A method of hole array geometry design, embedded structure and device

Abstract

The application relates to the technical field of hypersonic vehicle thermal protection, and provides a hole array geometric design method, an embedded structure and equipment, which comprises the following steps: determining the upper limit of a hole arrangement area according to a spherical head radius, an insulation layer thickness and the like; generating a ring radius sequence by taking a first ring projection radius and a spherical arc length as intervals; determining the angular position by superimposing a continuous deflection component which monotonously accumulates with the arc length, so that the relative offset amount of adjacent rings changes from ring to ring; and generating the coordinates and normal vectors of the hole centers. The application cooperatively regulates the electric field through the parameterized spiral dislocation layout and the embedded electrode, effectively suppresses the space charge effect, and improves the electron transpiration cooling efficiency.

Description

Technical Field

[0001] This invention relates to the field of thermal protection technology for hypersonic vehicles, and particularly to a method for designing hole array geometry, an embedded structure, and a device. Background Technology

[0002] Aerodynamic heating in the sharp leading-edge region of hypersonic vehicles is a key factor restricting their performance and reliability. Achieving efficient, lightweight, and reusable active thermal protection has become a hot topic of ongoing research in this field. Electron transpiration cooling (ETC), as a novel active thermal protection mechanism, utilizes the emission of electrons from heated thermoelectric materials, which then migrate to the collector electrode to form a cycle. This achieves adaptive cooling without the need for a working fluid and without ablation, and is considered a highly promising technological approach to solving the "thermal barrier" problem at sharp leading edges.

[0003] Existing technologies have developed various ETC (Electronic Toll Collection) structural schemes for engineering applications. For example, early research proposed an internal ETC structure, which uses a emitting layer and anode arranged on the inner wall of the wing's leading edge and filled with vapor to suppress the space charge effect. Later research proposed an external ETC structure, consisting of a leading-edge emitting layer and a tail-mounted collecting electrode, simplifying system complexity. More recently, some schemes have attempted to introduce magnetic fields to control electron movement or coat the emitting surface with specific materials to enhance emission capabilities. These schemes have, to some extent, verified the physical feasibility of ETC and accumulated preliminary experience for structural design.

[0004] However, the aforementioned solutions face an inherent dilemma in practical applications: they cannot simultaneously achieve both electron migration efficiency and structural engineering feasibility. The fundamental reason lies in the fact that existing ETC structural designs all follow the static, pre-defined thinking of traditional fluid cooling or simple electrode stacking. Electron migration in vacuum or rarefied gases is dominated by the space charge effect, a highly nonlinear dynamic physical process. Specifically, simple structures lack active means to control the local electric field, leading to the formation of "virtual cathodes" near the emission surface that suppress subsequent electron emission. While complex structures attempt to improve the electric field, the numerous components and extremely difficult fabrication and assembly, coupled with the lack of a systematic parametric geometric design method, make it impossible to establish a precise quantitative relationship between emission area, electric field coverage, and structural manufacturability. More critically, existing design methods involving aperture array layouts are largely derived from the field of fluid jet impact cooling. Their aperture variation aims to compensate for fluid pressure drop to ensure uniform jet velocity, which is fundamentally different from the mechanism in electron emission physics that requires adjusting the radial distribution of current density to suppress the space charge effect. Therefore, directly applying fluid cooling design paradigms cannot meet the ETC's need for active control of electron migration.

[0005] Therefore, to achieve efficient ETC in extreme thermal environments with sharp leading edges, we must break away from the conventional framework of traditional fluid cooling or static electrode design and instead seek a new parametric design paradigm based on electron emission physics that can achieve dynamic matching between geometric structure and electric field distribution, fundamentally breaking the deadlock between space charge effect suppression and structural engineering practicality. Summary of the Invention

[0006] This invention provides a method for designing the geometry of a hole array, an embedded structure, and a device. It addresses the limitations of related technologies' ETC structures due to space charge effects and the lack of parametric geometric design methods based on electron emission physics, which prevents a balance between cooling efficiency and engineering practicality. The technical solution is as follows: On the one hand, a method for geometric design of aperture arrays is provided, the method comprising: step S1, based on the radius of the sphere head... Insulation layer thickness Aperture and boundary safety margin Determine the maximum allowable projected radius of the perforated area on the ball head surface. and maximum available arc length Step S2: Using the projection radius of the first ring Determine the position of the first ring and calculate the spherical arc length corresponding to the first ring. , at equal intervals Generate subsequent rings such that the arc length position of the k-th ring is... satisfy until When the generation of new rings stops, the actual number of holes in the k-th ring is [not specified]. The geometric capacity of the ring and the actual number of holes in the previous ring are determined by the geometric capacity of the ring. and preset capacity utilization factor Jointly determined; Step S3: Based on the basic uniform angle, superimpose the odd-even ring alternating component and the continuous cumulative deflection component, wherein the continuous cumulative deflection component is related to the arc length position of the k-th ring on the sphere. Proportional to, and follows the ring number The relative angular offset between any two adjacent rings increases monotonically and accumulates, causing the offset to change ring by ring; Step S4: Based on the arc length position of the k-th ring. The angular position of the j-th hole in the k-th ring Generate the center coordinates and unit normal vector of each hole on the sphere.

[0007] On the other hand, this application also provides an embedded structure for electron evaporation cooling, including a spherical substrate with a multi-ring concentric hole array arranged on its surface. The spherical substrate includes an emitter located at the front end of the spherical head, embedded electrodes nested in each hole, and an insulating ring surrounding the embedded electrodes. A voltage is applied to the embedded electrodes to form an electric field near the emitter surface to modulate electron emission. In the multi-ring concentric hole array, each concentric ring is arranged at equal intervals along the arc length of the spherical surface. The number of holes is determined by the geometric capacity of the ring, the actual number of holes in the previous ring, and the preset capacity utilization coefficient, and decreases non-decreasing ring by ring in the radial direction; the angular position of each hole on each ring includes a basic uniform angular component, an odd-even ring alternating component, and a continuously accumulated deflection component. The continuously accumulated deflection component is linearly related to the arc length position of each ring on the spherical surface, and accumulates monotonically as the ring number increases, so that the relative angular offset between any two adjacent rings changes ring by ring to suppress the alignment of the hole positions of each ring in the radial projection direction of the spherical surface; the diameter of each hole is an independent design variable.

[0008] On the other hand, this application also provides a computer device, which includes a memory and a processor. The memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory to implement the steps of the above-described hole array geometry design method.

[0009] On the other hand, this application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the above-described hole array geometry design method.

