This paper revisits the Space-Time Gradient(STG) method which was developed for efficient analysis of unsteady flows due to rotor–stator interaction and presents the method from an alternative time-clocking perspecti...This paper revisits the Space-Time Gradient(STG) method which was developed for efficient analysis of unsteady flows due to rotor–stator interaction and presents the method from an alternative time-clocking perspective. The STG method requires reordering of blade passages according to their relative clocking positions with respect to blades of an adjacent blade row. As the space-clocking is linked to an equivalent time-clocking, the passage reordering can be performed according to the alternative time-clocking. With the time-clocking perspective, unsteady flow solutions from different passages of the same blade row are mapped to flow solutions of the same passage at different time instants or phase angles. Accordingly, the time derivative of the unsteady flow equation is discretized in time directly, which is more natural than transforming the time derivative to a spatial one as with the original STG method. To improve the solution accuracy, a ninth order difference scheme has been investigated for discretizing the time derivative. To achieve a stable solution for the high order scheme, the implicit solution method of Lower-Upper Symmetric GaussSeidel/Gauss-Seidel(LU-SGS/GS) has been employed. The NASA Stage 35 and its blade-countreduced variant are used to demonstrate the validity of the time-clocking based passage reordering and the advantages of the high order difference scheme for the STG method. Results from an existing harmonic balance flow solver are also provided to contrast the two methods in terms of solution stability and computational cost.展开更多
Resin transfer molding(RTM)is among the most used manufacturing processes for composite parts.Initially,the resin cure is initiated by heat supply to the mold.The supplementary heat generated during the reaction can c...Resin transfer molding(RTM)is among the most used manufacturing processes for composite parts.Initially,the resin cure is initiated by heat supply to the mold.The supplementary heat generated during the reaction can cause thermal gradients in the composite,potentially leading to undesired residual stresses which can cause shrinkage and warpage.In the present numerical study of these processes,a one-dimensional finite difference method is used to predict the temperature evolution and the degree of cure in the course of the resin polymerization;the effect of some parameters on the thermal gradient is then analyzed,namely:the fiber nature,the use of multiple layers of reinforcement with different thermal properties and also the temperature cycle variation.The validity of this numerical model is tested by comparison with experimental and numerical results in the existing literature.展开更多
In this paper, we propose a method to solve coupled problem. Our computational method is mainly based on conjugate gradient algorithm. We use finite difference method for the structure and finite element method for th...In this paper, we propose a method to solve coupled problem. Our computational method is mainly based on conjugate gradient algorithm. We use finite difference method for the structure and finite element method for the fluid. Conjugate gradient method gives suitable numerical results according to some papers.展开更多
An inverse analysis is presented to estimate line heat source in two-dimensional steady-state and transient heat transfer problems.A constant heat source is considered in the steady-state heat transfer problem(a param...An inverse analysis is presented to estimate line heat source in two-dimensional steady-state and transient heat transfer problems.A constant heat source is considered in the steady-state heat transfer problem(a parameter estimation problem)and a time-varying heat source is considered in the transient heat transfer problem(a function estimation problem).Since a general irregular 2D heat conducting body is considered,a body-fitted grid generation is used to mesh the domain.Then governing equations and associated boundary and initial conditions are transformed from the physical domain to the computational domain and finite difference method is used to solve the governing equations to obtain the temperature distribution in the body.Using an efficient,accurate,and very easy to implement sensitivity analysis incorporated in a gradient based minimization method(here,steepest descentmethod),the unknown heat source is estimated accurately.In the function estimation part,it is assumed that there is no prior information on the functional form of the heat source and the estimation process can be performed with a reasonable initial guess for the heat source.The main advantage of the proposed inverse analysis is that the sensitivity matrix(and hence,the objective function gradient with respect to the unknown variables)can be computed during the direct heat transfer solution through newyet simple explicit expressions with no need to solve extra equations such as the sensitivity and adjoint problems and impose additional computational costs comparable to the direct problem solution ones.Some test cases are presented to investigate the accuracy,efficiency,and effect of measurement error on the estimated parameter and function for the line heat source.展开更多
A hybrid finite difference method and vortex method (HDV), which is based on domain decomposition and proposed by the authors (1992), is improved by using a modified incomplete LU decomposition conjugate gradient meth...A hybrid finite difference method and vortex method (HDV), which is based on domain decomposition and proposed by the authors (1992), is improved by using a modified incomplete LU decomposition conjugate gradient method (MILU-CG), and a high order implicit difference algorithm. The flow around a rotating circular cylinder at Reynolds number R-e = 1000, 200 and the angular to rectilinear speed ratio alpha is an element of (0.5, 3.25) is studied numerically. The long-time full developed features about the variations of the vortex patterns in the wake, and drag, lift forces on the cylinder are given. The calculated streamline contours agreed well with the experimental visualized flow pictures. The existence of critical states and the vortex patterns at the states are given for the first time. The maximum lift to drag force ratio can be obtained nearby the critical states.展开更多
