張儷安,刁永發(fā),楚明浩,王如歌,沈恒根
單纖維捕集過程中亞微米顆粒的布朗團聚
張儷安,刁永發(fā)*,楚明浩,王如歌,沈恒根
(東華大學環(huán)境科學與工程學院,上海 201620)
針對亞微米顆粒(0.1~0.5μm)在單纖維捕集過程中的布朗團聚規(guī)律,基于計算流體動力學-顆粒群平衡模型(CFD-PBM)對粉塵顆粒在單纖維捕集過程中的布朗團聚行為進行了數(shù)值模擬研究,采用分區(qū)法對顆粒群平衡方程(PBE)進行求解,綜合考慮了停留時間、入口粉塵粒徑、氣流溫度、數(shù)對布朗團聚的影響,并將數(shù)值模擬與實驗結果進行對比.結果表明,布朗團聚核UDF符合數(shù)值模擬計算要求.粉塵顆粒的布朗團聚貫穿整個過程,團聚有效時間=/(速度方向模型尺寸長度/入口流速);粉塵顆粒越小,布朗團聚越強,Bin-7與Bin-0區(qū)間的數(shù)量濃度差距越小,粒徑與布朗團聚強度呈負相關;氣流溫度是通過改變氣流動力黏度以及聚并系數(shù)來影響布朗團聚,與布朗團聚強度呈正相關,當=300K,p30.5μm時,顆粒的布朗團聚效應可以忽略;數(shù)通過擴散系數(shù)的變化影響布朗團聚,與布朗團聚強度呈負相關.
亞微米顆粒;CFD-PBM;布朗團聚;分區(qū)法;單纖維
PM2.5等微細顆粒物對人體免疫系統(tǒng)、呼吸系統(tǒng)和中樞神經(jīng)系統(tǒng)都有著不良影響[1].目前工業(yè)上袋式除塵器對于PM2.5以下的顆粒存在穿透區(qū),纖維難以捕集[2].
目前國內外對于纖維捕集顆粒物的研究主要包括纖維截面形狀(異型纖維)[3-4]、纖維直徑[5]、填充率[6]、顆粒物沉積特性[7-9]以及纖維排列結構[1,10]和纖維交叉角度[11]等參數(shù)的變化對捕集效率和壓降的影響.所研究的粒徑區(qū)間主要集中在兩個范圍,一方面p>0.5μm粒徑段范圍,該區(qū)間粒徑較大,布朗運動效應基本可以忽略,其纖維捕集顆粒時主要依靠慣性碰撞和攔截效應.另一方面p£0.5μm粒徑段時存在一部分亞微米級顆粒(0.1~0.5μm)[12],在流場中會由于布朗效應做無規(guī)則運動,此時布朗運動已經(jīng)不能忽略,纖維捕集顆粒主要依靠粉塵顆粒的布朗效應,且顆粒由于布朗擴散作用被纖維捕集的效率計算公式繁多[13-16].基于計算流體動力學-離散相模型(CFD-DPM),添加布朗力UDF或Boltzmann法模擬可以計算出粉塵顆粒因布朗運動而被纖維捕集的運動軌跡或過濾性能,進而得出顆粒做布朗運動的相關信息[17-18].但是,布朗團聚信息僅僅依靠CFD-DPM等方法并不能很好的得出計算結果,該方法在計算時忽略了顆粒與顆粒之間的相互作用[19].
為了更好地探究出單纖維捕集過程中亞微米級顆粒因布朗運動而團聚的現(xiàn)象,基于CFD-PBM,采用分區(qū)法對顆粒群平衡方程進行求解,進而對整個過程進行數(shù)值模擬,而對于分區(qū)法則是把顆粒尺寸分布曲線進行離散,劃分為有限數(shù)目的個區(qū)間,認為每個區(qū)間內顆粒尺度分布滿足一個統(tǒng)一的分布函數(shù),在每個區(qū)間內針對某個顆粒屬性的分布函數(shù),建立平衡方程,聯(lián)立求解平衡方程,可以得到某個顆粒屬性的分布函數(shù)隨時間演變的過程.
同時,模擬的顆粒尺寸范圍選擇0.1~0.5μm粒徑段.根據(jù)文獻[20]研究結果,當0.1μm£p£0.4μm,隨著粒徑的減小,布朗團聚開始逐漸增強.在研究亞微米顆粒布朗團聚過程中,通過編寫UDF在PBM模型中添加布朗團聚核函數(shù),以實現(xiàn)顆粒在流場中的布朗團聚過程,改變停留時間、入口粉塵粒徑、氣流溫度、數(shù)等工況來探究對流場中亞微米顆粒布朗團聚的影響.為后續(xù)開展纖維捕集亞微米顆粒的數(shù)值模擬提供借鑒.
