離心式壓縮機(jī)設(shè)計(jì)-離心壓縮機(jī)氣動(dòng)及結(jié)構(gòu)設(shè)計(jì)含6張CAD圖
離心式壓縮機(jī)設(shè)計(jì)-離心壓縮機(jī)氣動(dòng)及結(jié)構(gòu)設(shè)計(jì)含6張CAD圖,離心,壓縮機(jī),設(shè)計(jì),氣動(dòng),結(jié)構(gòu)設(shè)計(jì),cad
設(shè)計(jì)任務(wù)書畢業(yè)設(shè)計(jì)(論文)題目:離心壓縮機(jī)氣動(dòng)及結(jié)構(gòu)設(shè)計(jì)設(shè)計(jì)(論文)的基本內(nèi)容:一、設(shè)計(jì)工作圖一套:1、離心式壓縮機(jī)總裝配圖1張0#;2、離心式壓縮機(jī)零件圖共5張;設(shè)計(jì)原始參數(shù): 1) 空氣流量m: 2.5kg/s2) 壓強(qiáng)比: 2.43) 環(huán)境壓強(qiáng)p: 1.01310Pa4) 環(huán)境溫度T: 293K5) 環(huán)境密度: 1.205kg/m6) 空氣氣體常數(shù)R: 287J/(kg.K)7) 空氣絕熱指數(shù)k: 1.48) 交流電機(jī)驅(qū)動(dòng)設(shè)計(jì)(XX)開(kāi)題報(bào)告論文題目離心式壓縮機(jī)設(shè)計(jì)一、選題原因離心式壓縮機(jī)是一種速度式壓縮機(jī),氣體在壓縮機(jī)中沿垂直于壓縮機(jī)軸的徑向進(jìn)行運(yùn)動(dòng),工作輪在旋轉(zhuǎn)的過(guò)程中,利用離心旋轉(zhuǎn)力和工作輪中的擴(kuò)壓流動(dòng)作用來(lái)提高氣體壓力和速度。早期,離心式壓縮機(jī)只用來(lái)壓縮空氣,且只適用于中、低壓力及氣量很大的場(chǎng)合。隨著石油、化工生產(chǎn)規(guī)模的擴(kuò)大和機(jī)械加工工藝的發(fā)展。從60年代開(kāi)始,離心式壓縮機(jī)在我國(guó)石油化工生產(chǎn)中應(yīng)用越來(lái)越廣泛。近幾十年來(lái)新建的大型合成氨廠、乙烯廠均采用了離心式壓縮機(jī),并實(shí)現(xiàn)了單機(jī)配套。此外離心式壓縮機(jī)還廣泛地應(yīng)用在制氧、尿素、酸、堿等工業(yè)以及原子能工業(yè)的惰性氣體的壓縮和核工業(yè)特殊元素的制取方面。隨著離心式壓縮機(jī)技術(shù)的不斷提高,其在許多場(chǎng)合已經(jīng)逐漸替代活塞式壓縮機(jī)而成為主要的動(dòng)力機(jī)械。而且,近些年來(lái),由于科學(xué)技術(shù)的飛速發(fā)展,離心式壓縮機(jī)因其可靠性高、體積小、質(zhì)量輕等諸多優(yōu)點(diǎn)在航空航天、能源動(dòng)力、石油化工及冶金等行業(yè)日益發(fā)揮著極其重要的作用?;谙M麑?duì)離心式壓縮機(jī)的機(jī)構(gòu)及其研究發(fā)展有更進(jìn)一步的了解,我選擇了該課題。二、論文框架摘 要3第一章 前言51.1 TJ020離心式壓縮機(jī)技術(shù)現(xiàn)狀和發(fā)展趨勢(shì)51.2 TJ020離心式壓縮機(jī)發(fā)展方向6第二章 離心壓縮機(jī)氣動(dòng)參數(shù)計(jì)算82.1 原始數(shù)據(jù)82.2 進(jìn)氣道參數(shù)92.3 壓縮機(jī)葉輪參數(shù)102.4 無(wú)葉擴(kuò)壓器段參數(shù)152.5 葉片擴(kuò)壓器參數(shù)172.6 蝸殼參數(shù)192.7 壓縮機(jī)參數(shù)校核202.8 軸的強(qiáng)度校核212.9 軸承和鍵的選擇212.10 軸承蓋的參數(shù)計(jì)算21第三章 結(jié)論參考文獻(xiàn)致謝附錄三、時(shí)間及進(jìn)度安排(此項(xiàng)內(nèi)容參照畢業(yè)設(shè)計(jì)(論文)進(jìn)度安排表,依據(jù)自身寫作進(jìn)度填寫)第一階段: 7月24日 選題; 第二階段: 7月25日至8月14日 開(kāi)題報(bào)告寫作;第三階段: 8月15日至8月25日 查找相關(guān)文獻(xiàn);第四階段: 8月26日至9月14日 初稿寫作;第五階段: 9月15日至10月14日 二稿寫作; 第六階段: 10月15日至31日 終稿寫作 學(xué)生(簽名):年 月 日指導(dǎo)教師意見(jiàn):指導(dǎo)教師(簽名):年 月 日三、時(shí)間及進(jìn)度安排第一階段: 7月24日 選題; 第二階段: 7月25日至8月14日 開(kāi)題報(bào)告寫作;第三階段: 8月15日至 8月22日 查找相關(guān)文獻(xiàn);第四階段: 8月23日至9月14日 初稿寫作; 第五階段: 9月15日至10月14日 二稿寫作; 第六階段: 10月15日至10月31日 終稿寫作。 學(xué)生(簽名):年 月 日指導(dǎo)教師意見(jiàn):指導(dǎo)教師:年 月 日注:(1)封面:題目:宋體,二號(hào);其他填寫內(nèi)容:宋體,三號(hào);(2)填表字體:宋體,小四號(hào); (3)括號(hào)內(nèi)的文字為提示性語(yǔ)句,一律不準(zhǔn)出現(xiàn)在最終要上傳的開(kāi)題報(bào)告中。離心式壓縮機(jī)的設(shè)計(jì)摘要離心式壓縮機(jī)的用途很廣。例如氨化肥生產(chǎn)中的氮、氫氣體的離心壓縮機(jī),空氣分離工程、煉油和石化工業(yè)中普遍使用的各種壓縮機(jī),天然氣輸送和制冷等場(chǎng)合的各種壓縮機(jī)。在動(dòng)力工程中,離心式壓縮機(jī)主要用于小功率的燃?xì)廨啓C(jī)、內(nèi)燃機(jī)增壓以及動(dòng)力風(fēng)源等。本課題研究的內(nèi)容是設(shè)計(jì)一臺(tái)離心式壓縮機(jī)。葉輪和擴(kuò)壓器是離心式壓縮機(jī)的關(guān)鍵部件,葉輪設(shè)計(jì)制造的好壞及其與擴(kuò)壓器的匹配將對(duì)壓縮機(jī)的性能產(chǎn)生決定性的影響。關(guān)鍵詞:進(jìn)氣道 葉輪 擴(kuò)壓器The Design of Centrifugal CompressorAbstract:Centrifugal compressor is very versatile. A variety of occasions such as nitrogen, hydrogen, ammonia fertilizer production in the centrifugal compressor, air separation engineering, commonly used in the refining and petrochemical industries, compressors, natural gas transportation and refrigeration compressors. In power engineering, the centrifugal compressor is mainly used for low-power gas turbines, internal combustion engine supercharged and dynamic wind source. The content of this research is the design of a centrifugal compressor. Impeller and diffuser is a key component of the centrifugal compressor impeller design and manufacture of the good or bad a decisive impact on the match will be the compressor diffuser performance.Key words:Inlet;Impeller;Diffuser目錄摘 要31 前言51.1 離心式壓縮機(jī)技術(shù)現(xiàn)狀和發(fā)展趨勢(shì)51.2 離心式壓縮機(jī)發(fā)展方向62. 離心壓縮機(jī)氣動(dòng)參數(shù)計(jì)算82.1 原始數(shù)據(jù)82.2 進(jìn)氣道參數(shù)92.3 壓縮機(jī)葉輪參數(shù)102.4 無(wú)葉擴(kuò)壓器段參數(shù)152.5 葉片擴(kuò)壓器參數(shù)172.6 蝸殼參數(shù)192.7 壓縮機(jī)參數(shù)校核202.8 軸的強(qiáng)度校核212.9 軸承和鍵的選擇212.10 軸承蓋的參數(shù)計(jì)算213 結(jié)論22參 考 文 獻(xiàn)23致 謝241 前言1.1離心式壓縮機(jī)技術(shù)現(xiàn)狀和發(fā)展趨勢(shì)18世紀(jì)初期,Papin給出了最早的離心式葉輪機(jī)械的設(shè)計(jì)方法,在他出版的著作中介紹了離心泵的設(shè)計(jì)方法。從那以后,離心式葉輪機(jī)械開(kāi)始逐步得到發(fā)展。19世紀(jì),離心式壓縮機(jī)伴隨著葉輪機(jī)械理論的發(fā)展而得到了迅速的發(fā)展。在這一時(shí)期,Leonhard Eular建立了葉輪機(jī)械中的基本能量方程;Lazare Carnot指出在葉輪進(jìn)口流體應(yīng)光滑順利的流入葉輪,即零攻角狀態(tài),他還指出為了獲得高效率應(yīng)減小葉輪出口動(dòng)能。這一階段的標(biāo)志性成果是離心壓縮機(jī)中開(kāi)始使用有葉擴(kuò)壓器。從20世紀(jì)開(kāi)始至今是離心壓縮機(jī)技術(shù)迅猛發(fā)展的時(shí)代。在這一時(shí)期,產(chǎn)生了對(duì)離心壓縮機(jī)發(fā)展具有劃時(shí)代意義的理論和方法。正是這些理論和方法的誕生,使得離心壓縮機(jī)在全世界范圍內(nèi)得到了極為廣泛的應(yīng)用。1930年,F(xiàn)rank Whittle申請(qǐng)了他的第一項(xiàng)專利,在國(guó)際上首次應(yīng)用了雙向進(jìn)氣單級(jí)離心壓縮機(jī),這個(gè)離心壓縮機(jī)由軸向透平驅(qū)動(dòng),采用雙向進(jìn)氣不但可以避免在轉(zhuǎn)子進(jìn)口葉尖產(chǎn)生超音速流動(dòng),而且可以減小軸向推力。從那時(shí)開(kāi)始,F(xiàn)rank Whittle就將目標(biāo)瞄準(zhǔn)單級(jí)壓比達(dá)到4,而此前單級(jí)壓比最高值只達(dá)到2.5。離心壓縮機(jī)因?yàn)槭苄D(zhuǎn)、曲率及粘性等諸多因素的影響及相互作用而使其內(nèi)部流動(dòng)表現(xiàn)為相當(dāng)復(fù)雜的非定常、有粘性的三維湍流流動(dòng)。但在早期,因?yàn)槿碚摷坝?jì)算手段的缺乏,使得離心壓縮機(jī)的設(shè)計(jì)主要采用幾何設(shè)計(jì)或二維氣動(dòng)設(shè)計(jì)方法進(jìn)行。20世紀(jì)50年代,我國(guó)著名的科學(xué)家吳仲華教授提出了對(duì)離心壓縮機(jī)發(fā)展具有劃時(shí)代意義的兩簇流面理論,奠定了葉輪機(jī)械內(nèi)部三元流場(chǎng)求解的基礎(chǔ)。他首先提出葉輪機(jī)械葉片通道內(nèi)的三元流動(dòng)可以看作是兩類相交的流面(S1、S2流面,S1流面為是從一個(gè)葉片到相鄰葉片之間的周向扭曲流面,S2流面是從輪轂導(dǎo)輪蓋的徑向扭曲流面)之和,這樣就可以把一個(gè)復(fù)雜的三元問(wèn)題轉(zhuǎn)化為兩個(gè)二元問(wèn)題,從而使計(jì)算簡(jiǎn)化。隨著吳氏三元理論的提出,離心壓縮機(jī)的設(shè)計(jì)方法開(kāi)始由幾何設(shè)計(jì)或二維氣動(dòng)設(shè)計(jì)向準(zhǔn)三維氣動(dòng)設(shè)計(jì)及全三維氣動(dòng)設(shè)計(jì)方法轉(zhuǎn)變。