Optimal combustion control with application to engine design and development

The need to reduce development time whilst simultaneously improving engine performance has motivated this application of optimal control to product development processes for engines and powertrains. The optimisation of the fuel consumption is formulated as a constrained Optimal Control Problem (OCP) and solved using pseudospectral methods, giving the optimum heat release and injection profiles in the presence of cylinder pressure rate and cylinder pressure constraints. The technique is applied to an engine design problem and used to reduce fuel consumption by optimising compression ratio within a cylinder pressure limit, also providing new insights into the combustion processes.     

An elastic hollow cylinder under axial tension containing a crack and two rigid inclusions of ring shape

This paper is concerned with the fracture of an axisymmetric hollow cylindrical bar containing rigid inclusions. The cylinder is under the action of uniformly distributed axial tension applied at infinity. The bar contains a ring-shaped crack at the symmetry plane whose surfaces are free of tractions and two ring-shaped rigid inclusions with negligible thickness symmetrically located on both sides of the crack. It is assumed that the material of the cylinder is linearly elastic and isotropic. The mixed boundary conditions of the problem lead the analysis to a system of three singular integral equations for crack surface displacement derivative and normal and shearing stress jumps on rigid inclusions. These integral equations are solved numerically and the stress intensity factors are calculated.     

发动机汽缸内工作过程仿真计算

为了能够直观地分析发动机工作过程内汽缸各参数的变化情况,便于发动机的试验研究,该文在零维假设的前提下构建了发动机汽缸的仿真模型。从质量,能量的守恒关系和热力学原理推导方程式,并根据汽缸燃烧过程中各个阶段的不同特点进行求解,按给定的步长得到整个工作循环内汽缸主要参数的数值,从而模拟出它们在工作过程中的变化情况。用此模型进行测试,其计算时间少,实时性好,计算结果与实测数据相比能够准确地反应发动机汽缸内主要参数在一个工作循环内的变化情况。     

The finite element solution of laminar combined convection from a horizontal cylinder

The purpose of this investigation is to study the flow and heat-transfer characteristics of laminar combined convection from an isothermal cylinder. The full Navier-Stokes and energy equations are solved by a finite element method. The variations of surface shear stress, pressure and Nusselt number are obtained over the whole cylinder surface including the zone beyond the separation point. The predicted values of the average Nusselt number as well as the angle of separation, and the results of the pressure distribution and the local Nusselt number are compared with the available experimental correlations and previous numerical investigations. The agreement is satisfactory.     

A numerical method for predicting natural convection in horizontal cylinders with asymmetric boundary conditions

A numerical technique is developed to predict the two-dimensional transient natural convection heat transfer within a horizontal cylinder. Finite difference analogs of the Navier-Stokes and thermal energy equations are solved in the stream function-vorticity framework. The solution method, which is a modification of an alternating-direction implicit (ADI) scheme wherein the convective terms are evaluated explicitly, is found to be computationally more efficient than either an ADI or an explicit method. Unlike previous work, the present technique will accommodate completely arbitrary temperature boundary conditions. Thus, rather than considering an annular space or half of a symmetric cylinder, the solutions are determined for a full cylinder. A Cartesian form of the governing equations is employed at the point $\text{r= 0}$ where the polar coordinate equations become singular. The computed results are found to be in good agreement with previously published experimental data.     

High Order Accurate Solution of Flow Past a Circular Cylinder

A high order method is applied to time-dependent incompressible flow around a circular cylinder geometry. The space discretization employs compact fourth-order difference operators. In time we discretize with a second-order semi-implicit scheme. A large linear system of equations is solved in each time step by a combination of outer and inner iterations. An approximate block factorization of the system matrix is used for preconditioning. Well posed boundary conditions are obtained by an integral formulation of boundary data including a condition on the pressure. Two-dimensional flow around a circular cylinder is studied for Reynolds numbers in the range 7 ≤ R ≤ 180. The results agree very well with the data known from numerical and experimental studies in the literature.     

正弦曲线三点拟合问题的一种新方法

根据三个样本点拟合一条正弦曲线是计算机仿真和信号测量中的一个基本问题。目前流行的方法是最小二乘法。这种问题是一个三维以上的非线性最小化问题,计算规模与拟合具有三个参数一般曲线的计算规模相当。根据正弦曲线对应于某平面与某圆柱面交线的规律,提出了一种新的用于信号测量的正弦曲线拟合方法,它将原问题转化成为一个关于周期的单变量函数的最小化问题。新方法几何意义明确,算法实现简洁,结果可靠。     

On numerical computations in mixed boundary problems

A technique of solving mixed boundary value problems is formulated. The problem is essentially reduced to solving a set of linear algebraic equations, which can be solved efficiently on a computer. The technique is illustrated by two examples. The first deals with the electrostatic potential distribution on a partially grounded annulus. The other concerns with a contact of hollow cylinder, bonded inside to a rigid core.     