[0010] Compared to existing technologies, this application constructs a concentric ring array of holes on the surface of the spherical head substrate, based on equal spacing of spherical arc lengths and multidimensional angular control. This forms a parameterizable geometric basis for electric field control near the emitter surface, effectively improving the matching accuracy of electron emission and collection in the electron evaporation cooling structure. Simultaneously, since the aperture, ring spacing, and angular gradient coefficients are decoupled from fluid dynamic constraints as independent design variables, each geometric parameter can be independently adjusted according to the needs of the electron emission physical mechanism, thus breaking the inherent contradiction between the fluid pressure drop compensation logic and the space charge effect suppression requirements in existing designs. Furthermore, based on this parameterized geometric generation capability, this application further provides an active electron migration control dimension that traditional fluid cooling design paradigms cannot achieve for the multidisciplinary optimization design of active thermal protection systems for hypersonic vehicles, enabling the engineering design of ETC structures to move from empirical trial and error to a new stage of physical-driven precise modeling. Attached Figure Description

[0011] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0012] Figure 1 This is a flowchart of the aperture array geometry design method according to an embodiment of this application; Figure 2 This is a schematic diagram of the overall embedded structure for electronic evaporation cooling according to an embodiment of this application; Figure 3 This is a front view of the embedded structure for electronic evaporation cooling according to an embodiment of this application; Figure 4 This is a velocity distribution diagram of the emitted electron trajectory according to an embodiment of this application; Figure 5 This is a velocity distribution diagram of the emitted electron trajectory according to an embodiment of this application; Figure 6 This is a hardware architecture diagram of a computer device provided in an embodiment of the present invention. Detailed Implementation

[0013] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0014] As mentioned earlier, existing ETC structural designs often directly apply the design paradigm from the fluid jet impingement cooling field, with the aperture variation aimed at compensating for fluid pressure drop to ensure uniform jet velocity. However, this design paradigm is fundamentally mismatched with the electron emission physics mechanism of ETC: fluid cooling focuses on fluid dynamic pressure distribution, while ETC requires regulating the electric field distribution near the emitter surface, thus affecting the radial uniformity of the electron emission current density. This embodiment provides an aperture array geometry design method guided by the electron emission physics mechanism to address the technical problem of the mismatch between the aforementioned fluid cooling design paradigm and the actual needs of ETC. Embodiment 1 below describes the specific implementation of this concept.

[0015] Example 1 like Figure 1As shown, this embodiment provides a hole array geometry design method, which is applied to the spherical substrate of an embedded structure with electron evaporation cooling.

[0016] Step S1: Based on the ball head radius Insulation layer thickness Aperture and boundary safety margin Determine the maximum allowable projected radius of the perforated area on the ball head surface. and maximum available arc length ; Step S2, using the projection radius of the first ring Determine the position of the first ring and calculate the spherical arc length corresponding to the first ring. , at equal intervals Generate subsequent rings such that the arc length position of the k-th ring is... satisfy until When the generation of new rings stops, the actual number of holes in the k-th ring is [not specified]. The geometric capacity of the ring and the actual number of holes in the previous ring are determined by the geometric capacity of the ring. and preset capacity utilization factor Jointly determined; Step S3: Using the basic uniform angle as a reference, superimpose the odd-even ring alternating component and the continuous cumulative deflection component. The continuous cumulative deflection component is related to the arc length position of the k-th ring on the sphere. Proportional to, and follows the ring number The increase and monotonically accumulates, causing the relative angular offset between any two adjacent rings to change ring by ring; Step S4: Based on the position of the arc length of the k-th ring The angular position of the j-th hole in the k-th ring Generate the center coordinates and unit normal vector of each hole on the sphere.

[0017] In this embodiment of the invention, the method inputs structural constraint parameters and array design variables into a deterministic geometric generation process, ultimately outputting the center coordinates and unit normal vectors of each hole on the spherical head surface. This provides an accurate geometric model foundation for subsequent electric field simulation, particle tracking, and structure fabrication. The entire process can be summarized as four sequentially executed steps, with clear input-output dependencies between each step, forming a parameterized driven logical closed loop.

[0018] Example 2 The following description Figure 1 The execution method of each step is shown. Step S1, based on the radius of the ball head. Insulation layer thickness Aperture and boundary safety margin Determine the maximum allowable projected radius of the perforated area on the ball head surface. and maximum available arc length .

[0019] The core task of this step is to define the effective distribution range of the aperture array on the spherical surface. In practical engineering, not the entire surface of the spherical substrate can be used for aperture placement: each aperture needs to contain an embedded electrode, which is surrounded by an insulating ring to achieve electrical insulation from the emitter. The insulating ring itself occupies a certain radial space, and a safety margin needs to be reserved at the outermost edge of the aperture-placement area to prevent structural interference or electric field edge effects. Therefore, step S1 integrates the three physical constraints of aperture diameter, insulating layer thickness, and boundary safety margin into an equivalent outer edge constraint radius, and then maps it to the upper limit of the projected radius and the upper limit of the arc length through the spherical geometry. These two upper limits constitute the hard boundary for the subsequent generation of the ring sequence: once the arc length of any ring exceeds the limit... If a loop is detected as exceeding the valid region, no new loop will be generated. It can be understood that the output of step S1 directly determines the termination condition of the loop sequence in step S2.

[0020] Step S2, with the projected radius of the first ring Determine the position of the first ring and calculate the spherical arc length corresponding to the first ring. , at equal intervals Generate subsequent rings such that the arc length position of the k-th ring is... satisfy until When the generation of new rings stops, the actual number of holes in the k-th ring is [not specified]. The geometric capacity of the ring and the actual number of holes in the previous ring are determined by the ring's geometric capacity. and preset capacity utilization factor Determined jointly.

[0021] This step accomplishes two closely coupled tasks: radial generation of the ring sequence and determination of the number of holes in each ring. The position of the first ring is determined by design variables. Independent control, This refers to the projected radius of the first ring on a plane perpendicular to the axis of the spherical head, not the spherical arc length. The reason for using the projected radius as the positioning parameter for the first ring is that in the region near the stagnation point of the spherical head, the polar angle is extremely sensitive to changes in the projected radius. Using the projected radius as input makes it easier for engineers to intuitively control the distance between the first ring and the stagnation point. After the position of the first ring is determined, subsequent rings expand outwards sequentially at equal intervals of spherical arc length (dr). Equal intervals of spherical arc length are used here instead of equal intervals of projected radius because the spherical arc length directly corresponds to the true geometric scale of the spherical head surface: in areas with large spherical curvature, the same increase in projected radius corresponds to significantly different increases in spherical arc length. Using equal intervals of projected radius would result in uneven density of the hole rings on the spherical surface, which is detrimental to the uniformity of subsequent electric field control. Simultaneously with the generation of each ring, step S2 also determines the actual number of holes in that ring. The determination of the number of holes is not simply based on the maximum value of the ring's geometric capacity, but rather takes into account three factors: the maximum number of holes the ring can accommodate under the minimum hole spacing constraint (geometric capacity), the actual number of holes in the previous ring (ensuring that the number of holes does not decrease abruptly along the radial direction), and the capacity utilization coefficient. (Global control of overall aperture density). This joint determination mechanism ensures that the number of apertures exhibits a smooth, non-decreasing trend along the radial direction, avoiding electron emission hotspots that may be caused by sudden changes in local aperture density. The ring number, arc length position of each ring, and number of apertures in each ring output in step S2 provide complete ring-level parameters for the angular allocation in step S3.