許多國(guó)內(nèi)外專家學(xué)者利用這一理論對(duì)離心壓縮機(jī)進(jìn)行了研究并取得了許多有益的成果8離心式空氣壓縮機(jī)屬于速度式壓縮機(jī),在用氣負(fù)荷穩(wěn)定時(shí)離心式空氣壓縮機(jī)工作穩(wěn)定、可靠。 優(yōu)點(diǎn)是結(jié)構(gòu)緊湊、重量輕,排氣量范圍大; 易損件少,運(yùn)轉(zhuǎn)可靠、壽命長(zhǎng); 排氣不受潤(rùn)滑油污染,供氣品質(zhì)高; 大排量時(shí)效率高、且有利于節(jié)能。目前 離心式壓縮機(jī)發(fā)展趨勢(shì)是:容量不斷增大,以滿足石化生產(chǎn)規(guī)模不斷擴(kuò)大的要求隨著新技術(shù)的發(fā)展,新型氣體密封、磁力軸承和無(wú)潤(rùn)滑聯(lián)軸器的出現(xiàn),不斷開(kāi)發(fā)高壓壓縮機(jī)和小流量壓縮機(jī)產(chǎn)品進(jìn)一步研究三元流動(dòng)理論,不僅應(yīng)用到葉輪設(shè)計(jì),還發(fā)展到葉片擴(kuò)壓器靜止元件設(shè)計(jì)中,以期達(dá)到最高的機(jī)組效率低噪聲化,采用噪聲防護(hù)以改善操作環(huán)境。 國(guó)內(nèi)可以生產(chǎn)石化用離心壓縮機(jī)的制造企業(yè)主要有沈陽(yáng)鼓風(fēng)機(jī)廠、上海鼓風(fēng)機(jī)廠、陜西鼓風(fēng)機(jī)廠等。他們引進(jìn)國(guó)外技術(shù),經(jīng)過(guò)消化吸收,可以生產(chǎn)石化用大型離心壓縮機(jī)。沈陽(yáng)鼓風(fēng)機(jī)廠從意大利新比隆公司引進(jìn)了MCL、BCL、PCL三個(gè)離心壓縮機(jī)系列的全套設(shè)計(jì)制造專利技術(shù)從日本日立公司引進(jìn)了DH型離心壓縮機(jī)、HS型工業(yè)冷凍機(jī)設(shè)計(jì)制造專利技術(shù),從美國(guó)費(fèi)城齒輪公司引進(jìn)了MHS、HS、HSS、HSD四個(gè)系列的高速齒輪變速器的設(shè)計(jì)制造專利技術(shù)從德國(guó)德馬格公司引進(jìn)了VK8型組裝式離心壓縮機(jī)設(shè)計(jì)制造專利技術(shù)和從日本川崎重工株式會(huì)社引進(jìn)了GM型污水處理鼓風(fēng)機(jī)技術(shù)。沈陽(yáng)鼓風(fēng)機(jī)廠生產(chǎn)的離心壓縮機(jī)在國(guó)內(nèi)石化企業(yè)已經(jīng)應(yīng)用200多臺(tái),市場(chǎng)占有率已達(dá)80以上。沈鼓廠生產(chǎn)的300萬(wàn)t/a催化裂化裝置富氣壓縮機(jī)進(jìn)口流量達(dá)到81 600Nm 3 /h,功率達(dá)到7 166kW離心式循環(huán)氫壓縮機(jī)流量達(dá)到250 000Nm 3 /h,功率達(dá)到1 600kW,出口壓力達(dá)到18MPa,已經(jīng)應(yīng)用于120萬(wàn)t/a加氫裂化裝置沈鼓廠自行設(shè)計(jì)、制造的裂解氣壓縮機(jī)流量達(dá)到120 000Nm 3 /h,功率達(dá)到18 000kW同國(guó)外合作設(shè)計(jì)、制造的丙烯壓縮機(jī)流量達(dá)到58 000Nm 3 /h,功率達(dá)到7 500kW乙烯壓縮機(jī)流量達(dá)到74 000Nm 3 /h,功率達(dá)到5 500kW,已經(jīng)應(yīng)用到3050萬(wàn)t/a乙烯裂解裝置。沈鼓廠自行設(shè)計(jì)和制造的大化肥裝置的空氣壓縮機(jī)、天然氣壓縮機(jī)、氨壓縮機(jī)、二氧化碳?jí)嚎s機(jī)已應(yīng)用于2030萬(wàn)t/a化肥裝置沈鼓設(shè)計(jì)制造的空氣壓縮機(jī)流量達(dá)到220 000Nm 3 /h,功率達(dá)到17 580kW,已經(jīng)應(yīng)用于40 000Nm 3空分裝置1。目前國(guó)內(nèi)離心壓縮機(jī)在高技術(shù)、高參數(shù)、高質(zhì)量和特殊產(chǎn)品方面還不能滿足國(guó)內(nèi)需要。另外在技術(shù)水平、質(zhì)量、成套性上和國(guó)外還有差距。隨著石化生產(chǎn)規(guī)模不斷擴(kuò)大,離心壓縮機(jī)大型化方面面臨新的課題。100萬(wàn)t/a乙烯三機(jī)中的裂解氣壓縮機(jī),進(jìn)口流量達(dá)到403 000kg/h,出口壓力達(dá)到3.89MPa,軸功率達(dá)到45770kW。45萬(wàn)t/aPTA裝置原料空氣壓縮機(jī)帶尾氣透平進(jìn)口流量162 413Nm 3 /h,進(jìn)出口壓力0.1/1.46MPa,軸功率22 000kW,國(guó)內(nèi)在設(shè)計(jì)制造這些大型氣體壓縮機(jī)上還沒(méi)有成熟的經(jīng)驗(yàn)。因此,對(duì) 離心式壓縮機(jī)的設(shè)計(jì)理論進(jìn)行深入、系統(tǒng)的研究非常有必要,從而設(shè)計(jì)出符合實(shí)際工作要求的 離心式壓縮機(jī)。1.2 離心式壓縮機(jī)發(fā)展方向 大型離心壓縮機(jī)組屬技術(shù)密集型、高難度產(chǎn)品,必須擁有先進(jìn)的專業(yè)設(shè)計(jì)制造技術(shù)。由于化工和石油化工裝置不斷向大型化發(fā)展,用戶對(duì)壓縮機(jī)組的能耗、可靠性、配套水平等技術(shù)指標(biāo)的要求也越來(lái)越高。 在二氧化碳?jí)嚎s機(jī)方面,過(guò)去出現(xiàn)了一些壓縮機(jī)性能與工藝條件不匹配的事故?,F(xiàn)在西安交大、沈陽(yáng)鼓風(fēng)機(jī)廠都有自己的二氧化碳閉式試驗(yàn)臺(tái),問(wèn)題已得到解決。因此,對(duì)大型化肥和石油化工壓縮機(jī)的改進(jìn)已基本上集中在壓縮機(jī)性能本身的改進(jìn)上。目前,世界上先進(jìn)的壓縮機(jī)制造廠家都在致力于這方面的研究。如在壓縮機(jī)的氣動(dòng)性能設(shè)計(jì)上使用的程序,能夠適用于幾百個(gè)大氣壓,在近臨界區(qū)域條件下適用于幾十種復(fù)雜氣體,大大提高了計(jì)算精度;在轉(zhuǎn)子穩(wěn)定性研究上,已經(jīng)研制出超二階、三階的高柔性轉(zhuǎn)子,并已成功使用;還在部件成套技術(shù)上有了很大發(fā)展,如在密封、軸承、調(diào)節(jié)系統(tǒng)、輔機(jī)配套水平等方面。因此,如何跟蹤世界上先進(jìn)的壓縮機(jī)設(shè)計(jì)制造技術(shù)是當(dāng)務(wù)之急。大型離心壓縮機(jī)組的改進(jìn),需要加強(qiáng)以下方面研究。1三維工程設(shè)計(jì)CAD開(kāi)發(fā)。采用三維工程設(shè)計(jì)可以優(yōu)化設(shè)計(jì)機(jī)組布置,使機(jī)組布置美觀,且具有自動(dòng)進(jìn)行干涉檢查的功能,避免設(shè)計(jì)缺陷。能夠自動(dòng)進(jìn)行結(jié)構(gòu)分析,提高設(shè)計(jì)精度和設(shè)計(jì)效率。CAD的主要開(kāi)發(fā)內(nèi)容有:建立三維實(shí)體造型設(shè)計(jì)模型,建立三維實(shí)體設(shè)備圖庫(kù)、數(shù)據(jù)庫(kù)等。2轉(zhuǎn)子-軸承系統(tǒng)動(dòng)力特性設(shè)計(jì)專家系統(tǒng)的開(kāi)發(fā)。在設(shè)計(jì)過(guò)程中,當(dāng)轉(zhuǎn)子-軸承系統(tǒng)動(dòng)力特性不能滿足設(shè)計(jì)規(guī)范的要求,或已經(jīng)制造出來(lái)的機(jī)組出現(xiàn)振動(dòng)過(guò)大、運(yùn)行不穩(wěn)定等情況時(shí),就必須修改原機(jī)組的結(jié)構(gòu)參數(shù)、物性參數(shù)值。但是影響轉(zhuǎn)子-軸承系統(tǒng)動(dòng)力特性的結(jié)構(gòu)參數(shù)有很多,修改哪一個(gè)或幾個(gè)結(jié)構(gòu)參數(shù)最有效,能立竿見(jiàn)影地解決設(shè)計(jì)和機(jī)組穩(wěn)定運(yùn)行問(wèn)題,是建立該專家系統(tǒng)軟件的目標(biāo)。主要研究?jī)?nèi)容有:各種轉(zhuǎn)子結(jié)構(gòu)、軸承結(jié)構(gòu)參數(shù)對(duì)轉(zhuǎn)子-軸承系統(tǒng)動(dòng)力特性的影響、建立智能型專家系統(tǒng)設(shè)計(jì)計(jì)算軟件包等。3智能型計(jì)算機(jī)控制系統(tǒng)開(kāi)發(fā)。目前世界上已廣泛采用了微機(jī)控制的三重冗余、容錯(cuò)控制器、多功能防喘振、性能調(diào)節(jié)、安全保護(hù)綜合控制系統(tǒng),使離心壓縮機(jī)控制由傳統(tǒng)的模擬儀表控制變?yōu)槎喙δ艿膶<铱刂葡到y(tǒng)。主要研究?jī)?nèi)容有:研制大化肥裝置用離心壓縮機(jī)組專用的、具有防喘振、性能調(diào)節(jié)、安全保護(hù)的數(shù)字式微機(jī)綜合控制系統(tǒng)2。德國(guó)宇航院(DFVLR)Krain博士基于準(zhǔn)三維氣動(dòng)設(shè)計(jì)方法,通過(guò)計(jì)算機(jī)輔助設(shè)計(jì)完成了離心壓縮機(jī)后向三元葉輪的設(shè)計(jì),并應(yīng)用激光測(cè)試技術(shù)對(duì)該葉輪內(nèi)部流場(chǎng)進(jìn)行了非常詳細(xì)地測(cè)量9。迄今為止,Krain葉輪仍然是許多研究人員校驗(yàn)自己設(shè)計(jì)方法的對(duì)象。國(guó)內(nèi)在離心壓縮機(jī)三元葉輪的各類反命題設(shè)計(jì)方法中,以角動(dòng)量的不同分布來(lái)控制葉片幾何型線的方法應(yīng)用較廣10。角動(dòng)量的分布規(guī)律直接決定葉片載荷的大小并影響流動(dòng)方向、跨盤蓋方向的速度分布,而速度分布對(duì)葉輪二次流的強(qiáng)度及葉片表面邊界層的發(fā)展有決定性的影響,這必然影響到對(duì)葉輪邊界層損失、分離損失和二次流損失的控制,因此合適的角動(dòng)量分布是設(shè)計(jì)高性能葉輪最有效的手段。席光等人以上文提到的德國(guó)宇航院(DFVLR)Krain博士設(shè)計(jì)并試驗(yàn)的后向三元葉輪為研究對(duì)象,對(duì)其內(nèi)部流動(dòng)及氣動(dòng)性能進(jìn)行了計(jì)算,在保留子午型線的前提下,改變角動(dòng)量分布,對(duì)葉片重新設(shè)計(jì),以研究角動(dòng)量分布對(duì)葉輪內(nèi)部三維流場(chǎng)及總體性能的影響,發(fā)展了一種以三維粘性分析為參考準(zhǔn)則的實(shí)用設(shè)計(jì)方法,并利用CFD軟件FLUENT5.4進(jìn)行了數(shù)值計(jì)算,計(jì)算結(jié)果表明:角動(dòng)量的不同分布對(duì)離心壓縮機(jī)葉輪的壓比和效率有明顯的影響。在發(fā)展以三維粘性分析為參考準(zhǔn)則的離心壓縮機(jī)三元葉輪的實(shí)用設(shè)計(jì)方法的基礎(chǔ)上,王曉峰等人又探討了將離心葉輪內(nèi)部的三維粘性流動(dòng)求解與試驗(yàn)設(shè)計(jì)技術(shù)以及響應(yīng)面方法相結(jié)合的優(yōu)化設(shè)計(jì)方法。響應(yīng)面方法是試驗(yàn)設(shè)計(jì)與數(shù)理統(tǒng)計(jì)相結(jié)合的優(yōu)化方法,在試驗(yàn)測(cè)量、經(jīng)驗(yàn)公式或數(shù)值分析的基礎(chǔ)上,對(duì)指定的設(shè)計(jì)點(diǎn)集合進(jìn)行連續(xù)的試驗(yàn),并在設(shè)計(jì)空間構(gòu)造測(cè)定量的全局逼近,這樣便可以全面觀察響應(yīng)變量在設(shè)計(jì)空間的變化12。