CN110442959B - Method for predicting and maintaining light-gathering performance of solar disc type light-gathering system - Google Patents

Method for predicting and maintaining light-gathering performance of solar disc type light-gathering system Download PDF

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CN110442959B
CN110442959B CN201910706050.4A CN201910706050A CN110442959B CN 110442959 B CN110442959 B CN 110442959B CN 201910706050 A CN201910706050 A CN 201910706050A CN 110442959 B CN110442959 B CN 110442959B
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颜健
彭佑多
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Hunan University of Science and Technology
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F24—HEATING; RANGES; VENTILATING
    • F24S—SOLAR HEAT COLLECTORS; SOLAR HEAT SYSTEMS
    • F24S50/00—Arrangements for controlling solar heat collectors
    • F24S50/20—Arrangements for controlling solar heat collectors for tracking
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E10/00—Energy generation through renewable energy sources
    • Y02E10/40—Solar thermal energy, e.g. solar towers
    • Y02E10/46—Conversion of thermal power into mechanical power, e.g. Rankine, Stirling or solar thermal engines
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E10/00—Energy generation through renewable energy sources
    • Y02E10/40—Solar thermal energy, e.g. solar towers
    • Y02E10/47—Mountings or tracking

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Abstract

The invention discloses a method for predicting and maintaining the light-gathering performance of a solar disc-type light-gathering system, which comprises the following steps: 1) Establishing a finite element model of the disc type condenser system, and calculating optical information of the disc type condenser under the working condition of no optical error and no load; 2) Calculating optical parameters of each plane infinitesimal grid of the reflecting mirror surface of the condenser when boundary conditions of self weight and wind pressure load are applied; 3) Predicting the focusing energy flow distribution and the optical performance of the disc type light-gathering system under the action of a load by adopting a ray tracing method; 4) Fitting to obtain a function model of the tracking error angle value and the centroid position of the focusing light spot; 5) Determining the centroid position of the focusing light spot according to the operation condition, and reversely solving the output corner error value of the double-shaft tracking device; the output shaft of the double-shaft tracking device rotates by a corresponding angle, so that the light-gathering performance of the disc-type light-gathering system is kept. The method is simple to implement, can predict the light gathering performance of the disc type light gathering system under the bearing working condition and keep the energy flow distribution, and guides the design of the disc type system.

Description

Method for predicting and maintaining light-gathering performance of solar disc type light-gathering system
Technical Field
The invention belongs to the technical field of solar condensation utilization, and particularly relates to a method for predicting and maintaining the condensation performance of a solar disc type condensation system.
Background
Solar energy is a clean, environmentally friendly, abundant and widely distributed renewable energy source. Concentrated solar thermal power generation is an important technology for developing and utilizing solar energy resources, and is considered as an important approach for solving the problems of energy shortage and environmental pollution. The disc-Stirling solar thermal power generation system collects sunlight to the surface of a metal coil in a receiver through a parabolic disc condenser, and is used for heating a gas working medium (usually hydrogen or helium) in the metal coil, and then the heated gas working medium can drive a Stirling heat engine to work to drive a generator to work to output electric energy. The disc-Stirling solar thermal power generation system has the advantages of high solar energy-electric energy conversion efficiency, flexible arrangement, high modularization degree and the like, so that the disc-Stirling solar thermal power generation system is considered to be high-grade solar thermal utilization equipment with a wide application prospect.
The disc type Stirling system relates to sunlight, a mechanical structure, a heat absorber and internal working media thereof, and multi-link and multi-interface energy transfer of a Stirling heat engine, a generator and the like, and is a complex optical-mechanical-thermal-electrical multidisciplinary integration/coupling system. The dish-type light-gathering system is a mechanical carrier for effectively and efficiently gathering solar energy and keeping the focused energy flow on the surface of the heat absorber reasonably distributed, and the geometric shape of the mirror surface of the light-gathering device and the spatial relative position of the mirror surface and a receiver need to be ensured. However, the disc-type light-gathering system in the engineering service cycle is subjected to the action of self weight and wind load to generate structural deformation, so that the indexes of the focusing performance, the radiation energy flow distribution and the like of the disc-type light-gathering system are further deteriorated, the solar radiation energy received by the surface of the heat absorber of the Stirling heat engine is unbalanced, the light-heat-work-electricity conversion efficiency is reduced, and the safety problems of ablation or burnthrough and the like caused by high-temperature hot spots formed on the coil of the heat absorber are further serious. Especially, the more severe requirements of commercial power stations require that the disc-type light-focusing system normally focuses light to generate electricity within a certain wind speed (usually, eighth-order wind), which brings more serious challenges to the safe and efficient operation of the disc-type light-focusing system. Therefore, it is particularly important to provide a universal method for realizing the prediction and evaluation of the optical performance and the focusing energy flow distribution under the load action of the designed disc-type light-condensing system, and the universal method is also the basis for the structural design and optimization of the disc-type light-condensing system. On the other hand, the load effect in the service cycle always exists, a method is provided to realize the 'keeping' of the energy flow distribution on the surface of the heat absorber of the disc-type light-condensing system under the load effect, the power generation efficiency, the operation reliability and the safety of the disc-type Stirling system can be effectively improved, and the common technical problem which needs to be solved urgently in the field of disc-type light condensation is also solved.
Disclosure of Invention
In order to solve the technical problems, the invention provides a universal and simple-to-implement method for predicting and maintaining the light condensation performance of a solar disc type light condensation system under a bearing working condition, which can predict the light condensation performance of the solar disc type light condensation system under the bearing working condition, is used for guiding the design of a rack structure of the disc type system and a cavity of a heat absorber, and predicting the energy flow distribution of the designed disc type solar light condensation system under the wind load effect, thereby providing an evaluation basis for the light condensation performance of the disc type system in wind-resistant operation.
The technical scheme adopted by the invention is as follows: a method for predicting and maintaining the light-gathering performance of a solar disc-type light-gathering system comprises the following steps:
1) Establishing a finite element model of the disc type light condensing system, dividing a grid into the structural finite element model of the disc type light condensing system, outputting space coordinate information of each node of each plane infinitesimal grid of a reflecting mirror surface of the light condenser under a non-bearing working condition, and calculating optical information of the disc type light condenser under the non-bearing working condition without optical errors;
2) Applying boundary conditions of self weight and wind pressure load to the established finite element model of the disc type light-gathering system, calculating structural deformation under the action of the self weight and the wind load, and calculating the geometric centroid, the normal vector and the effective daylighting area of each plane infinitesimal grid of the reflecting mirror surface of the light-gathering device at the moment;
3) Calculating the bearing deformation of the disc type light condensing system to obtain a space displacement value of the cavity receiver, and predicting the focusing energy flow distribution and the optical performance of the disc type light condensing system under the action of a load by adopting a ray tracing method;
4) Introducing a tracking error angle of a double-shaft tracking device into the disc type light condensing system, calculating the centroid position of a focusing light spot on the surface of the plane receiver under the condition of different tracking errors, and fitting to obtain a function model of the tracking error angle value and the centroid position of the focusing light spot;
5) Establishing a corresponding relation between the bearing working condition of the disc type light condensing system and the centroid position of the focusing light spot under the bearing working condition of the disc type light condensing system, reversely solving a tracking error angle value according to the centroid position of the focusing light spot under the bearing working condition, and establishing a data table in which the bearing working condition of the disc type light condensing system and the output corner error value of the double-shaft tracking device are in one-to-one correspondence; acquiring an output corner error value of the double-shaft tracking device by a data table according to the bearing working condition measured in the operation of the disc type light-gathering system; then the drive controller makes the output shaft of the double-shaft tracking device rotate by a corresponding angle, and the light-gathering performance of the solar disc type light-gathering system is kept under the bearing working condition.
