轴流式压气机非均匀栅距时序效应的影响研究

本文采用LU-SGS隐式解法与双时间方法相结合,求解圆柱面二维流动的雷诺平均非定常N-S方程,数值模拟了时序效应对动叶非定常气动力的影响,研究表明:时序效应对动叶非定常气动力的影响较大,主要影响基频处的气动力幅值,导叶排和静叶排均为非均匀结构的新型时序效应可以大大降低基频处的非定常气动力,但气动力的大小随工况的变化比较大。     

氧碘化学激光器组分超音速混合反应数值模拟

采用数值方法求解二维可压缩非定常N-S方程及组分连续方程,计算氧碘化学激光器中的组分超音速混合反应流场.空间离散格式为AUSM -up格式,用四步龙格-库塔方法作显式时间推进,湍流粘性系数使用k-ε两方程湍流模型进行求解.假设混合气体为热力学完全而热值非完全气体,化学反应模型采用有限速率反应模型.使用一种松弛迭代的方法来处理化学源项的刚性问题.给出了出口处碘分子的质量分数分布,数值模拟结果与文献结果符合良好.     

输电线雾凇覆冰过程的二维数值模拟

基于拉格朗日法提出了一种输电线表面雾凇覆冰过程的二维数值模拟方法.采用同位网格上的SIMPLE算法求解非定常不可压缩流动的RANS方程和SST-κ-ω湍流模型以获得空气流场;采取拉格朗日法跟踪流场中过冷水滴的运动轨迹得到输电线表面各控制体的瞬时局部碰撞率;求解基于Messinger控制容积法建立的覆冰热力学方程以获得各...     

某跨音速高压涡轮非定常流动数值模拟研究

通过求解三维非定常雷诺平均N-S方程模拟某跨音速高压涡轮非定常流场,研究涡轮内非定常流动特征。通过对静子尾迹及静子尾缘激波和转子叶排之间的相互干涉过程进行详细分析,发现定常/非定常模拟方法获得的涡轮总体性能参数基本一致但流场存在较大差异。静子尾迹是导致涡轮流场非定常性的重要因素之一:在转子叶栅通道中部和下部,静子尾迹和转子叶片附面层及下通道涡发生明显干涉,并导致通道中下部损失周期性波动幅度较大,此外尾迹和下通道涡间的干涉作用在转子尾缘处诱导出高频脱落涡。静子尾缘激波也是导致涡轮流场非定常性的原因之一,激波和转子叶片作用形成复杂的波系结构,对涡轮流场影响显著:一方面激波/附面层干涉导致转子和静子的吸力面产生周期性变化的高温区域;另一方面激波撞击叶片导致叶片表面的气流在激波后出现分离,对转子静压分布产生影响,使得转子叶片表面载荷出现明显的非定常性,进而导致涡轮输出功的周期性波动十分剧烈。     

修正局部Crank-Nicolson方法对二维非定常对流扩散方程的应用

本文利用修正局部Crank-Nicolson方法求解二维非定常对流扩散方程.首先,将二维非定常对流扩散方程转化为二维非定常热传导方程.其次,将二维非定常热传导方程转化为常微分方程组,利用指数函数的Trotter积公式近似该常微分方程组的系数矩阵并将其分离成分块小矩阵及Crank-Nicolson法求出结果,从而推出二维非定常对流扩散方程的修正局部Crank-Nicolson方法.所提方法具有计算量少,精度较高,无条件稳定的显著优点.最后,利用数值实验验证了所提方法的有效性,实验结果表明,所提方法能够得到与真解吻合的计算结果,因而具有很好的应用价值与推广意义.     

Cartesian网格结合无网格法处理的二维柱体

本文发展了基于四叉树数据结构的网格生成和二维流动的N-S方程数值求解器及动边界问题的Euler方程求解方法。采用压力梯度或者密度梯度的绝对值作为网格自适应的控制参量,同时采用基于最小二乘法的无网格方法处理对于一般Cartesian网格难于处理的物面边界条件。文中采取了绕方柱流动和绕圆柱流动的经典算例对所发展的方法进行了验证。计算的结果验证了所发展的方法在处理绕流流动时的合理性和有效性。采用Naca0012翼型的几种工况验证了所发展的动网格技术在处理无粘流动的合理性和可行性。从而为数值模拟具有复杂几何外形的流动提供了一种网格布局合理、高效,边界处理简单易行的新思路。     