在詳細(xì)探討響應(yīng)面優(yōu)化設(shè)計(jì)方法的基礎(chǔ)上,他們以某工業(yè)離心壓縮機(jī)中間級(jí)葉輪為研究對(duì)象,采用響應(yīng)面方法對(duì)其進(jìn)行優(yōu)化設(shè)計(jì),結(jié)果表明:與原始葉輪相比,性能有較大改進(jìn)。為減小離心壓縮機(jī)葉輪進(jìn)口的沖擊損失,降低葉片厚度對(duì)進(jìn)氣的阻塞,避免葉輪出口圓周上相鄰兩葉片間距過(guò)大等,目前國(guó)內(nèi)外的高效率離心壓縮機(jī)葉輪廣泛采用了長(zhǎng)、短葉片(分流葉片)的形式。劉瑞韜等人運(yùn)用三維粘性流動(dòng)數(shù)值計(jì)算程序Fine/Turbo對(duì)含分流葉片的離心壓縮機(jī)級(jí)內(nèi)三維粘性流場(chǎng)進(jìn)行了數(shù)值分析,為該類葉輪的優(yōu)化設(shè)計(jì)及改進(jìn)研究打下了基礎(chǔ)14。在此基礎(chǔ)上,劉瑞韜等人又對(duì)分流葉片位置對(duì)高轉(zhuǎn)速離心壓縮機(jī)性能的影響進(jìn)行了研究,重點(diǎn)分析了分流葉片不同起始位置及不同周向位置對(duì)壓縮機(jī)內(nèi)三維粘性流場(chǎng)及整級(jí)性能的影響。計(jì)算結(jié)果表明:采用分流葉片在進(jìn)口處會(huì)減少葉片阻塞;不同分流葉片起始位置時(shí)長(zhǎng)葉片進(jìn)口流場(chǎng)具有相同的分布規(guī)律;分流葉片越短,長(zhǎng)葉片壓力面無(wú)量綱靜壓載荷越大;當(dāng)分流葉片長(zhǎng)度達(dá)到某一數(shù)值后,長(zhǎng)葉片載荷變化趨于平緩;就文獻(xiàn)15中研究的葉輪來(lái)說(shuō),分流葉片起始位置位于圖2所示位置,分流葉片與長(zhǎng)葉片吸力面夾角為22.5時(shí)的葉輪模型級(jí)效率最高,壓縮機(jī)性能最好15。初雷哲、杜建一等人采用CFD軟件對(duì)微型燃機(jī)的離心葉輪進(jìn)行數(shù)值模擬,討論了葉片數(shù)及分流葉片位置對(duì)葉輪性能的影響,并進(jìn)行了流場(chǎng)分析。分析結(jié)果表明:葉片數(shù)增加使得性能曲線左移,單個(gè)葉片載荷減小,損失增加,葉輪效率下降,但是增壓效果得到改善;分流葉片位置靠近主葉片壓力面時(shí),性能曲線右移,流通能力提高,同時(shí)會(huì)使分流葉片的載荷增大,當(dāng)分流葉片位置靠近主葉片吸力面時(shí),情況正好相反16。楊策等人開(kāi)發(fā)了一套將初步設(shè)計(jì)、性能優(yōu)化計(jì)算、性能預(yù)測(cè)、葉片成型和葉輪應(yīng)力分析包含在內(nèi)的離心式葉輪輔助設(shè)計(jì)系統(tǒng),并用其設(shè)計(jì)出一種小型高轉(zhuǎn)速離心壓縮機(jī),然后對(duì)其性能進(jìn)行了詳細(xì)地分析研究。楊策等人的研究結(jié)果表明:在進(jìn)口條件和轉(zhuǎn)速相同情況下,后向葉輪壓比小于徑向葉輪,效率高于徑向葉輪,后向葉輪的流量特性曲線的斜率大于徑向葉輪的流量特性曲線的斜率,后向葉輪的流量特性更接近軸流壓縮機(jī)的特性;頂部間隙增大時(shí),離心壓縮機(jī)壓比減小,效率下降;對(duì)于小流量的離心壓縮機(jī),葉輪進(jìn)口彎曲對(duì)葉輪在設(shè)計(jì)點(diǎn)的絕熱效率影響不大,葉輪出口彎曲對(duì)離心壓縮機(jī)在設(shè)計(jì)點(diǎn)的效率影響很??;葉輪正彎時(shí)存在一個(gè)最高效率點(diǎn),當(dāng)葉輪正彎度大于或小于這個(gè)數(shù)值時(shí)效率均下降;采用前傾葉輪可以提高壓縮機(jī)的效率,但降低了壓縮機(jī)的壓比;在較低轉(zhuǎn)速下,前傾葉輪在大部分工作范圍內(nèi)效率高于普通葉輪,在較高轉(zhuǎn)速下,前傾葉輪在全工況范圍內(nèi)效率都高于普通葉輪;前傾葉輪比普通葉輪有更大的喘振裕度,工作范圍更寬廣;前傾葉輪改善了出口的氣流分離現(xiàn)象,能夠減少摻混損失。綜上所述,國(guó)內(nèi)研究人員對(duì)離心壓縮機(jī)的研究主要是通過(guò)數(shù)值計(jì)算來(lái)進(jìn)行,一般是先用自己開(kāi)發(fā)的計(jì)算程序或應(yīng)用軟件計(jì)算國(guó)外文獻(xiàn)提到的有詳細(xì)試驗(yàn)結(jié)果的離心壓縮機(jī)或葉輪(一般多用前文提及的德國(guó)宇航院(DFVLR)Krain博士研究的葉輪),經(jīng)過(guò)驗(yàn)證可行后,再用于自己的研發(fā)。一直以來(lái),國(guó)內(nèi)外在采用先進(jìn)技術(shù)進(jìn)行離心壓縮機(jī)流場(chǎng)測(cè)試方面的研究較之設(shè)計(jì)方法的研究則稍顯滯后。運(yùn)行中的離心壓縮機(jī)內(nèi)部流場(chǎng)測(cè)試技術(shù)的重大突破是伴隨著激光速度測(cè)量學(xué)的成功發(fā)展而實(shí)現(xiàn)的。1970年,Eckardt運(yùn)用Schodld的2倍焦距激光測(cè)速計(jì)(Laser-2focus-Velocimeter)對(duì)壓比為3的壓縮機(jī)內(nèi)部流場(chǎng)進(jìn)行了研究。在20世紀(jì)60年代初出現(xiàn)的激光多普勒測(cè)速技術(shù)和2倍焦距激光測(cè)速技術(shù)幾乎同時(shí)被應(yīng)用于離心壓縮機(jī)內(nèi)部流場(chǎng)的測(cè)量。國(guó)內(nèi)上海交通大學(xué)的繆俊、谷傳綱等人研究了激光相位多普勒測(cè)速技術(shù)(PDA)在離心壓縮機(jī)葉輪內(nèi)部流場(chǎng)測(cè)量中的應(yīng)用,他們采用PDA技術(shù)對(duì)試驗(yàn)用離心壓縮機(jī)在小流量工況下葉輪內(nèi)部的流動(dòng)進(jìn)行了測(cè)量,對(duì)如何在原有適合粒子圖像速度場(chǎng)儀(PIV)測(cè)量的試驗(yàn)臺(tái)上進(jìn)行PDA測(cè)量,并提出了改進(jìn)意見(jiàn),分析了小流量工況下流道內(nèi)氣流速度矢量的變化趨勢(shì)等流動(dòng)特性17。測(cè)試技術(shù)的發(fā)展必將進(jìn)一步推動(dòng)離心壓縮機(jī)技術(shù)的發(fā)展。前述國(guó)內(nèi)外研究人員在各自的研究過(guò)程中基本都針對(duì)的是較大流量的離心壓縮機(jī),所提及的楊策等人研究的一種小型高轉(zhuǎn)速離心壓縮機(jī)其流量也是0.kg/s,難以完全說(shuō)明小流量(0.kg/s以下)下的情形。F.Gui et al進(jìn)行了高速小流量離心壓縮機(jī)的設(shè)計(jì)和試驗(yàn)研究。在他的文獻(xiàn)里介紹了一種小流量高轉(zhuǎn)速的離心壓縮機(jī)的研究結(jié)果,結(jié)果表明:小流量高轉(zhuǎn)速離心壓縮機(jī)在幾何特征與整機(jī)性能上與大型離心壓縮機(jī)存在區(qū)別,小流量高轉(zhuǎn)速的離心壓縮機(jī)在進(jìn)口處輪蓋與輪轂的直徑比較大,葉輪外徑與進(jìn)口輪蓋直徑之比及葉尖間隙與葉片高度之比比大型離心壓縮機(jī)大許多;在設(shè)計(jì)范圍內(nèi),大型離心壓縮機(jī)的流量壓比曲線要比小流量高轉(zhuǎn)速離心壓縮機(jī)的流量壓比曲線平坦得多,這也暗示著小流量高轉(zhuǎn)速離心壓縮機(jī)與大型離心壓縮機(jī)的設(shè)計(jì)是有區(qū)別的,大型離心壓縮機(jī)設(shè)計(jì)的經(jīng)驗(yàn)方法不能完全應(yīng)用于小流量高轉(zhuǎn)速離心壓縮機(jī)的設(shè)計(jì)。F.Gui et al設(shè)計(jì)了一個(gè)葉輪直徑僅為63mm的小流量高轉(zhuǎn)速離心壓縮機(jī),其效率可達(dá)84,這個(gè)數(shù)值較之從20世紀(jì)50年代起一直未有太大提高的60%左右的效率則是有了相當(dāng)大的進(jìn)步,這也表明:設(shè)計(jì)一個(gè)用于飛行器空氣循環(huán)制冷系統(tǒng)和小型蒸汽壓縮制冷系統(tǒng)用的小流量高轉(zhuǎn)速離心壓縮機(jī)是可以實(shí)現(xiàn)的。經(jīng)過(guò)研究人員的長(zhǎng)期努力,對(duì)離心壓縮機(jī)的研究,無(wú)論是設(shè)計(jì)理論、方法還是試驗(yàn)手段都取得了巨大的進(jìn)步,但因?yàn)槿S流場(chǎng)本身的復(fù)雜性及相關(guān)技術(shù)發(fā)展的限制,使得仍有一些問(wèn)題有待完善和解決。葉輪和擴(kuò)壓器是離心壓縮機(jī)的關(guān)鍵部件,葉輪設(shè)計(jì)與制造的好壞及其與擴(kuò)壓器的匹配情況將對(duì)壓縮機(jī)的性能產(chǎn)生決定性的影響。作為整個(gè)壓縮機(jī)來(lái)說(shuō),軸承的性能及潤(rùn)滑、密封情況也將會(huì)對(duì)壓縮機(jī)性能產(chǎn)生影響。隨著計(jì)算機(jī)技術(shù)及計(jì)算流體動(dòng)力學(xué)(CFD)的發(fā)展,相繼出現(xiàn)了一批可以應(yīng)用于離心壓縮機(jī)研究的CFD應(yīng)用軟件。目前市場(chǎng)上較常見(jiàn)的有:FLUENT、NUMECA、NREC、CFX、STAR-CD等,這些軟件一般都集中了造型、網(wǎng)格生成、流場(chǎng)計(jì)算及后處理功能。這些軟件的發(fā)展極大地豐富了三元葉輪的設(shè)計(jì)手段,提高了工程設(shè)計(jì)的效率,為設(shè)計(jì)性能優(yōu)良的三元葉輪創(chuàng)造了更好的條件。用三元理論設(shè)計(jì)的葉輪葉片形狀一般為空間曲面,葉片及葉輪的加工成型是制造的重點(diǎn),也是難點(diǎn)。對(duì)于三元葉輪,常用的加工方法主要有兩種:三體焊形式,也即對(duì)輪盤、葉片、輪蓋分別加工然后再焊裝;整體銑制,也就是輪盤和葉片在一起利用多坐標(biāo)設(shè)備進(jìn)行整體銑制而得到一個(gè)半開(kāi)式葉輪。為避免干涉,目前國(guó)際上對(duì)這種葉輪的加工大都是利用價(jià)格很高的五坐標(biāo)加工中心進(jìn)行。在離心壓縮機(jī)的設(shè)計(jì)過(guò)程中,葉輪與擴(kuò)壓器的匹配問(wèn)題一直以來(lái)都是困擾設(shè)計(jì)人員的難題之一。影響葉輪與擴(kuò)壓器匹配的主要因素有:有葉擴(kuò)壓器的喉部面積,葉輪與擴(kuò)壓器之間的間隙,氣動(dòng)葉型擴(kuò)壓器的稠度,擴(kuò)壓器葉片前緣形狀等。研究發(fā)現(xiàn)改變有葉擴(kuò)壓器的喉部面積可以改變?nèi)~輪與擴(kuò)壓器的匹配范圍。當(dāng)有葉擴(kuò)壓器的喉部面積較大時(shí),葉輪與擴(kuò)壓器在流量較大區(qū)域內(nèi)匹配;當(dāng)有葉擴(kuò)壓器的喉部面積較小時(shí),葉輪與擴(kuò)壓器在流量較小區(qū)域內(nèi)匹配。低稠度的氣動(dòng)葉型擴(kuò)壓器具有較寬的工作范圍,能明顯改善喘振邊界限制。關(guān)于擴(kuò)壓器葉片前緣的最佳位置目前尚未有明確的答案,只是估計(jì)擴(kuò)壓器葉片前緣所在的半徑與葉輪半徑之比在1.15以上。Kenny認(rèn)為:在擴(kuò)壓器葉片前緣采用燕尾槽的方式可以使流出葉輪的渦破碎,從而使流動(dòng)更加穩(wěn)定??傊?,影響葉輪與擴(kuò)壓器匹配問(wèn)題的因素仍有待進(jìn)一步發(fā)現(xiàn)和解決。