Investigation of drag crisis phenomenon using CFD methods

When fluid flow passes a cylinder, the drag crisis phenomenon occurs between the sub-critical and the super-critical Reynolds numbers. The focus of the present studies was on the numerical prediction of the drag crisis based on CFD methods. In this work, block structured meshes with refined grids near the cylinder surface and in the downstream were employed. Both 2D and 3D simulations were performed using various turbulence models, including the SST k − ω model, the k − ϵ model, the SST with LCTM, the DES model, and the LES model. In the convergence studies, the effects of the grid size, the time step, the first grid size and the aspect ratio (for 3D simulations) on the solutions were examined. The errors due to spatial and time discretizations were quantified according to a V&V procedure. Validation studies were carried out for various Reynolds numbers between Re = 6.31 × 10⁴ and 7.57 × 10⁵. The averaged drag force, the RMS of lift force and the Strouhal number were compared with experimental data. The studies indicated that standard 2D and 3D RANS methods were inadequate to capture the drag crisis phenomenon. The LES method however has the potential to address the problem.     

Large eddy simulations of a circular cylinder at Reynolds numbers surrounding the drag crisis

Large eddy simulations of the flow around a circular cylinder at high Reynolds numbers are reported. Five Reynolds numbers were chosen, such that the drag crisis was captured. A total of 18 cases were computed to investigate the effect of gridding strategy, turbulence modelling, numerical schemes and domain width on the results. It was found that unstructured grids provide better resolution of key flow features, when a ‘reasonable’ grid size is to be maintained.When using coarse grids for large eddy simulation, the effect of turbulence models and numerical schemes becomes more pronounced. The dynamic mixed Smagorinsky model was found to be superior to the Smagorinsky model, since the model coefficient is allowed to dynamically adjust based on the local flow and grid size. A blended upwind-central convection scheme was also found to provide the best accuracy, since a fully central scheme exhibits artificial wiggles, due to dispersion errors, which pollute the solution.Mean drag, fluctuating lift Strouhal number and base pressure are compared to experiments and empirical estimates for Reynolds numbers ranging from 6.31 × 10⁴ to 5.06 × 10⁵. In terms of the drag coefficient, the drag crisis is well captured by the present simulations, although the other integral quantities (rms lift and Strouhal number) show larger discrepancies. For the lowest Reynolds number, the drag is seen to be more sensitive to the domain width than the spanwise grid spacing, while at the higher Reynolds numbers the grid resolution plays a more important role, due to the larger extent of the turbulent boundary layer.     

Numerical simulation of flow around a circular cylinder close to a flat seabed at high Reynolds numbers using a k–ε model

High Reynolds number flows around a circular cylinder close to a flat seabed have been computed using a two-dimensional standard high Reynolds number k–ε turbulence model. The effects of gap to diameter ratio, Reynolds number and flat seabed roughness for a given boundary layer thickness of the inlet flow upstream of the cylinder have been investigated. Hydrodynamic quantities and the resulting bedload transport have been predicted, and the vortex shedding mechanisms have been investigated. Predictions of hydrodynamic quantities around a cylinder located far away from the bed (so that the effect of the bed is negligible) are in satisfactory agreement with published experimental data and numerical results obtained for the flow around an isolated cylinder. Results for lower Reynolds number flows have also been computed for comparison with the high Reynolds number flow results. Overall it appears that the present approach is suitable for design purposes at high Reynolds numbers which are present near the seabed in the real ocean.     

Reynolds number variation in oscillatory boundary layers: Part I. Purely oscillatory motion

A numerical model based upon a low Reynolds number turbulence closure is proposed to study Reynolds number variation in reciprocating oscillatory boundary layers. The model is used to compute the boundary layer for flow regimes ranging from smooth laminar to rough turbulent. Criteria for fully developed turbulence are derived for walls of the smooth and rough types. In particular, a new criterion to identify the rough turbulent regime is determined based on the time-averaged turbulence intensity. The reliability of the present model is assessed through comparisons with detailed experimental data collected by other investigators. The model globally improves upon standard high Reynolds number closures. Variation through the wave cycle of the main flow variables (ensemble-averaged velocity, shear stress, turbulent kinetic energy) is remarkably well-predicted for smooth walls. Predictions are satisfactory for rough walls as well. Yet, the turbulence level in the rough turbulent regime is overpredicted in the vicinity of the bed.     

