多纖維捕集過(guò)程中細(xì)顆粒湍流團(tuán)聚模擬研究

張儷安,刁永發(fā),楚明浩,賈中堅(jiān),沈恒根,孫 靜

多纖維捕集過(guò)程中細(xì)顆粒湍流團(tuán)聚模擬研究

張儷安1,刁永發(fā)1*,楚明浩1,賈中堅(jiān)1,沈恒根1,孫 靜2

(1.東華大學(xué)環(huán)境科學(xué)與工程學(xué)院,上海 201620；2.甘肅蘭菲環(huán)?？萍加邢薰?蘭州 730030)

基于隨機(jī)多層纖維過(guò)濾介質(zhì)算法建立了平板式三維擬態(tài)化結(jié)構(gòu).利用計(jì)算流體力學(xué)-顆粒群平衡模型(CFD-PBM)對(duì)多纖維捕集過(guò)程中細(xì)顆粒湍流團(tuán)聚進(jìn)行數(shù)值模擬研究,并采用分區(qū)法求解顆粒群平衡方程(PBE).通過(guò)控制變量法分析表明:多纖維捕集過(guò)程中存在著明顯的顆粒團(tuán)聚行為.粉塵顆粒的團(tuán)聚程度隨停留時(shí)間增加而增強(qiáng),當(dāng)3/(速度方向模型尺寸長(zhǎng)度/入口風(fēng)速),團(tuán)聚逐漸趨于穩(wěn)定;當(dāng)max·￡,入口風(fēng)速越大,顆粒團(tuán)聚程度和團(tuán)聚速率越大,最終的團(tuán)聚程度取決于入口風(fēng)速和停留時(shí)間;顆粒粒徑越大,粉塵顆粒的團(tuán)聚程度和團(tuán)聚速率越小.出口顆粒平均粒徑與初始粒徑相比增長(zhǎng)倍數(shù)越小.粉塵顆粒體積分?jǐn)?shù)越大,顆粒團(tuán)聚程度以及團(tuán)聚速率越大.當(dāng)= 0.1m/s,p= 1.0μm,VF > 0.003636, Bin-7～Bin-0區(qū)間數(shù)量濃度對(duì)數(shù)分布呈線性比例關(guān)系.

計(jì)算流體力學(xué)-顆粒群平衡模型；顆粒群平衡方程；分區(qū)法；湍流團(tuán)聚；多纖維

顆粒物通過(guò)呼吸道進(jìn)入肺部會(huì)產(chǎn)生沉積和滯留.粒徑在2.5μm以下以及2.5～5.0μm的顆粒物能夠進(jìn)入肺泡,進(jìn)而干擾肺部的氣體交換,損傷肺泡和粘膜,引起肺組織的慢性纖維化等一系列病變,甚至?xí)绊懭梭w免疫功能,呼吸和中樞神經(jīng)系統(tǒng)[1].目前最常見(jiàn)的去除工業(yè)廢氣中顆粒物的方法是依靠纖維濾料捕集技術(shù).

