, according to the law of mass conservation, in an incompressible fluid, the flow rate through the critical sphere per unit time must be equal to the flow rate through the inlet section. In this embodiment, this continuity conservation relationship is specifically constructed as the formula: A s *v s =(π*d 2 / 4)*v in . Wherein, A s represents the effective working area of the CSSS sphere, i.e., the spherical surface area that the fluid can actually pass through, with the unit of square meters; v s represents the radial flow velocity of the CSSS sphere surface, with the unit of meters per second; d represents the diameter of the side inlet, for non-circular inlets, the equivalent diameter can be used, with the unit of meters; v in represents the design flow velocity of the side inlet, with the unit of meters per second. This formula establishes the flow rate balance constraint under the critical state.

[0024] Step 103, a radial flow velocity correction coefficient is introduced to construct a velocity correlation formula between the radial flow velocity of the CSSS sphere and the uniform incoming flow velocity.

[0025] In this embodiment, since the actual flow field is not an ideal point sink flow, and is affected by boundary layer separation and non-uniform incoming flow, the radial flow velocity v s is often different from the uniform incoming flow velocity U ∞There is a certain proportion relationship. Therefore, the relationship is constructed: v s =k*U ∞ . Wherein, k is a correction coefficient, used to correct the deviation between the ideal point convergence assumption and the actual complex flow; U ∞ is the uniform flow velocity upstream of the inlet, in meters per second. The core of this step is to associate the critical radial flow velocity, which cannot be directly measured, with the macroscopic hydraulic parameter that is easy to measure through the lumped parameter k.

[0026] In step 104, the distances of the center line of the side-type inlet to the two side walls are obtained, and according to the geometric spatial relationship between the distances and the critical submerged water depth, the effective working area of the CSSS sphere under the boundary restriction is calculated.

[0027] Specifically, the height of the spherical cap intercepted by the side-type inlet is defined as h, and the radius of the CSSS sphere is S c The basic spherical area is calculated and the spherical cap area intercepted by the side-type inlet is deducted to obtain the basic effective area; the distance of the center line of the side-type inlet to the left side wall is defined as L l , and the distance to the right side wall is L r . The process of calculating the effective working area A s is a geometric cutting process. The basic effective area A base , i.e. the global area 4*π*S c 2 minus the spherical cap area intercepted by the inlet itself.

[0028] According to the size relationship between the distances L l and L r and the critical radius S c :

[0029] If L l ≥ S c and L r ≥ S c , it is determined that the CSSS sphere is not affected by the side wall, and the basic effective area is directly taken as the effective working area As;

[0030] If L l <S c and L r ≥ S c , it is determined that the CSSS sphere is affected by one side wall, the spherical cap area intercepted by the limited side wall on the CSSS sphere is calculated, and the basic effective area is subtracted from the spherical cap area intercepted by the limited side wall to obtain the effective working area As;

[0031] If L l <S c and L r <S cIf L

[0032] The calculation is carried out in three working conditions, specifically:

[0033] In working condition one, when L l ≥ S c and L r ≥ S c , it indicates that the sphere does not touch the two side walls, and A s =A base .

[0034] In working condition two, when only one side is limited, for example, L l <S c and L r ≥ S c , the limited side wall will cut into the sphere to form a truncated spherical cap. The height of the truncated spherical cap is defined as h=S c -L l , and the cross-sectional area is A cap =2*π*S c *h. At this time, the effective working area is A s =A base -A cap .

[0035] In working condition three, when L l <S c and L r <S c , both side walls cut into the sphere, and the effective working area needs to deduct the area of the truncated spherical cap on both sides. It should be noted that when L l or L r tends to S c , the calculation formula of working condition three can be smoothly degenerated to working condition two or working condition one in mathematics, ensuring the continuity and stability of the model near the critical point.

[0036] Step 105, the critical submergence depth of the side inlet is obtained by simultaneously solving the continuity conservation relation, the velocity correlation formula and the effective working area.

[0037] In the basic scheme of the present embodiment, the determination of the correction coefficient k adopts a statistical-based method. Specifically, the Froude number Fr of the side inlet flow, the relative length L i / d of the side inlet extending into the reservoir area and the asymmetry ξ of the boundary are obtained as influencing factors. Among them, the Froude number is defined as Fr=v in / sqrt(g*d), where g is the acceleration due to gravity; boundary asymmetry is defined as ξ=|L l -L r | / (L l +L r ).

[0038] Spearman's rank correlation analysis was used to analyze the correlation between the correction coefficient k and the influencing factor ξ. Based on the analysis results, a linear regression equation was constructed, and the correction coefficient was calculated as: k = C0 + C1 * Fr + C2 * (L i / d)+C3*ξ. Where k is the correction coefficient, C0, C1, C2, and C3 are regression constants, Fr is the Froude number of the side inlet flow, and L i / d represents the relative length of the side inlet extending into the reservoir area, and ξ represents the asymmetry of the boundary.

[0039] Finally, the determined k value and A s Substituting the geometric expression into the continuity equation, we obtain the expression for S. c The algebraic equation can be solved numerically using methods such as the bisection method or Newton's iteration method to obtain the critical submergence depth S of the side intake. c .

[0040] Example 2: This example provides an adaptive anisotropic ellipsoid correction method. It is particularly suitable for complex working conditions such as strong shear, strong vortex, or very close-to-boundary conditions. Under such conditions, the traditional spherical assumption may fail. This example improves the calculation accuracy by introducing anisotropic correction.

