Nonstationary dynamics of turbulent axisymmetric jets in a stratified fluid: Part 2. Mechanism of excitation of axisymmetric oscillations in a submerged jet

It was shown based on laboratory experiments in a Large Thermally Stratified Tank (LTST) at the Institute of Applied Physics of the Russian Academy of Sciences that a turbulent axisymmetric jet in a stratified fluid with a sharp density drop (a pycnocline) intensively generates internal waves. An axisymmetric oscillation mode, for which a sufficient condition of stability in the parallel flow approximation is met, served as their source. This paper studies the stability of a nonparallel flow (with self-similar velocity profiles) that simulates a jet flow in the lower part of the pycnocline with respect to the axisymmetric mode. The estimates of the axisymmetric mode near the pycnocline are in agreement with the experimental data. The signs of the self-oscillating mode of the jet were experimentally revealed and the possibility of self-oscillations was theoretically proved: it was shown that the flow in the pycnocline vicinity is absolutely unstable.     

On the onset of the instability of a three-dimensional jet in a stratified fluid

The onset of a three-dimensional jet flow in a stratified fluid is studied with the aid of a direct numerical simulation. An initially cylindrical jet with a Gaussian velocity profile is considered in a fluid with stable linear density stratification. The results indicate that, if an initial small perturbation of the velocity field has a wide spectrum, an exponential growth of the isolated quasi-two-dimensional mode occurs and its spectral maximum is shifted toward smaller wave numbers in comparison with the maximum of the helical mode of the instability of a nonstratified jet. The growth rate is proportional to Ri^0.5, where Ri is the global Richardson number. The onset of the instability leads to the formation of the flow’s vortex structure, which consists of a collection of different-polarity quasi-two-dimensional vortices located in a horizontal plane near the longitudinal axis of the jet. At sufficiently long times (Nt > 100, where N is the buoyancy frequency and t is time), the growth of instability reaches the saturation stage and further fluctuations in velocity and density decay under the effect of viscous diffusion. At this stage, the flow becomes self-similar and the time dependences of the transverse and vertical widths of the jet are consistent with the asymptotic behaviors of integral parameters of the flow that are observed experimentally in the far stratified wake. The results suggest that the onset of the instability of a quasitwo-dimensional mode can play the determining role in the dynamics of flow in the far stratified wake.     

Numerical Simulation of the Vortex-Induced Vibration of A Curved Flexible Riser in Shear Flow

A series of fully three-dimensional(3 D) numerical simulations of flow past a free-to-oscillate curved flexible riser in shear flow were conducted at Reynolds number of 185–1015. The numerical results obtained by the two-way fluid–structure interaction(FSI) simulations are in good agreement with the experimental results reported in the earlier study. It is further found that the frequency transition is out of phase not only in the inline(IL) and crossflow(CF) directions but also along the span direction. The mode competition leads to the non-zero nodes of the rootmean-square(RMS) amplitude and the relatively chaotic trajectories. The fluid–structure interaction is to some extent reflected by the transverse velocity of the ambient fluid, which reaches the maximum value when the riser reaches the equilibrium position. Moreover, the local maximum transverse velocities occur at the peak CF amplitudes, and the values are relatively large when the vibration is in the resonance regions. The 3 D vortex columns are shed nearly parallel to the axis of the curved flexible riser. As the local Reynolds number increases from 0 at the bottom of the riser to the maximum value at the top, the wake undergoes a transition from a two-dimensional structure to a 3 D one. More irregular small-scale vortices appeared at the wake region of the riser, undergoing large amplitude responses.     