吸附式扩压叶栅流动仿真与试验研究

利用附面层抽吸技术,对大弯角平面扩压叶栅端壁流场进行试验研究,通过叶栅吸力面开槽抽吸的方式,研究不同吸气位置、吸气量对叶栅气动性能的影响,结合平面叶栅流动试验和数值仿真结果,分析叶栅抽吸和不抽吸的分离线形态及流场结构,探索叶栅附面层流动机理和端壁流动对叶栅气动性能的影响。结果表明:控制附面层流动的吸出技术是改善压气机叶栅性能的关键手段之一,对于高亚音速叶栅采用吸力面附面层吸出技术,可以提高叶栅气动性能。     

振荡压气机叶栅叶片表面非定常响应以及气弹稳定性分析

发展并验证了一种适用于叶轮机内部非定常跨音流动诱导的叶片气弹问题的高效、准确的数值模拟方法。采用有限体积的多块结构化网格形式,多重网格方法加速收敛,隐式的双时间步时间推进,Spalart-Allmaras（S-A）湍流模型求解非定常雷诺平均Navier-Stokes方程。通过气动弹性标准算例10,叶片在高亚音和跨音流动下做弯曲振动,分析了流动状态、折合频率以及叶片间相位角对叶片表面非定常气动力响应以及叶栅气弹稳定性的影响。分析结果表明激波在此跨音振荡压气机叶栅中起失稳作用,叶片间相位角对气弹稳定性的影响在高折合频率下被加强。     

基于投影法求解不可压缩流的高精度紧致格式

本文建立了一种基于投影法的求解不可压缩Navier-Stokes(N-S)方程的高精度紧致差分格式。该方法时间上采用Kim和Moin二阶投影法离散,空间上采用高精度紧致格式离散,并提出了一种新的离散压力边界的紧致格式,同时对计算结果进行分析以验证该投影法的精度和格式稳定性。文中Taylor涡列数值计算结果表明,Kim和Moin投影法能使得压力场和速度场均达到时间二阶精度,且高精度紧致格式投影法也具有空间高阶精度。驱动方腔数值模拟结果显示,本文对N-S方程的离散格式具有很好的可靠性,适用于对复杂流体流动的小尺度问题的数值模拟和研究。     

三维定常/非定常Stokes方程的维数分裂算法

本文针对三维柱形区域提出了定常/非定常Stokes方程基于一致分裂格式的维数分裂算法(DSA).文章推导了三维定常/非定常Stokes方程维数分裂方法的数值迭代格式.新算法的优势在于一系列的二维问题能够并行执行,而且数值计算中避免了三维网格的生成.大量的数值结果表明新算法既能获得最优收敛阶,而且能获得比采用四面体元求解更精确的逼近解.最后,通过采用并行求解新算法能够得到比较好的加速比和并行效率.     

A two-layer model for a non-Newtonian gravity current subjected to wind shear

Summary.  A theoretical model is developed for the gravity current resulting from the sudden release of a fixed volume of fluid of non-Newtonian power law rheology on top of a slightly denser Newtonian fluid layer in the presence of wind stress. The model incorporates the flow of both layers and accounts for the effects of inertial and viscous forces, and is suited for moderate Reynolds number flows. The governing equations are obtained by depth-averaging the unsteady equations of motion in accordance with the von Kármán's momentum integral method, and constitute a hyperbolic system of four equations for the flow rates and thicknesses of the fluid layers. Results are obtained by a well established numerical scheme for systems of nonlinear hyperbolic equations. For a particular case analytical results are obtained by employing an asymptotic matching approach. Good agreement is obtained between the numerical and analytical results. The effects of the thickness of the ambient layer, wind stress, Reynolds numbers, and rheology on the gravity current are discussed. Received July 22, 2002; revised November 27, 2002 Published online: May 8, 2003     

Simulation of micro flows with moving boundaries using high-order upwind FV method on unstructured grids

