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        基于CFD-DEM的超細(xì)碳酸鈣螺旋輸送仿真分析

        2024-09-29 00:00:00蔡文源王利強(qiáng)徐立敏
        中國粉體技術(shù) 2024年3期

        摘要:【目的】為提高螺旋輸送機(jī)的輸送效率,降低輸送機(jī)的功耗與磨損,探究在不同進(jìn)料速率、螺旋軸轉(zhuǎn)速與幾何體摩擦系數(shù)下,超細(xì)碳酸鈣在水平變徑變距螺旋輸送機(jī)內(nèi)的顆粒流動(dòng)狀態(tài)、出口質(zhì)量流量、輸送機(jī)功耗與磨損分布?!痉椒ā渴褂糜?jì)算流體動(dòng)力學(xué)(computational fluid dynamics,CFD)與離散單元法(discrete element method,DEM)雙向耦合數(shù)值模擬的方法,對(duì)螺旋輸送機(jī)在不同轉(zhuǎn)速下的質(zhì)量流率進(jìn)行分析對(duì)比,驗(yàn)證數(shù)值模型的正確性?!窘Y(jié)果】摩擦系數(shù)對(duì)顆粒的運(yùn)動(dòng)有較大影響,顆粒流的軸向速度峰值和質(zhì)量流率峰值隨著摩擦系數(shù)的增加先增大再減??;隨著下料速度和摩擦系數(shù)的增大,輸送機(jī)功率明顯增大,且摩擦系數(shù)在高進(jìn)料速度與低轉(zhuǎn)速的情況下對(duì)功耗的影響相對(duì)于低進(jìn)料速度和高轉(zhuǎn)速更加明顯;磨損較嚴(yán)重的區(qū)域集中在下料口處的螺旋軸與螺旋葉片的邊緣處。【結(jié)論】簡單增大或減小摩擦系數(shù)并不能提高顆粒的軸向速度和質(zhì)量流量,而是存在一個(gè)局部最優(yōu)參數(shù)組合;適當(dāng)?shù)靥岣咿D(zhuǎn)速能夠減小顆粒密實(shí)度與顆粒停留時(shí)間,從而減小輸送機(jī)的功耗與幾何體磨損。

        關(guān)鍵詞:超細(xì)碳酸鈣;計(jì)算流體動(dòng)力學(xué);離散單元法;螺旋輸送機(jī);顆粒流動(dòng)

        中圖分類號(hào):TB44;TH224文獻(xiàn)標(biāo)志碼:A

        引用格式:

        蔡文源,王利強(qiáng),徐立敏.基于CFD-DEM的超細(xì)碳酸鈣螺旋輸送仿真分析[J].中國粉體技術(shù),2024,30(3):100-111.

        CAI W Y,WANG L Q,XU L M.Simulation analysis of ultrafine calcium carbonate spiral transportation based on CFD-DEM[J].China Powder Science and Technology,2024,30(3):100?111.

        在現(xiàn)代工業(yè)過程中,螺旋輸送機(jī)作為一種高效的固體物料輸送設(shè)備,因結(jié)構(gòu)簡單、維護(hù)成本低并且能夠在水平、傾斜或垂直方向上輸送物料而被廣泛應(yīng)用[1]。在粉體工業(yè)中,螺旋輸送機(jī)展現(xiàn)出獨(dú)特的優(yōu)勢,特別是在輸送超細(xì)粉體材料時(shí),螺旋輸送機(jī)通過螺旋葉片的旋轉(zhuǎn)運(yùn)動(dòng)和密封的輸送管道可實(shí)現(xiàn)高效率輸送并能夠有效減少粉塵飛揚(yáng)。超細(xì)碳酸鈣作為一種重要的無機(jī)非金屬粉體材料,在塑料、橡膠、涂料、造紙等行業(yè)中得到了廣泛應(yīng)用[2]。由于超細(xì)碳酸鈣粒徑極小且具有一定的黏附性,在輸送過程中易導(dǎo)致輸送效率下降和設(shè)備磨損增加,因此對(duì)輸送設(shè)備的設(shè)計(jì)和操作提出了更高的要求。

        隨著計(jì)算機(jī)模擬技術(shù)的進(jìn)步,離散元單元法(discrete element method,DEM)已成為研究螺旋輸送機(jī)輸送過程中顆粒流動(dòng)和相互作用的重要方法[3-4]。Wang等[5]運(yùn)用DEM對(duì)不同轉(zhuǎn)速和填充水平條件下顆粒流動(dòng)狀態(tài)及輸送過程進(jìn)行了模擬研究,并預(yù)測了顆粒速度的空間分布和速度分布;賈宏禹等[6-7]運(yùn)用DEM對(duì)傾角為45°的螺旋輸送機(jī)進(jìn)行仿真,分析物料在輸送機(jī)內(nèi)的速度分布與流動(dòng)行為,并研究了摩擦因數(shù)對(duì)顆粒速度的影響規(guī)律。Karwat等[8]基于DEM分析物料運(yùn)動(dòng)速度,研究在不同螺桿螺距下物料顆粒尺寸、摩擦系數(shù)和恢復(fù)系數(shù)與螺旋輸送機(jī)輸送能力之間的關(guān)系。

