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        高溫合金定向凝固過(guò)程中枝晶生長(zhǎng)與溶質(zhì)對(duì)流數(shù)值模擬

        2023-10-18 02:57:52張勇佳周建新殷亞軍沈旭計(jì)效園李文
        精密成形工程 2023年10期
        關(guān)鍵詞:羽流枝晶溶質(zhì)

        張勇佳,周建新,殷亞軍,沈旭,計(jì)效園,李文

        高溫合金定向凝固過(guò)程中枝晶生長(zhǎng)與溶質(zhì)對(duì)流數(shù)值模擬

        張勇佳,周建新*,殷亞軍,沈旭,計(jì)效園,李文

        (華中科技大學(xué) 材料成形與模具技術(shù)全國(guó)重點(diǎn)實(shí)驗(yàn)室,武漢 430074)

        針對(duì)高溫合金葉片在定向凝固過(guò)程中容易出現(xiàn)雀斑缺陷,從而導(dǎo)致葉片報(bào)廢的問(wèn)題,對(duì)定向凝固枝晶生長(zhǎng)與溶質(zhì)對(duì)流進(jìn)行模擬研究,以揭示雀斑缺陷的形成規(guī)律。針對(duì)CM247LC合金定向凝固過(guò)程,采用相場(chǎng)模型模擬凝固過(guò)程枝晶生長(zhǎng),采用格子Boltzmann模型模擬溶質(zhì)濃度差引起的自然對(duì)流。采用基于雙重網(wǎng)格的GPU并行算法對(duì)相場(chǎng)-格子Boltzmann模型進(jìn)行數(shù)值求解。研究在不同晶體取向角度與取向差條件下的枝晶形貌、對(duì)流速度及溶質(zhì)羽流的演變規(guī)律。當(dāng)晶體取向角度不同時(shí),在枝晶生長(zhǎng)過(guò)程中,液相區(qū)域的平均對(duì)流速度均表現(xiàn)為周期性變化。當(dāng)晶體取向角度較大時(shí),隨著晶體取向角度的變大,一次枝晶臂間距變大。當(dāng)枝晶間存在晶體取向差時(shí),溶質(zhì)羽流傾向于在發(fā)散型晶界附近發(fā)起;隨著晶體取向差的增大,溶質(zhì)羽流發(fā)起時(shí)間提前。溶質(zhì)羽流的形成阻礙了枝晶尖端及附近枝晶側(cè)臂的生長(zhǎng)。晶體取向角度對(duì)溶質(zhì)羽流形成的影響較小,較大的晶體取向差對(duì)溶質(zhì)羽流的形成有促進(jìn)作用。

        高溫合金;定向凝固;枝晶生長(zhǎng);溶質(zhì)對(duì)流;相場(chǎng)模擬

        高溫合金定向凝固技術(shù)是制造航空發(fā)動(dòng)機(jī)和燃?xì)廨啓C(jī)渦輪葉片的主要成形工藝。高溫合金葉片包括等軸晶葉片、定向凝固柱狀晶葉片及單晶葉片。其中,定向凝固柱狀晶葉片與單晶葉片消除了橫向晶界,具有優(yōu)異的高溫力學(xué)性能。由于高溫合金葉片的結(jié)構(gòu)較為復(fù)雜,其凝固過(guò)程中的溫度場(chǎng)難以穩(wěn)定控制,所以在定向凝固過(guò)程中容易出現(xiàn)雀斑缺陷。定向凝固雀斑缺陷的形成與凝固過(guò)程中枝晶組織與溶質(zhì)對(duì)流之間的相互作用有關(guān)。

