Continuous-time state-space unsteady aerodynamic modeling based on boundary element method

In this paper a continuous-time state-space aerodynamic model is developed based on the boundary element method. Boundary integral equations governing the unsteady potential flow around lifting bodies are presented and modified for thin wing configurations. Next, the BEM discretized problem of unsteady flow around flat wing equivalent to the original geometry is recast into the standard form of a continuous-time state-space model considering some auxiliary assumptions. The system inputs are time derivative of the instantaneous effective angle of attack and thickness/camber correction terms while the outputs are unsteady aerodynamic coefficients. To validate the model, its predictions for aerodynamic coefficients variations due to the various unsteady motions about different wing geometries are compared to the results of the direct BEM computations and verified numerical and theoretical solutions. This comparison indicates a good agreement. Since the resulting aerodynamic model is in the continuous-time domain, it is particularly useful for optimization and nonlinear analysis purposes. Moreover, its state-space representation is the appropriate form for an aerodynamic model in design or control applications.     

On the parallelization of unsteady BEM problems with variable mesh size

This paper presents code acceleration strategies for a boundary element method (BEM) simulation of an unsteady free-surface problem with a variable mesh size. The evolution of the film and droplet field emanating from a classical swirl injector/nozzle is used as a test case for the methodology. The unsteady free-surface problem (dynamic grid problem) presents challenges for load balancing the inversion of a matrix that is changing size with time. Since inversion of the matrix of linear equation coefficients represents the dominant computational cost for large problems, the parallelization of the second-order BEM code is implemented using a portable computation library, ScaLAPACK. A different processor grid topology using ScaLAPACK has been implemented and compared to the recommendation of ScaLAPACK guide. Implementation of ScaLAPACK in the solver routine of BEM has been successful and a significant simulation time reduction is demonstrated on an Opteron Dual Processor high-performance computing cluster employing two processors per node.     

Effect of flapping kinematics on aerodynamic force of a flapping two-dimensional flat plate

Potential applications of flapping-wing micro-aerial vehicles (MAVs) have prompted enthusiasm among the engineers and researchers to understand the flow physics associated with flapping flight. An incompressible Navier–Stokes solver that is capable of handling flapping flight kind of moving boundary problem is developed. Arbitrary Lagrangian–Eulerian (ALE) method is used to handle the moving boundaries of the problem. The solver is validated with the results of problems like inline oscillation of a circular cylinder in still fluid and a flat plate rapidly accelerating at constant angle of attack. Numerical simulations of flapping flat plate mimicking the kinematics of those like insect wings are simulated, and the unsteady fluid dynamic phenomena that enhance the aerodynamic force are studied. The solution methodology provides the velocity field and pressure field details, which are used to derive the force coefficients and the vorticity field. Time history of force coefficients and vortical structures gives insight into the unsteady mechanism associated with the unsteady aerodynamic force production. The scope of the work is to develop a computational fluid dynamic (CFD) solver with the ALE method that is capable of handling moving boundary problems, and to understand the flow physics associated with the flapping-wing aerofoil kinematics and flow parameters on aerodynamic forces. Results show that delayed stall, wing–wake interaction and rotational effect are the important unsteady mechanisms that enhance the aerodynamic forces. Major contribution to the lift force is due to the presence of leading edge vortex in delayed stall mechanism.     

High frequency oscillating viscous flow over elliptic cylinder at incidence

Summary The problem of high frequency oscillating viscous flow over an elliptic cylinder at incidence is investigated. The method of matched inner-outer asymptotic expansion to second order is used to solve the governing equations. The steady and the unsteady modes of flow, related to the present work, are identified and separated. Both steady and unsteady drag and lift coefficients are presented and discussed. The effect of different parameters such as the Strouhal number, Reynolds number, focal length and angle of attack are explored.     

The flow due to a slender ship moving over a wavy wall in shallow water

Summary The problem under investigation is the unsteady subcritical potential flow generated by a slender ship translating over a wavy wall in shallow water. The method of matched asymptotic expansions is used to take advantage of the simplified governing equations in the near and far fields. The vertical force and pitching moment coefficients are calculated as functions of the reduced frequency and Froude number with a view towards possible application to ship safety considerations.     