        DEM中單一的固相分析無法準(zhǔn)確地描述螺旋輸送機(jī)內(nèi)顆粒與氣體之間的關(guān)系。近年來計(jì)算流體動(dòng)力學(xué)(computational fluid dynamics,CFD)與DEM耦合方法應(yīng)運(yùn)而生[9]。CFD-DEM耦合方法相對(duì)DEM能夠更精確地模擬顆粒之間的碰撞、顆粒與輸送機(jī)壁面的相互作用以及顆粒流與氣體流的動(dòng)態(tài)相互影響。近年來有眾多的研究者通過CFD-DEM耦合方法對(duì)螺旋輸送性能進(jìn)行研究。Liu等[10]采用CFD-DEM耦合方法詳細(xì)分析了稻谷的運(yùn)動(dòng)和氣流場,通過改變水平螺旋輸送機(jī)的風(fēng)機(jī)速度、填充系數(shù)、轉(zhuǎn)速,大大提高了顆粒的輸送速度、物料分散性以及質(zhì)量流量。Wang等[11]和Banooni等[12]對(duì)螺旋輸送機(jī)內(nèi)顆粒流動(dòng)行為進(jìn)行了對(duì)比分析模擬,與單一DEM固相模擬結(jié)果相比,使用CFD-DEM耦合方法預(yù)測的質(zhì)量流量更加貼合實(shí)際,說明螺旋輸送器內(nèi)部的氣體流動(dòng)不可忽略。Xiong等[13]和Lang等[14]使用CFD-DEM耦合方法模擬了不同粒徑分布、流體流速、顆粒密度對(duì)顆粒遷移和應(yīng)力傳遞的影響?,F(xiàn)有的基于CFD-DEM耦合方法對(duì)物料螺旋輸送的研究,通常集中于對(duì)較大顆粒物料在螺旋輸送過程中的操作參數(shù)。相比之下,對(duì)于超細(xì)粉體螺旋輸送過程中的幾何摩擦系數(shù)的研究較少。

        本研究中采用CFD-DEM耦合方法,使用流體動(dòng)力學(xué)軟件Fluent與離散元軟件EDEM,深入探討不同操作參數(shù)與幾何參數(shù)下超細(xì)碳酸鈣粉體在水平變徑變距螺旋輸送過程中的氣固兩相流動(dòng)特性,為超細(xì)粉體的有效輸送提供理論和技術(shù)支持,同時(shí)也為相關(guān)領(lǐng)域的工程應(yīng)用和科學(xué)研究提供新的視角和方法論基礎(chǔ)。

        1輸送理論

        在CFD-DEM氣固耦合中氣相視為連續(xù)相,并滿足連續(xù)性方程與動(dòng)量守恒方程,湍流模型采用更加符合螺旋輸送機(jī)內(nèi)部復(fù)雜湍流流動(dòng)的RNG k-ε模型;顆粒視為離散相,通過牛頓動(dòng)力學(xué)方程來描述其運(yùn)動(dòng)行為[15-17]。

        1.1連續(xù)相

        連續(xù)性方程為

        (φgρg)+??(φgρg vg)=0,

        式中:t為時(shí)間;φg為氣體體積分?jǐn)?shù);ρg為氣體密度;vg為氣體速度。

        動(dòng)量守恒方程為

        (φgρg vg)+??(φgρgvg vg)=-φg?pg+??τg+φgρgg+Kgs(vs-vg),

        式中:pg為氣體壓力;τg為氣相應(yīng)力張量;g為重力加速度;vs為顆粒速度。

        湍流模型中湍動(dòng)能k和湍動(dòng)能耗散率ε的表達(dá)式為

        (ρgk)+(ρgkvg)=αkμg+Gk+Gb-ρgε,(ρgε)+(ρgεvg)=αεμg+(Cε1 Gk-Cε2ρgε)-Rε,

        式中:xi、xj為顆??臻g坐標(biāo);αk和αε分別為k和ε的有效普朗特?cái)?shù)倒數(shù);μg為氣體有效黏度;Gk和Gb分別為平均速度梯度和浮力引起的湍動(dòng)能;Cε1和Cε2的默認(rèn)值為1.42和1.68;Rε為RNG k-ε模型的附加項(xiàng)。

        顆粒的運(yùn)動(dòng)軌跡可以運(yùn)用拉格朗日坐標(biāo)系對(duì)顆粒運(yùn)動(dòng)方程進(jìn)行積分得到。在牛頓第二定律理論基礎(chǔ)上建立的顆粒離散相控制方程為

        mpFw-p+Fp-p-Ft+mpg,(5)

        Ip=Wp,(6)