Modeling of self-oscillations and a search for new self-oscillatory flows

A possible mechanism of self-oscillations in flows with shock waves and contact discontinuities is studied. Flows are investigated in the heliosphere, near a blunt cone in an inhomogeneous stream, and in the vicinity of a blunt cylinder with an outflowing supersonic jet, which is supposed to be, according to this mechanism, of a self-oscillatory nature. Two-dimensional Reynolds equations with algebraic turbulent viscosity are solved by the implicit third order Runge-Kutta scheme. The results of numerical studies are presented.     

一种面向VR多投影环幕设备的可视化结果显示方法

传统显示设备难以满足大规模复杂数据可视化结果显示的需求,而VR多投影环幕显示设备提供的沉浸式显示环境可以良好地应对复杂数据可视化显示的使用情景。提出一种面向VR多投影环幕设备的可视化结果显示方法,通过设计多投影环境中兼容2D与3D显示的渲染流程,解决了传统方法中出现的画面渲染模糊问题。同时,该方法通过3D运动模拟计算以及交互射线计算解决了在新渲染流程下的立体显示和交互坐标转换问题。实验结果表明,该方法有效地提高了多投影环境中可视化结果画面的清晰度,并支持立体显示与交互。     

吸附天然气储罐放气过程的数学模拟

吸附天然气储罐的放气行为与其实际应用密切相关,因而对此研究具有重要意义。描述该过程的数学模型是含积分约束条件的发展型偏微分方程组,其中的积分约束方程较难处理。针对文献中其他求解方法的不足,本文基于线上方法,采用正交配置离散空间变量,无需对模型本身另作特别处理,用Radu积分式即可以很容易地处理积分约束方程,并用DASSL软件求解所得隐式常微分方程组,解法方便、快捷、稳定。通过模拟计算分析了改善储罐放气性能的途径。指出增加床层导热系数并非改善放气性能的有效方法,而采用给罐壁加热的方式较易消除吸附热效应对放气过程的不利影响。     

Frequency dependence on image reconstruction for a buried imperfectly conducting cylinder

Frequency dependence on image reconstruction for a buried imperfectly conducting cylinder is investigated. A conducting cylinder of unknown shape and conductivity is buried in one half‐space and the incident wave is scattered from another half‐space. By using measured scattered field, the image problem is reformulated into an optimization problem and solved by the genetic algorithm. Frequency dependence on image reconstruction is investigated and numerical results show that the reconstruction is well in the resonant frequency range. On the contrary, if the frequency is too high or too low, then the reconstruction becomes bad. This work provides both comparative and quantitative information. © 2002 Wiley Periodicals, Inc. Int J RF and Microwave CAE 12: 144–147, 2002.     

Non-hydrostatic finite volume model for non-linear waves interacting with structures

An efficient non-hydrostatic finite volume model is developed and applied to simulate non-linear waves interacting with structures. The unsteady Navier–Stokes equations are solved in a 3D grid made of polyhedrons, which are built from a 2D horizontal unstructured grid by adding several horizontal layers. A new grid arrangement in the vertical direction is proposed, which renders the resulting model is relatively simple. Moreover, the discretized Poisson equation for pressure is symmetric and positive definite, and thus it can be solved effectively by the preconditioned conjugate gradient method. Several test cases including solitary wave interacting with a submerged structure, solitary wave scattering from a vertical circular cylinder and an array of four circular cylinders are used to demonstrate the capability of the model on simulating non-linear waves interacting with structures. In all cases, the model gives satisfactory results in comparison with analytical solutions, experimental data and other published numerical results.     

On the numerical analysis of compressible flow problems by the “modified FLIC method”

This paper presents a new computational technique for transonic flow problem analysis. This method, named Modified FLIC Method, is based on a time-marching technique of FLIC (fluid in cell) method and employs triangular elements conventionally used in finite element method. This technique can be applied to transonic flows with any complicated boundary shapes. Three problems were solved in this paper, the first was a supersonic flow around a circular cylinder, the second was a transonic flow between tubrine blade cascades and the last was an unsteady flow in a duct with a junction. The calculated results showed a good agreement with the experimental data.     

Optimal heat release shaping in a reactivity controlled compression ignition (RCCI) engine

The present paper addresses the optimal heat release (HR) law in a single cylinder engine operated under reactivity controlled compression ignition (RCCI) combustion mode to minimise the indicated specific fuel consumption (ISFC) subject to different constraints including pressure related limits (maximum cylinder pressure and maximum cylinder pressure gradient). With this aim, a 0-dimensional (0D) engine combustion model has been identified with experimental data. Then, the optimal control problem of minimising the ISFC of the engine at different operating conditions of the engine operating map has been stated and analytically solved. To evaluate the method viability a data-driven model is developed to obtain the control actions (gasoline fraction) leading to the calculated optimal HR, more precisely to the optimal ratio between premixed and diffusive combustion. The experimental results obtained with such controls and the differences with the optimal HR are finally explained and discussed.     

