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设计了大功率器件的液冷室结构,整体封装结构如图1(a)所示。电阻阵列芯片基底材质为硅,其大小为30 mm×30 mm×2 mm,正常工况下发热功率约为100 W,通过陶瓷电极板胶接到液冷室底板上。液冷室的材料为钼,在低温下具有良好的导热性。支柱采用导热性差的304L不锈钢材料,以减少热量泄漏。排气口、流体进出液口均采用纯铜材质,封装结构外壳采用可伐合金。
液冷室结构如图1(b)所示,在电阻阵列芯片周围设置换热区域,尺寸为35 mm×35 mm。共设计三种换热结构,分别为空腔结构、微槽道结构和多扰流柱结构。空腔结构中换热区域无特殊结构,微槽道结构中设置长度为35 mm、宽度和间隔均为2 mm、高度为6.2 mm的流道。多扰流柱结构的俯视图如图1(c)~图1(f)所示,共设置四种典型的扰流柱结构,分别为平行排布圆形扰流柱、交错排布圆形扰流柱、平行排布方形扰流柱和交错排布方形扰流柱。扰流柱的高度均为6.2 mm,扰流柱的边长或直径为d,在长、宽两方向上与相邻扰流柱的距离分别为l和w。其中,l=2d,在平行排布结构中l=w,交错排布中l=2w。扰流柱尺寸范围为1.0~4.0 mm。
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仿真分析时选用Fluent作为流体与热分析工具。两相流中气液界面与气体分布在热传导中起到了重要的作用,因此选取可以追踪气液界面的流体体积法(VOF)研究两相流的流动特性并分析不同结构液冷室的换热能力。在使用VOF进行多相流分析时,引入各流体的体积分数以完善流体的控制方程组。微元中混合流体的体积特性,例如密度和粘度,为各流体体积分数的加权平均值,且所有相共享共同的速度和温度场。热量和流体流动的物理过程可以用一组质量、动量和体积分数的方程来描述。对于不可压缩的牛顿流体,这些方程可以写成如下形式。
连续性方程:
$$ \frac{{\partial \rho }}{{\partial {\text{t}}}}{\text{ + }} \nabla( \rho {{{\boldsymbol{V}}} } ) = 0 $$ (1) 动量守恒方程:
$$ \begin{split} &\frac{{\partial (\rho {{{\boldsymbol{V}}} } ) }}{{\partial t}} + \nabla (\rho \mathbf{\mathit{{\boldsymbol{{\boldsymbol{V}}}}}} {{{\boldsymbol{V}}}}) = \\ &- \nabla p + \nabla (\mu (\nabla {{{\boldsymbol{V}}}} + \nabla {{{{\boldsymbol{V}}}}^{\rm{T}}})) + {F_s} \\ \end{split} $$ (2) 体积分数方程:
$$ \frac{{\partial \alpha }}{{\partial {\text{t}}}}{\text{ + }}{{{\boldsymbol{V}}} } \nabla \alpha = 0 $$ (3) 式中:V 为速度矢量;p 为压力;ρ 为密度;μ 为流体的动态粘度;Fs为界面附近的体积力,主要来源为气液界面的表面张力;α为液相或气相的体积分数。
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为了简化计算,首先采用二维模型对液氮流动进行模拟,在优化的结构上进行两相流的三维仿真分析。文中采用RNG k-ε湍流模型,较之标准k-ε湍流模型,该模型在流动中存在涡流时能够提供更高旋涡流动的精度,对流线弯曲流动的仿真效果更好。RNG k-ε湍流模型为双方程涡粘模型,它将涡粘系数μT表示为湍动能k和湍流耗散率ε的函数,引入的关于湍动能k和湍流耗散率ε的微分方程如下式所示:
$$ \begin{split} &\frac{\partial }{{\partial {{t}}}}\left( {\rho k} \right){\text{ + }}\frac{\partial }{{\partial {{x}_{i}}}}\left( {\rho k{u_i}} \right)=\frac{\partial }{{\partial {x_j}}}\left( {{\alpha _k}{\mu _{eff}}\frac{{\partial k}}{{\partial {x_j}}}} \right) + \\ & {G_k} + {G_b}- \rho \varepsilon - {Y_M} + {S_k} \end{split} $$ (4) $$ \begin{split} &\frac{\partial }{{\partial {t}}}\left( {\rho \varepsilon } \right){\text{ + }}\frac{\partial }{{\partial {{x}_{i}}}}\left( {\rho \varepsilon {{u}_{i}}} \right){\text{ = }} \frac{\partial }{{\partial {{x}_{j}}}}\left( {{\alpha _\varepsilon }{\mu _{{eff}}}\frac{{\partial \varepsilon }}{{\partial {{x}_{j}}}}} \right){\text{ + }} \\ &{C_{1\varepsilon }}\frac{\varepsilon }{{k}}\left( {{G_{k}}{\text{ + }}{C_{3\varepsilon }}{G_{b}}} \right) - {C_{2\varepsilon }}\rho \frac{{{\varepsilon ^2}}}{{k}} - {R_\varepsilon }{\text{ + }}{S_\varepsilon } \end{split} $$ (5) 式中:C1ε=1.42;C2ε=1.68;Gk为平均速度梯度引起的湍流动能;Gb为由浮力产生的湍流动能;YM为可压缩湍流中波动膨胀对总耗散率的贡献;αk和αε分别为k和ε有效普朗特数的倒数;Sk和Sε为可定义的源项。