[0022] Step S3: Using the basic uniform angle as a reference, superimpose the odd-even ring alternating component and the continuously accumulated deflection component. The continuously accumulated deflection component is related to the arc length position of the k-th ring on the sphere. Proportional to, and follows the ring number As it increases and accumulates monotonically, the relative angular offset between any two adjacent rings changes ring by ring.

[0023] This step is crucial in transitioning the aperture array from a "regular arrangement" to a "controlled irregular arrangement." The basic uniform angle ensures the angular equivalence of apertures within the same ring, which is fundamental for maintaining electron emission uniformity within a single ring. The odd-even ring staggered component introduces an angular misalignment of half an aperture spacing between adjacent rings, causing the aperture positions of odd-numbered and even-numbered rings to be offset in the radial projection direction, preventing the formation of continuous radial aperture arrays. The continuously accumulated deflection component further superimposes an angular offset proportional to the arc length position, and this offset monotonically accumulates as the ring number increases, ensuring that the relative angular offset between any two adjacent rings is not a fixed value but varies ring by ring. This design gives the aperture array a controlled spiral characteristic: the aperture positions of each ring are no longer aligned in the radial projection direction, but instead form a spatially speckled distribution pattern. The angular positions of each ring and aperture output in step S3, together with the arc length positions output in step S2, constitute the input for step S4.

[0024] Step S4, based on the position of the arc length of the k-th ring. Angular position of the j-th hole in the k-th ring Generate the center coordinates and unit normal vector of each hole on the sphere.

[0025] This step converts the arc length and angular positions generated in the previous steps into three-dimensional coordinates in the Cartesian coordinate system using spherical coordinate formulas, and simultaneously provides the spherical unit normal vector at the location of each hole. The center coordinates are used to accurately locate the spatial position of each hole on the spherical head surface, serving as the direct basis for subsequent geometric modeling, mesh generation, and machining path planning. The unit normal vector defines the axial direction of each hole: in the embedded structure, the mounting direction of the electrodes inside the hole and the nesting direction of the insulating ring must be consistent with the hole axis direction; the normal vector information provides the necessary geometric reference for these subsequent operations. Thus, a set of design parameters, after the complete process from S1 to S4, is uniquely mapped into a deterministic hole array geometric model.

[0026] It is important to emphasize that the four steps described above constitute a parameter-driven geometry generation process, rather than a simple drawing operation. The fundamental difference lies in the fact that drawing operations only focus on the final geometric shape of the graphic, while each step in this method embeds engineering constraints related to electron emission physics: step S1 embeds insulation and safety margin constraints, step S2 embeds minimum aperture spacing and aperture density control constraints, step S3 embeds an angular control strategy for suppressing space charge effects, and step S4 solidifies the geometric representation of the above physical constraints into manufacturable three-dimensional coordinates and normal vectors. Designers only need to adjust... , , , , A few design variables with clear physical meanings can drive the automatic regeneration of the entire aperture array without manual intervention in any intermediate geometric elements. This parameterized driving capability allows the method to be seamlessly integrated into multidisciplinary optimization processes, providing an efficient geometric engine for finding the optimal trade-off between emission area, electric field coverage, and structural manufacturability.

[0027] Example 3 This embodiment, within the framework of steps S1 and S2 described in Embodiment 2, further elaborates on its specific geometric derivation and parameter determination logic. (Refer to...) Figure 3 The front view shown provides a more intuitive understanding of the boundary constraints of the porous region on the surface of the spherical head substrate and the generation method of the concentric ring sequence.

[0028] In step S1, the maximum permissible projection radius and maximum available arc length Determine as follows: Further define the maximum polar angle of the orifice-deployable region on the ball head surface as: : in, The equivalent outer edge constraint radius is composed of three physical constraints superimposed: aperture. Half of the insulation layer thickness and border security margin These three constraints each correspond to insurmountable physical boundaries in practical engineering: Corresponding to the radial half-width of the hole itself, The radial thickness of the insulating ring surrounding the embedded electrode in the spherical projection direction. This refers to the additional safety distance reserved at the outermost edge of the perforated region, used to prevent interference between the outermost annular hole structure and the edge of the spherical head substrate, or to avoid unexpected edge effects generated by the electric field at geometric abrupt changes. The sum of these three factors... A cylindrical restricted area centered on the axis of the spherical head is defined: outside this cylindrical area, the projected distance from any point on the spherical surface to the axis satisfies the geometric conditions for hole placement. This cylindrical restricted area is mapped to the upper limit of the projected radius on the spherical surface using spherical geometry. Then, the corresponding maximum polar angle is obtained through the arcsine function. Finally, multiply by the ball head radius Obtain the maximum usable arc length from the stationary point. .

[0029] It is important to emphasize the thickness of the insulation layer. and boundary security margin This is not a dispensable auxiliary parameter, but an independent physical constraint that directly participates in defining the effective emission area. In practical engineering, the insulating ring must have sufficient radial thickness to ensure the reliability of electrical insulation between the embedded electrode and the emitter, especially under extreme conditions of high temperature and high electric field strength. The creepage distance requirements of the insulating material often determine the reliability of the insulation. The lower limit. Boundary safety margin. This provides a buffer for manufacturing tolerances and assembly deviations. If these two constraints are ignored and only the aperture is considered... Using this as a boundary criterion for aperture placement will result in the generated aperture array being too close to the edge of the ball head. In actual manufacturing, this may lead to problems such as the outer wall of the insulating ring penetrating the surface of the ball head or insufficient strength of the edge aperture structure. Therefore, the geometric derivation established in step S1 is essentially seeking a balance point quantitatively constrained by physical parameters between maximizing the emission area and structural reliability.

[0030] In step S2, the spherical arc length corresponding to the first ring And the position of the arc length of the kth ring Determine as follows: The polar angle corresponding to the first ring With spherical arc length They are respectively: Based on this, subsequent rings are generated at equal intervals according to the spherical arc length, and the arc length position of the kth concentric ring is... satisfy: , among which, when When that happens, stop generating new rings.