Further consideration of the effect of curvature on the stability of three-dimensional flows

The effect of curvature on the stability and transition of three-dimensional incompressible flows is examined. The stability equations with and without curvature terms are solved with the temporal eigenvalue formulations used by Malik and Poll. Calculations are performed for flow over a yawed circular cylinder and results are compared with the calculations of Malik and Poll with and without curvature effects. Results show that the effect of curvature on transition is much smaller than claimed previously.     

Steady and unsteady flow past a rotating circular cylinder at low Reynolds numbers

Results of calculations of the steady and unsteady flows past a circular cylinder which is rotating with constant angular velocity and translating with constant linear velocity are presented. The motion is assumed to be two-dimensional and to be governed by the Navier-Stokes equations for incompressible fluids. For the unsteady flow, the cylinder is started impulsively from rest and it is found that for low Reynolds numbers the flow approaches a steady state after a large enough time. Detailed results are given for the development of the flow with time for Reynolds numbers 5 and 20 based on the diameter of the cylinder. For comparison purposes the corresponding steady flow problem has been solved. The calculated values of the steady-state lift, drag and moment coefficients from the two methods are found to be in good agreement. Notable, however, are the discrepancies between these results and other recent numerical solutions to the steady-state Navier-Stokes equations. Some unsteady results are also given for the higher Reynolds numbers of 60, 100 and 200. In these cases the flow does not tend to be a steady state but develops a periodic pattern of vortex shedding.     

Numerical simulation of an oscillating cylinder in a cross-flow at low Reynolds number: Forced and free oscillations

A numerical simulation of the flow past a circular cylinder which is able to oscillate transversely to the incident stream is presented in this paper for a fixed Reynolds number equal to 100. The 2D Navier-Stokes equations are solved by a finite volume method with an industrial CFD code in which a coupling procedure has been implemented in order to obtain the cylinder displacement. A preliminary work is first conducted for a fixed cylinder to check the wake characteristics for Reynolds numbers smaller than 150 in the laminar regime. The Strouhal frequency f_S and the aerodynamic coefficients are thus controlled among other parameters. Simulations are then performed with forced oscillations characterized by the frequency ratio F = f₀/f_S, where f₀ is the forced oscillation frequency, and by the adimensional amplitude A. The wake characteristics are analyzed using the time series of the fluctuating aerodynamic coefficients and their power spectral densities (PSD). The frequency content is then linked to the shape of the phase portraits and to the vortex shedding mode. By choosing interesting couples (A, F), different vortex shedding modes have been observed, which are similar to those of the Williamson-Roshko map. A second batch of simulations involving free vibrations (so-called vortex-induced vibrations or VIV) is finally carried out. Oscillations of the cylinder are now directly induced by the vortex shedding process in the wake and therefore, the time integration of the motion is realized by an explicit staggered algorithm which provides the cylinder displacement according to the aerodynamic charges exerted on the cylinder wall. Amplitude and frequency response of the cylinder are thus investigated over a wide range of reduced velocities to observe the different phenomena at stake. In particular, the vortex shedding modes have also been related to the frequency response observed and our results at Re = 100 show a very good agreement with other studies using different numerical approaches.     

Comparison of image reconstruction by using near‐field and far‐field data for an imperfect conductor

Image reconstruction by using near‐field and far‐field data for an imperfectly conducting cylinder is investigated. A conducting cylinder of unknown shape and conductivity scatters the incident wave in free space and the scattered near and far fields are measured. By using measured fields, the imaging problem is reformulated into an optimization problem and solved by the genetic algorithm. Numerical results show that the convergence speed and final reconstructed results by using near‐field data are better than those obtained by using far‐field data. This work provides both comparative and quantitative information. © 2001 John Wiley & Sons, Inc. Int J RF and Microwave CAE 11: 69–73, 2001.     

Numerical studies of the flow around a circular cylinder by a finite element method

Numerical solutions of the steady, incompressible, viscous flow past a circular cylinder are presented for Reynolds numbers R ranging from 1 to 100. The governing Navier-Stokes equations in the form of a single, fourth order differential equation for stream function and the boundary conditions are replaced by an equivalent variational principle. The numerical method is based on a finite element approximation of this principle. The resulting non-linear system is solved by the Newton-Raphson process. The pressure field is obtained from a finite element solution of the Poisson equation once the stream function is known. The results are compared with those determined by other numerical techniques and experiments. In particular, the discussion is concerned with the development of the closed wake with Reynolds number, and the tendency of R ≥ 40 flow toward instability.