The method for predicting and maintaining the light-gathering performance of the solar disc-type light-gathering system comprises the following specific operations in the step 1):
1.1 To establish a global coordinate system for mechanical and optical analysis: establishing a global coordinate system O-xyz at the vertex O position of a parabolic reflector of the disc condenser, wherein the z axis points to a focus F of the parabolic curved surface, the position vector F of the focus F = [0, F ], and F is the focal length of the parabolic reflector; when the light gathering system bears deformation, the global coordinate system O-xyz is still fixed, namely the coordinate system O-xyz is not fixedly connected with the light gathering device;
1.2 Establish a local coordinate system of the cavity receiver: at the receiving window center point F of the cavity receiver 1 Establishing a local coordinate system F fixed with the receiver 1 -x 1 y 1 z 1 Center point F of receiving window of cavity receiver 1 Position vector F of 1 ＝[0，0，f](ii) a Local coordinate system F under non-bearing working condition 1 -x 1 y 1 z 1 Parallel to each corresponding axis of the global coordinate system O-xyz, and point F 1 Coincides with the position of the focal point F; local coordinate system F when the disc-type light-gathering system is deformed 1 -x 1 y 1 z 1 Rigid body motion with the receiver; three characteristic points are fixedly connected on the cavity receiver, and the three characteristic points are respectively taken as central points F of the receiving window 1 At + x 1 Points on the axis g and at + y 1 Point m, point g, point m and point F on the axis 1 Are all distances e 1 ；
1.3 Finite element modeling and mirror meshing: establishing a finite element model of the disc type light-gathering system by adopting a finite element method according to an elastic mechanics theory; dividing each reflecting mirror surface of the condenser into triangular plane micro-element grids or quadrilateral plane micro-element grids or mixed plane micro-element grids of the triangular plane micro-element grids and the quadrilateral plane micro-element grids;
1.4 Calculating the optical parameters of the reflecting mirror surface of the dish condenser without optical errors: and deriving the space coordinates of each node of the plane micro-element grid of each reflecting mirror surface under the non-bearing condition from a finite element model of the disc type light-gathering system, and calculating the geometric centroid, the normal vector and the effective daylighting area of each plane micro-element grid under the non-bearing working condition when no optical error exists.
In the method for predicting and maintaining the light-gathering performance of the solar disc type light-gathering system, the geometric centroid, the normal vector and the effective daylighting area of each plane infinitesimal grid under the non-bearing working condition in the step 1.4) are calculated as follows:
geometric centroid point p of each planar infinitesimal grid 1 Position vector p of 1 Comprises the following steps:
Figure BDA0002152157250000031
in the formula: the vectors a, b, c and d are position vectors of each node of the plane micro-element grid respectively;
unit normal vector N of plane infinitesimal grid p1 And effective daylighting area A p1 Respectively as follows:
Figure BDA0002152157250000032
Figure BDA0002152157250000033
in the formula: vector bc = c-b; vector ba = a-b; vector dc = c-d; vector da = a-d; angle phi 1 Is a unit normal vector N of a planar infinitesimal grid p1 The included angle between the central ray vector S and the incident light cone of the sun; vector S = [0,0, -1](ii) a Angle phi 1 Satisfies the following conditions:
Figure BDA0002152157250000034
the method for predicting and maintaining the light-gathering performance of the solar disc-type light-gathering system comprises the following specific operations in the step 2):
2.1 The load bearing deformation of the disc type light gathering system is calculated, wherein a dead weight and wind pressure load boundary condition is applied to the established finite element model of the disc type light gathering system, a wind pressure load is applied to the surface of a parabolic reflector of the light gathering device, and the structural deformation under the action of the dead weight and the wind load is calculated;
2.2 Calculating the displacement vector of each node of each plane micro-element grid of the reflecting mirror surface of the condenser under the bearing condition, and calculating the geometric centroid, the normal vector and the effective daylighting area of each plane micro-element grid; the specific calculation process is as follows: after the disc type light-gathering system bears deformation, the geometric centroid point p of each plane micro-element grid 1 Move to point p t Position, at this point p t The position vector of (a) is:
Figure BDA0002152157250000041
in the formula u a 、u b 、u c 、u d Respectively displacement vectors of each node of the plane infinitesimal grid under the action of load;
unit normal vector N of each plane infinitesimal grid pt And effective daylighting area A pt Respectively as follows:
Figure BDA0002152157250000042
Figure BDA0002152157250000043
in the formula: vector b 1 c 1 ＝c 1 -b 1 ；b 1 a 1 ＝a 1 -b 1 ；d 1 c 1 ＝c 1 -d 1 ；d 1 a 1 ＝a 1 -d 1 (ii) a Vector a 1 、b 1 、c 1 、d 1 And respectively the position vectors of all nodes of the plane infinitesimal after the condenser bears the deformation.
The method for predicting and maintaining the light-gathering performance of the solar disc-type light-gathering system comprises the following specific operations in the step 3):
3.1 Computing the feature point spatial coordinates of the cavity receiver: the disk-type light-gathering system bears deformation to cause the cavity receiver to generate rigid displacement, and the local coordinate system fixedly connected with the cavity receiver is also F 1 -x 1 y 1 z 1 Change to F t -x 2 y 2 z 2 (ii) a Three characteristic points F fixed on the cavity receiver 1 G and m move to point F respectively t 、g t And m t Position, relative geometric relation between three characteristic pointsIs kept unchanged; vector F t 、g t And m t Are respectively point F t 、g t And m t A position vector of (a); vector F 1 G and m are points F in the design state 1 Position vectors of g and m, vector F 1 G and M are known in advance and satisfy M 1 ＝F 1 、g＝M 1 +[e 1 ,0,0]And M = M 1 +[0,e 1 ,0](ii) a Vector u F ，u g And u m Respectively, the light-collecting system bearing deformation causes the point F 1 Displacement vectors generated by g and m; the position vectors of the three feature points satisfy the following equation:
Figure BDA0002152157250000044
3.2 Computing a spatial coordinate system variation relationship of the cavity receiver: calculating to obtain a local coordinate system F of the cavity receiver t -x 2 y 2 z 2 And the global coordinate system O-xyz are:
Figure BDA0002152157250000045
in the formula: vector M 1 Is the center point F of the receiving window 1 A position vector of, i.e. M 1 ＝F 1 Rot (A, β) is used to implement an arbitrary vector P ∈ R 1×3 Around an arbitrary unit vector a = [ a = x ,a y ,a z ]The matrix function of the rotation angle beta specifically comprises:
Figure BDA0002152157250000051
vector
Figure BDA0002152157250000052
Wherein: vector
Figure BDA0002152157250000053
Vector
Figure BDA0002152157250000054
Vector g 4 ＝(g-F 1 )Rot(n 3 ,β 1 )+F t (ii) a Vector
Figure BDA0002152157250000055
Vector
Figure BDA0002152157250000056
Vector m 3 ＝m+u F Vector of
Figure BDA0002152157250000057
Rotation angle
Figure BDA0002152157250000058
Vector F 1 m＝m-F 1 ；m 3 m t ＝m t -m 3 ＝u m -u F (ii) a Rotation angle
Figure BDA0002152157250000059
Vector F 1 g＝g-F 1 ；g 4 g t ＝g 4 -g t ；g 4 ＝(g-F 1 )Rot(n 3 ,β 1 )+F t (ii) a Angle of rotation beta 1 Angle of rotation beta 2 Is an intermediate variable;
3.3 Dispersion of the solar incident cone of light): in a global coordinate system O-xyz, dispersing a solar incident light cone with a half vertex angle delta of 4.65mrad into a large number of solar rays, and calculating incident vectors and carried energy density of each solar ray; the specific method comprises the following steps: establishing a sunlight cone model at the origin O of the global coordinate system, and constructing a focal plane of the parabolic mirror surface with the radius R s A disc of = F · tan (δ), which disc has a focal point F as the centre and a side length of 2R s The square is enveloped, then the square is respectively dispersed into W and N parts along the length and width directions, and W = N, so as to obtain a series of square grids; the center points of the w-th and n-th square grids wn of the square along the length and width directions are denoted as Qwn, and the point Q wn At a distance d from F wn ＝||Q wn -F |, vector F = [0, F | ]](ii) a Center point Q of square grid wn wn At a radius R s The disk of (1) is an effective grid, f wn =1; otherwise, it is an invalid grid, f wn =0, i.e. not participating in subsequent ray tracing calculations; the direction of the connecting line of the center point Qwn of the effective square grid wn and the origin O is the incident ray I of the sun wn Incident vector I of wn I.e. I wn ＝-Q wn /||Q wn | | where the vector
Figure BDA00021521572500000510
Solar ray I wn The energy density I (w, n) carried is:
Figure BDA00021521572500000511
in the formula: gamma ray wn For incident rays of the sun I wn The included angle between the central ray vector S of the incident light cone of the sun,
Figure BDA0002152157250000061
I 1 the radiation intensity of the central ray of the incident light cone of the sun,
Figure BDA0002152157250000062
W 0 is the intensity value of direct solar radiation, and the unit is W/m 2 ；f wn A decision parameter for whether the square grid wn participates in the calculation;
3.4 Coordinate system transformation of condenser reflected ray equation: in a global coordinate system O-xyz, the incident ray I of the sun is calculated based on the law of specular reflection wn Geometric centroid p of plane infinitesimal grid on reflecting mirror surface of dish type condenser t The equation of the reflected ray of (c); this reflected ray equation is then converted to the local coordinate system F of the cavity receiver 2 -x 2 y 2 z 2 In (1), the parametric equation is expressed as:
Figure BDA0002152157250000063