離心式壓縮機(jī)一般采用增速齒輪,轉(zhuǎn)子轉(zhuǎn)速一般都在5000r/min以上,目前一般采用滑動(dòng)軸承,滑動(dòng)軸承的設(shè)計(jì)也是研制離心壓縮機(jī)的一個(gè)重點(diǎn)。壓縮機(jī)轉(zhuǎn)速的增大必然要求減小軸承和軸之間的摩擦。國(guó)內(nèi)在這方面的研究已有多年,靜壓和動(dòng)壓空氣軸承已在許多透平機(jī)械中得到應(yīng)用。文獻(xiàn)18提出國(guó)外已有一種磁力軸承在被應(yīng)用于離心壓縮機(jī)后展示了其優(yōu)良的性能。磁力軸承的一個(gè)明顯的優(yōu)點(diǎn)就是它在轉(zhuǎn)軸旋轉(zhuǎn)后是懸浮于軸上的,只要空氣充滿磁力軸承和軸之間的狹小間隙,軸就懸浮在空氣(或其它工作介質(zhì))中旋轉(zhuǎn),以至于相對(duì)其它類型軸承來(lái)說(shuō),磁力軸承運(yùn)轉(zhuǎn)時(shí)的摩擦力是可以忽略不計(jì)的,從而轉(zhuǎn)子能夠真正實(shí)現(xiàn)在轉(zhuǎn)子強(qiáng)度和“堵塞”限制范圍內(nèi)以任何速度運(yùn)轉(zhuǎn)。因此有必要加快磁力軸承應(yīng)用技術(shù)研究。目前,國(guó)內(nèi)外對(duì)于高壓比(單級(jí)壓比5)離心壓縮機(jī)的應(yīng)用仍然較少,這主要是因?yàn)槠湫实?、流?dòng)范圍受限等原因所造成的。現(xiàn)代三維求解技術(shù)及先進(jìn)測(cè)試手段(PIV、PDA等)的應(yīng)用將使這些問(wèn)題有望得到解決,但仍需要大量的努力,一旦在這一領(lǐng)域?qū)崿F(xiàn)突破,將會(huì)使得離心壓縮機(jī)的使用成本大幅下降,從而使離心壓縮機(jī)得到更大范圍地應(yīng)用7。對(duì)于離心式制冷壓縮機(jī)研究,外一個(gè)有待突破的問(wèn)題即是實(shí)現(xiàn)其在小流量場(chǎng)合的應(yīng)用。離心壓縮機(jī)依賴于高流速實(shí)現(xiàn)增壓,這種高流速不可避免地會(huì)帶來(lái)摩擦及氣動(dòng)損失等流動(dòng)損失。對(duì)于小流量的離心壓縮機(jī),當(dāng)轉(zhuǎn)速不大時(shí),其流動(dòng)損失將顯著影響效率的提高。因此,對(duì)于小流量的壓縮機(jī),必須增加其轉(zhuǎn)速以保證達(dá)到一定的效率。隨著運(yùn)用CFD及三元理論進(jìn)行離心壓縮機(jī)研制技術(shù)的進(jìn)一步發(fā)展,高轉(zhuǎn)速軸承技術(shù)的日益成熟,相信有望在這一領(lǐng)域?qū)崿F(xiàn)突破。2. 離心壓縮機(jī)氣動(dòng)參數(shù)計(jì)算2.1 原始數(shù)據(jù)1) 空氣流量m: 2.5kg/s2) 壓強(qiáng)比: 2.43) 環(huán)境壓強(qiáng)p: 1.01310Pa4) 環(huán)境溫度T: 293K5) 環(huán)境密度: 1.205kg/m6) 空氣氣體常數(shù)R: 287J/(kg.K)7) 空氣絕熱指數(shù)k: 1.48) 交流電機(jī)驅(qū)動(dòng)2.2 進(jìn)氣道參數(shù)吸氣室是為了把氣體從進(jìn)氣管或中間冷卻器引到工作葉輪中去。設(shè)計(jì)時(shí)應(yīng)盡量減少氣體的流動(dòng)損失,避免出現(xiàn)氣流局部降速和分離。吸氣室的出口氣流要均勻,不產(chǎn)生切向的旋繞,以保證葉輪進(jìn)口有均勻的速度場(chǎng)與壓力場(chǎng)。除了上述氣動(dòng)要求外,還要注意到加工制造的方便。吸氣室的形式較多,常見(jiàn)的有:軸向進(jìn)氣的吸氣管、徑向進(jìn)氣的進(jìn)氣管、雙支承軸承所采用的徑向吸氣室、水平進(jìn)氣所采用的進(jìn)氣室。本設(shè)計(jì)采用的是軸向進(jìn)氣的吸氣管,如圖1,這種進(jìn)氣管形狀最簡(jiǎn)單,一般用于單機(jī)懸臂式鼓風(fēng)機(jī)或增壓器中。進(jìn)氣管可做成收斂狀,以使氣體能均勻進(jìn)入后面的葉輪。這種進(jìn)氣管形狀簡(jiǎn)單,氣流均勻,損失較小,故比其它形式的具有較好的性能。圖19) 葉輪對(duì)氣體所做的絕熱壓縮功ll=83739J/kg10) 葉輪出口的圓周速度=346m/s(取=0.70)11) 取進(jìn)氣道出口的速度C(=50150m/s)取 C=100m/s12) 進(jìn)氣道內(nèi)空氣降溫=4.98K13) 進(jìn)氣道出口溫度TT=T-=288.02K14) 進(jìn)氣道多變指數(shù)n(=1.371.39)n=1.3715) 進(jìn)氣道出口空氣壓強(qiáng)pp=0.9510P16) 進(jìn)氣道出口空氣密度=1.15kg/m17) 進(jìn)氣道出口面積ff=217cm2.3 壓縮機(jī)葉輪參數(shù)壓氣機(jī)葉輪一般分為兩部分:前一部分為導(dǎo)風(fēng)輪,后一部分叫工作輪。這是由于壓氣機(jī)葉片前緣部分彎曲較大,形狀復(fù)雜。大型的壓氣機(jī)為了便于制造把前后二部分分開(kāi)制造,而形成兩個(gè)輪子。尤其實(shí)對(duì)于徑向直葉片的工作輪(如圖2),前面設(shè)導(dǎo)風(fēng)輪是必要的。因?yàn)槿~輪進(jìn)口處從輪轂到輪緣的半徑是變化的,圓周速度也就是變化的,那么進(jìn)口氣流角是變化的。全進(jìn)口葉片角為,那么 式中為沖角,那么葉輪進(jìn)口葉片角也是變化的。圖2 徑向直葉片式的葉輪導(dǎo)風(fēng)輪也是一個(gè)擴(kuò)張性流道,出口速度大于進(jìn)口速度,故氣體靜壓有所提高。葉數(shù)的結(jié)構(gòu)形式分為以下幾種:(1) 閉式葉輪,由于輪盤、葉片、輪蓋三部分組成,由于輪蓋的強(qiáng)度不夠,使葉輪的轉(zhuǎn)速受到限制,一般閉式葉輪的周圍速度在320m/s以下。(2) 半開(kāi)式葉輪,這種葉輪強(qiáng)度和剛度均好,可達(dá)到450540m/s圓周速度,用于高壓比,高轉(zhuǎn)速壓氣機(jī)中,在內(nèi)燃機(jī)的透平增壓器和小功率燃?xì)廨啓C(jī)中得到廣泛應(yīng)用。(3) 此外還有雙進(jìn)氣葉輪,全開(kāi)式葉輪。本設(shè)計(jì)采用半開(kāi)式葉輪。18) 取葉輪外徑DD=290mm19) 轉(zhuǎn)速nn=22798r/min20) 取葉輪進(jìn)出口直徑比D取 =0.721) 導(dǎo)風(fēng)輪進(jìn)口外徑=203mm22) 導(dǎo)風(fēng)輪進(jìn)口內(nèi)徑=116mm(取110mm)23) 導(dǎo)風(fēng)輪進(jìn)口平均直徑=163mm24) 導(dǎo)風(fēng)輪進(jìn)口外徑處的圓周速度=242m/s25) 導(dǎo)風(fēng)輪進(jìn)口處的圓周速度=194m/s26) 導(dǎo)風(fēng)輪進(jìn)口處的圓周速度=131m/s27) 導(dǎo)風(fēng)輪葉片=1737取=2028) 取導(dǎo)風(fēng)輪進(jìn)口的阻塞系數(shù)=0.850.95取=0.9029) 導(dǎo)風(fēng)輪進(jìn)口軸向速度111m/s30) 導(dǎo)風(fēng)輪進(jìn)口相對(duì)速度266m/s31) 導(dǎo)風(fēng)輪進(jìn)口馬赫數(shù)0.782(0.7820.9則需要重新調(diào)整參數(shù)、重新計(jì)算)32) 導(dǎo)風(fēng)輪進(jìn)口處的氣流角=33) 導(dǎo)風(fēng)輪進(jìn)口處的氣流角34) 導(dǎo)風(fēng)輪進(jìn)口處的氣流角35) 取沖角ii=36) 導(dǎo)風(fēng)輪進(jìn)口處的葉片角=37) 取工作輪葉片數(shù)38) 滑移系數(shù)39) 工作輪出口氣流圓周向分速287m/s40) 工作輪出口氣流徑向分速取 111m/s41) 工作輪出口氣流速度308m/s42) 工作輪出口氣流角43) 取工作輪出口葉片角(徑向直葉片)44) 取工作輪出口葉片厚度1.6mm45) 工作輪出口阻塞系數(shù)0.96546) 取工作輪出口氣流密度取 =1.68kg/m47) 葉輪出口寬度15.3mm48) 取輪阻損失系數(shù)取 49) 葉輪出口氣溫=350K50) 取葉輪多變效率取 =0.8351) 多變指數(shù)項(xiàng)52) 多變指數(shù)1.5253) 葉輪出口氣體壓強(qiáng)1.6854) 葉輪出口氣體密度=1.67kg/m55) 氣體密度誤差=0.60%2%56) 葉輪出口馬赫數(shù)0.82 1認(rèn)可2.4 無(wú)葉擴(kuò)壓器段參數(shù)57) 無(wú)葉擴(kuò)壓器寬度 58) 入口氣流周向分速=287m/s59) 入口氣流徑向分速=107m/s60) 入口氣流角=61) 入口氣流速度=306m/s62) 入口氣流溫度=350.61K63) 入口氣流壓強(qiáng)=1.6964) 入口氣流密度=1.68kg/m65) 取出口直徑比取為1.1666) 出口直徑=336mm67) 出口密度(取)1.78kg/m68) 出口氣流速度=249m/s69) 出口氣流溫度366K70) 馬赫數(shù)=0.650.95認(rèn)可71) 取多變效率取為0.6072) 多變指數(shù)項(xiàng)=2.173) 出口空氣壓強(qiáng)=1.86Pa74) 出口空氣密度=1.77kg/m75) 密度誤差0.56%2%76) 出口寬度15.3mm77) 出口徑向分速=87.5m/s78) 出口周向分速=233m/s79) 出口氣流角=80) 長(zhǎng)度23mm2.5 葉片擴(kuò)壓器參數(shù)81) 取直徑比取為1.5082) 出口直徑435mm83) 出口寬度15.3mm84) 進(jìn)氣口沖角取85) 葉片進(jìn)口角86) 葉片出口角=87) 葉片進(jìn)口阻塞系數(shù),取=0.988) 進(jìn)口通道面積=56cm89) 葉片數(shù),取2990) 進(jìn)口喉部寬度12.6mm91) 設(shè)出口氣流密度=2.01kg/m92) 出口氣流速度=97m/s93) 出口空氣溫度=392K94) 多變效率,取為0.895) 多變指數(shù)項(xiàng)=2.896) 出口空氣壓強(qiáng)97) 出口空氣密度=0.49%2%2.6 蝸殼參數(shù)98) 蝸殼出口氣流速度=60m/s99) 出口空氣溫度=395K100) 多變效率,取為0.60101) 多變指數(shù)項(xiàng)102) 出口壓強(qiáng)103) 蝸殼出口密度kg/m104) 出口滯止溫度=396.8K105) 出口滯止壓強(qiáng)2.7 壓縮機(jī)參數(shù)校核106) 壓強(qiáng)比2.39107) 滯止壓強(qiáng)比=2.43108) 等熵壓縮功l=83194J109) 壓強(qiáng)系數(shù)=0.695110) 絕熱效率=0.77111) 功率=262kW2.8 軸的強(qiáng)度校核112) 軸的材料選45鋼,=25軸的扭轉(zhuǎn)強(qiáng)度條件為可得軸的直徑軸上有兩個(gè)鍵槽,應(yīng)增大(取30mm)2.9 軸承和鍵的選擇查閱機(jī)械設(shè)計(jì)手冊(cè),選用61806-2RZ型深溝球軸承,油潤(rùn)滑葉輪與軸采用雙平鍵聯(lián)接,鍵的規(guī)格為:鍵寬12,鍵高8,長(zhǎng)度50,B型,代號(hào)B2.10 軸承蓋的參數(shù)計(jì)算軸承蓋采用透蓋凸緣式,鑄鐵制造,無(wú)套杯,螺釘選用開(kāi)槽盤頭螺釘GB/T67 M412,材料為鋼113) e=1.2d=4.8mm,d-軸承蓋螺釘直徑114) mm115) mm116) ,取為36mm117) mm3 結(jié)論經(jīng)過(guò)了幾個(gè)月,我總算把畢業(yè)設(shè)計(jì)這個(gè)大難題攻克下來(lái)了。期間有過(guò)不少的不眠之夜,還有到珠海盈德氣體有限公司實(shí)習(xí)的經(jīng)歷。