A CFD Model to Evaluate Near-Surface Oil Spill from a Broken Loading Pipe in Shallow Coastal Waters

Oil spills continue to generate various issues and concerns regarding their effect and behavior in the marine environment,owing to the related potential for detrimental environmental,economic and social implications.It is essential to have a solid understanding of the ways in which oil interacts with the water and the coastal ecosystems that are located nearby.This study proposes a simplified model for predicting the plume-like transport behavior of heavy Bunker C fuel oil discharging downward from an acutely-angled broken pipeline located on the water surface.The results show that the spill overall profile is articulated in three major flow areas.The first,is the source field,i.e.,a region near the origin of the initial jet,followed by the intermediate or transport field,namely,the region where the jet oil flow transitions into an underwater oil plume flow and starts to move horizontally,and finally,the far-field,where the oil re-surface and spreads onto the shore at a significant distance from the spill site.The behavior of the oil in the intermediate field is investigated using a simplified injection-type oil spill model capable of mimicking the undersea trapping and lateral migration of an oil plume originating from a negatively buoyant jet spill.A rectangular domain with proper boundary conditions is used to implement the model.The Projection approach is used to discretize a modified version of the Navier-Stokes equations in two dimensions.A benchmark fluid flow issue is used to verify the model and the results indicate a reasonable relationship between specific gravity and depth as well as agreement with the aerial data and a vertical temperature profile plot.

A Third-Order Upwind Compact Scheme on Curvilinear Meshes for the Incompressible Navier-Stokes Equations

This paper presents a new version of the upwind compact finite difference scheme for solving the incompressible Navier-Stokes equations in generalized curvilinear coordinates.The artificial compressibility approach is used,which transforms the elliptic-parabolic equations into the hyperbolic-parabolic ones so that flux difference splitting can be applied.The convective terms are approximated by a third-order upwind compact scheme implemented with flux difference splitting,and the viscous terms are approximated by a fourth-order central compact scheme.The solution algorithm used is the Beam-Warming approximate factorization scheme.Numerical solutions to benchmark problems of the steady plane Couette-Poiseuille flow,the liddriven cavity flow,and the constricting channel flow with varying geometry are presented.The computed results are found in good agreement with established analytical and numerical results.The third-order accuracy of the scheme is verified on uniform rectangular meshes.

A FINITE-DIFFERENCE RELAXATION SCHEME BASED ON BOTH MULTIGRID TECHNIQUES AND HOMOTOPY METHOD FOR 2D STEADY-STATE NAVIER-STOKES EQUATIONS

In this paper, multigrid techniques together with homotopy method are applied to propose a kind of finite-difference relaxation scheme for 2D steady-state Navier-Stokes equations. The proposed numerical scheme can give convergent results for viscous flows with high Reynolds number. As an example, the results of shear-driven cavity flow with high Reynolds number up to 25000 on fine grid 257×257 are given.

Chaotic Lid-Driven Square Cavity Flows at Extreme Reynolds Numbers

This paper investigates the chaotic lid-driven square cavity flows at extreme Reynolds numbers.Several observations have been made from this study.Firstly,at extreme Reynolds numbers two principles add at the genesis of tiny,loose counterclockwise-or clockwise-rotating eddies.One concerns the arousing of them owing to the influence of the clockwise-or counterclockwise currents nearby;the other,the arousing of counterclockwise-rotating eddies near attached to the moving(lid)top wall which moves from left to right.Secondly,unexpectedly,the kinetic energy soon reaches the qualitative temporal limit’s pace,fluctuating briskly,randomly inside the total kinetic energy range,fluctuations which concentrate on two distinct fragments:one on its upper side,the upper fragment,the other on its lower side,the lower fragment,switching briskly,randomly from each other;and further on many small fragments arousing randomly within both,switching briskly,randomly from one another.As the Reynolds number Re→∞,both distance and then close,and the kinetic energy fluctuates shorter and shorter at the upper fragment and longer and longer at the lower fragment,displaying tall high spikes which enlarge and then disappear.As the time t→∞(at the Reynolds number Re fixed)they recur from time to time with roughly the same amplitude.For the most part,at the upper fragment the leading eddy rotates clockwise,and at the lower fragment,in stark contrast,it rotates counterclockwise.At Re=109 the leading eddy-at its qualitative temporal limit’s pace—appears to rotate solely counterclockwise.