In this paper, we are concerned with the numerical solution of second-order partial differential equations. We analyse the use of the Sine Transform precondilioners for the solution of linear systems arising from the ...In this paper, we are concerned with the numerical solution of second-order partial differential equations. We analyse the use of the Sine Transform precondilioners for the solution of linear systems arising from the discretization of p.d.e. via the preconditioned conjugate gradient method. For the second-order partial differential equations with Dirichlel boundary conditions, we prove that the condition number of the preconditioned system is O(1) while the condition number of the original system is O(m 2) Here m is the number of interior gridpoints in each direction. Such condition number produces a linear convergence rale.展开更多
基金co-supported by the National Natural Science Foundation of China(No.51976172)the National Science and Technology Major Project of China(No.2017-Ⅱ-0009-0023)。
文摘This paper revisits the Space-Time Gradient(STG) method which was developed for efficient analysis of unsteady flows due to rotor–stator interaction and presents the method from an alternative time-clocking perspective. The STG method requires reordering of blade passages according to their relative clocking positions with respect to blades of an adjacent blade row. As the space-clocking is linked to an equivalent time-clocking, the passage reordering can be performed according to the alternative time-clocking. With the time-clocking perspective, unsteady flow solutions from different passages of the same blade row are mapped to flow solutions of the same passage at different time instants or phase angles. Accordingly, the time derivative of the unsteady flow equation is discretized in time directly, which is more natural than transforming the time derivative to a spatial one as with the original STG method. To improve the solution accuracy, a ninth order difference scheme has been investigated for discretizing the time derivative. To achieve a stable solution for the high order scheme, the implicit solution method of Lower-Upper Symmetric GaussSeidel/Gauss-Seidel(LU-SGS/GS) has been employed. The NASA Stage 35 and its blade-countreduced variant are used to demonstrate the validity of the time-clocking based passage reordering and the advantages of the high order difference scheme for the STG method. Results from an existing harmonic balance flow solver are also provided to contrast the two methods in terms of solution stability and computational cost.
文摘Resin transfer molding(RTM)is among the most used manufacturing processes for composite parts.Initially,the resin cure is initiated by heat supply to the mold.The supplementary heat generated during the reaction can cause thermal gradients in the composite,potentially leading to undesired residual stresses which can cause shrinkage and warpage.In the present numerical study of these processes,a one-dimensional finite difference method is used to predict the temperature evolution and the degree of cure in the course of the resin polymerization;the effect of some parameters on the thermal gradient is then analyzed,namely:the fiber nature,the use of multiple layers of reinforcement with different thermal properties and also the temperature cycle variation.The validity of this numerical model is tested by comparison with experimental and numerical results in the existing literature.
文摘In this paper, we propose a method to solve coupled problem. Our computational method is mainly based on conjugate gradient algorithm. We use finite difference method for the structure and finite element method for the fluid. Conjugate gradient method gives suitable numerical results according to some papers.
文摘An inverse analysis is presented to estimate line heat source in two-dimensional steady-state and transient heat transfer problems.A constant heat source is considered in the steady-state heat transfer problem(a parameter estimation problem)and a time-varying heat source is considered in the transient heat transfer problem(a function estimation problem).Since a general irregular 2D heat conducting body is considered,a body-fitted grid generation is used to mesh the domain.Then governing equations and associated boundary and initial conditions are transformed from the physical domain to the computational domain and finite difference method is used to solve the governing equations to obtain the temperature distribution in the body.Using an efficient,accurate,and very easy to implement sensitivity analysis incorporated in a gradient based minimization method(here,steepest descentmethod),the unknown heat source is estimated accurately.In the function estimation part,it is assumed that there is no prior information on the functional form of the heat source and the estimation process can be performed with a reasonable initial guess for the heat source.The main advantage of the proposed inverse analysis is that the sensitivity matrix(and hence,the objective function gradient with respect to the unknown variables)can be computed during the direct heat transfer solution through newyet simple explicit expressions with no need to solve extra equations such as the sensitivity and adjoint problems and impose additional computational costs comparable to the direct problem solution ones.Some test cases are presented to investigate the accuracy,efficiency,and effect of measurement error on the estimated parameter and function for the line heat source.
文摘A hybrid finite difference method and vortex method (HDV), which is based on domain decomposition and proposed by the authors (1992), is improved by using a modified incomplete LU decomposition conjugate gradient method (MILU-CG), and a high order implicit difference algorithm. The flow around a rotating circular cylinder at Reynolds number R-e = 1000, 200 and the angular to rectilinear speed ratio alpha is an element of (0.5, 3.25) is studied numerically. The long-time full developed features about the variations of the vortex patterns in the wake, and drag, lift forces on the cylinder are given. The calculated streamline contours agreed well with the experimental visualized flow pictures. The existence of critical states and the vortex patterns at the states are given for the first time. The maximum lift to drag force ratio can be obtained nearby the critical states.
文摘In this paper, we are concerned with the numerical solution of second-order partial differential equations. We analyse the use of the Sine Transform precondilioners for the solution of linear systems arising from the discretization of p.d.e. via the preconditioned conjugate gradient method. For the second-order partial differential equations with Dirichlel boundary conditions, we prove that the condition number of the preconditioned system is O(1) while the condition number of the original system is O(m 2) Here m is the number of interior gridpoints in each direction. Such condition number produces a linear convergence rale.
基金国家自然科学基金项目(No.51109092No.11272137)+5 种基金中国博士后基金项目(No.2013M530237No.2014T70479)supported by the National Natural Science Foundation of China(5110909211272137)the Foundation for Post-doctoral Scientists of China(2013M5302372014T70479)