由于壁面处存在粘性层,为了较为准确地得出近壁面的流动状态,同时节省计算资源,使用半经验型的壁面函数计算壁面与充分发展的湍流区域之间的粘性影响区域。
为了对近壁面流动进行准确仿真,需要对流体模型近壁面处的网格进行细化,多使用y+作为近壁面网格划分的判据。对于文中的高雷诺数湍流模型,需要将第一层边界层厚度设定为y+处于对数率区间(20<y+<50),经多次迭代后,文中y+取值为30,对应的第一层边界层厚度为0.1 mm。确定第一层边界层厚度后,即可通过确定的柯朗数(Co)获得单次仿真的时间步长。柯朗数由下式定义:
$$ C{{o}} = \frac{{\Delta {{t}}}}{{\Delta {{x}}/{V_{{\text{fluid}}}}}} $$ (6) 式中:∆x 为第一层网格大小,即0.1 mm;Vfluid 是流体速度。
在当前的计算中设置了0.25的最大 Co 数,并使用基于0.25的固定Co数的可变时间步长来强制所有方程的时间步长相同,计算得出时间步长为2.5×10−5 s。仿真总时长设定为0.5 s,共进行20 000时间步长的计算。
在入口处,流体全部为液氮,温度为76.5 K,应用速度入口条件,为保证两相流拥有足够的冷却能力,流速设定为1 m/s。出口使用压力出口边界条件,压力设置为0 Pa。壁面采用非滑移边界条件。二维仿真模型中仅考虑不同结构对于流体流动的影响,因此不设外部热源,液冷室中流体全部为液氮。
三维仿真模型中需要考虑外部大功率热源对流体中相变与换热的影响。对于仿真中的相变,采取常用的Lee模型进行仿真。由于分析中主要考虑使用液氮-氮气两相流对大功率芯片进行散热,因此液体沸腾在相变中占据主导作用。
Lee模型用于计算相变时的相变率,当液体温度高于饱和温度时,即Tl>Tsat,液体气化,其相变率为:
$$ {\dot {\rm\mathit{m}}}_{\text{lv}}=coef f_{{\rm{eva}}}\times {\alpha }_{\text{l}}{\rho }_{\text{l}}\frac{({T}_{\text{l}}-{T}_{{\rm{sat}}})}{{T}_{{\rm{sat}}}} $$ (7) 式中:α为体积分数;ρ为密度;液氮-氮气的饱和温度为76.59 K;coeffeva
为蒸发频率;蒸发频率和液化频率设置在仿真软件中可以分别设置,考虑到沸腾换热时气化量远大于液化量,经多次迭代计算后,将蒸发频率设定为50,液化频率设置为0.1。 除拥有恒定热通量边界条件外,三维仿真模型的边界条件与二维一致。热边界条件设置如下。液冷室壁面与流体界面采用耦合方式连接,以仿真流体与固体中的换热现象。使用陶瓷加热片模拟电阻阵列芯片和陶瓷电极板组件,加热片通过环氧树脂胶结固定在钼质液冷室上,加热片的加热功率约为100 W,大小为30 mm×30 mm×2 mm。通过薄膜层模拟环氧树脂胶层的换热,薄膜层厚度为0.1 mm。以上仿真模型中涉及的材料参数如表1所示。
液冷室内流体的对流换热系数是衡量流体换热能力的主要指标。由于远离加热片的底面对换热贡献较小,因此后面分析时涉及的各结构对流换热系数为接近加热片的底面与侧面上的对流换热系数。对流换热系数的定义如公式(8)所示:
$$ h = \frac{q}{{{T_{{\rm{wall}}}} - {T_{{\rm{ref}}}}}} $$ (8) 式中:q为壁面处的热流密度;Twall为壁面温度;Tref为参考温度。
文中的液冷室结构较为复杂,因此将进出口流体平均温度作为参考温度。
表 1 仿真模型中涉及的材料物性参数表
Table 1. Material parameter used in the simulation model
Material ρ/kg·m−3 Cp/J·kg−1·K−1 λ/W·m−1·K−1 Liquid-N2 806 2041.5 0.14581 Gas-N2 1.138 1038 0.0242 Mo 10220 217 179 Ceramic 3960 126 449.8 Epoxy glue 1200 550 0.02
Flow and heat analysis of liquid nitrogen cooling structure by CFD method