Forces on a pitching plate: An experimental and numerical study

A flat plate in pitching motion is considered as a fundamental source of locomotion in the general context of marine propulsion. The experimental as well as numerical investigation is carried out at a relatively small Reynold number of 2000 based on the plate length c and the inflow velocity U_∞. The plate oscillates sinusoidally in pitch about its 1/3 − c axis and the peak to peak amplitude of motion is 20°. The reduced frequency of oscillation k = πfc/U_∞ is considered as a key parameter and it may vary between 1 and 5. The underlying fluid-structure problem is numerically solved using a compact finite-differences Navier–Stokes solution procedure and the numerical solution is compared with Particle Image Velocimetry (PIV) measurements of the flow field around the pitching foil experimental device mounted in a water-channel. A good agreement is found between the numerical and experimental results and the threshold oscillation frequency beyond which the wake exhibits a reverse von Kármán street pattern is determined. Above threshold, the mean velocity in the wake exhibits jet-like profiles with velocity excess, which is generally considered as the footprint of thrust production. The forces exerted on the plate are extracted from the numerical simulation results and it is shown, that reliable predictions for possible thrust production can be inferred from a conventional experimental control volume analysis, only when besides the wake's mean flow the contributions from the velocity fluctuation and the pressure term are taken into account.     

Direct numerical simulation of flow over a slotted cylinder at low Reynolds number

Direct numerical simulation was conducted to investigate the flow past a slotted cylinder at low Reynolds number (Re) of 100. The slotting of cylinder affects the boundary layer separation, vortex formation position, recirculation region length and wake width, which are determined by the type of slit. The streamwise slit (SS1), T-shaped slit (SS3) and Y-shaped slit (SS4) act as passive jets, while the transverse slit (SS2) achieves an alternate self-organized boundary layer suction and blowing. The flow rate in slits fluctuates over time due to the alternate vortex shedding and fluctuating pressure distribution around the cylinder surface. One fluctuation cycle of flow rate is caused by a pair of vortices shedding for SS2, SS3 and SS4, while it is created by each vortex shedding for SS1. The wall shear stress and flow impact on the slit wall partly contribute to the hydrodynamic forces acting on the slotted cylinder. Taking into account the internal wall of slit, the transverse slit plays the best role in suppressing the fluid forces with drag reduction of 1.7% and lift reduction of 17%.     

Surface manifestations of internal waves investigated by a subsurface buoyant Jet: 1. The mechanism of internal-wave generation

In a large test reservoir with artificial temperature stratification at the Institute of Applied Physics, Russian Academy of Sciences, we have performed a major laboratory simulation of the nonstationary dynamics of buoyant turbulent jets generated by wastewater flows from underwater collector diffusers. The interaction of buoyant jets with the pycnocline leads to an active generation of internal waves. An analysis of the dependence of wave amplitude on the control parameter proportional to the rate of liquid flow from the collector diffuser has indicated that this dependence is adequately described by a function that is characteristic for the presence in the Hopf bifurcation system, which occurs for a soft actuation mode of self-oscillations of the globally instable mode. To check the conditions for the actuation of the globally instable mode, we have performed an auxiliary experiment in a small reservoir with a salt stratification formulated similar to the experiment in the big reservoir. Using the particle image velocimetry (PIV) method, we have measured the velocity field in the buoyant jet and constructed the profiles of transverse velocity in several sections. When the jet approaches the pycnocline, a counterflow is generated at the edges. A stability analysis for the resulting profiles of flow velocities performed by the method of normal modes has revealed that, for the jet portions with counterflow, the condition of absolute instability by the Briggs criterion for axisymmetric jet oscillations is satisfied, which testifies to the fact that the globally instable mode is actuated. The estimates for oscillation frequencies of the globally instable mode are well consistent quantitatively with the measured spectrum of jet oscillations.     