波浪水槽中振动格栅湍流特征的实验研究

在波浪水槽中采用格栅振动的方式产生湍流,研究振动格栅产生湍流的特征。本文开展了4类实验,调节测量点到格栅平均位置的距离、格栅振动频率、振动冲程,采用ADV测量水体中单点的脉动速度。实验结果显示,湍流强度在一定范围内随离格栅距离的增大而逐渐减小,随着振动频率的增大而呈幂指数增大,随着振动冲程的增大而呈幂指数增大。同时还比较了两个不同格栅产生湍流的不同。结果显示,在波浪水槽中,振动格栅产生湍流的强度还与格栅的长度尺寸有关,这与在水箱中振动格栅产生湍流的特征不同。     

海洋湍流数据实时压缩方法研究

海洋湍流因具有随机性特点,目前多采用统计学理论进行研究,因此需要获取大量的湍流观测数据,这给湍流观测设备的数据存储和传输带来挑战。针对上述问题,本文在分析海洋湍流数据特征的基础上,提出了一种高效实时的无损数据压缩方法。以大量的湍流数据增量信息作为数据源构建霍夫曼编码表,并以此作为湍流压缩和解压的字典,从而提高了压缩效率。通过对历史海洋湍流数据进行压缩实验,证明该方法的湍流数据压缩比低至25%,并且具有压缩速度快、处理器占用率低等特点。     

Numerical simulation of micro-bubble drag reduction using population balance model

The phenomenon of drag reduction by the injection of micro-bubbles into turbulent boundary layer has been investigated using an Eulerian-Eulerian two-fluid model. Multiple-size group (MUSIG) based on population balance models, which resolve a wide range of bubble sizes taking into account the bubble break-up and coalescence have been used for this purpose. The simulated results are compared against the experimental findings of Madavan et al. [1984. Reduction of turbulent skin friction by micro-bubbles. Physics of Fluids 27, 356-363] and also other numerical studies explaining the sophisticated phenomena of drag reduction. For the two Reynolds number cases considered, the buoyancy with the plate on the bottom configuration is investigated, as from the experiments it is seen that buoyancy seem to play a role in the drag reduction. Numerical model employed in the investigation comprises of a micro-bubble laden flow wherein two independent sets of Reynolds averaged Navier-Stokes (RANS) transport equations were used to describe both the phases of the flow. The shear stress transport (SST) turbulence model is used as the turbulent closure for the primary phase and a zero equation turbulence model is used for the micro-bubbles. Change in the mean streamwise velocity profiles, void fraction, turbulence modification and other results are presented and discussed with corresponding change in the gas injection rates. The complex mechanism of drag reduction are scrutinised and explained in context to our numerical findings. Special attentions have been also devoted to divulge the effect of bubble coalescence and break-up caused by random collision and turbulent impact. Numerical results showed good agreement for the skin-friction coefficients against experimental data throughout various air injection rates. The MUSIG model was found to be one of the best candidates to resolve the bubble dynamics in micro-bubble-induced drag reduction problems.     

A generalized coordinate ocean model and a comparison of the bottom boundary layer dynamics in terrain-following and in z-level grids