        式中:mp為顆粒p的質(zhì)量;vp為平移速度;Fw-p和Fp-p分別為顆粒-幾何體與顆粒-顆粒的作用力;Ff為顆粒-流體作用力;Ip為顆粒的轉(zhuǎn)動(dòng)慣量;ωp為顆粒的角速度;Wp為顆粒所受力矩。

        1.2連續(xù)相與離散相耦合

        依據(jù)公式(2)和公式(5),通過動(dòng)量交換來實(shí)現(xiàn)連續(xù)相與離散相的耦合,顆粒-流體作用力Ff的表達(dá)式為Ff=Kgs(vg-vs),(7)

        式中,Kgs為動(dòng)量交換系數(shù)。本文中曳力模型采用Gidaspow模型[18],其表達(dá)式如下

        K(K)g(g)s(s)50(C)φ(D)p(φ)2 g(v)s 1(φ)g(-)75(2.65)pρd(g|)pvg-vs|),φ(φ)p(p)0(0).(.)8(8),(,)(8)

        式中:φp為顆粒體積分?jǐn)?shù);dp為顆粒粒徑;CD為曳力系數(shù),表達(dá)式為

        顆粒雷諾數(shù)Res表達(dá)式為

        Res=dp|vg-vs|φg。(10)

        1.3磨損模型

        在本研究中,采用Archard磨損模型來描述螺旋葉片表面的磨損過程。根據(jù)Archard磨損模型,螺旋葉片表面被磨損的材料量與顆粒在該表面摩擦作用所施加的摩擦功之間呈正相關(guān)關(guān)系。Archard模型的數(shù)學(xué)表達(dá)式為

        V=WFn dt,(11)

        式中:V為材料被移除的體積;W為初始磨損常數(shù);Fn為顆粒與壁面接觸的法向力;dt為顆粒沿壁面的切向滑動(dòng)距離。其中磨損常數(shù)W的數(shù)學(xué)表達(dá)式為

        W=K/H,(12)

        式中:K為無量綱常數(shù),取K為3×10-3;H為材料的最軟表面布氏硬度,螺旋輸送機(jī)的材料為不銹鋼,取H為150。

        每個(gè)離散相單元的磨損深度Hp可表示為

        Hp=V/a,(13)

        式中,a為顆粒-幾何體接觸面積。

        2數(shù)值模擬

        2.1仿真模型與網(wǎng)格劃分

        本文中構(gòu)建的水平變徑變距螺旋輸送機(jī)仿真模型,是基于江蘇省創(chuàng)新包裝科技有限公司實(shí)際使用的輸送裝置進(jìn)行建模的,在保證模擬結(jié)果準(zhǔn)確性的前提下進(jìn)行了適當(dāng)簡化。螺旋輸送機(jī)仿真模型包括螺旋套筒、下料口、螺旋軸和螺旋葉片,其仿真模型和具體結(jié)構(gòu)如圖1、2所示。模型按照功能分為進(jìn)料段、密實(shí)段和卸料段。在該水平變徑變距螺旋輸送機(jī)仿真模型中,葉片厚度與高度分別為2、31 mm;下料口長度、寬度分別為180、60 mm;進(jìn)料段、密實(shí)段和卸料段的長度分別為205、205、330 mm,進(jìn)料段與卸料段的套筒直徑分別為108、85 mm,螺旋軸直徑分別為45、22 mm,螺距分別為80、90 mm。

        將上述幾何模型導(dǎo)入CFD的前處理軟件integrated computer engineering and manufacturing進(jìn)行網(wǎng)格劃分,將模型劃分為旋轉(zhuǎn)域和靜止域2個(gè)區(qū)域[19-23]。鑒于包含螺旋體的旋轉(zhuǎn)域結(jié)構(gòu)復(fù)雜,本研究中選擇應(yīng)用適應(yīng)性較高的四面體非結(jié)構(gòu)化網(wǎng)格進(jìn)行網(wǎng)格劃分,而在靜態(tài)域中則使用六面體結(jié)構(gòu)化網(wǎng)格來進(jìn)行劃分。圖3展示了詳細(xì)的網(wǎng)格劃分情況。在進(jìn)行模擬計(jì)算時(shí),針對(duì)旋轉(zhuǎn)域和靜態(tài)域采用不同的參考系進(jìn)行計(jì)算。其多重參考系的變換方程可表示為

        vr=v-ω×r,

        ?v=?vr+?(ω×r),

        式中:vr為氣體相對(duì)于旋轉(zhuǎn)參考系的速度;v為氣體靜止參考系下的絕對(duì)速度;ω為氣體旋轉(zhuǎn)域的角速度;r為氣體從旋轉(zhuǎn)軸到觀察點(diǎn)的距離;vt為氣體在旋轉(zhuǎn)參考系內(nèi)相對(duì)于靜止參考系的速度。

        2.2仿真參數(shù)

