A spherical disc concentrator and its design method

Abstract

This invention discloses a spherical dish-type concentrator and its design method, comprising a reflector and a receiver. The reflector is composed of multiple annular spherical mirrors spliced ​​together, and the circles formed by the transverse midpoints of any one of the annular spherical mirrors lie on the same paraboloid of revolution. The receiver is a flat plate receiver or a cavity receiver, mounted at the focal point of the paraboloid of revolution. This invention proposes using spliced ​​spherical reflectors as sub-mirrors to form a dish-type system reflector. Each sub-mirror is a part of a sphere. By controlling the width of the annular spherical reflector and designing a suitable spherical radius, spherical aberration can be effectively eliminated, and coma and astigmatism are also eliminated, achieving excellent light-gathering effect. This not only improves system efficiency by 4.25% but also reduces manufacturing difficulty and cost.

Description

Technical Field

[0001] This invention relates to the field of concentrated solar thermal utilization technology, and in particular to a dish concentrator and its design method. Background Technology

[0002] Concentrated solar thermal utilization uses concentrating technology to focus a large amount of low-density solar energy onto a small area, forming high-density solar energy, which can then generate high-temperature heat energy for solar thermal power generation. It is the most promising thermal power generation technology to replace coal-fired power plants. Currently, the main concentrated solar technologies include tower, trough, linear Fresnel, and dish concentrating solar technologies.

[0003] Typically, dish-type solar concentrators use a rotating parabolic mirror as the primary mirror and a two-way tracking device to ensure that incident sunlight always hits the dish mirror at an angle of approximately 0 degrees. The dish mirror then focuses the sunlight onto a focal point, using a receiver or by directly heating the working fluid to drive an engine mounted at the focal point to generate electricity. This method has the highest cosine factor and the highest efficiency, making it one of the most promising concentrated solar power technologies.

[0004] However, typical dish systems use parabolic spheres as primary mirrors. The manufacturing process of parabolic spheres is difficult, costly, and prone to errors, leading to a decline in system performance. The simplest solution is to use small-area plane mirrors pieced together to form the dish system mirrors. For example, Wang Yunfeng's doctoral dissertation at the University of Science and Technology of China studied the performance of this system, but the focusing power is significantly reduced, and the performance is much worse than that of a parabolic sphere dish system. Another approach is to use multiple spherical mirrors pieced together to form a mirror, simulating a parabolic sphere. Patent CN201220201616.1 and our optimization article published in Apply Science in 2022 both use square spherical mirrors pieced together to form the mirror, which reduces the manufacturing difficulty and cost. The literature also mentions the use of regular hexagonal and equilateral triangular spherical mirrors, but these all introduce spherical aberrations, including spherical aberration, meridional aberration, and sagittal aberration, which still significantly reduce system performance. The third solution is to use a spherical mirror as the primary mirror. In the field of astronomical telescopes, this has become one of the main choices for many giant telescopes. It can significantly reduce the manufacturing difficulty and cost of the primary mirror. However, it often requires multiple secondary mirrors to correct aberrations such as spherical aberration and coma, making the system structure very complex and increasing the manufacturing difficulty and cost, making it difficult to apply to the solar energy field. Patent CN200610041392.1 uses a spherical mirror instead of a paraboloid of revolution, without aberration correction, and uses a tubular receiver with a length equal to half the radius of the sphere. This means that the light-gathering power and performance of the spherical mirror are significantly reduced. CN201610278112.2 and CN201610278111.8 use multiple aspherical mirrors to construct an off-axis dish system, which actually increases the manufacturing difficulty and cost.

[0005] Using dual-mirror and multi-mirror telescopes is a common method in the field of astronomy. In the field of solar energy, multi-mirror systems are complex and technically difficult to implement, making them less feasible. However, dual-mirror schemes already exist. For example, the dual-mirror system designed by Pan Qikun et al. in "High-Magnification Solar Concentrator Based on Cassegrain Structure" (Chinese Optics, 2012, Vol5, No4) uses photovoltaic cells as the receiver, a rotating parabolic mirror as the primary mirror, and a rotating hyperboloid as the secondary mirror. Only spherical aberration is eliminated, and the theoretical concentration ratio is only 550 times. Moreover, the manufacturing process is difficult, and the actual concentration ratio is 500 times, which is lower than that of traditional dish systems.