        目前,主要采用實(shí)驗(yàn)與數(shù)值模擬的方法對(duì)雀斑缺陷的形成機(jī)制與規(guī)律進(jìn)行研究。Pollock等[1]研究了高溫合金定向凝固形成的雀斑缺陷,研究發(fā)現(xiàn),當(dāng)冷卻速率較低時(shí),一次枝晶臂間距較大,雀斑缺陷更容易形成,且不同高溫合金之間的雀斑缺陷形成傾向存在顯著差異。Tin等[2]研究發(fā)現(xiàn),將碳的質(zhì)量分?jǐn)?shù)增大至0.1%能夠顯著降低雀斑缺陷數(shù)量,這得益于富Ta的MC型碳化物析出。Tin等[3]采用回歸分析的方法得到了高溫合金試樣中雀斑缺陷數(shù)量與糊狀區(qū)密度差及一次枝晶臂間距的關(guān)系式,該關(guān)系式可用于高溫合金雀斑缺陷形成傾向的評(píng)估。Ma等[4]研究了試樣幾何形狀對(duì)雀斑缺陷的影響,發(fā)現(xiàn)在試樣截面擴(kuò)張與收縮位置容易形成雀斑缺陷。Shevchenko等[5]采用同步輻射技術(shù)觀察了Ga-In合金定向凝固過(guò)程中溶質(zhì)羽流的形成,結(jié)果表明,富集的溶質(zhì)促進(jìn)了偏析通道的形成。Reinhart等[6]采用同步輻射技術(shù)觀察了CMSX-4合金凝固過(guò)程中枝晶生長(zhǎng)與溶質(zhì)羽流的相互作用。

        研究者采用數(shù)值模擬的方法研究了定向凝固枝晶生長(zhǎng)與溶質(zhì)對(duì)流現(xiàn)象,以揭示雀斑缺陷的形成機(jī)制。Schneider等[7]基于高溫合金熱力學(xué)數(shù)據(jù)庫(kù)對(duì)定向凝固過(guò)程中溶質(zhì)羽流的發(fā)起進(jìn)行了模擬,結(jié)果表明,隨著冷卻速率的減小,凝固前沿的溶質(zhì)分布轉(zhuǎn)變?yōu)椴环€(wěn)定狀態(tài),進(jìn)而出現(xiàn)了通道偏析。Felicelli等[8]對(duì)Pb-10%(質(zhì)量分?jǐn)?shù))Sn合金定向凝固過(guò)程中的溶質(zhì)對(duì)流現(xiàn)象進(jìn)行了三維模擬,模擬結(jié)果表明,在壁面位置出現(xiàn)了間隔一定距離的偏析通道。Yuan等[9]采用元胞自動(dòng)機(jī)模型研究了Pb-Sn合金定向凝固過(guò)程中的溶質(zhì)對(duì)流現(xiàn)象,結(jié)果表明,由對(duì)流引起的枝晶間富集的溶質(zhì)使枝晶干和二次枝晶重熔,進(jìn)而形成了通道偏析。Karagadde等[10]采用元胞自動(dòng)機(jī)模型對(duì)Ga-25%(質(zhì)量分?jǐn)?shù))In合金定向凝固過(guò)程進(jìn)行了模擬,發(fā)現(xiàn)溶質(zhì)羽流的形成與枝晶取向及一次枝晶臂間距密切相關(guān),且形成溶質(zhì)羽流的臨界瑞利數(shù)為150~170。Kao等[11]研究了固液界面形狀對(duì)定向凝固枝晶生長(zhǎng)與溶質(zhì)對(duì)流的影響,模擬結(jié)果表明,當(dāng)固液界面為凸界面時(shí),溶質(zhì)羽流傾向于在中間位置發(fā)起,而當(dāng)固液界面為凹界面時(shí),則在兩側(cè)壁面位置發(fā)起。由于溶質(zhì)對(duì)流過(guò)程中的流動(dòng)場(chǎng)求解計(jì)算量較大,開(kāi)展大規(guī)模模擬需要極大的計(jì)算量。為提高模擬速度,Sakane等[12]提出了基于多個(gè)GPU的并行求解算法,采用格子Boltzmann模型對(duì)溶質(zhì)差引起的浮力驅(qū)動(dòng)流動(dòng)過(guò)程進(jìn)行了快速求解。Guo等[13-14]采用自適應(yīng)網(wǎng)格算法對(duì)熱溶質(zhì)對(duì)流條件下的枝晶生長(zhǎng)過(guò)程進(jìn)行了并行求解。Yang等[15]提出了基于耦合熱力學(xué)數(shù)據(jù)庫(kù)的GPU并行算法,并對(duì)CMSX-4合金凝固過(guò)程中的枝晶生長(zhǎng)與溶質(zhì)對(duì)流現(xiàn)象進(jìn)行了模擬。Takaki等[16]采用二維相場(chǎng)模型研究了自然對(duì)流條件下Al-Cu合金枝晶生長(zhǎng)過(guò)程中的競(jìng)爭(zhēng)生長(zhǎng)規(guī)律。Takaki等[17]對(duì)Al-Cu合金自然對(duì)流條件下的枝晶生長(zhǎng)過(guò)程進(jìn)行了大規(guī)模相場(chǎng)模擬,得到了不同重力加速度條件下一次枝晶臂隨時(shí)間的變化規(guī)律。Sakane等[18]采用多套網(wǎng)格系統(tǒng)對(duì)枝晶生長(zhǎng)過(guò)程中的相場(chǎng)、流動(dòng)場(chǎng)與溫度場(chǎng)模型進(jìn)行求解,有效提高了模擬計(jì)算速度。Watanabe等[19]提出了一種用于多相場(chǎng)模型的自適應(yīng)結(jié)構(gòu)化網(wǎng)格區(qū)域分解算法,以提高計(jì)算速度。此外,也有模型考慮了凝固過(guò)程中的枝晶運(yùn)動(dòng)[20]、碰撞[21]及枝晶與氣孔的相互作用[22-23]等。