Determination of thermophysical properties of semiconductors from measurement of Ettingshausen effect by method of variation of magnetic field

A method is proposed for determination of the thermophysical coefficients of semiconductors by measurement of the Ettingshausen effect in the unsteady state following the application or removal of a magnetic field.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 36, No. 3, pp. 460–465, March, 1979.     

Kinetic mesh-free method for flutter prediction in turbomachines

The present paper deals with the development and application of a kinetic theory-based mesh-free method for unsteady flows. The method has the capability to compute on any arbitrary distribution of moving nodes. In general, computation of unsteady flow past multiple moving boundaries using conventional finite volume solvers are quite involved. They invariably require repeated grid generation or an efficient grid movement strategy. This approach becomes more difficult when there are many moving boundaries. In the present work, we propose a simple and an effective node movement strategy for the mesh-free solver. This can tackle the unsteady problems with moving boundaries in a much easier way. Using the present method we have computed unsteady flow in oscillating turbomachinery blades. A simple energy method has been used to predict flutter using the unsteady computations. The results compare well with the available experiments and other computations.     

突风作用下圆柱结构气动特性的试验研究

突风(平均风速随时间快速变化)作用在结构或构件上时,结构的气动力和振动状态与平稳风作用下的结果有何不同,是值得研究的问题。在风洞实验室,利用电压控制的方法,实现了具有一定风速加速度的突升和突降的风速变化过程,测试了圆柱结构在突变风速平稳风速作用下的气动力和振动状态,试验结果表明：当突升风速作用在模型上时,采用瞬时风速和气动力算得的力系数和在平稳风速下的结果一致;当突降风速作用在模型上时,采用瞬时风速和气动力算得的力系数虽然在大小上和在平稳风速下的结果一致,但是其对应的临界雷诺数范围比平稳风速对应的临界雷诺数范围,整体向小的方向上偏移了一定的量值。当不涉及到临界雷诺数时,本文的突变风速不会激发模型的大幅振动;当风速升至或降至临界雷诺数区域时,模型将发生稳定的大幅振动;当风速经过临界雷诺数时,在临界雷诺数对应的风速下发生大幅振动,随着风速的升高或降低使得对应的雷诺数离开临界区域时,振动逐渐消失     

Experimental investigation of the temperature dependence of the accommodation coefficients for the gases He,Ne, Ar,and Xe on a Pt surface

This paper presents measurements of accommodation coefficients for the gases He, Ne, Ar, and Xe on a Pt surface in the temperature range 100–500°K. An improved unsteady hot-wire method at low pressure is used.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 34, No. 5, pp. 880–884, May, 1978.     

General boundary element method for non-linear heat transfer problems governed by hyperbolic heat conduction equation

The general Boundary Element Method (BEM) for strongly non-linear problems proposed by Liao (1995) is further applied to solve a two-dimensional unsteady non-linear heat transfer problem in the time domain, governed by the hyperbolic heat conduction equation (HHCE) with the temperature-dependent thermal conductivity coefficients which are different in the x and y directions. This paper confirms that the general BEM can be used to solve even those non-linear unsteady heat transfer problems whose governing equations do not contain any linear terms in spatial domain.     

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.     

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.     

Transient response behavior of an axisymmetric stagnation flow on a circular cylinder due to time dependent free stream velocity

An analysis is presented to investigate the unsteady response behavior of an axisymmetric stagnation flow on a circular cylinder due to transient free stream velocity. The governing boundary layer equations are integrated by the steepest descent method. Numerical results have been presented for the unsteady wall stress by assuming explicit time dependent forms for the free stream velocity.     

A panel method computation for oscillating aerofoil in compressible flow

A panel method using source and doublet singularity has been proposed to solve for subcritical aerodynamics of a two dimensional steady and unsteady aerofoil. The source singularities are placed on the aerofoil surface. The doublet singularity is distributed by a function along the chordline of the aerofoil; this distribution is further projected downstream into infinity. The aerodynamics of an oscillating aerofoil is investigated. The governing unsteady linearized potential equation has a Hankel function as its fundamental solution, which is a source type function. A combination of source and doublet singularity is therefore used for solving the unsteady compressible problem by means of the panel method, this methodology being an extension of a steady aerofoil formulation. Incremental effects of profile change in aerofoil and wake geometry are accounted for. A surface boundary condition is applied on the stationary mean aerofoil surface with time dependent geometrical changes accounted for. An unsteady Kutta condition of equal pressure across the trailing edge is assumed. Results are presented on the aerodynamic influence of Mach number, oscillating frequency parameter, angle of incidence and change of pivoting point. Results are also compared with linear theory, a subsonic experimental result and a subcritical solution of a transonic model.     