[0006] One of our recent solutions, as described in patent 2023100678201, is to use ellipsoidal mirrors to form the primary reflector. Although this eliminates sub-mirror aberrations, including spherical aberration and astigmatism, maintains performance, reduces manufacturing difficulty, and increases actual performance, its manufacturing difficulty is still relatively high, and its manufacturing accuracy is not as good as that of spherical mirrors. Summary of the Invention

[0007] The purpose of this invention is to overcome the shortcomings of existing technologies, such as high processing difficulty, low precision, and low system performance, and to provide a spherical disc concentrator and its design method. This invention proposes to use annular spherical mirrors spliced ​​together to form a disc system mirror, and to eliminate aberrations by selecting appropriate transmission width and radius.

[0008] This invention is achieved through the following technical solution:

[0009] A spherical disc condenser includes a reflector and a receiver. The reflector is composed of multiple toroidal spherical mirrors, and the circles formed by the transverse midpoints of any one of the toroidal spherical mirrors lie on the same paraboloid of revolution. The receiver is a flat plate receiver or a cavity receiver, mounted at the focal point of the paraboloid of revolution. By using toroidal spherical mirrors instead of corresponding toroidal paraboloids of revolution, the light reflected from these mirrors shares a common focal point, even though they are some distance from the focal point of the entire spherical reflector. The smaller radius of the focused spot effectively eliminates most spherical aberration. By adjusting the position and radius of the spherical mirrors, the focal point of the toroidal spherical reflector is also aligned with the focal point of the paraboloid of revolution, thus eliminating spherical aberration.

[0010] If any point on the circumference formed by the transverse midpoints of the annular spherical mirror is d away from the principal axis of the paraboloid of revolution i The edge angle on the parabolic surface of revolution is The radius of the spherical surface of the annular spherical mirror is r. i ,but

[0011] The goal of optimizing a concentrated solar power (CSP) system is to maximize thermal energy gain. Increasing the receiver radius can improve the interception rate, allowing the absorber to absorb more energy. However, since the receiver operates at high temperatures, energy loss is proportional to the receiver's aperture area, thus increasing energy loss. Our research shows that when reflected light distributed within a 3σ angle range is intercepted, energy gain is close to maximum. Further increasing the receiver radius, while increasing the interception angle range, results in a small increase in intercepted energy, while the thermal energy loss increases significantly, making it counterproductive. Therefore, one conclusion we reached through our research is that the initial design should utilize a range of reflected sunlight with an interception angle less than or equal to 3σ. The receiver radius r of the dish system is then... c It can be calculated using the following formula:

[0012]

[0013] Where σ is the Gaussian distribution variance of reflected solar intensity, and R0 is the light transmission radius of the dish-type concentrating solar thermal collector system. The edge angle of the dish-type concentrating solar thermal system; the formula for calculating the Gaussian distribution variance σ of reflected solar intensity is:

[0014]

[0015] σ sun Let σ be the variance of the Gaussian distribution of the solar photosphere. slopex It is the variance of the reflector slope error distribution; σ tracking The variance of the tracking error is a Gaussian distribution; σ disp The variance of the system installation error is a Gaussian distribution; σ specular The variance of the Gaussian distribution of the reflector material error is usually very small and can be ignored. Referring to the measured data provided in the research report on trough systems published by Bendt et al., "Optical analysis and optimization of line focus solar collectors," the variance of the solar photosphere distribution σ can be taken as the variance. sun It is 4.1 mrad, σ slope This is the variance of the reflector slope error distribution; when using a spherical mirror, take 1.0 mrad; σ tracking The variance of the tracking error is a Gaussian distribution, taken as 1.0 mrad; σ disp The variance of the system installation error is a Gaussian distribution, taken as 1 mrad; σ specular The variance of the error, such as that of the mirror material, is a Gaussian distribution and is usually very small, so it can be ignored; the calculated value is σ = 4.776 mrad. The above results can be used as preliminary design values ​​for optimization.

