Simulation of transient gas flows in networks

A technique is presented for calculating the transient flow in high pressure transportation systems where both simple systems (without compressors) and systems with compressors have been taken into consideration. A partial differential equation characterizing the dynamic gas flow through a pipeline and a numerical scheme for its solution are considered. A method of computing node pressures is also characterized.     

A finite element method for transient compressible flow in pipelines

A finite element method is developed to solve the partial differential equations describing the unsteady flow of gas in pipelines. Excellent agreement is obtained between simulated results and experimental data from a fullscale gas pipeline. The method is used to describe very transient flow (blowout), and to determine the performance of leak detection systems, and proves to be very stable and reliable.     

A numerical method for simulating discontinuous shallow flow over an infiltrating surface

A numerical method based on the MacCormack finite difference scheme is presented. The method was developed for simulating two‐dimensional overland flow with spatially variable infiltration and microtopography using the hydrodynamic flow equations. The basic MacCormack scheme is enhanced by using the method of fractional steps to simplify application; treating the friction slope, a stiff source term, point‐implicitly, plus, for numerical oscillation control and stability, upwinding the convective acceleration term. A higher‐order smoothing operator is added to aid oscillation control when simulating flow over highly variable surfaces. Infiltration is simulated with the Green–Ampt model coupled to the surface water component in a manner that allows dynamic interaction. The developed method will also be useful for simulating irrigation, tidal flat and wetland circulation, and floods. Copyright © 2000 John Wiley & Sons, Ltd.     

An adjoint method for the calculation of remote sensitivities in supersonic flow

This paper presents an adjoint method for the calculation of remote sensitivities in supersonic flow. The goal is to develop a set of discrete adjoint equations and their corresponding boundary conditions in order to quantify the influence of geometry modifications on the pressure distribution at an arbitrary location within the domain of interest. First, this paper presents the complete formulation and discretization of the discrete adjoint equations. The special treatment of the adjoint boundary condition to obtain remote sensitivities or sensitivities of pressure distributions at points remotely located from the wing surface are discussed. Secondly, we present results that demonstrate the application of the theory to a three-dimensional remote inverse design problem using a low sweep biconvex wing and a highly swept blunt leading edge wing. Lastly, we present results that establish the added benefit of using an objective function that contains the sum of the remote inverse and drag minimization cost functions.     

Application of the centre implicit method for investigation of pressure transients in pipelines

This paper investigates the application of the centre implicit method for the determination of the pressure transient in a pipeline, and compares the results with those obtained using the method of characteristics and an experimental investigation. The study shows that there are unique values for the stability criterion (ratio of the linear and time increments) and the artificial viscosity term (a damping factor) used in the numerical computation. The time step and the number of nodes required for the accuracy of the method have been considered. The centre implicit method can be readily adapted to transient flow with variable wave speed provided the established conditions are used.     

Numerical study of short-circuiting flow and particles in a gas cyclone

Short-circuiting flow is an important secondary flow in gas cyclones, which has a negative impact on the separation performance. To improve the understanding of the short-circuiting flow and guide the optimization of gas cyclones, this paper presents a numerical study of a cyclone using computational fluid dynamics. Based on the steady flow field, three methods were adopted to investigate the formation mechanism and characteristics of the short-circuiting flow and particles. The temporal variation of the tracer species concentration distribution reveals that the formation mechanism of the short-circuiting flow is the squeeze between the airflows entering the annular space of the gas cyclone at different times. The short-circuiting flow region, distinguished through the spatial distribution of the moments of age, is characterized by a small mean age and a large coefficient of variation. The proportion of the short-circuiting particles increases with the increase of the inlet velocity only for small particles. But with the increase of particle size, the proportion of the short-circuiting particles decreases faster at higher inlet velocities, resulting in significant differences in collection efficiency curves.     

Unsteady compressible flow in long pipelines following a rupture

The unsteady frictional flow of a compressible fluid generated in a long pipeline after an accidental rupture is of considerable interest to the offshore gas industry. It answers several important questions concerning safety and pollution, e.g. the flow rate at the broken pipe end. Laboratory tests cannot simulate the rather complex phenomenon satisfactorily. The problem is highly non-linear and no general analytical solution is yet known. In this study, based on computational fluid dynamics, the simplifying assumptions of isothermal and low Mach number flow often applied in the case of unsteady compressible flows in pipelines, have not been used. Owing to the choking condition (Ma=1) which prevails for some time at the broken end. and the cumulative effect of friction over the 145 km long pipeline, we obtain (?p/?x)^t→?∞. This analytically established singularity leads to numerical difficulties which seriously affect the accuracy. For short tubes (such as shock tubes) this negative feature is much less severe. Special procedures were necessary to keep the accuracy within the chosen limit of 1 per cent.     