 Numerical methods are presented for the simulation of steady and unsteady micro gas flows with moving boundaries found in micro scale fluidic devices. Both steady and unsteady flows are calculated by using an implicit real-time discretization and a dual-time stepping scheme implemented in a high-order upwind finite-volume unstructured-grid Navier–Stokes solver. For moving boundary problems, a new dynamic mesh method has been developed which is shown to be robust in handling large mesh deformation. Micro-scale flows studied with the methods developed include flow in micro channels, unsteady flow around a micro cylinder in oscillation and transport processes in micro pumps. The simulation is based on the continuum fluid model (the compressible Navier–Stokes equations) with slip boundary conditions implemented in the context of unstructured grids as the micro flows studied are all in the slip flow regime. Results are presented to validate the methods and demonstrate their applications to the analysis and design of micro fluidic devices. The implicit dual-time stepping scheme is found to be robust and efficient in dealing with both steady and unsteady micro flows. The unstructured-grid solver proves to be very flexible in dealing with complex geometries such as micro pumps. This is the first known report on the use of finite-volume unstructured grid solver for studying micro flows based on the slip boundary condition with moving boundaries.     

Eigenanalysis and reduced-order modelling of unsteady partial cavity flows using the boundary element method

This paper presents an efficient reduced-order modelling approach to predict unsteady behaviour of partial cavity flows (PCROM). The boundary element method (BEM) along with the potential flow is used to analyze unsteady partial cavity flows. Partial cavity flow is modelled based on a new non-iterative approach and the PCROM is based on fluid eigenmodes. To construct fluid eigenmodes the spatial iterative scheme to find cavity extent is removed. The eigenvalue problem of the unsteady flows is defined based on the unknown wake singularities. Eigenanalysis and reduced-order modelling of unsteady flows over a NACA 16-006 section are performed using the PCROM. Numerical examples are presented to demonstrate the accuracy of the proposed method. Comparison between the obtained results of the proposed method and those of other and conventional method indicates that the present algorithm works well with sufficient accuracy. Moreover, it is shown that the PCROM is computationally more efficient than the conventional one for unsteady sheet cavitations analysis on hydrofoils.     

The method of fundamental solutions for solving incompressible Navier–Stokes problems

A novel meshless numerical procedure based on the method of fundamental solutions (MFS) is proposed to solve the primitive variables formulation of the Navier–Stokes equations. The MFS is a meshless method since it is free from the mesh generation and numerical integration. We will transform the Navier–Stokes equations into simple advection–diffusion and Poisson differential operators via the operator-splitting scheme or the so-called projection method, instead of directly using the more complicated fundamental solutions (Stokeslets) of the unsteady Stokes equations. The resultant velocity advection–diffusion equations and the pressure Poisson equation are then calculated by using the MFS together with the Eulerian–Lagrangian method (ELM) and the method of particular solutions (MPS). The proposed meshless numerical scheme is a first attempt to apply the MFS for solving the Navier–Stokes equations in the moderate-Reynolds-number flow regimes. The lid-driven cavity flows at the Reynolds numbers up to 3200 for two-dimensional (2D) and 1000 for three-dimensional (3D) are chosen to validate the present algorithm. Through further simulating the flows in the 2D circular cavity with an eccentric rotating cylinder and in the 3D cube with a fixed sphere inside, we are able to demonstrate the advantages and flexibility of the proposed meshless method in the irregular geometry and multi-dimensional flows, even though very coarse node points are used in this study as compared with other mesh-dependent numerical schemes.     

Finite element computation of unsteady viscous transonic flows past stationary airfoils

Results are presented for computations of unsteady viscous transonic flows past a stationary NACA0012 airfoil at various angles of attack. The Reynolds number, based on the chord-length of the airfoil, is 10,000 and the Mach number is 0.85. Stabilized finite-element formulations are employed to solve the compressible Navier-Stokes equations. The equation systems, resulting from the discretization, are solved iteratively by using the preconditioned GMRES technique. Time integration of the governing equations is carried out for large values of the non-dimensional time to understand the unsteady dynamics and long-term behavior of the flows. The results show interesting flow patterns and a complex interaction between the boundary/shear layers, shock/expansion waves and the lateral boundaries of the computational domain. For transonic flow past an airfoil at various angles of attack in a narrow channel/wind-tunnel one can observe solutions that are qualitatively different from each other. At low angles of attack an unsteady wake is observed. At moderate angles of attack the interaction between the shock system and the lateral walls becomes significant and the temporal activity in the wake decreases and eventually disappears. At high angles of attack a reflection shock is formed. Hysteresis is observed at an angle of attack 8^∘. For the flow in a domain with the lateral boundaries located far away, the unsteadiness in the flow increases with an increase in the angle of attack. Computations for a Mach 2, Re 106 flow past an airfoil at 10^∘ angle of attack compare well with numerical and experimental results from other researchers     