[0016] The light transmission width of any one of the annular spherical mirrors should not exceed the upper limit calculated as follows:

[0017] If the maximum angle between the line connecting any point of the annular spherical mirror to its focal point and the axis of symmetry of the paraboloid of revolution is ψ i Then the upper edge angle of the ring corresponding to the horizontal midpoint

[0018]

[0019] The upper limit of the light transmission width w of the annular spherical mirror is calculated using the following formula:

[0020]

[0021] According to the above design, the aberrations caused by spherical mirrors can be eliminated, thus eliminating the disadvantages of using spherical mirrors. At the same time, the advantages of spherical mirrors, such as easy processing and small optical errors, can be taken advantage of.

[0022] The annular spherical mirror is composed of spliced ​​sector spherical mirrors. Each sector spherical mirror that makes up the same annular spherical mirror has the same shape and spherical radius, which makes it easy to manufacture.

[0023] The edge angle range of the dish-type concentrating solar thermal collector system is 35-50 degrees, and a value is selected from this range to begin the design calculations. Typically, 45 degrees is used as the initial design value.

[0024] The dish-type concentrating solar thermal collector system is installed on a two-way tracking device.

[0025] When the receiver uses a cavity receiver, a spherical segment transparent glass cover is installed at the opening of the cavity receiver, with the concave side of the spherical segment transparent glass cover placed inside the cavity receiver.

[0026] To aid in the design of this system, we propose a design method for a spherical dish concentrator, with the following specific steps:

[0027] The first step is to determine the light transmission radius R0 of the dish concentrating solar thermal collector system based on the requirements;

[0028] The second step is to determine that the edge angle of the dish-type concentrating solar thermal collector system is 45 degrees.

[0029] The third step is to determine the focal length. receiver radius is

[0030] The fourth step is to first determine the width of the outermost annular spherical mirror, and then calculate the edge angle of the center of the annular spherical mirror on the paraboloid of revolution using the following formula.

[0031]

[0032] At this time The upper limit of the light transmission width w of the annular spherical mirror is calculated using the following formula:

[0033]

[0034] This allows us to determine the light transmission width w of the annular spherical mirror, and then determine the distance d from any point on the central circle of the annular spherical mirror to the principal axis. i Calculate using the following formula:

[0035]

[0036] Then the spherical radius r of the annular spherical mirror i The calculation formula is:

[0037]

[0038] Fifth, following the method in step four, calculate the maximum edge angle data of the second annular spherical mirror, and determine the light transmission width parameters of each annular spherical mirror in sequence according to the above method;

[0039] Step 6: Use a ray tracing program to simulate and calculate the system performance. If the results are not satisfactory, adjust the receiver radius or change the system edge angle, and re-complete the new design and performance calculation according to steps 4 to 6.

[0040] The advantages of this invention are: This invention proposes to use spherical mirrors spliced ​​together as sub-mirrors to form a dish system mirror. Each sub-mirror is a part of a sphere. By controlling the width of the annular spherical mirror, spherical aberration is better eliminated, and there is no coma or astigmatism. This can achieve a very good light-gathering effect, which not only improves the system efficiency, but also reduces the processing difficulty and cost. Attached Figure Description

[0041] Figure 1 Side view of the spherical splicing disc system;

[0042] Figure 2 A ring-shaped spherical mirror composed of fan-shaped spherical mirrors spliced ​​together in a spherical splicing disc system;

[0043] Figure 3 The outline of a fan-shaped spherical mirror;

[0044] Figure 4 This is a diagram showing the energy flux density distribution at the aperture (focal plane) of a novel dish-type receiver system. Detailed Implementation

[0045] like Figure 1-4 As shown, a spherical disc condenser includes a reflector 1 and a receiver 3. The reflector 1 is composed of multiple annular spherical mirrors 2 spliced ​​together. The circles formed by the transverse midpoints of any one of the annular spherical mirrors 2 are all on the same parabolic surface of rotation. The receiver 3 is a flat plate receiver or a cavity receiver, which is installed at the focal point of the parabolic surface of rotation.