早期對(duì)于多纖維捕集粉塵顆粒的研究主要分為兩類(lèi),一類(lèi)集中體現(xiàn)在多纖維建模[2-3],其方法是首先利用SEM、MRI以及X射線斷層攝影等技術(shù)獲得纖維隨機(jī)分布的微觀結(jié)構(gòu),利用Matlab進(jìn)行編碼生成腳本文件Txt,導(dǎo)入到建模軟件生成多纖維過(guò)濾介質(zhì)結(jié)構(gòu)模型,其中,典型的多纖維過(guò)濾介質(zhì)包括平板纖維過(guò)濾介質(zhì)[4-5]、V型褶式纖維過(guò)濾介質(zhì)[6]以及U型纖維過(guò)濾介質(zhì)[7].另一類(lèi)則體現(xiàn)在多纖維捕集顆粒數(shù)值模擬計(jì)算方法上.目前基于離散相模型進(jìn)行數(shù)值模擬能方便計(jì)算出多纖維捕集效率[8-9]以及顆粒在流場(chǎng)中的運(yùn)動(dòng)軌跡[1,10],但是該方法忽略了流場(chǎng)中顆粒對(duì)顆粒的相互作用.與此同時(shí),能夠計(jì)算流場(chǎng)中顆粒與顆粒相互作用的離散單元法多用來(lái)研究粉塵顆粒在纖維表面的團(tuán)聚沉積[4-5],并且計(jì)算時(shí)Fluent和EDEM兩軟件之間需要雙向耦合,使得該方法計(jì)算使用時(shí)存在周期時(shí)間長(zhǎng)的弊端.而基于CFD-PBM方法在計(jì)算顆粒之間相互作用的同時(shí)不需要考慮雙向耦合的問(wèn)題,因此可以很好的計(jì)算出顆粒與顆粒之間的團(tuán)聚行為[11-13].

通過(guò)計(jì)算多纖維捕集結(jié)構(gòu)中流體雷諾數(shù)Re<1,屬于層流運(yùn)動(dòng),運(yùn)用-湍流模型以及湍流團(tuán)聚核的合理性假設(shè)包括:(1)從宏觀角度,袋式除塵內(nèi)部是復(fù)雜的三維湍流流場(chǎng)[14],那么粉塵顆粒在被纖維捕集過(guò)程中必然經(jīng)歷著碰撞和湍流團(tuán)聚行為.同時(shí),根據(jù)研究表明[4],工況的改變可能導(dǎo)致纖維捕集過(guò)程湍流的變化;(2)若采用層流計(jì)算,默認(rèn)顆粒在流場(chǎng)中不發(fā)生碰撞,與實(shí)際有一定誤差;(3)使用層流和-湍流模型時(shí),多維捕集結(jié)構(gòu)內(nèi)部的速度分布相同.

為獲得纖維捕集過(guò)程中更為符合物理真實(shí)的氣固兩相流流動(dòng)特性,基于CFD-PBM方法對(duì)多纖維捕集顆粒過(guò)程中流場(chǎng)內(nèi)顆粒微觀變化團(tuán)聚現(xiàn)象進(jìn)行系統(tǒng)的研究.同時(shí),顆粒團(tuán)聚后的破碎問(wèn)題根據(jù)文獻(xiàn)[15]研究結(jié)果可忽略.在傳統(tǒng)歐拉雙流體模型的基礎(chǔ)上加載群體顆粒模型,綜合考慮了停留時(shí)間、入口風(fēng)速、粉塵粒徑、以及體積分?jǐn)?shù)對(duì)粉塵顆粒湍流團(tuán)聚的影響.為后續(xù)研究纖維捕集過(guò)程中的團(tuán)聚奠定了一定的基礎(chǔ).

1 數(shù)值計(jì)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(dòng)量方程如下[5]:

1.2 顆粒群平衡方程

顆粒團(tuán)聚可以用粒子的聚并動(dòng)力學(xué)方程(General Dynamic Equation,GDE/PBE)來(lái)進(jìn)行描述,即聚并動(dòng)力學(xué)方程如下[16]:

1.3 湍流聚并核函數(shù)

通過(guò)計(jì)算可知K的數(shù)值趨于0,根據(jù)Saffman和Turner所提出的零慣性顆粒湍流模型來(lái)進(jìn)行描述,顆粒湍流聚并核函數(shù)為[17]:

式中:V表示顆粒之間實(shí)際發(fā)生的碰撞次數(shù)與理論上發(fā)生碰撞的比例,即聚并系數(shù);N為粘性力與范德華力的比值;為顆粒變形率;表示湍流耗散率, m2/s3;為氣體的動(dòng)力黏度,Pa·s;為氣體的運(yùn)動(dòng)黏度,m2/s;d和d表示兩顆粒的直徑,μm;為Hamaker常數(shù).

