Method, device and equipment for determining critical conditions of rotating stall of pump turbine

Abstract

The invention relates to the technical field of pumped storage power stations, and discloses a method, a device and equipment for determining a critical condition of a rotating stall of a pump-turbine. The method comprises: establishing a simplified model of a pump-turbine, and determining a stability equation of the pump-turbine; determining an initial working condition of the simplified model of the pump-turbine, and performing unsteady flow field calculation of the pump-turbine under the initial working condition to obtain a flow field calculation result; solving a circumferential average velocity and a circumferential average pressure of a turbine runner based on the flow field calculation result, and obtaining a flow field velocity and a flow field pressure at each node on an intermediate surface of the pump-turbine; solving a disturbance amount when a disturbance exists based on the flow field velocity, the flow field pressure and a preset N-S equation; and obtaining a critical condition of a rotating stall of a pump-turbine based on the disturbance amount and the stability equation. The invention realizes the purpose of adopting a rotating stall theoretical analysis method using flow field calculation and solving a critical condition of a rotating stall.

Description

Technical Field

[0001] The invention relates to the technical field of pumped storage power stations, and in particular to a method, a device and equipment for determining critical conditions for rotational stall of a water pump turbine. Background Art

[0002] The core equipment of a pumped-storage power station is a pump-turbine. Unlike a general turbine that is only used for power generation, a pump-turbine needs to have the ability to operate in both directions of a pump and a turbine. According to changes in the load of the power grid, it is necessary to frequently switch between power generation and pumping conditions. This complex operating condition and transition process results in unstable flow characteristics inside it. Under turbine conditions and pump conditions, it will face extremely unstable flow areas in the S zone and the hump zone, respectively. Taking the S zone of the turbine condition as an example, when the pump-turbine is started and stopped under the turbine condition, the same speed can correspond to more than one (3 or four) operating points on the characteristic curve, which enables the pump-turbine to operate in any condition between these operating points, making it difficult to stabilize. In the S zone, there is a very unstable operating characteristic, namely, rotating stall.

[0003] Once rotating stall occurs, the flow field near the turbine runner and movable guide vanes will show obvious asymmetry in the entire circumference, with large flow in some flow channels and small flow in other flow channels. Such flow field distribution will induce strong low-frequency pressure pulsation, causing components such as the runner to be subjected to periodic alternating stress, and there is a risk of fatigue damage to important parts such as blades, which has a great impact on the safe and stable operation of the pump turbine.

[0004] For the analysis and research of rotating stall, the existing technology mainly uses unsteady numerical calculation methods or model test methods to analyze and study the designed flow channel to determine the rotating stall phenomenon within the operating range of the pump turbine. The unsteady numerical calculation method and the model test method have the following disadvantages:

[0005] 1. Unsteady numerical calculation. The entire flow channel of the pump turbine is modeled, including the volute, fixed guide vanes, movable guide vanes, runner and tailwater pipe. The full flow channel model is meshed, and unsteady numerical calculations are performed after boundary conditions are set. The flow process of more than 20 rotations of the runner needs to be calculated; the numerical calculation is mainly for the full flow channel model. The meshing of the flow channel such as the volute, runner and guide vanes is difficult, and the mesh units of the entire flow channel are generally in the millions to tens of millions, which places high demands on computer performance. In addition, rotating stall is an unsteady phenomenon with obvious dynamic characteristics. It is necessary to use unsteady numerical calculations to obtain its starting point and frequency and other characteristics. Even with a powerful computer, it takes a long time. In addition, numerical calculations can determine the flow field characteristics of rotating stall, but it is difficult to determine the starting point of rotating stall.

[0006] 2. Model test. According to the design plan, a proportionally reduced pump-turbine model is manufactured and installed on a general hydraulic machinery test platform for testing. The test process is strictly carried out in accordance with IEC international standards. Model testing can obtain more accurate rotating stall information, but it requires the processing and manufacturing of proportionally reduced pump-turbine models, and the model manufacturing cost of pump-turbine units is relatively high. During the design stage, it is impossible to test every designed impeller in the design process for a certain pump-turbine unit. In addition, it is difficult to identify the operating point where rotating stall occurs in model testing;

[0007] In summary, the above two methods for analyzing rotating stall can usually only analyze the impact of rotating stall on the operating conditions where rotating stall has occurred, including pressure pulsation, vibration and noise. However, the above two methods are difficult to identify and determine the critical conditions of rotating stall. Summary of the invention

[0008] In view of this, the present invention provides a method, device and equipment for determining critical conditions for rotating stall of a pump-turbine, so as to solve the problem that critical conditions for rotating stall of a pump-turbine are difficult to identify and determine.

[0009] In a first aspect, the present invention provides a method for determining a critical condition of a rotating stall of a pump-turbine, the method comprising:

[0010] Establish a three-dimensional model of the entire flow path of the pump-turbine and determine the stability equation of the pump-turbine;

[0011] Determine the initial working condition of the three-dimensional model of the entire flow passage of the pump-turbine, and perform unsteady flow field calculation of the pump-turbine under the initial working condition to obtain the flow field calculation results;

[0012] Based on the flow field calculation results, the average circumferential velocity and average circumferential pressure of the turbine runner are solved;

[0013] Based on the circumferential average velocity and circumferential average pressure, the flow field velocity and flow field pressure at each node on the middle surface of the pump-turbine are obtained;

[0014] Solve the disturbance amount when disturbance exists based on flow field velocity, flow field pressure and preset NS equation;

[0015] The critical condition of rotating stall of pump-turbine is obtained based on the disturbance quantity and stability equation.

[0016] The method for determining the critical condition of rotational stall of a pump-turbine provided by the present invention establishes a three-dimensional model of the entire flow passage of the pump-turbine, determines the stability equation of the pump-turbine, and adopts a rotational stall theoretical analysis method of flow field calculation and a non-steady-state numerical calculation method of solving a disturbance quantity to obtain an operating condition point of the rotational stall. The critical condition of the rotational stall can be clearly determined through the operating condition point of the rotational stall, and the purpose of determining the critical condition of the predecessor disturbance wave of the rotational stall of the disturbance quantity flow field calculation result is achieved. The critical condition is accurately determined before the rotational stall condition of the pump-turbine occurs, and the situation that the rotational stall condition of the pump-turbine occurs is avoided, thereby solving the problem that the critical condition of the rotational stall of the pump-turbine is difficult to identify and determine.

[0017] In an optional implementation, establishing a three-dimensional model of the entire flow path of a pump-turbine and determining the stability equation of the pump-turbine includes:

[0018] The unit flow passage of the pump-turbine is simplified into a one-dimensional model including the runner inlet, runner flow passage and runner outlet, and the one-dimensional model is used as the three-dimensional model of the entire flow passage of the pump-turbine;

[0019] The stability equation of the pump-turbine is obtained based on the small disturbance theory and the three-dimensional model of the full flow path of the pump-turbine.