Numerical analysis of water exit for a sphere with constant velocity using the lattice Boltzmann method

In this paper, the three-dimensional water exit of a sphere with different vertical velocities is investigated numerically using the lattice Boltzmann method (LBM). In this method, the liquid-gas two-phase flow is simplified as a single-phase free surface flow. To capture the free surface, a mass tracking algorithm is incorporated into the LBM. The gravity as a body force is introduced in the form of calculating the equilibrium distribution with an altered velocity, while the surface tension is neglected. Besides, the employed bounce-back boundary conditions are used for a moving sphere. What’s more, the Wall-Adapting Local Eddy (WALE) viscosity model is employed to capture the turbulent structures of the flow and stabilize the simulation. The accuracy of the numerical results is demonstrated through comparisons with the previous numerical and experimental results in the literature. The results show that the spike height is significantly influenced under the Froude number (Fr) below 4.12 and slightly affected under the Fr varying from 4.12 to 8.24. After the sphere exits water totally, the evolution of the free surface waterfall can be described as two phases and becomes more intense with the Froude number increasing. The non-uniform distribution of velocity results in the breaking of the free surface after the sphere completely exits the water. Moreover, the Reynolds number greatly affects the wake dynamics and hydrodynamics acting on the sphere when it moves beneath the water surface.     

潮流能水轮机仿真及尾流场分析

为了研究潮流能水轮机尾流场的变化规律,本文在水平轴水轮机现有理论基础上,采用计算流体力学技术建立了数值模型,计算了水轮机的功率特性,进行了网格独立性验证,比较了模型中旋转区域不同对结果的影响。仿真结果与试验结果进行了对比分析,验证了数值模型的有效性。研究了全工况下尾流场速度衰减随尖速比和距离变化的规律,结果显示在小尖速比下尾流场速度恢复情况相对大尖速比下较好;靠近水轮机轮毂中心线位置处,衰减相对较大。研究建议水轮机在同等功率表现下尽量选择在小尖速比下工作,水轮机组在实际排列时避免采用成列布置,水轮机设计阶段应综合考虑功率特性和尾流场衰减。本文研究内容可以为潮流能水轮机的研究以及阵列式应用提供参考。     

Numerical Investigation on Severe Slugging in A Catenary Riser

A mathematical model is presented to study the main characteristics of severe slugging in a downward inclined pipeline followed by a catenary riser. In this model, both simplified transient model and phase distribution model are included so that the flow characteristics of each stage for severe slugging can be accurately reproduced, especially for blowout stage. The results show that the flow features of severe slugging can be simulated by the proposed mathematical model. A good agreement between the experimental data and the numerical results is observed. The model can predict the transient fluctuation of many respects, such as the superficial gas velocity at the bottom of the riser and the average velocity at the outlet of the riser.     

Computation of the inertia-dominated forces on horizontal circular cylinders placed in oblique waves and near to a plane bed

Wave-force coefficients of horizontal circular cylinders inclined with respect to the incoming waves, are studied numerically under conditions when the effects of flow separation are insignificant. The mathematical model is set in terms of a boundary-value problem for the velocity potential of the wave, which is formulated under the assumption of the linear diffraction theory, and solved numerically by the boundary element method. The numerical calculations are performed in the vertical plane, assuming uniform water depths in the direction along the axis of the cylinder. A first-order correction to the pressures is introduced to take account of the asymmetry of the velocity field around the cylinder when it is close to the plane bed. The correction procedure is found to be highly effective in computing the transverse forces for small gap ratios. The numerical results show that irrespective of the values of the gap ratio, the in-line forces are always sensitive to the wave directionality. The transverse forces, however, show sensitivity only for the smaller gap ratios. It is also shown that by accounting for the wave directionality effects in the wave kinematics only, the forces could be estimated to a certain extent by using the hydrodynamic force coefficients of inertia and lift corresponding to the normal waves.     

Flow-induced vibration analysis of elastic propellers in a cyclic inflow: An experimental and numerical study

In this paper, the flow-induced vibrations of marine propellers in cyclic inflows are investigated both experimentally and numerically. A Laser-Doppler velocimetry (LDV) system is used to measure the axial flow velocity distributions produced by the seven-cycle wake screen in the water tunnel. A customized underwater slip ring and a single axis accelerometer sealed by silicon sealant are employed to measure the acceleration responses of rotating propeller blade. Numerical simulations of pressure fluctuations on the blades are performed using large eddy simulation (LES), while the forced vibrations of the propeller blades are obtained by a combined finite element and boundary element method. Experimental and numerical results are presented for two model propellers with the same geometries and different flexible properties, which show that the propeller blade vibrates at a frequency which is seven times as large as the axial passing frequency (APF) in the seven-cycle inflow. Moreover, the propeller blades are observed to resonance when the 7 APF excitation frequency is equal to the fundamental frequency of the propellers. The results indicate that both the inflow feature and the modal characteristic of blades contribute to flow-induced vibrations of elastic propellers.     