[0031] The location of the first ring here is determined by design variables. control, This is the projected radius of the first ring on a plane perpendicular to the axis of the ball head. The reason for using the projected radius instead of directly using the arc length or polar angle as the positioning parameter for the first ring is that, in the region near the ball head's stagnation point, the polar angle is extremely sensitive to changes in the projected radius: a small increment in the projected radius corresponds to a significant change in the polar angle. Using the projected radius as input, engineers can more intuitively control the spatial distance between the first ring and the stagnation point. For example, on a ball head with a diameter of 20mm, [the following parameters are used]. Setting it to 5mm means that the first ring is located on a circle 5mm from the axis. The physical meaning of this value is more intuitive than the corresponding polar angle or arc length.

[0032] Subsequent rings are spaced at equal intervals according to the spherical arc length. Instead of being spaced evenly according to the projected radius, the spacing expands outward sequentially. The difference between these two spacing strategies is particularly significant in regions with high spherical curvature: when using equal spacing by the projected radius, in the region near the equatorial plane of the spherical head, the increase in spherical arc length corresponding to the same increase in projected radius gradually decreases, resulting in a non-uniform distribution of the hole rings on the spherical surface, characterized by "sparser inside and denser outside." In contrast, equal spacing by spherical arc length ensures uniform expansion between adjacent rings on the true geometric scale of the spherical surface, keeping the increase in spherical area corresponding to each ring relatively stable. For electron evaporation cooling, this uniform expansion facilitates the formation of a uniform electric field coverage gradient along the generatrix of the spherical surface by the embedded electrodes, avoiding local electric field concentration or sparseness caused by uneven density between rings, thus providing a uniform geometric basis for the radial smooth control of electron emission density.

[0033] Furthermore, the actual number of holes in the k-th ring in step S2 Determine as follows: Maximum number of holes that can be placed in the k-th ring: in, Let be the projected radius of the k-th ring. The physical meaning of this formula is: on the small circle containing the k-th ring, with the minimum hole spacing... Given the chord length constraint between the centers of adjacent holes, calculate the maximum number of holes that the small circumference can accommodate. (The denominator contains...) Indicates a radius of On the circle, the chord length is The corresponding central angle, Divide by the central angle to get the maximum number of holes that can be placed.

[0034] Actual number of holes Then determine it according to the following formula: in, To preset the capacity utilization factor, , This represents the actual number of holes in the (k-1)th ring.

[0035] The rule for determining the number of holes comprehensively reflects the synergistic effect of three engineering constraints. The first constraint comes from the upper limit of geometric capacity. The actual number of holes in any ring must not exceed the maximum value that the ring can accommodate under the minimum hole spacing constraint. This is a hard boundary to ensure sufficient material wall thickness between adjacent holes to maintain structural strength. The second constraint comes from the requirement that the number of holes does not decrease radially: through... Ensure that the actual number of holes is at least one more than the previous ring, that is... This ensures that the number of holes increases or at least remains constant along the radial direction from the inside out, avoiding the "inverted" phenomenon where the number of holes in the outer ring is less than that in the inner ring. The third constraint comes from the capacity utilization factor. Global control of overall pore density: The closer it is to 1, the closer the actual number of holes in each ring is to its geometric capacity limit, and the higher the hole density. The smaller the size, the sparser the number of holes in each ring, leaving more room for structural strength and manufacturing process.

[0036] The engineering significance of the non-decreasing aperture number constraint lies in achieving a smooth radial transition in electron emission density. In electron evaporation cooling structures, the positive bias applied by the embedded electrodes within each ring aperture creates a strong local electric field near the emitter surface. The aperture number density is directly related to the electron emission capability of that ring region. If the number of apertures in the outer ring is less than that in the inner ring, it will cause a discontinuous, abrupt decrease in electron emission density along the radial direction. Local electric field distortion and electron emission hotspots are easily formed at the abrupt aperture number interface, further exacerbating the local space charge effect. By forcing... The number of holes exhibits a monotonically non-decreasing smooth expansion trend along the radial direction, and the electron emission density changes gradually accordingly, effectively suppressing the generation of local hot spots.

[0037] Taking a set of preferred parameters as an example: sphere head radius Insulation layer thickness Minimum hole spacing Border security margin aperture Ring spacing Capacity utilization coefficient First ring projection radius Under this parameter combination, the equivalent outer edge constraint radius Maximum permissible projection radius Maximum polar angle Maximum available arc length First ring polar angle First ring arc length .by Subsequent rings are generated at equal intervals, with the second ring having an arc length of... The arc length of the third ring ,at this time Exceeded Therefore, only two rings are generated. The projected radii of each ring are respectively... , The maximum number of holes that can be distributed in the first ring. Actual number of holes The maximum number of holes that can be distributed in the second ring. Actual number of holes It can be seen that the number of holes smoothly transitions from 20 in the inner ring to 33 in the outer ring, satisfying the non-decreasing constraint.

[0038] It should be understood that the above parameters are for illustrative purposes only. In practical applications, the capacity utilization factor... The value can be selected according to specific needs. arrive The values ​​can be adjusted flexibly. When higher structural strength is required, a smaller value can be chosen. Values, such as 0.5 or 0.6, can be used to increase the wall thickness between holes; when maximizing the emission area is desired, larger values ​​can be chosen. Values, such as 0.85 or 0.9, bring the number of holes in each ring closer to its geometric capacity limit. Ring spacing. Similarly, adjustments can be made based on the ball head size and the required total number of perforated rings; smaller ones... This will generate a denser sequence of rings, suitable for scenarios requiring higher uniformity of electric field coverage. Furthermore, although this embodiment uses a uniform aperture... This example is used for illustration, but in other embodiments, the aperture of each ring can also be varied radially as an independent design variable to adapt to different electron emission density distribution requirements.

[0039] This embodiment, within the framework of steps S3 and S4 described in Embodiment 2, further elaborates on the specific implementation mechanism of angular control and the logic for generating spherical coordinates. (Refer to...) Figure 3 The front view shown can be seen intuitively as to the fact that the distribution of each annular hole position in the angular direction is not a simple uniform division, but rather presents a controlled irregular arrangement.

[0040] In step S3, the angular position of the j-th hole in the k-th ring... Determine as follows: in, Based on uniform angles, It is a component with alternating odd and even rings. For continuous accumulation of deflection components; Preset angular gradient coefficients and , It is a position function based on arc length normalization.

