CN108647391B - Centripetal turbine all-condition simulation modeling method and system based on particle swarm optimization - Google Patents
Centripetal turbine all-condition simulation modeling method and system based on particle swarm optimization Download PDFInfo
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Abstract
The invention discloses a particle swarm algorithm-based modeling method and a particle swarm algorithm-based modeling system for a centripetal turbine full-working-condition simulation model for compressed air energy storage, wherein the method comprises the following steps: determining input quantity, output quantity and model parameters of a centripetal turbine dynamic simulation model; establishing a centripetal turbine simulation model considering the friction loss and the attack angle loss of the centripetal turbine, and optimizing the process of solving the centripetal turbine simulation model; solving the optimization problem by adopting a particle swarm algorithm to obtain the output quantity of the centripetal turbine simulation model; a processing method of loop iteration is adopted to reduce simulation errors caused by falling into a local optimal value; a centripetal turbine full-working-condition simulation module based on a particle swarm algorithm is built on a Matlab/Simulink platform, and the module can be freely combined with other models in the Matlab/Simulink. The simulation model obtained by the method can effectively show the running condition of the centripetal turbine under all working conditions, and has lower simulation error.
Description
Technical Field
The invention belongs to the field of system simulation modeling, and particularly relates to a centripetal turbine all-condition simulation modeling method and system based on a particle swarm algorithm.
Background
Compressed-Air Energy Storage (CAES) technology has the advantages of low cost, long service life, large capacity, relatively few site selection constraints and the like, and is considered to be a large-scale Energy Storage technology with the greatest development prospect. However, the conventional compressed air energy storage technology has three obvious disadvantages: depends on fossil fuel, has low cycle efficiency and needs a large-scale gas storage chamber. Among them, the supercritical compressed air energy storage (SC-CAES) technology is considered as one of the most effective ways to solve the above three drawbacks. At present, multiple SC-CAES demonstration projects are built in China. In an SC-CAES system, a turbine is a main component for converting internal energy of air into mechanical energy, and the performance of the operation characteristics of the turbine seriously affects the overall performance of the system. Among various turbine types, the centripetal turbine has the advantages of simple structure, high efficiency and the like, and has wide application prospect in small and medium-scale CAES systems. The 1.5MW SC-CAES demonstration system which is established in the corridor of Hebei in China at present adopts a 4-stage centripetal turbine as an expansion machine. Therefore, the research on the full-working-condition operation characteristics of the centripetal turbine and the simulation modeling method of the centripetal turbine have important significance, and are important bases for the overall performance optimization and dynamic characteristic analysis of the SC-CAES system.
In the current simulation modeling research on the turbine, most of the simulation modeling researches are based on a static thermodynamic model of the turbine or dynamic simulation modeling is carried out on the piston type turbine, and relatively few simulation modeling methods are researched for the centripetal turbine.
Disclosure of Invention
Aiming at the defects or improvement requirements of the prior art, the invention provides a centripetal turbine full-operating-condition simulation modeling method and system based on a particle swarm optimization, so that the technical problem that in the simulation modeling research of the turbine at the present stage, most of the simulation modeling methods are based on a static thermodynamic model of the turbine or dynamic simulation modeling is carried out aiming at the piston turbine, and the research on the simulation modeling methods aiming at the centripetal turbine is relatively few is solved.
In order to achieve the above object, according to an aspect of the present invention, there is provided a full-condition simulation modeling method for a radial inflow turbine based on a particle swarm algorithm, including:
(1) determining input quantity, output quantity and model parameters of the centripetal turbine full-condition simulation model;
(2) establishing a centripetal turbine simulation model for considering the friction loss and the attack angle loss of the centripetal turbine according to the input quantity, the output quantity and the model parameters;
(3) deleting the constraint that the mass flow of the gas flowing through the stator and the mass flow of the gas flowing through the rotor in the centripetal turbine simulation model are equal, and converting the solving process of the centripetal turbine simulation model into an optimization problem that the difference between the mass flow of the gas flowing through the stator and the mass flow of the gas flowing through the rotor is minimum;
(4) and solving the optimization problem of the centripetal turbine simulation model by adopting a particle swarm algorithm, and obtaining the output quantity of the centripetal turbine simulation model.
Preferably, the input quantity of the radial turbine all-condition simulation model is as follows: turbine inlet pressure p1Turbine inlet temperature T1And a rotational speed N; the output quantity of the centripetal turbine full-working-condition simulation model is as follows: turbine outlet pressure p3Turbine outlet temperature T3Output power P of the turbine, mass flow of gas through the turbine
Turbine output torque τ, turbine efficiency η, reaction DR, and difference in mass flow between stator and rotor of centripetal turbine
The model parameters of the centripetal turbine all-condition simulation model are as follows: outer diameter d of rotor2Average rotor inner diameter d3Height b of blade at rotor inlet2Height b of blade at rotor outlet3Rotor inlet absolute angle α2Rotor inlet relative angle β2Rotor outlet relative angle β3Stator friction loss coefficient ξ2Coefficient of rotor friction loss ξ3And expansion ratio.
