Optimal control of unsteady compressible viscous flows

The control of complex, unsteady flows is a pacing technology for advances in fluid mechanics. Recently, optimal control theory has become popular as a means of predicting best case controls that can guide the design of practical flow control systems. However, most of the prior work in this area has focused on incompressible flow which precludes many of the important physical flow phenomena that must be controlled in practice including the coupling of fluid dynamics, acoustics, and heat transfer. This paper presents the formulation and numerical solution of a class of optimal boundary control problems governed by the unsteady two‐dimensional compressible Navier–Stokes equations. Fundamental issues including the choice of the control space and the associated regularization term in the objective function, as well as issues in the gradient computation via the adjoint equation method are discussed. Numerical results are presented for a model problem consisting of two counter‐rotating viscous vortices above an infinite wall which, due to the self‐induced velocity field, propagate downward and interact with the wall. The wall boundary control is the temporal and spatial distribution of wall‐normal velocity. Optimal controls for objective functions that target kinetic energy, heat transfer, and wall shear stress are presented along with the influence of control regularization for each case. Copyright © 2002 John Wiley & Sons, Ltd.     

On estimating pressure build-up in severely accelerated,shocked flow

A new approach to the calculation of the high pressures characterizing the flow field in front of a piston undergoing severe acceleration over the short term is presented. In contrast with previous approaches where the computational domain is altered but which stop short of transforming velocities, here the problem is solved in an accelerating non-Euclidean co-ordinate system where the piston is stationary. The method is applied to a study of the problem of premature sabot separation. Through use of Harten's second-order-accurate TVD scheme, flow simulations are performed for both 1D and 3D axisymmetric geometries. The simple 1D model gives pressure profiles surprisingly close to those of the more physical 3D model.     

沉浮,俯仰及控制面振动引起的跨音速非定常气动载荷计算

本文将文献[9]提出改进的通量分裂方法,应用于随时间变化的贴体网格中,建立了可用于求解非定常Euler方程的通量分裂方法.该方法是以连续的特征值分离为基础,它具有方法简单,便于推广使用的特点.同时克服了Steger-Warming通量分裂方法存在的问题.对通量分裂后的Euler方程.利用MUSCL型迎风差分建立了具有二阶精度的有限体积方程.文中以NACA64A—10翼型为例,对其在跨音速流场中进行沉浮、俯仰及带有振动控制面引起的非定常气动载荷进行了计算.部分计算结果与相应的实验结果进行了比较,吻合良好     

Influence of Relative Permeability on the Stability Characteristics of Immiscible Flow in Porous Media

Relative permeability functions for immiscible displacements in porous media show a wide range of profiles. Although, this behavior is well known, its impact on the stability of the displacement process is unexplored. Our analysis clearly demonstrates for the first time that the viscous instability characteristics of two-phase flows are governed not only by their end point values, but are strongly dependent on the actual profile of relative permeability functions. Linear stability analysis predicts the capacity of the flow to develop large scale fingers which can result in substantial bypassing of the resident fluid. It is observed that relative permeability functions attributed to drainage processes yield a more unstable displacement as compared to functions related to imbibition processes. Moreover, instability is observed to increase for those relative permeability functions which result from increased wettability of the wetting fluid. High accuracy numerical simulations show agreement with these predictions and demonstrate how large amplitude viscous fingers result in significant bypassing for certain relative permeability functions. In the nonlinear regime, the finger amplitude grows at a rate ∝ t^1/2 initially, drops to t^1/4 at a later time and finally grows ∝ t. The basic mechanisms of finger interaction, however, are not substantially influenced by relative permeability functions.     

Measurements and simulations of particle dispersion in a turbulent flow

A particle imaging technique has been used to collect droplet displacement statistics in a round turbulent jet of air. Droplets are injected on the jet axis, and a laser sheet and position-sensitive photomultiplier tube are used to track their radial displacement and time-of-flight. Dispersion statistics can be computed which are Lagrangian or Eulerian in nature. The experiments have been simulated numerically using a second-order closure scheme for the jet and a stochastic simulation for the particle trajectories. Results are presented for non-vaporizing droplets of sizes from 35 to 160 μm. The simulations have underscored the importance of initial conditions and early droplet displacement history on the droplet trajectory for droplets with large inertia relative to the turbulence. Estimates of initial conditions have been made and their effect on dispersion is quantified.     

Application of heat flow calorimetry to the study of oilwell cements

The majority of previous studies of the hydration of cements using heat flow calorimetry have been carried out isothermally. However, with oilwell cements the slurry is mixed on the surface at ambient temperature and then gradually increases in temperature as it is pumped down the well. A Setaram C-80 calorimeter has been used to simulate the temperature ramp in API oilwell cement test schedules. This approach has enabled cementing reactions to be studied for the first time under conditions approaching those encountered in the field, and has shown that the results obtained from isothermal experiments may be misleading.The permission of the British Petroleum Company PLC to publish this paper is gratefully acknowledged.     

Averaged topological equations for dispersed two-phase flows

A general relationship between the volume fraction and the specific interfacial area for averaged dispersed two-phase flows is proposed. This relationship, expressed as a basic set of two scalar evolution equations and two vectorial non-uniformity state equations, is an analytical result obtained by a systematic approach using the derivatives of some generalized functions and a local volume-averaging technique. The proposed set of equations was expressed for measurable macroscopic parameters of the system and has the same generality as the averaged transport equations of two-phase flows. By combination of the basic set of equations, called the averaged topological equations (ATEs), second-order ATEs for the volume fraction were found. The second-order ATEs were expressed both by a Lagrangian formulation and by a Eulerian formulation. The importance and physical meaning of the ATEs developed in this study were clarified within the framework of the theory of kinematic waves.     

纬向对称准地转流的非线性稳定性定理

建立了周期域上准地转流在一般的边界条件下对应于Arnold第二定理的非线性稳定性定理。将扰动能量与扰动拟能的上界用初始扰动场的显示表示出来，从而建立了Liapunov意义下的非线性稳定性定理。     

Modélisation du champ des vitesses de l'urine dans un bolus urétéralModelling of urine flow in an ureteral bolus

Urine transport is made from the kidney to the bladder through the ureter by isolated pockets called bolus. To determine the urine flow in a bolus, we use an adherence condition on the interface urine/wall. It gives us an infinite linear system verified by a set of parameters. An iterative and convergent algorithm allows us to solve this system and to determine analytically the components of the velocity vector in the bolus. To cite this article: A. Vogel et al., C. R. Mecanique 332 (2004).