多相流模型采用歐拉-歐拉雙流體模型,連續(xù)性方程和動量方程如下[7]:
式中:為流體的密度,kg/m3;為體積分數(shù)項;是流體的速度,m/s;為計算單元的壓力,N;為流體黏附性應力張量;為重力加速度,m/s2;為網(wǎng)格單元內受到的綜合作用力,N.
顆粒的團聚可以用粒子聚并的動力學方程(GDE/PBE)來進行描述,聚并動力學方程如下[21]:
Knudesn數(shù)可用來表征顆粒和環(huán)境氣體之間的質量、動量和能量的交換和轉移,且根據(jù)顆粒的數(shù)將顆粒分為自由分子區(qū)、過渡區(qū)、近連續(xù)區(qū)(或滑流區(qū))和連續(xù)區(qū),其表達式如下[22]:
式中:為空氣分子的平均自由程,nm;為顆粒的半徑,μm;p為顆粒直徑,μm.
根據(jù)Allen等[23]空氣的平均自由程的計算式如下:
表1 不同直徑顆粒的Kn值大小(300K)
通過大小和表2的范圍可知,0.2~0.5μm范圍內的顆粒屬于近連續(xù)區(qū)/滑流區(qū)(0.1££1),當p=0.1μm時,=1.368,但由于0.1μm的顆粒仍接近于近連續(xù)區(qū)間,為了簡化研究,考慮同樣屬于近連續(xù)區(qū)間.
對于近連續(xù)區(qū)/滑流區(qū)的布朗團聚核為[22]:
式中:d和d分別為顆粒的直徑,μm;co為連續(xù)區(qū)及近似連續(xù)區(qū)的碰撞系數(shù);B為玻爾茲曼常數(shù), 1.380649×10-23J/K;為氣流的動力黏度,Pa·s;0= 1.83245×10-5Pa·s;為氣流的絕對溫度,K;0和S為溫度常數(shù),K;為環(huán)境氣體的絕對溫度,K.
表2 不同直徑顆粒的Kn數(shù)和區(qū)域(溫度300~2000K)[22]
對于連續(xù)區(qū),Stokes-Cunningham,滑移修正系數(shù)c=1,對于近似連續(xù)區(qū),一般c的計算式如下[24]:
對顆粒群平衡方程PBE采用分區(qū)算法,初始顆粒分布為單分散相體系,以入口顆粒粒徑為0.2μm為例,將顆粒群大小劃分為8個子區(qū)間, Bin-7~Bin-0區(qū)間粒徑大小由初始通入顆粒的粒徑計算得來,(分區(qū)后,相鄰區(qū)間后一區(qū)間顆粒體積與前一區(qū)間顆粒體積滿足k+1=sk, 1.08£s£3.0),Ratio Exponent數(shù)值取1.0滿足要求,在每個子區(qū)間內對群體平衡模型進行積分即可得到一系列離散的方程,表3為初始計算時各區(qū)間對應的粒徑大小和體積分數(shù).
圖1 計算區(qū)域及邊界條件示意
表3 Bin-7-Bin-0區(qū)間粒徑大小以及初始體積分數(shù)
注:不同的入口粒徑對應不同組的Bin-7~Bin-0.
對于模型的正確性驗證包括網(wǎng)格獨立性檢驗以及布朗團聚核UDF檢驗,單纖維捕集結構模型根據(jù)[26]計算結果選取50多萬六面體結構化網(wǎng)格進行數(shù)值模擬計算,對比進出口壓降,與Darcy壓降經(jīng)驗公式(8)誤差在5%范圍內.
而對于布朗團聚核的正確性根據(jù)徐俊波等[27]的實驗數(shù)據(jù)進行驗證,以0.5μm聚并乙烯標準微球通入凝并器為例,物理和化學特性比較穩(wěn)定,密度為783kg/m3,顆粒入口的固含率為10-6,入口氣流速度為3.5L/min,通過計算<2300,流動為層流,顆粒間不存在湍流團聚.空氣為連續(xù)相,并采用不可壓縮流體描述,密度為1.225kg/m3,氣固兩相流的曳力系數(shù)根據(jù)Schiller-naumann關聯(lián)式,由于p=0.5μm,= 0.2736,處于近連續(xù)區(qū)/滑流區(qū),符合布朗團聚核UDF的驗證,數(shù)值模擬結果如圖2所示:
由圖2可知,凝并器出口顆粒分布呈多分散相分布,粒徑尺寸趨向于大顆粒偏移,且分布主要集中在0.5~1.0μm之間,模擬結果與實驗結果定性一致,而在實驗結果中出現(xiàn)的低于0.5μm的顆粒原因可能是實驗過程中凝并器被環(huán)境氣體污染及實驗過程污染等因素,數(shù)值模擬結果0.5μm顆粒較多是由于團聚時間短,大量的初始顆粒還未團聚.