Preferably, step (2) comprises:
from the outer diameter d of the rotor2Average rotor inner diameter d3And the rotational speed N determines the peripheral speed u of the rotor outer diameter2And the speed u of the rotor bore3；
From degree of reaction DR, turbine inlet pressure p1And turbine outlet pressure p3Determining rotor inletPressure p2；
Coefficient of friction loss ξ from stator2Turbine inlet temperature T1Turbine inlet pressure p1And the pressure p at the rotor inlet2Determining rotor inlet absolute velocity c2；
From turbine inlet temperature T1Absolute speed of rotor inlet c2Rotor inlet absolute angle α2Rotor inlet relative angle β2And the peripheral speed u of the rotor outer diameter2Determining rotor inlet temperature T before incidence loss occurs2And rotor inlet temperature T 'after incidence loss'2；
By rotor inlet temperature T before incidence loss2Rotor inlet temperature T 'after incidence loss'2Absolute speed of rotor inlet c2Rotor inlet absolute angle α2Rotor inlet relative angle β2And the peripheral speed u of the rotor outer diameter2Determining rotor inlet relative speed w 'after incidence angle loss'2And rotor inlet absolute speed c'2And rotor inlet absolute angle α'2；
Coefficient of friction loss ξ from rotor3And rotor inlet relative speed w'2And rotor inlet temperature T'2Turbine outlet pressure p3Pressure p at the rotor inlet2Circumferential speed u of rotor inner diameter3Outer diameter of rotor2And rotor outlet relative angle β3Determining rotor exit relative velocity w3Absolute speed of rotor outlet c3And rotor outlet absolute angle α3；
From rotor inlet temperature T 'after angle of attack loss'2Circumferential speed u of rotor inner diameter3Outer diameter of rotor2Rotor outlet relative velocity w3And rotor inlet relative speed w'2Determining the temperature T at the turbine outlet3；
From rotor inlet absolute speed c2Rotor inlet absolute angle α2Rotor before incidence lossInlet temperature T2Rotor inlet temperature T 'after incidence loss'2Rotor inlet relative angle β2Outer diameter of rotor2Outer diameter d of rotor2And rotor inlet absolute speed c'2α 'rotor inlet absolute angle'2Absolute speed of rotor outlet c3Rotor outlet absolute angle α3And rotor average inner diameter d3Determining the torque per mass flow tau caused by sudden deflection of the air flowsAnd the torque per unit mass flow tau resulting from the expansion of the air flow in the rotor channelr；
From rotor inlet absolute speed c2Rotor inlet absolute angle α2Outer diameter d of rotor2Height b of blade at rotor inlet2Turbine inlet pressure p1Pressure p at the rotor inlet2Absolute speed of rotor outlet c3Rotor outlet absolute angle α3Average rotor inner diameter d3Height b of blade at rotor outlet3Rotor inlet temperature T before incidence loss2Rotor inlet temperature T 'after incidence loss'2And turbine outlet pressure p3Determining the mass flow of gas flowing through a turbine stator
And the mass flow of gas through the rotor
Wherein the content of the first and second substances,
torque per unit mass flow tau caused by sudden deflection of the air flowsTorque per unit mass flow tau produced by expansion of the air flow in the rotor flow channelrAnd the mass flow of gas through the turbine
Determining the output torque tau of the turbine;
determining the output power P of the turbine according to the output torque tau and the rotating speed N of the turbine;
from the output power P of the turbine, the mass flow of the gas flowing through the turbine
Turbine inlet temperature T1Turbine inlet pressure p1And turbine outlet pressure p3The output efficiency of the turbine is determined η.
Preferably, step (3) comprises:
deleting the mass flow of the gas flowing through the stator in the centripetal turbine simulation model
And the mass flow of gas through the rotor
Equal constraint
And will be
As an optimization target, the reaction degree DR is used as a decision variable of an optimization problem, DR is more than or equal to 0 and less than or equal to 1, and the circumferential speed u of the outer diameter of the rotor2Calculation formula, and circumferential velocity u of rotor inner diameter3Formula of calculation, pressure p at rotor inlet2Calculation formula, rotor inlet absolute velocity c2Calculation formula, rotor inlet temperature T before incidence loss occurs2Calculating formula, rotor inlet temperature T 'after incidence angle loss'2Calculating formula, and rotor inlet relative speed w 'after incidence angle loss'2Calculation formula, rotor inlet absolute speed c'2Calculation formula, rotor inlet absolute angle α'2Calculation formula, rotor outlet relative speed w3Calculation formula, rotor outlet absolute velocity c3Calculation formula, rotor outlet absolute angle α3Calculation formula, turbine outlet temperature T3Unit of calculation formula caused by sudden deflection of air flowMass flow torque τsCalculating formula, unit mass flow torque tau produced by air flow expansion in rotor flow channelrFormula of calculation, mass flow of gas flowing through stator of turbine
Formula of calculation, mass flow of gas flowing through rotor
And (3) taking a calculation formula, a calculation formula of the output torque tau of the turbine, a calculation formula of the output power P of the turbine and a calculation formula of the output efficiency η of the turbine as constraint conditions of the optimization problem, and solving the optimal value of the centripetal turbine simulation model converted into the optimization problem.