Sensitivity studies with a new generalized coordinate ocean model are performed in order to compare the behavior of bottom boundary layers (BBLs) when terrain-following (sigma or combined sigma and z-level) or z-level vertical grids are used, but most other numerical aspects remain unchanged. The model uses a second-order turbulence closure scheme that provides surface and BBL mixing and results in a quite realistic climatology and deep water masses after 100 year simulations with a coarse resolution (1° × 1°) basin-scale terrain-following grid. However, with the same turbulence scheme but using a z-level grid, the model was unable to produce dense water masses in the deep ocean. The latter is a known problem for coarse resolution z-level models, unless they include highly empirical BBL schemes.A set of dense water overflow experiments with high-resolution grids (10 and 2.5 km) are used to investigate the influence of model parameters such as horizontal diffusivity, vertical mixing, horizontal resolution, and vertical resolution on the simulation of bottom layers for the different coordinate systems. Increasing horizontal diffusivity causes a thinner BBL and a bottom plume that extends further downslope in a sigma grid, but causes a thicker BBL and limited downslope plume extension in a z-level grid. A major difference in the behavior of the BBL in the two grids is due to the larger vertical mixing generated by the turbulence scheme over the step-like topography in the z-level grid, compared to a smaller vertical mixing and a more stably stratified BBL in the sigma grid. Therefore, the dense plume is able to maintain its water mass better and penetrates farther downslope in the sigma grid than in the z-level grid. Increasing horizontal and vertical resolution in the z-level grid converges the results toward those obtained by a much coarser resolution sigma coordinate grid, but some differences remain due to the basic differences in the mixing process in the BBL.     

高雷诺数下近壁圆柱绕流数值模拟与分析

近壁圆柱绕流问题在海底悬跨管道的研究中具有重要的意义。在绕流阻力、升力以及海底土壤的耦合作用下,海底管道所发生的移位、悬跨等现象对于海底管道的安全运行构成了很大的威胁。正确预测各种绕流条件下管流之间的作用力是保证油气管道安全的首要任务。海底管道在极端海洋环境条件下的管、流相互作用为高雷诺数绕流问题,处于高雷诺数下的绕流模拟比处于低雷诺数下的绕流模拟要复杂很多,它需要更精细的网格以及合适的湍流模型。此文对处于悬跨状态下的海底管道进行数值研究,给出不同间隙比下海流绕流海底管道的流场结构形态,分析了间隙比对绕流阻力和绕流升力的影响,为进一步研究海底悬跨管道的受力和变形提供载荷边界数据。     

Numerical evaluation of passive control of VIV by small control rods

Flow past a circular cylinder with multiple small control rods is studied by numerical simulation for Re_D ranging from 1161.3 to 6387.1. The Reynolds-Averaged-Navier–Stokes (RANS) equations and shear stress transport (SST) k − ω turbulence model are used to calculate the vortex field, while a fourth-order Runge–Kutta method is employed for evaluating the structure dynamics of the cylinder group. Comparisons with experimental results demonstrate the validation of this method. This study is concerned with the vortex induced vibration (VIV) suppression efficacy of small control rods placed around a main cylinder. The effects of control rod number, diameter ratio, spacing ratio and Reynolds number on the hydrodynamics and vibration responses of the main cylinder are investigated. The reduced percents of in-line and cross-flow amplitudes and the increased percents of the whole cross-sectional area of cylinders and the drag coefficient are used to give a comprehensive evaluation. Results of simulation indicate that placing small rods with appropriate number at appropriate locations can achieve good suppression effectiveness at a wide range of Reynolds number. The numerical result for the case with nine control rods, diameter ratio of 0.15 and spacing ratio of 0.6 shows the best suppression effect among the cases investigated in this study.     

Turbulent free-surface flow around a Wigley hull using the slightly compressible flow formulation

The slightly compressible flow formulation is applied to the free-surface, three-dimensional turbulent flow around a Wigley hull. Two turbulence models (large eddy simulation and Baldwin–Lomax) are used and compared. The simulation conditions are the ones for which experimental and numerical results exist. The computational grid is built using an algebraic grid generator with the model fixed in space. The codes use the interface-capturing technique for computing the free-surface displacements and the Beam and Warming scheme for marching in time the numerical model. The results compare well with the experimental data available.     

Numerical solution of a mathematical model for water wavesin large coastal areas

on the evolution equation for water waves,a mathematical model for wave propagation in large mild-slope areas is derived.The model is solved by the finite difference method with the staggered grid system.The computational results are in good agreement with experimental data and show that the model can obtain better results with relatively coarser grids.The model can be used to simulate water wave propagation in large coastal areas and can be efficiently solved without much programming effort.     