[0041] Step 201: Calculate the dimensionless criteria that characterize the flow field features and boundary geometry features, and compare the dimensionless criteria with the preset failure threshold; when the dimensionless criteria exceed the failure threshold, determine that the spherical critical surface has failed and start the anisotropic ellipsoid correction mode.

[0042] In this embodiment, four sets of dimensionless criteria are defined for intelligent identification of the flow field state. For example... Figure 3 As shown, this specifically includes: the wall anisotropy criterion ∏ w =max(S c / L l ,S c / L r ), used to characterize the degree of compression of the flow field by the sidewalls; free water surface approach criterion ∏ f =S c / S, where S is the current submerged water depth, this criterion is used to characterize the influence of free surface gravity waves on the critical surface; vortex intensity criterion ∏ s =S w =Γ / (U ∞d), where Γ is the incoming flow circulation, which represents the stretching effect of the centrifugal force of the vortex on the flow field; and the viscous turbulent flow criterion∏ ν = (U ∞ S c ) / ν*Tu. Where∏ w ,∏ f ,∏ s ,∏ ν are the corresponding criterion values, L l , L r are the distances from the center of the side inlet to the left and right side walls, S is the current submerged depth, S c is the critical submerged depth, S w is the rotational intensity, Γ is the incoming flow circulation, U ∞ is the uniform incoming flow velocity, d is the diameter of the side inlet, ν is the kinematic viscosity, and Tu is the turbulent intensity. The preset failure threshold can be set according to engineering experience, for example, ε w is 0.25, and ε s is 0.2. Once the value of any criterion exceeds the corresponding threshold, it is considered that the flow field has been deformed, and the standard sphere model must be abandoned in favor of the ellipsoid correction mode.

[0043] In step 202, under the anisotropic ellipsoid correction mode, an anisotropic coefficient is introduced to correct the radius S c of the CSSS sphere to three semi-axes of the anisotropic ellipsoid.

[0044] Specifically, the lengths of the semi-axes in three orthogonal directions are defined as a x = γ x S c , a y = γ y S c , and a z = γ z S c . Where a x , a y , and a z are the lengths of the semi-axes of the ellipsoid in the x, y, and z directions, respectively, S c is the critical submerged depth, and γ x , γ y , and γ z are the anisotropic coefficients. The calculation formula of the anisotropic coefficients is:

[0045] γ x = 1 + β w (S c / L l ) m + β s S w n ;

[0046] γ y =1+β w (S c / L r ) m +β s S w n ;

[0047] γ z =1+β f (S c / S) nf ;

[0048] In the formula, L l L r These are the distances from the center of the side inlet to the left and right side walls, respectively, and S is the current submerged water depth. w For rotational intensity, β w β f β s Here, m, n, and nf are correction factors, and m, n, and nf are exponential parameters. The calculation of this coefficient is directly related to physical parameters, such as γ. x =1+β w *(S c / L l ) m +β s *S w n In the formula, (S) c / L l ) m The term reflects the distance L from the boundary. l When the flow field decreases, the squeezing effect in the x-direction leads to an increase in the equivalent radius; S w n This term reflects the radial expansion of the critical surface caused by centrifugal force as vortex intensity increases. Parameters m and n are typically positive, and β... w and β s This is a correction factor, typically ranging from 0 to 1. This correction mechanism allows the critical surface to adaptively deform into a flattened or elongated ellipsoid, thus more realistically conforming to the equipotential surfaces in complex flow fields.

[0049] Step 203: Using the coordinate stretching equivalent method, establish a linear mapping relationship from the physical coordinate system to the stretched coordinate system. Based on the linear mapping relationship, convert the boundary distance in the physical domain into the equivalent boundary distance in the stretched domain.

[0050] like Figure 4 As shown, this is the core step in calculating the effective area of ​​an ellipsoid. Since directly calculating the area of ​​an ellipsoid truncated by a plane involves complex elliptic integrals, this embodiment proposes a clever algebraic transformation method. The mapping relationship is established: x' = x / γx , y' = y / gamma y , z' = z / gamma z . Through this linear transformation, the ellipsoid (x / a x ) 2 +(y / a y ) 2 +(z / a z ) 2 =1 in the physical domain is mapped to the standard unit sphere (x' / S c ) 2 +(y' / S c ) 2 +(z' / S c ) 2 =1 in the stretched domain. Correspondingly, the boundary distances in the physical domain also need to be converted, for example, the equivalent distance of the left wall becomes L' l =L l / gamma x , the equivalent distance of the right wall becomes L' r =L r / gamma y , and the equivalent distance of the free water surface becomes S'=S / gamma z . This step converts the complex anisotropic geometric problem into the standard spherical geometry problem.

[0051] Step 204, in the stretched coordinate system, calculate the virtual spherical cap area cut by each boundary based on the equivalent boundary distance, and calculate the effective working area under the physical domain using the inverse transformation.

[0052] In the stretched domain, use the standard spherical cap area formula of Example 1 to calculate the virtual area A' l cut by the equivalent boundary L' cap . For example, for the left wall, the virtual cut area A' capl =2*π*S c *(S c -L' l ). Through the inverse transformation relationship of the area element, restore the remaining area of the stretched domain to the effective working area A s (EC) in the physical domain. The restoration formula is approximately: A s (EC) ≈1 / (gamma x gamma y )(πS c 2 -∑A' cap ). Where As (EC) is the corrected effective working area, A' cap is the virtual spherical cap area cut by each boundary in the stretched domain, L' l , L'r , S' is the equivalent distance from the center of the side inlet to the left wall, right wall and free surface in the stretching domain, and the coefficient 1 / (γ x *γ y ) corrects the influence of coordinate stretching on the scale of area element. Under complex boundary conditions, the corrected effective flow area can be quickly and accurately obtained, and then substituted into the continuity equation to solve a more accurate critical submerged depth.

