Computer-implemented method for systematically configuring, evaluating and optimizing heat transfer device

Abstract

A computer-implemented method for systematically configuring, evaluating and optimizing a heat transfer device comprising a plurality of heat transfer elements arranged in a structured manner, each heat transfer element extending along an axial path, the method comprising: starting from an initial geometric design of the plurality of heat transfer elements; a computer simulation of fluid dynamics and heat transfer at least around the heat transfer elements is performed during an intended operation of the heat transfer device using an optimization framework with a computational model to perform a geometric design optimization for each heat transfer element based on an optimization algorithm targeting a predetermined criterion, the optimization framework is configured to iteratively improve the geometric design of the respective heat transfer elements, and to allow the geometric designs of the plurality of heat transfer elements to change independently of one another during optimization.

Description

Technical Field

[0001] The present invention relates to a computer-implemented method for systematically configuring, evaluating, and optimizing a heat transfer device, for providing an optimized design including a plurality of heat transfer elements arranged in a structured manner. Further, the present invention relates to a computing system for designing a heat transfer device. Additionally, the present invention relates to a non-transitory computer-readable medium including code configured to instruct a processor to perform steps of the computer-implemented method according to the present disclosure. Additionally, the present invention relates to a computer program product. Background Art

[0002] Optimizing heat transfer devices such as heat exchangers is generally challenging. One of the main concerns in the art is the high computational cost associated with the optimization process and the high complexity of the models. In some cases, to reduce the computational overhead, the models employed in the design and optimization of these devices are overly simplified. Such simplification typically results in suboptimal designs that do not fully realize the full potential of the devices.

[0003] A common approach to heat transfer device design involves optimizing a single shape of a tube or a fin and then replicating this shape throughout the design. This approach does not take into account the specific requirements and constraints of individual components within a larger system and thus typically results in a low-efficiency final design.

[0004] Topology optimization is another approach that has received attention in recent years, which focuses on strategically adding or removing material to achieve an optimal design. While this approach is promising, it is not without drawbacks. The computational requirements of topology optimization are very high, especially when modeling complex flow patterns such as turbulence. Additionally, traditional topology optimization techniques are typically defined based on volume, differentiating between solid or fluid volume elements. This volume-based approach makes it almost impossible to accurately model turbulence. Turbulence itself needs to be precisely defined based on walls or surfaces rather than just volume. Therefore, existing methods may only be able to provide a rough estimate of turbulent flow, which can affect the accuracy and efficiency of the design.

[0005] A promising alternative to the above-described topology optimization method is shape optimization. Different from topology optimization, shape optimization focuses on changing the surface, such as changing the shape of pipes or fins, rather than adding or removing materials. This method is not only computationally more efficient, but also provides higher accuracy for fluid simulation due to the use of predefined surfaces. A significant advantage of using shape optimization is that the influence of turbulence can be well captured during shape optimization due to the well-defined walls. However, this method often requires a large amount of design space. Therefore, a method is needed to improve the efficiency of shape design optimization of heat transfer devices to meet the evolving industrial needs. Summary of the Invention

[0006] An object of the present invention is to provide a method and system that overcome at least one of the above defects.

[0007] Additionally or alternatively, an object of the present invention is to provide a computer-implemented method and system capable of more effectively configuring, evaluating, and optimizing a heat transfer device.

[0008] Additionally or alternatively, an object of the present invention is to provide a computer-implemented method and system capable of improving the design process of a heat transfer device.

[0009] Additionally or alternatively, an object of the present invention is to provide a computer-implemented method and system that effectively promotes the systematic and iterative design optimization of heat transfer elements using computational simulations of fluid dynamics and heat transfer.

[0010] Accordingly, the present invention provides a computer-implemented method for systematically configuring, evaluating, and optimizing a heat transfer device. The heat transfer device includes a plurality of heat transfer elements arranged in a structured manner, wherein each heat transfer element extends along an axial path. The method includes: starting from an initial geometric design of the plurality of heat transfer elements; performing computer simulations of at least fluid dynamics and heat transfer around the heat transfer elements during the expected operation of the heat transfer device using an optimization framework having a computational model to geometrically design-optimize each heat transfer element based on an optimization algorithm targeting a predetermined criterion, wherein the optimization framework is configured to iteratively improve the geometric design of each heat transfer element, and wherein the geometric designs of the plurality of heat transfer elements are allowed to change independently of each other during the optimization.

[0011] The method starts with a predefined geometric design of these elements. An optimization framework combined with a computational model is used to perform computerized simulations of fluid dynamics and heat transfer, particularly during the operation of the device, around these heat transfer elements. The aim is to optimize the geometric design of each element, and this optimization is controlled by an optimization algorithm targeting predefined criteria. The framework is designed to iteratively improve the geometric design of each element. During the entire optimization process, the geometric designs of various heat transfer elements can be modified independently.

[0012] Advantageously, a very rich design space can be explored for the heat transfer device while providing effective optimization. The improved design flexibility enables the design of customized heat exchangers in an effective manner.

[0013] A customized design of the heat transfer device for optimized performance can be obtained. A customized design means that the heat transfer device is personalized or specifically designed to meet these specific requirements. By ensuring that each element of the device is precisely shaped to function optimally under specific conditions, the overall efficiency and effectiveness of the device can be enhanced.

[0014] Utilizing an optimization framework with a computational model means integrating computational tools and algorithms to improve the design process. An optimization framework is a structured system that uses mathematical models / algorithms to find the best possible design solution based on set criteria. In this case, the criteria can be defined, for example, as achieving maximum heat transfer efficiency and / or optimal fluid dynamics.

[0015] Including a computational model in the process means that the framework does not rely solely on trial and error or empirical data. Instead, models based on mathematics and physics are used to simulate how the device will operate under various conditions. These models can simulate fluid flow (referring to computational fluid dynamics) and how heat is transferred between materials around the heat transfer elements (computational heat transfer). By utilizing these models, it is possible to predict how small changes in the design will affect performance, enabling informed decisions about which design changes will yield the best results.

[0016] The process is iterative, meaning that the design is continuously improved. The optimization framework using the computational model will adjust the design, test the results in a virtual environment (see computation), analyze the results, and then make further improvements. This cycle can continue until the improved design meets or exceeds the predefined operating criteria.

[0017] In some examples, a computer-implemented method can include configuring and evaluating a heat sink or heat exchanger having a plurality of fins or heat pipes, where each fin or pipe has an elongated shape. The process begins with an initial design of these fins or pipes. An optimization tool using a simulation model of fluid dynamics and heat transfer improves the design of each fin or pipe. The model targets certain criteria, and the tool improves the design of each fin or pipe. The design of each fin or pipe can be adjusted independently during this optimization process.

[0018] Optionally, output data representing the optimized geometric design of each heat transfer element.

[0019] Optionally, transmit the data representing the optimized geometric design to a production device configured to produce a heat transfer device.

[0020] Optionally, the production device includes an additive manufacturing system.

[0021] Optionally, use an additive manufacturing system configured to manufacture at least a portion of an optimized heat transfer device based on the optimized design parameters.

[0022] Optionally, transmit an output signal representing the optimized geometric design to a production device configured to produce an optimized physical object based on the output signal.

[0023] Optionally, the physical object is a heat transfer device or a part of a heat transfer device.

[0024] It should be understood that the term "physical object" refers to any tangible item that can be produced based on an optimized geometric design obtained from a computer-implemented method. The heat transfer device can be the main product for which the method is used to optimize. The heat transfer device can be considered an assembly including a plurality of heat transfer elements. The optimized design can aim to improve aspects such as the efficiency, effectiveness, and / or manufacturability of the device.

[0025] It should be understood that instead of producing the entire heat transfer device, the optimized design can be used to manufacture only certain parts or components of the heat transfer device. For example, if the heat transfer device consists of several different types of elements, the method can optimize the design of a specific type of element and can produce only that element based on the optimized design.

