中文赛题：给环境装空调：公共空间降温中的能源浪费建模
背景
大家都知道，敞着冷冻柜的门会造成浪费。冷空气逸出、暖空气进入，冷冻柜就必须消耗额外的能源来维持所需温度。然而，许多现代公共空间并未遵循这一原则，而是有意消耗能源，为并未完全封闭的区域降温。露天场所（Open-air venues），例如体育场公共通道或露天音乐剧场，以及半开放公共空间（Semi-open public spaces），例如公共交通站点、机场航站楼和公共等候区，尽管持续暴露于周围环境中，仍使用降温系统来保障顾客的舒适与安全。在这些场景下，一部分降温作用惠及目标人群，另一部分则散失到大气中。
随着城市气温升高、能源成本增加以及极端高温事件日益频繁，场所运营者面临一项艰巨挑战：既要提供舒适、安全的环境，又要负责任地使用能源。判断一种降温策略是否有效，不能只测量温度。设施设计、人群规模、天气状况、空气流动、运营成本，以及访客的舒适与安全等因素都发挥着作用。
“通过降温管理缓解热影响”（Heat impact Mitigation through Cooling Management，HiMCM）团队同时管理露天场所和半开放公共空间，目前正在重新评估其降温措施，希望了解其系统向访客提供有效降温的效率。由于不同设施和气候条件下的情况各异，该公司希望建立一个通用框架，用于比较不同降温方法，并识别改进机会。
你们团队受 HiMCM 委托研究这一问题。请建立一个数学模型，评估露天场所和半开放公共空间中降温系统的有效性，并就如何平衡舒适、安全、能源消耗和成本提出建议。
要求
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理解问题。杂货店中的敞开式冷冻陈列柜（Open freezer cases）持续消耗能源，从食品和周围空气中移除热量。在衡量降温效率时，应考虑冷冻陈列柜的哪些方面？效率是否应仅取决于能源消耗？论证降温效率指标应包含哪些量，并以此作为下述降温效率模型的设计依据。
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建立模型。某城市正在寻找方法，让人们在炎热夏日等候公交车或轨道交通时保持舒适。
a. 公交车站：一项提议是在四周开放的公交候车亭（Bus stop shelter）中安装降温系统。城市规划者希望确定哪种系统效率最高，但目前只掌握以下信息：
降温系统 对候车亭的影响 能源使用量 A. 风扇系统 使空间内体感温度最多降低 3°C 0.25 kW B. 蒸发式冷风机 使空气温度最多降低 5°C 1.2 kW C. 大型蒸发式冷风机 使空气温度最多降低 8°C 2.5 kW 为公交车站建立一个降温效率指标。你们可以考虑的因素包括但不限于：降温区域的大小、气候条件（Climate conditions）、能源消耗，以及受益于降温的人数。
b. 轨道交通站候车区：针对半开放的轨道交通站候车区，按需修订和改进模型，以衡量降温效率。清楚说明修改了什么、为什么有必要修改，以及这些修订如何提升模型的实用性或准确性。
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应用模型。你们的降温效率模型能否适用于不同规模的场景？将模型应用于至少两个具体场所。确保这些场所位于不同气候区，或采用不同类型的降温系统，以展示模型的稳健性。可选择的案例包括：
你们可以使用真实世界的数据；无法获得真实数据时，也可在明确假设的基础上采用合理估计。利用模型比较不同场所降温策略的效率，并识别对高效降温贡献最大的特征。
- 体育场公共通道；
- 露天音乐剧场；
- 餐厅户外露台；
- 温暖气候地区的露天机场航站楼；
- 露天购物中心的开放式步行通道；或
- 其他露天场所或半开放公共空间。
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扩展模型并反思分析。一种降温方案即使效率很高，也未必在总体上最有效。扩展模型，通过平衡降温表现、访客体验、能源消耗与成本来评估降温有效性。清楚描述模型如何处理这些相互竞争的目标。
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分享模型及其结果。为所选场所提出降温系统使用指南。讨论在极端高温期间，运营者如何在维持安全、有效环境的同时，平衡访客舒适度、可持续性与成本。
a. 备忘录：围绕所选场所之一，向 HiMCM 首席运营官提交一份1–2 页的备忘录。概述主要发现，并就该场所降温系统的使用提出可执行的建议。建议应说明如何平衡影响降温有效性的各项取舍。
b. 博客文章：撰写一篇博客文章，供 HiMCM 向公众解释这些结果。HiMCM 希望围绕以下问题开展公众科普：“在这些露天场所或半开放公共空间中，我们消耗的能源究竟换来了多少降温效果？”
提交要求
你们提交的 PDF 解决方案总页数不超过25 页，应包括：
- 一页摘要页。
- 目录。
- 完整的解决方案。
- 致首席运营官的 1–2 页备忘录。
- 参考文献列表。
- AI 工具使用报告（如使用了 AI 工具；此部分不计入 25 页限制）。
术语表
- Open-air venue（露天场所）：活动主要在户外举行、暴露于周围环境之中，而非由墙壁和屋顶封闭的场所。
- Semi-open public space（半开放公共空间）：可供公众进入、由屋顶、墙壁或其他结构部分围合，同时仍与室外保持大量空气交换的区域。
- Open freezer case（敞开式冷冻陈列柜）：杂货店或便利店使用的一种冷藏陈列设备，在保持商品低温的同时向周围空气敞开，使顾客无需开门即可方便地查看和取用商品。
- Bus Stop（公交车站）：道路旁指定的地点，公交车在此短暂停靠，供乘客上下车。
- Evaporative cooler（蒸发式冷风机）：使暖空气通过浸水湿帘来降低空气温度的降温设备。水分蒸发时从空气中吸收热量，产生较冷的空气，再通过风扇使其循环流动，其能耗低于传统空调。