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摘要: 低温应用的大功率器件需要设计高冷却效率的液冷室结构。采用计算流体动力学(CFD)方法模拟了以液氮-氮气两相流为制冷剂的空腔结构、微通道结构和扰流柱结构的流动与传热过程。结果表明,相比于空腔结构和微槽道结构,扰流柱结构具有较好的换热能力。圆形扰流柱易发展45°方向支流,而方形扰流柱结构有利于垂直方向流速均匀化。相较于平行排布,扰流柱交错排列时圆形和方形扰流柱结构中流速分布更为均匀。对比对流换热系数发现,交错排布优于平行排布,方形扰流柱优于圆形扰流柱。换热效果最好的结构为交错排布的2 mm方形扰流柱,对流换热系数为4223 W/(m2·K),较空腔结构提高125.83%。采用上述结构进行测试验证,在107.6 W加热功率工况下冷头测温点温度与相同功率下仿真结果有较好的对应性。Abstract: High-power devices for low-temperature applications require a liquid-cooled chamber structure with high cooling efficiency. The Computational Fluid Dynamics (CFD) method was used to simulate the flow and heat transfer process of the cavity structure, the microchannel structure, and the pin-fins structure under the condition of the liquid nitrogen-nitrogen two-phase flow as the refrigerant. The results show that the pin-fins structure has the best heat exchange effect among the three above structures. The circular pin-fins structure is easy to develop a branch in the direction of 45°, and the square pin-fins structure is conducive to the uniform flow velocity in the vertical direction. Compared with the parallel pin-fins structure, the flow velocity distribution in the circular and square pin-fins is more uniform when the pin-fins are staggered. Comparing the convective heat transfer coefficients in different liquid cooling chambers with pin-fin structures, under the same other parameters, the staggered arrangement is better than the parallel arrangement, and the square pin-fin is better than the circular pin-fin. The structure with the best heat transfer effect is the staggered 2 mm square pin-fin structure, and the convective heat transfer coefficient is 4223 W/(m2·K), which is 125.83% higher than cavity structure. The above structure is manufactured for physical verification. The temperature of the cold head under the 107.6 W heating power corresponds well with the simulation result under the same condition.
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Key words:
- high-power devices /
- pin-fin /
- two-phase flow /
- convective heat transfer coefficient
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图 5 不同尺寸交错排布扰流柱液冷室中的液氮流速图。 (a)方形扰流柱1.0 mm;(b)方形扰流柱3.0 mm;(c)方形扰流柱4.0 mm;(d)圆形扰流柱1.0 mm;(e)圆形扰流柱3.0 mm;(f)圆形扰流柱4.0 mm
Figure 5. Flow velocity diagram of liquid nitrogen in a liquid cooling chamber with staggered arrangement of different size pin-fins. (a) Square, 1.0 mm; (b) Square, 3.0 mm; (c) Square, 4.0 mm; (d) Circular, 1.0 mm; (e) Circular, 3.0 mm; (f) Circular, 4.0 mm
表 1 仿真模型中涉及的材料物性参数表
Table 1. Material parameter used in the simulation model
Material ρ/kg·m−3 Cp/J·kg−1·K−1 λ/W·m−1·K−1 Liquid-N2 806 2041.5 0.14581 Gas-N2 1.138 1038 0.0242 Mo 10220 217 179 Ceramic 3960 126 449.8 Epoxy glue 1200 550 0.02 -
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