[0026] Optionally, each heat transfer element is parameterized along a line in a cross-sectional view perpendicular to the axial path of each heat transfer element, wherein during iterative optimization, the optimization framework is configured to adjust the thickness distribution of each heat transfer element along the line to obtain the overall shape of each heat transfer element, and wherein a plurality of nodes are defined along the length of each heat transfer element, and wherein the thickness distribution of the heat transfer element is determined by the distance from each of these plurality of nodes to the line of the corresponding heat transfer element.

[0027] Each heat transfer element can be parameterized along a line observed in a cross-sectional view that is perpendicular to the axial path of the heat transfer element. During iterative optimization, the optimization framework is technically set to adjust the thickness distribution of each heat transfer element along the specified line. This adjustment is crucial in obtaining the overall shape of each heat transfer element. Additionally, a plurality of nodes are defined along the length of each element. The thickness distribution of the element is determined by measuring the distance from each of these nodes to the line of the associated heat transfer element.

[0028] Throughout the iterative optimization process, the framework adjusts the thickness distribution of each heat transfer element along the aforementioned line, thereby obtaining the overall shape of the heat transfer element. This process involves a number of nodes defined along the length of each heat transfer element. The thickness distribution is then determined by the distance from each of these nodes to the line of the corresponding element. Advantageously, fine and precise control of the shape and thickness of the heat transfer element is provided. The method ensures an effective way to optimally adapt the design to the specific requirements and constraints of a particular application. Compared to methods known in the art, the computational cost of the optimization process can be significantly reduced.

[0029] The design process of heat transfer elements is improved by introducing an improved parameterization method. Parameterization refers to the process of defining certain variables or parameters that can be adjusted to have an impact on the result. In this case, each heat transfer element is parameterized by defining it along a line in a cross-sectional view. The cross-sectional view is taken perpendicular to the axial path of the heat transfer element. Substantially, if the heat transfer element is imagined as a long rod, the cross-sectional view is a cut through the rod, thereby giving a cross-sectional view of the long rod.

[0030] It should be understood that iteration can be understood as repetitive, indicating that the optimization process goes through multiple improvement cycles. During each cycle, the thickness distribution of the heat transfer element along the defined line (as seen from the cross-sectional view) is adjusted. This adjustment is not arbitrary. Instead, the goal of this adjustment is to optimize the shape of the heat transfer element.

[0031] Nodes are specific points defined along the length of each heat transfer element. They can be understood as markers or reference points. The thickness of the heat transfer element at any given location is determined by the distance from these nodes to the defined line of the element in a cross-sectional view. By adjusting the positions of these nodes, the thickness and shape of the heat transfer element can be precisely controlled.

[0032] Introducing this parametric technique, combined with iterative optimization and the use of these nodes, provides an advantageous way to fine-tune the design of each heat transfer element with high precision. This fine control enables the adjustment of the shape and thickness of each element to meet specific requirements.

[0033] Different applications or operating conditions may have specific challenges or constraints. For example, some applications may require faster heat dissipation, while others may prioritize minimizing the use of materials. By precisely controlling the design of each heat transfer element, it is better ensured that the device is optimized for the intended purpose.

[0034] In some examples, the fin or heat pipe can be described by a curve in a view perpendicular to the extension line of each fin or heat pipe. During iterative improvement, the optimization tool can modify the thickness or width distribution of each fin or pipe based on this curve to determine the overall shape. Multiple reference points or nodes can be positioned along each fin or pipe. The thickness or width can be measured by the distance from each of these nodes to the described curve. In alternative examples, the curve can be a straight line or a curved path.

[0035] Optionally, the line is selected to be substantially parallel to the general flow direction between the inlet and outlet of the heat transfer device. Multiple heat transfer elements are arranged between this inlet and outlet.

[0036] In some examples, the selected line can be substantially parallel to the general flow direction connecting the inlet and outlet of the heat transfer device. The heat transfer elements can be systematically arranged between this inlet and outlet.

[0037] This arrangement of the line ensures the effective positioning of the heat transfer elements relative to the flow. This can improve the optimization process by reducing the computational time. By aligning the elements with the direction of fluid flow, improved heat transfer can be obtained. This alignment ensures that the fluid makes optimal contact with the elements, thereby facilitating efficient heat exchange.

[0038] In the design of such a fluid-based system, the direction of fluid flow is crucial. The line used for parameterizing the heat transfer elements can be aligned to be substantially parallel to the general flow direction between the inlet (the opening where the fluid enters) and outlet (the opening where the fluid leaves) of the device to ensure that the heat transfer elements are oriented in a way that complements the natural trajectory of the fluid.

[0039] This alignment ensures that the heat transfer element can be effectively positioned relative to the flow. The contact between the heat transfer element and the fluid is more effective than when the element is oriented in a way without such alignment. This strategic alignment improves the heat transfer efficiency. When the heat transfer element is aligned with the fluid flow direction, the surface area in direct contact between the element and the fluid is maximized. Since heat transfer is fundamentally affected by the contacted surface area, this alignment ensures more effective heat exchange between the fluid and the heat transfer element. In this way, the optimization process can be significantly improved, and thus the computational cost can be reduced.

[0040] In addition to alignment, orientation also ensures that the fluid better surrounds the element. This surrounding promotes closer and more persistent contact between the fluid and the element. The longer and closer the fluid contacts the heat transfer element, the more heat can be effectively transferred.

[0041] In some examples, a curve or line can be aligned almost parallel to the general flow direction from the inlet point to the outlet point of a radiator or exchanger, where fins or pipes are located inside the radiator or exchanger. In other examples, the curve or line can be oriented at a slightly inclined angle relative to the flow direction, or can follow a unique predefined path.

[0042] In some examples, the initial geometry or cross-sectional profile of the heat exchange element can be substantially circular. The term "circular" as used herein refers to such a shape or configuration where all points on the perimeter or boundary of the heat exchange element are equidistant from a central point or axis, resulting in a symmetric and continuous curve without any corners or edges.

[0043] This circular configuration of the heat exchange element can provide various advantages, including but not limited to efficient heat transfer due to the increased surface area and good structural integrity. The circular design can also enable uniform distribution of thermal stress, thereby reducing potential mechanical failure points and ensuring consistent performance of the entire heat exchange element.

[0044] It should be understood that although the present disclosure emphasizes the circular configuration as the initial geometry or cross-sectional profile of the heat exchange element as discussed in the above examples, the present invention is not limited thereto. Other initial geometric configurations, whether symmetric or asymmetric, can also be envisioned within the scope of the present invention.

[0045] Optionally, the initial geometric design in cross-section has a droplet shape.

[0046] In some examples, when observed in cross-section, the initial geometric design predominantly exhibits a droplet shape. This shape can form the basis design before any optimization. By its very nature, the droplet shape can facilitate smooth flow around it, reducing drag. Thereby, the efficiency and performance of the heat transfer device are enhanced by minimizing potential flow disruptions and maximizing the surface area in contact with the fluid. Thus, by using this shape as the initial geometric design, the optimization process can be significantly improved.

[0047] The droplet shape is typically rounded at its top (usually on the leading edge side) and smoothly tapers to a point or a narrower base (usually on the trailing edge). The aerodynamic properties inherent in the droplet shape confer technical advantages when interacting with a flowing fluid. When the fluid encounters the droplet-shaped heat transfer element, the fluid flows smoothly around the rounded contour of the droplet shape. Another advantage of the droplet shape is the ability to maximize the surface area in contact with the fluid. Compared to other possible shapes, the rounded and elongated nature of the droplet ensures a larger portion of the element's surface is in contact with the fluid. In heat transfer, the size of the surface area in contact with the fluid directly affects the efficiency of heat exchange. A larger contact surface area enables more heat to be exchanged between the fluid and the heat transfer element.

[0048] Advantageously, by starting with the droplet shape as the initial geometry, the number of iterations required to reach the optimum can be significantly reduced. The smooth fluid flow and the increased contact surface area result in a heat transfer device that operates with higher efficiency and performance.

[0049] In some examples, the starting geometric design in a cross-sectional view can resemble a teardrop shape. Optionally, the initial shape can reflect other geometries, such as an ellipse, a semi-circle, or a complex contour customized for a specific application.