in the formula: the vectors on the right side of the equation are all vectors represented in the global coordinate system O-xyz; vector
Figure BDA0002152157250000064
Wherein: (N) pt ) The right superscript T of T is the transposed symbol of the vector;
3.5 Calculating the light path transmission and energy absorption process of a single solar ray: local coordinate system F of receiver in cavity 2 -x 2 y 2 z 2 Giving a geometric equation, surface absorptivity and optical reflection characteristics of each surface in the cavity receiver; dividing the inner surface of the cavity receiver into U equal parts along the height direction and G equal parts along the circumferential direction; recording the transmission and energy absorption processes of the reflected light rays determined in the step 3.4) in the cavity receiver by adopting a known ray tracing method; that is, the coordinates of the intersection point of the light ray with the surface when the light ray is reflected for multiple times in the cavity receiver are calculated until the light ray escapes from the cavity receiver or the reflection times reach the maximum reflection times N r Until the end; then judging the coordinates of the intersection points in which numbered discrete grid area of the inner surface of the cavity receiver, and increasing the energy carried by the light to the grid area; when the energy carried by the sun rays is added to the discrete grid ug, the expression is:
E absorber (u,g)＝E absorber (u,g)+I(w,n)·A pt ·ρ mirror (1-σ absorber ) n1 ·(ρ wall ) n2 ·σ absorber (10)
in the formula: e habsorber (u, g) is an array element that stores the solar radiation energy received by the grid ug in the receiver surface, its initial value is 0 before the energy flow distribution calculation; rho mirror Is the reflectivity of the condenser mirror; sigma absorber Absorption rate for the area in the cavity receiver where the heat sink is mounted; ρ is a unit of a gradient wall Reflectivity of other surfaces inside the cavity receiver; n is 1 Is the number of times of reflection of the sun's rays by the surface of the heat absorber, n 1 ＝0,1,2,...N 1 ，N 1 The maximum reflection times of the solar rays on the surface of the heat absorber; n is 2 The number of times of reflection of the solar ray by the common wall surface in the cavity receiver, n 2 ＝0,1,2,...N 2 ，N 2 Is the maximum reflection number of the sun ray on the common wall surface, and N 1 +N 2 ≤N r ；
The receiver for receiving the solar radiation energy focused by the dish condenser is of a plane structure and is superposed with the focal plane of the parabolic reflector; taking a plane receiver as a square area with the side length of L, and equally dividing the square area into H parts and U parts along the directions of two sides, wherein H = U, and obtaining a small H multiplied by U square grid; calculating the coordinates of the intersection point of the reflected light ray and the plane receiver determined in the step 3.4), judging which numbered discrete grid area of the receiver the intersection point is in, and increasing the energy carried by the light ray to the grid area; when the energy carried by the sun rays is added to the discrete grid hu, the energy of the solar radiation received by the grid hu in the storage receiver surface is expressed as:
Eplan(h,u)＝Eplan(h,u)+I(w,n)·A pt ·ρ mirror (11)
where Eplan (h, u) is the energy of solar radiation received by grid hu in the storage receiver surface, its initial value is 0 before calculation of the energy flow distribution;
3.6 Focus performance prediction for a dish condensing system: calculating a reflected ray equation of all incident rays of the sun in the sunlight cone at the geometric centroid of all plane infinitesimal grids of the reflector surface of the disc-type condenser, calculating the transmission and energy absorption of all reflected rays in the cavity receiver through the step 3.5), finally obtaining the focusing energy flux density distribution of the inner surface of the heat absorber in the disc-type condenser system under the load-bearing working condition, counting the total energy received by the surface of the heat absorber and the total energy collected by the condenser, wherein the ratio of the total energy received by the inner wall surface of the cavity receiver to the total energy collected by the condenser is the optical efficiency of the disc-type condenser system under the load-bearing working condition; when the receiver for receiving the energy of the solar radiation focused by the dish concentrator is a planar receiver, the focused energy flux density distribution of the planar receiver surface is calculated.
The method for predicting and maintaining the light-gathering performance of the solar disc-type light-gathering system comprises the following specific operations in the step 4):
4.1 To establish a mathematical relationship between the output rotation angle error value of the dual-axis tracking device and the counterglow tracking error of the dish concentrator: the disc type light-gathering system realizes accurate tracking OF the position OF the sun through the double-shaft tracking device, and under the condition OF no tracking error, the focal axis OF OF the disc type light-gathering system is parallel to the central ray S OF the sunlight cone; the included angle between the focal axis OF OF the parabolic reflecting mirror surface OF the disc condenser and the ground plane is the height angle OF the disc condenser; the included angle between the projection OF the focal axis OF OF the parabolic reflecting mirror surface OF the disc condenser on the ground plane and the front south is the azimuth angle OF the disc condenser; the double-shaft tracking device comprises a height tracking device and an orientation tracking device, wherein the orientation tracking shaft is vertical to the ground plane, the height tracking shaft is parallel to the ground plane and vertical to the focal axis of the disc condenser, and the error values of output corners of the height tracking device and the orientation tracking device are respectively epsilon 1 And ε 2 The tracking error angle of the height angle of the disc condenser is epsilon 1r Satisfy epsilon 1r ＝ε 1 (ii) a Azimuth tracking error angle epsilon of disc condenser 2r Comprises the following steps: epsilon 2r ＝arcos[(cos(90-φ)) 2 ·(1-cosε 2 )+cosε 2 ]Wherein: phi is the elevation angle of the disc condenser when no tracking error exists;
4.2 Calculating the centroid coordinates of the focused light spots of the planar receiver of the disc condenser system under different sun tracking errors: calculating to obtain the focusing energy flux density distribution on the surface of the plane receiver through the steps 3.5) and 3.6), and then calculating to obtain the centroid coordinate of the focusing light spot as follows:
Figure BDA0002152157250000071
4.3 Fitting to establish a mathematical model of the sun tracking error of the disc type light-gathering system and the centroid coordinate of the focusing light spot: based on the data obtained in the step 4.2), a mathematical model of the sun tracking error of the disc type condenser system and the centroid coordinate of the focusing light spot is established by adopting a function fitting method, and the mathematical model is used for reversely solving the altitude angle and the azimuth angle tracking error angle of the disc type condenser by the centroid coordinate of the focusing light spot, and the formula is as follows:
Figure BDA0002152157250000081
in the formula: k 1 Is the undetermined coefficient and is determined by fitting a large amount of data.
The method for predicting and maintaining the light-gathering performance of the solar disc-type light-gathering system comprises the following specific operations in the step 5):
5.1 Calculating to obtain the centroid coordinates of the focusing light spots on the surface of the planar receiver of the disc type light condensing system under different bearing working conditions through the step 2) and the step 3);
5.2 Adopting the centroid of the focusing light spot obtained in the step 5.1), and reversely calculating the tracking error value of the disc condenser under each bearing working condition through the step 4.2);
5.3 The tracking error value of the disc condenser obtained in the step 5.2) passes through the azimuth angle tracking error angle epsilon of the disc condenser in the step 4.1) 2r The formula is used for reversely solving the output corner error value of the double-shaft tracking device; establishing a data table in which the bearing working conditions and the output corner error values of the double-shaft tracking device are in one-to-one correspondence, and storing the data table in a drive controller of the double-shaft tracking device;
5.4 According to the load-bearing working condition measured in the actual operation of the disc-type light-gathering system, inquiring the data table established in the step 5.3) to obtain the output corner error value epsilon of the double-shaft tracking device 1 And ε 2 (ii) a The drive controller sends the signal to the altitude angle and azimuth angle drive motors, so that two output shafts of the double-shaft tracking device respectively rotate to-epsilon 1 And-epsilon 2 An angle, wherein: the negative sign represents the opposite direction of rotation from the output corner error value; the light-gathering performance of the solar disc type light-gathering system is kept under the bearing working condition.
Compared with the prior art, the invention has the beneficial effects that:
1. the invention integrates two subjects of structural mechanics and optics, realizes data unification of finite element mechanical analysis and optical analysis, establishes an optical-mechanical integrated modeling method of the disc type condenser under the load action by transmitting and converting the deformation information of the reflecting mirror surface of the condenser to the optical information of the condenser, and realizes the prediction of the light condensing performance of the solar disc type condensing system under the load-bearing working condition. The method can be effectively used for guiding the design of the rack structure and the heat absorber cavity of the disc-type system, predicting the energy flow distribution of the heat absorber cavity of the designed disc-type solar light-gathering system under the action of wind load, and providing evaluation basis for the light-gathering performance of the disc-type system in wind-resistant operation.