        目前,晶體取向角度與取向差對(duì)高溫合金定向凝固枝晶生長(zhǎng)與溶質(zhì)對(duì)流的影響規(guī)律尚不清晰,本文采用相場(chǎng)-格子Boltzmann模型對(duì)高溫合金定向凝固過(guò)程進(jìn)行了枝晶尺度模擬,得到了不同晶體取向角度與取向差時(shí)溶質(zhì)羽流的形成傾向以及溶質(zhì)對(duì)流速度的變化規(guī)律。

        1 定向凝固過(guò)程中枝晶生長(zhǎng)數(shù)學(xué)模型

        在定向凝固過(guò)程中,枝晶生長(zhǎng)的數(shù)學(xué)模型包括相場(chǎng)模型與格子Boltzmann模型。其中,相場(chǎng)模型用于求解凝固過(guò)程中相界面的演化與溶質(zhì)濃度分布,格子Boltzmann模型用于求解溶質(zhì)差驅(qū)動(dòng)的流動(dòng)場(chǎng)。相場(chǎng)模型的控制方程如式(1)所示。

        采用格子Boltzmann模型對(duì)流動(dòng)場(chǎng)進(jìn)行求解,選取Bhatnagar-Gross-Krook(BGK)碰撞算子形式的格子Boltzmann方程,如式(5)所示。

        式中:為網(wǎng)格所在的空間位置矢量;f為方向的粒子分布函數(shù);feq為方向的平衡態(tài)粒子分布函數(shù);Δ為時(shí)間步長(zhǎng);為松弛時(shí)間;F為外力項(xiàng);為方向的離散格子速度。平衡態(tài)分布函數(shù)表達(dá)式如式(6)所示。

        式中:為流體密度;為流體速度矢量;s為格子聲速;w為權(quán)系數(shù)。這里采用D2Q9格子速度模型,w的取值如式(7)所示。

        采用Boussinesq假設(shè)來(lái)處理溶質(zhì)差引起的浮力,其計(jì)算式如式(8)所示。

        采用有限體積法對(duì)相場(chǎng)方程和溶質(zhì)場(chǎng)的對(duì)流擴(kuò)散方程進(jìn)行求解。采用一階Euler格式對(duì)時(shí)間導(dǎo)數(shù)進(jìn)行離散,采用迎風(fēng)格式離散對(duì)流項(xiàng),以文獻(xiàn)[24]中的通量形式對(duì)式(4)的右端項(xiàng)進(jìn)行處理。為減小計(jì)算量,分別在粗、細(xì)2套網(wǎng)格上求解格子Boltzmann方程和相場(chǎng)方程。參考文獻(xiàn)[25],粗細(xì)網(wǎng)格的邊長(zhǎng)比值為2,采用GPU并行算法進(jìn)行求解,粗、細(xì)網(wǎng)格上的場(chǎng)變量需要進(jìn)行相應(yīng)的插值。

        2 定向凝固過(guò)程中枝晶生長(zhǎng)的計(jì)算參數(shù)

