董芳,方立德,李小亭
(河北大學(xué)質(zhì)量技術(shù)監(jiān)督學(xué)院,河北保定 071002)
功率譜熵在垂直于水平流向的氣液兩相流壓差信號(hào)中的應(yīng)用
董芳,方立德,李小亭
(河北大學(xué)質(zhì)量技術(shù)監(jiān)督學(xué)院,河北保定 071002)
對(duì)垂直于水平流向的氣液兩相流壓差信號(hào)進(jìn)行了實(shí)際測(cè)量,對(duì)采集的信號(hào)提取其功率譜熵值.結(jié)果表明:壓差信號(hào)的功率譜熵受外界壓力變化影響較小,對(duì)兩相流流型變化是敏感的,通過分析功率譜熵值隨氣液兩相流氣相流速變化趨勢(shì),能夠較好地揭示水平管道氣液兩相流流動(dòng)特性,為兩相流流型的準(zhǔn)確識(shí)別方法提供有價(jià)值的參考.
氣液兩相流;壓差信號(hào);功率譜熵;流型
氣液兩相流動(dòng)存在于眾多工程領(lǐng)域中,例如石油、化工、動(dòng)力、制冷、冶金等工業(yè)中的管道傳輸和化學(xué)過程中,準(zhǔn)確地檢測(cè)出兩相流流動(dòng)參數(shù)對(duì)于系統(tǒng)的計(jì)量、控制、節(jié)能、環(huán)保和運(yùn)行可靠性等具有重要意義.在兩相流量、管道形狀、管道方向等因素的影響下,兩相分界面的形狀不斷改變,無規(guī)律可循,并且相間存在相對(duì)速度,相對(duì)速度不同也會(huì)引起流動(dòng)性質(zhì)和流動(dòng)結(jié)果發(fā)生很大變化,這些固有性質(zhì)使得多相流問題的復(fù)雜性要遠(yuǎn)遠(yuǎn)高于單相流問題.
氣液兩相流的壓差波動(dòng)信號(hào)容易準(zhǔn)確測(cè)量,并且攜帶大量關(guān)于流動(dòng)分布的信息,因此,近年來很多學(xué)者針對(duì)氣液兩相流壓差信號(hào)動(dòng)力學(xué)特征進(jìn)行研究[18],分別利用混沌分形理論、多尺度信息熵理論、符號(hào)序列統(tǒng)計(jì)分析、遞歸定量分析等多種先進(jìn)信息分析方法,對(duì)采集的壓差波動(dòng)信號(hào)進(jìn)行分析處理,探求氣液兩相流動(dòng)特性,以上研究均取得了良好的效果,為氣液兩相流流型識(shí)別方法研究提供了參考.然而,這些研究中的壓差信號(hào)都是提取的沿著流動(dòng)方向的兩點(diǎn)之間的壓差信號(hào),即水平管道在水平方向取壓,垂直管道在豎直方向取壓.這種取壓方法測(cè)取的壓差信號(hào)會(huì)受到沿程摩擦阻力的影響,導(dǎo)致在不同的實(shí)驗(yàn)參數(shù)下不能得到統(tǒng)一的結(jié)論.文中針對(duì)水平管道在垂直于流動(dòng)方向上提取壓差波動(dòng)信號(hào),此壓差信號(hào)與兩相流流動(dòng)的方向垂直,因此不會(huì)受沿程摩擦阻力的影響,對(duì)其進(jìn)行分析處理可以很方便地進(jìn)行流型識(shí)別.
功率譜熵分析作為一種非線性信息處理方法,具有計(jì)算過程簡(jiǎn)便、物理概念清晰等優(yōu)點(diǎn),已經(jīng)較好地應(yīng)用于一些復(fù)雜的非線性系統(tǒng)中[916].在水平管道中對(duì)豎直方向的氣液兩相流壓差信號(hào)進(jìn)行了測(cè)量,為了探討功率譜熵與氣液兩相流流動(dòng)特性之間關(guān)系,從實(shí)際測(cè)量的96組壓差信號(hào)中提取了功率譜熵,研究表明此功率譜熵值與水平管道氣液兩相流流型變化密切相關(guān),并且受外界壓力影響較小,是診斷與識(shí)別氣液兩相流流型的有效輔助工具.