2. The invention unifies the mirror surface optical information and the deformation information thereof, is also suitable for the light machine integration modeling and the light condensation performance prediction of other mirror surface reflection type solar light condensation systems, and has universality.
3. The invention can realize the maintenance of the energy flow distribution on the surface of the heat absorber in the disc-type light-gathering system under the action of load, can be used for improving the problems of the bias focus of a focusing light spot and the four-quadrant energy unbalance on the surface of the heat absorber, and the tracking compensation method of the invention offsets or weakens the influence of bearing deformation by introducing the tracking error in the opposite direction, namely converts the influence of the bearing deformation into the calibration problem of the tracking error of the light collector, and has simple implementation and no increase of the cost of the disc-type light-gathering system.
Drawings
FIG. 1 shows the deformation information and optical information of planar microelements on the mirror surface of a condenser.
FIG. 2 is a diagram of the change of the receiver pose under the condition of deformation of the disc type light condensing system under load.
FIG. 3 is a schematic illustration of a discrete cone of incident light from the sun; FIG. 3 (a) is a diagram of a model of creating a cone of sunlight at the origin of a global coordinate system; fig. 3 (b) is a discrete schematic of a disk constructed in the focal plane of a parabolic mirror.
Figure 4 is a schematic diagram of the centroid position of the focused spot.
FIG. 5 is a diagram of a finite element model of the XEM-Dish system.
FIG. 6 is a focusing energy flux density distribution diagram of the XEM-Dish system focal plane under the combined action of self-weight and wind load.
FIG. 7 is a focused energy flux density distribution plot of the inner surface of the cavity receiver of the XEM-Dish system under the combined action of self-weight and wind load.
FIG. 8 is a plot of focused energy flux density at the focal plane of the XEM-Dish system after the hold method of the present invention is employed.
FIG. 9 is a focused energy flux density profile of the inner surface of a cavity receiver of the XEM-Dish system after the present invention retention method is employed.
Detailed Description
The invention is further described below with reference to the figures and examples.
The invention comprises the following steps:
step 1: establishing a structural finite element model of the disc type light condensing system, dividing grids into the structural finite element model of the disc type light condensing system, outputting space coordinate information of each grid node of a reflector surface of the light condenser under a non-bearing working condition, and calculating optical information of the disc type light condenser under the conditions of no optical error and the non-bearing working condition. The specific operation is as follows:
step 1.1: a global coordinate system for mechanical and optical analysis is established. Establishing a global coordinate system O-xyz at the vertex O position of a parabolic reflector of the disc condenser, wherein the z axis points to a focus F of the parabolic curved surface, and the position vector F of the focus F is = [0, F ], wherein F is the focal length of the parabolic reflector; when the light-gathering system bears deformation, the global coordinate system O-xyz is still fixed, namely the coordinate system O-xyz is not fixed with the light-gathering device.
Step 1.2: a local coordinate system of the cavity receiver is established. At the receiving window center point F of the cavity receiver 1 (center point F of receiving window of cavity receiver) 1 Position vector F 1 ＝[0，0，f]) Establishing a local coordinate system F fixed with the receiver 1 -x 1 y 1 z 1 Parallel to each corresponding axis of the global coordinate system O-xyz under unloaded conditions, and point F 1 Coinciding with the focal point F. Local coordinate system F when the disc-type light-gathering system is deformed 1 -x 1 y 1 z 1 Will move rigidly with the receiver. 3 characteristic points are fixedly connected to the cavity receiver, and the 3 characteristic points form triangular distribution. Three characteristic points are respectively taken as central points F of the receiving window 1 In+x 1 Points on the axis g and at + y 1 Point m, point g and point F on the axis 1 A distance of e 1 Point m and point F 1 Is also a distance e 1 。
Step 1.3: finite element modeling and mirror meshing. And establishing a finite element model of the disc type light-gathering system by adopting a finite element method according to the theory of elastic mechanics. And dividing each reflecting mirror surface of the condenser into a triangular plane micro-element grid or a quadrilateral plane micro-element grid, or a mixed plane micro-element grid of the triangular plane micro-element grid and the quadrilateral plane micro-element grid.
Step 1.4: and calculating the optical parameters of the reflecting mirror surface of the disc condenser when no optical error exists. And deriving the space coordinates of each node of the plane micro-element grid of each reflecting mirror surface under the non-bearing condition from a finite element model of the disc type light-gathering system, and calculating optical parameters of the plane micro-element grid under the non-bearing working condition without optical errors, such as geometric centroids, normal vectors, effective daylighting areas and the like. The specific calculation process is as follows: geometric centroid point p of plane micro-element grid 1 Position vector p of 1 Comprises the following steps:
Figure BDA0002152157250000101
in the formula: the vectors a, b, c and d are position vectors of each node of the plane micro-element grid respectively; and directly obtaining the data from the finite element model derivation data of the disc type light-gathering system.
Unit normal vector N of plane infinitesimal grid p1 And effective daylighting area A p1 Respectively as follows:
Figure BDA0002152157250000102
Figure BDA0002152157250000103
vector b 1 c 1 ＝c 1 -b 1 ；b 1 a 1 ＝a 1 -b 1 ；d 1 c 1 ＝c 1 -d 1 ；d 1 a 1 ＝a 1 -d 1 (ii) a Vector a 1 、b 1 、c 1 、d 1 Respectively carrying the position vector of each node of the deformed plane infinitesimal by the condenser; angle phi 1 Is a vector N p1 The included angle between the central ray vector S of the incident light cone of the sun; vector S = [0,0, -1](ii) a Angle phi 1 Satisfy the requirement of
Figure BDA0002152157250000104
Step 2: and (3) applying the boundary conditions of the dead weight and the wind pressure load to the finite element model of the disc type light condensing system established in the step (1), calculating the structural deformation under the action of the dead weight and the wind load, and calculating the optical parameters such as the geometric centroid, the normal vector, the effective daylighting area and the like of each plane infinitesimal grid of the reflecting mirror surface of the light condenser at the moment. The specific operation is as follows:
step 2.1: and calculating the bearing deformation of the disc type light-gathering system. And (4) applying the boundary conditions of the self weight and the wind pressure load to the finite element model of the disc type light-gathering system established in the step (1.3), and calculating the structural deformation under the action of the self weight and the wind load. When a wind pressure load boundary condition is applied, a wind pressure load is applied to the surface of the parabolic reflector of the condenser, and the wind pressure load is obtained through numerical simulation by a computational fluid mechanics method or through outdoor actual measurement or a scaled wind tunnel experiment.
Step 2.2: and calculating the optical parameters of the disc condenser under the bearing working condition. And calculating displacement vectors of all nodes of all plane micro-element grids of the reflecting mirror surface of the condenser under a bearing working condition, and calculating optical parameters such as geometric centroids, normal vectors, effective daylighting areas and the like of all the plane micro-element grids according to the displacement vectors, as shown in figure 1. The calculation process is as follows: after the disc-type light-gathering system bears deformation, the geometric centroid point p of the plane micro-element grid 1 Move to point p t Position, point p at this time t The position vector of (a) is:
Figure BDA0002152157250000111
in the formula, u a 、u b 、u c 、u d Respectively displacement vectors of each node of the plane infinitesimal grid under the action of load; and calculating by a finite element model of the disc type light-gathering system.
At this time, the unit normal vector N of the planar infinitesimal grid i pt And effective daylighting area A pt Respectively as follows:
Figure BDA0002152157250000112
Figure BDA0002152157250000113
in the formula, vector b 1 c 1 ＝c 1 -b 1 ；b 1 a 1 ＝a 1 -b 1 ；d 1 c 1 ＝c 1 -d 1 ；d 1 a 1 ＝a 1 -d 1 (ii) a Vector a 1 、b 1 、c 1 、d 1 And respectively carrying position vectors corresponding to all nodes of the deformed plane infinitesimal for the condenser, and adding the position vectors under the non-carrying working condition and the carried deformation vectors to obtain the position vectors.