空调室内机贯流风扇流动噪音的仿真研究

空调室内机空气流动噪音是影响室内舒适性的重要因素,为此对室内机贯流风扇的非定常流场及噪音特性进行了数值分析。采用非均匀滑移网格和RNG k-ε湍流模型对不可压缩流体非定常流动的Navier-Stokes方程进行求解,并采用Ffowcs-Williams and Hawkings模型对空气流场和噪音进行关联,对空调室内机内空气非定常流场及流动噪音进行数值分析,并与实验结果进行比较。结果表明,采用此方法对计算的流动噪音的声音品质和声谱特性都与测量结果有较好的吻合,为空调器空气流场的优化设计和降低空调器风扇及空气流动噪音的研究提供了有效工具。     

用可压缩流涡方法模拟叶轮机动静叶的相互作用

本课题组发展了一种扰动涡方法,用以研究叶轮机内动、静叶相互作用。其优点是物理图画清楚,计算收敛快。它采用了一个重要假设：扰动胀量为零,从而大大简化 了计算过程。文章的目的是研究此假设的影响,并取消此假设,使扰动涡方法建立在完全严格的数学基础上。由于取消了“扰动胀量为零的假设,需要耦合求解扰动质量方程、扰动涡量输运方程和扰动能量输运方程。这是文章与文献[1,2]的主要区别。     

A three-step finite element method for unsteady incompressible flows

This paper describes a three-step finite element method and its applications to unsteady incompressible fluid flows. The stability analysis of the one-dimensional purely convection equation shows that this method has third-order accuracy and an extended numerical stability domain in comparison with the Lax-Wendroff finite element method. The method is cost effective for incompressible flows, because it permits less frequent updates of the pressure field with good accuracy. In contrast with the Taylor-Galerkin method, the present three-step finite element method does not contain any new higher-order derivatives, and is suitable for solving non-linear multi-dimensional problems and flows with complicated outlet boundary conditions. The three-step finite element method has been used to simulate unsteady incompressible flows, such as the vortex pairing in mixing layer. The properties of the flow fields are displayed by the marker and cell technique. The obtained numerical results are in good agreement with the literature.     

MFS with time-dependent fundamental solutions for unsteady Stokes equations

This paper describes the applications of the method of fundamental solutions (MFS) for 2D and 3D unsteady Stokes equations. The desired solutions are represented by a series of unsteady Stokeslets, which are the time-dependent fundamental solutions of the unsteady Stokes equations. To obtain the unknown intensities of the fundamental solutions, the source points are properly located in the time–space domain and then the initial and boundary conditions at the time–space field points are collocated. In the time-marching process, the prescribed collocation procedure is applied in a time–space box with suitable time increment, thus the solutions are advanced in time. Numerical experiments of unsteady Stokes problems in 2D and 3D peanut-shaped domains with unsteady analytical solutions are carried out and the effects of time increments and source points on the solution accuracy are studied. The time evolution of history of numerical results shows good agreement with the analytical solutions, so it demonstrates that the proposed meshless numerical method with the concept of space–time unification is a promising meshless numerical scheme to solve the unsteady Stokes equations. In the spirit of the method of fundamental solutions, the present meshless method is free from numerical integrations as well as singularities in the spatial variables.     

BEM simulations of potential flow with viscous effects as applied to a rising bubble

A model for the unsteady rise and deformation of non-oscillating bubbles under buoyancy force at high Reynolds numbers has been implemented using a boundary element method. Results such as the evolution of the bubble shape, variations of the transient velocity with rise height and the terminal velocity for different size bubbles have been compared to recent experimental data in clean water and to numerical solutions of the unsteady Navier–Stokes equation. The aim is to capture the essential physical ingredients that couple bubble deformation and the transient approach towards terminal velocity. This model requires very modest computational resources and yet has the flexibility to be extended to more general applications.