Evaluation of flow regime of turbidity currents entering Dez Reservoir using extended shallow water model

In this study, the performance of the extended shallow water model （ESWM） in evaluation of the flow regime of turbidity currents entering the Dez Reservoir was investigated. The continuity equations for fluid and particles and the Navier-Stokes equations govern the entire flow of turbidity currents. The shallow water equations governing the flow of the depositing phase of turbidity currents are derived from these equations. A case study was conducted on the flow regime of turbidity currents entering the Dez Reservoir in Iran from January 2002 to July 2003. Facing a serious sedimentation problem, the dead storage of the Dez Reservoir will be full in the coming 10 years, and the inflowing water in the hydropower conduit system is now becoming turbid. Based on the values of the dimensionless friction number （ Nf ≤1 ） and dimensionless entrainment number （ NE≤ 1 ） of turbidity currents, and the coefficient of determination between the observed and predicted deposit depths （R2 = 0.86） for the flow regime of negligible friction and negligible entrainment （NFNE）, the flow regime of turbidity currents coming into the Dez Reservoir is considered to be NFNE. The results suggest that the ESWM is an appropriate approach for evaluation of the flow regime of turbidity currents in dam reservoirs where the characteristics of turbidity currents, such as the deposit depth, must be evaluated.

A NUMERICAL AND ANALYTICAL STUDY ON A TAIL-FLAPPING MODEL FOR FISH FAST C-START

The force production physics and the flow control mechanism of fish fast C-start are studied numerically and theoretically by using a tail-flapping model.The problem is simplified to a 2-D foil that rotates rapidly to and fro on one side about its fixed leading edge in water medium.The study involves the simulation of the flow by solving the two-dimensional unsteady incompressible Navier- Stokes equations and employing a theoretical analytic modeling approach.Firstly,reasonable thrust magnitude and its time history are obtained and checked by fitting predicted results coming from these two approaches.Next,the flow fields and vortex structures are given,and the propulsive mechanism is interpreted.The results show that the induction of vortex distributions near the trailing edge of the tail are important in the time-averaged thrust generation,though the added inertial effect plays an important role in producing an instant large thrust especially in the first stage.Furthermore,dynamic and energetic effects of some kinematic controlling factors are discussed.For enhancing the time- averaged thrust but keeping a favorable ratio of it to time-averaged input power within the limitations of muscle ability,it is recommended to have a larger deflection amplitude in a limited time interval and with no time delay between the to-and-fro strokes.

Direct modeling for computational fluid dynamics

All fluid dynamic equations are valid under their modeling scales, such as the particle mean free path and mean collision time scale of the Boltzmann equation and the hydrodynamic scale of the Navier-Stokes （NS） equations. The current computational fluid dynamics （CFD） focuses on the numerical solution of partial differential equations （PDEs）, and its aim is to get the accurate solution of these governing equations. Under such a CFD practice, it is hard to develop a unified scheme that covers flow physics from kinetic to hydrodynamic scales continuously because there is no such governing equation which could make a smooth transition from the Boltzmann to the NS modeling. The study of fluid dynamics needs to go beyond the traditional numer- ical partial differential equations. The emerging engineering applications, such as air-vehicle design for near-space flight and flow and heat transfer in micro-devices, do require fur- ther expansion of the concept of gas dynamics to a larger domain of physical reality, rather than the traditional dis- tinguishable governing equations. At the current stage, the non-equilibrium flow physics has not yet been well explored or clearly understood due to the lack of appropriate tools. Unfortunately, under the current numerical PDE approach, it is hard to develop such a meaningful tool due to the absence of valid PDEs. In order to construct multiscale and multiphysics simulation methods similar to the modeling process of con- structing the Boltzmann or the NS governing equations, the development of a numerical algorithm should be based on the first principle of physical modeling. In this paper, instead of following the traditional numerical PDE path, we introduce direct modeling as a principle for CFD algorithm develop- ment. Since all computations are conducted in a discretized space with limited cell resolution, the flow physics to be mod- eled has to be done in the mesh size and time step scales. Here, the CFD is more or less a direct construction of dis- crete numerical evolution equations, where the mesh size and time step will play dynamic roles in the modeling process. With the variation of the ratio between mesh size and local particle mean free path, the scheme will capture flow physics from the kinetic particle transport and collision to the hydro- dynamic wave propagation. Based on the direct modeling, a continuous dynamics of flow motion will be captured in the unified gas-kinetic scheme. This scheme can be faithfully used to study the unexplored non-equilibrium flow physics in the transition regime.