        在仿真實(shí)驗(yàn)中,超細(xì)碳酸鈣的直徑設(shè)定為1 mm,密度設(shè)定為2 800 kg/m3,泊松比設(shè)定為0.28,剪切模量設(shè)定為5×107 Pa;不銹鋼的密度設(shè)定為7 800 kg/m3,泊松比設(shè)定為0.3,剪切模量設(shè)定為7×107 Pa;超細(xì)碳酸鈣與超細(xì)碳酸鈣之間的恢復(fù)系數(shù)為0.3,摩擦系數(shù)為0.36;超細(xì)碳酸鈣與不銹鋼之間的恢復(fù)系數(shù)為0.3,摩擦系數(shù)設(shè)定三種不同的變量值(f1=0.15、f2=0.3、f3=0.45),JKR表面能為0.032 1 J/m2;仿真實(shí)驗(yàn)的計(jì)算時(shí)間步長設(shè)定為8.66×10-6 s,網(wǎng)格尺寸為3 R,并采用三種不同的螺旋軸轉(zhuǎn)速(vn1=275 r/min、vn2=300 r/min、vn3=325 r/min)和三種不同的進(jìn)料速度(vq1=1.5 kg/s、vq2=2 kg/s、vq3=2.5 kg/s)進(jìn)行仿真實(shí)驗(yàn)。在EDEM軟件中選擇能夠準(zhǔn)確反映具有一定黏結(jié)性特征顆粒的Hertz-Mindlin with JKR接觸模型。在Fluent軟件中,將空氣視為不可壓縮相,設(shè)定氣體的初始速度為0.5 m/s,并選擇壓力出口作為出口邊界條件,湍流模型采用更加符合螺旋輸送機(jī)內(nèi)部復(fù)雜湍流流動(dòng)的RNG k-ε模型。求解器采用壓力基進(jìn)行求解[24-26]。

        3結(jié)果與分析

        3.1模型驗(yàn)證

        試驗(yàn)材料選用江蘇省創(chuàng)新包裝科技有限公司生產(chǎn)的超細(xì)碳酸鈣,平均粒徑為26.78μm,密度約為2 800 kg/m3。在試驗(yàn)過程中,以水平變徑變距螺旋輸送機(jī)為對(duì)象,設(shè)定超細(xì)碳酸鈣-不銹鋼摩擦系數(shù)為0.3,設(shè)置下料速度vq為2 kg/s,3組不同的螺旋轉(zhuǎn)速vn分別為275、300、325 r/min進(jìn)行實(shí)驗(yàn)。

        實(shí)驗(yàn)裝置基于江蘇創(chuàng)新包裝科技有限公司,總體裝置示意圖如圖4所示。在超細(xì)碳酸鈣螺旋輸送過程中,物料首先被送入下料筒,在輔助下料裝置的攪拌作用下實(shí)現(xiàn)均勻分散,之后被輸送入水平變徑變距螺旋輸送機(jī)中。螺旋軸由內(nèi)置編碼器的伺服電動(dòng)機(jī)驅(qū)動(dòng)以精準(zhǔn)轉(zhuǎn)速旋轉(zhuǎn),將物料水平向左推送,經(jīng)過下料段、密實(shí)段與卸料段掉入固定在輸送機(jī)出口處的包裝袋中,包裝袋由振動(dòng)托盤承托,當(dāng)包裝袋內(nèi)的粉體達(dá)到一定質(zhì)量時(shí),托盤下方的稱重傳感器將發(fā)出信號(hào),標(biāo)志著一次充填過程的結(jié)束。

        在試驗(yàn)中,通過調(diào)節(jié)進(jìn)口閘門來控制進(jìn)料量,并利用電動(dòng)機(jī)帶動(dòng)同步帶調(diào)整螺旋軸的轉(zhuǎn)速。通過連接電子天平和傳感器,統(tǒng)計(jì)在不同的轉(zhuǎn)速下輸送機(jī)的平均質(zhì)量流率,具體的實(shí)驗(yàn)數(shù)據(jù)和同一工況下的模擬數(shù)據(jù)如圖5所示。從圖中可知,部分實(shí)驗(yàn)數(shù)據(jù)在2 s后出現(xiàn)些許波動(dòng),但總體而言,實(shí)驗(yàn)數(shù)據(jù)與模擬曲線基本一致,誤差較小,因此,可以認(rèn)為該模型對(duì)超細(xì)碳酸鈣的輸送模擬精度較高,可作為研究超細(xì)碳酸鈣螺旋輸送過程仿真模擬的可靠模型。