And step 3: and calculating the bearing deformation of the disc type light condensing system to obtain a space displacement value of the cavity receiver, and predicting the focusing energy flow distribution and the optical performance of the disc type light condensing system under the action of a load by adopting a ray tracing method. The specific operation is as follows:
step 3.1: and calculating the space coordinates of the characteristic points of the cavity receiver. Based on the calculation of the bearing deformation of the disc-type light-focusing system in step 2.1, the bearing deformation of the disc-type light-focusing system can cause the cavity receiver to generate rigid displacement. As shown in fig. 2, the local coordinate system fixedly connected to the cavity receiver is also represented by F 1 -x 1 y 1 z 1 Change to F t -x 2 y 2 z 2 (ii) a Three characteristic points F fixed on the cavity receiver 1 G andm move to points F respectively t 、g t And m t The relative geometric relationship (e.g., the vertical relationship of the coordinate axes) between the three fixed feature points on the cavity receiver remains unchanged. Vector F t 、g t And m t Are respectively point F t 、g t And m t A position vector of (a); vector F 1 Point F under the condition that g and m are not bearing working conditions respectively 1 G and M, and satisfies M 1 ＝F 1 、g＝M 1 +[e 1 ,0,0]And M = M 1 +[0,e 1 ,0]. Vector u F ，u g And u m Respectively, the light-collecting system bearing deformation causes the point F 1 The displacement vectors generated by g and m are determined by the calculation of step 2.1. The position vectors of the three feature points satisfy:
Figure BDA0002152157250000114
step 3.2: and calculating the space coordinate system change relation of the cavity receiver. Calculating to obtain a local coordinate system F of the cavity receiver t -x 2 y 2 z 2 And the global coordinate system O-xyz are:
Figure BDA0002152157250000121
in the formula: vector M 1 Is the center point F of the receiving window 1 Of position vectors, i.e. M 1 = F, which is also the local coordinate system F 1 -x 1 y 1 z 1 A translation matrix with a global coordinate system O-xyz; rot (A, beta) is used to realize an arbitrary vector P ∈ R 1×3 Around an arbitrary unit vector a = [ a = x ,a y ,a z ]The matrix function of the rotation angle beta specifically comprises:
Figure BDA0002152157250000122
vector
Figure BDA0002152157250000123
Wherein: vector
Figure BDA0002152157250000124
Vector
Figure BDA0002152157250000125
Vector g 4 ＝(g-F 1 )Rot(n 3 ,β 1 )+F t (ii) a Vector
Figure BDA0002152157250000126
Vector
Figure BDA0002152157250000127
Vector m 3 ＝m+u F Vector of
Figure BDA0002152157250000128
Rotation angle
Figure BDA0002152157250000129
Vector F 1 m＝m-F 1 ；m 3 m t ＝m t -m 3 ＝u m -u F (ii) a Rotation angle
Figure BDA00021521572500001210
Vector F 1 g＝g-F 1 ；g 4 g t ＝g 4 -g t ；g 4 ＝(g-F 1 )Rot(n 3 ,β 1 )+F t (ii) a Angle of rotation beta 1 Angle of rotation beta 2 Is an intermediate variable;
step 3.3: dispersion of the cone of incident light from the sun. As shown in fig. 3, in the global coordinate system O-xyz, the solar incident light cone with the half apex angle δ of 4.65mrad is dispersed into a large number of solar rays, and the incident vector and the carried energy density of each solar ray are calculated. The specific method comprises the following steps: establishing a sunlight cone model at the origin O of the global coordinate system, and constructing a focal plane of the parabolic mirror surface with the radius R s ＝f·tan (delta) disc having a focal point F as the centre and having a side length of 2R s The square is respectively dispersed into W and N parts along the length and width directions, and W = N, so as to obtain a series of square grids; the central points of the squares respectively as the w-th square grid wn and the n-th square grid wn along the length and the width directions are recorded as Q wn Point Q of wn At a distance d from F wn ＝||Q wn -F |, vector F = [0, F | ]](ii) a Center point Q of square grid wn wn At a radius R s The disk of (1) is an effective grid, f wn =1; otherwise, it is an invalid grid, f wn =0, i.e. not participating in subsequent ray tracing calculations; center point Q of effective square grid wn wn The direction of the line connecting the origin O is the incident ray I of the sun wn Incident vector I of wn I.e. I wn ＝-Q wn /||Q wn | |, in which the vector
Figure BDA0002152157250000131
Solar ray I wn The energy density carried, I (w, n), is:
Figure BDA0002152157250000132
in the formula: gamma ray wn For incident rays of the sun I wn The included angle with the central ray vector S of the incident light cone of the sun,
Figure BDA0002152157250000133
I 1 the intensity of the radiation of the central ray of the incident light cone of the sun,
Figure BDA0002152157250000134
W 0 is the intensity value of direct solar radiation, and the unit is W/m 2 。f wn A decision parameter for whether the square grid wn participates in the calculation.
Step 3.4: and converting the coordinate system of the condenser reflected ray equation. In a global coordinate system O-xyz, the incident ray I of the sun is calculated based on the law of specular reflection wn Dish type condenserGeometric centroid p of plane infinitesimal grid i of reflecting mirror surface t The reflected ray equation of (a). This reflected ray equation is then converted to the local coordinate system F of the cavity receiver 2 -x 2 y 2 z 2 In (1), the parametric equation is expressed as:
Figure BDA0002152157250000135
in the formula, vectors on the right side of the equation are all expressed based on a global coordinate system O-xyz; vector
Figure BDA0002152157250000136
Where the right superscript T is the transposed sign of the vector.
Step 3.5: and calculating the light path transmission and energy absorption process of the single solar ray. Local coordinate system F of receiver in cavity 2 -x 2 y 2 z 2 Given the geometric equations, surface absorptance, and optical reflectance characteristics (i.e., specular or diffuse reflectance characteristics) of the various surfaces within the cavity receiver; dividing the inner surface of the cavity receiver into U equal parts along the height direction and G equal parts along the circumferential direction; the transmission and energy absorption process of the reflected ray determined in step 3.4 inside the cavity receiver is traced back using a well-known ray tracing method. Namely, the coordinates of the intersection point of the light ray and the surface when the light ray is reflected in the cavity receiver for multiple times are calculated until the light ray escapes from the cavity receiver or the reflection times reach the maximum reflection times N r Until the end; and then judging the coordinates of the intersection points in which numbered discrete grid area of the inner surface of the cavity receiver, and adding the energy carried by the light rays to the grid area. If the energy carried by the sun's rays is added to the discrete grid ug, it is expressed as:
E absorber (u,g)＝E absorber (u,g)+I(w,n)·A pt ·ρ mirror (1-σ absorber ) n1 ·(ρ wall ) n2 ·σ absorber (10)
in the formula, E habsorber (u, g) is the storage of solar radiation energy received by the grid ug in the receiver surfaceAn array element whose initial value before power flow distribution calculation is 0; rho mirror The reflectivity of the condenser mirror; sigma absorber Is the absorption rate of the cavity receiver in the area where the heat sink is mounted (referred to as the heat sink surface); rho wall Reflectivity of other surfaces (referred to as common walls) inside the cavity receiver; n is 1 Is the number of times of reflection of the sun's rays by the surface of the heat absorber, n 1 ＝0,1,2,...N 1 ，N 1 The maximum reflection times of the solar rays on the surface of the heat absorber; n is 2 The number of times of reflection of the solar ray by the common wall surface in the cavity receiver, n 2 ＝0,1,2,...N 2 ，N 2 Is the maximum reflection number of the sun ray on the common wall surface, and N 1 +N 2 ≤N r 。
When the receiver for receiving the energy of the solar radiation focused by the dish concentrator is of a planar configuration, it coincides with the focal plane of the parabolic mirror surface. Taking a plane receiver as a square area with the side length of L, and equally dividing the square area into H parts and U parts (H = U) along the directions of two sides to obtain a small H multiplied by U square grid; and (3) calculating the coordinates of the intersection point of the reflected light ray and the plane receiver determined in the step (3.4), judging which numbered discrete grid area of the receiver the intersection point is in, and adding the energy carried by the light ray to the grid area. If the energy carried by the sun's rays is added to the grid hu, the energy of the solar radiation received by the grid hu in the storage receiver surface is expressed as:
Eplan(h,u)＝Eplan(h,u)+I(w,n)·A pt ·ρ mirror (11)
where Eplan (h, u) is the stored solar radiation energy received by the grid hu in the receiver surface, its initial value is 0 prior to the energy flow distribution calculation.