[0046] If any point on the circumference formed by the transverse midpoints of the annular spherical mirror is d away from the principal axis of the paraboloid of revolution i The edge angle on the parabolic surface of revolution is The radius of the spherical surface of the annular spherical mirror is r. i ,but

[0047] The receiver radius r c Calculate using the following formula:

[0048]

[0049] Where σ is the Gaussian distribution variance of reflected solar intensity, and R0 is the light transmission radius of the dish-type concentrating solar thermal collector system. The edge angle of the dish-type concentrating solar thermal system; the formula for calculating the Gaussian distribution variance σ of reflected solar intensity is:

[0050]

[0051] σ sun Let σ be the variance of the Gaussian distribution of the solar photosphere. slopex It is the variance of the reflector slope error distribution; σ tracking The variance of the tracking error is a Gaussian distribution; σ disp The variance of the system installation error is a Gaussian distribution; σ specular It is the Gaussian distribution variance of the error in the reflector material.

[0052] The upper limit of the light transmission width of any one annular spherical mirror is calculated as follows:

[0053] If the maximum angle between the line connecting any point of the annular spherical mirror to its focal point and the axis of symmetry of the paraboloid of revolution is ψ i Then the upper edge angle of the ring corresponding to the horizontal midpoint

[0054]

[0055] The upper limit of the light transmission width w of the annular spherical mirror is calculated using the following formula:

[0056]

[0057] The annular spherical mirror is composed of sector spherical mirrors 5 spliced ​​together, and each sector spherical mirror that makes up the same annular spherical mirror has the same shape and spherical radius.

[0058] The edge angle range of the dish-type concentrating solar thermal collector system is 35-50 degrees. A value is selected from this range to begin the design calculation.

[0059] The dish-type concentrating solar thermal collector system is installed on a two-way tracking device.

[0060] When the receiver uses a cavity receiver, a spherical segment transparent glass cover plate 4 is installed at the opening of the cavity receiver, and the concave surface of the spherical segment transparent glass cover plate 4 is placed inside the cavity receiver.

[0061] A design method for a spherical dish concentrator, the specific steps of which are as follows:

[0062] The first step is to determine the light transmission radius R0 of the dish concentrating solar thermal collector system based on the requirements;

[0063] The second step is to determine that the edge angle of the dish-type concentrating solar thermal collector system is 45 degrees.

[0064] The third step is to determine the focal length. receiver radius is

[0065] The fourth step is to first determine the width of the outermost annular spherical mirror, and then calculate the edge angle of the center of the annular spherical mirror on the paraboloid of revolution using the following formula.

[0066]

[0067] At this time The upper limit of the light transmission width w of the annular spherical mirror is calculated using the following formula:

[0068]

[0069] This allows us to determine the light transmission width w of the annular spherical mirror, and then determine the distance d from any point on the central circle of the annular spherical mirror to the principal axis. i Calculate using the following formula:

[0070]

[0071] Then the spherical radius r of the annular spherical mirror i The calculation formula is:

[0072]

[0073] Fifth, following the method in step four, calculate the maximum edge angle data of the second annular spherical mirror, and determine the light transmission width parameters of each annular spherical mirror in sequence according to the above method;

[0074] Step 6: Use a ray tracing program to simulate and calculate the system performance. If the results are not satisfactory, adjust the receiver radius or change the system edge angle, and re-complete the new design and performance calculation according to steps 4 to 6.

[0075] The following example uses a dish system with a light transmission radius R0 = 4.1 meters, constructed by splicing together ring-shaped spherical mirrors, to illustrate the main design parameters. As mentioned earlier, the Gaussian distribution variance of the reflected light intensity is σ = 4.776 mrad. Using a cavity receiver, at maximum focusing ratio, the system edge angle... The angle is 45 degrees, the receiver radius rc = 117.5 mm, and the light concentration ratio is 12:14. System focal length. For the solar array, we selected a spherical reflector width of 0.4 meters and used a total of 10 annular spherical mirrors. In actual manufacturing, multiple sector-shaped spherical reflectors are spliced ​​together to form an annular spherical mirror, with the width of each sector-shaped spherical reflector flexibly chosen to be approximately 0.5 meters. The cavity receiver is installed at the focal point of the parabolic rotating surface, and the system is then mounted on a two-way tracking device to form a dish-like system capable of collecting solar energy. Our established ray tracing program calculated the focal plane energy flux density distribution, such as... Figure 4 As shown, the interception rate reaches 99.8%. If a rotating parabolic surface is used to construct the same dish system, the light transmission radius and receiver radius are the same, but the radial error of the parabolic surface is 3 mrad and the optical error is 7.4 mrad, resulting in an interception rate of 95.1%, which is 4.7% lower than the spliced ​​dish system. Moreover, it is more complex to manufacture and more expensive. Therefore, this solution not only improves system efficiency but also reduces manufacturing costs.

