An implicit numerical scheme is developed based on the simplified marker and cell （SMAC） method to solve Reynolds-averaged equations in general curvilinear coordinates for three-dimensional （3-D） unsteady incompre...An implicit numerical scheme is developed based on the simplified marker and cell （SMAC） method to solve Reynolds-averaged equations in general curvilinear coordinates for three-dimensional （3-D） unsteady incompressible turbulent flow. The governing equations include the Reynolds-averaged momentum equations, in which contravariant velocities are unknown variables, pressure-correction Poisson equation and k- s turbulent equations. The governing equations are discretized in a 3-D MAC staggered grid system. To improve the numerical stability of the implicit SMAC scheme, the higherorder high-resolution Chakravarthy-Osher total variation diminishing （TVD） scheme is used to discretize the convective terms in momentum equations and k- e equations. The discretized algebraic momentum equations and k- s equations are solved by the time-diversion multiple access （CTDMA） method. The algebraic Poisson equations are solved by the Tschebyscheff SLOR （successive linear over relaxation） method with alternating computational directions. At the end of the paper, the unsteady flow at high Reynolds numbers through a simplified cascade made up of NACA65-410 blade are simulated with the program written according to the implicit numerical scheme. The reliability and accuracy of the implicit numerical scheme are verified through the satisfactory agreement between the numerical results of the surface pressure coefficient and experimental data. The numerical results indicate that Reynolds number and angle of attack are two primary factors affecting the characteristics of unsteady flow.展开更多
基于SMAC(simplified marker and cell)方法和交错网格技术,发展了一套在贴体坐标系下求解三维不可压缩流动的数值算法,并应用该方法求解以逆变速度和压力为未知变量的Navier-Stokes方程,对弯曲度为2.3的三维90°方形截面弯管内部...基于SMAC(simplified marker and cell)方法和交错网格技术,发展了一套在贴体坐标系下求解三维不可压缩流动的数值算法,并应用该方法求解以逆变速度和压力为未知变量的Navier-Stokes方程,对弯曲度为2.3的三维90°方形截面弯管内部不可压缩流场进行了数值模拟.结果表明:文中提出的SMAC方法对强曲率弯管内流有较强的预测能力,能够较准确地模拟其主流和两次流的运动规律,从而证明了本算法的可靠性和有效性.展开更多
基于简化标记和单元(Simplified marker and cell,SMAC)方法,发展一种在任意曲线坐标系中求解三维非定常不可压湍流Reynolds时均方程的隐式数值方法。控制方程包括以逆变速度为变量的动量方程、压力Poisson方程和k-ε湍流模型方程,控制...基于简化标记和单元(Simplified marker and cell,SMAC)方法,发展一种在任意曲线坐标系中求解三维非定常不可压湍流Reynolds时均方程的隐式数值方法。控制方程包括以逆变速度为变量的动量方程、压力Poisson方程和k-ε湍流模型方程,控制方程的离散在三维标记和单元(Marker and cell,MAC)交错网格系统中进行。为提高方程数值计算的稳定性,动量方程、k方程和ε方程对流项离散均采用Chakravarthy-Osher总变差衰减(Total variation diminishing,TVD)格式。动量方程、k方程和ε方程离散后的代数方程组采用循环三对角阵算法(Cyclic tridiagonal matrix algorithm,CTDMA)方法进行求解,Poisson方程离散后的代数方程组采用Tschebyscheff超线性松弛(successive linear over relaxation,SLOR)方法交替方向迭代求解。用该方法自编程序对简化后的射流放水阀内非定常流场进行数值模拟,计算结果和试验结果吻合。展开更多
该文基于SMAC(simplified marker and cell)方法,发展了一种在任意曲线坐标系中求解不可压黏性层流的全隐数值格式。基本方程是以逆变速度为未知变量的动量方程和关于压力修正量的Poisson方程。所有方程离散在MAC交错网格系统中进行。...该文基于SMAC(simplified marker and cell)方法,发展了一种在任意曲线坐标系中求解不可压黏性层流的全隐数值格式。基本方程是以逆变速度为未知变量的动量方程和关于压力修正量的Poisson方程。所有方程离散在MAC交错网格系统中进行。根据构造的全隐数值格式自编程序对一可简化成二维层流的后台阶流场进行计算,通过与已有的实验结果和计算结果进行比较,确认目前的计算结果优于比较的计算结果,和实验结果也相当吻合。为进一步验证该数值格式的可靠性,扩展程序对三维后台阶层流进行计算,结果表明,三维计算结果比二维计算结果更加接近实验结果。展开更多
该文基于SM AC(s im p lified m arker and ce ll)方法,发展了一种在任意曲线坐标系中求解三维粘性不可压湍流R eyno lds时均方程的全隐式数值方法。基本方程是以逆变速度为变量的R eyno lds时均动量方程和椭圆型压力Po isson方程,并采...该文基于SM AC(s im p lified m arker and ce ll)方法,发展了一种在任意曲线坐标系中求解三维粘性不可压湍流R eyno lds时均方程的全隐式数值方法。基本方程是以逆变速度为变量的R eyno lds时均动量方程和椭圆型压力Po isson方程,并采用标准k-ε湍流模型封闭方程组。压力Po isson方程用T schebyscheff SLOR方法交替方向迭代求解。R eyno lds时均动量方程、k方程和ε方程对流项均采用Chakravarthy-O sher TVD格式离散,该格式不但有助于提高数值稳定性,而且能有效消除网格扭曲较大的地方产生的非物理振荡误差。用自编程序对后台阶方腔流场进行了计算,计算结果和实验结果吻合较好。展开更多
SMAC method is adopted to solve Navier-Stokes equations, by using fifth-order WENO scheme and TVD R-K scheme, LevelSet methods are used to capture moving interfaces with improved Ghost techniques. Some examples, e.g. ...SMAC method is adopted to solve Navier-Stokes equations, by using fifth-order WENO scheme and TVD R-K scheme, LevelSet methods are used to capture moving interfaces with improved Ghost techniques. Some examples, e.g. the incompressible inviscid flame interfaces of one and two dimensions and the rising-merging of oil bubbles in water, are computed and the comparison with the result of commercial CFD software Fluent has been done. The rationality of LevelSet methods with Ghost technique in capturing moving interfaces with jump conditions is affirmed. It is shown that Level Set method can capture interfaces sharply without complicated reconstruction and can be easily programmed.展开更多