Step 3.6: and predicting the focusing performance of the disc type light condensing system. Calculating a reflection ray equation of all solar incident rays in the solar cone at the geometric centroids of all plane micro-element grids of the reflecting mirror surface of the disc type condenser through the step 3.4, and paying attention to that the geometric centroid of each plane micro-element grid of the reflecting mirror surface of the disc type condenser receives one solar cone; and calculating the transmission and energy absorption processes of all the reflected light rays in the cavity receiver through the step 3.5, finally obtaining the focusing energy flux density distribution of the inner surface of the heat absorber in the disc type light condensing system under the bearing working condition, counting the total energy received by the surface of the heat absorber and the total energy collected by the condenser, wherein the ratio of the total energy received by the inner wall surface of the cavity receiver to the total energy collected by the condenser is the optical efficiency of the disc type light condensing system under the bearing working condition. When the receiver for receiving the solar radiation energy focused by the disc condenser is a plane receiver, the flow density distribution of the focusing energy on the surface of the plane receiver is obtained through calculation, and the prediction of the light focusing performance of the solar disc condenser system under the bearing working condition is completed.
And 4, step 4: introducing a tracking error angle of a double-shaft tracking device into the disc type light-gathering system; and calculating the centroid position of the focusing light spot on the surface of the plane receiver under different tracking errors, and fitting to obtain a function model of the tracking error angle value and the centroid position of the focusing light spot under corresponding working conditions. The specific operation is as follows:
step 4.1: and establishing a mathematical relation between the output corner error value of the double-shaft tracking device and the counterglow tracking error of the disc condenser. The disc type light-gathering system realizes accurate tracking OF the position OF the sun through the double-shaft tracking device, and under the condition OF no tracking error, the focal axis OF OF the disc type light-gathering system is parallel to the central ray S OF the sunlight cone; the included angle between the focal axis OF OF the parabolic reflector surface OF the disc condenser and the ground plane is the height angle OF the disc condenser; the included angle between the projection OF the focal axis OF OF the parabolic reflecting mirror surface OF the disc condenser on the ground plane and the front south is the azimuth angle OF the disc condenser; the double-shaft tracking device consists of a height tracking device and an azimuth tracking device, wherein an azimuth tracking shaft is vertical to a ground plane, the height tracking shaft is parallel to the ground plane and is vertical to a focal axis of the disc condenser, and output corner error values of the height tracking device and the azimuth tracking device are respectively epsilon 1 And ε 2 The tracking error angle of the height angle of the disc condenser is epsilon 1r Satisfy epsilon 1r ＝ε 1 (ii) a Azimuth tracking error angle epsilon of disc condenser 2r Comprises the following steps: epsilon 2r ＝arcos[(cos(90-φ)) 2 ·(1-cosε 2 )+cosε 2 ]Wherein: phi is no tracking errorThe elevation angle of the dish concentrator is poor.
Step 4.2: and calculating the centroid coordinates of the focusing light spots of the plane receiver of the disc type light-condensing system under different sun-tracking errors. Introducing a double-axis tracking error of the disc condenser, calculating through steps 3.5 and 3.6 to obtain the focusing energy flux density distribution on the surface of the plane receiver, and then calculating to obtain the centroid coordinate of the focusing spot, wherein the schematic diagram of the centroid position of the focusing spot is shown in fig. 4:
Figure BDA0002152157250000151
step 4.3: and fitting and establishing a mathematical model of the sun tracking error of the disc type light condensing system and the centroid coordinate of the focusing light spot. According to the mass data obtained in the step 4.2, a mathematical model of the sun tracking error of the disc type condenser system and the centroid coordinate of the focusing light spot is established by adopting a function fitting method, so that the height angle and the azimuth angle tracking error angle of the disc type condenser can be reversely solved through the centroid coordinate of the focusing light spot, and the mathematical expression is as follows:
Figure BDA0002152157250000152
in the formula, K 1 The undetermined coefficient can be determined by fitting a large amount of data; it is related to the focal length f and the lighting radius of the disc-type light-gathering system.
And 5: establishing a data table in which the bearing working condition and the output corner error value of the double-shaft tracking device correspond to the output corner error value of the double-shaft tracking device one by one, and obtaining the output corner error value of the double-shaft tracking device according to the bearing working condition measured in operation; then the drive controller makes the output shaft of the double-shaft tracking device rotate by a corresponding angle, and the light-gathering performance of the solar disc type light-gathering system is kept under the bearing working condition. The method comprises the following specific steps:
step 5.1: and (3) calculating to obtain the centroid coordinates of the focusing light spots on the surface of the plane receiver of the disc type light condensing system under different bearing working conditions through the step 2 and the step 3.
And step 5.2: and 4.3, solving the tracking error value of the disc condenser under each bearing working condition by using the centroid coordinates of the focusing light spots obtained in the step 5.1 and performing reflection in the step.
Step 5.3: the tracking error value of the disc condenser obtained in the step 5.2) passes through the azimuth angle tracking error angle epsilon of the disc condenser in the step 4.1) 2r A formula is used for reversely solving the output corner error value (comprising numerical value and rotation direction information) of the double-shaft tracking device; and then establishing a data table in which the bearing working conditions and the output corner error values of the double-shaft tracking device are in one-to-one correspondence, and storing the data table in a driving controller of the double-shaft tracking device.
Step 5.4: according to the load-bearing condition measured in operation, directly inquiring the data table in the drive controller to obtain the output corner error value epsilon of the double-shaft tracking device 1 And ε 2 (ii) a The drive controller then sends this signal to the elevation and azimuth drive motors, causing the output shaft of the dual-axis tracking device to rotate-epsilon 1 And- ε 2 An angle, wherein: the negative sign represents that the rotation direction of the error value of the output rotation angle is opposite, and the light-gathering performance of the solar disc type light-gathering system is kept under the bearing working condition.
The method for predicting and maintaining the light-gathering performance of the solar disc type light-gathering system under the load-bearing working condition is briefly described by a case XEM-Dish system. The calculation parameters are as follows: the collector has a light collecting radius of 8.85m, a focal length f =9.49m, a specular reflectivity of 0.90 and a direct solar radiation intensity value of 1000W/m 2 . A finite element model of the disc type light condensing system is established as shown in fig. 5, the bearing deformation of the disc type light condensing system under the action of 17.1m/s wind speed when the height angle is 45 degrees is calculated (the wind direction angle under the action of wind load is 30 degrees, namely the working condition of 45-30 degrees), the energy flow density distribution of the focal plane and the cavity receiver at the moment is respectively shown in fig. 6 and 7, and the problems of focus bias and uneven distribution of focusing light spots are solved.
The centroid shift function of the focused light spot of the XEM-Dish system calculated by the step 4 is as follows:
Figure BDA0002152157250000161
as can be seen from FIG. 6, the XEM-Dish system has the centroid coordinates of x =45.02mm and y =25.11mm under the working condition of 45-30 degrees; after the tracking compensation is performed in step 5, the energy flux density distributions of the focal plane and the cavity receiver obtained by calculation are respectively shown in fig. 8 and fig. 9, and it can be seen that the problem of off-focus on the surface of the planar receiver and the problem of uneven distribution of the focused energy flux on the inner surface of the cavity receiver are significantly improved.

Claims (7)

1. A method for predicting and maintaining the light-gathering performance of a solar disc-type light-gathering system comprises the following steps:
1) Establishing a finite element model of the disc type light condensing system, dividing a grid into the structural finite element model of the disc type light condensing system, outputting space coordinate information of each node of each plane micro-element grid of a reflector surface of the light condenser under a non-bearing working condition, and calculating optical information of the disc type light condenser under the conditions of no optical error and the non-bearing working condition;
2) Applying boundary conditions of self weight and wind pressure load to the established finite element model of the disc type light-gathering system, calculating structural deformation under the action of the self weight and the wind load, and calculating the geometric centroid, the normal vector and the effective daylighting area of each plane infinitesimal grid of the reflecting mirror surface of the light-gathering device at the moment;
3) Calculating the bearing deformation of the disc type light-gathering system to obtain a space displacement value of the cavity receiver, and predicting the focusing energy flow distribution and the optical performance of the disc type light-gathering system under the action of a load by adopting a ray tracing method;
4) Introducing a tracking error angle of a double-shaft tracking device into the disc type light condensing system, calculating the centroid position of a focusing light spot on the surface of the plane receiver under the condition of different tracking errors, and fitting to obtain a function model of the tracking error angle value and the centroid position of the focusing light spot;
5) Establishing a corresponding relation between the bearing working condition of the disc type light condensing system and the centroid position of the focusing light spot under the bearing working condition of the disc type light condensing system, reversely solving a tracking error angle value according to the centroid position of the focusing light spot under the bearing working condition, and establishing a data table in which the bearing working condition of the disc type light condensing system and the output corner error value of the double-shaft tracking device are in one-to-one correspondence; acquiring an output corner error value of the double-shaft tracking device through a data table according to the bearing working condition measured in the operation of the disc type light-gathering system; then the drive controller makes the output shaft of the double-shaft tracking device rotate by a corresponding angle, and the light-gathering performance of the solar disc-type light-gathering system is kept under the bearing working condition.