Preferably, step (4) comprises:
(4.1) taking the reaction degree DR of the centripetal turbine as a particle position, and initializing the particle position and the particle speed, wherein the particle position meets the constraint that DR is more than or equal to 0 and less than or equal to 1;
(4.2) by
Is a fitness function value;
(4.3) from xi(t+1)＝xi(t)+vi(t) updating the particle position by vi(t+1)＝wvi(t)+c1r1(Pi,best(t)-xi(t))+c2r2(Pg,best(t)-xi(t)) updating the particle velocity and recalculating the fitness function value, where vi(t) represents the velocity of the t-th iteration of particle i, w represents the inertial weight, c1And c2Represents a learning factor, r1And r2Is a random number, xi(t) denotes the position of the t-th iteration of particle i, Pi,best(t) represents the individual optimum of particle i after the t-th iteration, Pg,best(t) representing the global optimal value of the population after the t iteration;
and (4.4) judging whether the particle iteration number reaches a preset iteration number, if so, obtaining the output quantity of the centripetal turbine simulation model, and if not, returning to the step (4.3) until the particle iteration number reaches the preset iteration number.
Preferably, after reaching the preset number of iterations and before obtaining the output of the radial turbine simulation model, the method further includes:
judging the optimal fitness value after reaching the preset iteration number
Whether the difference is smaller than a preset threshold value delta or not;
if it is
Calculating the solving result of the centripetal turbine by adopting the particle swarm algorithm again until the solving result is up to
If the optimal fitness value is obtained after the preset maximum cycle number solution
If the maximum cycle number is still greater than the preset threshold value delta, the optimal fitness value after the maximum cycle number is preset
As the final output.
According to another aspect of the present invention, there is provided a centripetal turbine full-condition simulation modeling system based on a particle swarm optimization, comprising:
the parameter determination module is used for determining the input quantity, the output quantity and the model parameters of the centripetal turbine all-condition simulation model;
the simulation model building module is used for building a centripetal turbine simulation model for considering the friction loss and the attack angle loss of the centripetal turbine according to the input quantity, the output quantity and the model parameters;
the optimization module is used for deleting the constraint that the mass flow of the gas flowing through the stator and the mass flow of the gas flowing through the rotor in the centripetal turbine simulation model are equal, and converting the solving process of the centripetal turbine simulation model into an optimization problem that the difference between the mass flow of the gas flowing through the stator and the mass flow of the gas flowing through the rotor is minimum;
and the solving module is used for solving the optimization problem of the centripetal turbine simulation model by adopting a particle swarm algorithm and obtaining the output quantity of the centripetal turbine simulation model.
In general, compared with the prior art, the above technical solution contemplated by the present invention can achieve the following beneficial effects:
the method is based on a centripetal turbine mathematical model considering friction loss and attack angle loss, the solving process of the centripetal turbine mathematical model is converted into an optimization problem, the optimization problem is solved through a particle swarm algorithm, a cyclic iteration method is adopted to reduce simulation errors caused by the fact that particle swarm falls into local optimal values, and finally, a simulation model based on the particle swarm algorithm is built on a Matlab/Simulink simulation platform. The simulation model obtained by the method can effectively show the running condition of the centripetal turbine under all working conditions, and has lower simulation error.
Drawings
FIG. 1 is a schematic external view of a simulation module for a radial inflow turbine according to an embodiment of the present invention;
FIG. 2 is a schematic flow chart of a centripetal turbine full-condition simulation modeling method based on a particle swarm optimization according to an embodiment of the present invention;
FIG. 3 is a simulation result comparison diagram of a centripetal turbine full-condition simulation modeling method based on a particle swarm optimization according to an embodiment of the present invention;
fig. 4 is a simulation result diagram of the centripetal turbine full-condition simulation modeling method based on the particle swarm optimization according to the embodiment of the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
Fig. 2 is a schematic flow chart of a centripetal turbine full-condition simulation modeling method based on a particle swarm optimization according to an embodiment of the present invention, including:
(1) and determining the input quantity, the output quantity and the model parameters of the centripetal turbine full-condition simulation model.
The input quantity of the CAES system-oriented centripetal turbine all-condition simulation model is as follows: turbine inlet air pressure, turbine inlet temperature, rotational speed; the output quantity of the centripetal turbine full-condition simulation model is as follows: the turbine outlet air pressure, the turbine outlet temperature, the output power of the turbine, the mass flow of gas flowing through the turbine, the output torque of the turbine, the efficiency of the turbine, the reaction degree and the difference of the mass flow between the stator and the rotor of the centripetal turbine; the model parameters of the centripetal turbine are as follows: rotor outside diameter, rotor average inside diameter, rotor inlet vane height, rotor outlet vane height, rotor inlet absolute angle, rotor inlet relative angle, rotor outlet relative angle, stator friction loss coefficient, rotor friction loss coefficient, expansion ratio.