圖2 數(shù)值模擬與實驗結果對比
式中:D為進出口壓降,Pa;為填充率;為流體的動力黏度,Pa·s;顆粒入口風速,m/s;為過濾層厚度,μm;f為纖維直徑,μm.
如圖3(a)所示,單纖維捕集過程中存在明顯的布朗團聚行為,粉塵顆粒的布朗團聚貫穿整個過程,隨著停留時間的增加,Bin-7區(qū)間顆粒數(shù)量濃度逐漸減小,粉塵顆粒逐漸向大顆粒偏移,布朗團聚的效果越來越明顯,當=/時(速度方向模型尺寸長度/入口流速),顆粒數(shù)量濃度基本不變,顆粒流出單纖維捕集結構,布朗團聚過程結束.
通過多項式擬合,由圖3(b)出口平均粒徑與停留時間變化曲線可知,隨著停留時間的增加,出口平均粒徑隨著停留時間是逐漸增加的,且逐漸趨于穩(wěn)定,出口顆粒平均粒徑與停留時間滿足一元二次多項式關系,表達式如下:
Ave=+-2(、、均為常數(shù))(9)
如圖4(a)可知,入口粒徑越小,Bin-7與Bin-0區(qū)間顆粒數(shù)量濃度差距越小,粉塵顆粒的布朗團聚效果越強.這是因為粉塵顆粒粒徑越小,布朗運動強度越強,碰撞幾率越大;同時,粉塵顆粒體積分數(shù)一定時,粒徑越小,則單纖維捕集結構中所含有的顆粒數(shù)越多,同樣增加了粉塵顆粒的碰撞幾率,對于顆粒的團聚有促進作用,粒徑的大小與布朗團聚強度呈負相關.
對于曲線中凸點的出現(xiàn)是因為亞微米顆粒在流場中發(fā)生布朗團聚后,顆粒變化過程是(Bin-7→Bin-6→Bin-5→Bin-4→Bin-3→Bin-2→Bin-1→Bin-0),Bin-7區(qū)間的顆粒數(shù)量濃度會減小,逐漸由小顆粒向大顆粒變化,Bin-6~Bin-0區(qū)間的顆粒數(shù)量濃度會增加,若布朗團聚效果明顯,有效團聚時間內, Bin-7區(qū)間顆粒數(shù)量濃度下降多,此時凸點就會產(chǎn)生,若布朗團聚效果不明顯,Bin-7區(qū)間顆粒數(shù)量濃度下降少,Bin-6~Bin-0區(qū)間顆粒數(shù)量濃度小于Bin-7時就不會產(chǎn)生凸點.
Ave=A-Bp+Cp2-Dp3+Ep4
(A、B、C、D均為常數(shù))(10)
如圖5(a)所示,圖中3條曲線分別為流體溫度為300,400和500K時的數(shù)值模擬結果.由圖可知,粉塵顆粒的布朗團聚效果隨著氣流溫度的提高而增大,這是因為氣流溫度改變導致氣流的動力黏度以及聚并系數(shù)發(fā)生改變,當溫度由300K增加到500K時,聚并系數(shù)co由1.492′10-16增加到1.719′10-16,聚并系數(shù)的增加直接導致團聚的增強.同時溫度升高,顆粒的布朗運動越劇烈,促進了粉塵顆粒的團聚,氣流溫度對于粉塵顆粒的布朗團聚效果呈正相關.
通過多項式擬合,由圖5(b)出口平均粒徑與氣流溫度變化曲線可知,隨著氣流溫度的增加,出口處平均粒徑隨著氣流溫度變化逐漸增加,出口處平均粒徑與氣流溫度滿足一次函數(shù)關系式,表達式如下:
Ave=A+B(A、B均為常數(shù))(11)
數(shù)對于布朗擴散的影響主要來源于與粉塵顆粒的擴散系數(shù)有直接的關系,由公式(12)可知,數(shù)與擴散系數(shù)成反比關系,數(shù)越小,此時粉塵顆粒的擴散系數(shù)越大,粉塵顆粒的運動越劇烈,加劇了布朗擴散運動,因此團聚強度增強,計算公式如下:
對于顆粒的擴散,又稱布朗擴散,擴散系數(shù)由斯托克斯-愛因斯坦提出[28]:
式中:B為玻爾茲曼常數(shù),B=1.380649′10-23J/K;為環(huán)境氣體的絕對溫度,K;為動力黏度,Pa·s;C為庫寧漢滑移修正系數(shù);為粒子的遷移速率,m2/(N·s).