[0041] The angular position formula is composed of three independent components, each of which performs a different regulatory function. (Basic uniform angle) The circumference of the k-th ring is determined by the actual number of holes in that ring. Dividing the ring into equal parts ensures that the angular spacing between adjacent holes on the same ring is basically uniform, which is the basis for maintaining the uniformity of electron emission within a single ring. Based on this, the odd and even rings are alternately divided. An angular misalignment of half a hole spacing is introduced between adjacent rings, causing the hole positions of odd-numbered and even-numbered rings to be offset from each other in the radial projection direction, thus avoiding the formation of a continuous radial hole array. Continuous accumulation of deflection components. This is further superimposed with an angular offset related to the arc length position, and this offset varies with the ring number. The increasing and monotonically accumulating properties mean that the relative angular offset between any two adjacent rings is not a fixed value, but varies ring by ring. The superposition order of the three components does not affect the final result, but their respective functional boundaries are clear and non-redundant; the basic uniform angle is responsible for the uniformity within the ring, the odd-even alternation is responsible for the misalignment between rings, and the continuous cumulative deflection is responsible for the global spiralization.

[0042] Furthermore, the odd-even ring alternating component Determined as follows: When When it is an odd number, When k is even, Position function Determine as follows: .

[0043] The design logic of alternating odd and even ring components lies in: for odd rings ( The angular position of each hole is based on the uniform angle of the foundation, without applying any additional misalignment; for even-numbered rings ( Each hole was rotated by half the distance between the holes. In this way, in the radial projection direction, each hole in the even-numbered ring falls precisely in the gap between two adjacent holes in the odd-numbered ring. When viewed from the front of the spherical head, the holes in the inner and outer rings appear to be arranged in an alternating pattern. This alternating arrangement of odd and even numbers effectively avoids the accumulation of electrons along the radial straight line, reducing the probability of overlap of electron beams from adjacent rings in the radial projection direction.

[0044] Position function Using a linear mapping form based on arc length normalization, the arc length position of the k-th ring is determined. Linear mapping to interval Above: When (i.e., the location of the outpost) ;when (i.e., at the outermost edge of the perforation area) This normalization process allows for the continuous accumulation of deflection components. The physical meaning is clear and unambiguous: The absolute value of θ directly determines the total cumulative angular deflection from the innermost ring to the outermost ring, while This describes the proportion of deflection along the arc length. Because Follow Monotonically increasing, the continuously accumulating deflection components also increase with the ring number. The increasing and monotonous accumulation causes each annular hole to exhibit a gradual spiral rotation trend in the angular direction.

[0045] In step S4, the center coordinates of the j-th hole in the k-th ring are generated according to the spherical coordinate formula, with the spherical head facing the -x direction and the stationary point located at the origin: in, The polar angle corresponding to the k-th ring. Let be the projected radius of the k-th ring. Let j be the angular position of the j-th hole in the k-th ring; The corresponding unit normal vector for: It is the unit normal vector at the j-th hole of the k-th ring, which is obtained by normalizing the coordinate vector of the hole center and is directed radially outward along the sphere.

[0046] This coordinate generation process will output the arc length position from the previous steps. and angular position Through the standard spherical coordinate to Cartesian coordinate transformation, the coordinates of the hole center in three-dimensional space are uniquely mapped. The x-coordinate is along the axis of the spherical head (the -x direction is in front of the spherical head), and the y and z coordinates define the projected position of the hole on a plane perpendicular to the axis. Simultaneously, the unit normal vector at each hole location can be obtained from... It is found that the normal vector is radially outward along the sphere, providing the necessary geometric reference for the subsequent installation direction of the embedded electrode, the nesting direction of the insulating ring, and the setting of boundary conditions for electric field simulation.

[0047] Taking a set of preferred parameters as an example: sphere head radius Ring spacing Capacity utilization coefficient Angular gradient coefficient First ring projection radius aperture Under this parameter combination, as described in Example 3, two rings are generated, with the first ring having a certain number of holes. Number of holes in the second ring First ring arc length The second ring arc length Maximum available arc length For the first ring ( (Odd ring), alternating odd and even ring components Position function Continuous cumulative deflection components The angular position of the j-th hole in the first ring. For the second ring ( Even rings), alternating odd and even ring components Position function Continuous cumulative deflection components The angular position of the j-th hole in the second ring. It can be seen that from the first ring to the second ring, the continuously accumulated deflection component... Change to The cumulative deflection increment is approximately (Approximately 23.2°) The relative angular offset between two adjacent rings is not a simple fixed misalignment, but includes an additional deflection caused by the difference in arc length position. By substituting the arc length position and angular position of each ring into the spherical coordinate formula, the three-dimensional coordinates and unit normal vector of each hole can be uniquely determined.

[0048] The above describes the basic calculation process for angular control and coordinate generation. However, if the above formulas are merely understood as a geometric arrangement rule, the core technical value of this solution is not yet fully grasped. The following further analyzes this angular control mechanism, particularly the deep physical problems solved by the continuous accumulation of deflection components in the specific application scenario of electron evaporation cooling.

[0049] In an electron evaporation cooling structure, the embedded electrodes within each hole on the emitter surface are positively biased, creating a localized strong electric field near the emitter surface to promote electron emission. When the hole array employs a conventional uniform arrangement (i.e....), When only the basic uniform angle and the odd-even ring alternation components are retained, although the positions of the holes in each ring are offset in the radial projection direction due to the odd-even alternation, the relative angular relationship between the holes in adjacent rings is fixed due to the lack of continuous angular deflection accumulation. For example, if a hole in the first ring is located at 0°, the hole closest to it in the second ring is always located at a certain fixed deflection angle, and the third ring returns to an angular position close to that of the first ring. This fixed angular relationship is acceptable under weak electric field and low emission current density conditions, but under strong electric field and high emission current density conditions, it will cause a serious problem: the positions of the holes in each ring form a quasi-periodic alignment pattern in the radial projection direction. After electrons are emitted from each hole, they gather in the radial direction along several "virtual rays," forming radial electron beam channels. The electron density in these channels is much higher than in the surrounding area, the local space charge effect is sharply enhanced, and an unstable virtual cathode structure is formed near the emission surface, which in turn inhibits the emission of subsequent electrons, resulting in a significant decrease in overall cooling efficiency.

[0050] This scheme introduces a continuously accumulating deflection component. This fundamentally breaks this quasi-periodic alignment. Because... Position with arc length Linear change, and Each ring generates an additional angular deflection relative to the previous ring, and this deflection accumulates ring by ring. As a result, the relative angular offset between any two adjacent rings is not a fixed value, but varies ring by ring: the deflection angle between the first and second rings, and between the second and third rings, are all different. When viewed from the front of the ball head, the holes in each ring are no longer aligned in the radial projection direction, but instead exhibit a spatially speckled distribution pattern: the holes that might have been arranged in a radial straight line are "scattered" to different angular positions, and the electron emission source achieves spatial decorrelation in the two-dimensional projection plane.