In the simulation model, the unit and symbol expression of each input quantity, output quantity, and model parameter are shown in table 1:
TABLE 1 units of the model for each physical quantity in the International System of units
(2) Establishing a centripetal turbine mathematical model considering the friction loss and the attack angle loss of the centripetal turbine, and converting the process of solving the centripetal turbine mathematical model into an optimization problem.
1) Centripetal turbine mathematic model
For centripetal turbines used in CAES systems, where the compressed gas flows in at different peripheral speeds from the outer diameter and out at the inner diameter of the turbine rotor, these turbines can generally be considered as purely resistive flow components, with negligible accumulation of mass, momentum and energy in the turbine flow path. Therefore, the mathematical model does not take into account the flow instability inside the turbine.
Solving formulas of the outer diameter wheel speed and the inner diameter wheel speed of the rotor are respectively as follows:
in the formula u2And u3The outer diameter and inner diameter peripheral speeds of the rotor are indicated, respectively.
The formula for calculating the air pressure at the rotor inlet based on the reaction power is:
in the formula, p2Indicating the air pressure at the rotor inlet; κ represents the specific heat ratio of air.
The formula for calculating the absolute speed at the rotor inlet is:
in the formula, cpRepresents the isobaric specific heat capacity of air; c. C2Indicating the rotor inlet absolute velocity.
During off-design operation, sudden changes in airflow at the rotor inlet can produce angle of attack losses.
The calculation formulas of the rotor inlet temperature before and after the incidence angle loss is generated are respectively as follows:
in the formula, T2And T'2The rotor inlet temperatures before and after the incidence loss occurred are respectively shown.
The calculation formulas of the rotor inlet relative speed, the rotor inlet absolute speed and the rotor inlet absolute angle after the attack angle loss is generated are respectively as follows:
w 'of'2、c′2And α'2The rotor inlet relative speed, rotor inlet absolute speed and rotor inlet absolute angle after the incidence angle loss occurs are respectively represented.
The calculation formulas of the rotor outlet relative speed, the rotor outlet absolute speed and the rotor outlet absolute angle are respectively as follows:
in the formula, w3、c3And α3Indicating the rotor outlet relative speed, the rotor outlet absolute speed and the rotor outlet absolute angle.
The calculation formula of the temperature at the turbine outlet is as follows:
the unit mass flow rate torque caused by the sudden deflection of the air flow and the unit mass flow rate torque generated by the expansion of the air flow in the rotor flow passage are respectively expressed as follows:
in the formula, τsAnd τrRespectively representing the torque per mass flow caused by the sudden deflection of the air flow and the torque per mass flow caused by the expansion of the air flow in the rotor flow channel.
The gas mass flow through the turbine stator and the gas mass flow through the rotor are each expressed as follows:
in the formula (I), the compound is shown in the specification,
and
representing the gas mass flow through the turbine stator and the gas mass flow through the rotor, respectively; rho1And ρ2The mean densities of the gases expanded in the stator and rotor channels, respectively, are expressed by the following calculation formulas:
Rgrepresenting the ideal gas state constant.
According to the principle of conservation of mass, the mass flow of gas through the stator and rotor should be equal, namely:
the output torque of the turbine is calculated by the formula:
the output power calculation formula of the turbine is as follows:
the output efficiency calculation formula of the turbine is as follows:
2) converting the process of solving the centripetal turbine model into an optimization problem
The 23 formulas form a mathematical model capable of reflecting the design/non-design working condition operation condition of the centripetal turbine, but the mathematical model is a pure algebraic ring problem and cannot be solved by directly building a simulation model on a Matlab/Simulink simulation platform. We transform the solution process of the above mathematical model into an optimization problem.
First, the algebraic ring problem composed of the above 23 equations needs to be solved: the constraint that the gas mass flow through the stator and the gas mass flow through the rotor are equal is removed, i.e. formula (14) is removed; by eliminating equation (14), the mass flow of gas through the stator and the mass flow of gas through the rotor can be determined separately, and the only non-input and non-model parameters that affect the mass flow of gas through the stator/rotor are the turbine reaction (DR).
Thus, the optimization objectives can be set to:
the decision variables for the optimization problem are: DR (digital radiography)
The constraints of the optimization problem are equations (0) to (13), (14) to (15) and the following equation:
0≤DR≤1 (17)
(3) and (3) solving the centripetal turbine optimization problem established in the step (2) by adopting a particle swarm algorithm, and obtaining the output quantity of the centripetal turbine simulation model.
The solving process of the particle swarm optimization is as follows:
the first step is as follows: the particle position and the particle velocity are initialized by using the reaction rate (DR) of the centripetal turbine as the particle position, and the particle position satisfies the constraint of the formula (17).
The second step is that: the fitness function is expressed by the formula (18), and the fitness function value can be obtained from the formulas (0) to (6), (10) to (13) according to the particle position.