Dynamic coupling of fluid and structural mechanics for simulating particle motion and interaction in high speed compressible gas particle laden flow

In this work, structural finite element analyses of particles moving and interacting within high speed compressible flow are directly coupled to computational fluid dynamics and heat transfer analyses to provide more detailed and improved simulations of particle laden flow under these operating conditions. For a given solid material model, stresses and displacements throughout the solid body are determined with the particle–particle contact following an element to element local spring force model and local fluid induced forces directly calculated from the finite volume flow solution. Plasticity and particle deformation common in such a flow regime can be incorporated in a more rigorous manner than typical discrete element models where structural conditions are not directly modeled. Using the developed techniques, simulations of normal collisions between two 1 mm radius particles with initial particle velocities of 50–150 m/s are conducted with different levels of pressure driven gas flow moving normal to the initial particle motion for elastic and elastic–plastic with strain hardening based solid material models. In this manner, the relationships between the collision velocity, the material behavior models, and the fluid flow and the particle motion and deformation can be investigated. The elastic–plastic material behavior results in post collision velocities 16–50% of their pre-collision values while the elastic-based particle collisions nearly regained their initial velocity upon rebound. The elastic–plastic material models produce contact forces less than half of those for elastic collisions, longer contact times, and greater particle deformation. Fluid flow forces affect the particle motion even at high collision speeds regardless of the solid material behavior model. With the elastic models, the collision force varied little with the strength of the gas flow driver. For the elastic–plastic models, the larger particle deformation and the resulting increasingly asymmetric loading lead to growing differences in the collision force magnitudes and directions as the gas flow strength increased. The coupled finite volume flow and finite element structural analyses provide a capability to capture the interdependencies between the interaction of the particles, the particle deformation, the fluid flow and the particle motion.     

A decoupling numerical method for fluid flow

A first-order non-conforming numerical methodology, Separation method, for fluid flow problems with a 3-point exponential interpolation scheme has been developed. The flow problem is decoupled into multiple one-dimensional subproblems and assembled to form the solutions. A fully staggered grid and a conservational domain centred at the node of interest make the decoupling scheme first-order-accurate. The discretization of each one-dimensional subproblem is based on a 3-point interpolation function and a conservational domain centred at the node of interest. The proposed scheme gives a guaranteed first-order accuracy. It is shown that the traditional upwind (or exponentially weighted upstream) scheme is less than first-order-accurate. The pressure is decoupled from the velocity field using the pressure correction method of SIMPLE. Thomas algorithm (tri-diagonal solver) is used to solve the algebraic equations iteratively. The numerical advantage of the proposed scheme is tested for laminar fluid flows in a torus and in a square-driven cavity. The convergence rates are compared with the traditional schemes for the square-driven cavity problem. Good behaviour of the proposed scheme is ascertained.     

Multiphase flow model developed for simulating gas hydrate transport in horizontal pipe

The hydrate formation or dissociation in deep subsea flow lines is a challenging problem in oil and gas transport systems. The study of multiphase flows is complex while necessary due to the phase changes (i.e., liquid, solid, and gas) that occur with increasing the temperature and decreasing the pressure. A one-dimensional multiphase flow model coupled with a transient hydrate kinetic model is developed to study the characteristics of the multiphase flows for the hydrates formed by the phase changes in the pipes. The multiphase flow model is derived from a multi-fluid model, while has been widely used in modelling multiphase flows. The heat convection between the fluid and the ambient through the pipe wall is considered in the energy balance equation. The developed multiphase flow model is used to simulate the procedure of the hydrate transport. The results show that the formation of the hydrates can cause hold-up oscillations of water and gas.     

含高阶余项的非线性动力系统数值计算法

建立了一种求解非线性动力系统高精度数值计算的新方法,重构了等价的非线性动力系统方程,该方程考虑了非线性函数的任意高阶项,并给出了该方程的Duhamel积分表达式,在时间步长内用Newton-Raphson法进行数值迭代求解,该方法能连续满足微分方程而不只是在离散的步长端点满足方程,从而打破了传统的Euler型有限差分法。计算实例表明,该方法计算精度高于传统的Runge-Kutta,Newmark-β和Wilson-θ等方法。     

Assessment of 2D/3D numerical modeling for deep dynamic stall experiments

The results of computational fluid dynamics (CFD) simulations in two and three spatial dimensions are compared to pressure measurements and particle image velocimetry (PIV) flow surveys to assess the suitability of numerical models for the simulation of deep dynamic stall experiments carried out on a pitching NACA 23012 airfoil. A sinusoidal pitching motion with a 10° amplitude and a reduced frequency of 0.1 is imposed around two different mean angles of attack of 10° and 15°. The comparison of the airloads curves and of the pressure distribution over the airfoil surface shows that a three-dimensional numerical model can better reproduce the flow structures and the airfoil performance for the deep dynamic stall regime. Also, the vortical structures observed by PIV in the flow field are better captured by the three-dimensional model. This feature highlighted the relevance of three-dimensional effects on the flow field in deep dynamic stall.     