2. The method for predicting and maintaining the light-gathering performance of the solar disc-type light-gathering system as claimed in claim 1, wherein the specific operation of step 1) is as follows:
1.1 A global coordinate system O-xyz is established at the vertex O position of the parabolic reflector of the dish condenser, the z axis points to the focus F of the parabolic curved surface, the position vector F of the focus F is = [0, F ], and F is the focal length of the parabolic reflector; when the light gathering system bears deformation, the global coordinate system O-xyz is still fixed, namely the coordinate system O-xyz is not fixedly connected with the light gathering device;
1.2 At the center point F of the receiving window of the cavity receiver 1 Establishing a local coordinate system F fixed with the receiver 1 -x 1 y 1 z 1 Center point F of receiving window of cavity receiver 1 Position vector F of 1 ＝[0，0，f](ii) a Local coordinate system F under non-bearing working condition 1 -x 1 y 1 z 1 Parallel to each corresponding axis of the global coordinate system O-xyz, and point F 1 Coincides with the position of the focal point F; local coordinate system F when the disc-type light-gathering system is deformed 1 -x 1 y 1 z 1 Rigid body motion with the receiver; three characteristic points are fixedly connected on the cavity receiver, and the three characteristic points are respectively taken as central points F of the receiving window 1 At + x 1 Points on the axis g and at + y 1 Point m, point g, point m and point F on the axis 1 Are all distances e 1 ；
1.3 According to the theory of elastic mechanics, a finite element method is adopted to establish a structural finite element model of the disc type light-gathering system; dividing each reflecting mirror surface of the condenser into triangular plane micro-element grids or quadrilateral plane micro-element grids or mixed plane micro-element grids of the triangular plane micro-element grids and the quadrilateral plane micro-element grids;
1.4 Deriving the space coordinates of each node of the plane micro-element grid of each reflecting mirror surface under the non-bearing condition from the finite element model of the disc type light-gathering system, and calculating the geometric centroid, the normal vector and the effective daylighting area of each plane micro-element grid under the non-bearing working condition without optical errors.
3. The method for predicting and maintaining the light condensing performance of the solar disc-type light condensing system according to claim 2, wherein the geometric centroid, the normal vector and the effective daylighting area of each planar infinitesimal grid under the non-load-bearing working condition in the step 1.4) are calculated as follows:
geometric centroid point p of each planar infinitesimal grid 1 Position vector p of 1 Comprises the following steps:
Figure FDA0002152157240000021
in the formula: the vectors a, b, c and d are position vectors of each node of the plane micro-element grid respectively;
unit normal vector N of plane infinitesimal grid p1 And effective daylighting area A p1 Respectively as follows:
Figure FDA0002152157240000022
Figure FDA0002152157240000023
in the formula: vector bc = c-b; vector ba = a-b; vector dc = c-d; vector da = a-d; angle phi 1 Is the unit normal vector N of a planar infinitesimal grid p1 The included angle between the central ray vector S and the incident light cone of the sun; vector S = [0,0, -1](ii) a Angle phi 1 Satisfy the requirement of
Figure FDA0002152157240000024
4. The method for predicting and maintaining the light-gathering performance of the solar disc-type light-gathering system as claimed in claim 3, wherein the specific operation of step 2) is as follows:
2.1 Applying a self-weight and wind pressure load boundary condition to the established finite element model of the disc type light-gathering system, applying a wind pressure load to the surface of the parabolic reflector of the light-gathering device, and calculating the structural deformation under the action of the self-weight and the wind load;
2.2 Calculating displacement vectors of all nodes of all plane micro-element grids of the reflecting mirror surface of the condenser under a bearing condition, and calculating geometric centroids, normal vectors and effective daylighting areas of all the plane micro-element grids; the specific calculation process is as follows: after the disc-type light-gathering system bears deformation, the geometric centroid point p of each plane micro-element grid 1 Move to point p t Position, at this point p t The position vector of (a) is:
Figure FDA0002152157240000025
in the formula u a 、u b 、u c 、u d Respectively displacement vectors of each node of the plane infinitesimal grid under the action of load;
unit normal vector N of each planar infinitesimal grid pt And effective daylighting area A pt Respectively as follows:
Figure FDA0002152157240000031
Figure FDA0002152157240000032
in the formula: vector b 1 c 1 ＝c 1 -b 1 ；b 1 a 1 ＝a 1 -b 1 ；d 1 c 1 ＝c 1 -d 1 ；d 1 a 1 ＝a 1 -d 1 (ii) a Vector a 1 、b 1 、c 1 、d 1 And respectively the position vectors of all nodes of the plane infinitesimal after the condenser bears the deformation.
5. The method for predicting and maintaining the light-gathering performance of the solar disc-type light-gathering system as recited in claim 4, wherein the specific operation of step 3) is as follows:
3.1 The disk-type condensing system is deformed to cause rigid displacement of the cavity receiver, and the local coordinate system fixedly connected with the cavity receiver is also F 1 -x 1 y 1 z 1 Change to F t -x 2 y 2 z 2 (ii) a Three characteristic points F fixed on the cavity receiver 1 G and m move to point F respectively t 、g t And m t The position, the relative geometric relation among the three characteristic points is kept unchanged; vector F t 、g t And m t Are respectively point F t 、g t And m t A position vector of (a); vector F 1 G and m are points F in the design state 1 Position vectors of g and m, vector F 1 G and M are known in advance and satisfy M 1 ＝F 1 、g＝M 1 +[e 1 ,0,0]And M = M 1 +[0,e 1 ,0](ii) a Vector u F ，u g And u m Respectively, the light-focusing system bearing deformation causes the point F 1 Displacement vectors generated by g and m; the position vectors of the three feature points satisfy the following equation:
Figure FDA0002152157240000033
3.2 Computing a local coordinate system F of the cavity receiver t -x 2 y 2 z 2 And the global coordinate system O-xyz are:
Figure FDA0002152157240000038
in the formula: vector M 1 Is the center point F of the receiving window 1 A position vector of, i.e. M 1 ＝F 1 Rot (A, β) is used to implement an arbitrary vector P ∈ R 1×3 Around an arbitrary unit vector a = [ a = x ,a y ,a z ]The matrix function of the rotation angle beta specifically comprises:
Figure FDA0002152157240000034
vector
Figure FDA0002152157240000035
Wherein: vector
Figure FDA0002152157240000036
Vector
Figure FDA0002152157240000037
Vector g 4 ＝(g-F 1 )Rot(n 3 ,β 1 )+F t (ii) a Vector
Figure FDA0002152157240000041
Vector
Figure FDA0002152157240000042
Vector m 3 ＝m+u F Vector of
Figure FDA0002152157240000043
Rotation angle
Figure FDA0002152157240000044
Vector F 1 m＝m-F 1 ；m 3 m t ＝m t -m 3 ＝u m -u F (ii) a Rotation angle
Figure FDA0002152157240000045
Vector F 1 g＝g-F 1 ；g 4 g t ＝g 4 -g t ；g 4 ＝(g-F 1 )Rot(n 3 ,β 1 )+F t (ii) a Angle of rotation beta 1 Angle of rotation beta 2 Is an intermediate variable;
3.3 In a global coordinate system O-xyz, dispersing a solar incident light cone with a half vertex angle delta of 4.65mrad into a large number of solar rays, and calculating an incident vector and carried energy density of each solar ray; the calculation method is as follows: establishing a sunlight cone model at the origin O of the global coordinate system, and constructing a focal plane of the parabolic mirror surface with the radius R s A disk of = F · tan (δ), the disk having a focal point F as the center and having a side length of 2R s The square is enveloped, then the square is respectively dispersed into W and N parts along the length and width directions, and W = N, so as to obtain a series of square grids; let the center points of the w-th and n-th square grids wn of the square along the length and width directions be denoted as Q wn Point Q of wn At a distance d from F wn ＝||Q wn -F |, vector F = [0, F | ]](ii) a Center point Q of square grid wn wn At a radius R s The disk of (1) is an effective grid, f wn =1; otherwise, it is an invalid grid, f wn =0, i.e. not participating in subsequent ray trace calculations; center point Q of effective square grid wn wn The direction of the line connecting the origin O is the incident ray I of the sun wn Incident vector I of wn I.e. I wn ＝-Q wn /||Q wn | |, in which the vector
Figure FDA0002152157240000046
Solar ray I wn The energy density carried, I (w, n), is:
Figure FDA0002152157240000047
in the formula: gamma ray wn For incident rays of the sun I wn The included angle between the central ray vector S of the incident light cone of the sun,
Figure FDA0002152157240000048
I 1 the radiation intensity of the central ray of the incident light cone of the sun,
Figure FDA0002152157240000049
W 0 is the intensity value of direct solar radiation, and the unit is W/m 2 ；f wn A decision parameter for whether the square grid wn participates in the calculation;