當(dāng)初決定要做 離心式壓縮機(jī)的設(shè)計(jì)這課題就是因?yàn)楸挥落浻?,想做個(gè)跟自己以后工作相關(guān)的畢業(yè)設(shè)計(jì)。當(dāng)初沒(méi)有太多考慮做這個(gè)課題的難度,后來(lái)在資料匱乏的條件下才發(fā)現(xiàn)做起來(lái)步步維艱。特別是在繪圖過(guò)程中出現(xiàn)了很多問(wèn)題。比如說(shuō)繪制葉輪,一開(kāi)始根本不知道計(jì)算出來(lái)的參數(shù)在模型上應(yīng)該怎么表示,結(jié)果畫出來(lái)的圖總感覺(jué)不對(duì)勁。后來(lái)終于畫出一個(gè)自己覺(jué)得可以的,過(guò)了幾天又感覺(jué)不對(duì),又重畫了一個(gè)。因?yàn)閷?duì)proE使用不熟悉,繪圖很不順利,比如想把一個(gè)邊界掃描加厚,往往不成功,后來(lái)去網(wǎng)上找方法,經(jīng)過(guò)多次嘗試才把問(wèn)題給解決了。從一開(kāi)始我不知道 離心式壓縮機(jī)是什么,到我完成這個(gè)設(shè)計(jì),我覺(jué)得自己實(shí)現(xiàn)了一個(gè)巨大的跨越。現(xiàn)在我已經(jīng)對(duì) 離心式壓縮機(jī)有了一定的理解,這對(duì)我以后的工作有很大的幫助。本設(shè)計(jì)由于制作時(shí)間及本人水平有限,部分細(xì)節(jié)難免存在不足之處,懇請(qǐng)各位老師和學(xué)友批評(píng)和指正!參 考 文 獻(xiàn)1 不詳.氣體壓縮機(jī)在石化工業(yè)的應(yīng)用和發(fā)展 EB/OL. http:/www.asiapump.cn/news/news_info.asp?newsid=8872,2008-11-212 不詳. 化工用離心壓縮機(jī)現(xiàn)狀分析 EB/OL. http:/www.kongyaji.info/news_view.asp?id=86,2009-11-243 徐忠. 離心式壓縮機(jī)原理M. 3版. 北京:機(jī)械工業(yè)出版社,1988.4 B.里斯. 離心壓縮機(jī)械M. 北京:機(jī)械工業(yè)出版社,1986.5 朱報(bào)禎,郭濤. 離心壓縮機(jī)M. 西安:西安交通大學(xué)出版社,1989.6 T. B. 弗格遜. 離心壓縮機(jī)的級(jí)M. 1980.7 吳玉林,陳慶光,劉樹(shù)紅. 通風(fēng)機(jī)和壓縮機(jī)M. 北京:清華大學(xué)出版社,2005. 8 吳克啟. 透平壓縮機(jī)械M. 北京:機(jī)械工業(yè)出版社,2003.9 陸玉,馮立艷. 機(jī)械設(shè)計(jì)課程設(shè)計(jì)M. 北京:機(jī)械工業(yè)出版社,2006.10 濮良貴,紀(jì)名剛,陳國(guó)定等. 機(jī)械設(shè)計(jì)M. 北京:高等教育出版社,2006.11 成大先. 機(jī)械設(shè)計(jì)手冊(cè)M. 北京:化工工業(yè)出版社,2004.致 謝本文是在劉江濤老師悉心指導(dǎo)下完成的。他廣博的專業(yè)知識(shí)、嚴(yán)肅的科學(xué)態(tài)度、精益求精的工作作風(fēng)深深地影響著我,這一切使我受益匪淺。他經(jīng)常從百忙中抽時(shí)間解答我們遇到的問(wèn)題,并悉心指導(dǎo)我們下一步的工作。在此我表示衷心感謝,并致以崇高的敬意。要感謝學(xué)校和學(xué)院四年的專業(yè)栽培,并給我們良好的學(xué)習(xí)和生活環(huán)境。最后感謝所有關(guān)心、支持和幫助過(guò)我的老師、同學(xué)、同事和朋友。Journal of Engineering Mathematics 44: 5782, 2002. 2002 Kluwer Academic Publishers. Printed in the Netherlands. Modelling gas motion in a rapid-compression machine M.G. MEERE 1 , B. GLEESON 1 and J.M. SIMMIE 2 Department of Mathematical Physics, NUI, Galway, Ireland 2 Department of Chemistry, NUI, Galway, Ireland Received 25 July 2001; accepted in revised form 8 May 2002 Abstract. In this paper, a model which describes the behaviour of the pressure, density and temperature of a gas mixture in a rapid compression machine is developed and analyzed. The model consists of a coupled system of nonlinear partial differential equations, and both formal asymptotic and numerical solutions are presented. Using asymptotic techniques, a simple discrete algorithm which tracks the time evolution of the pressure, temperature and density of the gas in the chamber core is derived. The results which this algorithm predict are in good agreement with experimental data. Key words: gasdynamics, rapid-compression machines, shock-waves, singular perturbation theory 1. Introduction 1.1. RAPID-COMPRESSION MACHINES A rapid-compression machine is a device used to study the auto-ignition of gas mixtures at high pressures and temperatures, with particular reference to auto-ignition in internal combus- tion engines; see 13. A typical combustion engine is a very dirty and complex environment, and this has prompted the development of rapid-compression machines which enable the scientific study of compression and ignition in engines in a cleaner and simpler setting. In Figure 1 we schematically illustrate a two-piston rapid-compression machine, such as the one in the department of Chemistry at NUI, Galway. However, single-piston machines, with a piston at one end and a stationary solid wall at the other, are more typical. The analysis developed in this paper is appropriate to both single- and two-piston machines. The operation of a rapid-compression machine is very simple - the pistons are simul- taneously driven in pneumatically, compressing the enclosed gas mixture, thereby causing the gas pressure, temperature and density to rise quickly. In Figures 1(a), 1(b) and 1(c) we schematically represent a rapid-compression machine prior to, during, and after compression, respectively. The ratio of the final volume to the initial volume of the compression chamber for the machine at NUI, Galway is about 1:12, this value being typical of other machines. At the end of the compression, the gas mixture will typically have been pushed into a pressure and temperature regime where auto-ignition can occur. In Figure 2, we display an experimental pressure profile for a H 2 /O 2 /N 2 /Ar mixture which has been taken from Brett et al. 4, with the kind permission of the authors. In this graph, the time t = 0 corresponds to the end of the compression time. We note that, for the greater part of the compression, the pressure in the chamber is rising quite gently, but that towards the end of the compression (that is, just before t = 0), there is a steep rise in the pressure. After compression, the pressure profile levels off as expected; the extremely steep rise at the end of 58 M.G. Meere et al. Figure 1. Schematic illustrating the operation of a rapid-compression machine; we have shown the configuration (a) prior to compression, (b) during compression and (c) after compression. Figure 2. An experimental pressure profile for a gas mixture H 2 /O 2 /N 2 /Ar = 2/1/2/3, as measured in the rapid-compression machine at NUI, Galway. It is taken from 4, and has an initial pressure of 005 MPa and an initial temperature of 344 K. Modelling gas motion in a rapid-compression machine 59 the profile corresponds to the ignition of the mixture. We note that the compression