[0050] Optionally, a first subset of heat transfer elements is selected, which includes at least one or more front heat transfer elements and one or more rear heat transfer elements arranged within the device. Wherein, during optimization, the heat transfer elements in the first subset are allowed to independently assume different geometric designs. And wherein, a second subset of these heat transfer elements is selected, where, during optimization, the heat transfer elements in the second subset are constrained not to be allowed to independently change their geometric designs.

[0051] A specific subset of heat transfer elements including front heat transfer elements and rear heat transfer elements located within the device is selected. During the optimization phase, the elements in this first subset can have the freedom to independently exhibit different geometric designs. At the same time, a second subset of heat transfer elements is also identified. It should be noted that the elements in this second subset are subject to some constraints such that they cannot independently change their geometric designs.

[0052] The advantage of this selective design method is that it preserves the critical flow dynamics around the key components while allowing flexibility for other components. By controlling the design of the front and rear components, the present invention ensures that the initial and final stages of heat transfer are optimal, and other components between the front and rear components can be similarly changed for the overall device efficiency. Generally, even if the shapes of the components between the front and rear components are allowed to be changed individually during the optimization process, the designs of these components will not be very different from each other.

[0053] In this method, the design optimization of the heat transfer components is carried out by dividing them into different subsets based on their positioning and / or function within the device. The first subset includes the "front" and "rear" components, where the terms represent the positions of these components. The "front" component is the first component that the fluid encounters when entering the space where the components are arranged, and the "rear" component is the last component that the fluid contacts before leaving the space. During the optimization process, the first subset of components is allowed to have design flexibility, which means that these components can have different geometric designs. This makes sense because it means that the front and rear components can be customized individually to address the specific fluid dynamics and heat transfer challenges at the beginning and end of the process of the fluid passing through the device. Different from the first subset, another group of heat transfer components is not given the same design autonomy. These components that make up the second subset are restricted so that they do not undergo individual geometric design changes during the optimization. This shows that although the front and rear components can be optimized individually, the components between the front and rear components have some constraints to maintain consistency or follow specific design criteria.

[0054] This separate design strategy provides a combination of flexibility and consistency. By allowing the front and rear components to have different designs, the device can ensure the optimization of the fluid entering and leaving the device. These stages are crucial because any turbulence or inefficiency at the beginning will pervade the entire device, and any inefficiency at the end will reduce the overall heat transfer efficiency. Although the front and rear components are customized for specific flow dynamics, the other components (the second subset) in the device maintain a certain degree of consistency. Thus, a balance is achieved between customization and consistency, ensuring that while certain components can adapt to specific challenges, the entire device maintains consistent performance characteristics.

[0055] Therefore, the present invention ensures the mutual harmony between the performance of individual components and the efficiency of the overall device by differentiating the design methods of the front heat transfer components, the rear heat transfer components, and the intermediate heat transfer components. The ability to customize specific components while maintaining the consistency of other components ensures that the device can address specific fluid dynamics challenges while maintaining optimal heat transfer.

[0056] In some examples, a primary set of fins or tubes can be selected that can consist of one or more front fins or tubes and one or more rear fins or tubes within the device. During improvement, these fins or tubes in the primary set can independently adopt a specific design. During this improvement, a secondary set of fins or tubes can be constrained from making independent geometric changes. In other examples, multiple subsets can be selected for differential optimization constraints.

[0057] Optionally, the second set includes heat transfer elements located between one or more front heat transfer elements and one or more rear heat transfer elements in the heat transfer device.

[0058] The second subset can include heat transfer elements located between the front heat transfer elements and the rear heat transfer elements within the device. Specifically, the second subset includes heat transfer elements located between the front heat transfer elements and the rear heat transfer elements within the device. This positioning ensures that the core of the device maintains consistent flow dynamics, while the periphery (front heat transfer and rear heat transfer elements) can be customized according to specific requirements. Thus, a balance can be achieved between design flexibility and maintaining a consistent core design.

[0059] In some examples, during optimization, a distinction is made between the elements at the periphery and the core. The periphery consists of front and rear elements that have design flexibility. In contrast, the core, represented by the second subset, is intended for a consistent design. This can also result in consistent flow dynamics within the core. In this way, modeling can be significantly simplified, thereby reducing computational costs.

[0060] The elements located in the core play a crucial role in maintaining a stable and consistent flow dynamic through the device body. When the fluid moves through the central part of the device, this consistent flow is essential for ensuring that the interaction between the fluid and the heat transfer elements remains stable and predictable. This consistency helps to achieve a uniform heat transfer rate and minimize the likelihood of unstable flow patterns that can reduce efficiency.

[0061] The elements at the core are designed for consistency, while the front and rear elements at the periphery are given design flexibility. This flexibility ensures that these elements can be optimized for the specific challenges presented at the entry and exit points where the fluid travels through the device. For example, the front elements can be designed to ensure a smooth entry of the fluid, while the rear elements can be customized to maximize heat extraction before the fluid exits.

[0062] On the one hand, the periphery has design flexibility, enabling the device to adapt to specific operating requirements or challenges. On the other hand, the consistent performance at the core ensures that once the fluid effectively enters the device, it will experience stable and predictable flow dynamics, which is conducive to efficient heat transfer.

[0063] In some examples, the secondary group can consist of fins or ducts located between the front fins or ducts and the rear fins or ducts within the device. In alternative examples, the secondary group can include fins or ducts located in the middle, near the periphery, or at any other predetermined arrangement within the radiator or exchanger.

[0064] Optionally, one or more front heat transfer elements include at least one row of heat transfer elements at the front side of the plurality of heat transfer elements within the device; and wherein, one or more rear heat transfer elements include at least one row of heat transfer elements at the rear side of the plurality of heat transfer elements within the device.

[0065] The front heat transfer elements include the foremost row of these elements among the heat transfer elements located within the device. In contrast, the rear heat transfer elements include a row of elements located at the rear end of the heat transfer elements within the device.

[0066] In some examples, a row-based arrangement can be provided. In some examples, the front heat transfer elements can be not just sporadically located at the front of the device, but can be systematically organized into at least one row. Similarly, the rear elements can be arranged into at least one row at the rear end of the device. This row-based organization provides a structured and organized layout, ensuring that the fluid encounters a clearly defined set of heat transfer elements when entering and leaving the device.

[0067] The presence of these rows establishes clear entry and exit points for fluid flow. When the fluid enters the device, it first contacts a row of front elements, setting the tone for its flow dynamics and heat transfer. Similarly, when about to leave, the fluid finally interacts with a row of rear elements, ensuring that any final heat transfer opportunities can be utilized. This clear demarcation ensures that the interaction between the fluid and the device begins and ends in a structured manner.

[0068] In some examples, the front fins or ducts can consist of one or more rows at the leading edge of the device, and the rear fins or ducts can include one or more rows at the trailing edge. In other examples, the front group or the rear group can span multiple rows or form a specific pattern within the device.

[0069] Optionally, the optimization framework is configured to further adjust at least one of the following: the spacing distance in the length direction between the heat transfer elements, or the pitch in the direction perpendicular to the length direction between the heat transfer elements.

[0070] The optimization framework can be configured to further modify the spacing between heat transfer elements in their longitudinal direction or the pitch between these elements in a direction perpendicular to their length. This ability to adjust the element spacing provides the advantage of optimizing the spacing for fluid flow and / or heat transfer. By controlling this distance, the design ensures optimal flow velocity and heat transfer efficiency throughout the device.

[0071] In some examples, the optimization framework can also modify the longitudinal distance between fins or tubes, or modify the perpendicular gap between fins or tubes. In other variations, the tool can adjust other parameters, such as the angle, curvature, or alignment of fins or tubes relative to the flow direction.

[0072] This method can be used for two-dimensional (2D) and / or three-dimensional (3D) design optimization.

[0073] Optionally, three-dimensional shape optimization is performed by using multiple lines for each heat transfer element, each line being in a plane spaced a certain distance apart along the axial path of the corresponding heat transfer element to define the three-dimensional geometry of the heat transfer element.

