求解滑移流区外掠圆柱体气流流动与传热特性的数值模型
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摘要
为了更精确地求解滑移流区稀薄气体外掠圆柱体流动与传热问题,基于有限容积法的ANSYS FLUENT平台提出了一种滑移边界修正的数值模型,该模型考虑了完整的一阶速度滑移和温度跳跃,其中一阶速度滑移包括了轴向温度引起的热蠕动影响和壁面曲率影响。将模型计算值与实验数据进行了充分对比,结果表明:当气体流动处于连续流区时,滑移边界修正模型与无滑移边界直接模拟计算误差很小;当气体流态处于滑移流区时,采用滑移边界修正模型可实现对该流态气体流动与传热的精确预示(相对误差在±2.5%);稀薄效应对低压气体外掠圆柱体的流动特性影响显著,随着克努森数增加,最大无量纲滑移速度呈线性增加,而最大表面摩擦系数呈线性降低。本文方法可广泛应用于工程之中,以探索低压气体的换热机理,为研究稀薄气体滑移流区流动与传热问题提供了一种有效的数值计算方法。
To more accurately solve the problem of rarefied gas flow and heat transfer over a cylinder in slip flow regime,based on the ANSYS FLUENT platform of finite volume method,a modified numerical model of slip boundary is proposed.The first-order velocity slip and temperature jump are considered in this model,and the first-order velocity slip includes the effects of the thermal creep caused by axial temperature and the curvature of wall surface.Compared with experimental data,the errors of the values calculated by modified model of slip boundary and by direct simulation without slip boundary are very small when the rarefied gas flow is in the continuous flow regime.The precise prediction of flow and heat transfer characteristics can be achieved by using the present model,and the relative error is±2.5% when the rarefied gas flow is in the slip flow regime.Rarefying effect has significant influence on theflow characteristics of low pressure gas over a cylinder.With the increase of Knudsen number,the maximum dimensionless slip velocity increases linearly,while the maximum surface friction coefficient decreases linearly.This method can be widely used in engineering to explore the heat transfer mechanism of low pressure gases,and may become an effective numerical method for the study on the flow and heat transfer of rarefied gases in slip flow regime.
To more accurately solve the problem of rarefied gas flow and heat transfer over a cylinder in slip flow regime,based on the ANSYS FLUENT platform of finite volume method,a modified numerical model of slip boundary is proposed.The first-order velocity slip and temperature jump are considered in this model,and the first-order velocity slip includes the effects of the thermal creep caused by axial temperature and the curvature of wall surface.Compared with experimental data,the errors of the values calculated by modified model of slip boundary and by direct simulation without slip boundary are very small when the rarefied gas flow is in the continuous flow regime.The precise prediction of flow and heat transfer characteristics can be achieved by using the present model,and the relative error is±2.5% when the rarefied gas flow is in the slip flow regime.Rarefying effect has significant influence on theflow characteristics of low pressure gas over a cylinder.With the increase of Knudsen number,the maximum dimensionless slip velocity increases linearly,while the maximum surface friction coefficient decreases linearly.This method can be widely used in engineering to explore the heat transfer mechanism of low pressure gases,and may become an effective numerical method for the study on the flow and heat transfer of rarefied gases in slip flow regime.
引文
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[2]黄飞,吕俊明,程晓丽,等.火星进入器高空稀薄气动特性[J].航空学报,2017,38(5):120457.HUANG Fei,LJunming,CHENG Xiaoli,et al.Aerodynamics of Mars entry vehicles under hypersonic rarefied condition[J].Acta Aeronautica et Astronautica Sinica,2017,38(5):120457.
[3]KHAMSHAH N,ABDALLA A N,KOH S P,et al.Issues and temperature compensation techniques for hot wire thermal flow sensor:a review[J].International Journal of Physical Sciences,2011,7979(4):193-196.
[4]KIM T K,KIM K H,KWON H B.Aerodynamic characteristics of a tube train[J].Journal of Wind Engineering&Industrial Aerodynamics,2011,99(12):1187-1196.
[5]KISHORE N,RAMTEKE R R.Forced convective heat transfer from spheres to Newtonian fluids in steady axisymmetric flow regime with velocity slip at fluid-solid interface[J].International Journal of Thermal Sciences,2016,105:206-217.
[6]KISHORE N,RAMTEKE R R.Slip in flows of power-law liquids past smooth spherical particles[J].Acta Mechanica,2015,226(8):2555-2571.
[7]CHOI Y J,KWON O J.Numerical study of effects of accommodation coefficients on slip phenomena[J].Journal of Mechanical Science&Technology,2015,29(5):1883-1888.
[8]LI D,LI S,XUE Y,et al.The effect of slip distribution on flow past a circular cylinder[J].Journal of Fluids&Structures,2014,51:211-224.
[9]STROM H,SASIC S.Heat transfer effects on particle motion under rarefied conditions[J].International Journal of Heat&Fluid Flow,2013,43(43):277-284.
[10]索晓娜,王秋旺,罗来勤.压缩性和稀薄性对微通道气体流动换热的影响[J].工程热物理学报,2005,26(4):659-661.SUO Xiaona,WANG Qiuwang,LUO Laiqin.Effects of compressibility and rarefaction on gaseous flow and heat transfer in micro-channels[J].Journal of Engineering Thermophysics,2005,26(4):659-661.
[11]XIE F S,LI Y Z,WANG X B,et al.Numerical study on flow and heat transfer characteristics of low pressure gas in slip flow regime[J].International Journal of Thermal Sciences,2018,124:131-145.
[12]LOCKERBY D A,REESE J M,EMERSON D R,et al.Velocity boundary condition at solid walls in rarefied gas calculations[J].Phys Rev:E Stat Nonlin Soft Matter Phys,2004,70(2):017303.
[13]XIE F S,LI Y Z,LIU Z,et al.A forced convection heat transfer correlation of rarefied gases cross-flowing over a circular cylinder[J].Experimental Thermal&Fluid Science,2016,80:327-336.
[14]谢福寿,厉彦忠,王鑫宝,等.低真空压力下横掠圆柱体强制对流传热特性的实验研究[J].西安交通大学学报,2017,51(3):43-61.XIE Fushou,LI Yanzhong,WANG Xinbao,et al.Experimental study on the forced convection heat transfer characteristics of air flow across a cylinder under low vacuum pressures[J].Journal of Xi’an Jiaotong University,2017,51(3):43-61.
[15]MAXWELL J C.On stresses in rarified gases arising from inequalities of temperature[J].Philosophical Transactions of the Royal Society of London,1879,170:231-256.
[16]ANBARSOOZ M,NIAZMAND H.Heat transfer characteristics of slip flow over solid spheres[J].Proc IMechE:Part C J Mechanical Engineering Science,2016,230(19):3431-3441.
[17]LEONTIDIS V,CHEN J,BALDSA L,et al.Numerical design of a Knudsen pump with curved channels operating in the slip flow regime[J].Heat and Mass Transfer,2014,80(8):1065.
[18]FAND R M.Heat transfer by forced convection from a cylinder to water in crossflow[J].International Journal of Heat&Mass Transfer,1965,8(7):995-1010.
[19]HILPERT R.Heat transfer from cylinders[J].Forsch Geb Ingenieurwes,1933,4:215.
[20]MCADAMS W H.Heat Transmission[M].New York,USA:McGraw-Hill,1954:31-35.
[21]COLLIS D C,WILLIAMS M J.Two-dimensional convection from heated wires at low Reynolds numbers[J].Journal of Fluid Mechanics,1959,6(3):357-384.