time and the time delay to ignition after compression are both O(10) ms. The pressure history is the only quantity which is measured in experiments. However, the temperature in the core after compression is the quantity which is of primary interest to chemists since reaction rates depend mainly on temperature for almost all systems, although there may also be some weaker pressure dependence. Measuring temperature accurately in the core can be problematic because of the presence of a thermal boundary layer; see the comments below on roll-up vortices. However, with the experimental pressure data in hand, the corresponding temperatures can be estimated using the isentropic relation ln(p/p i ) = integraldisplay T T i (s) s(s) 1) ds, (1) where (T i ,p i ) are the initial values for the core temperature and pressure, (T,p) are these quantities at some later time, and (s)is the specific heat ratio at temperature s. In exper- iments, the initial core temperature is typically O(300 K), while the core temperature after compression is usually O(1000 K). In this paper, we shall consider only the behaviour of the gas mixture during compression; the post-compression behaviour is not considered here, but this will form the subject for future work. Nevertheless, the model presented here does provide a reasonable description of the post-compression behaviour of a single species pure gas, or an inert gas mixture; see Section 3.5. 1.2. THE MODEL We suppose that the compression chamber is located along 0 x 0. This assumption is actually quite a strong one in this context since higher-dimensional effects are frequently observed in experiments, roll-up vortices near the corner regions defined by the piston heads and the chamber wall being particularly noteworthy; see, for example, 5. These vortices arise due to the scraping by the pistons of the thermal boundary layer at the chamber wall, and they can, and frequently do, disturb the gas motion in the core of the compression chamber. However, the justification for the one-dimensional model studied here is twofold: (i) the corner vortices can be successfully suppressed by introducing crevices at the piston heads which swallow the thermal boundary layer as the pistons move in (see Lee 6), rendering the gas motion away from the chamber walls one-dimensional to a good approximation, and, (ii) the study of the one-dimensional model provides a useful preliminary to the study of higher-dimensional models. We now give the governing equations for our one-dimensional model. A reasonably com- plete derivation of the governing equations for a multi-component reacting gas can be found in the appendices of 7; these standard derivations are not reproduced here. The model which we shall study includes a number of simplifying assumptions and these will be clearly stated as they arise. The equation expressing conservation of mass is given by t + x (v) = 0, 60 M.G. Meere et al. where = (x,t)and v = v(x,t) are the density and the velocity of the gas, respectively, at location x and time t. It should be emphasized that these quantities refer to a gas mixture, so that if there are N different species in the mixture then = N summationdisplay i=1 i , where i = i (x,t) is the density of species i. Also, the velocity v above refers to the mass- averaged velocity of the mixture, that is, v = N summationdisplay i=1 Y i v i , where Y i = i / and v i = v i (x,t) are the mass fraction and velocity, respectively, of species i; see 7. Neglecting body forces and viscous effects, the equation expressing conservation of mo- mentum is given by v t +v v x = 1 p x , where p = p(x,t)is the pressure. We assume that the gas mixture is ideal, so that the equation of state is given by p = R M T, (2) where T = T(x,t)is the temperature, R is the universal gas constant (8314 JK 1 mol 1 ), and M is the average molecular mass of the mixture. This last quantity is given by M = N summationdisplay i=1 n i W i (mA), where n i and W i give the number fraction and molecular weight, respectively, of species i, m is the atomic mass unit (1661 10 27 kg) and A is Avogadros number (6022 10 23 molecules mol 1 ). The equation expressing conservation of energy is given by (see 7 or 8) parenleftbigg u t +v u x parenrightbigg =M parenleftbigg q x +p v x parenrightbigg , (3) where u = u(x,t) is the internal energy of the gas mixture and q = q(x,t) is the heat flux. We also have the thermodynamic identity u= N summationdisplay i=1 h i Y i Mp/, (4) where the enthalpies h i = h i (T) are given by h i (T) = h i (T 0 )+ integraldisplay T T 0 c p,i (s)ds, i = 1,2,.,N, (5) Modelling gas motion in a rapid-compression machine 61 where T 0 is some reference temperature and the c p,i (T) are the specific heats at constant pressure for the N species. When diffusion velocities and the radiant heat (again, see 7 for more details) are neglected, the expression for the heat flux is given by q =(T) T x , (6) where (T) is the thermal conductivity. The mass fractions Y i = i / are not necessarily constant since chemical reactions can change the composition of the mixture. However, for many systems such chemical effects can be neglected in the analysis of the compression because the gas mixture is cold for most of the compression time. The core temperature will only rise to a level where chemical reactions can have a significant effect near the end of the compression, and the duration