[0020] The method for determining the critical condition of rotating stall of a pump-turbine provided by the present invention simplifies the unit flow passage of the pump-turbine into a one-dimensional model including a runner inlet, a runner flow passage and a runner outlet, and uses the one-dimensional model as a three-dimensional model of the entire flow passage of the pump-turbine; the stability equation of the pump-turbine is obtained based on the small disturbance theory and the simplified model of the pump-turbine, thereby achieving the purpose of using the three-dimensional model of the entire flow passage of the pump-turbine to determine the stability equation of the pump-turbine, overcoming the defect that the existing model experiments and numerical calculation methods are difficult to determine the stable state of the pump-turbine, and providing a model basis for solving the disturbance quantity when a subsequent disturbance wave exists.

[0021] In an optional implementation, the initial operating condition of the three-dimensional model of the entire flow channel of the pump-turbine is determined, and the unsteady flow field of the pump-turbine is calculated under the initial operating condition, and the flow field calculation results obtained include:

[0022] The operating condition of any guide vane opening curve in the operating area of ​​the three-dimensional model of the whole flow passage of the pump-turbine is taken as the initial operating condition;

[0023] The unsteady flow field of the pump-turbine inlet flow rate linearly decreasing process is calculated under the initial working condition, and the flow field calculation results are obtained.

[0024] The method for determining the critical condition of rotating stall of a pump-turbine provided by the present invention takes the operating condition of the operating area where any guide vane opening curve of the three-dimensional model of the full flow passage of the pump-turbine is located as the initial condition; under the initial condition, the unsteady flow field of the process of linear reduction of the pump-turbine inlet flow is calculated to obtain the flow field calculation result, thereby achieving the purpose of using the three-dimensional model of the full flow passage of the pump-turbine to calculate the unsteady flow field and obtain the flow field calculation result, and providing numerical conditions for subsequently obtaining the flow field velocity and flow field pressure.

[0025] In an optional embodiment, obtaining the flow field velocity and flow field pressure at each node on the middle surface of the pump-turbine based on the circumferential average velocity and the circumferential average pressure includes:

[0026] The middle surface of the pump-turbine runner is determined, and the circumferential average velocity and circumferential average pressure are interpolated onto the middle surface to obtain the flow field velocity and flow field pressure at each node on the middle surface.

[0027] The method for determining the critical condition of rotating stall of a pump-turbine provided by the present invention determines the intermediate surface of the runner of the pump-turbine, interpolates the circumferential average velocity and the circumferential average pressure onto the intermediate surface, and obtains the flow field velocity and flow field pressure at each node on the intermediate surface, thereby simplifying the calculation process and providing boundary conditions for subsequent calculation of disturbance quantities.

[0028] In an optional implementation, solving the disturbance amount when the disturbance exists based on the flow field velocity and the flow field pressure and the preset NS equation includes:

[0029] Obtain the circumferential velocity of the inlet edge of the runner blade where the disturbed flow field exists, the radius at the inlet of the runner, the angular velocity of the circumferential rotation of the disturbance amount, and the disturbance amount of the angular velocity of the runner rotation;

[0030] The circumferential velocity of the inlet edge of the runner blade, the radius at the inlet of the runner, the angular velocity of the circumferential rotation of the disturbance, and the disturbance of the angular velocity of the rotation of the runner are dimensionless.

[0031] Substitute the dimensionless circumferential velocity of the inlet edge of the runner blade, the radius at the inlet of the runner, the angular velocity of the circumferential rotation of the disturbance, and the disturbance of the angular velocity of the rotation of the runner into the preset NS equation to obtain the disturbance equation;

[0032] The disturbance quantity equation is solved with flow field velocity and flow field pressure as boundary conditions to obtain the disturbance quantity when the disturbance exists.

[0033] The method for determining the critical condition of rotating stall of a pump turbine provided by the present invention determines the disturbance amount of the disturbance wave of the predecessor of rotating stall based on the rotating stall theoretical analysis method and the numerical calculation method, converts the disturbance wave when the disturbance exists into the numerical calculation for solving the disturbance amount, and the solving process is clear and complete. Compared with the expensive model test method and the non-steady-state numerical calculation method, the calculation process is simple and the cost investment is low, which provides a basis for the subsequent determination of the critical condition of rotating stall.

[0034] In an optional implementation, the disturbance quantity equation is solved with the flow field velocity and the flow field pressure as boundary conditions to obtain the disturbance quantity when the disturbance exists, including:

[0035] Obtain the polar coordinates of the nodes on the flow surface of runner S2;

[0036] The partial derivatives in the perturbation equation are transformed based on the node polar coordinates to obtain the transformed partial derivatives;

[0037] Determine the number of periods of the corresponding simple harmonic wave in the perturbation quantity equation;

[0038] Substitute the preset Jacobian determinant, the converted partial derivatives and the number of periods of the simple harmonic wave into the disturbance equation, and discretize the disturbance equation using the flow field velocity and flow field pressure as boundary conditions to obtain a non-homogeneous linear equation system;

[0039] The singular value decomposition technique is used to solve the nonhomogeneous linear equations and obtain the disturbance amount when the disturbance exists.

[0040] The method for determining the critical condition of rotating stall of a pump-turbine provided by the present invention obtains the disturbance quantity when the disturbance exists by converting and calculating the disturbance quantity equation, thereby simplifying the calculation process, reducing the amount of calculation when solving the disturbance quantity, and clearly and completely expressing the numerical calculation process of the solution, thus building a path between theory and application.

[0041] In an optional implementation, obtaining the critical condition of the pump-turbine rotating stall based on the disturbance quantity and the stability equation includes:

[0042] Substitute the disturbance into the stability equation to obtain the first parameter and the second parameter;

[0043] The operating condition point when the first parameter is greater than the first preset threshold and the second parameter is less than or equal to the second preset threshold is used as the critical condition for the rotational stall of the pump turbine.

[0044] The method for determining the critical condition of rotational stall of a pump-turbine provided by the present invention substitutes the disturbance into the stability equation to obtain a first parameter and a second parameter; the operating condition point when the first parameter is greater than a first preset threshold value and the second parameter is less than or equal to the second preset threshold value is used as the critical condition of rotational stall of the pump-turbine, the disturbance is combined with the stability equation of the pump-turbine, and the operating condition point of rotational stall of the pump-turbine is determined. The critical condition of rotational stall can be clearly determined through the operating condition point of rotational stall, and the critical condition can be accurately determined before the rotational stall condition of the pump-turbine occurs, thereby avoiding the situation where the rotational stall condition of the pump-turbine occurs.

[0045] In a second aspect, the present invention provides a device for determining a critical condition of a rotating stall of a pump turbine, the device comprising:

[0046] Establishing a module for establishing a three-dimensional model of the entire flow path of a pump-turbine and determining the stability equation of the pump-turbine;

[0047] A determination module is used to determine the initial working condition of the three-dimensional model of the entire flow passage of the pump-turbine, and to perform unsteady flow field calculation of the pump-turbine under the initial working condition to obtain flow field calculation results;

[0048] The first solving module is used to solve the circumferential average velocity and circumferential average pressure of the turbine runner based on the flow field calculation results;

[0049] The second solving module is used to obtain the flow field velocity and flow field pressure at each node on the middle surface of the pump-turbine based on the circumferential average velocity and the circumferential average pressure;

[0050] The third solution module is used to solve the disturbance amount when the disturbance exists based on the flow field velocity, the flow field pressure and the preset NS equation;

[0051] The fourth solving module is used to obtain the critical condition of the rotating stall of the pump turbine based on the disturbance quantity and the stability equation.