3.4 In the global coordinate system O-xyz) the solar incident ray I is calculated on the basis of the law of specular reflection wn Geometric centroid p of plane infinitesimal grid on reflecting mirror surface of dish type condenser t The equation of the reflected ray of (c); this reflected ray equation is then converted to the local coordinate system F of the cavity receiver 2 -x 2 y 2 z 2 In (1), the parametric equation is expressed as:
Figure FDA0002152157240000051
in the formula: the vectors on the right side of the equation are all expressed based on a global coordinate system O-xyz; vector
Figure FDA0002152157240000052
Wherein the upper right label T is the transposed symbol of the vector;
3.5 In the local coordinate system F of the cavity receiver 2 -x 2 y 2 z 2 Giving a geometric equation, surface absorptivity and optical reflection characteristics of each surface in the cavity receiver; dividing the inner surface of the cavity receiver into U equal parts along the height direction and G equal parts along the circumferential direction; recording the transmission and energy absorption processes of the reflected light rays determined in the step 3.4) in the cavity receiver by adopting a known ray tracing method; that is, the coordinates of the intersection point of the light ray with the surface when the light ray is reflected for multiple times in the cavity receiver are calculated until the light ray escapes from the cavity receiver or the reflection times reach the maximum reflection times N r Until the end; then judging the coordinates of the intersection points in which numbered discrete grid area of the inner surface of the cavity receiverAnd increasing the energy carried by the light to the grid area; when the energy carried by the sun rays is added to the discrete grid ug, it is expressed as:
E absorber (u,g)＝E absorber (u,g)+I(w,n)·A pt ·ρ mirror (1-σ absorber ) n1 ·(ρ wall ) n2 ·σ absorber (10)
in the formula: e habsorber (u, g) is an array element that stores the solar radiation energy received by the grid ug in the receiver surface, its initial value is 0 before the energy flow distribution calculation; ρ is a unit of a gradient mirror Is the reflectivity of the condenser mirror; sigma absorber Absorption rate for the area in the cavity receiver where the heat absorber is mounted; rho wall Reflectivity of other surfaces inside the cavity receiver; n is 1 Is the number of times of reflection of the sun's rays by the surface of the heat absorber, n 1 ＝0,1,2,...N 1 ，N 1 The maximum reflection times of the solar rays on the surface of the heat absorber; n is a radical of an alkyl radical 2 The number of times of reflection of the solar ray by the common wall surface in the cavity receiver, n 2 ＝0,1,2,...N 2 ，N 2 Is the maximum reflection number of the sun ray on the common wall surface, and N 1 +N 2 ≤N r ；
The receiver for receiving the solar radiation energy focused by the dish condenser is of a plane structure and is superposed with the focal plane of the parabolic reflector; taking a plane receiver as a square area with the side length of L, and equally dividing the square area into H parts and U parts along the directions of two sides, wherein H = U, and obtaining a small H multiplied by U square grid; calculating the coordinates of the intersection point of the reflected light ray and the plane receiver determined in the step 3.4), judging which numbered discrete grid area of the receiver the intersection point is in, and increasing the energy carried by the light ray to the grid area; when the energy carried by the sun rays is added to the discrete grid hu, the energy of the solar radiation received by the grid hu in the storage receiver surface is expressed as:
Eplan(h,u)＝Eplan(h,u)+I(w,n)·A pt ·ρ mirror (11)
where Eplan (h, u) is the energy of solar radiation received by grid hu in the storage receiver surface, its initial value is 0 before calculation of the energy flow distribution;
3.6 Calculating a reflection ray equation of all solar incident rays in a solar cone at the geometric centroid of all plane micro-element grids of a reflecting mirror surface of the disc type condenser, and calculating transmission and energy absorption of all reflection rays in the cavity receiver through the step 3.5), finally obtaining focusing energy flux density distribution of the inner surface of a heat absorber in the disc type condenser system under a bearing working condition, and counting total energy received by the surface of the heat absorber and total energy collected by the condenser, wherein the ratio of the total energy received by the inner wall surface of the cavity receiver to the total energy collected by the condenser is the optical efficiency of the disc type condenser system under the bearing working condition; when the receiver for receiving the energy of the solar radiation focused by the dish concentrator is a planar receiver, the distribution of the focused energy flux density at the surface of the planar receiver is calculated.
6. The method for predicting and maintaining the light-gathering performance of the solar disc-type light-gathering system as claimed in claim 5, wherein the specific operation of step 4) is as follows:
4.1 The disc type light-condensing system realizes accurate tracking OF the position OF the sun through a double-shaft tracking device, and under the condition OF no tracking error, the focal axis OF OF the disc type light-condensing system is parallel to the central ray S OF the sunlight cone; the included angle between the focal axis OF OF the parabolic reflecting mirror surface OF the disc condenser and the ground plane is the height angle OF the disc condenser; the included angle between the projection OF the focal axis OF OF the parabolic reflecting mirror surface OF the disc condenser on the ground plane and the front south is the azimuth angle OF the disc condenser; the double-shaft tracking device consists of a height tracking device and an azimuth tracking device, wherein an azimuth tracking shaft is vertical to a ground plane, the height tracking shaft is parallel to the ground plane and is vertical to a focal axis of the disc condenser, and output corner error values of the height tracking device and the azimuth tracking device are respectively epsilon 1 And ε 2 The tracking error angle of the height angle of the disc condenser is epsilon 1r Satisfy epsilon 1r ＝ε 1 (ii) a Azimuth tracking error angle epsilon of disc condenser 2r Comprises the following steps: epsilon 2r ＝arcos[(cos(90-φ)) 2 ·(1-cosε 2 )+cosε 2 ]Wherein: phi is the elevation angle of the disc condenser when no tracking error exists;
4.2 The focusing energy flux density distribution of the surface of the plane receiver is obtained through the calculation of the steps 3.5) and 3.6), and the centroid coordinate of the focusing light spot is obtained through calculation:
Figure FDA0002152157240000061
4.3 Based on the data obtained in step 4.2), a mathematical model of the sun tracking error of the disc type light condensing system and the centroid coordinate of the focusing light spot is established by adopting a function fitting method, and the mathematical model is used for reversely solving the altitude angle and the azimuth angle tracking error angle of the disc type light condenser by the centroid coordinate of the focusing light spot, and the formula is as follows:
Figure FDA0002152157240000062
in the formula: k 1 Is the undetermined coefficient and is determined by fitting a large amount of data.
7. The method for predicting and maintaining the light-gathering performance of the solar disc-type light-gathering system as recited in claim 6, wherein the specific operation of step 5) is as follows:
5.1 Calculating to obtain the centroid coordinates of the focusing light spots on the surface of the planar receiver of the disc type light condensing system under different bearing working conditions through the step 2) and the step 3);
5.2 Adopting the centroid of the focusing light spot obtained in the step 5.1), and reversely calculating the tracking error value of the disc condenser under each bearing working condition through the step 4.2);
5.3 The tracking error value of the disc condenser obtained in the step 5.2) passes through the azimuth angle tracking error angle epsilon of the disc condenser in the step 4.1) 2r The formula is used for reversely solving the output corner error value of the double-shaft tracking device; establishing a data table in which the bearing working conditions and the output corner error values of the double-shaft tracking device are in one-to-one correspondence, and storing the data table in a drive controller of the double-shaft tracking device;
5.4 ) querying the number established in step 5.3) according to the load-bearing condition determined in the actual operation of the disc-type light-condensing systemObtaining an output corner error value epsilon of the double-shaft tracking device according to a table 1 And ε 2 (ii) a The drive controller sends the signal to the elevation angle and azimuth angle drive motors to enable two output shafts of the double-shaft tracking device to rotate to the position of-epsilon respectively 1 And- ε 2 An angle, wherein: the negative sign represents the opposite direction of rotation from the output corner error value; the light-gathering performance of the solar disc type light-gathering system is kept under the bearing working condition.
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