如圖6(a)所示, 圖中3條曲線分別為數(shù)為88.03、66.42和51.81時的數(shù)值模擬結果.粉塵顆粒的布朗團聚效果隨著數(shù)的減小而增大,這是因為數(shù)由88.03減小到51.81時,擴散系數(shù)由2.272× 10-10m2/s增加到3.860×10-10m2/s,擴散系數(shù)的增加直接導致布朗團聚的增強.
通過多項式擬合,由圖6(b)出口平均粒徑與變化曲線可知,隨著數(shù)的增加,出口處平均粒徑隨著逐漸減小的,出口處平均粒徑與數(shù)滿足一元二次多項式關系,表達式如下:
Ave=-2(、、均為常數(shù))(14)
5.1 對于亞微米級顆粒來說,單纖維捕集結構中存在明顯的布朗團聚行為,且貫穿整個捕集過程,團聚有效時間=/,出口平均粒徑與停留時間呈一元二次多項式關系.
5.2 粉塵顆粒越小,布朗運動的強度越大,布朗團聚效果越強,出口處平均粒徑與入口粒徑相比增加的倍率越大,當=300K,p30.5μm時,顆粒的布朗團聚效應可以忽略,粒徑的大小與布朗團聚強度呈負相關.
5.3 粉塵顆粒的布朗團聚效果隨著溫度的提高而增大,氣流溫度越大,顆粒的布朗運動越劇烈,粉塵顆粒的布朗團聚效果越強,對于粉塵顆粒的布朗團聚強度呈正相關,出口平均粒徑與氣流溫度呈一次函數(shù)關系;
5.4數(shù)與擴散系數(shù)成反比關系,數(shù)越小,粉塵顆粒的運動越劇烈,粉塵顆粒的布朗團聚效果越強,數(shù)與布朗團聚強度呈負相關,出口平均粒徑與數(shù)呈一元二次關系式.
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Brownian aggregation in the process of submicron particles captured by single fiber.
ZHANG Li-an, DIAO Yong-fa*, CHU Ming-hao, WANG Ru-ge, SHEN Heng-gen
(College of Environmental Science and Engineering, Donghua University, Shanghai 201620, China)., 2021,41(4):1548~1554
In view of the Brownian aggregation law in the process of submicron particles (0.1~0.5μm) captured by single fiber, the Brownian aggregation behavior in the process of the dust particles captured by single fiber was numerically studied based on computational fluid dynamics-population balance model (CFD-PBM), and the partition method was used to solve population balance equation (PBE). The effects of residence time, inlet particle diameter, airflow temperature, andnumber on the Brownian aggregation were considered comprehensively, and the numerical simulation and experimental results were compared. The results showed that the Brownian aggregation kernel met the requirements of numerical simulation calculation. The Brownian aggregation of dust particles run through the entire process, aggregation effective time=/(dimension length along with flow field direction/face velocity). The smaller the dust particles, the stronger the intensity of the Brownian motion, the smaller the number density gap between Bin-7 and Bin-0, and the particle diameter was negatively correlated with the Brownian aggregation intensity. Brownian aggregation was affected by airflow temperature by changing flow field dynamic viscosity and aggregation coefficient, which was positively correlated with the Brownian aggregation intensity, when=300K,p30.5μm, the Brownian aggregation effect of particles can be ignored; Brownian aggregation was influenced by the change ofnumber through the change of diffusion coefficient, which was negatively correlated with the Brownian aggregation intensity.
submicron particles;CFD-PBM;Brownian aggregation;partition method;single fiber
X513
A
1000-6923(2021)04-1548-07
張儷安(1990-),男,安徽省淮北市人,東華大學博士研究生,主要從事粉塵磁團聚研究.發(fā)表論文4篇.
2020-08-16
國家重點研發(fā)計劃項目(2018YFC0705300);中央高?;究蒲袠I(yè)務費重點項目(2232017A-09);中央高?;究蒲袠I(yè)務費專項資金、東華大學研究生創(chuàng)新基金資助項目(CUSF-DH-D-2020067)
* 責任作者, 教授, diaoyongfa@dhu.edu.cn