内波场中水平桩柱波阻的实验研究

分析水平阻力与内波波要素的关系,采用实验室实验的方法,研究了水平桩柱与内波的相互作用,焦点是研究内波波要素与波阻之间的关系。实验中的密度分层采用典型跃层型剖面,而内波是由自行研制的造波机生成。实验结果表明,当内波的频率不变时,水平桩柱所受到的阻力随着内波的振幅增加而增加,它的量值与分层有关。对于强跃层的密度分布,当桩柱处在跃层中时,受到的水平波阻较小,而在跃层之外则受到较大的水平波阻。     

太平洋不同海水层结条件下的内波波致声场起伏研究

基于Argo资料对太平洋海域海水层结进行分类区划,利用内波动力学方法对内波致声起伏进行数值求解,对不同层结状况下的内波致声起伏进行模拟试验。结果表明:垂直方向海水层结的不均匀和跃层的存在,使海洋内波斜压模态受到了歪曲变形。层结峰的个数和深度与声速起伏存在很好的对应关系。有内波的声传播特征总体上与没有内波时的相似。不同层结情况下,声场对内波扰动的响应不一致。     

Tsunami inundation modeling in constructed environments: A physical and numerical comparison of free-surface elevation,velocity, and momentum flux

A laboratory benchmark test for tsunami inundation through an urban waterfront including free surface elevation, velocity, and specific momentum flux is presented and compared with a numerical model (COULWAVE). The physical model was a 1:50 scale idealization of the town Seaside, Oregon, designed to observe the complex tsunami flow around the macro-roughness such as buildings idealized as impermeable, rectangular blocks. Free surface elevation and velocity time series were measured and analyzed at 31 points along 4 transects. Optical measurements of the leading bore front were used in conjunction with the in-situ velocity and free surface measurements to estimate the time-dependent specific momentum flux at each location. The maximum free surface elevation and specific momentum flux sharply decreased from the shoreline to the landward measurement locations, while the cross-shore velocity slowly decreased linearly. The experimental results show that the maximum specific momentum flux is overestimated by 60 to 260%, if it is calculated using the each maximum values of the free surface elevation and cross-shore velocity. Comparisons show that the numerical model is in good agreement with the physical model at most locations when tuned to a friction factor of 0.005. When the friction factor decreased by a factor of 10 (from 0.01 to 0.001), the average maximum free surface elevation increased 15%, and the average cross-shore velocity and specific momentum flux increased 95 and 208%, respectively. This highlights the importance of comparing velocity in the validation and verification process of numerical models of tsunami inundation.     

基于Boussinesq水波模型的聚焦波模拟

基于最高导数为3阶的单层Boussinesq方程,建立了聚焦波的时域波浪计算模型。数值模型求解采用了预报?校正的有限差分法。对于时间差分格式,预报和校正分别采用3阶Adams-Bashforth格式和4阶Adams-Moulton格式。首先,针对不同水深条件下水槽中传播的强非线性波进行模拟,并将数值结果与流函数的数值解析解进行了比较,结果表明无论是波面位移、波面处的水平速度和垂向速度均与解析解符合较好,最大波峰面的速度分布伴随水深的增加与解析解吻合程度变差,非线性速度分布的适用范围与线性解析解适应范围kh<3.5基本一致。其次,对深水聚焦波演化进行了模拟研究,研究中聚焦波的生成采用在边界点累加不同频率线性规则波的方法。应用聚焦波物理模型实验结果验证模型,计算聚焦位置处的波面位移和沿水深的速度分布与实验结果的对比表明,波面位移吻合程度较好,垂向的水平速度分布基本吻合。最后,保持中心频率(周期)不变,数值模拟了周期范围变化下最大聚焦波峰面以及波峰面水平速度的变化趋势,结果表明波峰面值和波峰面水平速度随着周期范围缩小而增大。     