of this period is typically very short (a couple of milliseconds usually). Nevertheless, it is possible for some chemical reactions to proceed sufficiently rapidly for them to significantly influence the compression behaviour. However, we do not attempt to model systems which exhibit this behaviour here and take the Y i to be constant during compression. Substituting (4) and (6) in (3), and using (5), we have the final form of the equation expressing conservation of energy: T t +v T x = M (c p (T)R) parenleftbigg x parenleftbigg (T) T x parenrightbigg p v x parenrightbigg , where c p = N summationdisplay i=1 Y i c p,i is the mass-averaged specific heat. 1.3. BOUNDARY AND INITIAL CONDITIONS We suppose that the left and right pistons move with constant velocities V 0 and V 0 ,re- spectively, so that their motions are given by x = V 0 t and x = 2L V 0 t. In reality, the pistons in a rapid-compression machine will spend some of the compression time accelerating from rest and decelerating to rest, and this is not difficult to incorporate into the analysis given below. However, rather than complicate the analysis unnecessarily at the outset by considering variable piston velocity, we shall simply quote the results for general piston motion once the constant velocity case has been completed; see Section 3.4. Throughout the compression, we assume that the temperature of the walls of the chamber remain at their initial constant value, which we denote by T 0 . Hence, at the left piston, we impose v = V 0 ,T= T 0 on x = V 0 t, while at the right piston we set v =V 0 ,T= T 0 on x = 2LV 0 t. The gas in the chamber is initially at rest and we suppose that v = 0,T= T 0 ,p= p 0 ,= 0 at t = 0, 62 M.G. Meere et al. where p 0 and 0 are constants. Clearly, in view of (2), we have p 0 = R M 0 T 0 . However, the above are not quite the boundary and initial conditions that are considered in this paper. For the conditions described above above we have the symmetry v(x,t)=v(2Lx,t), T(x,t)= T(2Lx,t), p(x,t)= p(2Lx,t), (x,t)= (2Lx,t). We exploit this behaviour by halving the spatial domain, considering the gas motion in V 0 t xq + ,wehavev = 0, p = = T = 1. For x 0, but this amounts to nothing more than requiring that the pistons travel at velocities which do not exceed the speed of sound in the gas. Recall that the maximum speed of the pistons is O(10 ms 1 ), while the speed of sound in gases under typical conditions is frequently O(300 ms 1 ). Substituting (17) in (16) 3 , and integrating subject to the conditions v 0 0,p 0 1as z +,wehave Modelling gas motion in a rapid-compression machine 71 p 0 = 1 +q + 0 v 0 /. (19) Letting z in (19) we obtain P s (t) = 1 +q + 0 /, (20) so that, T c (t) = (1 +q + 0 /)(1 1/q + 0 ), (21) both of which are constant since, as we shall now show, q + 0 is constant. The prediction that (p,T)are constant to leading order in the outer region behind the wave-front is clearly consistent with the numerical solution displayed in Figure 3. Substituting (17) and (19) in (16) 4 and integrating subject tov 0 0,T 0 1,T 0 /z 0asz +,weget q + 0 (T 0 ) = (T 0 ) T 0 z (v 0 +q + 0 v 2 0 /2), (22) where (T 0 ) = integraldisplay T 0 1 ds (s) 1 . Letting z in (22), we obtain q + 0 parenleftbig (1 +q + 0 /)(1 1/q + 0 ) parenrightbig = 1 +q + 0 /2, (23) which determines q + 0 , completing the specification of the leading order outer problem. It is clear that the solution for q + 0 to (23) does not depend on t,sothatq + 0 has the form t where is a constant. Using (9), we have (T 0 ) = 1 1 ln parenleftbigg 0 + 1 T 0 1 0 + 1 1 parenrightbigg , so that (23) becomes q + 0 1 ln parenleftbigg 0 1 + 1 (1 +q + 0 /)(1 1/q + 0 ) 0 + 1 1 parenrightbigg = 1 +q + 0 /2, (24) which is an equation that is easily solved numerically for q + 0 for given values of 0 , 1 and . In the limit 1 0 (so that (T) 0 ) this expression reduces to a quadratic in q + 0 which can be solved to give q + 0 = 1 4 parenleftBig 0 + 1 radicalbig ( 0 + 1) 2 + 16 0 parenrightBig , with the positive solution being clearly the relevant one here. The numerical solution of (24) for 1 negationslash= 0 is usually unnecessary. Recalling that = O(10 3 ) typically, and considering the behaviour of (24) for greatermuch 1, we can easily show that q + 0 radicalbig ( 0 + 1 ) for greatermuch 1. (25) In dimensional terms, this expression for q + 0 is 72 M.G. Meere et al. radicalBigg (T 0 )p 0 0 , which is the familiar expression for the speed of sound in an ideal gas. We favour the simpler expression (25) over (24) for the algorithm described in Section 3.4. It is worth noting here that the relations (18), (20) and (23) could also have been obtained using integral forms for the conservation laws, and it is not necessary (although it is preferable) to consider the detail of the transition layer. For example, conservation of mass implies that d dt parenleftbiggintegraldisplay 1 t (x,t)dx parenrightbigg = 0, which at leading order gives d dt parenleftBigg integraldisplay q + 0 t 0 (x,t)dx + integraldisplay 1 q + 0 1dx parenrightBigg = 0, and this leads to (18). 3.1.4. Summary The motion of the wave-front, x = q + (t;), is such that as 0, q + (t;) q + 0 (t),where q + 0 (t) is determined by solving (24) subject to q + 0 (0) = 0. For xq + , p = = T = 1andv = 0. 