| 摘要: | 在2012年，普林斯頓大學Law之研究團隊(Chaudhri et al.)首度提出一向外傳
播預混紊流球狀火焰具有自我相似之傳播特性，他們發現正規化紊流火焰傳播速率[(1/SbL)d/dt]與一火焰紊流雷諾數(ReT,flame = u'/DT < 2,500)呈現1/2冪次之自我相似傳播關係，其中SbL為未作密度校正之層流燃燒速率(生成物SL)，為平均紊焰半徑，t為時間，u'為方均根紊流擾動速度，以及DT為熱擴散係數。我們特別用下標flame來清楚顯示ReT,flame與一般所認知之流場紊流雷諾數ReT,flow = u'LI/相當地不同，其中LI為積分長度尺度，而則為為運動黏滯係數。值得一提的是，Law團隊所量測紊流火焰速率(d/dt)之方法，與傳統量測紊流火焰速率(SF)有所異同，相同之處為兩者均需先量測與t之函數關係，並取中段vs. t之資料作分析，以避開前段引燃和後段容器尺寸限制之影響；不同之處僅在傳統SF = /t，是以線性耦合中段 vs. t之資料，而d/dt是將中段所有值對t作微分。事實上，由Law團隊和本實驗室所獲得之資料，均顯示d/dt會隨t之增加而近似線性增加，故SF可看作d/dt對時間之平均值。本研究主要回答下列兩大問題:(1)若使用SF數據，d/dt與ReT,flame之自我相似傳播特性是否仍存在?(2)若是，此自我相似傳播特性是否仍適用於ReT,flame遠大於2,500?
為釐清前述之問題，本論文採用本實驗室已建立之大型高壓雙腔體設計之十字形預混紊流燃燒設備，其可產生可控制之近似等向性紊流並使燃燒實驗可在固定系統壓力條件下進行，實驗使用與Law團隊相同之當量比 = 0.9的甲烷/空氣燃氣，進行一系列不同固定系統壓力(p = 0.1 ~ 0.5 MPa)及不同u'值(u' = 1.43 ~ 5.60m/s)之燃燒實驗，使用Schlieren光學技術(100 × 100 mm2)和直接火焰拍攝法(170 × 170 mm2)，以擷取平均球狀紊焰半徑隨時間變化之資料，即找到(t)。實驗結果顯示，在不同p及u'下，對ReT,flame關係之數據不僅仍具有自我相似傳播特性，且本研究所量得之(1/SbL)d/dt資料與Law團隊之資料有高度重合性，我們並找到前述球狀紊焰之自我相似傳播特性於ReT,flame高達10,000時，仍存在之証據。此研究結果對預混紊流燃燒領域有重要之貢獻。
In 2012, Law and his co-workers at Princeton university (Chaudhri et al.) found that a constant-pressure, unity Lewis number expanding turbulent premixed flame has the self-similar propagation, in which the normalized turbulent flame speed [(1/SbL)d/dt] as a function of the average flame radius () scales as a flame turbulent Reynolds number (ReT,flame = u'/DT < 2,500) to the one-half power.
is laminar burning velocity before density correlation, and the superscript b indicates the burnt side, t is time, u' is the r.m.s. turbulent fluctuation velocity, and DT is the
thermal diffusivity. Here the subscript flame is used to clearly distinguish ReT,flame from the fenerally-used flow turbulent Reynolds number (ReT,flow = u'LI/ , where LI
is the integral length scale of turbulence and is the kinematic viscosity of reactants. It is worthy of noting that there are similarity and difference on the determination of turbulent flame speed between d/dt and SF (the tradition method). The similarity is that both methods need to measure as a function of t first, and then analyze some middle part of vs. t data in order to avoid the influence of ignition in the beginning of flame growth and circumvent the influence of the chamber walls in the latter flame propagation. The only one difference is that SF = /t which is the slope of the traditional method uses the linear fitting to obtain middle part of vs. t data and thus SF if an average turbulent flame speed, while d/dt is to differentiate all available data within the middle part of vs. t data that increases nearly linearly with time. Actually, SF can be viewed as the average value of d/dt within the same time period of vs. t data. We aim to address two key questions: (1)what happen if SF data are applied to replace d/dt and whether does the self-similar propagation still exist?(2)Can aforesaid self-similar propagation, [(1/SbL)d/dt] ~ ReT,flame 0.5, be valid for ReT,flame 2,500?
In order to address the aforesaid questions, a series of lean methane/air mixtures, experiments at the equivalence ratio = 0.9 and carried out in the large high-pressure,
dual-chamber turbulent premixed combustion facility which can produce controllable near-isotropic turbulence with u' varying from 1.43 m/s to 5.60 m/s at constant vessel
pressure conditions varying from 1atm to 5atm. Both the Schlieren optical imaging a view field of 100mm × 100mm and the direct flame imaging with a large view field of 170mm × 170mm are applied to measure the average flame radius as a function of time, that is (t). Each of data is ensemble averaged from six identical runs. Results show that at different p and u', the data of scale as ReT,flame
0.5, which is the same as that of (1/SbL)d/dt, both showing self-similar propagation. Most importantly, such self-similar propagation is fund to be varied even at much higher values of ReT,flame up to 10,000. |
