基于螺旋貝殼仿生的發(fā)動(dòng)機(jī)增壓器渦輪蝸殼設(shè)計(jì)提升渦輪性能

吳 娜，張克松，王希波，馬云海

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基于螺旋貝殼仿生的發(fā)動(dòng)機(jī)增壓器渦輪蝸殼設(shè)計(jì)提升渦輪性能

吳 娜1，張克松1，王希波1，馬云海2※

（1. 山東交通學(xué)院汽車(chē)工程學(xué)院，濟(jì)南 250357；2. 吉林大學(xué)工程仿生教育部重點(diǎn)實(shí)驗(yàn)室，長(zhǎng)春 130022）

增壓器蝸殼性能直接影響增壓器整體效率和性能。通過(guò)降低蝸殼內(nèi)腔流動(dòng)阻力、減少蝸殼能量損失對(duì)提高增壓器效率和性能具有重要意義。海洋螺旋形貝殼在進(jìn)化過(guò)程中形成了減少流體阻力、降低運(yùn)動(dòng)過(guò)程中流體能量損耗的結(jié)構(gòu)特征。該文以螺旋貝殼為仿生原型，通過(guò)逆向工程技術(shù)獲取貝殼內(nèi)腔數(shù)據(jù)，在幾何分析的基礎(chǔ)上提取內(nèi)腔截面部分?jǐn)?shù)據(jù)作為仿生蝸殼設(shè)計(jì)原始數(shù)據(jù)，并完成數(shù)學(xué)建模。通過(guò)數(shù)據(jù)優(yōu)化得到增壓器渦輪蝸殼仿生設(shè)計(jì)截面曲線，實(shí)現(xiàn)蝸殼仿生曲面設(shè)計(jì)。建立原型增壓器和仿生增壓器計(jì)算模型，在原型增壓器仿真模型與臺(tái)架試驗(yàn)吻合較好的條件下，采用流體力學(xué)軟件對(duì)原型及仿生優(yōu)化增壓器渦輪效率、流通特性及蝸殼內(nèi)流態(tài)等性能進(jìn)行仿真分析。結(jié)果表明，渦輪流通能力不變情況下，仿生蝸殼使渦輪效率提升3%，最大可提升5%以上；流場(chǎng)分析結(jié)果表明，仿生優(yōu)化蝸殼減小蝸殼壁面附近的流動(dòng)損失和流道內(nèi)氣流摩擦，殼內(nèi)流動(dòng)平穩(wěn)均勻，無(wú)旋流，是渦輪效率明顯提高的根源。本文所采用的方法對(duì)增壓器渦輪性能的提升顯著，可以為汽車(chē)和農(nóng)業(yè)機(jī)械渦輪增壓系統(tǒng)設(shè)計(jì)和優(yōu)化提供參考和借鑒。

仿生；設(shè)計(jì)；試驗(yàn)；渦輪蝸殼；渦輪效率；螺旋貝殼；流通能力

0 引 言

渦輪增壓器已成為柴油機(jī)和汽油機(jī)的重要部件。渦輪增壓器的使用可以大幅提升內(nèi)燃機(jī)的動(dòng)力性能和燃油經(jīng)濟(jì)性，也是內(nèi)燃機(jī)小型化的關(guān)鍵手段。研究提升增壓器性能得到國(guó)內(nèi)外工程人員的重視[1-5]。增壓器蝸殼對(duì)渦輪和增壓器性能有著重要影響[6-9]，蝸殼的不同幾何設(shè)計(jì)參數(shù)影響蝸殼的曲率變化、蝸殼腔內(nèi)流體與壁面間的摩擦力及壓力梯度分布，改變蝸殼腔內(nèi)流場(chǎng)分布，影響蝸殼腔內(nèi)的流體運(yùn)動(dòng)規(guī)律、壓力分布及能量損失，影響蝸殼工作性能[10-13]，增壓器蝸輪蝸殼流道設(shè)計(jì)水平對(duì)渦輪的效率和流通能力起著關(guān)鍵作用[14-17]。目前還沒(méi)有成熟的蝸殼流道截面的設(shè)計(jì)方法，蝸殼結(jié)構(gòu)的優(yōu)化設(shè)計(jì)方法還處在不斷發(fā)展完善中[18-20 ]。