2 邊界條件

2.1 多纖維建模

為建立纖維隨機(jī)分布,基于Poisson(泊松)隨機(jī)直線過(guò)程[18-19],生成過(guò)濾介質(zhì)三維隨機(jī)模型的控制算法.直線L用直線到原點(diǎn)的距離X和方向角M描述,隨機(jī)X可以是任意實(shí)數(shù),隨機(jī)方向角M在[0, π]之間取值.采用Poisson隨機(jī)過(guò)程對(duì)相互獨(dú)立的隨機(jī)序列(1,1), (2,2),…,(X,M)進(jìn)行描述,由直線簇L中所有相互交叉的直線(1,1),(2,2),… ,(X,M)構(gòu)成多纖維結(jié)構(gòu).對(duì)于多纖維的建模引用文獻(xiàn)[20]的方法,模型如圖1所示:

圖1 多纖維過(guò)濾介質(zhì)結(jié)構(gòu)模型

2.2 多纖維捕集模型建立

對(duì)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,以入口粉塵粒徑為1.0μm為例,Ratio Exponent數(shù)值取1.0,根據(jù)Gelbard[22]提出的分區(qū)方法,將顆粒群大小劃分為8個(gè)子區(qū)間,如表1所示.

表1 Bin-7～Bin-0區(qū)間粒徑大小以及區(qū)間顆粒初始占比

Bin-7～Bin-0區(qū)間粒徑大小由初始粒徑計(jì)算得來(lái),(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V+1=fV,比例系數(shù)1.08￡f￡3.0).不同初始粒徑對(duì)應(yīng)不同組的Bin-7～Bin-0.通過(guò)計(jì)算, 0.5～5.0μm對(duì)應(yīng)的Bin-7～Bin-0如表2所示.團(tuán)聚過(guò)程為Bin-7→Bin-6→Bin-5→Bin-4→Bin-3→Bin-2→Bin-1→Bin-0.在每個(gè)子區(qū)間內(nèi)對(duì)群體平衡模型進(jìn)行積分即可得到一系列離散的方程.同時(shí),使用EWF模型結(jié)合計(jì)算粉塵顆粒在纖維表面的沉積.

圖2 計(jì)算區(qū)域及邊界條件示意

表2 不同初始粒徑下Bin-7～Bin-0區(qū)間對(duì)應(yīng)的粒徑值

3 正確性驗(yàn)證

3.1 網(wǎng)格獨(dú)立性檢驗(yàn)

為排除多纖維網(wǎng)格數(shù)量對(duì)數(shù)值模擬的影響,對(duì)其進(jìn)行了網(wǎng)格獨(dú)立性檢驗(yàn)(=3,=10,=3μm),計(jì)算不同網(wǎng)格密度下的壓力損失,結(jié)果見(jiàn)表3,當(dāng)網(wǎng)格數(shù)量由Mesh1增長(zhǎng)到Mesh2時(shí),壓降的變化為4.009 %,網(wǎng)格數(shù)量由Mesh2增長(zhǎng)到Mesh4時(shí),壓降的變化為0.5694 %,即多纖維捕集結(jié)構(gòu)網(wǎng)格達(dá)到270萬(wàn)左右時(shí),進(jìn)出口的壓降基本保持不變,因此選擇270萬(wàn)的網(wǎng)格進(jìn)行數(shù)值模擬計(jì)算,計(jì)算所使用的網(wǎng)格為四面體非結(jié)構(gòu)化網(wǎng)格,在劃分網(wǎng)格時(shí)將固體域纖維體定義為Solid,流體域定義為Fluid.

