耦合辐射的三维热化学非平衡流数值模拟

发展耦合辐射的三维热化学非平衡流场计算方法,可用于非结构网格.采用Jameson有限体积法求解耦合辐射源项的三维N-S方程.辐射源项通过求解辐射输运方程(Radiative Transport Equation RTE)获得.在空间方向上离散后,采用有限体积法求解辐射输运方程.化学模型包含11个组元,20个化学反应.采用该数值方法计算MUSES-C模型在速度为11.6 km·s^-1时的绕流流场及前驻点处的辐射热流密度.并通过对比,分析热辐射对流场的影响.     

龙格库塔间断有限元方法在计算爆轰问题中的应用

构造求解带源项守恒律方程组的龙格库塔间断有限元(RKDG)方法,并分别结合源项的Strang分裂法和无分裂法数值求解模型守恒律方程和反应欧拉方程.为了和有限体积型WENO方法进行比较,设计计算源项的WENO重构格式.对一维带源项守恒律的计算表明,对于非刚性问题,RKDG方法比有限体积型WENO方法的误差更小;对于刚性问题,RKDG方法对于间断面位置的捕捉更为精确.对于一二维爆轰波问题的计算结果表明,RKDG方法对爆轰波结构的分辨和爆轰波位置的捕捉能力更强.     

Euler及N-S方程的二维四边形/叉树混合网格自适应算法

描述了一种基于直角叉树网格的Euler和N-S方程自适应算法.由于考虑了粘性的作用,提出并使用了四边形叉树混合网格的方法,在几何表面附近生成贴体的四边形网格,外流场使用直角叉树网格.采用中心有限体积法,对Euler及N-S方程进行数值求解,对N-S方程的计算中加入了B-L代数湍流模型.在流场中,运用了网格自适应算法,提高了数值计算对激波、流动分离等特性的捕捉和分辨能力.采用上述方法,数值分析了单段和多段翼型的绕流问题.     

空冷透平静叶气膜冷却数值研究

为了深入了解空冷透平气膜冷却机理及三维流动特性,对某型燃气轮机透平静叶进行了详细的数值模拟。计算采用三维N-S方程有限体积解法,湍流模型为标准k-ε模型加改进的壁面函数方法,网格为非结构。计算域扩展到多排气膜冷却孔及与其相连的冷气通道内,求解亦包含所有冷却孔内部流动。根据计算结果重点对前缘气膜冷却复杂三维流动以及整个叶片的气膜冷却特性进行分析。     

基于非结构网格的不可压流动耦合求解器

采用非结构化网格有限容积法求解了不可压N-S方程组,对流项采用GAMMA格式,扩散项采用二阶中心差分格式建立离散方程,用SOAR算法处理压力与速度的耦合关系,得到了一种求解不可压N-S方程的非结构网格耦合求解器。通过方腔顶盖驱动流、后台阶绕流以及方腔自然对流等几个典型的算例,考察了求解器的计算精度及收敛特性,并与SIMPLE算法进行了比较,结果表明该求解器是有效可行的。     

基于CFD/CSD的舵面控制气动弹性数值模拟方法

在动态网格上通过耦合求解流动控制方程和结构动力学方程, 发展了一种舵面控制下飞行器运动响应过程中气动弹性数值模拟研究方法.流动控制方程采用N-S方程, 结构动力学采用线性模态叠加方法, 其中流动控制方程空间离散采用基于非结构网格的有限体积方法, 对流通量采用计算HLLC格式, 非定常时间离散采用基于LU-SGS的双时间步长方法.模拟中, 气动运动和结构变形在双时间步长方法推进过程中采用改进松耦合方法, 气动网格与结构网格之间信息交换采用无限平板样条法实现, 飞行器的运动和变形采用基于重叠网格和Delaunay图映射变形网格相结合的方法进行处理.采用多个考核算例对发展的数值方法进行考核验证, 结果表明该方法可以高效精确模拟舵面开环控制下飞行器运动响应过程中的气动弹性特性.      

旋翼的非定常流动及表面载荷的数值模拟

旋翼的流场呈现很强的非定常现象.目前,对旋翼定常流场的计算已经基本成熟,非定常流场的计算仍在探索之中。本文基于有限体积法的思想,利用较成熟的商用软件NUMECA/IGG生成计算所需的网格。对N-S方程进行离散,选用Baldwin-Lomax湍流模型,Dual-Time时间推进格式模拟了旋翼的非定常流场。计算的结果与文献给出的实验结果符合得较好。     

湍流模型在复杂流场数值模拟中的应用

采用4种湍流模型:代数Baldwin Lomax(B-L)模型、半方程Johnson King(J-K)模型的两个版本(J-K90A和J K92)以及两方程k-g模型,分别数值模拟了导弹超音速流动、NASATND-712标模和民机翼身组合体(两区C-O网格)跨音速流动.采用中心有限体积和多步Runge-Kutta方法数值积分三维可压缩雷诺平均Navier-Stokes(N-S)方程组.k-g湍流模型方程的求解采用类似于N-S方程组的方法进行.所有湍流模型均能很好地模拟附体及小分离流动;对于大攻角、分离剧烈的导弹流动,k-g和J-K92模型与实验吻合更好;B-L模型在模拟民机跨音速流动时,它所捕捉的激波位置较其余3种模型靠后.利用多块网格模拟民机翼身组合体流场时,k-g模型的模拟能力强于其余3种模型.     