旋成体射弹倾斜入水运动仿真

为了研究运动参数和弹头外形对弹体斜入水过程的影响规律,采用气液两相流体积分数和水汽空化模型,通过嵌套网格实现刚体三自由度运动学和动力学耦合,模拟了弹体以80~100 m/s速度倾斜入水开空泡阶段的运动过程。经文献实验验证,入水弹体速度与位移的误差为0~6%和-8%~0,转动角度误差为-6%~0。通过对入水速度和入水角度的多工况模拟研究,发现入水速度增大,弹体轴向冲击载荷增大,最大载荷与速度的平方呈线性关系,弹体速度非线性衰减率大;入水角增大,弹体转动角速率减小,运动稳定性强,速度衰减率不受入水角影响。与圆锥头部弹体相比,采用头部阶梯状修型后的弹体的平均速度衰减率、转动角速率和最大轴向冲击载荷分别降低到66.7%、40%和77.2%,显著提高了运动稳定性。

Assessment of advanced RANS turbulence models for prediction of complex flows in compressors

Reynolds-Averaged Navier-Stokes(RANS) Computational Fluid Dynamics(CFD) has been widely used in compressor design and analysis. However, reasonable prediction of compressor flow and its impact on compressor performance remains challenging. In this study, Menter’s Shear Stress Transport(SST) model and its variants, as well as the ω-based Reynolds stress model(Stress-BSL) are assessed. For a single rotor(Rotor 67), under the peak efficiency operating condition, all studied turbulence models predict its performance with reasonable accuracy;under the off-design conditions, SST with Helicity correction(SST-Helicity) shows superiority in predicting the effect of flow on the spanwise distribution of aerodynamic parameters. For Darmstadt’s 1.5-stage transonic axial compressor, SST-Helicity outperforms SST, SST with the Quadratic Constitutive Relation(SST-QCR) and Stress-BSL in predicting the performance as well as the spanwise distribution of aerodynamic parameters. At the design rotating speed, the stall margin given by SST-Helicity(20.90%) is the closest to the experimental measurement(24.81%), which is more than twice that by SST(8.71%) and 1.5 times that by SST-QCR(14.14%). This paper demonstrates that SSTHelicity model, together with a good quality and sufficiently refined grid, can capture the compressor flow features with reasonable accuracy, which results in a credible prediction of compressor performance and stage matching.

十三点格子Boltzmann模型仿真

格子气和格子Boltzmann方法的迅速发展提供了一类求解流体力学问题的新方法。格子Boltzmann方法在保留了格子气模型优点的同时，克服了它的不足之处。本文讨论了一种三迭加HPP十三点模型，通过选择适当的平衡分布及参数，并用Chapman－Enskog展开和多尺度技术导出了Navier－Stokes方程。在微机上模拟了空腔流的流动问题，并与传统方法的计算结果进行了比较，结果表明该模型能较好的模拟复杂流动现象，并具有较好的工程应用背景。

CAVITATION MODELING WITH A CFD APPROACH

A CFD model of two-dimensional cavity flow is developed using the full Navier-Stokes equations. Based on pseudo-compressibillty and time marching techniques, the cavity surface evolves with the flow field during the time marching process. The cavitation boundary conditions are enforced on the cavity surface. Numerical computations are carried out for a wide range of two-dimensional cavity flows over various hydrofoils, including leading edge cavities and midchord cavities. Extensions to three dimensional nows are, in principle, straight forward.