The third step: and updating the positions and the speeds of the particles according to the position updating formula and the speed updating formula of the particle swarm, and recalculating the fitness function value. The particle velocity update formula and the position update formula are respectively expressed by the formulas (19) and (20).
vi(t+1)＝wvi(t)+c1r1(Pi,best(t)-xi(t))+c2r2(Pg,best(t)-xi(t)) (19)
xi(t+1)＝xi(t)+vi(t) (20)
In the formula, vi(t) represents the velocity of the t-th iteration of particle i; w represents an inertial weight; c. C1And c2Represents a learning factor; r is1And r2Is [0,1 ]]The random number of (2); x is the number ofi(t) represents the position of the t-th iteration of particle i; pi,best(t) represents the individual optimum of particle i after the t-th iteration; pg,bestAnd (t) represents the population global optimum value after the t iteration.
The fourth step: and judging whether the particle iteration times reach the preset iteration times, if so, obtaining the output quantity of the centripetal turbine simulation model, and if not, repeating the third step until the preset iteration times are reached.
The preset iteration number can be determined according to actual needs.
(4) The problem that the optimization problem is solved by adopting the particle swarm optimization may fall into local optimization, so that a simulation result has a large error. Aiming at the problem, a loop iteration method can be adopted for processing, and the processing process is as follows:
firstly, judging the optimal fitness value after the solution is completed
Whether the value is smaller than a preset threshold value delta or not, wherein the value delta can be a decimal smaller than 0.1 under the normal condition, and the closer the value delta is to 0, the higher the required solving precision is; if it is
If the solution is trapped in the local optimal value, the particle swarm algorithm is adopted again to calculate the solution result of the once centripetal turbine until the solution result is trapped in the local optimal value
If the solution is performed in multiple cycles (the maximum cycle number is set as C)max) The optimal fitness value obtained after
Still greater than the predetermined threshold δ indicates that the trap is not due to occasional local optima
Thus, output CmaxOptimum fitness value after sub-cycle
At this time, if
Larger (in general)
Should be less than 0.1), it indicates that the given input quantity or input parameter in the model is incorrect and cannot be realized
And finally, a centripetal turbine full-working-condition simulation module based on a particle swarm algorithm can be built on the Matlab/Simulink platform. The appearance of the built centripetal turbine simulation module under the Matlab/Simulink platform is shown in figure 1.
The solution results of the simulation model of the centripetal turbine in the invention are compared with the experimental data in the published literature (as comparative examples) (author: analysis C. Jones, literature name: design and test of a small, high pressure biological turbine) to verify the effectiveness of the simulation model. The parameters of the centripetal turbine in the examples are shown in Table 2.
TABLE 2 System optimization results under different scenarios
Turbine inlet pressure is maintained at 5.8 x 105Pa, inlet temperature was maintained at 1057K.
Comparing the turbine expansion ratios of 4, 5 and 5.7 respectively, the difference between the turbine efficiency output by the simulation model and the turbine efficiency experimentally measured in the comparative example is used for verifying the effectiveness of the centripetal turbine simulation model.
(1) When the expansion ratio of the centripetal turbine is 4, the isentropic ideal expansion speed c of the turbinesComprises the following steps:
simulating the turbine operation condition (u) when the ratio of the outer diameter wheel peripheral speed of the rotor to the isentropic ideal expansion speed is 0.5-0.82/cs0.5 to 0.8), namely the simulated rotor outer diameter wheel peripheral speed u2For turbine operating conditions of 68586-109737 rpm, the change curve of turbine efficiency η is shown in FIG. 3 (a).
(2) When the expansion ratio of the centripetal turbine is 5, the isentropic ideal expansion speed c of the turbinesComprises the following steps:
simulating the turbine operation condition (u) when the ratio of the outer diameter wheel peripheral speed of the rotor to the isentropic ideal expansion speed is 0.5-0.82/cs0.5 to 0.8), namely the simulated rotor outer diameter wheel peripheral speed u2For the turbine operating conditions at 72815-116503 rpm, the η curve of the turbine efficiency is shown in FIG. 3 (b).
(3) When the expansion ratio of the centripetal turbine is 5.7, the isentropic ideal expansion speed c of the turbinesComprises the following steps:
simulating the turbine operation condition (u) when the ratio of the outer diameter wheel peripheral speed of the rotor to the isentropic ideal expansion speed is 0.5-0.82/cs0.5 to 0.8), namely the simulated rotor outer diameter wheel peripheral speed u2For the turbine operating conditions at 75159-120255 rpm, the η curve of the turbine efficiency is shown in FIG. 3 (c).
When the radial inflow expansion ratios are 4, 5 and 5.7, respectively, the absolute values of the differences in mass flow rates between the stator and rotor of the radial inflow are shown in fig. 4(a) to 4(c), respectively.