傳統(tǒng)增壓器蝸殼的設(shè)計(jì)采用公式計(jì)算并修正的方法進(jìn)行，常用計(jì)算方法為周向平均速度法和等環(huán)量法。這2種傳統(tǒng)設(shè)計(jì)方法完全依據(jù)理論計(jì)算得出。盡管設(shè)計(jì)結(jié)果也會(huì)根據(jù)實(shí)驗(yàn)數(shù)據(jù)進(jìn)行微調(diào)整，但完全依據(jù)理論計(jì)算的蝸殼設(shè)計(jì)方法單一，且阻礙了蝸殼設(shè)計(jì)技術(shù)的快速發(fā)展。

仿生設(shè)計(jì)通過(guò)對(duì)生物結(jié)構(gòu)、生物功能和生命過(guò)程的認(rèn)識(shí)為解決工程和機(jī)械設(shè)計(jì)中的難題提供巧妙的設(shè)計(jì)思路和靈感[21-25]。采用仿生技術(shù)進(jìn)行渦輪蝸殼設(shè)計(jì)可實(shí)現(xiàn)蝸殼設(shè)計(jì)技術(shù)的創(chuàng)新和發(fā)展。螺旋貝殼是軟體動(dòng)物的保護(hù)外套，在億萬(wàn)年的進(jìn)化過(guò)程中，已進(jìn)化出適應(yīng)海洋生存，減小流動(dòng)摩擦阻力的宏觀流線形結(jié)構(gòu)和形體，這為增壓器蝸殼設(shè)計(jì)提供了新的思路和方法。本文以螺旋貝殼為研究對(duì)象，采用仿生學(xué)方法對(duì)現(xiàn)有增壓器渦輪蝸殼進(jìn)行優(yōu)化設(shè)計(jì)，采用數(shù)值模擬方法對(duì)優(yōu)化前后的渦輪結(jié)構(gòu)進(jìn)行全面分析研究，對(duì)比研究仿生蝸殼性能。

1 仿生增壓器渦輪蝸殼設(shè)計(jì)

1.1 螺旋貝殼內(nèi)腔截面輪廓線建模

螺旋貝殼如圖1a所示。利用逆向工程技術(shù)，獲取螺旋貝殼內(nèi)腔的數(shù)字化點(diǎn)云如圖1b所示。考慮到增壓器蝸殼入口和出口的比值大小直接影響增壓器整體效率，由螺殼大端入口按螺旋方向取其270°內(nèi)的螺旋貝殼曲面模型，過(guò)螺殼正投影圓心均角度依次截取16個(gè)截面，角度間隔18°，如圖2a所示。螺殼內(nèi)腔截面輪廓線形狀如圖2b所示。對(duì)第1條截面輪廓曲線進(jìn)行幾何特征分析，結(jié)合增壓器蝸殼流道設(shè)計(jì)原理，提取輪廓線的曲率變化均勻、流線型較好的部分?jǐn)?shù)據(jù)點(diǎn)云，擬合處理后作為蝸殼流道截面設(shè)計(jì)的部分基準(zhǔn)輪廓線（如圖2b所示）。將曲線在數(shù)學(xué)分析軟件中進(jìn)行幾何特征分析可知，點(diǎn)云擬合曲線是長(zhǎng)軸為17.54，短軸為14.18橢圓的一部分。

圖1 螺旋貝殼和內(nèi)腔點(diǎn)云

采用最小二乘法完成曲線數(shù)學(xué)建模。曲線數(shù)學(xué)模型方程為

通過(guò)曲線鏡像獲得增壓器仿生蝸殼通道最大截面幾何形狀如圖2c所示，其形狀類(lèi)似水滴形。依次處理獲得其余15條螺殼內(nèi)腔截面輪廓部分曲線，數(shù)學(xué)模型如表1所示，其中。軟件鏡像處理后獲得增壓器渦輪蝸殼流道截面設(shè)計(jì)曲線。

表1 螺殼內(nèi)腔截面部分輪廓曲線的數(shù)學(xué)模型

1.2 仿生增壓器渦輪蝸殼設(shè)計(jì)

將獲得的截面曲線依據(jù)面積由小到大的次序沿360°圓周向展開(kāi)排列，作為增壓器蝸殼流道設(shè)計(jì)的截面線，每個(gè)截面線分隔間距為22.5°，具體形式如圖3所示。以16條截面輪廓線為基礎(chǔ)數(shù)據(jù)實(shí)現(xiàn)增壓器渦輪蝸殼的曲面設(shè)計(jì)，蝸殼流道出口處曲面與蝸殼通道曲面相切過(guò)渡，將造型曲面依據(jù)實(shí)際增壓器渦輪蝸殼厚度進(jìn)行加厚處理，實(shí)現(xiàn)仿生增壓器渦輪蝸殼流道設(shè)計(jì)，如圖4所示。