[0076] The principle of a solar dish concentrator is similar to that of an astronomical reflecting telescope. Astronomical telescopes primarily focus on the low-intensity light of stars and planets, requiring a high degree of accuracy in reproducing the target structure—a requirement far more stringent than that of a solar concentrator. Solar dish systems, on the other hand, can use non-imaging systems, with the primary goal of achieving a high light-gathering ratio to reduce heat loss and maximize energy gain. Low-cost astronomical reflecting telescopes often use spherical mirrors instead of parabolic mirrors due to the simplicity and low cost of manufacturing spherical mirrors, but they typically employ long focal lengths to eliminate spherical aberration. In a solar dish system, spherical mirrors can also be used instead of parabolic mirrors. The main drawback is that while increasing the focal length can eliminate spherical aberration, the spot radius is proportional to the focal length, leading to a decrease in light-gathering ratio and increased heat loss. This invention proposes a method of stitching together multiple annular spherical mirrors. By using spherical mirrors of different radii and limiting the width of the annular spherical mirrors, spherical aberration is eliminated, overcoming the drawbacks of using spherical mirrors while leveraging their ease of manufacture and lower optical error. In practice, it is necessary to select appropriate annular spherical mirror width, spherical radius, and focal length, as well as receiver radius, based on system properties such as condenser lens optical error, solar intensity distribution parameters, and receiver heat loss. We have established the relationship between the light concentration ratio and the spherical radius, focal length, and the receiver radius determined by the width of the intercepted reflected light intensity distribution. This allows us to calculate the optimal design parameters and obtain the maximum net energy. Below is our established analytical calculation method:

[0077] See our 2013 article, "Optical analysis and optimization of parabolic dish solar concentrator with a cavity receiver" (solar energy, 2013, Vol 92, pp288-297). Considering that the incident energy is constant, our optimization objective can also be to maximize the system's annual average net thermal efficiency η, calculated as follows:

[0078]

[0079] ρ is the specular reflectivity, τ is the transmittance of the receiver with a transparent cover (1.0 without a cover), α is the receiver absorptivity, and γ is the receiver interception rate, which can be calculated using a ray tracing program or estimated using the method proposed in this paper (see below). The last term in the expression is the reciprocal of the geometric concentration ratio. q is the receiver's heat loss per unit area (in W / m²). 2 ξ is the ratio of heat loss energy per unit receiver area to direct solar energy received per unit area of ​​concentrator per year, which we call the system heat loss coefficient. We use a clear-day model to approximate the annual average ξ, as shown in the following formula:

[0080]

[0081] Here, the integral of g represents the total operating time within a year when the solar altitude is greater than 15 degrees, and the denominator is the total amount of direct solar radiation per unit area within a year. At a certain operating temperature, the heat loss q per unit area of ​​the receiver can be approximated as a constant. For example, at an operating temperature of 800℃, the total heat loss power of a WGA cavity receiver with an opening diameter of 0.14m is approximately 0.260kW, varying slightly with the solar altitude angle, changing by about 2% when the maximum change in solar altitude angle is 60 degrees (FRASER 2008). Generally, we can use the following formula to calculate the heat loss of the cavity receiver (Siebers DL, Kraabel JS. Estimating convective energy losses from solar central receivers. Sandia National Laboratories; 1984).

[0082]

[0083] Where T w It is the average temperature of the receiving surface, T a Here, ε is the ambient temperature, A is the opening area of ​​the cavity receiver, ε is the emissivity, and σ is the Boltzmann constant = 5.67 * 10⁻⁶. -8W / (m 2 K 4 ).

[0084] Using a sunny-day model or measured data, the annual average DNI can be calculated, yielding the heat loss coefficient ξ. This allows for simulation calculation of the system's annual average net thermal efficiency η under different design parameters. heat This allows us to obtain optimized design parameters.