        3.2顆粒軸向速度與周向速度

        圖6所示為在vn=300 r/min、vq=2 kg/s和f=0.3條件下顆粒在水平變徑變距螺旋輸送機(jī)卸料段內(nèi)的速度場,其中箭頭代表顆粒的運(yùn)動(dòng)方向,顏色表示顆粒運(yùn)動(dòng)速度的大小。由圖6可知,所有顆粒朝向螺旋軸出口方向移動(dòng),其中絕大多數(shù)顆粒展現(xiàn)出平穩(wěn)的流動(dòng)狀態(tài),反映出螺旋輸送機(jī)擁有較為穩(wěn)定的輸送性能。圖中顯示,位于顆粒流表面的少數(shù)顆粒呈現(xiàn)紅色,代表這些位于上層的顆粒流相較于底部的顆粒具有更快的移動(dòng)速度。進(jìn)一步觀察發(fā)現(xiàn),緊靠螺旋葉片的顆粒傾向于沿葉片表面向上移動(dòng),而上層顆粒流傾向于順著顆粒流表面向下流動(dòng),形成一定的傾角,表明在螺旋輸送機(jī)的每一節(jié)內(nèi),顆粒流存在循環(huán)流動(dòng)的現(xiàn)象。

        圖7為顆粒沿螺旋軸的速度分布。圖7(a)呈現(xiàn)了在轉(zhuǎn)速為300 r/min、進(jìn)料質(zhì)量流量為2 kg/s的工況下,螺旋輸送機(jī)內(nèi)不同摩擦系數(shù)的顆粒沿螺旋軸的軸向速度分布。摩擦系數(shù)為f1條件下的顆粒在下料段時(shí),由于摩擦系數(shù)小,受螺旋葉片的推動(dòng)力不足,且活動(dòng)空間大,因此顆粒易沿著螺旋葉片滑動(dòng),從而導(dǎo)致平均軸向速度最小。摩擦系數(shù)為f3條件下的顆粒在下料段時(shí),顆粒在受到螺旋推動(dòng)時(shí)更容易沿螺旋前進(jìn)而不是在管道內(nèi)打滑或掉落至上一節(jié)螺旋中,因此在初始階段f3條件下的顆粒速度最大。隨著進(jìn)入密實(shí)段與卸料段,螺旋軸軸徑和套筒直徑逐漸減小,空間變得更加擁擠,顆粒與幾何體之間的摩擦力逐漸增大,使顆粒之間排列緊密,增大了粉體密實(shí)度,提高了螺旋輸送效率。對(duì)于f3條件下的顆粒,更小的空間意味著與筒壁之間有更大的阻力且顆粒更容易翻越螺旋軸掉入上一節(jié),使得顆粒平均軸向速度增速減小,而f1和f2條件下的顆粒的速度增速逐漸增大。在最后的卸料段中,由于輸送機(jī)的軸徑和套筒直徑最小,此時(shí)顆粒已經(jīng)處于較為密實(shí)的狀態(tài),顆粒之間的相互作用以及與螺旋和套筒的摩擦相對(duì)穩(wěn)定,在這個(gè)狀態(tài)下,所有顆粒的軸向速度都會(huì)增加并達(dá)到峰值。對(duì)f2條件下的顆粒,顆粒既能有效利用螺旋的推動(dòng)力,又不像f3條件下的顆粒在狹小空間下受到過大的阻力,因此在卸料段f2條件下的顆粒具有最大的軸向平均速度。綜上所述,在水平變徑變距螺旋輸送機(jī)中,顆粒與幾何體之間的摩擦系數(shù)在不同輸送段對(duì)顆粒的表現(xiàn)具有重要影響,但并不是摩擦系數(shù)越大或越小就能確保最佳的輸送效果,而是存在一個(gè)適當(dāng)?shù)钠胶恻c(diǎn)。

        圖7(b)呈現(xiàn)了在轉(zhuǎn)速為300 r/min、進(jìn)料質(zhì)量流量為2 kg/s的工況下,螺旋輸送機(jī)卸料段內(nèi)某一節(jié)的顆粒周向速度的分布。顆粒的周向速度為正值,表示其趨向上移;反之,若為負(fù)值,則指示下移趨勢。結(jié)果顯示,顆粒的最大上升速度超過其最大下降速度,且所有顆粒在此區(qū)段中間的速度分量最小。這是螺旋葉片帶動(dòng)顆粒運(yùn)動(dòng)的結(jié)果,接近螺旋葉片的顆粒被螺旋葉片帶動(dòng)從而有較大的周向速度,而在區(qū)段中間的顆粒周向速度較小。這反映了螺旋葉片對(duì)顆粒運(yùn)動(dòng)的驅(qū)動(dòng)作用:靠近螺旋葉片的顆粒由于受到葉片的推動(dòng)而具有較大的周向速度,而區(qū)段中心的顆粒周向速度則較小。

        3.3質(zhì)量流率

        螺旋輸送機(jī)的輸送性能可以通過在出口面設(shè)置質(zhì)量流率檢測面來定量評(píng)價(jià),通過記錄離開設(shè)備的顆粒的總質(zhì)量代表設(shè)備的吞吐量。圖8所示為不同工況下顆粒的質(zhì)量流率隨時(shí)間的關(guān)系。圖8(a)—(c)分別顯示了在恒定轉(zhuǎn)速為300 r/min、進(jìn)料質(zhì)量流量vq分別為1.5、2.0、2.5 kg/s的情況下,不同摩擦系數(shù)下輸送機(jī)出口的質(zhì)量流量隨時(shí)間的變化。

