Injection Profiling Through Temperature Warmback Analysis Under Variable Injection Rate and Variable Injection Temperature

Transport in Porous Media - Temperature warmback analysis has been recently adopted to quantitatively infer the injection profile during injection of cold fluids in stratified and heterogeneous...     

Adaptive Boundary Conditions for Exterior Flow Problems

We consider the problem of solving numerically the stationary incompressible Navier–Stokes equations in an exterior domain in two dimensions. This corresponds to studying the stationary fluid flow past a body. The necessity to truncate for numerical purposes the infinite exterior domain to a finite domain leads to the problem of finding appropriate boundary conditions on the surface of the truncated domain. We solve this problem by providing a vector field describing the leading asymptotic behavior of the solution. This vector field is given in the form of an explicit expression depending on a real parameter. We show that this parameter can be determined from the total drag exerted on the body. Using this fact we set up a self-consistent numerical scheme that determines the parameter, and hence the boundary conditions and the drag, as part of the solution process. We compare the values of the drag obtained with our adaptive scheme with the results from using traditional constant boundary conditions. Computational times are typically reduced by several orders of magnitude.     

Transient Characterization of the Reattachment of a Massively Separated Turbulent Boundary Layer Under Flow Control

The transient dynamics of a high Reynolds number separated flow over a two-dimensional ramp submitted to pulsed fluidic control is investigated. A spanwise array of 22 round jets, located upstream of the flap leading edge, is used as actuator to generate co-rotating vortical structures. Simultaneous measurements of wall friction using hot-film anemometry and phase-averaged velocity using 2D2C PIV are conducted. The PIV plane encompasses the incoming boundary layer upstream the flap leading edge, the separation bubble and the natural reattachment region. The dynamics of the separated flow is studied for successive sequences of pulsed actuation. Pockets of turbulence are periodically generated by the separation process and pushed downstream. After the transition period, the controlled flow shows large amplitude oscillations around a steady mean, particularly for the separation area. The transient dynamics of the flow at the actuation activation is also studied. The separated flow is strongly modified by the actuation from the first pulse. Characteristic times of the transient dynamics can be determined by fitting a first-order model with delay on the data. For the reattachment, the dimensionless characteristic rising times defined as \(\tau _{r}^{+} = \tau _{r} ~ U_{0} ~/~ L_{sep}\) of 11.7 for the friction gain, 4.8 for the separation length and 4.1 for the first mode of a Conditional Proper Orthogonal Decomposition analysis of the phase-averaged velocity fields were found. These values are in good agreement with previous studies and are of particular interest for modeling the transients and for further closed-loop control applications.     

Time-Dependent Shape Factors for Uniform and Non-Uniform Pressure Boundary Conditions

Matrix–fracture transfer functions are the backbone of any dual-porosity or dual-permeability formulation. The chief feature within them is the accurate definition of shape factors. To date, there is no completely accepted formulation of a matrix–fracture transfer function. Many formulations of shape factors for instantly-filled fractures with uniform pressure distribution have been presented and used; however, they differ by up to five times in magnitude. Based on a recently presented transfer function, time-dependent shape factors for water imbibing from fracture to matrix under pressure driven flow are proposed. Also new matrix–fracture transfer pressure-based shape factors for instantly-filled fractures with non-uniform pressure distribution are presented in this article. These are the boundary conditions for a case for porous media with clusters of parallel and disconnected fractures, for instance. These new pressure-based shape factors were obtained by solving the pressure diffusivity equation for a single phase using non-uniform boundary conditions. This leads to time-dependent shape factors because of the transient part of the solution for pressure. However, approximating the solution with an exponential function, one obtains constant shape factors that can be easily implemented in current dual-porosity reservoir simulators. The approximate shape factors provide good results for systems where the transient behavior of pressure is short (a case commonly encountered in fractured reservoirs).     

广义边界梁的动力学建模与动态特征

对于广义边界条件Euler-Bernoulli梁,采用相对描述方式建立了可描述梁整体运动和相对变形的几何非线性及其线性化动力学模型,应用线性变换得到了该类梁的线性经典动力学方程,得到了广义边界条件下梁的横向振动代数特征方程、特征函数及特征值的退化表达式.算例分析了边界小扰动对固支-固支梁横向振动特征的影响规律.     