- Climate conditions（气候条件）：可包括纬度或地理位置、温度、湿度、日照或风。
- Blog post（博客文章）：在网站上发布的文章或文字内容。
Problem B: Air Conditioning the Environment: Modeling Energy Waste in Public Cooling
Background
Everyone knows it is wasteful to leave the door of the freezer open. As cold air escapes and warm air enters, the freezer must use additional energy to maintain the desired temperature. Yet many modern public spaces do not follow this principle, as they intentionally expend energy to cool areas that are not fully enclosed.Open-air venues, like stadium concourses or concert amphitheaters, and,semi-open public spaces, like transit stations, airport terminals, and public waiting areas, use cooling systems to keep customers comfortable and safe, despite constant exposure to the surrounding environment. In these settings, some of the cooling reaches its intended audience, while some dissipates into the atmosphere.
As cities become warmer, energy costs increase, and extreme heat events become more frequent, venue operators face a difficult challenge trying to provide comfortable and safe environments while using energy responsibly. Determining whether a cooling strategy is effective requires more than measuring temperature alone. Factors such as facility design, crowd size, weather conditions, airflow, operating costs, and visitor comfort and safety all play a role.
The Heat impact Mitigation through Cooling Management (HiMCM) team that manages both open-air venues and semi-open public spaces is reevaluating its cooling practices and wants to understand how efficiently its systems deliver useful cooling to visitors. Because conditions vary across facilities and climates, the company seeks a general framework that can be used to compare different cooling approaches and identify opportunities for improvement.
Your team has been hired by HiMCM to investigate the problem. Develop a mathematical model to evaluate the effectiveness of cooling systems in both open-air venues and semi-open public spaces and provide recommendations for balancing comfort, safety, energy consumption, and cost.
Requirements
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Understand the Problem.Open freezer casesin grocery stores continuously use energy to remove heat from food and the surrounding air. What aspects of a freezer case should be considered when measuring cooling efficiency? Should efficiency depend only on energy use? Justify the quantities that should be included in a measure of cooling efficiency. Use your response to motivate the design of your cooling efficiency models below.