圖3 蝸殼流道截面仿生設(shè)計(jì)曲線

圖4 仿生蝸殼設(shè)計(jì)模型

2 仿生增壓器渦輪蝸殼性能仿真分析

本文以某型排量1.5 L的車(chē)用汽油機(jī)用增壓器為研究對(duì)象，采用數(shù)值模擬方法分析常用工況范圍內(nèi)原型蝸殼和仿生設(shè)計(jì)蝸殼的性能差異。首先以原型蝸殼建立數(shù)值模型，并驗(yàn)證其可靠性。然后以原型蝸殼為基礎(chǔ)，匹配仿生蝸殼。在常用工況范圍內(nèi)對(duì)仿生蝸殼和原型蝸殼進(jìn)行數(shù)值仿真，并從微觀流場(chǎng)探索兩者差別，從而實(shí)現(xiàn)對(duì)增壓器蝸殼的優(yōu)化。

2.1 仿真模型建立

原型蝸殼與仿生蝸殼的三維建模結(jié)構(gòu)如圖5所示。建模過(guò)程中2個(gè)增壓器蝸殼/保持一致，蝸殼出口寬度與出口直徑保持一致。仿真模擬中渦輪形式采用全輪盤(pán)向心徑流式結(jié)構(gòu)，葉片數(shù)為11片，進(jìn)口直徑為37 mm，出口直徑為32.1 mm，值為12.56 mm，相應(yīng)壓氣機(jī)葉輪直徑為44.2 mm，蝸殼噴嘴寬度4.8 mm。

圖5 原型與仿生蝸殼結(jié)構(gòu)對(duì)比

仿真數(shù)學(xué)模型采用雷諾時(shí)均N-S方程組[26]，選用RNG方程模型。計(jì)算域分為蝸殼進(jìn)口延長(zhǎng)段、蝸殼、轉(zhuǎn)子和渦輪出口延長(zhǎng)段共4個(gè)域，轉(zhuǎn)子區(qū)域采用結(jié)構(gòu)化網(wǎng)格，在葉片周?chē)砑覱型結(jié)構(gòu)網(wǎng)格；而蝸殼由于流道造型復(fù)雜，采用非結(jié)構(gòu)網(wǎng)格；在渦輪和蝸殼的各個(gè)壁面附近均添加了附面層網(wǎng)格[26]，2種結(jié)構(gòu)的蝸殼在劃分網(wǎng)格時(shí)采用同樣的網(wǎng)格參數(shù)和方法。仿真模擬中，共用的渦殼進(jìn)口延長(zhǎng)段、轉(zhuǎn)子區(qū)域和渦輪出口延長(zhǎng)段的網(wǎng)格單元數(shù)分別為119 595，2 769 008和116 085；原型渦殼網(wǎng)格數(shù)為752 431，仿生渦殼的網(wǎng)格數(shù)為784 168，仿生渦殼由于和原型渦殼保持相同的值而增大了流道截面，其網(wǎng)格總數(shù)比原型渦輪模型多3.1萬(wàn)。

蝸殼和出口延長(zhǎng)段設(shè)定為靜止域，轉(zhuǎn)子部分設(shè)定為旋轉(zhuǎn)域，流體域之間用凍結(jié)交接面連接。模型壁面均設(shè)定為光滑、無(wú)滑移、絕熱的狀態(tài)，流體定義為理想氣體，流體粘度設(shè)置為溫度的函數(shù)，各物性參數(shù)根據(jù)試驗(yàn)數(shù)據(jù)查表而得[27]。模擬計(jì)算中，2種蝸殼所匹配的渦輪轉(zhuǎn)子域完全相同。

2.2 數(shù)值仿真模型驗(yàn)證

數(shù)值仿真模型的試驗(yàn)驗(yàn)證在QYZ-2型增壓器試驗(yàn)臺(tái)進(jìn)行，如圖6所示。圖6a為試驗(yàn)臺(tái)照片，圖6b為試驗(yàn)臺(tái)工作流程圖。壓氣機(jī)進(jìn)口流量采用雙紐線流量計(jì)測(cè)量，最大測(cè)量誤差小于2%FS。壓氣機(jī)入口和出口均設(shè)有有壓力傳感器和溫度傳感器，渦輪進(jìn)口處設(shè)置有有渦輪進(jìn)氣壓力和進(jìn)氣溫度傳感器，渦輪出口的延長(zhǎng)管道中有渦輪排氣壓力和排氣溫度傳感器。壓力傳感器最大誤差小于2.5%FS，溫度傳感器最大誤差小于3%FS。