压力梯度对边界层两相流动稳定性的影响

分析了有压力梯度的边界层两相流动稳定性,推导出类似于Saffman理论的修正的稳定性方程,数值计算采用高精度的谱方法。结果说明,压力梯度对边界层两相流动稳定性有显著的影响,顺压梯度增强流动稳定性,而逆压梯度则促进流动失稳。在不同的压力梯度和浓度下,Stokes数对流动稳定性的影响是一致的,存在一个临界Stokes数,小Stokes数促进流动失稳,而大Stokes数则提高临界雷诺数,抑制流动失稳的最佳Stokes数为10的量级。     

Solution of Dynamic Problems for Thin-Walled Structural Elements with Nonuniform Dynamic Boundary Conditions

The characteristics of the stress–strain state of thin-walled structural elements are determined in the case where dynamic boundary loads or displacements described by pulse functions are specified. A general scheme for realization of the method of natural-mode expansion is stated as applied to differential equations with unknown functions of one spatial coordinate and time. Theoretical relations for rods, plates, and shells are given. The potential of the approach developed is illustrated by solving specific problems     

Analysis of Boundary Conditions for Crystal Defect Atomistic Simulations

Numerical simulations of crystal defects are necessarily restricted to finite computational domains, supplying artificial boundary conditions that emulate the effect of embedding the defect in an effectively infinite crystalline environment. This work develops a rigorous framework within which the accuracy of different types of boundary conditions can be precisely assessed. We formulate the equilibration of crystal defects as variational problems in a discrete energy space and establish qualitatively sharp regularity estimates for minimisers. Using this foundation we then present rigorous error estimates for (i) a truncation method (Dirichlet boundary conditions), (ii) periodic boundary conditions, (iii) boundary conditions from linear elasticity, and (iv) boundary conditions from nonlinear elasticity. Numerical results confirm the sharpness of the analysis.     

Artificial Boundary Conditions of Pressure Type for Viscous Flows in a System of Pipes

In a three-dimensional domain Ω with J cylindrical outlets to infinity the problem is treated how solutions to the stationary Stokes and Navier–Stokes system with pressure conditions at infinity can be approximated by solutions on bounded subdomains. The optimal artificial boundary conditions turn out to have singular coefficients. Existence, uniqueness and asymptotically precise estimates for the truncation error are proved for the linear problem and for the nonlinear problem with small data. The results include also estimates for the so called “do-nothing” condition.     

The Poiseuille Flow in a Pipe with Temperature Dependent Viscosity and Prescribed Flow Rate

This note studies the stationary Poiseuille flow in a cylindrical channel of arbitrary cross-section with temperature dependent viscosity and internal dissipation. We assume the flow-rate given and we treat the axial pressure gradient as an unknown. Theorems of existence and uniqueness are proved using a special transformation.     

Short Communication Finite Element Analysis of Visco-elastic Flow Under High Shear Rate Using the GSMAC-method

In the present work, we carry out a finite element analysis of visco-elastic flows for the multi-mode Giesekus model at high shear rales flow. We have already proposed a new numerical scheme suitable for the analysis of visco-elastic fluids in the previous paper. It is mainly composed of two parts: the MUSCL (Monotone Upstream-centered Scheme for Conservation Law)-TVD (Total Variation Diminishing) for the numerical analysis of the constitutive equation and the GSMAC (Generalized Simplified Maker and Cell)-FEM (Finite Element Method) for the momentum equation. We apply the new scheme for the flows through the contraction plane for the multi-mode Giesekus model that considers eight relaxation modes. It shows suitable matching with experimental data at low shear rates, and we confirm that the results are stable at high shear rates.     

Heated and Salted Below Porous Convection with Generalized Temperature and Solute Boundary Conditions

Transport in Porous Media - We address the problem of initiation of convective motion in the case of a fluid saturated porous layer, containing a salt in solution, which is heated and salted below....     

Nonstationary Displacements in an Axisymmetric Problem for an Elastic Half-Space Under Mixed Boundary Conditions*

International Applied Mechanics - The strain state of an elastic half-space under a non-stationary normal load acting on its boundary is determined. A mixed boundary-value problem is stated. Its...     