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Create Your Model.A city is looking for ways to keep people comfortable while they wait for public transportation by bus or rail on hot summer days.
a.For the bus, one proposal is to install a cooling system in an open-sidedbus stop shelter. City planners want to determine which system is the most efficient, but at this time, only know the following:
Cooling System Effect on Shelter Energy Use A. Fan System Makes space feel up to 3°C cooler 0.25 kW B. Evaporative Cooler Lowers air temperature up to 5°C 1.2 kW C. Large Evaporative Cooler Lowers air temperature up to 8°C 2.5 kW Develop a measure of cooling efficiency for the bus stop. You may want to consider factors, including, but not limited to, the size of the cooled area,climate conditions, energy use, and the number of people benefiting from the cooling.
b.For a semi-open rail-station waiting area, revise and improve your model as necessary to measure cooling efficiency. Clearly explaining what changed, why the change was necessary, and how the revision improved the model’s usefulness or accuracy.
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Apply Your Model.Does your cooling efficiency model scale? Apply your model to at least two specific venues. Ensure these venues are in different climates or that they use different types of cooling systems to demonstrate the robustness of your model. Possible case studies include:
You may use real-world data or reasonable estimates with assumptions when real-world data is not available. Use your model to compare the efficiency of cooling strategies across venues and identify the characteristics that contribute most to efficient cooling.
- Stadium concourses,
- Concert amphitheaters,
- Outdoor restaurant patios,
- Open-air airport terminals in warm climates,
- Open walkways in outdoor malls, or
- Other open-air venues or semi-open public spaces.
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Expand Your Model and Reflect on Your Analysis.A cooling solution that is highly efficient may not be the most effective overall. Extend your model to evaluate cooling effectiveness by balancing cooling performance, visitor experience, energy consumption and cost. Clearly describe how your model accounts for these competing objectives.
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Share Your Model and its Results.Propose guidelines for the use of cooling systems in your venues. Discuss strategies for how operators can balance visitor comfort, sustainability, and cost while maintaining safe and effective environments during periods of extreme heat.
a.Prepare a one-to-two-page memorandum to the Chief Operations Officer of HiMCM about one of your chosen venues. In your memorandum, summarize your major findings and provide actionable recommendations regarding the use of cooling systems for that venue. Your recommendations should address balancing the trade-offs of cooling effectiveness.
b.Create a blog post that HiMCM can use to explain these results to the public. HiMCM wants to educate the public surrounding the question of “How much cooling are we getting for the energy we use in these open-air venue or semi-open public spaces?”.
Submission Guidelines
Your PDF solution of no more than 25 total pages should include:
- One-page Summary Sheet.
- Table of Contents.
- Your complete solution.
- One-to-two-page memorandum to the Chief Operations Officer.
- References list.
- Report on Use of AI Tools (If used does not count toward the 25-page limit.).
Glossary
- Open-air venue– a place where events are held primarily outdoors and are exposed to the surrounding environment rather than being enclosed by walls and a roof.
- Semi-open public space– a publicly accessible area that is partially enclosed by roofs, walls or other structures while still allowing for a significant air exchange with the outdoors.
- Open freezer case– a refrigerated display used in grocery or convenient stores that keeps products cold while remaining open to the surrounding air, allowing customers to easily view and access items without opening a door.
- Bus Stop– A designated roadside location where a bus briefly halts to let passengers get on or off.
- Evaporative cooler– cooling device that lowers air temperature by passing warm air through water-soaked pads. As the water evaporates, it absorbs heat for the air, producing cooler air that is then circulated by a fan, using less energy than traditional air conditioners.
- Climate conditions– could include latitude or location, temperature, humidity, solar exposure or wind.
- Blog post– an article or piece of written content published on a website.