高壓氣源的空氣經(jīng)過(guò)燃燒室的加熱達(dá)到試驗(yàn)設(shè)定的渦輪進(jìn)氣溫度，燃燒室的燃油為柴油。渦輪流量等于壓氣機(jī)流量加上燃油流量。試驗(yàn)時(shí)，增壓器轉(zhuǎn)速誤差控制在±200 r/min，在增壓器工作工況穩(wěn)定3 min后通過(guò)數(shù)據(jù)采集器同時(shí)采集所有相關(guān)參數(shù)。

圖6 增壓器試驗(yàn)臺(tái)及結(jié)構(gòu)原理圖

驗(yàn)證試驗(yàn)以原型蝸殼進(jìn)行，對(duì)比在相同轉(zhuǎn)速、相同進(jìn)口絕對(duì)壓力和進(jìn)氣溫度條件下，試驗(yàn)流量和模擬流量。選取12×104、16×104和20×104r/min作為典型工況點(diǎn)進(jìn)行驗(yàn)證，3個(gè)工況對(duì)應(yīng)的蝸殼進(jìn)口絕對(duì)壓力、溫度、實(shí)測(cè)流量和模擬仿真得到的流量如表2所示。

對(duì)比表2中實(shí)測(cè)流量與模擬流量，可以發(fā)現(xiàn)在中、低轉(zhuǎn)速工況下，模擬和試驗(yàn)吻合較好；而在高轉(zhuǎn)速工況下，模擬值與試驗(yàn)值相差略大，最大誤差為2.68%。這與模型的簡(jiǎn)化、試驗(yàn)傳感器精度、測(cè)量不確定性等因素有關(guān)[28-29]?？傮w而言，模擬計(jì)算的最大誤差在允許范圍內(nèi)，認(rèn)為仿真模型與試驗(yàn)吻合較好，模型具有較好的可靠性，可以滿足后續(xù)研究的要求。

表2 原型蝸殼的模擬計(jì)算和試驗(yàn)對(duì)比

3 原型蝸殼與仿生蝸殼仿真結(jié)果分析

對(duì)2種蝸殼進(jìn)行典型工況的模擬計(jì)算，選擇12× 104、16×104和20×104r/min三個(gè)轉(zhuǎn)速，分別代表渦輪運(yùn)行的低中高轉(zhuǎn)速。模擬計(jì)算后，對(duì)所涉及的工況進(jìn)行宏觀性能分析，評(píng)價(jià)參數(shù)為渦輪效率、流通特性和蝸殼總壓損失系數(shù)。

3.1 渦輪效率分析

渦輪效率是評(píng)價(jià)渦輪工作性能的最重要參數(shù)之一。兩種蝸殼對(duì)渦輪效率的影響如圖7所示。在不同轉(zhuǎn)速工況下，隨著膨脹比的增加，渦輪效率先增大而后減小。轉(zhuǎn)速越低，渦輪效率變化越快。

由效率對(duì)比分析可知，所有工況下，配有仿生優(yōu)化蝸殼的渦輪效率均高于原型蝸殼的渦輪效率，2種情況下渦輪效率差值均在1.3%以上。固定轉(zhuǎn)速條件下，渦輪進(jìn)口壓力越小，兩者效率的差值越大；在中低轉(zhuǎn)速工況下，普遍相差3%以上。渦輪轉(zhuǎn)速越低，效率差值越大，當(dāng)轉(zhuǎn)速為12×104r/min、進(jìn)口膨脹比為1.2的工況時(shí)，效率最大差值為5.56%。這些趨勢(shì)說(shuō)明，相對(duì)原型蝸殼，仿生優(yōu)化蝸殼不但效率高，而且在低工況時(shí)明顯提升了渦輪效率。中低轉(zhuǎn)速工況下普遍提升3%以上，最大提升效率5%以上。這有利于增壓器改善發(fā)動(dòng)機(jī)的換氣情況，特別是低速工況，有效改善廢氣渦輪增壓器低速響應(yīng)特性，從而提升發(fā)動(dòng)機(jī)低速扭矩和加速性能，有利于改善車(chē)輛的燃油經(jīng)濟(jì)性能和動(dòng)力性能。