煤层气三孔双渗流动模型及压力分析

通过对美国Antrim页岩气藏及一些别的低阶煤层的研究表明,在基质颗粒中也有相当一部分自由气存在。本文建立了低阶煤层中单相煤层气三孔双渗流动的试井模型,并获得了模型在拉氏空间上的解析解以及模型的数值解,讨论了储层外边界条件、弹性储容比、窜流系数以及吸附系数等参数对于压力动态响应的影响。结果表明：外边界条件决定着早期过渡段出现的早晚;窜流系数和弹性储容比影响窜流阶段出现的早晚;而吸附系数对晚期过渡段影响明显。     

各种边界条件平行四边形功能梯度板的动力特性解析解

本文基于斜坐标系,建立起平行四边形功能梯度板的基本微分方程及变分方程,用梁函数组合法对平行四边形及菱形功能梯度板进行动力特性分析,提出了适用于每边任取简支、固定、自由边界之一(包括36种边界)平行四边形功能梯度板固有频率与振型的解析解;在简化情况下,给出了各种边界条件平行四边形功能梯度板各阶固有频率解的统一表达式。     

Computational Modelling of Turbulent Mixing in Confined Swirling Environment Under Constant and Variable Density Conditions

A high-intensity swirling flow in a model combustor subjected to large density variations has been examined computationally. The focus is on the Favre-averaged Navier–Stokes computations of the momentum and scalar transport employing turbulence models based on the differential second-moment closure (SMC) strategy. An updated version of the basic, high-Reynolds number SMC model accounting for a quadratic expansion of both the pressure–strain and dissipation tensors and a near-wall SMC model were used for predicting the mean velocity and turbulence fields. The accompanied mixing between the annular swirling air flow and the central non-swirling helium jet was studied by applying three scalar flux models differing mainly in the model formulation for the pressure-scalar gradient correlation. The computed axial and circumferential velocities agree fairly well with the reference experiment [So et al., NASA Contractor Report 3832, 1984; Ahmed and So, Exp. Fluids 4 (1986) 107], reproducing important features of such a weakly supercritical flow configuration (tendency of the flow core to separate). Although the length at which the mixing was completed was reproduced in reasonable agreement with the experimental results, the mixing activity in terms of the spreading rate of the shear/mixing layer, that is its thickness, was somewhat more intensive. Prior to these investigations, the model applied was validated by computing the transport of the passive scalar in the non-swirling (Johnson and Bennet, Report NASA CR-165574, UTRC Report R81-915540-9, 1981) and swirling (Roback and Johnson, NASA Contractor Report 168252, 1983) flow in a model combustor.     

Second Order Adaptive Boundary Conditions for Exterior Flow Problems: Non-Symmetric Stationary Flows in Two Dimensions

We consider the problem of solving numerically the stationary incompressible Navier–Stokes equations in an exterior domain in two dimensions. For numerical purposes we truncate the domain to a finite sub-domain, which leads to the problem of finding so called “artificial boundary conditions” to replace the boundary conditions at infinity. To solve this problem we construct – by combining results from dynamical systems theory with matched asymptotic expansion techniques based on the old ideas of Goldstein and Van Dyke – a smooth divergence free vector field depending explicitly on drag and lift and describing the solution to second and dominant third order, asymptotically at large distances from the body. The resulting expression appears to be new, even on a formal level. This improves the method introduced by the authors in a previous paper and generalizes it to non-symmetric flows. The numerical scheme determines the boundary conditions and the forces on the body in a self-consistent way as an integral part of the solution process. When compared with our previous paper where first order asymptotic expressions were used on the boundary, the inclusion of second and third order asymptotic terms further reduces the computational cost for determining lift and drag to a given precision by typically another order of magnitude. Peter Wittwer: Supported in part by the Fonds National Suisse.     

Pressure Transient Analysis for Multi-stage Fractured Horizontal Wells in Shale Gas Reservoirs

This article presents the PTA on the multi-stage fractured horizontal well in shale gas reservoirs incorporating desorption and diffusive flow in the matrix. Currently, most PTA models are simply based on Darcy flow both in natural fractures and matrix without considering the mechanisms of desorption and diffusion in shale matrix. Source function and Laplace transform with the numerical discrete method are employed to solve the mathematical model. The solution is presented in the Laplace domain so that the wellbore storage effect and skin factor can be easily incorporated by convolution. Type curves are plotted with Stehfest algorithm and different flow regimes are identified. The presented model could be used to interpret pressure signals more accurately for shale gas reservoirs.     

颅内Willis环二维血液动力学计算分析

采用颅内二维Willis环模型,对血管在不同程度狭窄情况下的血液流动进行稳态计算与分析,计算中采用了进出口处的压力边界条件和无滑移固壁条件.计算得到完整环和交通动脉缺失情况下各进出口血管流量变化曲线.所获结果表明,完整Willis环中,前交通动脉的代偿能力在左颈内动脉狭窄率达到25%以后才能得到比较明显的体现;后交通动脉缺失情况下前交通动脉的代偿能力变弱;Willis环的前部和后部有相对独立性,只有在主要进口动脉严重阻塞的时候,单侧的独立性才丧失.