[0052] In a third aspect, the present invention provides a computer device, comprising: a memory and a processor, the memory and the processor being communicatively connected to each other, the memory storing computer instructions, and the processor executing the method for determining the critical conditions for rotational stall of a pump turbine according to the first aspect or any corresponding embodiment thereof by executing the computer instructions.

[0053] In a fourth aspect, the present invention provides a computer-readable storage medium having computer instructions stored thereon, the computer instructions being used to enable a computer to execute the method for determining the critical conditions for rotational stall of a pump-turbine according to the first aspect or any corresponding embodiment thereof. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] In order to more clearly illustrate the specific implementation methods of the present invention or the technical solutions in the prior art, the drawings required for use in the specific implementation methods or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some implementation methods of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0055] Figure 1 is a flow chart of a method for determining a critical condition of a pump-turbine rotating stall according to an embodiment of the present invention;

[0056] Figure 2 is a flow chart of another method for determining critical conditions of rotating stall of a pump-turbine according to an embodiment of the present invention;

[0057] Figure 3 is a flow chart of another method for determining critical conditions of rotating stall of a pump-turbine according to an embodiment of the present invention;

[0058] Figure 4 is a schematic diagram of a three-dimensional model of a full flow passage of a pump-turbine according to an embodiment of the present invention;

[0059] Figure 5 is a schematic diagram of selecting the initial working condition of the full flow passage three-dimensional model of a pump-turbine according to an embodiment of the present invention;

[0060] Figure 6 Schematic diagram of the flow surface coordinate transformation effect of the pump-turbine runner S2 according to an embodiment of the present invention;

[0061] Figure 7 is a structural block diagram of a device for determining a critical condition of a pump-turbine rotating stall according to an embodiment of the present invention;

[0062] Figure 8 It is a schematic diagram of the hardware structure of a computer device according to an embodiment of the present invention. DETAILED DESCRIPTION

[0063] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative work are within the scope of protection of the present invention.

[0064] According to an embodiment of the present invention, an embodiment of a method for determining critical conditions for rotating stall of a pump-turbine is provided. It should be noted that the steps shown in the flowchart of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and although a logical order is shown in the flowchart, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0065] In this embodiment, a method for determining a critical condition of a pump-turbine rotating stall is provided, which can be used for a pump-turbine. Figure 1 is a flow chart of a method for determining a critical condition of a pump turbine rotating stall according to an embodiment of the present invention. Figure 1 As shown, the process includes the following steps:

[0066] Step S101, establishing a three-dimensional model of the entire flow path of a pump-turbine and determining a stability equation of the pump-turbine.

[0067] Specifically, in order to subsequently solve the disturbance amount when there is a disturbance, the pump-turbine stability theory is first explained. According to the rotating stall theory in the relevant technology, a small disturbance in a fluid machine is the source of flow field instability and eventually develops into a rotating stall. Assume that a small flow disturbance is transmitted from upstream to the inlet of the pump-turbine runner. j , the disturbance is non-uniform in the circumferential direction, so it can be expressed as j ( θ ) has a periodic circumferential rotation with a rotation frequency of f (this frequency corresponds to the circumferential rotation frequency of the rotational stall obtained by its development) and an average flow rate of Q. The disturbance disappears at the runner outlet; based on the transmission process of this tiny flow disturbance, a three-dimensional model of the entire flow channel of the pump-turbine is established, and based on the three-dimensional model of the entire flow channel of the pump-turbine, the stability equation of the pump-turbine, that is, the critical condition for system stability, is determined.

[0068] Step S102, determining the initial working condition of the three-dimensional model of the entire flow passage of the pump-turbine, and performing unsteady flow field calculation of the pump-turbine under the initial working condition to obtain flow field calculation results.

[0069] Specifically, the unsteady flow field refers to the flow of unbalanced pump-turbine motion, in which the flow velocity at each point in the flow field changes with time, and the pressure, viscous force and inertial force at each point also change with the change of velocity.

[0070] like Figure 5 As shown, a curve of equal guide vane opening is selected from the turbine operating condition part of the full characteristic curve of the pump-turbine as the research condition, and a certain condition is selected in the operation area as the initial calculation condition, and the unsteady flow field calculation of the pump-turbine is carried out under the initial condition to obtain the flow field calculation result.

[0071] Step S103, solving the circumferential average velocity and circumferential average pressure of the turbine runner based on the flow field calculation results.

[0072] Specifically, the flow field data at the guide vane outlet and in the runner are extracted from the flow field calculation results of each saved working condition, including the coordinates, velocity, pressure and other data of each position in the flow field. The runner flow field is solved based on the flow field data at the guide vane outlet and in the runner to obtain the circumferential average flow field, and the circumferential average velocity and circumferential average pressure of the turbine runner can be obtained.

[0073] Step S104, obtaining the flow field velocity and flow field pressure at each node on the middle surface of the pump-turbine based on the circumferential average velocity and the circumferential average pressure.

[0074] Specifically, it is assumed that the circumferential flow of the non-rotating stall flow field is uniform and indifferent, that is, it satisfies the infinite blade assumption, and there are infinite blades inside the entire runner, and the blades can be equivalent to the S2 flow surface in the two-dimensional blade design theory. The fluid in the runner can only flow along the blade surface, that is, along the S2 flow surface. The circumferential average flow field solved in step S103 is used to approximate the flow field under this assumption.

[0075] The blade surface of the runner is taken as the middle surface, and the flow field velocity and flow field pressure at each node on the middle surface of the pump-turbine are obtained based on the circumferential average velocity and the circumferential average pressure.

[0076] Step S105, solving the disturbance amount when the disturbance exists based on the flow field velocity, the flow field pressure and the preset NS equation.

[0077] Specifically, the preset NS equations (numeric equations of Navier-Stokes equations) refer to the Navier-Stokes equations, which are motion equations that describe the conservation of momentum of viscous incompressible fluids. The flow field velocity and flow field pressure are used as boundary conditions, and the disturbance amount when the disturbance exists is solved based on the preset NS equations.

[0078] Step S106, obtaining the critical condition of the pump-turbine rotational stall based on the disturbance quantity and the stability equation.

[0079] Specifically, the disturbance quantity and the stability equation are combined, and a numerical calculation method is used to find the operating condition that approximately satisfies the critical condition of disturbance stability, that is, the critical condition of rotating stall of the pump-turbine is obtained.