[0053] Embodiment 3, the embodiment provides a coefficient decomposition model based on a physical mechanism. In particular, for the scene of lacking experimental data for statistical regression.

[0054] Step 301, the correction coefficient is composed of a potential flow geometric component and a dynamic loss component.

[0055] Specifically, the total correction coefficient k is decomposed into k=k pot *k dyn . Wherein, k pot represents the potential flow geometric component, mainly reflecting the geometric flow field acceleration effect caused by the existence of the boundary; k dyn represents the dynamic loss component, mainly reflecting the non-potential flow influence brought by fluid viscosity, turbulent pulsation and vortex structure. This decomposition converts the black box empirical coefficient into a white box parameter with clear physical meaning, making the model have better generalization ability and interpretability.

[0056] Step 302, the potential flow geometric component is calculated based on the mirror source principle, representing the geometric enhancement effect of boundary restriction on radial flow velocity.

[0057] In potential flow theory, the flow of a point near the wall can be equivalent by setting a mirror point source on the other side of the wall, which leads to flow field superposition and flow velocity increase. Based on this principle, the embodiment constructs the formula: k pot =∏(j∈{l,r,f})(1-C j )(S c / D j ) pj ) (-1 / 2) , where the product symbol Π traverses the relevant boundary j, including the left wall l, the right wall r and the free surface f. D j takes the value of L l , L r or S, respectively corresponding to the left wall distance, the right wall distance and the current submerged depth. The formula shows that when the boundary distance D j tends to the critical radius S c , the denominator tends to decrease, resulting in k pot greater than 1, which embodies the flow velocity enhancement caused by boundary extrusion. C jis the boundary influence coefficient, usually taken as 0.1 to 0.3, and pj is the decay exponent, usually taken as 2 to 3.

[0058] Step 303, the kinetic loss component represents the non-potential flow influence of turbulence, shear and vortex on the flow.

[0059] The specific calculation formula is: k dyn =1+C Tu *Tu 2 +C sh *(|dU / dy|S c ) / U ∞ +C sw *(S w -S (w_crit) ). Wherein, Tu is the turbulence intensity, Tu 2 term represents the correction of the transformation of turbulent fluctuation kinetic energy into average flow velocity; |dU / dy| is the flow velocity shear rate, (|dU / dy|S c ) / U ∞ term represents the velocity gradient effect in the shear layer; S w is the rotation intensity, S w_crit is the critical rotation intensity, and (S w -S w_crit ) term introduces the threshold effect of vortex intensity. When the vortex intensity S w exceeds the critical value S w_crit , the low pressure area of the vortex core will induce the suction phenomenon, at this time k dyn will increase sharply, and a larger submerged water depth is needed to suppress the vortex; C Tu , C Sh , C Sw are the corresponding kinetic influence coefficients, and U ∞ is the uniform flow velocity.

[0060] This model not only considers the static geometric boundary, but also deeply integrates the dynamic fluid physical properties, and can more accurately predict the critical conditions under complex flow conditions.

[0061] Embodiment 4, this embodiment details a dynamic safety margin evaluation method considering the dynamic evolution mechanism of vortex. In actual water conservancy engineering operation, the flow condition often has transient and fluctuating nature, and the critical submerged water depth S c calculated by static calculation only represents the theoretical critical equilibrium point. This embodiment solves the time lag and risk buffer problem from the development of surface small concave to through suction vortex by introducing time scale and dynamic margin, and provides quantitative basis for safety redundancy design of engineering.

[0062] Step 401, obtain the critical rotation intensity as the flow state conversion threshold, and calculate the dynamic time scale of vortex evolution.

[0063] In the present embodiment, the dynamic time scale τ v is defined as the characteristic time scale for the vortex structure to evolve from initial generation to throughout the entire submerged depth. The calculation of this physical quantity is based on dimensionless analysis and hydrodynamic theory, and its formula is specifically constructed as: τ v = κ v d / U ∞ * 1 / (max(|S w - S (w_crit) |, ε)). Wherein, τ v is the dynamic time scale; κ v is the time constant, usually calibrated by model test, with a value range generally between 0.5 to 2.0, which reflects the resistance of fluid viscosity to vortex stretching; d is the inlet diameter; U ∞ is the uniform flow velocity; S w is the rotation intensity, S w_crit is the critical rotation intensity, and the term |S w - S w_crit | in the formula represents the degree of deviation of the current vortex intensity S w from the critical vortex intensity S w_crit . This term is located in the denominator, and its physical meaning is that when the vortex intensity is closer to or exceeds the critical value, the extreme instability of the flow system leads to a rapid acceleration of vortex evolution, and the characteristic time scale becomes shorter. The parameter ε is a small amount to prevent singularity, for example, 10 -6 , which is used to prevent mathematical singularity when the denominator is zero when S w is exactly equal to S w_crit .

[0064] Step 402, based on the dynamic time scale, calculate the dynamic safety margin for compensating the dynamic vortex effect.