水平管氣液兩相流壓差信號(hào)是在天津大學(xué)可調(diào)壓中壓濕氣測(cè)量裝置上進(jìn)行兩相流動(dòng)態(tài)實(shí)驗(yàn)采集得到,此裝置壓力可調(diào),實(shí)驗(yàn)連接實(shí)物圖如圖1所示.
圖1 實(shí)驗(yàn)連接實(shí)物Fig.1 Physical map of the experimental facilities
實(shí)驗(yàn)中測(cè)量管段為方管,水平管段豎直方向的壓差信號(hào)采用新型分體式高頻壓差變送器測(cè)量得到,該壓差變送器分高壓端、低壓端2個(gè)探頭,將2個(gè)探頭直接與取壓孔連接,避免了傳統(tǒng)的壓差測(cè)量中引壓管造成的測(cè)量誤差.此次實(shí)驗(yàn)主要模擬氣相為主的氣液兩相流動(dòng),包括分層流、環(huán)狀流、波狀分層流,這3種流型特點(diǎn)是氣相體積流量比液相大很多,氣相的流速都高于液相.
實(shí)驗(yàn)溫度為16~21℃,選擇0.05MPa和0.1MPa 2個(gè)背景壓力點(diǎn),每個(gè)壓力點(diǎn)下設(shè)置6個(gè)液相流量點(diǎn)(0.05,0.15,0.25,0.35,0.45,0.55m3/h),每個(gè)液相流量點(diǎn)下又分別設(shè)置8個(gè)氣相流量點(diǎn)(20,40,60,80,90,120,150,180m3/h).實(shí)驗(yàn)時(shí),按照所設(shè)定的流動(dòng)工況逐一調(diào)整水流量和氣流量,流量穩(wěn)定時(shí)等待5min之后再進(jìn)行數(shù)據(jù)的記錄.采樣頻率為1kHz,采樣時(shí)間為15s,共采集96組壓差信號(hào).
2.1 功率譜熵的定義
Kapur等[17]指出:對(duì)于一個(gè)不確定性系統(tǒng),若其狀態(tài)特征可以用一個(gè)隨機(jī)變量X來表示,X的取值為
變量的不確定性越大,熵就越大.一個(gè)系統(tǒng)越是有序,信息熵就越低;反之,一個(gè)系統(tǒng)越是混亂,信息熵就越高.因此,信息熵可以作為系統(tǒng)有序化程度的一個(gè)度量.
Rezek等人[18]通過信息熵來定量計(jì)算不確定系統(tǒng)的功率譜的復(fù)雜性.采用FFT變換將時(shí)域信號(hào)轉(zhuǎn)換為頻域信號(hào),然后估計(jì)序列的功率譜.
設(shè)長(zhǎng)度為N的序列x(n)的DFT變換為x(f),則其功率譜密度的估計(jì)為
(8)式中pi表示第i個(gè)功率譜在整個(gè)頻譜中占的百分比.
功率譜熵是從頻域角度定義的信息熵,可作為系統(tǒng)在頻域內(nèi)的復(fù)雜程度的一種度量.構(gòu)成某時(shí)間序列信號(hào)的過程數(shù)目越多,序列越復(fù)雜,則不確定度(功率譜熵)越大,反之若過程數(shù)目越少,序列越簡(jiǎn)單,則不確定度(功率譜熵)越小.
2.2 功率譜熵對(duì)一些常規(guī)信號(hào)的識(shí)別
為了進(jìn)一步考察功率譜熵對(duì)不同復(fù)雜程度信號(hào)的辨別能力,對(duì)一些典型的時(shí)間序列選取4 096點(diǎn)計(jì)算功率譜熵,結(jié)果如表1所示.其中正弦周期信號(hào)的采樣間隔為π/32,混合信號(hào)為正弦信號(hào)與高斯白噪聲信號(hào)的混合序列,p為高斯白噪聲信號(hào)的混入比例.