[0080] The method for determining the critical conditions of rotating stall of a pump-turbine provided in this embodiment establishes a three-dimensional model of the entire flow passage of the pump-turbine, determines the stability equation of the pump-turbine, and adopts a rotating stall theoretical analysis method for flow field calculation and a non-steady-state numerical calculation method for solving the disturbance quantity to obtain the operating condition point of the rotating stall. The critical conditions of the rotating stall can be clearly determined through the operating condition point of the rotating stall, and the purpose of determining the critical conditions of the disturbance wave that is the predecessor of the rotating stall in the flow field calculation result of the disturbance quantity is achieved. The critical conditions are accurately determined before the rotating stall condition of the pump-turbine occurs, and the situation where the rotating stall condition of the pump-turbine occurs is avoided, thereby solving the problem that the critical conditions of the rotating stall of the pump-turbine are difficult to identify and determine.

[0081] In this embodiment, a method for determining a critical condition of a pump-turbine rotating stall is provided, which can be used for a pump-turbine. Figure 2 is a flow chart of a method for determining a critical condition of a pump turbine rotating stall according to an embodiment of the present invention. Figure 2 As shown, the process includes the following steps:

[0082] Step S201, establish a three-dimensional model of the entire flow path of the pump-turbine and determine the stability equation of the pump-turbine. Specifically, the above step S201 includes:

[0083] Step S2011, simplifying the unit flow path of the pump-turbine into a one-dimensional model including a runner inlet, a runner flow path and a runner outlet, and using the one-dimensional model as a three-dimensional model of the entire flow path of the pump-turbine.

[0084] Specifically, the unit flow passage of the pump-turbine is simplified into a one-dimensional model including the runner inlet, runner flow passage and runner outlet, and the one-dimensional model is used as the three-dimensional model of the entire flow passage of the pump-turbine. The three-dimensional model of the entire flow passage of the pump-turbine is as follows: Figure 4 As shown. In the simplified model of the pump-turbine, the runner flow path of the pump-turbine is divided into the inlet section, the runner section and the outlet section. Among them, the total pressure at the inlet of the runner is p T , the outlet pressure of the outlet section is p S .

[0085] Step S2012, obtaining the stability equation of the pump-turbine based on the small disturbance theory and the simplified model of the pump-turbine.

[0086] Specifically, small-perturbation theory is an approximate theory for analyzing and studying certain fluid mechanics problems. To simplify the calculation, it is assumed that the radial velocity perturbation at the inlet is R (1) = 1, the pressure disturbance at the inlet P (1)= PR(1)+ iPM (1). Finally, the stability equation of the pump turbine is obtained:

[0087] (1);

[0088] Equation (1) is the model's assumption that disturbance waves exist stably in the flow field, that is, the stability equation of the pump-turbine. f and n The disturbance wave characteristics assumed in the calculation, Q is the radial velocity coefficient, V r The speed of the high pressure side of the runner U The ratio, D is the diameter of the high pressure side of the runner, n is the disturbance circumferential wave number, f is the perturbation rotation speed, They represent the influence of hysteresis on the flow, the ratio of the flow area between the runner inlet and outlet, and the circumferential velocity coefficient of the simplified model outlet section. When the stability equation of the pump turbine mentioned above is established, it is considered that the small disturbance that can develop into rotating stall as assumed by the small disturbance theory exists. PR (1) and PM (1) is the amplitude of the disturbance at the runner inlet. Thus, the stability analysis of the pump turbine is transformed into solving the disturbance PR (1) and PM (1) PR (1) is the radial disturbance, i.e. the radial amplitude at the runner inlet, PM (1) is the circumferential disturbance, that is, the circumferential amplitude at the runner inlet.

[0089] Step S202, determining the initial working condition of the three-dimensional model of the entire flow passage of the pump-turbine, and performing unsteady flow field calculation of the pump-turbine under the initial working condition to obtain the flow field calculation result.

[0090] Specifically, the above step S202 includes:

[0091] Step S2021, taking the operating condition of the operating area where any guide vane opening curve of the full flow channel three-dimensional model of the pump-turbine is located as the initial operating condition.

[0092] Specifically, Figure 5 As shown in the figure, a curve with equal guide vane opening is selected from the turbine operating condition part of the full characteristic curve of the pump turbine as the research condition, and a condition is selected in the operation area as the initial calculation condition OP1, and the slope of the characteristic curve at its location dQ 11 / dn 11 <0, the slope is between -4 and -1;

[0093] Set a certain operating point OP f , as the end point of the flow change process, the operating condition corresponding to this point is within the turbine braking condition range of the characteristic curve, and the slope of the characteristic curve at its location is dQ 11 / dn 11 >0, the slope of this point is between 1 and 5.

[0094] Step S2022, calculating the unsteady flow field of the pump-turbine inlet flow rate linear reduction process under the initial working condition to obtain the flow field calculation result.

[0095] Specifically, the unsteady flow field is calculated for the initial working condition, and the calculation result is used as the initial condition to continue to calculate the unsteady flow field of the process of linear reduction of the inlet flow of the group. The flow field data of a process is recorded at a certain interval flow rate to obtain the flow field calculation result. The interval flow rate can be OP1 and OP f The flow field calculation results include the flow field data at the guide vane outlet and the runner, including the coordinates, velocity, pressure and other data of each position in the flow field.

[0096] Step S203, based on the flow field calculation results, solve the circumferential average velocity and circumferential average pressure of the turbine runner. Figure 1 Step S103 of the illustrated embodiment will not be described in detail here.

[0097] Step S204, obtaining the flow field velocity and flow field pressure at each node on the middle surface of the pump-turbine based on the circumferential average velocity and the circumferential average pressure.

[0098] Specifically, the middle surface of the pump-turbine runner is determined, and the circumferential average velocity and circumferential average pressure are interpolated onto the middle surface to obtain the flow field velocity and flow field pressure at each node on the middle surface. The middle surface of the pump-turbine runner is the blade surface of the runner assuming infinite blades.

[0099] Step S205, based on the flow field velocity, flow field pressure and the preset NS equation, solve the disturbance amount when the disturbance exists. Figure 1 Step S105 of the illustrated embodiment will not be described in detail here.

[0100] Step S206, obtaining the critical condition of the pump-turbine rotating stall based on the disturbance quantity and the stability equation.

[0101] For details, please see Figure 1 Step S106 of the illustrated embodiment will not be described in detail here.

[0102] The method for determining the critical condition of rotating stall of a pump-turbine provided in this embodiment simplifies the unit flow passage of the pump-turbine into a one-dimensional model including a runner inlet, a runner flow passage and a runner outlet, and uses the one-dimensional model as a three-dimensional model of the entire flow passage of the pump-turbine; obtains the stability equation of the pump-turbine based on the small disturbance theory and the three-dimensional model of the entire flow passage of the pump-turbine, thereby achieving the purpose of using the simplified model of the pump-turbine to determine the stability equation of the pump-turbine, and uses the operating condition of the operating area where any guide vane opening curve of the three-dimensional model of the entire flow passage of the pump-turbine is located as the initial condition; calculates the unsteady flow field of the process of linear reduction of the inlet flow of the pump-turbine under the initial condition to obtain the flow field calculation result, thereby achieving the purpose of using the three-dimensional model of the entire flow passage of the pump-turbine to calculate the unsteady flow field and obtain the flow field calculation result, providing numerical conditions for subsequently obtaining the flow field velocity and flow field pressure, overcoming the defect that the existing model experiment and numerical calculation method are difficult to determine the stable state of the pump-turbine, and providing a model basis for solving the disturbance quantity when the subsequent disturbance wave exists.