圖7 仿生蝸殼與原型蝸殼的渦輪效率對(duì)比

3.2 渦輪流通特性分析

2種蝸殼對(duì)渦輪流通特性的影響如圖8所示。隨著膨脹比的增加，渦輪流通能力增加，對(duì)應(yīng)變化關(guān)系基本呈線性關(guān)系。渦輪流通能力受轉(zhuǎn)速的影響較小，在中低轉(zhuǎn)速工況下，渦輪的流量曲線基本重合，在20×104r/min高轉(zhuǎn)速的高膨脹比工況時(shí)，仿生優(yōu)化蝸殼的渦輪流量略小于原型蝸殼，但沒(méi)有明顯差別，其流通特性基本相同。

3.3 流場(chǎng)分析

當(dāng)仿生渦輪的流通能力與原型渦輪基本保持一致情況下，渦輪效率有了明顯的提升。渦輪效率提升的主要原因是渦輪流場(chǎng)的優(yōu)化。由圖7可知，20×104r/min時(shí)渦輪雖具有最高效率點(diǎn)，但是效率曲線的最高點(diǎn)不在同一工況點(diǎn)，仿生蝸殼和原型蝸殼的渦輪最高效率點(diǎn)分別對(duì)應(yīng)的膨脹比為2.1和2.3，所以流場(chǎng)分析選取轉(zhuǎn)速為16× 104r/min、膨脹比為1.8的工況進(jìn)行。

圖8 仿生蝸殼與原型蝸殼的渦輪流量特性對(duì)比圖

圖9為原型和仿生蝸殼周向90°～220°范圍內(nèi)的軸向截面上的速度矢量分布。原型蝸殼在流道噴嘴出口附近出現(xiàn)2個(gè)氣流回旋渦，說(shuō)明蝸殼內(nèi)部有螺旋滾流，在上下壁面附近氣流的影響下，上下回旋渦的旋向相反，產(chǎn)生混流現(xiàn)象。蝸殼流道中產(chǎn)生的氣流螺旋滾流使得蝸殼內(nèi)部流動(dòng)特性變差，增加混流損失，影響渦輪葉輪內(nèi)部的流動(dòng)，降低了渦輪總體效率。而優(yōu)化后的蝸殼流道內(nèi)部的氣流則規(guī)律地流向蝸殼出口噴嘴，且呈上下對(duì)稱(chēng)分布，氣流的流動(dòng)方向一致性更好，氣流更為平滑地進(jìn)入葉輪流道中進(jìn)行膨脹做功，有利于下游的渦輪轉(zhuǎn)子做功，使增壓器性能提高。

圖9 相同周向位置的葉輪流道50%葉片高度截面上的速度矢量分布

4 結(jié) 論

1）以螺旋貝殼為研究對(duì)象，采用仿生方法實(shí)現(xiàn)增壓器渦輪蝸殼優(yōu)化設(shè)計(jì)。通過(guò)逆向工程技術(shù)獲取螺殼內(nèi)腔幾何數(shù)據(jù)，并提取16條螺殼截面部分?jǐn)?shù)據(jù)曲線作為蝸殼仿生優(yōu)化設(shè)計(jì)原始數(shù)據(jù)，完成數(shù)學(xué)建模。曲線經(jīng)軟件處理后生成增壓器渦輪仿生蝸殼設(shè)計(jì)。

2）2種蝸殼的增壓器渦輪流體仿真結(jié)果表明，在渦輪流通能力基本不變的情況下，優(yōu)化蝸殼渦輪的效率得到明顯提升，最大可提升5%以上，渦輪做功能力增加，仿生設(shè)計(jì)方法對(duì)渦輪性能的提升顯著。

3）渦輪流場(chǎng)分析結(jié)果表明，優(yōu)化后的渦輪內(nèi)部流體流動(dòng)更為合理，蝸殼流道內(nèi)的氣流上下對(duì)稱(chēng)平穩(wěn)流入下游渦輪葉輪內(nèi)部，內(nèi)部氣流較為順暢，改善了原型蝸殼內(nèi)的滾流現(xiàn)象，減小了由于混流引起的能量損失，蝸殼出口氣流的波動(dòng)較小，這些因素有效促進(jìn)廢氣的能量轉(zhuǎn)換，提升了渦輪總體效率。

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Bionic design of turbocharger volute based on spiral shellsimproving turbine performance