        選取CM247LC合金進(jìn)行定向凝固枝晶生長(zhǎng)模擬,合金成分如表1所示。采用偽二元近似方法[26]得到相場(chǎng)模型所需的液相線斜率和平衡分配系數(shù)等參數(shù)。相場(chǎng)的計(jì)算網(wǎng)格尺寸為1 μm,流動(dòng)場(chǎng)的計(jì)算網(wǎng)格尺寸為2 μm,界面寬度0為1.25 μm,時(shí)間步長(zhǎng)為2.0×10?5s,界面能各向異性系數(shù)為0.02,液相溶質(zhì)擴(kuò)散系數(shù)為3.6×10–9m2/s,液相的運(yùn)動(dòng)黏度為1.0× 10–6m2/s,重力加速度常量為?9.81 m/s2,耦合系數(shù)=33.27。前期研究表明[25],該耦合系數(shù)的取值能夠保證相場(chǎng)模擬結(jié)果具備收斂性。當(dāng)耦合系數(shù)采用該取值時(shí),CMSX-4合金定向凝固枝晶生長(zhǎng)的模擬結(jié)果表明,在溶質(zhì)羽流發(fā)起位置的枝晶生長(zhǎng)速度呈周期性振蕩,與同步輻射實(shí)驗(yàn)[6]觀測(cè)到的振蕩周期與幅值均具有較好的一致性[25]。因此,本文計(jì)算模型在模擬枝晶生長(zhǎng)與溶質(zhì)對(duì)流相互作用方面具有較高的準(zhǔn)確性。

        表1 CM247LC合金成分

        Tab.1 Composition of CM247LC alloy wt.%

        模擬的工藝參數(shù)如下:=10 K/mm,p=50 μm/s。前期的計(jì)算結(jié)果表明[25],在該工藝條件下,CM247LC合金中溶質(zhì)羽流的發(fā)起處于臨界穩(wěn)定條件。在該工藝條件下,有利于溶質(zhì)羽流的形成,從而研究溶質(zhì)對(duì)流條件下晶體取向角度與取向差的影響規(guī)律。在不同晶體取向角度的模擬過(guò)程中,在整個(gè)計(jì)算區(qū)域底部設(shè)置一層連續(xù)的固相,取向角度為0°~30°,取值間隔為5°。計(jì)算區(qū)域大小為2 048 μm× 4 096 μm。在不同晶體取向差的模擬過(guò)程中,計(jì)算區(qū)域初始條件與邊界條件設(shè)置如圖1所示。在底部區(qū)域設(shè)置2種不同取向的晶粒,計(jì)算區(qū)域的左右邊界均為周期性邊界條件,底部為等間距放置的初始晶粒,晶粒之間的間距0為穩(wěn)態(tài)時(shí)的一次枝晶間距,具體數(shù)值由前期的模擬結(jié)果得到[25]。在底部左右各設(shè)置4個(gè)初始晶粒,取向角度為0°,在中間設(shè)置8個(gè)初始晶粒,取向角度分別為5°、10°和15°,計(jì)算區(qū)域大小為4 096 μm×4 096 μm,采用移動(dòng)計(jì)算區(qū)域的方法以減小計(jì)算量。當(dāng)抽拉距離為10 mm時(shí),終止計(jì)算。模擬計(jì)算在單個(gè)NVIDIA V100 GPU上進(jìn)行。

        3 結(jié)果與分析

        當(dāng)晶體取向角度為5°時(shí),溶質(zhì)濃度分布與對(duì)流速度分布模擬結(jié)果如圖2所示,圖2中的為無(wú)量綱溶質(zhì)濃度??梢钥吹?,在凝固初期(40 s時(shí)),初始條件的平界面發(fā)展為樹(shù)枝晶,且由于競(jìng)爭(zhēng)生長(zhǎng),一次枝晶臂間距逐漸變大。當(dāng)凝固時(shí)間為100 s時(shí),凝固前沿的溶質(zhì)在對(duì)流作用下富集,并形成溶質(zhì)羽流,如圖2b中左起第2、3個(gè)枝晶間??梢钥闯?,該位置的枝晶臂間距較大。當(dāng)枝晶臂間距較大時(shí),溶質(zhì)對(duì)流的阻力較小,因而更容易形成溶質(zhì)羽流。隨著凝固過(guò)程的進(jìn)行(150 s和200 s),形成的溶質(zhì)羽流由于具有較低的密度而上浮,在上浮過(guò)程中,羽流中心的溶質(zhì)濃度在對(duì)流擴(kuò)散作用下有所降低,因而羽流上浮的速度有所減緩,開(kāi)始在環(huán)流式對(duì)流的作用下向兩側(cè)運(yùn)動(dòng),使得溶質(zhì)羽流呈現(xiàn)為“煙囪”狀。模擬結(jié)果表明,最大對(duì)流速度可達(dá)160 μm/s,遠(yuǎn)大于該工藝參數(shù)條件下枝晶生長(zhǎng)的穩(wěn)態(tài)速度50 μm/s。