[0074] Specific three-dimensional shape optimization can be performed. This involves using multiple lines for each heat transfer element, where each line is in a different plane spaced apart along the axial path of the corresponding element. This intricate method defines the three-dimensional geometry of the heat transfer element.

[0075] In some examples, three-dimensional shape optimization is performed using multiple lines for each heat transfer element, each of these lines being in a separate plane along the axial path of the corresponding element, thereby defining its three-dimensional geometry for 3D optimization. As a result, a more intricate and customized design is created for each element, ensuring optimization for three-dimensional hydrodynamics and heat transfer. The multiple lines for each heat transfer element can be used to define the shape of the heat transfer element using corresponding nodes. Different from using a single line in a cross-sectional view (see 2D), multiple such lines are used, where each line is in a separate plane spaced apart along the axial path of the element (see 3D). This method can capture the geometry of the element at different points along its length, providing a comprehensive representation of its three-dimensional shape.

[0076] By using multiple such lines in different planes, the claims provide a method for defining and optimizing the entire three-dimensional geometry of a heat transfer element. It reflects not only how the element appears in cross-section at a single point, but also how its shape evolves and changes over its entire length.

[0077] In this way, a more intricate and detailed design is created for each heat transfer element. The 3D optimization means that every curve, edge, and surface of the element can be carefully designed for optimal performance. This granularity ensures that optimization is carried out not only for 2D slices of the element but also for its entire volume.

[0078] The fluid moves in three dimensions, and its interaction with the surface is not limited to a plane. The design takes into account the complexity of three-dimensional hydrodynamics by using a 3D optimization method. This ensures that when the fluid surrounds and flows around the heat transfer element, every surface, curve, and edge of the element can be optimized for heat transfer. Thereby, the heat transfer element is customized not only for the instant of interaction between the heat transfer element and the fluid but also for the entire dynamic process.

[0079] In some examples, multiple curves for each fin or tube can be used for 3D shape optimization, where each curve lies in a plane spaced along the length of the fin or tube. These planes help to define the 3D geometry. In alternative examples, more than two curves or complex 3D profiles can be employed for each fin or tube.

[0080] Optionally, the cross-sectional shape is allowed to vary along the axial path during optimization.

[0081] Since the cross-sectional shape is allowed to undergo changes along the axial path during optimization, a dynamic design aspect is introduced, where each part of the element can be uniquely customized for specific flow conditions. Thereby, the ability to adapt the design to the changing flow and heat transfer requirements along the axial path of the element is provided. Thus, in this example, the cross-sectional shape of the heat transfer element is not static or uniform along its length. Instead, it is allowed to change or vary as it moves along the axial path of the element.

[0082] Allowing cross-sectional variations introduces a great degree of design versatility. As the fluid flows along the length of the heat transfer element, the fluid may encounter different flow conditions or challenges. By allowing the cross-sectional shape to vary along the axial path, each part of the element can be specifically designed to handle these particular flow scenarios.

[0083] By allowing flexibility in changing the cross-sectional shape along the axial path, the design ensures that the heat transfer element can remain adaptable. The geometry of the cross-section can be changed and adjusted to accommodate different flow rates, pressure variations, or heat transfer rates. Traditional designs that maintain a uniform cross-sectional shape may not be equipped to handle the different challenges that arise along the length of the element. In contrast, a design that allows the cross-section of the element to be changed ensures that each part of the element is optimized for its specific set of challenges. Whether it is a change in flow rate, a change in fluid density, or the need for local heat transfer, the adaptable design ensures that the element maintains optimal performance.

[0084] In some examples, the cross-sectional shape can be allowed to vary along the length of the element during refinement. Optionally, specific portions of the fins or ducts can remain constant while other portions are optimized.

[0085] Optionally, the length of the heat transfer element along its axial path is parameterized and the heat transfer element is allowed to vary in length along its axial path during optimization.

[0086] The length of the heat transfer element along its axial path is parameterized. This parameterization is crucial because it enables the length to be modified during the optimization process.

[0087] Unlike static or fixed-length designs, the length of each heat transfer element is not predetermined or locked, but rather a parameter that can be adjusted during the optimization process. This dynamic approach ensures that the element is not constrained by initial design assumptions and can be customized during the design phase. Different flow conditions and heat transfer requirements may call for heat transfer elements of different lengths. For example, parts of the device with higher flow rates can benefit from longer elements that provide a longer interaction with the fluid, ensuring efficient heat transfer. In contrast, slower-flowing regions may require shorter elements to avoid creating unnecessary drag or pressure drop. The ability to modify the element length ensures that each element is precisely customized according to its specific operating scenario.

[0088] By allowing the length of the heat transfer element to be a variable parameter, the design can ensure that each element has an optimal length, neither too short (which may affect heat transfer efficiency) nor too long (which may introduce flow resistance or inefficiency). This adaptability ensures that each element can be fine-tuned according to the specific requirements of its position within the device, resulting in an overall optimized design.

[0089] In some examples, the length of the fins or ducts can be described and the length of the fins or ducts is allowed to change during refinement. In other examples, only the length of the top, bottom, or middle portion of the fins or ducts is allowed to be adjusted.

[0090] Optionally, at least 6 nodes are used, preferably at least 10 nodes, and even more preferably at least 12 nodes.

[0091] In some examples, parameterization is performed using a minimum of 7 nodes, preferably 12 nodes or even 15 nodes.

[0092] By using a greater number of nodes, the method achieves a finer and more precise control over the shape and distribution of the heat transfer elements. The advantage of this is the ability to refine the design in more detail to ensure a highly optimized heat transfer device.

[0093] These nodes play an important role in defining and refining the geometry of the heat transfer elements. They serve as reference points or markers that help to determine the shape, thickness, and distribution of these elements. Substantially, they serve as control points that influence the overall geometry. The increase in the number of nodes is proportional to the level of control granularity that can be achieved in the design. As the number of nodes increases, there are more reference points to guide and refine the shape of the elements, enabling a more intricate design process.

[0094] The main advantage of increasing the number of nodes is the ability to improve the level of detail and accuracy in the design process. As the number of nodes increases, the curvature, thickness, and overall geometry of the heat transfer elements can be defined with higher accuracy. Additionally, potential inefficiencies or design challenges can be addressed more accurately, enabling fine-tuning to meet very local flow or heat transfer conditions. Furthermore, the overall design becomes more adaptable and responsive to the specific requirements of the device, ensuring that each segment of the element is optimized for its specific operating scenario.

[0095] In some examples, a minimum of 6 nodes can be employed, but in some embodiments, 10 nodes, 12 nodes, or even more nodes can be used. In other variations, the number of nodes can be customized according to the complexity of the design or optimization criteria.

[0096] In some examples, for computational efficiency, a maximum of 100 nodes are used, preferably a maximum of 80 nodes, and even more preferably a maximum of 40 nodes. It has been found that nodes in the range of 6 to 100, preferably 10 to 80, and even more preferably 12 to 40 provide a good balance in terms of accuracy and computational cost.

[0097] Optionally, a first-order optimization method that utilizes gradients is used to perform shape optimization, where the adjoint method is used to calculate the gradients.

[0098] A first-order optimization method that utilizes gradients is used to perform shape optimization. The adjoint method can be employed to calculate these gradients, ensuring accuracy and efficiency.

[0099] This method offers the advantages of high efficiency and precise optimization. By using the adjoint method for gradient calculation, the optimization process is computationally more efficient and accurate, ensuring the achievement of the optimal design in a shorter time.

[0100] First-order optimization methods utilize gradients, where the gradient represents the direction and rate of change of the objective function with respect to the design parameters. In the context of a heat transfer device, these gradients provide insights into how small changes in the design affect the performance of the device. Based on these gradients, the optimization process can converge towards a design that maximizes (or minimizes) the desired performance metric.