[0103] In this embodiment, a method for determining a critical condition of a pump-turbine rotating stall is provided, which can be used for a pump-turbine. Figure 3 is a flow chart of a method for determining a critical condition of a pump turbine rotating stall according to an embodiment of the present invention. Figure 3 As shown, the process includes the following steps:

[0104] Step S301, establish a three-dimensional model of the entire flow path of the pump-turbine and determine the stability equation of the pump-turbine. Figure 2 Step S201 of the illustrated embodiment will not be described in detail here.

[0105] Step S302, determine the initial working condition of the three-dimensional model of the entire flow channel of the pump-turbine, and perform unsteady flow field calculation of the pump-turbine under the initial working condition to obtain the flow field calculation result. Figure 2 Step S202 of the illustrated embodiment will not be described in detail here.

[0106] Step S303, based on the flow field calculation results, solve the circumferential average velocity and circumferential average pressure of the turbine runner. Figure 2 Step S203 of the illustrated embodiment will not be described in detail here.

[0107] Step S304, based on the circumferential average velocity and circumferential average pressure, obtain the flow field velocity and flow field pressure at each node on the middle surface of the pump turbine. Figure 2 Step S204 of the illustrated embodiment will not be described in detail here.

[0108] Step S305, solving the disturbance amount when the disturbance exists based on the flow field velocity, the flow field pressure and the preset NS equation.

[0109] Specifically, the above step S305 includes:

[0110] Step S3051, obtaining the circumferential velocity of the inlet edge of the runner blade where the disturbed flow field exists, the radius at the runner inlet, the angular velocity of the circumferential rotation of the disturbance amount, and the disturbance amount of the runner rotation angular velocity.

[0111] Specifically, in a disturbed flow field, the physical quantity of each node is expressed in the form of the sum of the non-disturbance quantity and the disturbance quantity, that is: N = N a + N ',in N is the total physical quantity, N a is the non-perturbing quantity, N ' is the disturbance quantity, which is an infinitesimal quantity, that is, the physical quantity has the following numerical value: N a >> N The disturbance of the pump turbine in the disturbed flow field includes the circumferential velocity of the inlet edge of the runner blade, that is, the linear velocity of the high-pressure edge of the runner. U , Radius of runner inlet R 1. Angular velocity of the disturbance's circumferential rotation F and the wheel rotation angular velocity ω The amount of disturbance.

[0112] Step S3052, non-dimensionalize the circumferential velocity of the inlet edge of the runner blade, the radius at the inlet of the runner, the angular velocity of the circumferential rotation of the disturbance, and the disturbance of the angular velocity of the rotation of the runner.

[0113] Specifically, each physical quantity is dimensionless using the following form:

[0114] (2);

[0115] in, U is the circumferential velocity of the runner blade inlet edge, also known as the runner high-pressure edge velocity. R 1 is the radius of the runner entrance, F is the angular velocity of the disturbance's circumferential rotation, ω is the angular velocity of the wheel, V is the viscosity coefficient, f is the perturbation rotation speed, , , Respectively represent the radial velocity coefficient, circumferential velocity coefficient and axial velocity coefficient of each node, , , Represent the radial velocity, circumferential velocity and axial velocity of each node respectively , denote the pressure coefficient and pressure respectively, , , They represent the radius, axial coordinate and dimensionless viscosity coefficient of each node respectively.

[0116] Step S3053, substitute the dimensionless circumferential velocity of the inlet edge of the runner blade, the radius at the inlet of the runner, the angular velocity of the circumferential rotation of the disturbance amount, and the disturbance amount of the angular velocity of the rotation of the runner into the preset NS equation to obtain the disturbance amount equation.

[0117] Specifically, the physical quantity in the NS equation of the disturbance quantity is replaced by the form of formula (2), and the dimensionless form of formula (2) is used. Finally, the second-order infinitesimal terms in the equation are ignored, and the disturbance quantity equation is obtained, which is as follows:

[0118] (3);

[0119] in, Represents the partial derivative operation.

[0120] Step S3054, solving the disturbance quantity equation with the flow field velocity and the flow field pressure as boundary conditions to obtain the disturbance quantity when the disturbance exists.

[0121] In some optional implementations, the above step S3054 includes:

[0122] Step a1, obtaining the polar coordinates of the nodes on the flow surface of the runner S2.

[0123] Specifically, the nodes on the flow surface of runner S2 are represented by polar coordinates, where θ yes r and z The function of the node polar coordinates is: θ = f ( r , z ).

[0124] Step a2, transforming the partial derivatives in the disturbance equation based on the node polar coordinates to obtain the transformed partial derivatives.

[0125] Specifically, based on the node polar coordinates and formula (4), the partial derivatives in the perturbation equation (3) are transformed to obtain the transformed partial derivatives. Formula (4) is as follows:

[0126] (4);

[0127] In order to discretize the perturbation equation (3), it is necessary to transform the coordinates of the grid on the S2 flow surface of the complex mechanism. The Jacobian determinant used for the transformation is:

[0128] (5);

[0129] Using the above coordinate transformation, the node coordinate system of the S2 flow surface is changed from rzθ Converted to ξηθ Coordinate system, S2 flow surface is perpendicular to θ The effect on the projection surface of the direction is as follows Figure 6 shown.

[0130] Step a3, determining the number of periods of the corresponding simple harmonic wave in the disturbance quantity equation.

[0131] Each disturbance quantity in the disturbance equation (3) is defined in the form of simple harmonic waves. n It represents the wave number of the disturbance wave within a whole circle, that is, the period number. The specific form of the period number of the corresponding simple harmonic wave is as follows:

[0132] (6);

[0133] Step a4, substitute the preset Jacobian determinant, the converted partial derivatives and the number of periods of the simple harmonic wave into the disturbance equation, and discretize the disturbance equation with the flow field velocity and flow field pressure as boundary conditions to obtain a non-homogeneous linear equation group.

[0134] Specifically, the flow field velocity includes the radial velocity disturbance at the impeller inlet, and the flow field pressure includes the pressure disturbance at the outlet. The relationship between formulas (4) to (6) is substituted into the disturbance equation (3). The impenetrable boundaries of the inlet radial velocity disturbance, the outlet pressure disturbance, and the disturbances on the upper and lower walls of the flow channel are used as boundary conditions for solving the disturbance equation. The disturbance equation is discretized and finally a non-homogeneous linear equation system AX=B is obtained.

[0135] Step a5, using singular value decomposition technology to solve the non-homogeneous linear equations to obtain the disturbance amount when the disturbance exists.