        圖1 計(jì)算區(qū)域初始條件與邊界條件

        圖2 晶體取向角度為5 °時(shí)的模擬結(jié)果

        晶體取向角度為15°時(shí)和30°時(shí)的模擬結(jié)果分別如圖3和圖4所示??梢钥吹剑M結(jié)果中均出現(xiàn)了溶質(zhì)羽流。當(dāng)晶體取向角度為30°時(shí),一次枝晶臂間距大于取向角度為15°時(shí)的一次枝晶臂間距,且在凝固200 s時(shí),晶體取向角度為30°時(shí)的對(duì)流速度最大可達(dá)180 μm/s,略高于15°時(shí)的150 μm/s。

        圖3 晶體取向角度為15°時(shí)的模擬結(jié)果

        圖4 晶體取向角度為30 °時(shí)的模擬結(jié)果

        圖5 不同晶體取向角度時(shí)的平均對(duì)流速度vtavg(a)及其時(shí)間平均值vavg(b)

        統(tǒng)計(jì)結(jié)果表明,當(dāng)晶體取向角度從0°變化到30°時(shí),在凝固初期(凝固時(shí)間小于50 s左右時(shí)),平均對(duì)流速度均保持在較小值(低于10 μm/s)。隨著凝固過(guò)程的進(jìn)行,平均對(duì)流速度迅速增大至峰值,速度峰值超過(guò)70 μm/s。之后,平均對(duì)流速度開(kāi)始衰減,并保持周期性振蕩。除了晶體取向角度為15°時(shí)平均對(duì)流速度增大至峰值較為滯后(在120 s左右速度出現(xiàn)明顯的增大)外,當(dāng)晶體取向角度為其他取值時(shí),平均對(duì)流速度開(kāi)始迅速增大的時(shí)間均較早(在60~80 s之間)。結(jié)果表明,當(dāng)晶體取向角度不同時(shí),平均對(duì)流速度時(shí)間平均值均大于50 μm/s,即大于抽拉速度,即對(duì)應(yīng)枝晶生長(zhǎng)速度的穩(wěn)態(tài)值。平均對(duì)流速度振蕩幅值較大(見(jiàn)圖5a),其時(shí)間平均值的分散度較大,這表明,平均對(duì)流速度時(shí)間平均值與晶體取向角度之間沒(méi)有明顯的依賴性。

        溶質(zhì)羽流的發(fā)起與一次枝晶臂間距密切相關(guān)。為此,統(tǒng)計(jì)了凝固終態(tài)時(shí)不同晶體取向角度對(duì)應(yīng)的一次枝晶臂間距的最大值、最小值及均值,結(jié)果如圖6所示。

        圖6 不同晶體取向角度時(shí)的一次枝晶臂間距的最大值、最小值及均值

        晶體取向差為5°時(shí)的溶質(zhì)分布與速度分布如圖7所示。結(jié)果表明,當(dāng)晶體取向差為5°時(shí),在右側(cè)發(fā)散型晶界處,對(duì)流速度較大。當(dāng)凝固時(shí)間為74 s時(shí),在發(fā)散型晶界兩側(cè)出現(xiàn)明顯的溶質(zhì)濃度起伏(見(jiàn)圖7a)。隨著凝固過(guò)程的進(jìn)行,在79 s時(shí),發(fā)散型晶界右側(cè)率先形成溶質(zhì)羽流(見(jiàn)圖7b)。隨后,溶質(zhì)羽流逐漸向上運(yùn)動(dòng)(見(jiàn)圖7c),之后,溶質(zhì)羽流從兩側(cè)向下方回流(見(jiàn)圖7d),溶質(zhì)羽流中心的濃度減小。在溶質(zhì)羽流發(fā)起的位置,傾斜枝晶生長(zhǎng)出的二次枝晶及其分枝的生長(zhǎng)被抑制,形成的枝晶間隙較大,進(jìn)而有利于溶質(zhì)羽流的發(fā)展。取向差為10°和15°時(shí)的模擬結(jié)果也呈現(xiàn)出類似的規(guī)律。