[0101] Although gradients are crucial for optimization, the calculation of these gradients can be computationally intensive, especially for complex systems. The adjoint method provides a mathematical technique that offers a more efficient way to calculate these gradients. Instead of directly calculating the gradients for each design parameter (which can be numerous), the adjoint method calculates "adjoint variables" from which all the required gradients can be obtained. This significantly reduces the computational effort and time required, especially when dealing with a large number of design parameters.

[0102] Combining this method with the method according to the present disclosure provides significant advantages. It is possible to explore a vast design space, and effective optimization can be achieved using the adjoint method. The adjoint method is not only efficient but also accurate. By providing precise gradients, it ensures that the optimization process is accurately guided towards the desired design goal, thereby reducing the likelihood of suboptimal solutions.

[0103] Optionally, the line is a central symmetry line that substantially passes through the heat transfer element along the length direction of the corresponding heat transfer element. The term "symmetry line" generally refers to a reflection line or a central axis around which the two halves of a structure such as a heat transfer element are mirror images of each other, meaning that each half is symmetric with respect to the other half along this line. In some cases, a symmetric design is required.

[0104] However, in certain examples, an asymmetric configuration can also be adopted. The heat transfer element can exhibit an asymmetric profile or shape such that the two halves separated by the symmetry line are not mirror images of each other. This asymmetry can be intentionally introduced to meet specific design objectives or operational requirements of the heat transfer device.

[0105] In some examples, the symmetry line can pass through or not pass through the heat transfer element, and the directions or configurations of multiple heat transfer elements in the device can be different, such that if each element has its own symmetry line, it will result in different geometric profiles.

[0106] In some examples, these heat transfer elements may be non-parallelly aligned. Such non-parallel alignment may be the result of considering a specific design or for achieving specific hydrodynamic or heat transfer results.

[0107] The flexibility of asymmetric, non-identical, and non-parallel configurations enables a greater range of design possibilities and operational efficiencies for the heat transfer device.

[0108] According to one aspect, the present invention provides a computing system for designing a heat transfer device. The computing system includes: a processor; a non-transitory machine-readable medium. The non-transitory machine-readable medium includes code configured to instruct the processor to perform steps in accordance with the present disclosure.

[0109] The system presents significant advantages by providing a vast design space for the heat transfer device. The optimization process is simplified and efficient, facilitating the mastery of designing customized heat exchangers.

[0110] According to one aspect, the present invention provides a non-transitory computer-readable medium including code configured to instruct a processor to perform steps in accordance with the present disclosure.

[0111] It should be understood that, according to various examples, the term "structured manner" may be understood to refer to an arrangement in which heat transfer elements are organized in a specific way to achieve a desired configuration (e.g., an array). In certain embodiments, the term "array" represents a consistent or predefined order of heat transfer elements. This consistent or predefined order may be characterized by the pattern, sequence, or any other organized layout of these heat transfer elements.

[0112] It should be understood that although a structured manner may represent a consistent or uniform distribution, it does not necessarily mean that it is uniform across all regions of the arrangement. In certain embodiments, the distribution of heat transfer elements within an array may be non-uniform. Such non-uniform distribution may be manifested as a variation in the spacing or distance between adjacent heat transfer elements. Specifically, the distance between heat transfer elements may be different at different positions within the array. Such variations may be deliberately designed to meet specific performance, hydrodynamic, or heat transfer requirements of the heat transfer device.

[0113] In some examples, the structured manner may provide a strategic arrangement or positioning of heat transfer elements to optimize the heat transfer efficiency, hydrodynamic performance, or other operating parameters of the device. Thus, the structured manner provides flexibility in the design and configuration of heat transfer elements while maintaining an organized arrangement.

[0114] It should be understood that, according to various examples, the term "axial path" refers to a predefined trajectory or direction along which a heat transfer element extends or is oriented. This axial path serves as a fundamental reference for defining the geometric and spatial properties of the heat transfer elements within a heat transfer device.

[0115] It should be understood that in some embodiments, the axial path of one heat transfer element may be substantially similar or identical to the axial path of another heat transfer element, which means that the orientations of multiple heat transfer elements are consistent or uniform with respect to a common reference point or a common reference plane. However, in other examples, the axial path of one heat transfer element may deviate from or be different from the axial path of another heat transfer element. Such variations can be introduced into the axial path to achieve specific design objectives, optimize heat transfer efficiency, or meet specific hydrodynamic requirements. The variability of the axial path enables enhanced customization and adaptability in the design and functionality of the heat transfer device, providing a wider range of configurations.

[0116] Therefore, the concept of "axial path" as disclosed herein encompasses both the case where heat transfer elements share the same axial path within the same heat transfer device and the case where heat transfer elements exhibit different axial paths within the same heat transfer device.

[0117] In some examples, in the context of computational simulations and modeling of heat transfer devices, the spanwise direction is generally defined as the direction perpendicular to the main flow direction of the pipe or the axial path. In some examples, to achieve efficient and accurate modeling, especially in scenarios where the pipe exhibits repetitive or cyclic patterns in the spanwise direction, periodic boundary conditions can be employed. The term "periodic boundary conditions" refers to a set of mathematical and computational conditions in which the properties, behaviors, and values at one boundary of the computational domain are set to be the same or congruent to those at the opposite boundary. This approach essentially creates a seamless and continuous modeling environment, eliminating abrupt or artificial boundaries that may interfere with the accuracy of the simulation.

[0118] By applying periodic boundary conditions in the spanwise direction, a representative segment or portion of a pipe array can be modeled instead of modeling the entire array. The modeled segment can be considered as a repeating unit cell that reflects the behaviors and characteristics of the entire pipe arrangement in the spanwise direction. This approach offers computational efficiency as it reduces the overall complexity and size of the simulation domain while still being able to capture the fundamental dynamics and interactions occurring across the entire span of the pipe.

[0119] Therefore, the method of using periodic boundary conditions in the spanwise direction helps to simplify and streamline the computational modeling process, ensuring an accurate representation of the behaviors and interactions of the pipes in the heat transfer device.

[0120] According to one aspect, the present invention provides a method for configuring and evaluating a heat transfer device having a plurality of elements, wherein each element is along an axial path. The process starts with an initial design of these elements. An optimization system and a computational model are used to simulate the hydrodynamics and heat transfer around the elements. The system iteratively improves the design of each element based on set criteria, allowing individual design variations for multiple elements during the optimization process.

[0121] It should be understood that although some heat transfer elements within the heat transfer device may be oriented or extend in a particular direction, it is not mandatory for all heat transfer elements to conform to a single, uniform direction of extension. Specifically, the design and configuration of the heat transfer device allow for a diversity of orientations among the constituent heat transfer elements of the heat transfer device.

[0122] In some embodiments, different heat transfer elements may be oriented or extend in different directions to accommodate specific design constraints, optimize heat transfer characteristics, address hydrodynamic considerations, or achieve other operational objectives. This flexibility in directional orientation enables a customized arrangement of heat transfer elements within the device to meet specific performance requirements or design criteria.

[0123] Accordingly, the present invention contemplates a heat transfer device in which the heat transfer elements may exhibit various directional extensions, not limited to the same or a single direction spanning all elements. This design approach enhances the adaptability and versatility of the heat transfer device under different applications and / or operating conditions.

[0124] It should be understood that any aspect, feature, and option described in view of a computer-implemented method equally apply to the computing system and the non-transitory computer-readable medium described. It will also be clear that any one or more of the above aspects, features, and options may be combined. BRIEF DESCRIPTION OF THE DRAWINGS

[0125] The present invention will be further elaborated based on exemplary embodiments to be represented in the drawings. The exemplary embodiments are given by way of non-limiting illustration. It should be noted that the drawings are only schematic representations of the embodiments of the present invention given by way of non-limiting examples.