表3 網(wǎng)格獨(dú)立性檢驗(yàn)(v=0.1m/s)

3.2 模型驗(yàn)證

圖3 多纖維過(guò)濾壓降數(shù)值模擬與經(jīng)驗(yàn)公式對(duì)比

同時(shí),將多纖維過(guò)濾效率與經(jīng)驗(yàn)公式(6)進(jìn)行對(duì)比[1,8-10],由于所研究的粒徑范圍為0.5～5.0μm,常溫[27]下當(dāng)p=0.5μm時(shí),粉塵顆粒的布朗團(tuán)聚可以忽略.由圖4可知,多纖維對(duì)粉塵顆粒進(jìn)行捕集時(shí),數(shù)值計(jì)算所得到的趨勢(shì)與經(jīng)驗(yàn)公式理論模型基本一致,基于CFD-PBM計(jì)算符合數(shù)值模擬計(jì)算的要求.

圖4 多纖維過(guò)濾效率數(shù)值模擬與經(jīng)驗(yàn)公式對(duì)比

4 數(shù)值計(jì)算結(jié)果

4.1 捕集過(guò)程中停留時(shí)間對(duì)顆粒湍流團(tuán)聚的影響

圖5 停留時(shí)間對(duì)顆粒湍流團(tuán)聚的影響

由圖5可知,Bin-7區(qū)間顆粒數(shù)量濃度減小,Bin- 6～Bin-0區(qū)間顆粒數(shù)量濃度增加,說(shuō)明顆粒在多纖維捕集模型中存在明顯的碰撞與團(tuán)聚,隨著時(shí)間的增加,粉塵顆粒的湍流團(tuán)聚效果逐漸增強(qiáng),粉塵顆粒在流場(chǎng)的作用下碰撞后受范德華力發(fā)生團(tuán)聚,粒徑逐漸向大顆粒偏移.當(dāng)3/,團(tuán)聚逐漸趨于穩(wěn)定.粒徑段越靠近初始顆粒,達(dá)到穩(wěn)定所需要的時(shí)間越短,小粒徑段顆粒相比較于大粒徑段顆粒團(tuán)聚速率較大.但單位時(shí)間內(nèi)小粒徑段顆粒數(shù)量濃度變化百分比較小.

4.2 捕集過(guò)程中入口風(fēng)速對(duì)顆粒湍流團(tuán)聚的影響

由圖6可知,團(tuán)聚呈現(xiàn)出不同的三段規(guī)律,Ⅰ段(Bin-7區(qū)間),入口風(fēng)速越大,穩(wěn)定后Bin-7區(qū)間顆粒數(shù)量濃度越大,表現(xiàn)出入口風(fēng)速越大,顆粒團(tuán)聚程度越小;Ⅱ段(Bin-6～Bin-2區(qū)間),入口風(fēng)速越大,穩(wěn)定后Bin-6～Bin-2區(qū)間顆粒數(shù)量濃度越小,表現(xiàn)出入口風(fēng)速越大,顆粒團(tuán)聚程度越小;Ⅲ段(Bin-1～Bin-0區(qū)間),入口風(fēng)速越大,穩(wěn)定后Bin-1～Bin-0區(qū)間的數(shù)量越大,表現(xiàn)出入口風(fēng)速越大,顆粒團(tuán)聚程度越大.

圖6 入口風(fēng)速對(duì)顆粒湍流團(tuán)聚的影響

圖7(a)表示Bin-7區(qū)間顆粒數(shù)量濃度在不同入口風(fēng)速下隨停留時(shí)間變化曲線.入口風(fēng)速越大,Bin-7區(qū)間顆粒數(shù)量濃度隨停留時(shí)間下降越快,即團(tuán)聚速率越大,但穩(wěn)定后Bin-7區(qū)間顆粒數(shù)量濃度越大,這是因?yàn)樗俣仍龃髮?dǎo)致顆粒在纖維捕集結(jié)構(gòu)中停留時(shí)間減少.通過(guò)圖7(b)和(c)可知,速度越大,粉塵顆粒的團(tuán)聚速率越大,唯一不同的是穩(wěn)定后7(b)中顆粒數(shù)量濃度大小與速度大小呈負(fù)相關(guān),7(c)中呈正相關(guān),根據(jù)圖5的規(guī)律,Bin-0相比于Bin-3區(qū)間顆粒粒徑較大,單位時(shí)間內(nèi)的Bin-0區(qū)間數(shù)量濃度變化百分比要大于Bin-3區(qū)間,速度增加導(dǎo)致停留時(shí)間減小,對(duì)于7(b)中的小顆粒,速度增加導(dǎo)致的顆粒數(shù)量濃度的增加量小于因?yàn)橥Ａ魰r(shí)間減小損失的顆粒數(shù)增加量;對(duì)于7(c)中的大顆粒,速度增加導(dǎo)致的顆粒數(shù)量濃度的增加量大于因停留時(shí)間減小損失的顆粒數(shù)增加量.