表1 不同類型信號(hào)的功率譜熵計(jì)算結(jié)果Tab.1 Results of spectral entropy for different type signals
從表1可以看出,從正弦信號(hào)到混合信號(hào)到高斯白噪聲,功率譜熵的值呈增大的趨勢(shì),對(duì)于混合信號(hào),其功率譜熵值隨著其白噪聲混入比例的增加而增大,介于正弦信號(hào)和高斯白噪聲之間.綜上所述,功率譜熵認(rèn)為周期正弦信號(hào)不確定性最小,復(fù)雜性最低;高斯白噪聲信號(hào)不確定性最大,復(fù)雜性最高;并且對(duì)不同隨機(jī)程度的信號(hào)也能有效地區(qū)分,能對(duì)時(shí)間序列的復(fù)雜性程度進(jìn)行有效地描述.
兩相流是一個(gè)復(fù)雜的非線性動(dòng)力學(xué)系統(tǒng),利用功率譜熵作為氣液兩相流壓差波動(dòng)信號(hào)的復(fù)雜性度量,揭示兩相流流動(dòng)特性以及流型演變的規(guī)律.
對(duì)采集的96組氣液兩相流差壓波動(dòng)信號(hào)進(jìn)行處理,其中每個(gè)壓力點(diǎn)下設(shè)置6個(gè)液相流量點(diǎn),每個(gè)液相流量點(diǎn)下又分別設(shè)置8個(gè)氣相流量點(diǎn).為了減小序列長(zhǎng)度對(duì)功率譜熵計(jì)算影響,對(duì)每種工況信號(hào)分別選取4 096個(gè)測(cè)量數(shù)據(jù)點(diǎn)計(jì)算其功率譜熵,結(jié)果如圖2和圖3所示.
圖2 在0.05MPa壓力點(diǎn)下,SE與氣相表觀速度關(guān)系Fig.2 Diagram of spectral entropy and gas superficial velocity under the pressure of 0.05MPa
圖3 在0.1MPa壓力點(diǎn)下,SE與氣相表觀速度關(guān)系Fig.3 Diagram of spectral entropy and gas superficial velocity under the pressure of 0.1MPa
從圖2圖3可以看出,在2個(gè)壓力點(diǎn)下,功率譜熵隨氣相表觀速度變化趨勢(shì)基本一致,表明用功率譜熵分析兩相流流動(dòng)特性受外界壓力影響很小.總的變化趨勢(shì)為隨著氣相表觀速度的增加,功率譜熵值逐漸增加,說明差壓波動(dòng)信號(hào)不確定性逐漸增大,氣液兩相流動(dòng)力學(xué)特性越來越復(fù)雜.