[0126] In the figures:

[0127] Figure 1A 、 Figure 1B shows a schematic diagram of an exemplary shape design;

[0128] Figure 2 shows a schematic diagram of an exemplary optimization method; and

[0129] Figure 3A 、 Figure 3B 、 Figure 3CA schematic diagram showing exemplary analysis results. Detailed implementation

[0130] Figure 1A 、 Figure 1B A schematic diagram showing exemplary shape designs of heat transfer elements 1a and 1b. The design can be adjusted during the optimization process. A computer-implemented method for systematically configuring, evaluating, and optimizing a heat transfer device is employed. The heat transfer device includes a plurality of heat transfer elements arranged in a structured manner, where each heat transfer element extends along an axial path. The method includes the following steps: starting from an initial geometric design of the plurality of heat transfer elements; using an optimization framework with a computational model to perform computer simulations of at least the hydrodynamics and heat transfer around the heat transfer elements during the expected operation of the heat transfer device, in order to perform geometric design optimization for each heat transfer element based on an optimization algorithm targeting a predetermined criterion, where the optimization framework is configured to iteratively improve the geometric design of each heat transfer element, and where the geometric designs of the plurality of heat transfer elements are allowed to change independently of each other during the optimization.

[0131] In the shown example, each heat transfer element is parameterized along line 3 in a cross-sectional view perpendicular to the axial path of each heat transfer element 1a, 1b, where during iterative optimization, the optimization framework is configured to adjust the thickness distribution of each heat transfer element along line 3 to obtain the overall shape of each heat transfer element 1a, 1b, and where a plurality of nodes 5 are defined along the length of each heat transfer element 1a, 1b, and where the thickness distribution of the heat transfer element is determined by the distance from each of these plurality of nodes 5 to line 3 of the corresponding heat transfer element 1a, 1b.

[0132] The line is selected to be substantially parallel to the general flow direction between the inlet and outlet of the heat transfer device, where the plurality of heat transfer elements are arranged between the inlet and outlet.

[0133] This computer-implemented method can provide an improved optimization method for the design of the heat transfer device, specifically focusing on the geometric optimization of each heat transfer element. Each heat transfer element can be parameterized around line 3, where the thickness distribution around this centerline determines the overall shape of the element. By adjusting the thickness distribution, the shape of each pipe can be optimized independently.

[0134] For each element, a plurality of nodes 5 are used to provide a comprehensive design space for the heat transfer device. This method improves the optimization efficiency while covering a rich design space.

[0135] The present invention uses shape optimization instead of topology optimization. This method is more efficient. Since a defined surface is used and the flow with wall modeling is adopted, viscosity and turbulence can be modeled more accurately.

[0136] The optimization framework can adopt, for example, a first-order optimization method using gradients. Different from computationally intensive traditional methods, the adjoint method can be used to calculate the gradients of all sensitivities simultaneously, thus significantly accelerating the optimization process.

[0137] This method can provide CAD-based parameterization, provide precise geometric control and allow effective setting of constraints and bounds on design parameters. The optimized design can significantly reduce the pressure drop and / or improve the hydrodynamic performance while constraining heat transfer, thus producing a more efficient heat transfer device.

[0138] In some examples, the method is configured to avoid complete remeshing. For this purpose, in some examples, after each optimization step, the mesh elements can be deformed based on the shape modification to ensure computational efficiency.

[0139] The optimization framework of the present invention can start from the initial geometric design of the heat transfer element. An optimization algorithm is used to iteratively improve the design. During the optimization process, the design of each heat transfer element is allowed to vary independently. In some examples, line 3 can be oriented along the general flow direction. In some examples, the initial design of the element is a teardrop shape. In some examples, the heat transfer element represents a pipe or a fin in a heat transfer device.

[0140] The distance from the baseline 3 determines the shape of the heat transfer element. By using multiple thick lines on each side of the heat transfer element (see nodes), a rich design space is ensured while maintaining an effective optimization process.

[0141] This method can handle geometric parameters and flow conditions such as flow velocity. This dual consideration ensures that the optimized shape directly affects the flow dynamics.

[0142] In some examples, the heat transfer element is a pipe in a tube heat exchanger, where the pipe is hollow and fluid flows through these pipes for heat exchange. However, the pipe can also be integrated with a resistor for resistive heating. In some examples, the heat flux of the heat transfer element is constant, which is particularly relevant to the design of radiators. In the 3D perspective, the design of the heat transfer element can consider different boundary conditions based on the heat transfer mechanism.

[0143] This method provides a method in which the geometric parameters of each pipe are (completely) independent of each other, which is very different from the existing methods where all pipes usually share the same design. By integrating advanced optimization techniques and providing a rich design space, the present invention ensures an efficient and effective heat exchanger design.

[0144] Figure 2 A schematic diagram shows an exemplary optimization method for parallel shape optimization of a heat transfer surface using CAD - based parameterization with the adjoint method for gradient - based optimization. The gradient - based optimizer enables faster convergence of multiple design variables, while the adjoint method reduces the computational cost of calculating gradients for a large number of design variables. Employing CAD - based parameterization in shape optimization provides enhanced control over the design surface, facilitating the imposition of geometric constraints. Thus, this method can improve the performance of the heat transfer surface. The optimization framework can utilize CFD simulation, adjoint calculation, and mesh deformation.

[0145] In Figure 2 an exemplary optimization framework is shown. The main components of the optimization framework include:

[0146] 1. Pre - processing: Input the mesh of the baseline design into a CAD parameterization tool to obtain an initial design vector (α 0 ), which contains the parameterized representation of all design surfaces in the baseline geometry.

[0147] 2. Optimizer: Start the optimization loop using the initial design vector.

[0148] 3. Surface generation: Generate the coordinates (X surf ) of the design surface, calculate the CAD sensitivity (dX surf / dα), and evaluate geometric constraints (c g ), such as perimeter, internal area, etc., and the sensitivity of geometric constraints (dc g / dα).

[0149] 4. Mesh deformation: Deform the mesh using the coordinates of the design surface to obtain the mesh output (X vol ).

[0150] 5. Flow solver: Perform CFD calculations and evaluate the objective function (J) and flow - related constraints (cf).

[0151] 6. Adjoint solver: Perform adjoint calculations to calculate the sensitivities of the cost function with respect to the mesh coordinates (dJ / dX vol , dc f / dX vol ).

[0152] 7. Optimizer: Utilize the gradients evaluated throughout the process and continue the optimization loop until the convergence criterion is met.

[0153] The optimization framework can be configured to accommodate multiple optimizers to obtain an optimal design of the heat transfer geometry. In some examples, one or more gradient-based optimizers are used. The gradient value can be obtained from the dot product of the nodal sensitivity (i.e., the sensitivity of the objective function with respect to the surface nodal coordinates) and the CAD sensitivity (i.e., the sensitivity of the nodal coordinates with respect to the design variables), as shown in the following equation:

[0154]

[0155] The CAD sensitivity can be obtained through surface generation. The nodal sensitivity can be calculated using the output of the adjoint solver and mesh deformation.

[0156] The heat transfer design surface can be parameterized using a generation / construction method that characterizes the geometry using, for example, Non-Uniform Rational B-Spline (NURBS) curves. The camber-thickness approach can be used, i.e., by utilizing a camber line and two thickness distributions (upper and lower) around the camber line, to parameterize each heat transfer design surface. The entire parameterized surface can be selected to be G 2 continuous.

[0157] The output of surface generation can be:

[0158] · Surface nodal coordinates (Xsurf)

[0159] · CAD sensitivity (dXsurf / dα), i.e., the sensitivity of the nodal coordinates with respect to the design variables

[0160] · Geometric constraint (c g ) value

[0161] · Sensitivity of the geometric constraint (dcg / dα)

[0162] The CAD sensitivity and the sensitivity of the geometric constraint can be calculated with machine precision using the complex-step method. Then, Xsurf can be fed into the mesh deformation section to obtain the corresponding mesh.

[0163] In an exemplary optimization framework, the volume deformation part can use a linear elastic mesh deformation method. This method is based on linear elastic equations, where the surface deformation is applied as a Dirichlet condition. The deformation can be performed, and a mesh (Xvol) for performing a flow simulation can be output. This volume deformation method provides an integrated, robust, and flexible method to obtain new meshes for different surface geometries. This method is computationally more efficient than remeshing. However, for large deformations, the mesh quality may be affected. Various other mesh deformation techniques can be used.

