結合過濾原理與風機性能曲線之空氣清淨機效能優化研究

Abstract

為避免濾材過度設計導致不必要之壓降損失與過濾性能下降，本研究建立一套整合濾材與風機特性之數值模擬方法，結合單一纖維理論、濾材阻抗模型與風機性能曲線(P-Q curve)，用以預測不同操作條件下的最佳濾材厚度(Topt)與潔淨空氣輸出率(Clean Air Delivery Rate, CADR)。本方法不僅可重現Rudnick(2004)所提出在擴散主導條件下「效率為82%時厚度為最適值」的特例，更可針對實務應用中常見之操作條件進行延伸應用，彌補既有研究未涵蓋風機特性與粒徑分布等限制。

本研究主要可分成數值方法的確立以及影響濾材設計厚度參數的探討等兩階段。前者是以Rudnick所使用的參數以及結果為基準，透過比對的方式，藉以驗證本研究所建立之數值分析方法的準確性與可行性。後者則應用該方法，擴大探討不同參數包括濾材纖維直徑、填充密度、風機特性曲線、過濾面積、與粒徑大小等對Topt與CADR的影響，同時驗證Topt下的收集效率並非為82%的主張。

第一階段驗證所建立之數值方法準確性，並探討濾材結構均勻性（以均勻係數ε表示）對厚度設計的影響。當ε增大時，單位厚度濾材之效率與阻抗同步下降，須透過厚度線性補償方可維持最大CADR；一旦達到Topt條件後，整體CADR並不會受到ε的變動所影響，顯示濾材結構不均可透過厚度調整予以修正。另分析指出，P-Q curve斜率亦影響Topt設計。對通過相同起始操作點，但斜率不同的P-Q curve而言，較平緩的P-Q curve允許以微幅減少厚度換取更大流量；而斜率較大者，則需設計較厚濾材。

第二階段則探討Topt與CADR如何受到風機類型與轉速、濾材參數（纖維直徑與填充密度）、過濾面積及目標粒徑等交互因素之影響。模擬結果顯示，設定P-Q curve最大流量為70,000 L/min，最大靜壓為4.5 mmH2O下，Concave down型P-Q curve可在相同阻抗下輸出更大流量，因此，可以適當地增加濾材的厚度，用部分風量的減少以換取較高的過濾效率，藉此提升整體的CADR。另一方面，若僅透過提高風機轉速來增加過濾風量，卻未同步調整濾材厚度，雖然整體CADR仍可提升，但與最佳設計條件相比，其效能差異最高可能達41%。因此，在實務應用上，若濾材厚度無法隨風機轉速同步調整，建議採用固定轉速運轉，以確保系統維持在最佳能源效率的狀態。

除了風機特性外，濾材面積增加可降低表面風速、並提升擴散機制的收集效率，但每單位濾材過濾面積下提供的CADR值隨過濾面積增加而遞減，設計時應考慮空氣清淨機所能容納的濾材體積；此外，纖維越細或填充密度越高，越能於較小厚度下達成設計效率；Topt主要取決於針對特定目標粒徑所需達成之效率。模擬結果亦指出，相同濾材條件及風速下，目標粒徑與最易穿透粒徑(Most Penetrating Particle Size, MPPS)之相對位置將決定厚度增減的變動趨勢。

綜合而言，Topt並無固定數值可供套用，須依據風機性能、濾材結構與目標粒徑條件逐項計算調整。本研究所提出之數值方法不僅較解析法更易操作，並將單一條件下之建議值延伸為多參數設計曲線，可作為高性能空氣清淨設備設計之參數化工具。未來若進一步結合駐極技術，則有機會在不增加濾材阻抗的情況下進一步提升CADR表現。

To mitigate unnecessary pressure drop losses and performance degradation caused by overdesigned filters, this study develops a numerical simulation framework that integrates filter and fan characteristics. By combining single fiber theory, filter pressure drop models, and fan performance curves (P-Q curves), the proposed method predicts the optimal filter thickness (Topt) and Clean Air Delivery Rate (CADR) under various operating conditions. This approach not only reproduces the specific case proposed by Rudnick (2004), in which a filter efficiency of 82% is optimal under diffusion-dominated conditions, but also extends its applicability to practical scenarios, addressing limitations in prior studies that overlooked fan characteristics and particle size distributions.

The research is organized into two phases: the development of the numerical method and the examination of parameters that influence filter thickness design. The first phase validates the accuracy and feasibility of the proposed numerical method by benchmarking it against Rudnick’s parameters and results. The second phase utilizes this method to investigate the effects of various parameters—including fiber diameter, packing density, fan performance curves, filter area, and particle size—on Topt and CADR, while questioning the assumption that Topt consistently corresponds to an 82% efficiency.

In the initial phase, the accuracy of the numerical method is validated, and the influence of filter structure uniformity—represented by the homogeneity factor (ε) on thickness design is analyzed. As ε increases, both the efficiency and impedance per unit thickness decrease, necessitating linear thickness compensation to sustain maximum CADR. Once Topt is achieved, CADR remains unaffected by variations in ε, indicating that structural non-uniformity can be corrected through thickness adjustments. Additionally, the slope of the P-Q curve significantly influences the design of Topt. For P-Q curves that pass through the same initial operating condition but exhibit different slopes, a flatter curve permits a slight reduction in thickness to achieve higher airflow, while a steeper curve necessitates a thicker filter.

The second phase examines how Topt and CADR are influenced by the interplay of fan type, rotational speed, filter parameters (such as fiber diameter and packing density), filter area, and target particle size. Simulation results indicate that, with a P-Q curve set at a maximum flow rate of 70,000 L/min and a maximum static pressure of 4.5 mmH2O, a concave-down P-Q curve delivers higher airflow at equivalent impedance. This configuration allows for a slightly thicker filter to achieve a greater CADR. Additionally, it provides a higher CADR per unit filter area compared to other types of P-Q curves. As fan speed increases, airflow scales proportionally; however, failing to adjust filter thickness to Topt can result in a CADR loss of up to 41%. Therefore, air purifiers should be designed with a single fan-filter combination operating at a fixed speed, rather than incorporating multiple flow settings, to maintain optimal operating conditions.

Beyond fan characteristics, increasing the filter area reduces face velocity, thereby enhancing the collection efficiency of diffusion-dominated mechanisms. However, the CADR contribution per unit filter area diminishes as the area increases, necessitating consideration of the volumetric constraints of the air purifier during the design process. Utilizing finer fibers or higher packing densities enables design efficiency to be achieved with thinner filters, while Topt primarily depends on the efficiency required for a specific target particle size. Simulations further indicate that, under identical filter conditions and face velocity, the relative position of the target particle size in relation to the Most Penetrating Particle Size (MPPS) influences the trend of thickness adjustments.

In summary, Topt is not a constant value; instead, it must be calculated and adjusted based on fan performance, filter structure, and target particle size. The proposed numerical method offers greater operational simplicity compared to analytical approaches and extends single-condition recommendations into multi-parameter design curves, serving as a parameterized tool for designing high-performance air purifiers. Future research that incorporates electret technology could further enhance CADR without increasing filter impedance, thereby unlocking additional performance improvements.