[0136] Specifically, for r Direction and z The number of nodes in the direction of the grid is m and n respectively. The matrix A is a 8mn×8mn matrix, and its elements increase exponentially with the increase of the number of grid nodes. The number of elements in the linear equation system AX=B is huge, and the singular value decomposition (SVD) technique is used to solve it. For any m × n ( m Greater than or equal to n ), we have:

[0137] (7);

[0138] in, M for m × n The column of the matrix is ​​orthogonal. n × n A diagonal matrix with the elements λ 1, λ 2,…, λ n For the matrix A The singular values ​​of . L yes n × n The original matrix is ​​transformed into an orthogonal matrix by singular value decomposition technology. A After decomposition, the matrix can be easily calculated A The inverse matrix (or pseudo-inverse matrix) of A -1 , and then through X = A -1 B Find the unknown vector X .

[0139] For the above large matrix operation, a graphics processing unit (GPU) is used to process the calculation to increase the calculation speed.

[0140] From the above calculation, we can know that X in AX=B is the solution of the velocity disturbance and pressure disturbance at each node. By solving X according to the above method, we can get the disturbance when the disturbance exists. PR (1) and PM (1).

[0141] The method for determining the critical condition of rotating stall of a pump-turbine provided in this embodiment obtains the disturbance quantity when the disturbance exists by converting and calculating the disturbance quantity equation, thereby simplifying the calculation process, reducing the amount of calculation when solving the disturbance quantity, and clearly and completely expressing the numerical calculation process of the solution, thus building a path between theory and application.

[0142] Step S306, obtaining the critical condition of the pump-turbine rotating stall based on the disturbance quantity and the stability equation.

[0143] Specifically, the above step S306 includes:

[0144] Step S301, substituting the disturbance into the stability equation to obtain a first parameter and a second parameter.

[0145] Specifically, the formulas for the first parameter and the second parameter are as follows:

[0146] (8);

[0147] in, is the first parameter, is the second parameter, which can be the damping of the disturbance wave.

[0148] Step S302: taking the operating condition point when the first parameter is greater than the first preset threshold and the second parameter is less than or equal to the second preset threshold as the critical condition for rotational stall of the pump-turbine.

[0149] Specifically, the first preset threshold and the second preset threshold are both set to 0. If the first parameter The operating range with a larger value indicates that the speed is f , the wave number is n The disturbance wave can exist; the second parameter represents the damping of the disturbance wave, if <0 means that the disturbance wave amplitude increases with time, that is, the small disturbance continues to grow and develops into a macroscopic rotational stall. So the first parameter is determined to be is greater than 0, and the second parameter The operating condition close to 0 is the starting condition of rotating stall, and the corresponding operating point is the critical condition of rotating stall. If the flow rate is further reduced based on this operating condition, rotating stall will inevitably occur.

[0150] The method for determining the critical condition of rotating stall of a pump-turbine provided in this embodiment determines the disturbance amount of the disturbance wave of the predecessor of rotating stall based on the rotating stall theoretical analysis method and the numerical calculation method, converts the disturbance wave when there is disturbance into the numerical calculation for solving the disturbance amount, and the solution process is clear and complete. Compared with the expensive model test method and the non-steady-state numerical calculation method, its calculation process is simple and the required cost investment is low, which provides a basis for the subsequent determination of the critical condition of rotating stall. Substitute the disturbance amount into the stability equation to obtain the first parameter and the second parameter; take the operating condition point when the first parameter is greater than the first preset threshold and the second parameter is less than or equal to the second preset threshold as the critical condition of rotating stall of the pump-turbine, combine the disturbance amount with the stability equation of the pump-turbine, determine the operating condition point of rotating stall of the pump-turbine, and the critical condition of rotating stall can be clearly determined through the operating condition point of rotating stall, and the critical condition can be accurately determined before the rotating stall condition of the pump-turbine occurs, so as to avoid the situation where the rotating stall condition of the pump-turbine occurs.

[0151] In this embodiment, a device for determining the critical condition of rotating stall of a pump turbine is also provided, and the device is used to implement the above-mentioned embodiments and preferred implementation modes, and the descriptions that have been made will not be repeated. As used below, the term "module" can implement a combination of software and / or hardware of a predetermined function. Although the device described in the following embodiments is preferably implemented in software, the implementation of hardware, or a combination of software and hardware, is also possible and conceivable.

[0152] This embodiment provides a device for determining critical conditions of rotational stall of a pump turbine, such as Figure 7 As shown, including:

[0153] The module 701 is established to establish a three-dimensional model of the entire flow path of the pump-turbine and determine the stability equation of the pump-turbine.

[0154] The determination module 702 is used to determine the initial working condition of the three-dimensional model of the entire flow passage of the pump-turbine, and perform unsteady flow field calculation of the pump-turbine under the initial working condition to obtain the flow field calculation result.

[0155] The first solving module 703 is used to solve the circumferential average velocity and circumferential average pressure of the turbine runner based on the flow field calculation results.

[0156] The second solving module 704 is used to obtain the flow field velocity and flow field pressure at each node on the middle surface of the pump-turbine based on the circumferential average velocity and the circumferential average pressure.

[0157] The third solution module 705 is used to solve the disturbance amount when the disturbance exists based on the flow field velocity, the flow field pressure and the preset NS equation.

[0158] The fourth solving module 706 is used to obtain the critical condition of the rotating stall of the pump turbine based on the disturbance quantity and the stability equation.

[0159] In some optional implementations, the establishing module 701 includes:

[0160] The simplified unit is used to simplify the unit flow path of the pump-turbine into a one-dimensional model including a runner inlet, a runner flow path and a runner outlet, and use the one-dimensional model as a three-dimensional model of the entire flow path of the pump-turbine.

[0161] The first solving unit is used to obtain the stability equation of the pump-turbine based on the small disturbance theory and the three-dimensional model of the whole flow passage of the pump-turbine.

[0162] In some optional implementations, the determining module 702 includes:

[0163] The selection unit is used to take the operating condition of an operating area where any guide vane opening curve of the full flow channel three-dimensional model of the pump-turbine as the initial operating condition.

[0164] The calculation unit is used to calculate the unsteady flow field of the pump-turbine inlet flow rate linear reduction process under the initial working condition to obtain the flow field calculation result.

[0165] In some optional implementations, the second solution module 704 includes:

[0166] A solution unit is determined to determine the middle surface of the pump-turbine runner, and the circumferential average velocity and the circumferential average pressure are interpolated to the middle surface to obtain the flow field velocity and the flow field pressure at each node on the middle surface.

[0167] In some optional implementations, the third solution module 705 includes:

[0168] The acquisition unit is used to obtain the circumferential velocity of the inlet edge of the runner blade where the disturbed flow field exists, the radius at the runner inlet, the angular velocity of the circumferential rotation of the disturbance amount, and the disturbance amount of the runner rotation angular velocity.

[0169] The dimensionless unit is used to dimensionlessly transform the circumferential velocity of the inlet edge of the runner blade, the radius at the inlet of the runner, the angular velocity of the circumferential rotation of the disturbance amount, and the disturbance amount of the angular velocity of the rotation of the runner.