Wu Na1, Zhang Kesong1, Wang Xibo1, Ma Yunhai2※

(1.250357,;2.130022,)

The performance of the supercharger volute directly affects the overall efficiency and capability of the turbocharger. It is important to improve the efficiency and performance of the turbocharger by reducing the flow resistance and decreasing the energy loss of the volute. Many measures are taken to improve the efficiency of the volute. Ocean spiral shells have evolved to reduce fluid resistance and cut down fluid energy loss during motion. In this paper, the spiral shell was taken as the biomimetic prototype, and the cavity data of the spiral shells were obtained by reverse engineering technology. The internal cavity cross-section data of shells were extracted in the range of 270 degrees. After the cross-section curves were optimized, they were taken as the section curves to construct the bionic volute. And then the volute bionic surface design was realized. The computational models of the prototype and bionic supercharger were finished. Taking the turbocharger volute of the gasoline engine with 1.5-liter displacement as the research object, the numerical analysis method was used to realize the performance difference between the bionic volute and the prototype volute. First, the prototype numerical model’s reliability was verified. Then the bionic volute was matched with the prototype turbine system. The numerical simulation of the bionic volute and the prototype volute was carried out in the range of common working conditions, and the difference between the two was explored from the microscopic flow field. During the modeling process, the A/R values of the two turbine volutes were the same, and the outlet width of the volute was consistent with the outlet diameter. The verification test was carried out on a QYZ-2 turbocharger test bench. The inlet flow of the compressor was measured by a double-line flowmeter, and the maximum measurement error was less than 2% FS. Both the inlet and the outlet of the compressor were provided with a pressure sensor and a temperature sensor. The turbine inlet was provided with a turbine inlet pressure sensor and an intake temperature sensor, and the turbine outlet had a turbine exhaust pressure sensor and an exhaust temperature sensor in the extension duct. The maximum error of the pressure sensor was less than 2.5% FS, and the maximum error of the temperature sensor was less than 3% FS. The maximum error of the simulation calculation was within the allowable range. The simulation results showed that the simulation model was in good agreement with the test bench, and has good reliability. Therefore, the numerical model can meet the requirements of subsequent research. In the simulation, 12×104, 16×104and 20×104r/min were selected to represent the low, medium and high operation speed of turbine respectively. The evaluation parameters included turbine efficiency, flow characteristics and total volute loss coefficient. The results showed that the turbine flow capacity increases with the increase of the expansion ratio increase. And the turbine flow characteristics of the two volutes were basically the same. The results showed that the turbine efficiency can be increased by 3% and by up to 5% under the condition of keeping the same turbine flow capacity matching two volutes. The flow field analysis results showed that the bionic optimization volute reduces the flow loss near the inner surface of the volute and the airflow friction in the flow channel. And the flow resistance was small, the whole flow in the bionic volute was smooth and uniform, and there was no swirling flow. Therefore, the turbine efficiency can be significantly improved. The bionic design method used in this paper had a significant improvement on turbocharger turbine performance, and can provide reference and method innovation for the design and optimization of automotive and agricultural machinery turbocharging systems.

bionic; design; experiments; turbine volute;turbine efficiency; spiral shells; flow capacity

10.11975/j.issn.1002-6819.2018.19.008

TB17

A

1002-6819(2018)-19-0060-06

2018-06-18

2018-08-16

國(guó)家自然科學(xué)基金資助項(xiàng)目（51505259，51475205）；山東省自然科學(xué)基金資助項(xiàng)目（ZR2015EL026）

吳 娜，副教授，博士，主要從事仿生機(jī)械工程研究。 Email：wuna1978@163.com

馬云海，教授，博士生導(dǎo)師，研究方向?yàn)榉律牧霞捌淠Σ翆W(xué)。 Email：myh@jlu.edu.cn

吳 娜，張克松，王希波，馬云海.基于螺旋貝殼仿生的發(fā)動(dòng)機(jī)增壓器渦輪蝸殼設(shè)計(jì)提升渦輪性能[J]. 農(nóng)業(yè)工程學(xué)報(bào)，2018，34(19)：60－65. doi：10.11975/j.issn.1002-6819.2018.19.008 http://www.tcsae.org

Wu Na, Zhang Kesong, Wang Xibo, Ma Yunhai.Bionic design of turbocharger volute based on spiral shellsimproving turbine performance[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2018, 34(19): 60－65. (in Chinese with English abstract) doi：10.11975/j.issn.1002-6819.2018.19.008 http://www.tcsae.org