喷雾干燥过程中雾滴内传质与传热方程的数值求解
|
摘要
将广义Navier-Stokes方程应用于喷雾干燥过程中雾滴内的传质与传热过程,简化后建立了雾滴内传质与传热模型。由于雾滴表面的边界条件为第三类边界条件,不能显式求解,将边界条件与雾滴内传递模型相结合,并采用中心差分格式将空间项离散,将传质、传热模型化为每个空间节点上关于时间的常微分方程组,再应用龙格-库塔法求解,建立了快速求解雾滴干燥模型的方法,与某特殊条件下解析解的比较表明,前述方法准确、可靠。将其应用于实际雾滴内浓度、温度变化过程的求解,结果合理。
General Navier-Stokes equation was applied to mass and heat transfer of aqueous droplets during spray drying process. After simplification, the transfer model of aqueous droplets was established. Because of the third boundary condition, the explicit solution at the boundary cannot be obtained. The boundary condition was combined with the transfer model, and the central difference schemes were used to discrete the spatial items. The model was converted to ordinary differential equations on each node, and Runge-Kutta method was used to solve these equations. An efficient numerical method to solve droplets drying model is established. Compared with the analytical solution under a special condition, it is shown that the proposed method is accurate and reliable. Later, the method was used to calculate the concentration and temperature profile in actual aqueous droplets, and the result is reasonable.
General Navier-Stokes equation was applied to mass and heat transfer of aqueous droplets during spray drying process. After simplification, the transfer model of aqueous droplets was established. Because of the third boundary condition, the explicit solution at the boundary cannot be obtained. The boundary condition was combined with the transfer model, and the central difference schemes were used to discrete the spatial items. The model was converted to ordinary differential equations on each node, and Runge-Kutta method was used to solve these equations. An efficient numerical method to solve droplets drying model is established. Compared with the analytical solution under a special condition, it is shown that the proposed method is accurate and reliable. Later, the method was used to calculate the concentration and temperature profile in actual aqueous droplets, and the result is reasonable.
引文
[1]朱洪法.催化剂成型[M].北京:中国石化出版社,1992,136.
[2]蒋维钧,雷良恒,刘茂林.化工原理(下册)[M].北京:清华大学出版社,1993,455.
[3]王喜忠,于才渊,周才君.喷雾干燥[M].北京:化学工业出版社,2003,168.
[4]李忠,张小兵,郭启海,等.喷雾干燥成型温度对浆态床合成甲醇CuO/ZnO/Al2O3催化剂活性及稳定性的影响[J].化工学报,2011,62(6):1554-1562.(LIZhong,ZHANG Xiaobing,GUO Qihai,et al.Influence of spray drying temperature on the performance of CuO/ZnO/Al2O3 catalyst for methanol synthesis in slurry reactor[J].CIESC Journal,2011,62(6):1554-1562.)
[5]朱远,许京荆,孙裕萍,等.喷雾干燥塔内的设计与数值模拟[J].计量与测试技术,2018,45(4):24-27.(ZHU Yuan,XU Jingjing,SUN Yuping,et al.Design and numerical simulation of a spray drying tower[J].Metrology&Measurement Technique,2018,45(4):24-27.)
[6]马川川,张丽丽.气流式喷雾干燥过程的计算流体力学模拟[J].中国粉体技术,2014,20(5):15-18.(MAChuangchuang,ZHANG Lili.Computational fluid dynamics simulation on spray drying process of pneumatic atomization[J].China Powder Science and Technology,2014,20(5):15-18.)
[7]周健.喷雾干燥及其对裂化催化剂性能影响的研究[D].北京:中国石油大学,2011.
[8]刘明珠,王建立,李建忠.球形活性氧化铝的制备及表征[J].轻金属,2018,1:1-4.(LIU Mingzhu,WANGJianli,LI Jianzhong.Preparation and characterization of spherical activated alumina[J].Light Metals,2018,1:1-4.)
[9]MASTERS K.Spray Drying Handbook[M].New York:Longman Scientific&Technical,1991:456.
[10]郭锴,唐小恒,周绪美.化学反应工程[M].北京:化学工业出版社,2000:188-189.
[11]陆金甫,关治.偏微分方程数值解法[M].北京:清华大学出版社,2004:97.
[12]赵秉新.求解一维对流扩散反应方程的高阶紧致格式[J].重庆理工大学学报(自然科学版),2012,26(7):100-104.(ZHAO Bingxin.A high-order compact difference scheme for solving 1Dconvection-differencereaction equation[J].Journal of Chongqing University of Technology(Natural science),2012,26(7):100-104.)
[13]张亚刚,马廷福,王燕,等.求解一维非定常对流扩散反应方程的高精度紧致差分格式[J].数学的实践与认识,2017,47(13):263-270.(ZHANG Yagang,MATingfu,WANG Yan,et al.High order compact difference scheme for solving the unsteady convection diffusion reaction equation[J].Mathematics in Practice and Theory,2017,47(13):263-270.)
[14]HIXON R.Prefactored small-stencil compact schemes[J].Journal of Computational Physics,2000,165:522-541.
[15]LELE S K.Compact finite difference scheme with spectral-like resolution[J].Journal of Computational Physics,1992,103:16-42.
[16]张亚刚,马廷福,王燕,等.求解一维非定常对流扩散反应议程的高精度紧致差分格式[J].数学的实验与认识,2017,47(13):263-270.(ZHANG Yagang,MATingfu,WANG Yan,et al.High order compact difference scheme for solving the unsteady convection diffusion reaction equation[J].Mathematics in Practice and Theory,2017,47(13):263-270.)