As can be seen from FIG. 3, the simulation results of the centripetal turbine established by the invention are basically consistent with the experimental data in the comparative example, and the effectiveness of the simulation model of the centripetal turbine is verified. As can be seen from FIGS. 4(a) -4 (c), the mass flow difference between the stator and the rotor of the radial turbine obtained by the model is very close to 0, that is, equation (20)
The method can basically meet the requirement, and shows that the solving method can effectively solve the radial inflow turbine models represented by the formulas (1) to (23), and the solving precision is high.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (8)
1. A centripetal turbine all-condition simulation modeling method based on particle swarm optimization is characterized by comprising the following steps:
(1) determining input quantity, output quantity and model parameters of the centripetal turbine full-condition simulation model;
(2) establishing a centripetal turbine simulation model for considering the friction loss and the attack angle loss of the centripetal turbine according to the input quantity, the output quantity and the model parameters;
(3) deleting the mass flow of the gas flowing through the stator in the centripetal turbine simulation model
And the mass flow of gas through the rotor
Equal constraint
And will be
As an optimization target, the reaction degree DR is used as a decision variable of an optimization problem, DR is more than or equal to 0 and less than or equal to 1, and the circumferential speed u of the outer diameter of the rotor2Calculation formula, and circumferential velocity u of rotor inner diameter3Formula of calculation, pressure p at rotor inlet2Calculation formula, rotor inlet absolute velocity c2Calculation formula, rotor inlet temperature T before incidence loss occurs2Calculation formula, rotor inlet temperature T after incidence loss2' calculation formula, rotor inlet relative velocity w ' after incidence loss '2Calculation formula, rotor inlet absolute speed c'2Calculation formula, rotor inlet absolute angle α'2Calculation formula, rotor outlet relative speed w3Calculation formula, rotor outlet absolute velocity c3Calculation formula, rotor outlet absolute angle α3Calculation formula, turbine outlet temperature T3Calculating formula, unit mass flow rate torque tau caused by sudden deflection of air flowsCalculating formula, unit mass flow torque tau produced by air flow expansion in rotor flow channelrFormula of calculation, mass flow of gas flowing through stator of turbine
Formula of calculation, mass flow of gas flowing through rotor
A calculation formula, a turbine output torque tau calculation formula, a turbine output power P calculation formula and a turbine output efficiency η calculation formula are used as constraint conditions of the optimization problem, and the optimal value of the centripetal turbine simulation model converted into the optimization problem is solved;
(4) and solving the optimization problem of the centripetal turbine simulation model by adopting a particle swarm algorithm, and obtaining the output quantity of the centripetal turbine simulation model.
2. The method of claim 1, wherein the input of the full-condition simulation model of the radial turbineThe input amount is as follows: turbine inlet pressure p1Turbine inlet temperature T1And the rotating speed N; the output quantity of the centripetal turbine full-working-condition simulation model is as follows: turbine outlet pressure p3Turbine outlet temperature T3Output power P of the turbine, mass flow of gas through the turbine
Turbine output torque tau, turbine efficiency η, reaction degree DR, difference of mass flow between centripetal turbine stator and rotor
The model parameters of the centripetal turbine all-condition simulation model are as follows: outer diameter d of rotor2Average rotor inner diameter d3Height b of blade at rotor inlet2Height b of blade at rotor outlet3Rotor inlet absolute angle α2Rotor inlet relative angle β2Rotor outlet relative angle β3Stator friction loss coefficient ξ2Coefficient of rotor friction loss ξ3And an expansion ratio.
3. The method of claim 2, wherein step (2) comprises:
from the outer diameter d of the rotor2Average rotor inner diameter d3And the rotational speed N determines the peripheral speed u of the rotor outer diameter2And the speed u of the rotor bore3；
From degree of reaction DR, turbine inlet pressure p1And turbine outlet pressure p3Determining the pressure p at the rotor inlet2；
Coefficient of friction loss ξ from stator2Turbine inlet temperature T1Turbine inlet pressure p1And the pressure p at the rotor inlet2Determining rotor inlet absolute velocity c2；
From turbine inlet temperature T1Absolute speed of rotor inlet c2Rotor inlet absolute angle α2Rotor inlet relative angle β2And rotatingPeripheral speed u of minor outer diameter2Determining rotor inlet temperature T before incidence loss occurs2And rotor inlet temperature T after incidence loss2′；
By rotor inlet temperature T before incidence loss2Rotor inlet temperature T after incidence loss2', rotor inlet absolute velocity c2Rotor inlet absolute angle α2Rotor inlet relative angle β2And the peripheral speed u of the rotor outer diameter2Determining rotor inlet relative speed w 'after incidence angle loss'2And rotor inlet absolute speed c'2And rotor inlet absolute angle α'2；
Coefficient of friction loss ξ from rotor3And rotor inlet relative speed w'2Rotor inlet temperature T2', turbine outlet pressure p3Pressure p at the rotor inlet2Circumferential speed u of rotor inner diameter3Outer diameter of rotor2And rotor outlet relative angle β3Determining rotor exit relative velocity w3Absolute speed of rotor outlet c3And rotor outlet absolute angle α3；
By rotor inlet temperature T after incidence loss2', peripheral speed u of rotor inner diameter3Outer diameter of rotor2Rotor outlet relative velocity w3And rotor inlet relative speed w'2Determining the temperature T at the turbine outlet3；
