喷注壁面楔状流层流边界层速度与温度相似解  

Velocity and temperature similarity solutions of wedge flow laminar boundary layer with wall injection

作　　者：赵国昌[1,2] 杜霞[1] 宋丽萍[3] 单龙[1] 孔敬儒 彭大维[1] 

机构地区：[1]沈阳航空航天大学航空航天工程学部(院),沈阳110136 [2]沈阳航空航天大学航空航天工程学部(院)辽宁省航空推进系统先进测试技术重点实验室,沈阳110136 [3]沈阳航空航天大学科学技术协会,沈阳110136

出　　处：《航空动力学报》2015年第7期1537-1545,共9页Journal of Aerospace Power

基　　金：航空科学基金(20131954004);辽宁省攀登学者基金(20132015)

摘　　要：建立了壁面有喷注的楔状流层流边界层冷却数学模型,求解经相似变换得到的描述无量纲流函数和无量纲温度的常微分方程,获得了楔状流层流边界层无量纲速度和温度的相似解,给出了考虑壁面喷注边界条件的形式简洁、物理意义明确的无量纲流函数拟合式;用Runge-Kutta法求解无量纲速度与温度的常微分方程,获得了壁面有喷注的楔状流层流边界层无量纲速度和温度随楔形角、吹风参数、冷却介质温度的变化规律.通过计算0°,18°和36°楔形角的楔状流层流边界冷却速度与温度分布得到以下结论:楔状流速度边界层和温度边界层厚度都随楔形角的增大而变小,随着吹风参数的增大而增大;当冷却介质温度越低、吹风参数越小、楔形角越大时,靠近壁面处楔状流层流边界层内温度梯度越大.The mathematical model of the wedge flow laminar boundary layer with wall injection boundary was established.Based on this model,the similarity solutions of dimensionless velocity and temperature distribution in the laminar boundary layer were obtained by solving the ordinary differential equations of the dimensionless stream function and dimensionless temperature.The ordinary differential equations were derived through similarity transformation from the partial differential equations describing the flow and heat transfer of wedge flow laminar boundary layer with wall injection.The curve fitting of dimensionlessstream function derived takes into account the wall injection effect of cooling gas.The Runge-Kutta method was used to solve the ordinary differential equations of dimensionless stream function and dimensionless temperature in order to analyze the variations in the dimensionless velocity and temperature distributions in the wedge flow laminar boundary layer with wall injection with changes in wedge angle,blowing parameter,and cooling medium temperature.The results of the dimensionless velocity and temperature similarity solutions in the laminar boundary layer of wedge flows with wedge angles of 0°,18°and 36°show that both the velocity boundary layer thickness and temperature boundary layer thickness of the laminar wedge flows with wall injection enlarge with the increase of blowing parameter and reduce with the increase of wedge angle;the boundary layer temperature gradient near the wall is larger with lower cooling media temperatures,smaller blowing parameters,and larger wedge angles.

关 键 词：楔状流 层流边界层 喷注壁面 相似解 吹风参数 

分 类 号：V211.19[航空宇航科学与技术—航空宇航推进理论与工程]