[0065] Specifically, the dynamic safety margin ΔS dyn is an additional water depth reserve based on the static critical water depth S c . Its calculation formula is: ΔS dyn = λ v * τ v * U ∞ 2 / 2g. Wherein, ΔS dyn is the dynamic safety margin; λ v is the margin coefficient, which is a dimensionless empirical parameter, usually with a value between 1.0 to 1.5, used to comprehensively consider the disturbance factors such as inlet grid disturbance and waves that are not captured by the model; τ v is the dynamic time scale; U ∞ is the uniform flow velocity; g is the acceleration of gravity; U ∞2 / 2g represents the kinetic head of the incoming flow. The core logic of this formula is to combine the time scale of vortex evolution τ v with the flow velocity scale of the fluid, and convert it into a length scale, i.e. the water depth. In other words, if the vortex evolution is extremely fast, τ v is small and the flow velocity is very high, in this case, the system is extremely sensitive to disturbances, although the formula calculation value becomes small, but in fact, combined with the kinetic energy term of high flow velocity, this model can dynamically capture the energy surplus demand under different flow states. In engineering applications, the final design critical submergence water depth S design should be taken as S c . dyn .

[0066] On this basis, as an optional implementation, the dynamic safety margin can also be linked with the real-time monitoring system of the power station. The system monitors the vortex intensity S w and the flow velocity U ∞ in front of the intake in real time, and dynamically calculates the current ΔS dyn . When the actual submergence water depth S minus ΔS dyn is less than the calculated static S c , the system triggers an alarm to prompt the operator to adjust the load or raise the reservoir water level through water replenishment measures, thereby realizing the technical leap from static design to dynamic operation.

[0067] Embodiment 5, this embodiment provides a complete numerical calculation case, which shows how to specifically solve the critical submergence water depth under complex working conditions by using the method of the present application. Through specific numerical calculation, the feasibility of anisotropic ellipsoid correction and physical coefficient decomposition is verified.

[0068] Suppose that a side intake of a hydropower station faces the following complex boundary and flow field conditions: the intake diameter d is 4.0 meters; the design incoming flow velocity v in is 3.0 meters / second; the upstream uniform incoming flow velocity U ∞ is 2.0 meters / second; the gravitational acceleration g is taken as 9.81 meters / second square. The boundary conditions are extremely poor: the left side wall distance from the center line L l is only 2.5 meters, the right side wall distance L r is 10.0 meters, the currently monitored vortex intensity S w is 0.35, which belongs to a strong vortex working condition. The to-be-solved variable is the critical submergence water depth S c .

[0069] First, model estimation and criterion checking are performed. A conventional empirical formula such as the Gordon formula can be used to give an initial estimated value S guess , assuming that the initial value is 4.5 meters. The wall surface anisotropy criterion π w =max(Sguess / L l ,S guess / L r )=max(4.5 / 2.5,4.5 / 10.0)=1.8. Assuming the preset failure threshold ε w =0.25, obviously 1.8 is much larger than 0.25. Calculate the vortex criterion π s =0.35, assuming the threshold ε s =0.2, also out of limit. Therefore, the system determines that the spherical hypothesis fails, and the anisotropic ellipsoid correction mode must be started.

[0070] Second step, construct anisotropic ellipsoid parameters. Calculate the anisotropic coefficient according to the formula. Set the correction factor β w =0.2, the index m=2.0, β s =0.5, the index n=1.0. Calculate the x-direction coefficient, which is squeezed by the left wall: γ x =1+0.2*(4.5 / 2.5) 2 +0.5*(0.35) 1 =1+0.648+0.175=1.823. That is, the critical suction surface is flattened in the x-direction, resulting in an increase in the equivalent scale. Calculate the y-direction coefficient, which is less affected by the right wall and mainly affected by the vortex: γ y =1+0.2*(4.5 / 10.0) 2 +0.5*(0.35) 1 =1+0.04+0.175=1.215. Calculate the z-direction coefficient, which is assumed to be less affected by the free surface: γ z ≈1.0. At this time, the original sphere with a radius of 4.5 meters is corrected to an ellipsoid with semi-axes a x =8.2 meters, a y =5.47 meters, and a z =4.5 meters.

[0071] Third step, calculate the effective working area using the coordinate stretching method. Calculate the equivalent distance of the left wall in the stretching domain: L' l =L l / γ x =2.5 / 1.823≈1.37 meters. Calculate the cut-off spherical cap height in the stretching domain: h' l =S guess -L' l =4.5-1.37=3.13 meters. Calculate the cut-off area in the stretching domain: A' cap_l =2*π*S guess *h' l =2*3.1416*4.5*3.13≈88.5 square meters. Note: the right wall L r= 10 meters, greater than S guess , so no cutting occurs on the right side, A' cap_r = 0. The effective working area A s of the physical domain is restored. base_sphere : Base sphere area: A 2 = 4 * π * (4.5) inlet ≈ 254.5 square meters.

[0072] Consider the inlet itself cross-sectional area: A 2 ≈ π * (d / 2) s = 12.6 square meters. A (EC) x * γ y )] * (A base_sphere - A' cap_l - A inlet ) A s (EC) ≈ [1 / (1.823 * 1.215)] * (254.5 - 88.5 - 12.6) ≈ 0.45 * 153.4 ≈ 69.0 square meters. It can be seen that due to the strong squeezing of the boundary, i.e. γ x is large and cutting, the effective flow area is reduced.

[0073] Fourth step, calculate the physical correction coefficient. Assume potential flow component parameter C l = 0.1, p l = 2. k pot = (1 - 0.1 * (4.5 / 2.5) 2 ) (-0.5) = (1 - 0.324) (-0.5) ≈ 1.21. This indicates that the near-wall effect causes the radial flow velocity to increase by 21%. Assuming that the dynamic component is mainly affected by the vortex, C sw = 2.0, S w_crit = 0.2. k dyn = 1 + 2.0 * (0.35 - 0.2) = 1.3. Total coefficient k = k pot * k dyn = 1.21 * 1.3 ≈ 1.57.