[17]刘晓,王小光,李文强.三对角四阶紧致差分格式的优化和初步应用[J].科技导报,2011,29(34):20-26.(LIU Xiao,WANG Xiaoguang,LI Wenqiang.Optimization of fourth-order compact finite difference triangular scheme and its initial applications[J].Science Guide,2011,29(34):20-26.)
[18]杨晓佳,田芳.一维非定常对流扩散反应议程的高精度紧致差分格式[J].河北大学学报(自然科学版),2017,37(1):5-12.(YANG Xiaojia,TIAN Fang.High order compact difference scheme for the one-dimensional unsteady convection diffusion reaction equation[J].Journal of Hebei university(Natural science edition),2017,37(1):5-12.)
[19]黄志刚,朱慧,李栋,等.颗粒物料传热传质过程的数值仿真与实验研究[J].计算机仿真,2006,23(9):330-332.(HUANG Zhigang,ZHU Hui,LI Dong,et al.Numerical simulation and test of particulate materials heat and mass transfer[J].Computer Simulation,2006,23(9):330-332.)
[2]蒋维钧,雷良恒,刘茂林.化工原理(下册)[M].北京:清华大学出版社,1993,455.
[3]王喜忠,于才渊,周才君.喷雾干燥[M].北京:化学工业出版社,2003,168.
[4]李忠,张小兵,郭启海,等.喷雾干燥成型温度对浆态床合成甲醇CuO/ZnO/Al2O3催化剂活性及稳定性的影响[J].化工学报,2011,62(6):1554-1562.(LIZhong,ZHANG Xiaobing,GUO Qihai,et al.Influence of spray drying temperature on the performance of CuO/ZnO/Al2O3 catalyst for methanol synthesis in slurry reactor[J].CIESC Journal,2011,62(6):1554-1562.)
[5]朱远,许京荆,孙裕萍,等.喷雾干燥塔内的设计与数值模拟[J].计量与测试技术,2018,45(4):24-27.(ZHU Yuan,XU Jingjing,SUN Yuping,et al.Design and numerical simulation of a spray drying tower[J].Metrology&Measurement Technique,2018,45(4):24-27.)
[6]马川川,张丽丽.气流式喷雾干燥过程的计算流体力学模拟[J].中国粉体技术,2014,20(5):15-18.(MAChuangchuang,ZHANG Lili.Computational fluid dynamics simulation on spray drying process of pneumatic atomization[J].China Powder Science and Technology,2014,20(5):15-18.)
[7]周健.喷雾干燥及其对裂化催化剂性能影响的研究[D].北京:中国石油大学,2011.
[8]刘明珠,王建立,李建忠.球形活性氧化铝的制备及表征[J].轻金属,2018,1:1-4.(LIU Mingzhu,WANGJianli,LI Jianzhong.Preparation and characterization of spherical activated alumina[J].Light Metals,2018,1:1-4.)
[9]MASTERS K.Spray Drying Handbook[M].New York:Longman Scientific&Technical,1991:456.
[10]郭锴,唐小恒,周绪美.化学反应工程[M].北京:化学工业出版社,2000:188-189.
[11]陆金甫,关治.偏微分方程数值解法[M].北京:清华大学出版社,2004:97.
[12]赵秉新.求解一维对流扩散反应方程的高阶紧致格式[J].重庆理工大学学报(自然科学版),2012,26(7):100-104.(ZHAO Bingxin.A high-order compact difference scheme for solving 1Dconvection-differencereaction equation[J].Journal of Chongqing University of Technology(Natural science),2012,26(7):100-104.)
[13]张亚刚,马廷福,王燕,等.求解一维非定常对流扩散反应方程的高精度紧致差分格式[J].数学的实践与认识,2017,47(13):263-270.(ZHANG Yagang,MATingfu,WANG Yan,et al.High order compact difference scheme for solving the unsteady convection diffusion reaction equation[J].Mathematics in Practice and Theory,2017,47(13):263-270.)
[14]HIXON R.Prefactored small-stencil compact schemes[J].Journal of Computational Physics,2000,165:522-541.
[15]LELE S K.Compact finite difference scheme with spectral-like resolution[J].Journal of Computational Physics,1992,103:16-42.
[16]张亚刚,马廷福,王燕,等.求解一维非定常对流扩散反应议程的高精度紧致差分格式[J].数学的实验与认识,2017,47(13):263-270.(ZHANG Yagang,MATingfu,WANG Yan,et al.High order compact difference scheme for solving the unsteady convection diffusion reaction equation[J].Mathematics in Practice and Theory,2017,47(13):263-270.)
[17]刘晓,王小光,李文强.三对角四阶紧致差分格式的优化和初步应用[J].科技导报,2011,29(34):20-26.(LIU Xiao,WANG Xiaoguang,LI Wenqiang.Optimization of fourth-order compact finite difference triangular scheme and its initial applications[J].Science Guide,2011,29(34):20-26.)
[18]杨晓佳,田芳.一维非定常对流扩散反应议程的高精度紧致差分格式[J].河北大学学报(自然科学版),2017,37(1):5-12.(YANG Xiaojia,TIAN Fang.High order compact difference scheme for the one-dimensional unsteady convection diffusion reaction equation[J].Journal of Hebei university(Natural science edition),2017,37(1):5-12.)
[19]黄志刚,朱慧,李栋,等.颗粒物料传热传质过程的数值仿真与实验研究[J].计算机仿真,2006,23(9):330-332.(HUANG Zhigang,ZHU Hui,LI Dong,et al.Numerical simulation and test of particulate materials heat and mass transfer[J].Computer Simulation,2006,23(9):330-332.)