充分发展槽道湍流的小波数值分析

数值计算了高斯子波变换Navier Stokes(N-S)方程后得到的积分方程.在利用高斯子波得到的以弯曲度为基本量的无穷域中N-S方程的基础上,得到了有界区域内的以弯曲度为基本量的N-S方程.将此N-S方程看作一个特殊的扩散方程,将压力项与对流项看作是源项,得到一个积分方程.利用特征线法对该方程求解,得到通解.并将所得结果运用于对称槽道湍流和非对称槽道湍流的研究中.将计算与实验所得的平均量与实验结果进行了对比.     

方柱绕流大涡模拟

采用有限体/有限元混合格式、非结构网格和大涡模拟方法求解可压缩的N-S方程,对Re=22 000的方柱绕流进行数值模拟,并对不同的边界条件进行详细的分析比较.通过对以往研究经验的总结和利用精细的边界条件,使得采用二阶精度的数值格式和较稀疏的网格仍然得到了令人满意的计算结果,甚至优于以往采用密网格的模拟结果.     

黏性激波管的有限体积WENO格式数值模拟

本文采用OpenFOAM软件下实现的一种可实现任意阶数,可应用于非结构网格的有限体积WENO格式对黏性激波管问题进行模拟。模拟中对流项离散采用3阶精度、4阶精度该类WENO格式,网格形式采用结构网格和三角形非结构网格。结果表明,采用该类格式,三角形非结构网格的算精度、效率优于结构网格,3阶精度格式计算效率优于4阶精度。该工作表明OpenFOAM下采用3阶精度该类格式及非结构网格对叶轮机械内部流动等复杂流场的模拟更具优势与应用潜力.     

Large-eddy simulation of evaporating spray in a coaxial combustor

Large-eddy simulation of an evaporating isopropyl alcohol spray in a coaxial combustor is performed. The Favre-averaged, variable density, low-Mach number Navier-Stokes equations are solved on unstructured grids with dynamic subgrid scale model to compute the turbulent gas-phase. The original incompressible flow algorithm for LES on unstructured grids by [Mahesh et al., J. Comp. Phys. 197 (2004) 215–240] is extended to include density variations and droplet evaporation. An efficient particle-tracking scheme on unstructured meshes is developed to compute the dispersed phase. Experimentally measured droplet size distribution and size-velocity correlation near the nozzle exit are used as the inlet conditions for the spray. The predictive capability of the LES approach on unstructured grids together with Lagrangian droplet dynamics models to capture the droplet dispersion characteristics, size distributions, and the spray evolution is examined in detail. The mean and turbulent quantities for the gas and particle phases are compared to experimental data to show good agreement. It is shown that for low evaporation rates considered in the present study, a well resolved large-eddy simulation together with simple subgrid models for droplet evaporation and motion provides good agreement of the mean and turbulent quantities for the gas and droplet phases compared to the experimental data. This work represents an important first step to assess the predictive capability of the unstructured grid LES approach applied to spray vaporization. The novelty of the results presented is that they establish a baseline fidelity in the ability to simulate complex flows on unstructured grids at conditions representative of gas-turbine combustors.     

Unstructured finite volume discretisation of bed friction and convective flux in solute transport models linked to the shallow water equations

The finite volume discretisation of the shallow water equations has been the subject of many previous studies, most of which deal with a well-balanced conservative discretisation of the convective flux and bathymetry. However, the bed friction discretisation has not been so profusely analysed in previous works, while it may play a leading role in certain applications of shallow water models. In this paper we analyse the numerical discretisation of the bed friction term in the two-dimensional shallow water equations, and we propose a new unstructured upwind finite volume discretisation for this term. The new discretisation proposed improves the accuracy of the model in problems in which the bed friction is a relevant force in the momentum equation, and it guarantees a perfect balance between gravity and bed friction under uniform flow conditions. The relation between the numerical scheme used to solve the hydrodynamic equations and the scheme used to solve a scalar transport model linked to the shallow water equations, is also analysed in the paper. It is shown that the scheme used in the scalar transport model must take into consideration the scheme used to solve the hydrodynamic equations. The most important implication is that a well-balanced and conservative scheme for the scalar transport equation cannot be formulated just from the water depth and velocity fields, but has to consider also the way in which the hydrodynamic equations have been solved.     

非结构网格上Level Set方程的间断有限元解法

针对间断有限元弱形式难于求解可压缩流场中Level Set方程的问题提出间断有限元强形式,从而在统-框架下解决Level Set方程在可压缩与不可压缩流场中的求解问题.通过非结构网格上采用Legendre-Gauss-Lobatto节点构造基函数,在复杂区域上可以达到任意高阶的精度.将若干-、二、三维算例与已有文献或解析解比较,验证方法追踪自由界面的有效性.结果表明,该方法适合各种情形下Level Set方程求解,易于在复杂区域的非结构网格上实施,精度高、分辨率高且具有高质量守恒性,既能避免重新初始化过程又方便向高维扩展.     