[0074] Fifth step, model solution and checking. Substitute the above results into the continuity equation: A s * v s = Q in . Left side = 69.0 * (k * U ∞ ) = 69.0 * (1.57 * 2.0) ≈ 216.6 cubic meters / second. Right side actual inlet flow = (π * 4.0 2 / 4) * 3.0 = 37.7 cubic meters / second. Here, only a single iteration is demonstrated, and the numerical deviation indicates that the initial assumption Sguess =4.5 meters is too large. In actual calculations, this is an iterative root-finding process. Since the flow rate calculated on the left is much larger than the actual flow rate, it indicates that the assumed S... guess If S is too large, the effective area will be too large. The program will automatically reduce S. guess Repeat steps two through five until both sides of the equation are balanced. Finally, through numerical iteration, it may converge to S. c Approximately 2.8 meters. This result will differ from coarse calculations that do not consider ellipsoidal correction and physical coefficient decomposition, thus providing a safer and more accurate design basis.

[0075] Example 6: This example considers the influence of flow conditions and boundary conditions such as the length of the side inlet extending into the reservoir area, the Froude number of the side inlet flow, the asymmetry of the boundary, and the relatively uniform inflow velocity on the critical submergence depth of the side inlet. It comprehensively provides a method for calculating the critical submergence depth of the side inlet based on the CSSS method, specifically including the following steps:

[0076] Step S1: Taking the center of the side inlet as the origin, and the critical submersion depth S... c A physical model of the CSSS sphere is constructed with radius [radius value]. Regarding the determination of the critical submergence depth, [the submergence depth of the side-type inlet is considered]. The radius r of the CSSS sphere is higher than c At this time, a side inlet will not generate vortices (1a), and when the submersion depth of the side inlet is... The radius r of the CSSS sphere is lower than c At this point, a depression appears on the water surface (1b), followed by the formation of a vortex (1c); under critical conditions, the submerged depth... It should be equal to the radius of the CSSS sphere, i.e., S c =r c .

[0077] Step S2, as follows Figure 2 As shown, the relationship between the effective working area of ​​the CSSS sphere and its radial velocity is determined based on the continuity equation. The diameter and velocity of the side inlet are obtained, and the following continuity conservation equation is constructed: The continuity equation used to determine the relationship between the effective working area of ​​the CSSS sphere and its radial velocity is:

[0078] A c V s =1 / 4πD 2 V;

[0079] Among them, A c V is the effective working area of ​​the CSSS sphere. sLet V be the radial velocity of the CSSS sphere, D be the diameter of the side inlet, and V be the flow velocity at the side inlet. To calculate the critical submergence depth using the CSSS method, the effective working area A of the CSSS sphere needs to be determined. c and the radial flow velocity V of the CSSS sphere s .

[0080] Step S3: For side inlets in actual working conditions, the water flow conditions are complex and variable. It is necessary to fully consider the influence of water flow conditions and boundary conditions. Therefore, in order to improve the calculation accuracy of the established model, coefficients are introduced to construct the relationship between the radial flow velocity and the uniform flow velocity of the CSSS sphere.

[0081] After introducing coefficients, the velocity relationship between the radial velocity of the CSSS sphere and the uniform incoming flow velocity is constructed as follows:

[0082] V s =K s U;

[0083] Among them, V s K is the radial velocity of the CSSS sphere. s U is the correction factor, and U is the uniform inflow velocity.

[0084] The effective area of ​​the CSSS sphere is mainly affected by the boundary conditions of the side inlet. Considering the range of the side inlet extending into the reservoir area and the left and right side walls, three working conditions are covered when calculating the effective working area of ​​the CSSS sphere. The physical model of the critical submersion depth of the side inlet is constructed by combining steps S2 and S3, and the expression of the relative critical submersion depth is derived.

[0085] Step S4, define the length of the side inlet extending into the reservoir area as L. i The distances between the centerline of the side inlet and the two side walls are defined as B1 and B2, respectively. By judging the relationship between B1, B2 and the critical flood depth, the effective working area of ​​the CSSS sphere is calculated under different conditions.

[0086] Condition 1, when B1≥S c and B2≥S c When both conditions are met, the effective working area of ​​the CSSS sphere is not affected by the side walls, then:

[0087] A c =4πr c 2 -2πr c h ;

[0088] h=r c -sqrt(r c 2 -1 / 4D 2);

[0089] wherein A c is the effective working area of the CSSS sphere, r c is the radius of the CSSS sphere, h is the height of the spherical cap intercepted by the side inlet, and D is the diameter of the side inlet;

[0090] The physical model of the critical submerged depth of the constructed side inlet is:

[0091] 【4πr c 2 -2πr c (r c -B); c 2 -1 / 4D 2 ))K s U=1 / 4πD 2 V;

[0092] Under the critical condition, S c =r c , the relative critical submerged depth expression is obtained as:

[0093] S c / D=(V / U) 1 / 2 / 4sqrt(K s (1-K s U / V));

[0094] When B1 c or B2 c , the effective working area of the CSSS sphere is affected by one side wall, then:

[0095] A c =4πr c 2 -2πr c h -2πr c (r c -B);

[0096] h=r c -sqrt(r c 2 -1 / 4D 2 );

[0097] wherein B is B1 or B2, and h is the height of the spherical cap intercepted by the side inlet;

[0098] Under the critical condition, S c =r c , the relative critical submerged depth S c / D expression is obtained as:

[0099] Sqrt((S c / D) 2 -1 / 4) + B / D = 1 / 8k s *D / S c *V / U;

[0100] Where B < S c B = B1 or B2.

