| 摘要: | 本論文針對貧油氫氣/空氣預混球狀火焰於不同壓力條件（p = 1、3、5 atm）下進行實驗，探討火焰不穩定性對球狀火焰傳遞行為、細胞狀結構發展、傳播速度及自我加速特性之影響。在層流球狀火焰向外傳遞過程中，主要受到兩種不穩定性影響：(1)熱擴散不穩定性（thermal-diffusional instability），由於貧油氫氣/空氣混合氣在當量比ϕ = 0.4、0.6、0.8時具有低Lewis數（Le = DT/DM ≈ 0.38、0.43、0.47 ≪ 1），使火焰於初始半徑還小時即產生表面皺褶並形成細胞狀結構；(2)流力不穩定性（hydrodynamic instability，又稱Darrieus–Landau instability），這由火焰燃燒所不可避免之熱膨脹所造成，尤其是在高壓條件下，因火焰厚度變薄，使細胞化結構更易產生。上述不穩定性使火焰表面形成細胞狀結構，增加火焰表面積並提升傳遞速率，進而導致球狀火焰的自我加速。過去研究多以R=R_0+A(t-t_0 )^α推求加速度指數α，然該方法易受初始條件設定影響。為降低此不確定性，本研究採用Wu et al. (2013) 所提出之方法，對R=At^α進行微分以求得球焰傳播速度S_b=dR/dt，並透過對數座標中S_b與R關係之斜率d=(α-1)/α來決定α值。實驗使用本實驗室已建立之雙腔體十字型高壓燃燒器，搭配高速紋影法攝影系統（15,000 frame/s，600 × 600 pixels）記錄火焰由平滑傳播至細胞增生與加速階段之時序紋影影像，並利用SAM2與Cellpose 2.0之人工智慧模型進行火焰輪廓、半徑及細胞數之自動化擷取。結果顯示，ϕ = 0.4（Le ≈ 0.38）條件下不穩定性最為顯著，球焰表面細胞化最早生成且最為密集，火焰亦最早進入自我加速。隨壓力提升至5 atm，因火焰厚度進一步變薄，使溫度與密度梯度增大，細胞化於更早期即大量出現，其α值相較於1 atm與3 atm條件更早上升且變化幅度更為明顯。以ϕ = 0.6、p = 5 atm為例，在12 mm ≤ R ≤ 30 mm時α ≈ 1.34，高於Wu et al. (2013)於10 mm ≤ R ≤ 20 mm內所獲得之α = 1.26；當半徑進一步增加至30 mm ≤ R ≤ 45 mm時，α值上升至約1.42。於1 atm與 3 atm條件下亦呈現類似之分段式成長趨勢，且壓力越高，加速現象越早出現。整體而言，貧油氫氣球狀火焰之α值並非固定常數，而是隨火焰半徑增加呈現兩段式上升，顯示火焰僅具有局部自我相似性（locally self-similar），與Wu et al (2013)所找到α值較小和為固定值不同。進一步分析細胞狀結構可知，火焰傳遞行為與細胞數增加及細胞尺寸縮小密切相關。以ϕ = 0.6、p = 5 atm為例，在R < 12 mm時，細胞數僅約50 ~ 120個；當進入第一加速階段（12 mm ≤ R ≤ 30 mm）後，細胞數增加至250 ~ 450個，且細胞平均半徑隨火焰半徑成長而呈現明顯下降趨勢；於第二加速階段（R ≥ 30 mm）時，細胞數進一步累積至600 ~ 850個，此外，在ϕ = 0.4、p = 5 atm條件下，由於低Lewis數所引發之熱擴散不穩定性，火焰於R ≈ 6 ~ 8 mm即會產生大量細胞狀結構，使加速度指數相較於高當量比條件更早上升。細胞尺寸持續細化，顯示細胞化發展與火焰表面積非線性增生及加速行為可能具有對應關係。在固定當量比(ϕ = 0.6)下，隨初始壓力由1 atm提升至5 atm，細胞平均半徑由約1.5 ~ 2.1 mm 降低至約0.26 ~ 0.30 mm，細胞平均半徑下降約84%。整體而言，在火焰半徑成長過程中，不同當量比與壓力條件下，細胞數量的累積與細胞尺寸的縮減，皆與加速度指數α的分段式上升呈現相似特徵，顯示火焰表面由稀疏皺褶逐漸轉為密集細胞化時，火焰傳遞速度隨火焰半徑成長而呈現加快趨勢，並與加速度指數α的階段性提升相互對應。本研究補足既有文獻於高壓貧油條件下，對中後期細胞化發展、火焰傳遞速度變化與自我加速行為關聯性之不足，並可作為高壓氫燃燒安全評估及火焰動力模型改良之重要基礎知識。;This thesis experimentally investigates lean hydrogen/air premixed spherical flames under different initial pressure conditions (p = 1, 3, and 5 atm), with a focus on the effects of flame instabilities on flame propagation behavior, cellular structure development, burning velocity, and self-acceleration characteristics. During outward propagation of laminar spherical flames, two major instabilities dominate the flame dynamics. The first is thermal–diffusional instability, which arises from the low Lewis numbers of lean hydrogen/air mixtures at equivalence ratios of ϕ = 0.4, 0.6, and 0.8 (Le = DT/DM ≈ 0.38, 0.43, and 0.47 ≪ 1). This instability induces surface wrinkling and cellular structures at very small flame radii. The second is hydrodynamic instability, also known as the Darrieus–Landau instability, which is inherently caused by thermal expansion across the flame front. Under elevated pressure conditions, the reduction in flame thickness further enhances this instability, promoting the early formation of cellular structures. The combined effects of these instabilities increase the flame surface area and propagation speed, ultimately leading to flame self-acceleration. Previous studies commonly determined the acceleration exponent α using the power-law relation R=R_0+A(t-t_0 )^α; however, this approach is sensitive to the selection of initial conditions. To reduce this uncertainty, the present study adopts the method proposed by Wu et al. (2013), in which the flame radius follows R=At^α. By differentiating this expression, the flame propagation speed S_b=dR/dtis obtained, and the acceleration exponent α is determined from the slope d=(α-1)/αin the logarithmic relationship between S_band R. Experiments were conducted using a