Benchmark computations for flows around a stationary cylinder with high Reynolds numbers by RANS-overset grid approach

The aim of this paper is to evaluate the accuracy, stability and efficiency of the overset grid approach coupled with the RANS (Reynolds Averaged Navier-Stokes) model via the benchmark computations of flows around a stationary smooth circular cylinder. Two dimensional numerical results are presented within a wide range of Reynolds numbers (6.31 × 10⁴ ∼ 7.57 × 10⁵) including the critical flow regime. All the simulations are carried out using the RANS solver pimpleFoam provided by OpenFOAM, an open source CFD (Computational Fluid Dynamics) toolkit. Firstly, a grid convergence study is performed. The results of the time-averaged drag and lift force coefficients, root-mean square value of lift force coefficient and Strouhal number (St number) are then compared with the experimental data. The velocity, vorticity fields and pressure distribution are also given. One main conclusion is that the numerical solutions in regard to a fixed cylinderare not deteriorated due to the implementation of the overset grid. Furthermore, it can be an appealing approach to facilitate simulations of Vortex Induced Vibrations (VIV), which involves grid deformation. The present study is a good start to implement the overset grid to solve VIV problems in the future.     

Numerical Investigation of Submarine Hydrodynamics and Flow Field in Steady Turn

This paper presents numerical simulations of viscous flow past a submarine model in steady turn by solving the Reynolds-Averaged Navier?Stokes Equations (RANSE) for incompressible, steady flows. The rotating coordinate system was adopted to deal with the rotation problem. The Coriolis force and centrifugal force due to the computation in a body-fixed rotating frame of reference were treated explicitly and added to momentum equations as source terms. Furthermore, velocities of entrances were coded to give the correct magnitude and direction needed. Two turbulence closure models (TCMs), the RNG model with wall functions and curvature correction and the Shear Stress Transport (SST) model without the use of wall functions, but with curvature correction and low-Re correction were introduced, respectively. Take DARPA SUBOFF model as the test case, a series of drift angle varying between 0° and 16° at a Reynolds number of 6.53×106 undergoing rotating arm test simulations were conducted. The computed forces and moment as a function of drift angle during the steady turn are mostly in close agreement with available experimental data. Though the difference between the pressure coefficients around the hull form was observed, they always show the same trend. It was demonstrated that using sufficiently fine grids and advanced turbulence models will lead to accurate prediction of the flow field as well as the forces and moments on the hull.     

近岸大区域水波数学模型及其数值求解

从水波发展方程出发,导出了大区域缓坡水波数学模型,并采用交错网格系统下的有限差分法对该数学模型进行了数值求解,计算结果表明该数学模型在粗网格下也能得到与实验结果比较一致的结果,从而表明该模型可用于较大区域的水波问题.该模型具有编程简单、求解比较快速、经济的优点.     

Wave deformation and vortex generation in water waves propagating over a submerged dike

The Navier–Stokes equations and the exact free surface boundary conditions are solved to simulate wave deformation and vortex generation in water waves propagating over a submerged dike. Incident waves are generated by a piston-type wavemaker set up in the computational domain. Numerical results are compared with experimental data in order to confirm the validity of the numerical model. The fast Fourier transform and a wave resolution technique are applied to decompose the transformed waves and the higher harmonics. Effects of different parameters on wave transformation and vortex generation are studied systematically. These parameters include the Ursell number, the Keulegan–Carpenter number, the water depth ratio, the Reynolds number, the length aspect ratio of the dike, and the type of dike.     

Experimental investigation of the hydrodynamics in pockmarks using particle tracking velocimetry

Water tank experiments were performed in order to investigate the behaviour of currents in pockmarks. A particle-seeded flow was visualised and quantified with the aid of the particle tracking velocimetry technique. The employed analogue pockmark is a 1:100 idealised scale model of a natural pockmark, while the highest Reynolds number in the experiments was one order of magnitude smaller than in nature. Interaction of the flow with the pockmark geometry resulted in an upwelling current downstream of the pockmark centre, along with enhanced water turbulence in the depression. Scaling-up the experimental measurements, it is found that the upwelling would be capable of preventing the settling of particles as large as very fine sand. Furthermore, the increased turbulence would support the suspended fine material, which can thus be transported away before settling. The net effect for a variable-direction near-bed current over long periods of time would be to winnow the settling sediments and reduce the sedimentation rate in pockmarks. These mechanisms may be responsible for the observed lack of sediment infill and the typical presence of relatively coarser sediments inside pockmarks compared to the surrounding bed. In contrast, sediments transported as bedload are likely to be deposited in pockmarks because of the weakening of near-bed currents as well as lateral flow convergence associated with the upwelling. Bedload, however, may not be the dominant mode of sediment transport in areas covered by cohesive sediments, where pockmarks are found.     