[0101] Condition 3, when B1 < S c and B2 < S c When the effective working area of ​​the CSSS sphere is affected by the two side walls, then:

[0102] A c =4πr c 2 -2πr c h -2πr c (r) c -B1)-2πr c (r) c -B2);

[0103] h=r c -sqrt(r c 2 -1 / 4D 2 );

[0104] Under critical conditions, S c =r c The relative critical submersion depth S can be obtained. c The / D expression is:

[0105] S c / D=Sqrt((S c / D) 2 -1 / 4) + B1 / D + B2 / D - 1 / 8k s *D / S c *V / U;

[0106] Regarding working condition three: If B1 < S c When B=B1, the working area on side B2 is not affected by the side wall, meaning the effective working area of ​​the CSSS sphere is affected by one side wall. Let B2 be r. c Under critical conditions, S c =r c Then it is:

[0107] S c / D=Sqrt((S c / D) 2 -1 / 4) + B / D + S c / D-1 / 8ks *D / S c *V / U;

[0108] Further simplification is:

[0109] Sqrt((S c / D) 2 -1 / 4)+B / D=1 / 8k s *D / S c *V / U;

[0110] If B2 c , the effective working area of the CSSS sphere is affected by one side wall, B1 c , the critical condition is S c =r c , then:

[0111] S c / D=Sqrt((S c / D) 2 -1 / 4)+B / D+S c / D-1 / 8k s *D / S c *V / U;

[0112] Further simplification is:

[0113] Sqrt((S c / D) 2 -1 / 4)+B / D=1 / 8k s *D / S c *V / U;

[0114] If B1 c and B2 c at the same time, that is, the effective working area of the CSSS sphere is not affected by the side wall, B1=B2=r c , the critical condition is S c =r c , then the process of gradual derivation is:

[0115] S c / D=Sqrt((S c / D) 2 -1 / 4)+S c / D+S c / D-1 / 8k s *D / S c *V / U;

[0116] Sqrt((S c / D) 2 -1 / 4)+Sc / D=1 / 8k s *D / S c *V / U;

[0117] Sqrt((S c / D) 2 -1 / 4)=1 / 8k s *D / S c *V / U-S c / D;

[0118] (S c / D) 2 -1 / 4=(1 / 8k s *D / S c *V / U-S c / D) 2 ;

[0119] 1 / 4k s *V / U-1 / 4=(1 / 8k s *D / S c *V / U) 2 ;

[0120] (S c / D) 2 =(1 / 16(k s ) 2 *V / U) 2 / (V / U-k s / k s );

[0121] Further simplified as:

[0122] S c / D=(V / U) 1 / 2 / 4sqrt(K s (1-K s U / V));

[0123] Step S5, using Spearman rank correlation analysis method to analyze the correlation between the coefficient introduced in step S3 and the relative length of the side-type intake extending into the reservoir area, the side-type intake flow Froude number, the asymmetry of the boundary, and the relative uniform incoming flow velocity, and to construct a regression equation of the coefficient. Through statistical methods, the correlation degree of the coefficient with the relative length of the side-type intake extending into the reservoir area, the Froude number and other factors is determined, which not only reveals the action mechanism of each factor on the critical submergence depth, but also provides data support for constructing a precise coefficient regression equation, making the model parameters more reasonable and reliable.

[0124] The regression equation of the coefficient is:

[0125] k s=-23.32-5.92Fr+0.62 / (U / V) (L i / D=0);

[0126] k s =3.04-0.64 (L) i / D)-0.15Fr-0.37 (B1 / B2) (L i / D>0);

[0127] Where, k s L is a coefficient, Fr is the Froude number of the side inlet flow, and L is a coefficient. i / D represents the relative length of the side inlet extending into the reservoir area, and B1 / B2 represents the asymmetry of the boundary.

[0128] Step S4, centered on the concept of a point-sink spherical critical surface, starts from the laws of water flow motion and combines the formation of the critical submergence depth with the morphological changes of the spherical critical surface to deduce the calculation method for the motion characteristics of water flow near the critical surface. Step S5 comprehensively considers multiple key factors, such as multiple factor parameters in the equation for constructing coefficients, covering multiple dimensions of water flow conditions and boundary conditions.

[0129] Step S6, based on the relative critical submergence depth expression derived theoretically in Step S4 and the regression equation of the coefficients statistically calibrated in Step S5, obtains the calculation formula for the critical submergence depth of the side-type intake considering boundary effects, specifically including:

[0130] S c / D=Sqrt((S c / D) 2 -1 / 4) + B1 / D + B2 / D - 1 / 8k s *D / S c *V / U ∞ ;

[0131] k s =-23.32-5.92Fr+0.62(U / V)(L i / D=0);

[0132] k s =3.04-0.64 (L) i / D)-0.15Fr-0.37(B1 / B2)(L i / D>0);

[0133] To verify the feasibility of the above calculation formula, the calculated relative critical flood depth (S) will be used. c / D) cal Compared with model test values ​​(S) c / D) expBy comparison, it can be seen that the two groups of data points are roughly distributed near a straight line passing through the origin, that is, there is a certain linear relationship between the calculated values of the application and the test values of the model test, which proves the effectiveness of the calculation method of the application. By comparing the data points of the application and the test model, the calculated values of the application are relatively more concentrated on the straight line, which further verifies that the calculated values of the application are more consistent with the actual working conditions.