[0085] Using a cavity receiver and adding a transparent cover to the opening can reduce heat loss, but it also reduces the amount of solar energy entering the receiver due to the transmittance being less than 1. Quartz glass is commonly used because it is both heat-resistant and has high transmittance. However, ordinary quartz glass has relatively low transmittance, which sometimes cannot offset heat loss. The main reason is the high reflectivity of sunlight incident on ordinary quartz glass. The main measure to reduce reflectivity is to add an anti-reflective coating to the surface of the quartz glass, thereby reducing surface reflection and increasing transmittance. Literature reports that this can increase transmittance from 93% to 99%.

[0086] We previously calculated the heat loss coefficients of two typical cavity receivers operating at 800℃, connected to a Stella engine. One type is a cavity receiver without a transparent cover, with a heat loss of 16.26 W / cm². 2 One type has a heat loss coefficient of 168.25; the other type is a cavity receiver with a transparent cover, with a heat loss of 1.67 W / cm². 2 The heat loss coefficient is 18.177. We advocate using a dish system to obtain thermal energy, and then concentrating the heat energy collected by a large number of dish systems to drive a steam turbine to generate electricity. The maximum operating temperature of the dish system is around 600℃, and the heat loss is much smaller. This system can group a large number of dish systems and operate them at different temperatures, which can further reduce heat loss. However, this also increases the workload for optimization design by several times.

[0087] This system is essentially a dish-like system of mirrors constructed by splicing together portions of multiple spherical mirrors. Since the central rays of the sun are incident perpendicularly on each spherical mirror, coma and astigmatism are very small and negligible. However, using spherical mirrors introduces spherical aberration. Our solution is to use a ring-shaped spherical mirror, eliminating spherical aberration by limiting the mirror width. The method for eliminating spherical aberration is discussed below. Spherical aberration refers to the large spot formed on the focal plane when parallel light rays are incident along the principal axis of a parallel spherical mirror. The spot radius δx is the lateral spherical aberration, which can be expressed by the following formula: (Soviet) Klópalova et al., *Studies and Tests of Optical Systems*, page 175:

[0088] δ x =r*tan(ψ)*sin 2 (ψ / 4) / cos(ψ / 2)

[0089] r is the radius of the spherical mirror sphere, and ψ is the maximum angle between the reflected ray from the spherical mirror and the principal axis.

[0090] Parabolic rotating disc systems generally do not exhibit spherical aberration, as the receiver primarily intercepts diffused reflected light. However, when a parabolic rotating disc system is constructed using spherical submirrors, spherical aberration inevitably arises. As described in the formula above, spherical aberration is related to the spherical size. Since the ratio of the spherical aperture R0 to the spherical radius r is R0 / r = sin(ψ / 2), according to the spherical aberration calculation formula, the larger R0 / r is, the greater the spherical aberration. Because increasing r increases the image spot radius, researchers primarily limit the aperture size of the mirrors to eliminate spherical mirror aberration. Our research indicates that if σ represents the Gaussian distribution variance of the reflected light intensity, at least the reflected light within the 3σ range should be completely intercepted. This allows us to obtain the receiver radius r. c It should be calculated using the following formula:

[0091]

[0092] R0 is the light transmission radius of the dish system. The edge angle of the dish system, where the Gaussian distribution variance σ of the reflected light intensity is calculated using the following formula:

[0093]

[0094] Referring to the measured data provided in the research report on trough systems published by Bendt et al., "Optical analysis and optimization of line focus solar collectors," the variance of the solar photosphere distribution σ can be taken as the value. sun It is 4.1 mrad, σ slope This is the variance of the reflector slope error distribution; when using a spherical mirror, take 1.0 mrad; σ tracking The variance of the tracking error is a Gaussian distribution, taken as 1.0 mrad; σ disp The variance of the system installation error is a Gaussian distribution, taken as 1 mrad; σ specular The variance of the error in the reflector material is a Gaussian distribution, which is usually very small and can be ignored; the calculated value is σ = 4.776 mrad.