[0051] The mechanism by which spatial speckle distortion suppresses the space charge effect lies in the following: after electrons are emitted from the emitting surface, during their migration towards the collecting electrode under the influence of the electric field, the electron beams emitted from adjacent holes are no longer superimposed along the same radial ray in space due to the radial projection of the holes. Instead, they diverge at different azimuth angles in three-dimensional space. This significantly reduces the peak electron density in the local space, effectively increasing the formation threshold of the virtual cathode, thereby improving the equivalent electron emission capability without reducing the aperture size or the emitting area. (Refer to...) Figure 4 The simulation diagram of the emitted electron trajectory shown is based on the parameters of this scheme ( Under this configuration, electrons emitted from the holes on the spherical head surface exhibit a divergent and uniform distribution in space, without significant radial beam aggregation, allowing electrons to migrate efficiently to the collecting electrode. In contrast, if a traditional uniform arrangement is used ( Under the same electric field conditions, electron trajectories will tend to converge along several radial directions, local electron density will increase, space charge effect will intensify, and collector current will decrease significantly.

[0052] It is important to note that the spiral arrangement in this scheme is fundamentally different from the orifice adjustment used in fluid jet impact cooling devices to compensate for pressure drop. Orifice adjustment in fluid cooling serves a fluid dynamics objective: compensating for pressure drop along the flow path by changing the position or angle of the orifices to ensure uniform jet impact velocity across all orifices. Its control logic is constrained by the fluid momentum equation and pressure drop distribution. In contrast, the continuous cumulative deflection in this scheme serves an electron optics objective: suppressing the spatial correlation of the electron beam through spatial speckle formation and reducing local space charge density. Its control logic is governed by electron emission physics and space charge effects. Although both appear as non-uniform orifice arrangements, their underlying physical mechanisms, design goals, and constraints are drastically different. Compared to traditional uniform arrangement schemes, this approach targets the specific pain point of space charge suppression, rather than simply focusing on geometric aesthetics or manufacturing convenience.

[0053] Furthermore, when faced with the problem of space charge effect in electron evaporation cooling structures, those skilled in the art might conventionally approach it by increasing the aperture to increase the single-aperture emission area, increasing the embedded electrode voltage to enhance the electric field pumping capability, or introducing an external magnetic field to deflect the electron trajectory. However, increasing the aperture is limited by the geometric space and structural strength constraints of the spherical head surface, increasing the voltage is limited by the breakdown field strength of the insulating ring, and introducing a magnetic field requires adding a magnetic field generating device, increasing system complexity. This solution takes an unconventional approach: without changing the aperture, increasing the voltage, or introducing an external magnetic field, it suppresses space charge accumulation solely through the spatial speckle distribution of the aperture angular direction, utilizing the geometric decorrelation effect of the electron beam in three-dimensional space. This approach, which extends the control dimension from "electric field strength" or "magnetic field configuration" to "emission source spatial correlation," provides a completely new degree of freedom for the optimized design of electron evaporation cooling structures.

[0054] It should be understood that the angular gradient coefficient The value can be flexibly adjusted according to specific working conditions. When a smaller value (e.g., 0.1 to 0.3) is used, the degree of spiralization is less pronounced, making it suitable for scenarios with low emission current density and minimal space charge effect. In this case, the aperture array is closer to a uniform arrangement, and processing and inspection are relatively simple. When a larger value is taken (such as 0.5 to 0.8), the spiralization characteristics are significant and the spatial speckle effect is stronger, making it suitable for extreme conditions with high emission current density and strong space charge effect. The sign (positive or negative) determines the direction of rotation of the helicalization, and has no essential impact on the space charge suppression effect. It can be selected according to processing habits or assembly requirements. Furthermore, the position function... It is not limited to linear mapping. In other implementations, nonlinear mapping (such as square root mapping or exponential mapping) can also be used to adjust the distribution gradient of the deflection along the arc length direction to adapt to different radial distribution requirements of electron emission density.

[0055] Example 5 Reference Figure 2 This embodiment provides an embedded structure for electron evaporation cooling. The structure includes a spherical substrate with multiple concentric ring-shaped holes arranged on its surface. The spherical substrate includes an emitter located at the front end of the spherical head, embedded electrodes nested in the holes, and an insulating ring surrounding the embedded electrodes. A voltage is applied to the embedded electrodes to form an electric field near the emitter surface to modulate electron emission.

[0056] Specifically, the spherical head substrate, serving as the main support of the entire embedded structure, has a spherical geometry at its front end, with its axis pointing in the -x direction and its stationary point located at the origin. The emitter, located on the front surface of the spherical head, is made of thermoelectric material capable of thermionic emission, emitting electrons when heated under high-temperature conditions. Multiple concentric rings of holes are arranged along the generatrix of the spherical surface, each hole containing an embedded electrode. The electrodes are surrounded by an insulating ring, which electrically isolates the embedded electrodes from the emitter substrate material. A collector is located behind the spherical head, forming a vacuum channel for electron migration between the collector and emitter. A positive bias voltage is applied to the embedded electrodes relative to the emitter, creating a strong local electric field near each hole on the emitter surface. This electric field reduces the effective work function of the emitter material to promote electron emission and applies an initial acceleration force to the emitted electrons, guiding them towards the collector.

[0057] In a multi-ring concentric hole array, each concentric ring is arranged at equal intervals along the arc length of the sphere. The number of holes in each ring is determined by the geometric capacity of the ring, the actual number of holes in the previous ring, and the preset capacity utilization coefficient, and decreases non-decreasing along the radial direction. The angular position of each hole on each ring includes a basic uniform angular component, an odd-even ring alternating component, and a continuously accumulated deflection component. The continuously accumulated deflection component is linearly related to the arc length position of each ring on the sphere and accumulates monotonically as the ring number increases, so that the relative angular offset between any two adjacent rings changes ring by ring to suppress the alignment of the hole positions of each ring in the radial projection direction of the sphere.

[0058] The above three structural features can be combined in the physical embodiment of the product. Figure 3 This can be understood by referring to the front view. The equidistant arc length arrangement means that, measured from the stagnation point of the sphere along the generatrix, the spherical distance between adjacent rings remains constant, rather than the projected radii being equally spaced. This characteristic manifests in the product's appearance as follows: in areas near the stagnation point with greater spherical curvature, the radial spacing between adjacent rings in the frontal projection is relatively large; while in areas closer to the equatorial plane, the radial spacing between adjacent rings in the frontal projection is relatively small. This equidistant arc length geometry allows the embedded electrodes to form a uniform spatial distribution gradient along the generatrix of the sphere, ensuring that the coverage of the electric field on the emitting surface by each ring electrode remains balanced across the spherical geometry.

