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(tuán)聚

張儷安,刁永發(fā)*,楚明浩,王如歌,沈恒根

(東華大學(xué)環(huán)境科學(xué)與工程學(xué)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(tuán)聚規(guī)律,基于計算流體動力學(xué)-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(tuán)聚行為進(jìn)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(jìn)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(tuán)聚的影響,并將數(shù)值模擬與實驗結(jié)果進(jìn)行對比.結(jié)果表明,布朗團(tuán)聚核UDF符合數(shù)值模擬計算要求.粉塵顆粒的布朗團(tuán)聚貫穿整個過程,團(tuán)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(tuán)聚越強(qiáng),Bin-7與Bin-0區(qū)間的數(shù)量濃度差距越小,粒徑與布朗團(tuán)聚強(qiáng)度呈負(fù)相關(guān);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(tuán)聚,與布朗團(tuán)聚強(qiáng)度呈正相關(guān),當(dāng)=300K,p30.5μm時,顆粒的布朗團(tuán)聚效應(yīng)可以忽略;數(shù)通過擴(kuò)散系數(shù)的變化影響布朗團(tuán)聚,與布朗團(tuán)聚強(qiáng)度呈負(fù)相關(guān).

亞微米顆粒；CFD-PBM；布朗團(tuán)聚；分區(qū)法；單纖維

PM2.5等微細(xì)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(nèi)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(jié)構(gòu)[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(yùn)動效應(yīng)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(yīng).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(yīng)做無規(guī)則運(yùn)動,此時布朗運(yùn)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(yīng),且顆粒由于布朗擴(kuò)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(xué)-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(yùn)動而被纖維捕集的運(yùn)動軌跡或過濾性能,進(jìn)而得出顆粒做布朗運(yùn)動的相關(guān)信息[17-18].但是,布朗團(tuán)聚信息僅僅依靠CFD-DPM等方法并不能很好的得出計算結(jié)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(yùn)動而團(tuán)聚的現(xiàn)象,基于CFD-PBM,采用分區(qū)法對顆粒群平衡方程進(jìn)行求解,進(jìn)而對整個過程進(jìn)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(jìn)行離散,劃分為有限數(shù)目的個區(qū)間,認(rèn)為每個區(qū)間內(nèi)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(nèi)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(xiàn)[20]研究結(jié)果,當(dāng)0.1μm￡p￡0.4μm,隨著粒徑的減小,布朗團(tuán)聚開始逐漸增強(qiáng).在研究亞微米顆粒布朗團(tuán)聚過程中,通過編寫UDF在PBM模型中添加布朗團(tuán)聚核函數(shù),以實現(xiàn)顆粒在流場中的布朗團(tuán)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(tuán)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.

1 數(shù)值計算模型

1.1 多相流模型

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?jǐn)?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(yīng)力張量;為重力加速度,m/s2;為網(wǎng)格單元內(nèi)受到的綜合作用力,N.

1.2 顆粒群平衡方程

顆粒的團(tuán)聚可以用粒子聚并的動力學(xué)方程(GDE/PBE)來進(jìn)行描述,聚并動力學(xué)方程如下[21]:

1.3 布朗團(tuán)聚核

Knudesn數(shù)可用來表征顆粒和環(huán)境氣體之間的質(zhì)量、動量和能量的交換和轉(zhuǎn)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(dá)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(nèi)的顆粒屬于近連續(xù)區(qū)/滑流區(qū)(0.1￡￡1),當(dāng)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(tuán)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]:

2 邊界條件

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(nèi)對群體平衡模型進(jìn)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(yīng)的粒徑大小和體積分?jǐn)?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?jǐn)?shù)

注:不同的入口粒徑對應(yīng)不同組的Bin-7~Bin-0.

3 模型正確性驗證

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(tuán)聚核UDF檢驗,單纖維捕集結(jié)構(gòu)模型根據(jù)[26]計算結(jié)果選取50多萬六面體結(jié)構(gòu)化網(wǎng)格進(jìn)行數(shù)值模擬計算,對比進(jìn)出口壓降,與Darcy壓降經(jīng)驗公式(8)誤差在5%范圍內(nèi).

而對于布朗團(tuán)聚核的正確性根據(jù)徐俊波等[27]的實驗數(shù)據(jù)進(jìn)行驗證,以0.5μm聚并乙烯標(biāo)準(zhǔn)微球通入凝并器為例,物理和化學(xué)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(tuán)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(guān)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(tuán)聚核UDF的驗證,數(shù)值模擬結(jié)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(jié)果與實驗結(jié)果定性一致,而在實驗結(jié)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(jié)果0.5μm顆粒較多是由于團(tuán)聚時間短,大量的初始顆粒還未團(tuán)聚.