From rotor inlet absolute speed c2Rotor inlet absolute angle α2Rotor inlet temperature T before incidence loss2Rotor inlet temperature T after incidence loss2' rotor inlet relative angle β2Outer diameter of rotor2Outer diameter d of rotor2And rotor inlet absolute speed c'2α 'rotor inlet absolute angle'2Absolute speed of rotor outlet c3Rotor outlet absolute angle α3And rotor average inner diameter d3Determining the torque per unit mass flow caused by sudden deflection of the gas flowτsAnd the torque per unit mass flow tau resulting from the expansion of the air flow in the rotor channelr；
From rotor inlet absolute speed c2Rotor inlet absolute angle α2Outer diameter d of rotor2Height b of blade at rotor inlet2Turbine inlet pressure p1Pressure p at the rotor inlet2Absolute speed of rotor outlet c3Rotor outlet absolute angle α3Average rotor inner diameter d3Height b of blade at rotor outlet3Rotor inlet temperature T before incidence loss2Rotor inlet temperature T after incidence loss2' and turbine outlet pressure p3Determining the mass flow of gas flowing through a turbine stator
And the mass flow of gas through the rotor
Wherein the content of the first and second substances,
torque per unit mass flow tau caused by sudden deflection of the air flowsTorque per unit mass flow tau produced by expansion of the air flow in the rotor flow channelrAnd the mass flow of gas through the turbine
Determining the output torque tau of the turbine;
determining the output power P of the turbine according to the output torque tau and the rotating speed N of the turbine;
from the output power P of the turbine, the mass flow of the gas flowing through the turbine
Turbine inlet temperature T1Turbine inlet pressure p1And turbine outlet pressure p3Determining turbine efficiencyη。
4. The method of claim 1, wherein step (4) comprises:
(4.1) taking the reaction degree DR of the centripetal turbine as a particle position, and initializing the particle position and the particle speed, wherein the particle position meets the constraint that DR is more than or equal to 0 and less than or equal to 1;
(4.2) by
Is a fitness function value;
(4.3) from xi(t+1)＝xi(t)+vi(t) updating the particle position by vi(t+1)＝wvi(t)+c1r1(Pi,best(t)-xi(t))+c2r2(Pg,best(t)-xi(t)) updating the particle velocity and recalculating the fitness function value, where vi(t) represents the velocity of the t-th iteration of particle i, w represents the inertial weight, c1And c2Represents a learning factor, r1And r2Is a random number, xi(t) denotes the position of the t-th iteration of particle i, Pi,best(t) represents the individual optimum of particle i after the t-th iteration, Pg,best(t) representing the global optimal value of the population after the t iteration;
and (4.4) judging whether the particle iteration number reaches a preset iteration number, if so, obtaining the output quantity of the centripetal turbine simulation model, and if not, returning to the step (4.3) until the particle iteration number reaches the preset iteration number.
5. The method of claim 4, wherein after a predetermined number of iterations is reached, before obtaining the output of the simulation model of the radial turbine, the method further comprises:
judging the optimal fitness value after reaching the preset iteration number
Whether the difference is smaller than a preset threshold value delta or not;
if it is
Calculating the solving result of the centripetal turbine by adopting the particle swarm algorithm again until the solving result is up to
If the optimal fitness value is obtained after the preset maximum cycle number solution
If the maximum cycle number is still greater than the preset threshold value delta, the optimal fitness value after the maximum cycle number is preset
As the final output.
6. A centripetal turbine all-condition simulation modeling system based on particle swarm optimization is characterized by comprising:
the parameter determination module is used for determining the input quantity, the output quantity and the model parameters of the centripetal turbine all-condition simulation model;
the simulation model building module is used for building a centripetal turbine simulation model for considering the friction loss and the attack angle loss of the centripetal turbine according to the input quantity, the output quantity and the model parameters;
an optimization module for deleting the gas mass flow passing through the stator in the centripetal turbine simulation model
And the mass flow of gas through the rotor
Equal constraint
And will be
As an optimization target, the reaction degree DR is used as a decision variable of an optimization problem, DR is more than or equal to 0 and less than or equal to 1, and the circumferential speed u of the outer diameter of the rotor2Calculation formula, and circumferential velocity u of rotor inner diameter3Formula of calculation, pressure p at rotor inlet2Calculation formula, rotor inlet absolute velocity c2Calculation formula, rotor inlet temperature T before incidence loss occurs2Calculation formula, rotor inlet temperature T after incidence loss2' calculation formula, rotor inlet relative velocity w ' after incidence loss '2Calculation formula, rotor inlet absolute speed c'2Calculation formula, rotor inlet absolute angle α'2Calculation formula, rotor outlet relative speed w3Calculation formula, rotor outlet absolute velocity c3Calculation formula, rotor outlet absolute angle α3Calculation formula, turbine outlet temperature T3Calculating formula, unit mass flow rate torque tau caused by sudden deflection of air flowsCalculating formula, unit mass flow torque tau produced by air flow expansion in rotor flow channelrFormula of calculation, mass flow of gas flowing through stator of turbine
Formula of calculation, mass flow of gas flowing through rotor
A calculation formula, a turbine output torque tau calculation formula, a turbine output power P calculation formula and a turbine output efficiency η calculation formula are used as constraint conditions of the optimization problem, and the optimal value of the centripetal turbine simulation model converted into the optimization problem is solved;
and the solving module is used for solving the optimization problem of the centripetal turbine simulation model by adopting a particle swarm algorithm and obtaining the output quantity of the centripetal turbine simulation model.