3.2. THE FIRST REFLECTION OF THE WAVE FROM THE CENTRE-LINE When the wave-front reaches the centre-line, it reflects off the identical opposing wave, and then moves from right to left towards the incoming piston. The leading-order behaviour ahead of the wave is now known from the calculations of the previous subsection. A numerical solution illustrating this case is given in Figure 4. The leading-order behaviour in the boundary layer near the piston is clearly unchanged from that considered in Section 3.1.1 and requires no further discussion. 3.2.1. Outer region We denote the motion of the reflected wave by x = q (t;).Forxq ,wehavev = o(1) and we pose p p + 0 (x,t), + 0 (x,t), T T + 0 (x,t) to obtain p + 0 = + 0 T + 0 , + 0 t = 0, p + 0 x = 0, T + 0 t = 0, so that p + 0 = P sr , + 0 = g(x), T + 0 = P sr /g(x), Modelling gas motion in a rapid-compression machine 73 where P sr , which is constant, and g(x) are determined below by matching. 3.2.2. Transition region This is located at z = O(1) where x = q (t;)+z . It gives the location of the narrow region over which v drops from v 1tov = o(1); the transition region is also clearly identifiable in the solutions for p, and T; see Figure 4. In z = O(1) we pose q q 0 (t), p p 0 (z ,t), 0 (z ,t),v v 0 (z ,t),T T 0 (z ,t), to obtain leading-order equations which have precisely the same form as (16). Integrating and matching in a manner similar to that described in Section 3.1.3, we obtain 0 = q + 0 (q 0 1) (q + 0 1)(q 0 v 0 ) , v 0 = 1 + (q + 0 1) q + 0 (q 0 1) (p 0 1 q + 0 /), q + 0 (q 0 1) q + 0 1 (T c )(T 0 ) = (T 0 ) T 0 z parenleftbigg (1 +q + 0 /)(v 0 1)+ q + 0 (q 0 1) 2(q + 0 1) (v 2 0 1) parenrightbigg . (27) Letting z +in (27) gives g(x) q + 0 (q 0 1) q 0 (q + 0 1) ,P sr = 1 + q + 0 (q + 0 q 0 ) (q + 0 1) , T + 0 = q 0 q + 0 (q 0 1) parenleftbigg q + 0 1 + q + 0 (q + 0 q 0 ) parenrightbigg , (28) where the constant reflected wave speed q 0 is determined as the negative solution to q + 0 (q 0 1) 1 (q + 0 1) ln parenleftbigg 0 1 + 1 T c 0 1 + 1 T + 0 parenrightbigg = 1 + q + 0 q + 0 (q 0 1) 2(q + 0 1) , (29) where T c is given by (21) and T + 0 is given in (28). Considering the behaviour of this last expression for greatermuch 1, we find that q 0 ( 0 + 1 ), the negative solution being the relevant one now. It is this simpler form which we shall use for the algorithm described in Section 3.4. 3.2.3. Summary The location of the reflected wave-front, x = q (t;), is such that as 0, q (t;) q 0 (t),whereq 0 (t) is determined as the solution to (29). For xq ,wehavev = o(1) and p 1 + q + 0 (q + 0 q 0 ) (q + 0 1) , q + 0 (q 0 1) q 0 (q + 0 1) , T q 0 q + 0 (q 0 1) parenleftbigg q + 0 1 + q + 0 (q + 0 q 0 ) parenrightbigg . 74 M.G. Meere et al. 3.3. THE WAVE TRAVELS OVER AND BACK IN THE CHAMBER FOR THE N th TIME Most of the notation required here has previously been introduced in Section 2.3. 3.3.1. The wave travels down the chamber for the N th time Denoting the location of the wave-front by q + N ,wehaveforxq + N ,wehavev = o(1) and p p 2N2 , 2N2 ,T T 2N2 , where (p 2N2 , 2N2 ,T 2N2 ) are constants. If we now consider the transition layer of thick- ness O() about q + N , and perform calculations which are almost identical to those of Sec- tion 3.1.3, we find that 2N1 = q + N0 q + N0 1 2N2 , p 2N1 = p 2N2 + q + N0 2N2 , T 2N1 = p 2N1 2N1 , q + N0 2N2 (T 2N1 )(T 2N2 ) = p 2N2 + q + N0 2 2N2 . (30) Using (9), and considering the behaviour of (30) 4 for greatermuch 1, we can easily show that q + N0 radicalbig (T 2N2 )T 2N2 = radicalBigg (T 2N2 )p 2N2 2N2 for greatermuch 1. We note from this expression that as the pistons compress the gas in the chamber core, the speed of the wave increases in proportion to the square root of the rising temperature (for (T)constant). If (T) 0 , then we can solve exactly for q + N0 to obtain q + N0 = 1 4 parenleftBig 0 + 1 + radicalbig ( 0 + 1) 2 + 16 0 T 2N2 parenrightBig . (31) 3.3.2. The wave reflects off the centre-line for the N th time We denote the location of the wave-front by x = q N .As 0, we have for xq N ,wehavev = o(1) and p p 2N , 2N ,T T 2N , with (p 2N , 2N ,T 2N ) constant. Considering the transition layer about q N , it is readily shown that Modelling gas motion in a rapid-compression machine 75 2N = q N0 1 q N0 2N1 , p 2N = p 2N1 q N0 2N , T 2N = p 2N 2N , q N0 2N (T 2N1 )(T 2N ) = p 2N + q N0 2 2N . (32) Considering the behaviour of (34) 4 for greatermuch 1, we have q N0 radicalbig (T 2N1 )T 2N1 = radicalBigg (T 2N1 )p 2N1 2N1 for greatermuch 1. For (T) 0 , we have the exact expression q N0 = 1 4 parenleftBig 3 0 radicalbig (3 0 ) 2 + 16 0 T 2N1 + 8( 0 1) parenrightBig . (33) 3.4. THE ALGORITHM 3.4.1. Constant piston velocity The calculations of the previous subsections yield the following simple iterative algorithm for the evolution of the pressure, density and temperature in the chamber core: p 0 = 0 = T 0 = 1,t 0 = 0, and for N = 1,2,3,.,wehave q + N = radicalbig (T 2N2 )T 2N2 , 2N1 = q + N q + N 1 2N2 , p 2N1 = p 2N2 + q + N 2N2 ,T 2N1 = p 2N1 2N1 , t 2N1 = t 2N2 + 1 t 2N2 q + N , q N = radicalbig (T 2N1 )T 2N1 , 2N = q N 1 q N 2N1 ,p 2N = p 2N1 q N 2N , T 2N = p 2N 2N ,t 2N = t 2N1 + 1 t 2N1 1 q N . (34) It is clear that this iterative scheme is trivial to implement on a computer. Once a calculation based on this algorithm has been completed, one could, for example, plot the pressure in the chamber during compression by simply passing a smooth curve through the data points (p i ,t i ), i = 0,1,2,. In Figure 6(a), we have p
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