圖2 數(shù)值模擬與實驗結(jié)果對比

式中:D為進(jìn)出口壓降,Pa;為填充率;為流體的動力黏度,Pa·s;顆粒入口風(fēng)速,m/s;為過濾層厚度,μm;f為纖維直徑,μm.

4 數(shù)值模擬計算

4.1 停留時間對布朗團(tuán)聚影響

如圖3(a)所示,單纖維捕集過程中存在明顯的布朗團(tuán)聚行為,粉塵顆粒的布朗團(tuán)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(tuán)聚的效果越來越明顯,當(dāng)=/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(jié)構(gòu),布朗團(tuán)聚過程結(jié)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(guān)系,表達(dá)式如下:

Ave=+-2(、、均為常數(shù))(9)

4.2 入口粉塵粒徑對布朗團(tuán)聚影響

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(tuán)聚效果越強(qiáng).這是因為粉塵顆粒粒徑越小,布朗運(yùn)動強(qiáng)度越強(qiáng),碰撞幾率越大;同時,粉塵顆粒體積分?jǐn)?shù)一定時,粒徑越小,則單纖維捕集結(jié)構(gòu)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(tuán)聚有促進(jìn)作用,粒徑的大小與布朗團(tuán)聚強(qiáng)度呈負(fù)相關(guān).

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(tuán)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(tuán)聚效果明顯,有效團(tuán)聚時間內(nèi), 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(tuán)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)

4.3 氣流溫度對布朗團(tuán)聚影響

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(jié)果.由圖可知,粉塵顆粒的布朗團(tuán)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(dǎo)致氣流的動力黏度以及聚并系數(shù)發(fā)生改變,當(dāng)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(dǎo)致團(tuán)聚的增強(qiáng).同時溫度升高,顆粒的布朗運(yùn)動越劇烈,促進(jìn)了粉塵顆粒的團(tuán)聚,氣流溫度對于粉塵顆粒的布朗團(tuán)聚效果呈正相關(guān).

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(guān)系式,表達(dá)式如下:

Ave=A+B(A、B均為常數(shù))(11)

4.4 Pe數(shù)對布朗團(tuán)聚影響

數(shù)對于布朗擴(kuò)散的影響主要來源于與粉塵顆粒的擴(kuò)散系數(shù)有直接的關(guān)系,由公式(12)可知,數(shù)與擴(kuò)散系數(shù)成反比關(guān)系,數(shù)越小,此時粉塵顆粒的擴(kuò)散系數(shù)越大,粉塵顆粒的運(yùn)動越劇烈,加劇了布朗擴(kuò)散運(yùn)動,因此團(tuán)聚強(qiáng)度增強(qiáng),計算公式如下:

對于顆粒的擴(kuò)散,又稱布朗擴(kuò)散,擴(kuò)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(jié)果.粉塵顆粒的布朗團(tuán)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(kuò)散系數(shù)由2.272× 10-10m2/s增加到3.860×10-10m2/s,擴(kuò)散系數(shù)的增加直接導(dǎo)致布朗團(tuán)聚的增強(qiáng).

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(guān)系,表達(dá)式如下:

Ave=-2(、、均為常數(shù))(14)

5 結(jié)論

5.1 對于亞微米級顆粒來說,單纖維捕集結(jié)構(gòu)中存在明顯的布朗團(tuán)聚行為,且貫穿整個捕集過程,團(tuán)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(guān)系.

5.2 粉塵顆粒越小,布朗運(yùn)動的強(qiáng)度越大,布朗團(tuán)聚效果越強(qiáng),出口處平均粒徑與入口粒徑相比增加的倍率越大,當(dāng)=300K,p30.5μm時,顆粒的布朗團(tuán)聚效應(yīng)可以忽略,粒徑的大小與布朗團(tuán)聚強(qiáng)度呈負(fù)相關(guān).

5.3 粉塵顆粒的布朗團(tuán)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(yùn)動越劇烈,粉塵顆粒的布朗團(tuán)聚效果越強(qiáng),對于粉塵顆粒的布朗團(tuán)聚強(qiáng)度呈正相關(guān),出口平均粒徑與氣流溫度呈一次函數(shù)關(guān)系;

5.4數(shù)與擴(kuò)散系數(shù)成反比關(guān)系,數(shù)越小,粉塵顆粒的運(yùn)動越劇烈,粉塵顆粒的布朗團(tuán)聚效果越強(qiáng),數(shù)與布朗團(tuán)聚強(qiáng)度呈負(fù)相關(guān),出口平均粒徑與數(shù)呈一元二次關(guān)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(xué)博士研究生,主要從事粉塵磁團(tuán)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(wù)費重點項目(2232017A-09);中央高?；究蒲袠I(yè)務(wù)費專項資金、東華大學(xué)研究生創(chuàng)新基金資助項目(CUSF-DH-D-2020067)

* 責(zé)任作者, 教授, diaoyongfa@dhu.edu.cn