[0164] A flow solver can be used to evaluate the performance of the heat transfer surface, and this flow solver uses the finite volume method to simulate steady-state, incompressible turbulent flow. In some examples, the flux-difference-splitting (FDS) method is used to discretize the convective flux. The Monotone Upstream-Centered Schemes for Conservation Laws (MUSCL) method is used to achieve second-order accuracy. The Green-Gauss theorem can be used to calculate the spatial gradients of the flow variables. For turbulence modeling, for example, the Spalart-Allmaras turbulence model can be used because this model has the advantage of lower computational cost for reasonable accuracy. The first-order scalar upwind method can be used to model the convection of turbulent variables. A pseudo-transient method with Euler implicit time integration can be used to achieve a steady-state solution. The flexible generalized minimum residual (FGMRES) method with an incomplete LU preconditioner can be used to solve the linearized governing equations. The flow state (U) is used to calculate the objective function (J) and the flow-related constraint value (c f ).

[0165] In some examples, an adjoint solver is employed. The adjoint solver forms an important part of this optimization framework due to its ability to efficiently calculate gradients. A discrete adjoint solver based on algorithmic differentiation (AD) can be configured to solve the adjoint equation. The discretization scheme of the adjoint solver can be the same as that of the flow solver. The adjoint state is used to calculate the objective function with respect to the volume coordinates dJ / dX volThe sensitivity. In addition, the surface node sensitivity can be calculated, that is, the sensitivity of the objective function with respect to the surface node coordinates

[0166] Figure 3A and Figure 3B and Figure 3C Fig. shows a schematic diagram of exemplary analysis results of a case study of a tubular heat exchanger.

[0167] For this case study, a bare-tube air-to-fluid heat exchanger was selected to demonstrate the potential of the optimization framework in improving the performance of heat transfer equipment. The selected reference geometry consists of a staggered tube arrangement, which is designed as a proof of concept to provide a heat transfer load similar to that of a small / microchannel heat exchanger but with a lower air-side pressure drop. In this case study, a geometry consisting of a staggered arrangement of 7 flow-through tubes was selected as the baseline geometry of the tubular heat exchanger.

[0168] Since the case study focuses on improving the air-side flow and heat transfer performance, the computational domain for the flow simulation was simplified to include only the air side, where the tubes were modeled as isothermal walls. The inlet is located at a distance of 1 widthlength (wt) from the leading edge of the first tube, while the outlet is 3 wt from the trailing edge of the last tube. These upstream and downstream computational domain distances were determined based on the sensitivity analysis performed to minimize the domain size without affecting the accuracy of the results. The flow conditions selected for this case study correspond to an air volume flow rate of 0.03 m 3 / s. At a temperature of 300 K, the inlet was specified to have a velocity of 3 m / s. The free-stream turbulence intensity at the inlet is 5%, and the ratio of turbulent to laminar viscosity is 10. A pressure outlet boundary condition with a value of 0 Pa was applied at the outlet. The top and bottom boundaries were set as periodic boundaries. For the tube walls, a constant-temperature no-slip boundary condition with a temperature value of 350 K was applied. At the characteristic length of the tube width, the Reynolds number is 530, and the turbulent effect is more prominent downstream of the domain. It is assumed that the fluid properties are constant.

[0169]

[0170] A CFL number of 10 was selected for the optimization study to ensure the stability of the flow solution. The flow simulation was carried out using a 5th-order convergence criterion.

[0171] In this case study, the objective is to minimize the pressure drop across the heat exchanger while maintaining the required minimum heat transfer rate.

[0172] The objective of the optimization problem is to minimize the air - side pressure drop (ΔPair) of the entire heat exchanger, which represents the pumping loss of the heat exchanger application. The pressure drop is evaluated using the output of the flow solver, while the sensitivity is calculated using the output of the adjoint solver.

[0173] In the camber - thickness method, the design variables are the upper and lower thickness distribution parameters. The initial values of these design variables are calculated by performing surface matching of the baseline design to obtain a suitable parametric representation. Bounds are imposed on the design variables to ensure that the optimized pipe shape is physically meaningful and to avoid self - intersecting pipes and pipes intersecting each other's surfaces.

[0174] The optimization problem includes constraints on the flow and geometric characteristics of the tube - type heat exchanger. Flow constraints are imposed on the heat transfer rate in the heat exchanger, represented by the temperature difference between the fluid outlet and inlet. This constraint ensures that the thermal performance of the heat exchanger remains at the desired level. The temperature difference is obtained from the output of the flow solver, and its sensitivity is calculated using the output of the adjoint calculation.

[0175] Geometric constraints are imposed on the area enclosed within each pipe (a) to ensure that the pressure drop of the fluid flow within the pipe (not modeled in the CFD simulation) does not become too high and thus does not adversely affect the overall performance of the heat exchanger. To calculate the area enclosed by each pipe, the shoelace method is used. The shoelace method, also known as the Gauss area formula, is a simple and effective technique for calculating the area of any non - intersecting polygon when the vertex coordinates are known.

[0176] The adjoint method allows for the calculation of gradients in a computationally efficient manner because each cost function requires only one adjoint calculation to compute its gradient values with respect to all design variables. On the other hand, the computational cost of gradient calculation using the finite - difference method is higher because the associated computational cost increases with the number of design variables.

[0177] Figure 3 shows the optimized non - identical pipe geometries. For the optimal non - identical pipe geometries, it is observed that all pipes except the first (pipe 1) and the last (pipe 4) gradually tilt forward near the leading edge in the flow - direction. Notably, the profiles of all pipes except pipes 1 and 4 are similar to but have some differences from the profiles in the case of the optimal identical - pipe geometry. This difference is evident near the leading edge, where a flatter region near the circular leading edge followed by a steeper rising region can be observed compared to the identical - case geometry. This can be attributed to the different incident - flow profiles on the central pipes due to the varying trailing - edge shape of pipe 1.

[0178] Further inspection revealed that the leading edge of duct 1 is more rounded, which potentially contributes to greater forming resistance. However, the shape of the remainder of the duct after the curvature of the leading edge ensures a smooth flow path to reduce flow separation. Compared to the same duct geometry, the flow path is wider and there are no repeated contractions and expansions in the flow path as seen in the baseline, resulting in a lower pressure drop in this case. This is particularly evident near duct 4. Compared to duct 1, a flatter leading edge and a more rounded trailing edge are observed at duct 4, which causes a mirror effect. Due to its gradual slope, this shape ensures a wider flow path compared to the other two cases and minimizes flow separation compared to the baseline. Figure 3B Velocity contours are shown, providing a more detailed picture of the flow effects. A significantly lower maximum velocity magnitude is observed for the non-identical duct cases when compared to the baseline throughout the internal flow path. This difference becomes more pronounced near duct 4 when compared to the same duct. Due to the gentler geometric slope, the maximum velocity is lower, and thus the pressure loss is reduced due to the decreased need for flow acceleration and deceleration. Figure 3A The corresponding pressure contours are shown. Figure 3C The temperature contours in [reference] indicate a similar trend for different geometries, suggesting that the heat transfer rate remains consistent even when significantly reduced.

[0179] In this example, an adjoint-based shape optimization method is combined with CAD-based parameterization to simultaneously optimize multiple heat transfer surfaces. CAD-based parameterization helps to fully control the design surface, enabling better imposition of functional and manufacturing-related geometric constraints. The adjoint method effectively calculates the gradient of the objective function with respect to the design variables used to parameterize the multiple heat transfer surfaces. However, other methods can also be used.

[0180] In Figures 3A to 3C the results, the optimization framework is applied to a case study of optimizing a finned-tube heat exchanger. The aim is to minimize the pressure drop of a tube heat exchanger with non-circular ducts while maintaining the heat transfer rate. In summary, using gradient-based optimization can lead to rapid optimization convergence. The best designs are obtained through 12 and 20 design iterations for the same duct and non-identical duct cases, respectively. Additionally, the local flow and heat transfer effects of each duct are considered to simultaneously optimize these ducts for higher performance improvement. Using the best identical tubes, the performance is improved by 19.41%, while using the best non-identical tubes, the pressure drop is 25.05% lower than when using the baseline design.