[0059] The characteristic of the number of holes not decreasing radially ring by ring is manifested in the product appearance as follows: when viewed from the inner ring to the outer ring, the number of holes in each ring shows a monotonically increasing or at least leveling trend, without the phenomenon of the number of holes in the outer ring suddenly being less than that in the inner ring. This feature ensures a smooth transition of electron emission source density radially, avoiding local current density concentration that may be caused by abrupt changes in the number of holes at the structural level.

[0060] The angular triple component characteristic manifests in the product's appearance as follows: the holes on the same ring are basically evenly distributed in the circumferential direction, but the hole positions between adjacent rings are not simply radially aligned or fixedly misaligned, but rather exhibit a gradual spiral rotation trend. Viewed from the front of the ball head, the hole positions of each ring are staggered in the radial projection direction, not forming a continuous radial hole array. This spatially speckled hole distribution pattern is the result of the superposition of three components: the basic uniform angle, the alternation of odd and even rings, and the continuous cumulative deflection. Its structural function is to suppress the beam accumulation of electrons emitted from each hole in the radial direction, thereby reducing the local space charge density.

[0061] The diameter of each hole is an independent design variable.

[0062] This feature means that the product structure allows the aperture of each hole to be set independently at the geometric level, without being constrained by ring number, arc length position, or other mandatory functional relationships of hole diameter. In other words, provided that minimum hole spacing and structural strength constraints are met, designers can specify different aperture values ​​for different rings or even different holes on the same ring according to the requirements of electron emission density distribution. For example, in one implementation, all holes use a uniform aperture, exemplarily, such as... or This uniform aperture scheme is itself an effective choice for independent design variables. In another implementation, the aperture can vary radially according to a certain pattern. For example, the inner ring aperture is smaller and the outer ring aperture is larger to accommodate the geometric condition that the outer ring has a larger projected circumference and can accommodate a larger aperture; or conversely, the inner ring aperture is larger to enhance the electron emission capability in the region near the stagnation point, and the outer ring aperture is smaller to ensure sufficient inter-aperture wall thickness. In yet another implementation, the aperture variation pattern can take the form of a gradient, that is, the rate of change of aperture between adjacent rings satisfies... ,in This is the aperture gradient coefficient, independent of the ring spacing. Capacity utilization coefficient Angular gradient coefficient and the first ring projection radius Other design variables, such as aperture variation, are also possible. Of course, the aperture variation is not limited to the linear gradient form described above; it can also employ piecewise constants, nonlinear increasing or decreasing patterns, or even aperture-specific distribution schemes based on local electric field simulation results.

[0063] Treating the aperture as an independent design variable, rather than one derived from other parameters, offers the engineering significance of providing a completely decoupled degree of freedom for controlling the radial distribution of electron emission current density, independent of the aperture placement. In existing fluid jet impingement cooling devices, the aperture is typically determined by pressure drop compensation requirements, and its variation along the flow path is strictly constrained by the fluid momentum equation, making independent adjustment impossible. However, in this embedded structure, the aperture selection serves the physical requirements of electron emission: increasing the aperture means increasing the single-aperture emission area and electrode surface area, thereby enhancing the local electron emission capability and electric field coverage at that aperture location; decreasing the aperture means increasing the wall thickness between apertures, improving structural strength, and reducing crosstalk between the electric fields of adjacent apertures. Since the aperture is independent of other geometric parameters such as ring spacing, number of apertures, and angular deflection, designers can flexibly make trade-offs in a multi-dimensional design space without being constrained by fluid dynamics.

[0064] It should be understood that, although Figure 2 The illustration shows a specific structure in which embedded electrodes are nested within holes and insulating rings surround the electrodes. However, in other embodiments, the material of the insulating ring can be selected from different high-temperature resistant insulating materials, such as hexagonal boron nitride, alumina ceramic, or silicon nitride, depending on the operating temperature and electrical insulation requirements. The fit between the embedded electrodes and the insulating ring can be achieved through different processes, such as interference fit, threaded connection, or welding. The shape of the collecting electrode is not limited to the large-area flat plate shown in the figure; it can also adopt configurations such as annular collecting electrode, segmented collecting electrode, or curved surface-fitting collecting electrode, as long as it can effectively collect electrons migrating from the emitter. Furthermore, the shape of the rear extension of the spherical head substrate can be cylindrical, conical, or any shape adapted to the inner cavity of the leading edge of the aircraft; this embodiment does not impose any restrictions on this.

[0065] This embodiment provides a computer device, which includes a memory and a processor. The memory is used to store computer programs, and the processor is used to execute the computer programs stored in the memory to implement the steps of the hole array geometry design method described in any of the above embodiments.

[0066] Specifically, the memory can be volatile or non-volatile, such as random access memory (RAM), read-only memory (ROM), flash memory, hard disk drive (HDD), solid-state drive (SSD), or any combination thereof. The processor can be a central processing unit (CPU), graphics processing unit (GPU), digital signal processor (DSP), field-programmable gate array (FPGA), or any general-purpose or special-purpose processing chip with instruction execution capability. The computer program stored in the memory contains the complete execution logic of steps S1 to S4 described in Embodiment 1 above. When the processor loads and runs the computer program, the designer only needs to provide the ball head radius to the program through an input interface or configuration file. Insulation layer thickness Aperture Boundary safety margin First ring projection radius Ring spacing Capacity utilization coefficient Angular gradient coefficient and minimum hole spacing Based on these parameters, the processor automatically determines the maximum allowable projected radius and maximum usable arc length of the hole-laying area according to step S1, generates a ring sequence and determines the number of holes in each ring according to step S2, calculates the angular position of each hole in each ring according to step S3, and generates the center coordinates and unit normal vector of each hole on the sphere according to step S4, finally outputting complete hole array geometric model data. This geometric model data can be directly imported into subsequent electric field simulation software, particle tracking numerical models, or computer-aided manufacturing (CAM) systems, realizing a fully digital process from parameter input to simulation verification to manufacturing.

[0067] It should be understood that the specific hardware form of the computer device can be a desktop workstation, an industrial control computer, an embedded industrial control computer, a server, or a cloud-based virtual computing instance, as long as it has sufficient computing power and storage space to execute the aforementioned geometry generation algorithm. In one embodiment, the computer device may also include a display and input peripherals to allow designers to preview the generated 3D model of the hole array in real time and interactively adjust design parameters. In another embodiment, the computer device can be deployed in a ground design platform for an aircraft's thermal protection system, serving as a geometry engine module for a multidisciplinary optimization process. It works collaboratively with other aerodynamic and thermodynamic simulation modules and structural mechanics analysis modules, automatically updating the hole array geometry model in iterative optimization loops.

[0068] This embodiment also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the hole array geometry design method described in any of the above embodiments.