        從圖8(a)中可以看出,在幾何體摩擦系數(shù)為f2條件下的顆粒的質(zhì)量流率增速最快,到達(dá)質(zhì)量流率峰值時(shí)間最短,而f3條件下的顆粒在前期的增速稍大于f1條件下的顆粒的,但是達(dá)到峰值的時(shí)間幾乎與f1條件下顆粒的相同,這一現(xiàn)象說明,隨著顆粒的增加,f3條件下的顆粒與幾何體之間的摩擦系數(shù)對(duì)顆粒造成的阻礙逐漸增大,而在f1條件下,由于摩擦系數(shù)較小,物料受到的相對(duì)阻力較小,導(dǎo)致其與f3條件下物料到達(dá)峰值的時(shí)間差異不大。

        進(jìn)一步分析圖8(b)、(c)可知,隨著下料質(zhì)量流量的增加,f1與f3條件下物料的質(zhì)量流量增長速度差異進(jìn)一步縮小。這表明,物料總量的增加加劇了摩擦系數(shù)對(duì)物料流動(dòng)的影響。在穩(wěn)定輸送階段,在進(jìn)料質(zhì)量流量設(shè)定為2 kg/s條件下,摩擦系數(shù)為f1時(shí),輸送機(jī)的平均質(zhì)量流量減小了0.05 kg/s,而在f3條件下,該減少量為0.07 kg/s;當(dāng)進(jìn)料質(zhì)量流量提高到2.5 kg/s時(shí),f1和f3條件下的輸送機(jī)質(zhì)量流量減少量分別為0.09、0.15 kg/s。質(zhì)量流量峰值的變化歸因于顆粒的軸向速度受到摩擦系數(shù)的影響。過大的摩擦系數(shù)阻礙了顆粒的流動(dòng),而過小的摩擦系數(shù)則導(dǎo)致顆粒前進(jìn)動(dòng)量不足,因此,摩擦系數(shù)過大和過小均會(huì)導(dǎo)致顆粒在設(shè)備中的堆積,從而使質(zhì)量流量造成輕微的減小。

        3.4功率

        在螺旋輸送機(jī)的研究領(lǐng)域,功耗的分析是評(píng)估設(shè)備運(yùn)行狀態(tài)并促進(jìn)能源節(jié)約的關(guān)鍵指標(biāo)之一。輸送機(jī)功率是通過將每個(gè)時(shí)間步長接觸點(diǎn)的速度與顆粒與螺桿之間的接觸力的點(diǎn)積求和來計(jì)算的[27]。計(jì)算公式如下

        Ptol=Fi?Vi,(15)

        式中:Ptol為設(shè)備的總功率;Fi為設(shè)備對(duì)顆粒在接觸點(diǎn)的接觸力;Vi為接觸點(diǎn)的速度;下標(biāo)i為每一個(gè)接觸點(diǎn);n為顆粒與設(shè)備在每個(gè)時(shí)間步長中接觸點(diǎn)的數(shù)量總和。

        圖9為不同參數(shù)下螺旋輸送機(jī)的功耗圖。圖9(a)展示了螺旋輸送機(jī)的恒定轉(zhuǎn)速為300 r/min時(shí),不同進(jìn)料質(zhì)量流量條件下,不同幾何體摩擦系數(shù)下的螺旋輸送機(jī)功耗特性。結(jié)果表明,螺旋輸送機(jī)的功耗隨著進(jìn)料質(zhì)量流量的增加而顯著增長,在低進(jìn)料質(zhì)量流量下不同摩擦系數(shù)的輸送設(shè)備功耗差異不大,而在高的進(jìn)料流量下摩擦系數(shù)對(duì)功率消耗的影響更加明顯。進(jìn)一步分析圖9(b)中的數(shù)據(jù),在恒定進(jìn)料速度為2 kg/s下,不同轉(zhuǎn)速與不同摩擦系數(shù)的裝置的功耗情況。結(jié)果顯示,螺旋輸送機(jī)的功耗隨轉(zhuǎn)速的增加而減小。在轉(zhuǎn)速較高時(shí),摩擦系數(shù)對(duì)功耗的影響逐漸減?。辉谵D(zhuǎn)速較低時(shí),幾何體的摩擦系數(shù)對(duì)功耗的影響更加顯著。這些結(jié)果為理解螺旋輸送機(jī)的功耗機(jī)制提供了新的視角,說明在設(shè)計(jì)和運(yùn)行螺旋輸送機(jī)時(shí),必須考慮摩擦系數(shù)對(duì)功耗的影響。