[0170] The second solving unit is used to substitute the dimensionless circumferential velocity of the inlet edge of the runner blade, the radius at the inlet of the runner, the angular velocity of the circumferential rotation of the disturbance amount, and the disturbance amount of the angular velocity of the rotation of the runner into the preset NS equation to obtain the disturbance amount equation.

[0171] The third solving unit is used to solve the disturbance quantity equation by taking the flow field velocity and the flow field pressure as boundary conditions to obtain the disturbance quantity when the disturbance exists.

[0172] In some optional implementations, the third solving unit includes:

[0173] The acquisition subunit is used to obtain the polar coordinates of the nodes on the flow surface of the runner S2.

[0174] The conversion subunit is used to convert the partial derivatives in the perturbation equation based on the node polar coordinates to obtain the converted partial derivatives.

[0175] The determination subunit is used to determine the number of periods of the corresponding simple harmonic wave in the disturbance quantity equation.

[0176] The discrete subunit is used to substitute the preset Jacobian determinant, the converted partial derivatives and the number of periods of the simple harmonic wave into the disturbance equation, and discretize the disturbance equation with the flow field velocity and flow field pressure as boundary conditions to obtain a non-homogeneous linear equation group.

[0177] The solving subunit is used to solve the non-homogeneous linear equations by adopting the singular value decomposition technique to obtain the disturbance amount when the disturbance exists.

[0178] In some optional implementations, the fourth solution module 706 includes:

[0179] Bring it into the solving unit to substitute the disturbance into the stability equation to obtain the first parameter and the second parameter;

[0180] The determination unit is used to take the operating condition point when the first parameter is greater than a first preset threshold and the second parameter is less than or equal to a second preset threshold as the critical condition for the rotational stall of the pump turbine.

[0181] The further functional description of each of the above modules and units is the same as that of the above corresponding embodiments and will not be repeated here.

[0182] In this embodiment, the device for determining the critical condition of rotating stall of the pump turbine is presented in the form of a functional unit, where the unit refers to an ASIC (Application Specific Integrated Circuit) circuit, a processor and memory that executes one or more software or fixed programs, and / or other devices that can provide the above functions.

[0183] The embodiment of the present invention also provides a computer device having the above Figure 7 The device for determining the critical condition of rotating stall of a pump turbine is shown.

[0184] See also Figure 8 , Figure 8 is a schematic diagram of the structure of a computer device provided by an optional embodiment of the present invention, such as Figure 8 As shown, the computer device includes: one or more processors 10, a memory 20, and interfaces for connecting various components, including high-speed interfaces and low-speed interfaces. Various components are connected to each other using different buses for communication, and can be installed on a common mainboard or installed in other ways as needed. The processor can process the instructions executed in the computer device, including instructions stored in or on the memory to display the graphical information of the GUI on an external input / output device (such as, a display device coupled to the interface). In some optional embodiments, if necessary, multiple processors and / or multiple buses can be used together with multiple memories and multiple memories. Similarly, multiple computer devices can be connected, and each device provides some necessary operations (for example, as a server array, a group of blade servers, or a multi-processor system). Figure 8 A processor 10 is taken as an example.

[0185] The processor 10 may be a central processing unit, a network processor or a combination thereof. The processor 10 may further include a hardware chip. The hardware chip may be a dedicated integrated circuit, a programmable logic device or a combination thereof. The programmable logic device may be a complex programmable logic device, a field programmable gate array, a general purpose array logic or any combination thereof.

[0186] The memory 20 stores instructions executable by at least one processor 10, so that the at least one processor 10 executes the method shown in the above embodiment.

[0187] The memory 20 may include a program storage area and a data storage area, wherein the program storage area may store an operating system, an application required for at least one function; the data storage area may store data created according to the use of the computer device, etc. In addition, the memory 20 may include a high-speed random access memory, and may also include a non-transient memory, such as at least one disk storage device, a flash memory device, or other non-transient solid-state storage device. In some optional embodiments, the memory 20 may optionally include a memory remotely arranged relative to the processor 10, and these remote memories may be connected to the computer device via a network. Examples of the above-mentioned network include, but are not limited to, the Internet, an intranet, a local area network, a mobile communication network, and combinations thereof.

[0188] The memory 20 may include a volatile memory, such as a random access memory; the memory may also include a non-volatile memory, such as a flash memory, a hard disk or a solid state drive; the memory 20 may also include a combination of the above types of memory.

[0189] The computer device also includes an input device 30 and an output device 40. The processor 10, the memory 20, the input device 30 and the output device 40 may be connected via a bus or other means. Figure 8 The example of connecting through bus is taken in the following.

[0190] The input device 30 can receive input digital or character information, and generate key signal input related to the user settings and function control of the computer device, such as a touch screen, a keypad, a mouse, a track pad, a touch pad, an indicator bar, one or more mouse buttons, a trackball, a joystick, etc. The output device 40 may include a display device, an auxiliary lighting device (e.g., an LED) and a tactile feedback device (e.g., a vibration motor), etc. The above-mentioned display device includes but is not limited to a liquid crystal display, a light emitting diode, a display and a plasma display. In some optional embodiments, the display device may be a touch screen.

[0191] The embodiment of the present invention also provides a computer-readable storage medium. The method according to the embodiment of the present invention can be implemented in hardware, firmware, or can be implemented as a computer code that can be recorded in a storage medium, or can be implemented as a computer code that is originally stored in a remote storage medium or a non-temporary machine-readable storage medium and will be stored in a local storage medium through a network download, so that the method described herein can be stored in such software processing on a storage medium using a general-purpose computer, a dedicated processor, or programmable or dedicated hardware. Among them, the storage medium can be a magnetic disk, an optical disk, a read-only storage memory, a random access memory, a flash memory, a hard disk or a solid-state hard disk, etc.; further, the storage medium can also include a combination of the above types of memories. It can be understood that a computer, a processor, a microprocessor controller, or programmable hardware includes a storage component that can store or receive software or computer code. When the software or computer code is accessed and executed by a computer, a processor, or hardware, the method shown in the above embodiment is implemented.

[0192] Although the embodiments of the present invention have been described in conjunction with the accompanying drawings, those skilled in the art may make various modifications and variations without departing from the spirit and scope of the present invention, and such modifications and variations are all within the scope defined by the appended claims.