隨著入口風(fēng)速的增加,湍流耗散率是逐漸增加的,由于在湍流團(tuán)聚核中,顆粒的團(tuán)聚與湍流耗散率成正比,故湍流耗散率越大,粉塵顆粒的團(tuán)聚速率越大,但最終的團(tuán)聚效果取決于入口風(fēng)速和粉塵顆粒在流場(chǎng)中的停留時(shí)間,當(dāng)max·￡,入口風(fēng)速越大,顆粒團(tuán)聚程度越大.

4.3 捕集過(guò)程中入口粒徑對(duì)顆粒湍流團(tuán)聚的影響

由圖8可知,入口粒徑越大,團(tuán)聚穩(wěn)定后Bin-7區(qū)間與Bin-0區(qū)間顆粒數(shù)量濃度的數(shù)量級(jí)差距越大,說(shuō)明入口粒徑越大,粉塵顆粒的團(tuán)聚程度越小.

圖8 粉塵粒徑對(duì)顆粒湍流團(tuán)聚的影響

由圖9可知,出口平均粒徑隨時(shí)間都呈現(xiàn)先增加后趨于平穩(wěn)的趨勢(shì),不同粒徑的粉塵顆粒達(dá)到團(tuán)聚穩(wěn)定的時(shí)刻不同,入口粉塵顆粒粒徑越大,流場(chǎng)中的顆粒數(shù)目越少,相同時(shí)間內(nèi)碰撞幾率減小,團(tuán)聚速率減小.同時(shí),出口處平均粒徑與原粒徑相比增加的倍率越小,這是因?yàn)轭w粒粒徑越小,擾動(dòng)性越強(qiáng),在流場(chǎng)中跟隨性好,使得流場(chǎng)中的粉塵顆粒更容易發(fā)生碰撞,而對(duì)于大粒徑顆粒,不容易受到擾動(dòng), 在流場(chǎng)中跟隨性較差,再加上流場(chǎng)中的顆粒數(shù)目由于粒徑增大減少,直接導(dǎo)致顆粒間碰撞幾率減小,顆粒的團(tuán)聚程度減小.

圖9 出口平均粒徑隨停留時(shí)間變化曲線

4.4 捕集過(guò)程中體積分?jǐn)?shù)對(duì)顆粒湍流團(tuán)聚的影響

圖10表明,粉塵顆粒的體積分?jǐn)?shù)越大,粉塵顆粒在流場(chǎng)中的團(tuán)聚效果越明顯,團(tuán)聚程度越大.這是由于粒徑不變時(shí),體積分?jǐn)?shù)增大直接導(dǎo)致流場(chǎng)內(nèi)顆粒數(shù)目增加,增加了粉塵顆粒碰撞的幾率.同時(shí),粉塵顆粒體積分?jǐn)?shù)越大,單位時(shí)間內(nèi)Bin-7區(qū)間顆粒數(shù)量濃度下降越快,即向大顆粒轉(zhuǎn)化的速度越快,說(shuō)明粉塵顆粒體積分?jǐn)?shù)越大,粉塵顆粒的團(tuán)聚速率越大,團(tuán)聚程度越大.當(dāng)=0.1m/s,p=1.0μm, VF>0.03636, Bin-7～Bin-0的顆粒數(shù)量濃度對(duì)數(shù)分布成線性比例關(guān)系.