[0095] When using spherical mirrors for splicing, the lateral spherical aberration δ x This involves increasing the radius of the intercepted reflected light spot. The receiver radius is then calculated using the following formula:

[0096]

[0097] Eliminating spherical aberration means reducing its impact. For the dish system proposed in this paper, our research results show that when the spherical aberration δ... x ≤30%r cThe impact can be ignored, that is:

[0098]

[0099] For a toroidal spherical mirror, the image spot radius or lateral spherical aberration can be calculated using the following formula:

[0100]

[0101] The radius of the spherical surface of the annular spherical mirror Substituting into the above equation, we get:

[0102]

[0103] ψ can be obtained numerically. If the width of the toroidal spherical mirror is w, then...

[0104]

[0105] This yields the maximum width w required to eliminate spherical aberration in a toroidal spherical mirror. Alternatively, the maximum width w can be approximated using the following method:

[0106] Since spherical aberration increases rapidly with increasing ψ, we only need to estimate the case where ψ is at its maximum, in which case it equals the system's edge angle. It can then be approximately calculated using the following formula:

[0107]

[0108] The width w of the annular spherical mirror can then be calculated according to the formula. Under such design requirements, the system can eliminate the spherical aberration caused by the applicable spherical mirror, thereby achieving a good focusing effect.

[0109] The following analysis examines the beneficial effects of using a cavity receiver.

[0110] Using a cavity receiver is superior to using a planar receiver because the cavity receiver has a high absorption rate. When light enters the cavity, it is almost entirely absorbed by the receiver, while a planar receiver reflects a portion of the intercepted sunlight, typically about 5%-10%, resulting in a lower absorption rate. This is the main advantage of using a cavity receiver.

[0111] In addition, see Figure 4In disc-type rotating parabolic reflectors, the energy flux density distribution on the focal plane is highly uneven, with a high density at the center and a low density at the edges. This results in uneven temperature distribution on the receiving surface, leading to significant heat loss, poor thermal stability, and a higher risk of burning out the receiving surface. Using a cavity receiver, the distance from the focal point can be varied to adjust the energy flux density on the receiving surface, maintaining a more uniform energy flux density and temperature distribution within the cavity. This method, by adjusting the internal structure of the receiving surface, achieves a more uniform energy flux density and temperature distribution, resulting in lower heat loss, more stable thermal performance, and higher heat collection efficiency compared to planar receivers.

[0112] The design method proposed in this invention can quickly and conveniently determine various optical design parameters for a ring-spherical disc system. Typically, selecting system design parameters, including the system's light-transmitting radius, focal length, edge angle, receiver radius, ring sub-mirror width, and spherical radius, often requires extensive simulations to calculate system performance under different conditions and comprehensively consider the influence of multiple factors, as illustrated in the research report on slotted systems published by Bendt et al., "Optical analysis and optimization of line focus solar collectors." This method is complex, labor-intensive, and does not necessarily yield an optimized design. This method, however, derives a formula for calculating the light-gathering ratio based on the receiver size calculation formula proposed in this invention, thereby determining the optimal edge angle and receiver size, and thus the various system design parameters. Regarding the design of the splicing sub-mirrors, it establishes conditions and calculation formulas for eliminating spherical aberration, thereby determining the ring-spherical mirror width parameter. The design method proposed in this invention has a simple calculation process, a clear approach, and can easily yield a reliable design, superior to designs obtained through traditional optical methods. Furthermore, it can be optimized to obtain the optimal design.

[0113] After optimization, the preliminary design provides the following parameters for the actual system: primary mirror light transmission radius of 4.1 meters, edge angle of 45 degrees, receiver radius of 117.5 millimeters, and geometric focusing ratio of 1214.4 times. Using a Gaussian reflected light intensity distribution with a variance of 4.776 mrad, simulation calculations show a system performance interception rate of 99.8%. Figure 4 This is the calculated energy flux density distribution on the receiving surface. The net energy efficiency is 90.15%. Compared to using a parabolic rotating surface, the slope error increases to 2 to 4 mrad. Using an average of 3 mrad, with the same receiver and geometric focusing ratio, the interception rate drops to 95.1%, 4.7% lower than the system proposed in this paper, and the net energy efficiency decreases to 85.9%, 4.25% lower than the system in this paper.