Optimal design of gas distributor in fluidized bed for synthesis of silicone monomer

The structure of the gas distributor is closely related to the production efficiency of organosilicon monomers. To improve the production efficiency of organosilicon monomers, this study uses Eulerian-Eulerian two fluid model and proposes a design formula for the gas distributor to optimize the gas distributor. It is proposed that the pressure drop of the gas distributor, the velocity nonuniformity coefficient, the relative standard deviation of the solid holdup, and the solid particle dispersion coefficient are used to evaluate the performance of the gas distributor. The results show that the performance of the gas distributor is significantly improved when the opening ratio Φ = 0.53% is optimized to Φ = 0.18%, in which the relative standard deviation of the solid holdup is reduced by 22%, and the solid particle dispersion coefficient is reduced by 40%. On this basis, this article studies the influence of different arrangements of vent holes on gas-solid fluidization characteristics. The results show that the circular arrangement of vent holes is helpful to the mixing of gas and solid.     

The numerical solution of the transient two‐phase flow in rigid pipelines

Consideration is given in this paper to the numerical solution of the transient two‐phase flow in rigid pipelines. The governing equations for such flows are two coupled, non‐linear, hyperbolic, partial differential equations with pressure dependent coefficients. The fluid pressure and velocity are considered as two principle dependent variables. The fluid is a homogeneous gas–liquid mixture for which the density is defined by an expression averaging the two‐component densities where a polytropic process of the gaseous phase is admitted. Instead of the void fraction, which varies with the pressure, the gas–fluid mass ratio (or the quality) is assumed to be constant, and is used in the mathematical formulation. The problem has been solved by the method of non‐linear characteristics and the finite difference conservative scheme. To verify their validity, the computed results of the two numerical techniques are compared for different values of the quality, in the case where the liquid compressibility and the pipe wall elasticity are neglected. Copyright © 1999 John Wiley & Sons, Ltd.     

Two-dimensional analysis of pressure transients in pipelines

The paper presents a two-dimensional model for the investigation of pressure transients in pipelines. The governing equations have been established and a method of solving the equations using the centre implicit method is presented. The theoretically predicted values are compared with the experimentally determined pressure transients for horizontal pipelines with a valve at the end. The two-dimensional model gives results which are accurate than those of the one-dimensional model and are in good agreement with the experimental results.     

浅埋高压输气管道爆炸地面振动的原型试验与数值模拟研究

针对浅埋高压输气管道爆炸产生的地面振动效应,采用现场试验结合数值模拟的方法展开研究。组织实施了全尺寸天然气管道爆炸试验,掌握了高压输气管道爆炸地面振动的量级范围以及衰减规律。经试验数据分析得到,埋地高压天然气管道爆炸造成的地面振动主要产生于物理爆炸过程中,随后发生的天然气爆燃过程并未产生明显的地面振动。基于非线性有限元程序 LS-Dyna建立了高压输气管道爆炸试验计算模型,计算结果与试验现象吻合较好,验证了模型参数设计的合理性。进一步分析了管道爆炸瞬间管内气体-管壁-土体的相互作用机理、应力分布以及裂纹扩展规律。由计算结果分析得到,管道开裂是由于内部高压气体推动管壁向两侧扩展在裂纹尖端处形成了应力集中,管壁冲击土体的速度可达50 m/s,冲击产生的塑性状态向远处传播逐渐衰减为弹性应力波,即形成了地面振动效应。研究成果揭示了高压气体管道爆炸地面振动的主要成因,可为爆炸事故振动预防提供理论参考和技术支持。     

On a network method for unsteady incompressible fluid flow on triangular grids

The dual variable method for Delaunay triangulations is a network-theoretic method that transforms a set of primitive variable finite difference or finite element equations for incompressible flow into an equivalent system which is one-fifth the size of the original. Additionally, it eliminates the pressures from the system and produces velocities that are exactly discretely divergence-free. In this paper new discretizations of the convection term are presented for Delaunay triangulations, the dual variable method is extended to tessellations that contain obstacles, and an efficient algorithm for the solution of the dual variable system is described.