圖10 粉塵體積分?jǐn)?shù)對(duì)顆粒湍流團(tuán)聚的影響

5 結(jié)論

5.1 粉塵顆粒在流場(chǎng)的作用下碰撞后受范德華力的作用發(fā)生湍流團(tuán)聚,粒徑逐漸向大顆粒偏移,當(dāng)3/,團(tuán)聚逐漸趨于穩(wěn)定.小粒徑段顆粒相比較于大粒徑段顆粒團(tuán)聚速率較大. 但單位時(shí)間內(nèi)小粒徑段顆粒數(shù)量濃度變化百分比較小.

5.3 入口初始粉塵粒徑越大,出口處平均粒徑與初始粒徑相比增加的倍數(shù)越小,即團(tuán)聚程度和團(tuán)聚速率越小;粉塵顆粒體積分?jǐn)?shù)越大,顆粒之間碰撞的幾率越大,粉塵顆粒的湍流團(tuán)聚速率以及團(tuán)聚程度越大,當(dāng)=0.1m/s,p=1.0μm,VF>0.03636,Bin-7～Bin-0的顆粒數(shù)量濃度對(duì)數(shù)分布成線性比例關(guān)系.

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Study on turbulent aggregation characteristics in the process of fine-particle captured by multi-fiber.

ZHANG Li-An1, DIAO Yong-fa1*, CHU Ming-Hao1, JIA Zhong-Jian1, SHEN Heng-Gen1, SUN Jing2

(1.School of Environmental Science and Engineering College, Dong Hua University, Shanghai 201620, China；2.Gansu Lanfei Environment Protection Co., Ltd. Lanzhou 730030, China)., 2021,41(10)：4572～4578

This paper established the flat 3-D mimic structure that was based on the random multi-fiber filter media algorithm. The computational fluid dynamics-population balance model (CFD-PBM) was used to simulate the turbulent aggregation of fine particles during the multi-fiber capture. The partition method was used to solve the population balance equation (PBE). The analysis by the controlled variable method shows that there was apparent particle aggregation behavior in the multi-fiber capturing process. The particle aggregation degree increased with the increasing residence time and gradually stabilizes while3/(dimensional length along with the flow field direction/inlet velocity). Whenmax·￡, the larger the velocity inlet, the larger the particle aggregation degree and the aggregation rate, but the final aggregation degree depends on the velocity inlet and residence time; the larger the particle diameter, the smaller the particle aggregation degree and the aggregation rate. Also, the smaller the ratio of the average particle diameter of the outlet compared with the initial particle diameter. The larger the volume fraction of dust particles, the larger the particle aggregation degree and the aggregation rate. When=0.1m/s,p=1.0μm, VF > 0.003636, the number concentration logarithmic distribution between Bin-7～Bin-0 shows a linear proportional relationship.

computational fluid dynamics-population balance model；population balance equation；partition method；turbulent aggregation；multi-fiber

X513

A

1000-6923(2021)10-4572-07

張儷安(1990-),男,安徽省淮北人,東華大學(xué)博士研究生,主要從事工業(yè)煙氣PM2.5控制技術(shù)研究.發(fā)表論文4篇.

2021-02-09

國(guó)家重點(diǎn)研發(fā)計(jì)劃項(xiàng)目(2018YFC0705300);中央高校基本科研業(yè)務(wù)費(fèi)重點(diǎn)項(xiàng)目(2232017A-09);中央高?；究蒲袠I(yè)務(wù)費(fèi)專(zhuān)項(xiàng)資金、東華大學(xué)研究生創(chuàng)新基金項(xiàng)目(CUSF-DH-D-2020067);蘭州市人才創(chuàng)新項(xiàng)目(2019-RC-7)

* 責(zé)任作者, 教授, diaoyongfa@dhu.edu.cn