7. The system of claim 6, wherein the input variables of the full-condition simulation model of the centripetal turbine are: turbine inlet pressure p1Turbine inlet temperature T1And a rotational speed N; the output quantity of the centripetal turbine full-working-condition simulation model is as follows: turbine outlet pressure p3Turbine outlet temperature T3Output power P of the turbine, mass flow of gas through the turbine
Turbine output torque τ, turbine efficiency η, reaction DR, and difference in mass flow between stator and rotor of centripetal turbine
The model parameters of the centripetal turbine all-condition simulation model are as follows: outer diameter d of rotor2Average rotor inner diameter d3Height b of blade at rotor inlet2Height b of blade at rotor outlet3Rotor inlet absolute angle α2Rotor inlet relative angle β2Rotor outlet relative angle β3Stator friction loss coefficient ξ2Coefficient of rotor friction loss ξ3And expansion ratio.
8. The system of claim 7, wherein the rotor is defined by an outer diameter d of the rotor2Average rotor inner diameter d3And the rotational speed N determines the peripheral speed u of the rotor outer diameter2And the speed u of the rotor bore3(ii) a From degree of reaction DR, turbine inlet pressure p1And turbine outlet pressure p3Determining the pressure p at the rotor inlet2Coefficient of friction loss ξ from stator2Turbine inlet temperature T1Turbine inlet pressure p1And the pressure p at the rotor inlet2Determining rotor inlet absolute velocity c2(ii) a From turbine inlet temperature T1Absolute speed of rotor inlet c2Rotor inlet absolute angle α2Rotor inlet relative angle β2And rotatingPeripheral speed u of minor outer diameter2Determining rotor inlet temperature T before incidence loss occurs2And rotor inlet temperature T after incidence loss2'; by rotor inlet temperature T before incidence loss2Rotor inlet temperature T after incidence loss2', rotor inlet absolute velocity c2Rotor inlet absolute angle α2Rotor inlet relative angle β2And the peripheral speed u of the rotor outer diameter2Determining rotor inlet relative speed w 'after incidence angle loss'2And rotor inlet absolute speed c'2And rotor inlet absolute angle α'2ξ coefficient of friction loss from rotor3And rotor inlet relative speed w'2Rotor inlet temperature T2', turbine outlet pressure p3Pressure p at the rotor inlet2Circumferential speed u of rotor inner diameter3Outer diameter of rotor2And rotor outlet relative angle β3Determining rotor exit relative velocity w3Absolute speed of rotor outlet c3And rotor outlet absolute angle α3(ii) a By rotor inlet temperature T after incidence loss2', peripheral speed u of rotor inner diameter3Outer diameter of rotor2Rotor outlet relative velocity w3And rotor inlet relative speed w'2Determining the temperature T at the turbine outlet3(ii) a From rotor inlet absolute speed c2Rotor inlet absolute angle α2Rotor inlet temperature T before incidence loss2Rotor inlet temperature T after incidence loss2' rotor inlet relative angle β2Outer diameter of rotor2Outer diameter d of rotor2And rotor inlet absolute speed c'2α 'rotor inlet absolute angle'2Absolute speed of rotor outlet c3Rotor outlet absolute angle α3And rotor average inner diameter d3Determining the torque per mass flow tau caused by sudden deflection of the air flowsAnd the torque per unit mass flow tau resulting from the expansion of the air flow in the rotor channelr(ii) a From rotor inlet absolute speed c2Rotor inlet absolute angle α2Outer diameter d of rotor2Height b of blade at rotor inlet2Turbine inlet pressure p1Pressure p at the rotor inlet2Absolute speed of rotor outlet c3Rotor outlet absolute angle α3Average rotor inner diameter d3Height b of blade at rotor outlet3Rotor inlet temperature T before incidence loss2Rotor inlet temperature T after incidence loss2' and turbine outlet pressure p3Determining the mass flow of gas flowing through a turbine stator
And the mass flow of gas through the rotor
Wherein the content of the first and second substances,
torque per unit mass flow tau caused by sudden deflection of the air flowsTorque per unit mass flow tau produced by expansion of the air flow in the rotor flow channelrAnd the mass flow of gas through the turbine
Determining the output torque tau of the turbine; determining the output power P of the turbine according to the output torque tau and the rotating speed N of the turbine; from the output power P of the turbine, the mass flow of the gas flowing through the turbine
Turbine inlet temperature T1Turbine inlet pressure p1And turbine outlet pressure p3Turbine efficiency is determined η.
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