Hydrodynamics of oil jets without and with dispersant: Experimental and numerical characterization

In this paper, we present the analysis of an underwater horizontal oil jet experimental measurement and Computational Fluid Dynamics (CFD) using the Reynolds Averaged Navier Stokes (RANS) equations. Two oil subsurface releases were conducted: one with crude oil and another with crude oil premixed with dispersant at the dispersant to oil ratio (DOR) of 1:20. The jet profile was captured by a camera at moderate resolution, and the instantaneous velocity was measured by a Vectrino Profiler. The velocity components, turbulence kinetic energy, and turbulence dissipation rate from the experiment agreed well with those from the CFD simulation using the k-epsilon turbulence model. The spread angle of the jet was found to be around 21° and 24° from the experiment measurement, for oil without dispersant and oil with dispersant, respectively. The latter is close to the angle of miscible jets at 23°. The jet profile of oil with dispersant had a smaller buoyancy than that without dispersant, which is probably due to the large water entrainment for the oil with dispersant jet. The cross sections of the jet for both cases gradually became flattened with distance, as the plume turned upward.     

A numerical study of swash flows generated by bores

The dynamic processes of bore propagation over a uniform slope are studied numerically using a 2-D Reynolds Averaged Navier–Stokes (RANS) solver, coupled to a non-linear k − ε turbulence closure and a volume of fluid (VOF) method. The dam-break mechanism is used to generate bores in a constant depth region. Present numerical results for the ensemble-averaged flow field are compared with existing experimental data as well as theoretical and numerical results based on non-linear shallow water (NSW) equations. Reasonable agreement between the present numerical solutions and experimental data is observed. Using the numerical results, small-scale bore behaviors and flow features, such as the bore collapse process near the still-water shoreline, the ‘mini-collapse’ during the runup phase and the ‘back-wash bore’ in the down-rush phase, are described. In the case of a strong bore, the evolution of the averaged turbulence kinetic energy (TKE) over the swash zone consists of two phases: in the region near the still-water shoreline, the production and the dissipation of TKE are roughly in balance; in the region farther landwards of the still-water shoreline, the TKE decay rate is very close to that of homogeneous grid turbulence. On the other hand, in the case of a weak bore, the bore collapse generated turbulence is confined near the bottom boundary layer and the TKE decays at a much slower rate.     

Reynolds and Mass-Damping Effect on Prediction of the Peak Amplitude of A Freely Vibrating Cylinder

The Reynolds effect and mass-damping effect on the peak amplitude of a freely vibrating cylinder is studied by using forced oscillating data from Gopalkrishnan＇ s research in 1993, in which all experimental cases were carried out at a fixed Reynolds and the tested cylinder was recognized as a body that had no mass and damping. However, the Reynolds and roass-damping are the very important parameters for the peak amplitude of a freely vibrating cylinder. In the present study, a function F is introduced to connect the forced oscillation and free vibration. Firstly the peak amplitude AG^＊ can be obtained from the function F using forced oscillation data of Gopalkrishnan＇ s experimental at Re = 10^4, and then the Reynolds effect is taken into account in the function f（Re）, while the mass-damping effect is considered in the function K（ α ）, where a is the mass-damping ratio. So the peak amplitude of a freely vibrating cylinder can be predicted by the expression： A ^＊ = K（ α ）f（ Re ）AG^＊ . It is found that the peak transverse amplitudes predicted by the above equation agree very well with many recent experimental data under both high and low Reynolds conditions while roass-damping varies. Furthermore, it is seen that the Reynolds number does have a great effect on the peak amplitude of a freely vibrating cylinder. The present idea in this paper can be applied as an update in the empirical models that also use forced oscillation data to predict the vortex induced vibration （VIV） response of a long riser in the frequency domain.