        3.5磨損

        磨損主要發(fā)生在顆粒與螺旋葉片表面碰撞過程中,這種相互作用對(duì)螺旋輸送機(jī)的輸送效率和使用壽命造成一定影響[28]。當(dāng)顆粒與葉片表面接觸時(shí),會(huì)發(fā)生附著或位移現(xiàn)象,從而加劇磨損,因此,深入研究螺旋輸送機(jī)的磨損機(jī)制對(duì)于實(shí)現(xiàn)設(shè)備的高效穩(wěn)定運(yùn)行具有重要的科學(xué)意義。

        圖10所示為在轉(zhuǎn)速設(shè)為300 r/min、進(jìn)料質(zhì)量流量為1.5 kg/s、幾何體摩擦系數(shù)為f2的條件下,螺旋葉片及螺旋軸的磨損速率分布。受到螺旋軸旋轉(zhuǎn)方向影響,葉片背側(cè)的磨損率較低。在螺旋輸送機(jī)的出口區(qū)域,隨著顆粒釋放,顆粒與葉片間的相互作用力降低,進(jìn)而顯著減少了螺桿末端葉片的磨損。磨損分布從螺桿軸向葉片邊緣逐漸增加,并在邊緣處觀察到最大磨損,原因主要是螺桿葉片邊緣受到較大的沖擊力和顆粒的高速運(yùn)動(dòng)影響。

        圖11所示為不同模擬情況下裝置的總磨損情況。由圖可見,總磨損率隨進(jìn)料質(zhì)量流量與摩擦系數(shù)的增加而增大,隨轉(zhuǎn)速的增大而減小。這是由于隨著進(jìn)料質(zhì)量流量的增大,物料通過葉片的數(shù)量增加,從而提高了物料與葉片接觸的頻率和擠壓強(qiáng)度。較高的轉(zhuǎn)速可以減少物料在葉片表面的停留時(shí)間,從而降低物料與葉片之間的相互作用次數(shù),因此在高轉(zhuǎn)速操作下,螺旋葉片的總磨損率較小。同時(shí),摩擦系數(shù)的增加會(huì)導(dǎo)致總磨損量顯著增加,較大的摩擦系數(shù)意味著物料在葉片表面的滑動(dòng)或滾動(dòng)阻力增加,增大了物料與葉片之間的磨擦作用,從而導(dǎo)致更高的磨損率,特別是在較低轉(zhuǎn)速和較高進(jìn)料質(zhì)量流量的條件下,摩擦系數(shù)的影響更加顯著。

        4結(jié)論

        1)在螺旋輸送機(jī)內(nèi),各個(gè)區(qū)段的物料在軸向移動(dòng)的同時(shí)以循環(huán)流的形式在每一節(jié)內(nèi)運(yùn)動(dòng)。顆粒與幾何體之間的摩擦系數(shù)對(duì)顆粒流動(dòng)狀態(tài)具有顯著影響。簡單的增加或減少摩擦系數(shù)并不能實(shí)現(xiàn)顆粒軸向速度和輸送機(jī)質(zhì)量流率的提高,而是存在一個(gè)局部最優(yōu)參數(shù)組合。

        2)隨著下料質(zhì)量流量和摩擦系數(shù)的增大,輸送機(jī)功率明顯增大,適當(dāng)?shù)靥岣咿D(zhuǎn)速能夠降低功耗,且摩擦系數(shù)在高進(jìn)料質(zhì)量流量與低轉(zhuǎn)速的情況下對(duì)功耗的影響相對(duì)于低進(jìn)料速度和高轉(zhuǎn)速更加明顯。

        3)磨損較嚴(yán)重的區(qū)域集中在下料口處的螺旋軸與螺旋葉片的邊緣處。轉(zhuǎn)速相同的情況下,顆粒與幾何體之間的摩擦系數(shù)和進(jìn)料速度越大,螺旋葉片與螺旋軸的磨損越嚴(yán)重,而螺旋軸轉(zhuǎn)速越大,整體磨損速率越小。

        利益沖突聲明(Conflict of Interests)

        所有作者聲明不存在利益沖突。

        All authors disclose no relevant conflict of interests.

        作者貢獻(xiàn)(Author’s Contributions)

        蔡文源和徐立敏進(jìn)行了方案設(shè)計(jì),蔡文源和王利強(qiáng)參與了論文的寫作和修改。所有作者均閱讀并同意了最終稿件的提交。

        The study was designed by CAI Wenyuan and XU Limin.The manuscript was written and revised by CAI Wenyuan and WANG Liqiang.All authors have read the last version of paper and consented for submission.