        圖7 不同凝固時(shí)間下晶體取向差為5°時(shí)的模擬結(jié)果

        統(tǒng)計(jì)了不同晶體取向差時(shí)的平均對(duì)流速度,如圖8所示??梢钥吹?,當(dāng)晶體取向差不同時(shí),平均對(duì)流速度均在增大至峰值后,在一定范圍內(nèi)呈周期性振蕩,但達(dá)到峰值的時(shí)間不同。隨著晶體取向差變大,平均對(duì)流速度達(dá)到峰值的時(shí)間逐漸減小。從圖8可以看出,當(dāng)晶體取向差為5°、10°、15°時(shí),達(dá)到峰值的時(shí)間(如圖8中豎直黑色虛線所示)分別為98、84、63 s。平均對(duì)流速度達(dá)到峰值的時(shí)間越小,表明對(duì)流過(guò)程中溶質(zhì)羽流出現(xiàn)得越早。因此,模擬結(jié)果表明,晶體取向差越大,溶質(zhì)羽流越容易發(fā)起。

        圖8 不同晶體取向差時(shí)的平均對(duì)流速度

        4 結(jié)論

        CM247LC合金在溫度梯度為10 K/mm、抽拉速度為50 μm/s條件下的相場(chǎng)模擬結(jié)果表明,當(dāng)晶體取向角度不同時(shí),在枝晶生長(zhǎng)過(guò)程中,液相區(qū)域的平均對(duì)流速度均表現(xiàn)出周期性變化。在溶質(zhì)對(duì)流條件下,當(dāng)晶體取向角度較大時(shí),定向凝固的一次枝晶臂間距隨晶體取向角度的變大而變大,但與Gandin等[27]提出的冪函數(shù)關(guān)系存在一定偏離。晶體取向差越大,溶質(zhì)羽流越容易發(fā)起。

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        Numerical Simulation of Dendrite Growth and Solute Convection during Directional Solidification of Superalloy

        ZHANG Yong-jia, ZHOU Jian-xin*, YIN Ya-jun, SHEN Xu, JI Xiao-yuan, LI Wen

        (State Key Laboratory of Materials Processing and Die & Mould Technology, Huazhong University of Science and Technology, Wuhan 430074, China)

        Superalloy blades are prone to freckle defects during directional solidification, which leads to scrap. Therefore, the work aims to simulate the dendrite growth and solute convection during directional solidification to reveal the formation of freckle defects. The dendrite growth of CM247LC alloy was simulated by phase field model and natural convection caused by solute concentration difference was simulated by the lattice Boltzmann model. The phase field-lattice Boltzmann model was solved by GPU-based parallel algorithm based on two different meshes. The dendrite morphology, convection velocity and evolution of solute plumes under different crystal orientation angles and orientation differences were studied. The average fluid velocity in the liquid phase during dendrite growth varied periodically with different crystal orientation angles. When the crystal orientation angle was large, the distance between the primary dendrite arm spacings increased with the increase of the crystal orientation angle. When there was a difference in crystal orientation between dendrites, solute plumes tended to start near divergent grain boundaries. With the increase of crystal orientation difference, the onset time of solute plume advanced. The formation of solute plumes inhibited the growth of dendrite tips and adjacent dendrite side arms. The angle of crystal orientation has slight effect on the formation of solute plumes, and the larger difference of crystal orientation can promote the formation of solute plumes.

        superalloy; directional solidification; dendrite growth; solute convection; phase field simulation

        10.3969/j.issn.1674-6457.2023.010.002

        TG244.3

        A

        1674-6457(2023)010-0013-08

        2023-08-04

        2023-08-04

        國(guó)家重點(diǎn)研發(fā)計(jì)劃(2020YFB1710100)

        The National Key R&D Program of China (2020YFB1710100)

        張勇佳, 周建新, 殷亞軍, 等. 高溫合金定向凝固過(guò)程中枝晶生長(zhǎng)與溶質(zhì)對(duì)流數(shù)值模擬[J]. 精密成形工程, 2023, 15(10): 13-20.

        ZHANG Yong-jia, ZHOU Jian-xin, YIN Ya-jun, et al. Numerical Simulation of Dendrite Growth and Solute Convection during Directional Solidification of Superalloy[J]. Journal of Netshape Forming Engineering, 2023, 15(10): 13-20.

        責(zé)任編輯:蔣紅晨

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