當(dāng)氣相表觀速度小于5m/s時(shí),水平管內(nèi)呈現(xiàn)為典型的分層流流型,由于重力作用,氣相分布在管道上部,液相分布在管道下部,氣液兩相之間存在較穩(wěn)定的分界面,流動(dòng)過程比較穩(wěn)定,功率譜熵相比其他2種流型來說是最小的,并且在同一氣相流速下,當(dāng)液相流速不同時(shí)功率譜熵值差異較大.隨著氣相流速逐漸增加,當(dāng)氣相表觀速度大于5m/s時(shí),兩相間穩(wěn)定的分界面在氣流帶動(dòng)下,沿流動(dòng)方向出現(xiàn)連續(xù)波動(dòng),呈波浪狀,氣相流速越大,波動(dòng)越劇烈,此時(shí)分層流轉(zhuǎn)變?yōu)椴盍?,其?dòng)力學(xué)特性較分層流復(fù)雜,因此其功率譜熵值高于分層流.在同一氣相流速下,當(dāng)液相流速不同時(shí)功率譜熵值差異也較大,這一特點(diǎn)和分層流相似,說明分層流和波狀流壓差波動(dòng)信號(hào)變化受液相流速影響較大.氣相表觀速度繼續(xù)增加,當(dāng)氣相表觀速度大于15m/s之后,氣液分界面出現(xiàn)更為劇烈的波動(dòng),波峰甚至達(dá)到管道的頂部,氣相將管頂部的液相波峰擊碎,氣相變?yōu)檫B續(xù)相,被擊碎的液相在管頂部形成液膜,在氣相帶動(dòng)下沿軸向緩慢流動(dòng),同時(shí)由于重力的存在,部分液體還向下流動(dòng),使得整個(gè)管道的圓周方向逐漸被液膜覆蓋,環(huán)狀流形成.在液相的重力和氣相較高的表觀流速的共同作用下,環(huán)狀流的氣液兩相分界面出現(xiàn)毫無規(guī)律的隨機(jī)波動(dòng),功率譜熵達(dá)到最大.但環(huán)狀流型下,氣相流速不變時(shí),隨液相流速變化壓差信號(hào)的功率譜熵變化較小,說明環(huán)狀流壓差波動(dòng)信號(hào)變化受液相流速的影響較小.
綜上所述,功率譜熵對(duì)氣液兩相流流型變化是敏感的,不同流型下功率譜熵值有較明顯的差異.通過分析功率譜熵值隨兩相流氣相表觀速度的變化規(guī)律,可以更深刻地揭示動(dòng)力學(xué)系統(tǒng)內(nèi)在特性,能夠更好地反映水平管道典型流型轉(zhuǎn)換規(guī)律,是理解氣液兩相流流型現(xiàn)象的有效指示器.
1)將功率譜熵應(yīng)用于水平管氣液兩相流豎直方向的壓差波動(dòng)信號(hào)中,計(jì)算過程簡(jiǎn)便,物理意義明確,并且受外界壓力影響較小,為分析氣液兩相流流型轉(zhuǎn)換特性提供了一種有效的新方法.
2)功率譜熵作為一種復(fù)雜性度量對(duì)氣液兩相流流型變化比較敏感,通過分析功率譜熵隨兩相流氣相表觀速度變化規(guī)律,表明此復(fù)雜性度量可以作為理解兩相流流型現(xiàn)象的有效工具,為實(shí)現(xiàn)兩相流流型的準(zhǔn)確識(shí)別提供有價(jià)值的參考.
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(責(zé)任編輯:孟素蘭)
Application of spectral entropy on the differential pressure signals against to the horizontal flow direction in gas-liquid two-phase flow
DONG Fang,F(xiàn)ANG Lide,LI Xiaoting
(College of Quality and Technical Supervision,Hebei University,Baoding 071002,China)
The differential pressure fluctuation signals against to the horizontal flow direction were measured in gas-liquid two-phase flow,and then the spectral entropy was extracted from these signals.The results indicated that the spectral entropy was less affected by ambient pressure and sensitive to the flow pattern.By analyzing the rules of spectral entropy with the changes of gas phase velocity,the movement characteristic of gas-liquid two-phase flow was revealed deeply.It could serve as valuable references for precise identification of flow pattern.
gas-liquid two-phase flow;differential pressure signals;spectral entropy;flow pattern
董芳(1980-),女,河北青縣人,河北大學(xué)講師,主要從事多相流檢測(cè)技術(shù)方向研究.Email:dongfang1023@163.com
TP29
A
1000 -1565(2014)05 -0541 06
10.3969/j.issn.1000 -1565.2014.05.017
2014-03 -12
國(guó)家自然科學(xué)專項(xiàng)基金資助項(xiàng)目(61340028);河北省高等學(xué)校科學(xué)技術(shù)研究指導(dǎo)項(xiàng)目(Z2013123);河北大學(xué)自然科學(xué)研究計(jì)劃項(xiàng)目(2010Q14)