        參考文獻(xiàn)(References)

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        Simulation analysis of ultrafine calcium carbonate spiral transportation based on CFD-DEM

        CAI Wenyuan1,WANG Liqiang1,XU Limin2

        1.Jiangsu Key Laboratory of Advanced Food Manufacturing Equipment and Technology,School of Mechanical Engineering,Jiangnan University,Wuxi 214122,China;

        2.Jiangsu Innovative Packaging Technology Co.,Ltd.,Yangzhou 225600,China

        Abstract

        Objective As an important inorganic non-metallic powder material,ultrafine calcium carbonate is widely used in plastics,rub‐ber,coatings,and paper making,etc.Due to its extremely small particle size and adhesive nature,there are difficulties in its conveying process leading to lower conveying efficiency and increased equipment wear.Therefore,it requires improved design and operation of conveying equipment.Screw conveyor,as an efficient and widely used solid material conveying equipment,is characterized by its simple structure,low maintenance costs,and ability to convey materials in horizontal,inclined,or verticaldirections.With the advancement of computer simulation technology,the discrete element method(DEM)technique has become an important tool to study the particle flow and interactions in screw conveyor conveying process.Current research on CFD-DEM coupling method for screw conveyors typically focuses on operational parameters for large particle materials.How‐ever,they overlook investigations into the role of geometric friction coefficients in the ultrafine powder conveying.In order to improve the efficiency of screw conveyors and reduce power consumption and wear,the study was conducted to examine the par‐ticle flow state,outlet mass flow rate,conveyor power consumption,and wear distribution of ultrafine calcium carbonate in a horizontal screw conveyor with variable diameter and pitch.This study provided theoretical and technical support for effective transport of ultrafine powders,as well as new perspectives and methodological foundation for engineering applications and scien‐tific research in related fields.

        Methods In this study,we adopted the CFD-DEM coupling method,using FLUENT,a fluid dynamics software,and EDEM,a discrete element software,to explore the gas-solid two-phase flow characteristics of ultrafine calcium carbonate powder during horizontal conveying with variable diameter and pitch of the spiral.It also explored the effects of different operational and geo‐metric parameters on the conveying process.In CFD-DEM gas-solid coupling,the gas phase was treated as a continuous phase,governed by continuity and momentum conservation equations.RNG k-εmodel was used in the turbulence model,which was more suited for the complex turbulent flow inside the screw conveyor.The particles were regarded as a discrete phase,and their motion was described by the Newtonian kinetic equations.The Archard wear model was used to simulate the wear process on the spiral blade surfaces correlating the amount of material worn on the surface of the spiral blade to the friction work exerted by the frictional action of the particles on that surface.The simulation model of the horizontal screw conveyor with variable diameter and pitch was constructed in this paper and its specific structure was shown in Fig.1 and 2.A tetrahedral unstructured mesh with high adaptability was chosen to be applied for meshing in this study,as shown in Fig.3.Parameters of the simulation experiment were detailed in Tab.1.

        Results Simulated mass flow rates at different rotational speeds closely aligned with experimental results,showing a small mar‐gin of error.This high level of accuracy confirmed the model's reliability for simulating the screw conveying of ultrafine calcium carbonate.In the horizontal screw conveyor with variable diameter and pitch,particles uniformly flowed towards the outlet along the screw shaft,demonstrating stable conveying performance.The coefficient of friction between particles and geometry signifi‐cantly influenced particle behavior in various conveying sections.However,optimal conveying relied not solely on higher or lower friction coefficients but instead on finding an appropriate balance.Variations in peak mass flow rates were linked to par‐ticle axial velocity,which was influenced by friction coefficients.Excessive friction impeded particle flow,while insufficient friction reduced particle forward momentum,leading to equipment clogging and reduced mass flow rates.Power consumption analysis at a constant feed rate of 2 kg/s revealed decreasing consumption with increasing rotational speed,with the impact of the friction coefficient diminishing at higher speeds.Wear simulation results indicated that higher rotational speeds reduced material residence time on blade surfaces,thus reducing wear interactions.Conversely,increased friction coefficients significantly elevated wear rates due to heightened sliding or rolling resistance between material and blade surfaces.This abrasive interaction intensified wear rates under conditions of higher friction.

        Conclusion In a screw conveyor,materials moved axially and in a circular flow within each section.The coefficient of friction between the particles and the geometry had a significant effect on the particle flow state.Changes in the friction coefficient did not necessarily result in increased axial velocity of the particles or the mass flow rate of the conveyor.Instead,there existed a locally optimal combination of parameters that could be achieved.As the discharge speed and friction coefficient increased,the power consumption of the conveyor also rose.An appropriate increase in rotational speed could reduce power consumption.How‐ever,the influence of the friction coefficient on power consumption was more pronounced at high feed speeds and low rotational speeds,compared to low feed speeds and high rotational speeds.The more serious wear area concentrated at the edges of the spi‐ral shaft and spiral blades near the lower feed opening.For any given rotational speed,higher coefficient of friction between the particles and the geometry with greater feed speed resulted in more severe wear of the spiral blades and spiral shaft.Conversely,higher rotational speeds of the spiral shaft led to lower overall wear rates.The study provides theoretical and technical support for efficient conveying of ultrafine powders,and offers new perspectives and methodological basis for its engineering applications and scientific research in related fields.

        Keywords:ultrafine calcium carbonate;computational fluid dynamics;discrete element method;screw conveyor;particle flow

        (責(zé)任編輯:吳敬濤)

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