格子Boltzmann方程模拟高雷诺数三维方腔流

为分析方腔流内部流场的特性和验证格子Boltzmann方法模拟湍流的能力,应用标准Smagorinsky涡粘性模型与多松弛时间格子Boltzmann方程(Multiple Relaxation Time Lattice Boltzmann Equation,MRT-LBE)组合对高雷诺数(Re=10 000)三维方腔流进行数值研究,计算了时间平均量,如速度,均方根速度、雷诺应力以及中心断面(y=W/2)处的流线等高线。模拟结果与已有实验和数值模型结果比较可知,MRT-LBE能够精准地计算剪切驱动方腔内流场的变化。另外,将基于图形处理(graphic processor unit,GPU)的计算统一设备架构(Compute Unified Device Architecture,CUDA)并行技术引入到基于MRT-LBE的Smagorinsky模型以提高计算效率,计算效率提高达200倍。

IMPROVEMENT OF BUBBLE MODEL FOR CAVITATING FLOW SIMULATIONS

In the present research, a bubble dynamics based model for cavitating flow simulations is extended to higher void fraction region for wider range of applications. The present bubble model is based on the so-called Rayleigh-Plesset equation that calculates a temporal bubble radius with the surrounding liquid pressure and is considered to be valid in an area below a certain void fraction. The solution algorithm is modified so that the Rayleigh-Plesset equation is no more solved once the bubble radius （or void fraction） reaches at a certain value till the liquid pressure recovers above the vapor pressure in order to overcome this problem. This procedure is expected to stabilize the numerical calculation. The results of simple two-dimensional flow field are presented compared with the existing bubble model.

High accuracy compact finite difference methods and their applications

Numerical simulation of complex flow fields with multi-scale structures is one of the most important and challenging branches of computational fluid dynamics. From linear analysis and numerical experiments it has been discovered that the higher-order accurate method can give reliable and efficient computational results, as well as better resolution of the complex flow fields with multi-scale structures. Compact finite difference schemes, which feature higher-order accuracy and spectral-like resolution with smaller stencils and easier application of boundary conditions, has attracted more and more interest and attention.

Incompressible Laminar Flow Over a Three-Dimensional Rectangular Cavity

This paper investigates unsteady incompressible flow over cavities. Previous research in incompressible cavity-flow has included flow inside and past a 2-dimensional cavity, and flow inside a 3-dimensional cavity, driven by a moving lid. The present research is focused on incompressible flow past a 3-dimensional open shallow cavity. This involves the complex interaction between the external flow and the re-circulating flow within the cavity. In particular, computation was performed on a 3-dimensional shallow rectangular cavity with a laminar boundary layer at the cavity and a Reynolds number of 5,000 and 10,000, respectively. A CFD approach, based on the unsteady Navier-Stokes equations for 3-dimensional incompressible flow, was used in the study. Typical results of the computation are presented. These results reveal the highly unsteady and complex vortical structures at high Reynolds numbers.