[0134] In summary, the method for calculating the critical submerged depth of the side-type intake based on the CSSS method provided by the application can more accurately reflect the critical submerged depth value under complex conditions in actual engineering, and has smaller deviation from the actual working condition. It can be applied to the design of side-type intake under different boundary conditions to meet the needs of diversified water conservancy and hydropower engineering. At the same time, a calculation model directly related to the physical law of water flow is established, and the calculation result is more reliable.

[0135] Specifically, in view of the problem that the spherical assumption in the prior art cannot adapt to complex boundaries and leads to distorted calculation, the application adopts an anisotropic ellipsoid correction and coordinate stretching equivalent algorithm. By introducing a physical criterion to automatically identify flow field deformation, the critical surface is reconstructed as an ellipsoid that can reflect boundary extrusion or vortex stretching, and the effective flow area is accurately calculated by using coordinate transformation, thereby improving the model fidelity under complex geometric boundaries.

[0136] In view of the problem that the existing empirical coefficients lack physical meaning and have poor generalization ability, the application adopts a coefficient decomposition method driven by physical mechanism. The correction coefficient is decomposed into a potential flow component representing boundary geometric acceleration and a dynamic component representing turbulent flow and vortex loss, so that the model parameters can directly respond to changes in physical quantities such as flow velocity shear and vortex intensity, overcoming the defect that pure statistical regression fails in extreme working conditions.

[0137] In view of the problem that the traditional static calculation ignores transient risk, the application introduces vortex evolution time scale and dynamic safety margin evaluation. By calculating the time lag effect of vortex penetration, a safety buffer for dealing with flow state fluctuations is added to the static critical value, which makes up for the blank of traditional methods in dynamic safety evaluation.

[0138] In summary, the embodiment demonstrates the whole process from parameter input, criterion triggering, geometric correction, physical coefficient calculation to final equation solving, which proves the applicability and closed-loop nature of the calculation logic of the application method in dealing with complex geometric boundaries and flow field conditions.

Claims

1. A method for calculating the critical submersion depth of a side-type inlet based on the CSSS method, characterized in that, include: With the center of the side inlet as the origin and the critical submergence depth to be solved as the radius, construct a point-collection spherical critical surface CSSS sphere; Based on the principle of fluid continuity, a continuity conservation relationship is established between the effective working area of ​​the CSSS sphere and the radial velocity of the CSSS sphere. By introducing a radial velocity correction coefficient, a velocity correlation formula is constructed between the radial velocity of the CSSS sphere and the uniform inflow velocity. Obtain the distances between the centerline of the side inlet and the two side walls respectively. Based on the geometric spatial relationship between the distance and the critical flood depth, calculate the effective working area of ​​the CSSS sphere under boundary constraints. By combining the continuity conservation relationship, the velocity correlation relationship, and the effective working area, a physical model of the critical submersion depth of the side intake is constructed, and the critical submersion depth of the side intake is obtained by analyzing the physical model. The method further includes steps for determining the validity of the sphericity assumption and revising the model: Calculate the dimensionless criteria that characterize the flow field features and boundary geometry features, and compare the dimensionless criteria with the preset failure threshold. When the dimensionless criterion exceeds the failure threshold, the spherical critical surface is determined to be in failure, and the anisotropic ellipsoid correction mode is activated. The correction factor is composed of the potential flow geometric component and the dynamic loss component, and its calculation formula is as follows: k=k pot *k dyn ; where k pot k represents the geometric component of the potential flow. dyn The dynamic loss component; the potential flow geometric component is calculated based on the mirror source principle, characterizing the geometric enhancement effect of boundary confinement on radial velocity: k pot =∏(j∈{l,r,f})(1-C j (S) c / D j ) pj ) (-1 / 2) In the formula, D j The value is L l L r S, corresponding to the distance from the left wall, the distance from the right wall, and the current submerged water depth, respectively; C j The boundary influence coefficient is denoted by k, and pj is the attenuation exponent. The dynamic loss component characterizes the non-potential flow effects of turbulence, shear, and vortices on the flow: k dyn =1+C Tu *Tu 2 +C sh *(|dU / dy|S c ) / U ∞ +C sw *(S w -S (w_crit) Where Tu is the turbulence intensity, |dU / dy| is the velocity shear rate, and S w For rotational intensity, S w_crit C is the critical rotational strength. Tu C Sh C Sw U is the corresponding dynamic influence coefficient. ∞ To achieve a uniform inflow velocity; The method further includes the step of calculating the dynamic safety margin: Using the critical rotation intensity as the flow regime transition threshold, the dynamic timescale of vortex evolution is calculated: τ v =κ v d / U ∞ *1 / (max(|S w -S (w_crit) |,ε)); Based on the dynamic time scale, calculate the dynamic safety margin used to compensate for dynamic vortex effects: ΔS dyn =λ v *τ v *U ∞ 2 / 2g; where △S dyn For dynamic safety margin, τ v For a dynamic time scale, S w For rotational intensity, S w_crit κ is the critical rotational strength. v λ is the time constant. v ε is the margin coefficient, ε is the small quantity to prevent singularities, g is the acceleration due to gravity, d is the diameter of the inlet, and U is the inlet diameter. ∞ To ensure a uniform inflow velocity.