Claims

1. A method for determining critical conditions of rotating stall of a pump turbine, characterized in that: The method comprises: Establish a three-dimensional model of the entire flow path of the pump-turbine and determine the stability equation of the pump-turbine; Determining the initial working condition of the three-dimensional model of the entire flow passage of the pump-turbine, and performing unsteady flow field calculation of the pump-turbine under the initial working condition to obtain flow field calculation results; Determining the circumferential average velocity and circumferential average pressure of the turbine runner based on the flow field calculation results; Based on the circumferential average velocity and the circumferential average pressure, the flow field velocity and the flow field pressure at each node on the middle surface of the pump-turbine are obtained; Solving the disturbance amount when the disturbance exists based on the flow field velocity, flow field pressure and the preset NS equation; solving the disturbance amount when the disturbance exists based on the flow field velocity and flow field pressure and the preset NS equation includes: Obtain the circumferential velocity of the inlet edge of the runner blade where the disturbed flow field exists, the radius at the inlet of the runner, the angular velocity of the circumferential rotation of the disturbance amount, and the disturbance amount of the angular velocity of the runner rotation; Non-dimensionalizing the circumferential velocity of the inlet edge of the runner blade, the radius at the inlet of the runner, the angular velocity of the circumferential rotation of the disturbance amount, and the disturbance amount of the angular velocity of the rotation of the runner; Substituting the dimensionless circumferential velocity of the inlet edge of the runner blade, the radius at the inlet of the runner, the angular velocity of the circumferential rotation of the disturbance amount, and the disturbance amount of the angular velocity of the rotation of the runner into the preset NS equation to obtain the disturbance amount equation; The disturbance quantity equation is solved with the flow field velocity and flow field pressure as boundary conditions to obtain the disturbance quantity when the disturbance exists; The disturbance quantity equation is solved by taking the flow field velocity and the flow field pressure as boundary conditions to obtain the disturbance quantity when the disturbance exists, which includes: Obtain the polar coordinates of the nodes on the flow surface of runner S2; Transforming the partial derivatives in the disturbance quantity equation based on the node polar coordinates to obtain transformed partial derivatives; Determine the number of periods of the simple harmonic wave corresponding to the disturbance quantity equation; Substituting the preset Jacobian determinant, the converted partial derivatives and the number of periods of the simple harmonic wave into the disturbance quantity equation, and discretizing the disturbance quantity equation with the flow field velocity and the flow field pressure as boundary conditions to obtain a non-homogeneous linear equation system; The singular value decomposition technique is used to solve the non-homogeneous linear equations to obtain the disturbance amount when the disturbance exists; Based on the disturbance quantity and the stability equation, the critical condition of the pump-turbine rotating stall is obtained.

2. The method according to claim 1, characterized in that The three-dimensional model of the entire flow channel of the pump-turbine is established, and the stability equation of the pump-turbine is determined, including: Simplifying the unit flow passage of the pump-turbine into a one-dimensional model including a runner inlet, a runner flow passage and a runner outlet, and using the one-dimensional model as a three-dimensional model of the entire flow passage of the pump-turbine; The stability equation of the pump-turbine is obtained based on the small disturbance theory and the three-dimensional model of the full flow passage of the pump-turbine.

3. The method according to claim 1, characterized in that The initial working condition of the three-dimensional model of the entire flow channel of the pump-turbine is determined, and the unsteady flow field calculation of the pump-turbine is performed under the initial working condition to obtain the flow field calculation results, including: The operating condition of any guide vane opening curve in the operating area of ​​the three-dimensional model of the whole flow passage of the pump-turbine is taken as the initial operating condition; The unsteady flow field of the pump-turbine inlet flow rate linearly decreasing process is calculated under the initial working condition, and the flow field calculation results are obtained.

4. The method according to claim 1, characterized in that: The flow field velocity and flow field pressure at each node on the middle surface of the pump-turbine are obtained based on the circumferential average velocity and the circumferential average pressure, including: The middle surface of the pump-turbine runner is determined, and the circumferential average velocity and the circumferential average pressure are interpolated onto the middle surface to obtain the flow field velocity and the flow field pressure at each node on the middle surface.

5. The method according to claim 1, characterized in that Based on the disturbance and stability equation, the critical conditions for pump turbine rotation stall include: Substituting the disturbance into the stability equation to obtain a first parameter and a second parameter; The operating condition point when the first parameter is greater than a first preset threshold and the second parameter is less than or equal to a second preset threshold is used as the critical condition for rotational stall of the pump-turbine.

6. A device for determining critical conditions of rotating stall of a pump turbine, characterized in that: The device comprises: Establishing a module for establishing a three-dimensional model of the entire flow path of a pump-turbine and determining the stability equation of the pump-turbine; A determination module is used to determine the initial working condition of the three-dimensional model of the full flow passage of the pump-turbine, and perform unsteady flow field calculation of the pump-turbine under the initial working condition to obtain a flow field calculation result; A first solving module, used for solving the circumferential average velocity and circumferential average pressure of the turbine runner based on the flow field calculation result; A second solving module is used to obtain the flow field velocity and flow field pressure at each node on the middle surface of the pump-turbine based on the circumferential average velocity and the circumferential average pressure; The third solution module is used to solve the disturbance amount when the disturbance exists based on the flow field velocity, the flow field pressure and the preset NS equation; the disturbance amount when the disturbance exists based on the flow field velocity and the flow field pressure and the preset NS equation includes: Obtain the circumferential velocity of the inlet edge of the runner blade where the disturbed flow field exists, the radius at the inlet of the runner, the angular velocity of the circumferential rotation of the disturbance amount, and the disturbance amount of the angular velocity of the runner rotation; Non-dimensionalizing the circumferential velocity of the inlet edge of the runner blade, the radius at the inlet of the runner, the angular velocity of the circumferential rotation of the disturbance amount, and the disturbance amount of the angular velocity of the rotation of the runner; Substituting the dimensionless circumferential velocity of the inlet edge of the runner blade, the radius at the inlet of the runner, the angular velocity of the circumferential rotation of the disturbance amount, and the disturbance amount of the angular velocity of the rotation of the runner into the preset NS equation to obtain the disturbance amount equation; The disturbance quantity equation is solved with the flow field velocity and flow field pressure as boundary conditions to obtain the disturbance quantity when the disturbance exists; The disturbance quantity equation is solved by taking the flow field velocity and the flow field pressure as boundary conditions to obtain the disturbance quantity when the disturbance exists, which includes: Obtain the polar coordinates of the nodes on the flow surface of runner S2; Transforming the partial derivatives in the disturbance quantity equation based on the node polar coordinates to obtain transformed partial derivatives; Determine the number of periods of the simple harmonic wave corresponding to the disturbance quantity equation; Substituting the preset Jacobian determinant, the converted partial derivatives and the number of periods of the simple harmonic wave into the disturbance quantity equation, and discretizing the disturbance quantity equation with the flow field velocity and the flow field pressure as boundary conditions to obtain a non-homogeneous linear equation system; The singular value decomposition technique is used to solve the non-homogeneous linear equations to obtain the disturbance amount when the disturbance exists; The fourth solving module is used to obtain the critical condition of the rotating stall of the pump turbine based on the disturbance quantity and the stability equation.

7. A computer device, characterized in that: include: A memory and a processor, wherein the memory and the processor are communicatively connected to each other, the memory stores computer instructions, and the processor executes the method for determining the critical condition of rotational stall of a pump-turbine according to any one of claims 1 to 5 by executing the computer instructions.

8. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores computer instructions, and the computer instructions are used to enable a computer to execute the method for determining the critical condition of rotating stall of a pump-turbine according to any one of claims 1 to 5.

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