文摘An implicit numerical scheme is developed based on the simplified marker and cell （SMAC） method to solve Reynolds-averaged equations in general curvilinear coordinates for three-dimensional （3-D） unsteady incompressible turbulent flow. The governing equations include the Reynolds-averaged momentum equations, in which contravariant velocities are unknown variables, pressure-correction Poisson equation and k- s turbulent equations. The governing equations are discretized in a 3-D MAC staggered grid system. To improve the numerical stability of the implicit SMAC scheme, the higherorder high-resolution Chakravarthy-Osher total variation diminishing （TVD） scheme is used to discretize the convective terms in momentum equations and k- e equations. The discretized algebraic momentum equations and k- s equations are solved by the time-diversion multiple access （CTDMA） method. The algebraic Poisson equations are solved by the Tschebyscheff SLOR （successive linear over relaxation） method with alternating computational directions. At the end of the paper, the unsteady flow at high Reynolds numbers through a simplified cascade made up of NACA65-410 blade are simulated with the program written according to the implicit numerical scheme. The reliability and accuracy of the implicit numerical scheme are verified through the satisfactory agreement between the numerical results of the surface pressure coefficient and experimental data. The numerical results indicate that Reynolds number and angle of attack are two primary factors affecting the characteristics of unsteady flow.
文摘基于SMAC(simplified marker and cell)方法和交错网格技术,发展了一套在贴体坐标系下求解三维不可压缩流动的数值算法,并应用该方法求解以逆变速度和压力为未知变量的Navier-Stokes方程,对弯曲度为2.3的三维90°方形截面弯管内部不可压缩流场进行了数值模拟.结果表明:文中提出的SMAC方法对强曲率弯管内流有较强的预测能力,能够较准确地模拟其主流和两次流的运动规律,从而证明了本算法的可靠性和有效性.
文摘基于简化标记和单元(Simplified marker and cell,SMAC)方法,发展一种在任意曲线坐标系中求解三维非定常不可压湍流Reynolds时均方程的隐式数值方法。控制方程包括以逆变速度为变量的动量方程、压力Poisson方程和k-ε湍流模型方程,控制方程的离散在三维标记和单元(Marker and cell,MAC)交错网格系统中进行。为提高方程数值计算的稳定性,动量方程、k方程和ε方程对流项离散均采用Chakravarthy-Osher总变差衰减(Total variation diminishing,TVD)格式。动量方程、k方程和ε方程离散后的代数方程组采用循环三对角阵算法(Cyclic tridiagonal matrix algorithm,CTDMA)方法进行求解,Poisson方程离散后的代数方程组采用Tschebyscheff超线性松弛(successive linear over relaxation,SLOR)方法交替方向迭代求解。用该方法自编程序对简化后的射流放水阀内非定常流场进行数值模拟,计算结果和试验结果吻合。
文摘该文基于SMAC(simplified marker and cell)方法,发展了一种在任意曲线坐标系中求解不可压黏性层流的全隐数值格式。基本方程是以逆变速度为未知变量的动量方程和关于压力修正量的Poisson方程。所有方程离散在MAC交错网格系统中进行。根据构造的全隐数值格式自编程序对一可简化成二维层流的后台阶流场进行计算,通过与已有的实验结果和计算结果进行比较,确认目前的计算结果优于比较的计算结果,和实验结果也相当吻合。为进一步验证该数值格式的可靠性,扩展程序对三维后台阶层流进行计算,结果表明,三维计算结果比二维计算结果更加接近实验结果。
文摘该文基于SM AC(s im p lified m arker and ce ll)方法,发展了一种在任意曲线坐标系中求解三维粘性不可压湍流R eyno lds时均方程的全隐式数值方法。基本方程是以逆变速度为变量的R eyno lds时均动量方程和椭圆型压力Po isson方程,并采用标准k-ε湍流模型封闭方程组。压力Po isson方程用T schebyscheff SLOR方法交替方向迭代求解。R eyno lds时均动量方程、k方程和ε方程对流项均采用Chakravarthy-O sher TVD格式离散,该格式不但有助于提高数值稳定性,而且能有效消除网格扭曲较大的地方产生的非物理振荡误差。用自编程序对后台阶方腔流场进行了计算,计算结果和实验结果吻合较好。
基金The authors wish to express their gratitude to CAS&973 Project for sponsoring the research,Proj No:KZCX2-YW-302National Natural Science Foundation of China,Proj No:40501017
文摘SMAC method is adopted to solve Navier-Stokes equations, by using fifth-order WENO scheme and TVD R-K scheme, LevelSet methods are used to capture moving interfaces with improved Ghost techniques. Some examples, e.g. the incompressible inviscid flame interfaces of one and two dimensions and the rising-merging of oil bubbles in water, are computed and the comparison with the result of commercial CFD software Fluent has been done. The rationality of LevelSet methods with Ghost technique in capturing moving interfaces with jump conditions is affirmed. It is shown that Level Set method can capture interfaces sharply without complicated reconstruction and can be easily programmed.