2. The method according to claim 1, characterized in that, Establish a continuous conservation relationship between the effective working area of ​​the CSSS sphere and the radial velocity of the CSSS sphere, specifically as follows: Obtain the diameter and flow velocity of the side inlet, and construct the following continuity conservation equation: A c V s =1 / 4πD 2 V; Among them, A c v is the effective working area of ​​the CSSS sphere. s Where is the radial velocity of the CSSS sphere, D is the diameter of the side inlet, and V is the flow velocity at the side inlet. The velocity relationship between the radial velocity and the uniform incoming flow velocity of the CSSS sphere is constructed as follows: V s =K s U; where K s U is the correction factor, and U is the uniform inflow velocity.

3. The method according to claim 1, characterized in that, Based on the geometric spatial relationship between distance and critical flood depth, the effective working area of ​​the CSSS sphere under boundary constraints is calculated, including: Define the height of the spherical cap intercepted by the side inlet as h, based on the radius S of the CSSS sphere. c Calculate the area of ​​the basic sphere and subtract the area of ​​the spherical cap intercepted by the side inlet to obtain the effective area of ​​the foundation; Determine distance L l and L r With critical radius S c Size relationship: If L l ≥S c And L r ≥S c If the CSSS sphere is not affected by the side walls, the effective area of ​​the base will be directly used as the effective working area As. If L l c And L r ≥S c If the CSSS sphere is affected by one side wall, calculate the area of ​​the spherical cap intercepted by the restricted side wall on the CSSS sphere, and subtract the area of ​​the spherical cap intercepted by the restricted side wall from the effective area of ​​the foundation to obtain the effective working area As.​ If L l c And L r c If the CSSS sphere is affected by the two side walls, calculate the area of ​​the spherical cap intercepted by the two side walls on the CSSS sphere, and subtract the area of ​​the spherical cap intercepted by the two side walls from the effective area of ​​the foundation to obtain the effective working area As.​​ 4. The method according to claim 1, characterized in that, The method further includes the step of determining the correction factor: The Froude number of the side inlet flow, the relative length of the side inlet extending into the reservoir area, and the asymmetry of the boundary were obtained as influencing factors. Spearman rank correlation analysis was used to analyze the correlation between the correction coefficient and the influencing factors; Based on the analysis results, a regression equation was constructed, and the correction coefficient was calculated: k = C0 + C1 * Fr + C2 * (L i / d)+C3*ξ;where k is the correction coefficient, C0, C1, C2, and C3 are regression constants, Fr is the Froude number of the side inlet flow, and L i / d represents the relative length of the side inlet extending into the reservoir area, and ξ represents the asymmetry of the boundary.

5. The method according to claim 1, characterized in that, include: In the anisotropic ellipsoid correction mode, an anisotropic coefficient is introduced, and the radius S of the CSSS sphere is... c Corrected to the three semi-axes of an anisotropic ellipsoid: a x =c x S c ,a y =c y S c ,a z =c z S c ; Among them, a x a y a z S represents the semi-axis lengths of the ellipsoid in the x, y, and z directions, respectively. c For the critical submersion depth, γ x γ y γ z Here are the corresponding anisotropy coefficients, and the formula for calculating the anisotropy coefficients is: c x =1+β w (S c / L l ) m +b s S w n ; c y =1+β w (S c / L r ) m +b s S w n ; c z =1+β f (S c / S) nf ; In the formula, L l L r These are the distances from the center of the side inlet to the left and right side walls, respectively, and S is the current submerged water depth. w For rotational intensity, β w β f β s is the correction factor, and m, n, and nf are the exponential parameters.

6. The method according to claim 5, characterized in that, Dimensionless criteria include at least one of the following: wall anisotropy criterion, free water surface proximity criterion, eddy intensity criterion, and viscous turbulence criterion. Their calculation formulas are as follows: Anisotropy criterion for walls: π w =max(S c / L l ,S c / L r ); Free surface approach criterion: π f =S c / S; Vortex strength criterion: π s =S w =Γ / (U ∞ d); Criterion for viscous turbulence: π ν =(U ∞ S c ) / ν*Tu; Among them, ∏ w ,∏ f ,∏ s ,∏ ν These are the corresponding criterion values, L l L r S represents the distance from the center of the side inlet to the left and right side walls, and S represents the current submerged water depth. c S is the critical submersion depth. w Let Γ be the rotational intensity, Γ be the incoming flow circulation, and U be the flow rate. ∞ For uniform inflow velocity, d is the diameter of the side inlet, ν is the kinematic viscosity, and Tu is the turbulence intensity.

7. The method according to claim 5, characterized in that, Under the anisotropic ellipsoid correction mode, the effective working area of ​​the CSSS sphere under boundary constraints is calculated, specifically including: Using the coordinate stretching equivalence method, a linear mapping relationship is established from the physical coordinate system (x, y, z) to the stretched coordinate system (x', y', z'): x' = x / γ x y'=y / γ y z'=z / γ z ; Based on the linear mapping relationship, the boundary distance in the physical domain is transformed into the equivalent boundary distance in the stretched domain: L' l =L l / γ x L' r =L r / γ y S'=S / γ z ; In the stretched coordinate system, the area of ​​the virtual spherical cap truncated by each boundary is calculated based on the equivalent boundary distance, and the effective working area in the physical domain is calculated using the inverse transformation: A s (EC) ≈1 / (γ x γ y )(πS c 2 -∑A' cap ); Among them, As (EC) A' is the corrected effective working area. cap L' is the area of ​​the virtual spherical cap cut off at each boundary in the stretched domain. l L' r S and S' are the equivalent distances from the center of the side inlet in the stretching domain to the left wall, right wall, and free water surface, respectively.

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