[0069] Specifically, a computer-readable storage medium can be any tangible medium capable of persistently storing computer program instructions, including but not limited to: optical discs (such as CD-ROM, DVD-ROM, Blu-ray discs), USB flash drives, portable hard drives, magneto-optical discs, independent storage partitions in solid-state drives, embedded multimedia cards (eMMC), universal flash storage (UFS), and server storage space where program installation packages distributed over a network reside. The computer program stored in the storage medium can exist in the form of source code, compiled executable binary form, or intermediate bytecode. When executed by a processor, it completely replicates all the steps of the aperture array geometric design method described in Embodiments 1 to 5, including the maximum allowable projection radius in step S1. and maximum available arc length The determination process, the generation of the ring sequence and the number of holes in each ring in step S2 The joint determination process, the superposition calculation process of the basic uniform angle, the odd-even ring alternating component and the continuous cumulative deflection component in step S3, and the generation process of spherical coordinates and unit normal vector in step S4.

[0070] Through the aforementioned computer equipment and computer-readable storage media, the aperture array geometry design method described in the above embodiments obtains independent protection at the hardware level. This ensures that the method is protected not only as a design process but also its software carrier and hardware execution platform. Whether designers or aircraft manufacturers distribute the geometry design program as a standalone software product, pre-install it in a dedicated thermal protection design workstation, or provide the geometry generation capability to users through cloud services, they must obtain the appropriate authorization. This provides a complete intellectual property protection chain for the parametric design method of electron evaporation-cooled embedded structures, from method to equipment to medium.

[0071] For ease of description, the above systems or devices are described separately as various modules or units based on their functions. Of course, in implementing this application, the functions of each unit can be implemented in one or more software and / or hardware components.

[0072] As can be seen from the above description of the embodiments, those skilled in the art can clearly understand that this application can be implemented by means of software plus necessary general-purpose hardware platforms. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in various embodiments or some parts of the embodiments of this application.

[0073] Finally, it should be noted that in this document, relational terms such as first, second, third, and fourth are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0074] The above description is only a preferred embodiment of this application. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of this application, and these improvements and modifications should also be considered within the scope of protection of this application.

Claims

1. A method for designing the geometry of a hole array, applied to a spherical substrate of an embedded structure with electron evaporation cooling, characterized in that, include: Step S1: Based on the ball head radius Insulation layer thickness Aperture and boundary safety margin Determine the maximum allowable projected radius of the perforated area on the ball head surface. and maximum available arc length ; Step S2, using the projection radius of the first ring Determine the position of the first ring and calculate the spherical arc length corresponding to the first ring. , at equal intervals Generate subsequent rings such that the arc length position of the k-th ring is... satisfy until When the generation of new rings stops, the actual number of holes in the k-th ring is [not specified]. The geometric capacity of the ring and the actual number of holes in the previous ring are determined by the geometric capacity of the ring. and preset capacity utilization factor Jointly determined; Step S3: Using the basic uniform angle as a reference, superimpose the odd-even ring alternating component and the continuous cumulative deflection component. The continuous cumulative deflection component is related to the arc length position of the k-th ring on the sphere. Proportional to, and follows the ring number The increase and monotonically accumulates, causing the relative angular offset between any two adjacent rings to change ring by ring; Step S4: Based on the position of the arc length of the k-th ring The angular position of the j-th hole in the k-th ring Generate the center coordinates and unit normal vector of each hole on the sphere.

2. The method according to claim 1, characterized in that, The maximum permissible projection radius mentioned in step S1 and the maximum available arc length Determine as follows: From the geometric relationships of a sphere, its corresponding maximum permissible projected radius is... : Further define the maximum polar angle of the orifice-deployable region on the ball head surface as: : The maximum usable arc length on the sphere from the stationary point to the boundary of the canopy is: : 。 3. The method according to claim 1, characterized in that, In step S2, the spherical arc length s1 corresponding to the first ring and the arc length position of the kth ring are... Determine as follows: Calculate the polar angle corresponding to the first ring. The arc length s1 of the sphere is respectively: Based on this, subsequent rings are generated at equal intervals according to the spherical arc length, and the arc length position of the kth concentric ring is... satisfy: Among them, when When that happens, stop generating new rings.

4. The method according to claim 1, characterized in that, The actual number of holes in the k-th ring in step S2 Determine as follows: Maximum number of holes that can be placed in the k-th ring: in, Let be the projected radius of the k-th ring; Where nsc is the preset capacity utilization factor, 0 <nsc≤1, This represents the actual number of holes in the (k-1)th ring.

5. The method according to claim 1, characterized in that, The angular position of the j-th hole in the k-th ring in step S4 Determine as follows: in, Based on uniform angles, It is a component with alternating odd and even rings. For continuous accumulation of deflection components; For the preset angular gradient coefficients and , It is a position function based on arc length normalization.

6. The method according to claim 5, characterized in that, The odd-even ring interleaved component Determine as follows: When k is odd When k is even, ; The position function Determine as follows: .

7. The method according to claim 1, characterized in that, In step S4, the center coordinates of the j-th hole in the k-th ring are generated using the spherical coordinate formula, with the spherical head facing the -x direction and the stationary point located at the origin. in, The polar angle corresponding to the k-th ring. Let be the projected radius of the k-th ring. The angular position of the j-th hole in the k-th ring; the corresponding unit normal vector. for: 。 8. An embedded structure for electron evaporation cooling, comprising a spherical substrate, wherein a plurality of concentric ring-shaped holes are arranged on the surface of the spherical substrate, characterized in that: The ball head substrate includes an emitter located at the front end of the ball head, embedded electrodes nested in each hole, and an insulating ring surrounding the embedded electrodes; A voltage is applied to the embedded electrode to create an electric field near the surface of the emitter to modulate electron emission; In the multi-ring concentric hole array, each concentric ring is arranged at equal intervals along the arc length of the sphere. The number of holes in each ring is determined by the geometric capacity of that ring, the actual number of holes in the previous ring, and the preset capacity utilization coefficient, and it does not decrease from ring to ring in the radial direction; The angular position of each hole on each ring includes a basic uniform angular component, an odd-even ring alternating component, and a continuously accumulated deflection component. The continuously accumulated deflection component is linearly related to the arc length position of each ring on the sphere and accumulates monotonically as the ring number increases, so that the relative angular offset between any two adjacent rings changes ring by ring to suppress the alignment of the hole positions on the radial projection direction of the sphere. The hole diameter of each hole is an independent design variable.

9. A computer device, characterized in that, The computer device includes a memory and a processor. The memory is used to store computer programs, and the processor is used to execute the computer programs stored in the memory to implement the steps of the method according to any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The storage medium stores a computer program, which, when executed by a processor, implements the steps of the method described in any one of claims 1-7.

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