非结构混合网格上的NS方程求解方法

提出了一套较为通用的,完全自动化的非结构混合网格生成方法.在物面粘性作用区,采用一种改进的推进层方法生成三棱柱形和金字塔形网格;在其他流动区域采用阵面推进方法生成四面体网格.采用一种改进精度的格心有限体积法对三维NS方程进行了求解,在加速收敛措施方面,提出了一种新的当地时间步长取定方法来减小质量较差的网格单元对流场计算稳定性和收敛速度的不利影响.以M6机翼和DLR/F4翼身组合体外形的粘性流场作为数值算例,验证了上述网格生成和流场求解方法的正确性和实用性.     

钝体后湍流预混燃烧的PDF模拟

本文采用PDF方法对矩形燃烧室内钝体后的湍流预混火焰进行了数值模拟。脉动速度-频率-标量联合的PDF输运方程用Monte Carlo方法求解,质量、动量和能量的平均值由基于无结构网格的有限体积法求解,压力通过状态方程获得。PDF方程中所需的平均密度、平均速度和压力由有限体积法提供,并将用Monte Carlo方法求出的雷诺应力、化学反应源项和比热比传递给有限体积法。本文对丙烷和空气燃烧的不同简化化学反应机理进行了研究,并与实验结果进行比较,获得满意的结果。     

Implicit LU-SGS algorithm for high-order methods on unstructured grid with p-multigrid strategy for solving the steady Navier–Stokes equations

The fluid dynamic equations are discretized by a high-order spectral volume (SV) method on unstructured tetrahedral grids. We solve the steady state equations by advancing in time using a backward Euler (BE) scheme. To avoid the inversion of a large matrix we approximate BE by an implicit lower–upper symmetric Gauss–Seidel (LU-SGS) algorithm. The implicit method addresses the stiffness in the discrete Navier–Stokes equations associated with stretched meshes. The LU-SGS algorithm is then used as a smoother for a p-multigrid approach. A Von Neumann stability analysis is applied to the two-dimensional linear advection equation to determine its damping properties. The implicit LU-SGS scheme is used to solve the two-dimensional (2D) compressible laminar Navier–Stokes equations. We compute the solution of a laminar external flow over a cylinder and around an airfoil at low Mach number. We compare the convergence rates with explicit Runge–Kutta (E-RK) schemes employed as a smoother. The effects of the cell aspect ratio and the low Mach number on the convergence are investigated. With the p-multigrid method and the implicit smoother the computational time can be reduced by a factor of up to 5–10 compared with a well tuned E-RK scheme.     

A robust numerical model for premixed flames with high density ratios based on new pressure correction and IMEX schemes

In this study we present a model for the interaction of premixed flames with obstacles in a channel flow. Although the flow equations are solved with Direct Numerical Simulation using a low Mach number approximation, the resolution used in the computation is limited (∼1 mm) hence the inner structure of the flame and the chemical scales are not solved. The species equations are substituted with a source term in the energy equation that simulates a one-step global reaction. A level set method is applied to track the position of the flame and its zero level is used to activate the source term in the energy equation only at the flame front. An immersed boundary method reproduces the geometry of the obstacles. The main contribution of the paper is represented by the proposed numerical approach: an IMEX (implicit–explicit) Runge–Kutta scheme is used for the time integration of the energy equation and a new pressure correction algorithm is introduced for the time integration of the momentum equations. The approach presented here allows to calculate flames which produce high density ratios between burnt and unburnt regions. The model is verified by simulating first simple solutions for one- and two-dimensional flames. At last, the experiments performed by Masri and Ibrahim with square and rectangular bodies are calculated.     

Multigrid method based on the transformation-free HOC scheme on nonuniform grids for 2D convection diffusion problems

In this paper, a multigrid method based on the high order compact (HOC) difference scheme on nonuniform grids, which has been proposed by Kalita et al. [J.C. Kalita, A.K. Dass, D.C. Dalal, A transformation-free HOC scheme for steady convection–diffusion on non-uniform grids, Int. J. Numer. Methods Fluids 44 (2004) 33–53], is proposed to solve the two-dimensional (2D) convection diffusion equation. The HOC scheme is not involved in any grid transformation to map the nonuniform grids to uniform grids, consequently, the multigrid method is brand-new for solving the discrete system arising from the difference equation on nonuniform grids. The corresponding multigrid projection and interpolation operators are constructed by the area ratio. Some boundary layer and local singularity problems are used to demonstrate the superiority of the present method. Numerical results show that the multigrid method with the HOC scheme on nonuniform grids almost gets as equally efficient convergence rate as on uniform grids and the computed solution on nonuniform grids retains fourth order accuracy while on uniform grids just gets very poor solution for very steep boundary layer or high local singularity problems. The present method is also applied to solve the 2D incompressible Navier–Stokes equations using the stream function–vorticity formulation and the numerical solutions of the lid-driven cavity flow problem are obtained and compared with solutions available in the literature.