Claims

1. A spherical disc-type concentrator, comprising a reflector and a receiver, characterized in that: The reflector is composed of multiple annular spherical mirrors spliced ​​together. The circle formed by the transverse midpoint of any one of the annular spherical mirrors is on the same parabolic surface of rotation. The receiver is a flat plate receiver or a cavity receiver, which is installed at the focal point of the parabolic surface of rotation. The distance d from any point on the circumference formed by the transverse midpoints of the annular spherical mirror to the principal axis of the paraboloid of revolution is... i The edge angle on the parabolic surface of revolution is The radius of the spherical surface of the annular spherical mirror is r. i ,but The upper limit of the light transmission width of any one of the aforementioned annular spherical mirrors is calculated as follows: The maximum angle between the line connecting any point on the annular spherical mirror to its focal point and the axis of symmetry of the paraboloid of revolution is ψ. i Then the upper edge angle of the ring corresponding to the horizontal midpoint Where σ is the variance of the Gaussian distribution of reflected solar intensity; The upper limit of the light transmission width w of the annular spherical mirror is calculated using the following formula: R0 is the light transmission radius of the dish-type concentrating solar thermal collector system; This allows us to determine the light transmission width w of the annular spherical mirror, and then determine the distance d from any point on the central circle of the annular spherical mirror to the principal axis. i Calculate using the following formula: Where f is the focal length.

2. The spherical dish concentrator according to claim 1, characterized in that: receiver radius r c Calculate using the following formula: Where σ is the Gaussian distribution variance of reflected solar intensity, and R0 is the light transmission radius of the dish-type concentrating solar thermal collector system. The edge angle of the dish-type concentrating solar thermal system; the formula for calculating the Gaussian distribution variance σ of reflected solar intensity is: σ sun Let σ be the variance of the Gaussian distribution of the solar photosphere. slopex It is the variance of the reflector slope error distribution; σ tracking The variance of the tracking error is a Gaussian distribution; σ disp The variance of the system installation error is a Gaussian distribution; σ specular It is the Gaussian distribution variance of the error in the reflector material.

3. A spherical dish concentrator according to claim 1, characterized in that: The annular spherical mirror is composed of spliced ​​sector spherical mirrors, and each sector spherical mirror that makes up the same annular spherical mirror has the same shape and spherical radius.

4. A spherical dish concentrator according to claim 3, characterized in that: The edge angle range of a dish-type concentrating solar thermal collector system is 35-50 degrees. Select a value from this range to begin the design calculations.

5. A spherical dish concentrator according to claim 4, characterized in that: The dish-type concentrating solar thermal collector system is installed on the two-way tracking device.

6. A spherical dish concentrator according to claim 5, characterized in that: When the receiver uses a cavity receiver, a spherical segment transparent glass cover is installed at the opening of the cavity receiver, with the concave side of the spherical segment transparent glass cover placed inside the cavity receiver.

7. The design method of a spherical dish concentrator according to claim 1, characterized in that: The specific steps are as follows: The first step is to determine the light transmission radius R0 of the dish concentrating solar thermal collector system based on the requirements; The second step is to determine that the edge angle of the dish-type concentrating solar thermal collector system is 45 degrees. The third step is to determine the focal length. receiver radius is The fourth step is to first determine the width of the outermost annular spherical mirror, and then calculate the edge angle of the center of the annular spherical mirror on the paraboloid of revolution using the following formula. At this time For the edge angle of the dish-type concentrating solar thermal system, the upper limit of the light transmission width w of the annular spherical mirror is calculated by the following formula: This allows us to determine the light transmission width w of the annular spherical mirror, and then determine the distance d from any point on the central circle of the annular spherical mirror to the principal axis. i Calculate using the following formula: Then the spherical radius r of the annular spherical mirror i The calculation formula is: Fifth, following the method in step four, calculate the maximum edge angle data of the second annular spherical mirror, and determine the light transmission width parameters of each annular spherical mirror in sequence according to the above method; Step 6: Use a ray tracing program to simulate and calculate the system performance. If the results are not satisfactory, adjust the receiver radius or change the system edge angle, and re-complete the new design and performance calculation according to steps 4 to 6.

Images