Numerical simulation of unsteady cavitating flows using a homogenous equilibrium model

 Numerical simulations of two-dimensional cavity flows around a flat plate normal to flow and flows through a 90^∘ bent duct are performed to clarify unsteady behavior under various cavitation conditions. A numerical method applying a TVD-MacCormack scheme with a cavitation model based on a homogenous equilibrium model of compressible gas-liquid two-phase media proposed by the present authors, is applied to solve the cavitating flow. This method permits the simple treatment of the whole gas-liquid two-phase flow field including wave propagation and large interface deformation. Numerical results including detailed observations of unsteady cavity flows and comparisons of predicted results with experimental data are provided. Received: 5 August 2002 / Accepted: 6 January 2003     

Large eddy simulation of turbulent flows in external flow field using three-step FEM–BEM model

An innovative computational model is presented for the large eddy simulation (LES) modeling of multi-dimensional unsteady turbulent flow problems in external flow field. Based on the LES principles, the model uses a pressure projection method to solve the Navier–Stokes equations in transient condition. The turbulent motion is simulated by Smagorinsky sub-grid scale (SGS) eddy viscosity model. The momentum equation of the flow motion is solved using a three-step finite element method (FEM). The external flow field is simulated using a boundary element method (BEM) by solving a pressure Poisson equation that assumes the pressure as zero at the infinity. Through extracting the boundary effects on a specified finite computational domain, the model is able to solve the infinite boundary value problems. The present model is used to simulate the flows past a two-dimensional square rib and a three-dimensional cube at high Reynolds number. The simulation results are found to be reasonable and comparable with other models available in the literature even for coarse meshes.     

A dual-time method for two-dimensional unsteady incompressible flow calculations

A method for computing unsteady incompressible viscous flows on moving or deforming meshes is described. It uses a well-established time-marching finite-volume flow solver, developed for steady compressible flows past rigid bodies. Time-marching methods cannot be applied directly to incompressible flows because the governing equations are not hyperbolic. Such methods can be extended to steady incompressible flows using an artificial compressibility scheme. A time-accurate scheme for unsteady incompressible flows is achieved by using an implicit real-time discretization and a dual-time approach, which uses a technique similar to the artificial compressibility scheme. Results are presented for test cases on both fixed and deforming meshes. Experimental, numerical and theoretical data have been included for comparison where available and reasonable agreement has been achieved. © 1998 John Wiley & Sons, Ltd.     

Some simple unsteady unidirectional flows of a binary mixture of incompressible Newtonian fluids

The problems dealing with some simple unsteady unidirectional flows of a mixture of two incompressible Newtonian fluids are investigated. By using the constitutive equations appeared in the literature for binary mixtures of chemically inert incompressible Newtonian fluids, the equations governing the motion of the binary mixture are reduced to a system of coupled partial differential equations. By means of integral transforms, the exact solutions of these equations are obtained for the following three problems: (i) unsteady Couette flow, (ii) unsteady plane Poiseuille flow, (iii) unsteady axisymmetric Poiseuille flow.     

Measuring flows in partially-filled pipes in siphonic roof drainage systems

While a variety of flow measurement devices are available to measure the flow of water through closed pipe systems, these devices generally only function correctly when the pipes are completely full of water. Accurate measurement of water flows in partially-filled pipes is extremely difficult. In siphonic drainage systems, this problem is further compounded by the unsteady flow conditions that occur in the pipework during the priming process. This has been a major obstacle to understanding the performance of these systems in practice. In order to accurately model the priming process in multioutlet siphonic roof drainage systems, a method of estimating the instantaneous flows through the partially-filled individual pipes needs to be developed. This paper describes an experimental method of determining flows in partially-filled pipes using a propeller-type current meter to measure flow velocity and a pressure transducer to measure water depth and a modified version of the continuity equation. A computational model is presented which estimates the unsteady flows passing through partially-filled pipework. Overall, the experimental results are promising and correspond well with the model. The results of this study will ultimately be used to develop an unsteady flow model of the priming process in multi-outlet siphonic roof drainage systems.