A Multiple Temperature Kinetic Model and its Application to Near Continuum Flows

In an early approach,we proposed a kinetic model with multiple translational temperature[K.Xu,H.Liu and J.Jiang,Phys.Fluids 19,016101(2007)].Based on this model,the stress strain relationship in the Navier-Stokes(NS)equations is replaced by the translational temperature relaxation terms.The kinetic model has been successfully used in both continuum and near continuum flow computations.In this paper,we will further validate the multiple translational temperature kinetic model to flow problems in multiple dimensions.First,a generalized boundary condition incorporating the physics of Knudsen layer will be introduced into the model.Second,the direct particle collision with the wall will be considered as well for the further modification of particle collision time,subsequently a new effective viscosity coefficient will be defined.In order to apply the kinetic model to near continuum flow computations,the gas-kinetic scheme will be constructed.The first example is the pressure-driven Poiseuille flow at Knudsen number 0.1,where the anomalous phenomena between the results of theNS equations and the Direct SimulationMonte Carlo(DSMC)method will be resolved through the multiple temperaturemodel.The so-called Burnett-order effects can be captured as well by algebraic temperature relaxation terms.Another test case is the force-driven Poiseuille flow at various Knudsen numbers.With the effective viscosity approach and the generalized second-order slip boundary condition,the Knudsen minimum can be accurately obtained.The current study indicates that it is useful to use multiple temperature concept to model the non-equilibrium state in near continuum flow limit.In the continuum flow regime,the multiple temperature model will automatically recover the single temperature NS equations due to the efficient energy exchange in different directions.

NUMERICAL SIMULATIONS OF 2D PERIODIC UNSTEADY CAVITATING FLOWS

A two-phase mixture model was established to study unsteady cavitating flows. A local compressible system of equations was derived by introducing a density-pressure function to account for the two-phase flow of water/vapor and the transition from one phase to the other. An algorithm for solving the variable-density Navier-Stokes equations of cavitating flow problem was put forward. The numerical results for unsteady characteristics of cavitating flows on a 2D NACA hydrofoil coincide well with experimental data.

NUMERICAL SIMULATIONS OF CAVITATING FLOWS

A new model, which involves viscous and multi-phase effects, was given to study cavitating flows. A local compressible model was established by introducing a density-pressure function to account for the two-phase flow of water/vapor and the transition from one phase to the other. An algorithm for calculating variable-density N-S equations of cavitating flow problem was put forward. The present method yields reasonable results for both steady and unsteady cavitating flows in 2D and 3D cases. The numerical results of unsteady character of cavitating flows around hydrofoils coincide well with experimental data. It indicates the feasibility to apply this method to a variety of cavitating flows of practical problems.

A coupling VWM/CFD/CSD method for rotor airload prediction

A coupling fluid-structure method with a combination of viscous wake model（VWM）,computational fluid dynamics（CFD） and comprehensive structural dynamics（CSD） modules is developed in this paper for rotor unsteady airload prediction. The hybrid VWM/CFD solver is employed to model the nonlinear aerodynamic phenomena and complicated rotor wake dynamics;the moderate deflection beam theory is implemented to predict the blade structural deformation; the loose coupling strategy based on the ‘delt method＇ is used to couple the fluid and structure solvers.Several cases of Helishape 7A rotor are performed first to investigate the effect of elastic deformation on airloads. Then, two challenging forward flight conditions of UH-60 A helicopter rotor are investigated, and the simulated results of wake geometry, chordwise pressure distribution and sectional normal force show excellent agreement with available test data; a comparison with traditional CFD/CSD method is also presented to illustrate the efficiency of the developed method.

NUMERICAL SIMULATION OF 3-D TURBULENT FLOWS IN A CUT-OFF VALVE AND ANALYSIS OF FLOW CHARACTERISTICS IN PIPE

The 3-D turbulent flows in a valve pipe were described by the incompressibleReynolds-averaged Navier-Stokes equations with an RNG k-ε turbulence model. With the finite volumemethod and a body-fitted coordinate system, the discretised equations were solved by the SIMPLESTalgorithm. The numerical result of a cut-off valve with curved inlet shows the flow characteristicsand the main cause of energy loss when fluid flows through a valve. And then, the boundaries ofvalve were modified in order to reduce the energy loss. The computational results of modified valveshow that the numerical value of turbulent kinetic energy is lower, and that the modified design ofthe 3-D valve boundaries is much better. The analysis of the result also shows that RNG k-εturbulence model can successfully be used to predict the 3-D turbulent separated flows and thesecondary flow inside valve pipes.