[0181] It should be understood that in some examples, the term "computerized simulation of hydrodynamics" refers to computational methods and processes used to model, analyze, and predict the behavior of fluids within or around a specific structure such as a heat transfer element in a computer / virtual environment.

[0182] It should be understood that these computerized simulations include a series of fluid-related simulations. For example, in some embodiments, factors such as fluid viscosity, turbulence, and boundary conditions are considered, and "flow simulation" is used to model and analyze the movement or propagation of fluid through or around a heat transfer element.

[0183] In addition, "flow rate simulation" can be employed to predict and evaluate the volume or mass of fluid passing through a given section of a heat transfer device per unit time. Such simulation can provide insights into the efficiency and effectiveness of fluid flow within the system.

[0184] Furthermore, "flow direction simulation" is designed to model and determine the main trajectories or orientations of fluid movement relative to a heat transfer element and other components of the heat transfer device. This can assist in understanding the impact of design changes on fluid dynamics and optimizing the orientation and configuration of the heat transfer element.

[0185] In summary, these computerized simulations of fluid dynamics are used to provide a comprehensive understanding of fluid behavior in the context of a heat transfer device. By leveraging these simulations, design parameters can be iteratively improved and optimized to achieve desired performance results and ensure the effective operation of the heat transfer device.

[0186] It should be understood that the method may include computer-implemented steps. All of the above steps can be computer-implemented steps. Embodiments may include a computer device in which the process is executed. The present invention also extends to a computer program suitable for putting the present invention into practice, particularly a computer program on or in a carrier. The program may be in the form of source code or object code, or any other form suitable for implementing the process according to the present invention. The carrier can be any entity or device capable of carrying the program. For example, the carrier may include a storage medium such as a read-only memory (ROM), such as a semiconductor ROM or a hard disk. In addition, the carrier can be a transmissible carrier such as an electrical or optical signal, and the signal can be transmitted via a cable or optical fiber or by radio or other means (such as via the Internet or the cloud).

[0187] Some embodiments can be implemented, for example, using a machine or a tangible computer-readable medium or article that can store instructions or a set of instructions, which, if executed by the machine, can cause the machine to perform the method and / or operations according to the embodiments.

[0188] Various embodiments may be implemented using hardware elements, software elements, or a combination of both. Examples of hardware elements may include a processor, a microprocessor, a circuit, an application specific integrated circuit (ASIC), a programmable logic device (PLD), a digital signal processor (DSP), a field programmable gate array (FPGA), logic gates, registers, semiconductor devices, microchips, chip sets, etc. Examples of software may include software components, programs, applications, computer programs, application programs, system programs, machine programs, operating system software, mobile applications, middleware, firmware, software modules, routines, subroutines, functions, computer-implemented methods, processes, software interfaces, application program interfaces (APIs), methods, instruction sets, computing code, computer code, etc.

[0189] In this document, the present invention is described with reference to specific examples of embodiments of the invention. However, it is apparent that various modifications, variations, substitutions, and alterations can be made to the present invention without departing from its essence. For purposes of clear and concise description, features are described herein as part of the same or separate embodiments, however, alternative embodiments having combinations of all or some of the features described in these separate embodiments are also contemplated and are understood to fall within the framework of the present invention outlined by the claims. Accordingly, the specification, drawings, and examples are considered illustrative rather than restrictive. The present invention is intended to cover all alternatives, modifications, and variations falling within the scope of the appended claims. Additionally, many of the elements described are functional entities that may be implemented as discrete or distributed components in any suitable combination and location or in combination with other components.

[0190] In a claim, any reference numeral placed between parentheses shall not be construed as limiting the claim. The word “comprising” does not exclude the presence of other features or steps than those listed in a claim. Further, the word “a / an” shall not be construed as limited to “only one,” but rather is used to mean “at least one,” and does not exclude a plurality. As used herein, the term “and / or” includes any and all combinations of one or more of the associated listed items. The fact that certain measures are recited in different claims does not indicate that a combination of these measures cannot be used to advantage.

Claims

1. A computer-implemented method for systematically configuring, evaluating, and optimizing a heat transfer device, the heat transfer device comprising a plurality of heat transfer elements arranged in a structured manner, each heat transfer element extending along an axial path, the method comprising: Starting with an initial geometric design of the plurality of heat transfer elements; performing computer simulations of fluid dynamics and heat transfer around at least the heat transfer elements during expected operation of the heat transfer device using an optimization framework having a computational model to perform geometric design optimization for each heat transfer element based on an optimization algorithm targeting a predetermined criterion, wherein the optimization framework is configured to iteratively improve the geometric design of each heat transfer element; and wherein The geometric designs of the plurality of heat transfer elements are allowed to be varied independently of each other during optimization.

2. The method according to claim 1, wherein: Each heat transfer element is parameterized along a line in a cross-sectional view perpendicular to an axial path of the heat transfer element, wherein during iterative optimization, the optimization framework is configured to adjust a thickness distribution of each heat transfer element along the line to obtain an overall shape of each heat transfer element, wherein a plurality of nodes are defined along the length of each heat transfer element, and wherein the thickness distribution of the heat transfer element is determined by a distance from each of the plurality of nodes to the line of the corresponding heat transfer element.

3. The method according to claim 2, wherein: The line is selected to be substantially parallel to a general flow direction between an inlet and an outlet of the heat transfer device, the plurality of heat transfer elements being arranged between the inlet and the outlet.

4. A method according to any one of the preceding claims, wherein: The initial geometry of the cross section was designed as a droplet shape.

5. A method according to any one of the preceding claims, wherein: A first subset of the heat transfer elements is selected, the first subset comprising at least one or more front heat transfer elements and one or more rear heat transfer elements arranged within the device, wherein, during optimization, the heat transfer elements in the first subset are allowed to independently assume different geometric designs, and wherein a second subset of the heat transfer elements is selected, wherein, during optimization, the heat transfer elements in the second subset are constrained not to be allowed to independently change their geometric designs.

6. The method according to claim 5, wherein: The second subset includes heat transfer elements located between the one or more front heat transfer elements and the one or more rear heat transfer elements in the heat transfer device.

7. The method according to claim 5 or 6, wherein: The one or more front heat transfer elements include at least one row of heat transfer elements at the front side of the plurality of heat transfer elements in the device, and wherein the one or more rear heat transfer elements include at least one row of heat transfer elements at the rear side of the plurality of heat transfer elements in the device.

8. A method according to any one of the preceding claims, wherein: The optimization framework is configured to further adjust at least one of: a spacing distance between the heat transfer elements in a length direction, or a spacing distance between the heat transfer elements in a direction perpendicular to the length direction of the heat transfer elements.

9. A method according to any one of the preceding claims, wherein: The three-dimensional shape optimization is performed by using a plurality of lines for each heat transfer element, each line being located in a plane at a distance from one another in the axial path of the respective heat transfer element to define the three-dimensional geometry of the heat transfer element.

10. The method according to claim 9, wherein: The shape of the cross section is allowed to vary along the axial path during optimization.

11. A method according to any one of the preceding claims, wherein: The length of the heat transfer element along its axial path is parameterized and allows the length to be varied during optimization.

12. The method according to any one of the preceding claims 2 to 11, wherein: At least 6 nodes are used, preferably at least 10 nodes are used, and more preferably at least 12 nodes are used.

13. A method according to any one of the preceding claims, wherein: Shape optimization is performed using a first order optimization method utilizing gradients calculated using the adjoint method.

14. A computing system for designing a heat transfer device, comprising: processor; as well as A non-transitory machine-readable medium comprising code configured to instruct the processor to perform the steps according to any one of the preceding claims 1 to 13.

15. A non-transitory computer-readable medium comprising code configured to instruct a processor to perform the steps according to any one of the preceding claims 1 to 13.

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