laboratory-developed dual-chamber cross-type high-pressure combustion vessel. A high-speed schlieren imaging system operating at 15,000 frames per second with a spatial resolution of 600 × 600 pixels was employed to capture the temporal evolution of flames from smooth propagation to cellular growth and acceleration stages. Artificial intelligence-based models, including SAM2 and Cellpose 2.0, were utilized to automatically extract flame contours, flame radii, and cellular statistics. The results indicate that flame instabilities are most pronounced at ϕ = 0.4 (Le ≈ 0.38), where cellular structures appear earliest and with the highest density, leading to the earliest onset of flame self-acceleration. As the pressure increases to 5 atm, the flame thickness decreases further, intensifying temperature and density gradients and causing cellular structures to emerge at even smaller flame radii. Consequently, the acceleration exponent α increases earlier and exhibits a larger variation compared to the 1 atm and 3 atm cases. For example, at ϕ = 0.6 and p = 5 atm, α ≈ 1.34 in the range of 12 mm ≤ R ≤ 30 mm, which is higher than the value of α = 1.26 reported by Wu et al. (2013) for 10 mm ≤ R ≤ 20 mm. When the flame radius further increases to 30 mm ≤ R ≤ 45 mm, α rises to approximately 1.42. Similar two-stage growth behavior of α is also observed at 1 atm and 3 atm, with higher pressures leading to earlier acceleration. Overall, the acceleration exponent α of lean hydrogen spherical flames is not a constant but exhibits a two-stage increase with flame radius, indicating that the flame is only locally self-similar rather than globally self-similar. This behavior differs from the constant and relatively lower α values reported by Wu et al. (2013). Further analysis of cellular structures reveals a strong correlation between flame propagation behavior, cellular number accumulation, and cellular size reduction. For instance, at ϕ = 0.6 and p = 5 atm, the number of cells increases from approximately 50 ~ 120 at R < 12 mm to 250 ~ 450 during the first acceleration stage (12 mm ≤ R ≤ 30 mm), accompanied by a clear decrease in the mean cell radius. During the second acceleration stage (R ≥ 30 mm), the cell number further increases to 600 ~ 850. Under ϕ = 0.4 and p = 5 atm, thermal–diffusional instability induced by the low Lewis number leads to the formation of dense cellular structures as early as R ≈ 6 ~ 8 mm, resulting in an earlier increase in α compared to higher equivalence ratio conditions. At a fixed equivalence ratio of ϕ = 0.6, increasing the initial pressure from 1 atm to 5 atm reduces the mean cell radius from approximately 1.5 ~ 2.1 mm to 0.26 ~ 0.30 mm, a nearly 84% decrease in values of mean cell radii. In summary, under various equivalence ratio and pressure conditions, the accumulation of cellular structures and the continuous reduction in cell size exhibit trends consistent with the staged increase of the acceleration exponent α. As the flame surface evolves from sparse wrinkling to dense cellular structures, the flame propagation speed increases with flame radius and corresponds closely to the stepwise growth of α. This study complements existing literature by providing detailed insights into the relationship between mid-to-late-stage cellular development, flame propagation, and self-acceleration under high-pressure lean hydrogen conditions, and offers valuable fundamental knowledge for high-pressure hydrogen combustion safety assessment and the improvement of flame dynamic models. |