基于致动线模型的错列式两风机尾流场数值模拟

风电场中风机之间存在十分复杂尾流相互干扰现象,尾流相互干扰效应对风机的功率输出、叶片载荷等产生十分显著的影响。采用致动线模型以及计算流体力学方法,研究两风机之间的复杂尾流干扰效应。在保持两风机纵向间距一样的情况下,考虑两风机在不同横向间距下,数值模拟两风机的部分尾流相互干扰现象,分析两风机的气动功率输出特性、尾流速度变化特性、风轮平面附近轴向诱导因子分布特性,尾涡结构以及尾流干扰效应。数值模拟结果表明:在上下游风机在沿着流向方向距离保持不变的情况下,随着横向间距的变化,上下游风机的尾流存在十分复杂的尾流相互干扰效应,对下游风机的气动功率输出以及两风机风电场的整体流场产生了显著的影响。     

Comparison of flow patterns in the near wake of a circular cylinder and a square cylinder placed near a plane wall

The flow patterns in the near wake of a cylinder (either circular or square in shape, D=25 mm) placed in the proximity of a fully developed turbulent boundary layer (thickness δ=0.4D) are investigated experimentally using particle image velocimetry (PIV). The effects of changing the gap height (S) between the cylinder bottom and the wall surface, over the gap ratio range S/D=0.1–1.0, have been investigated. The results show that both the ensemble-averaged and instantaneous flow fields are strongly dependent on S/D. The flow patterns for the two types of cylinders share many similarities with respect to the change in S/D, such as the reduced recirculation length and increased velocity fluctuation in the near wake with increasing S/D, as well as the trend of suppression of vortex shedding at small S/D and onset of vortex shedding at large S/D. However, developments of the shear layers, in terms of wake width, flow curvature, etc., are considerably different for these two types of cylinders. In general, the wake development and momentum exchange for the square cylinder are slower those for the circular cylinder at the same gap ratio. Correspondingly, it is shown that the periodic vortex shedding is delayed and weakened in the case of square cylinder, as compared to that of the circular cylinder at the same S/D.     

Numerical simulation of viscous cavitating flow around a ship propeller

In the present study, cavitation and a ship propeller wake are reported by computed fluid dynamics based on viscous multiphase flow theory. Some recent validation results with a hybrid grid based on unsteady Navier-Stokes (N-S) and bubble dynamics equations are presented to predict velocity, pressure and vapor volume fraction in propeller wake in a uniform inflow. Numerical predictions of sheet cavitation, tip vortex cavitation and hub vortex cavitation are in agreement with the experimental data, same as numerical predictions of longitudinal and transversal evolution of the axial velocity. Blade and shaft rate frequency of propeller is well predicted by the computed results of pressure, and tip vortex is the most important to generate the pressure field within the near wake. The overall results indicate that the present approach is reliable for prediction of cavitation and propeller wake on the condition of uniform inflow.     

Effects of Degrees of Motion Freedom on Free-Fall of A Sphere in Fluid

Free-fall of a sphere in fluid is investigated at a Galileo number of 204 by direct numerical simulations (DNS). We mainly focus on the effects of different degrees-of-freedom (DOFs) of the sphere motion during free-fall. The characteristics of free-fall are compared with those of flow past a fixed sphere. Additional numerical tests are conducted with constraints placed on the translational or rotational DOFs of the sphere motion to analyze different DOFs of sphere motion. The transverse motion contributes significantly to the characteristics of free-fall; it results in the retardation of the vortex shedding, leading to the decrease of the Strouhal number. In addition, the transversal sphere motion exhibits the tendency to promote the sphere rotation. On the contrary, the effects of the sphere rotation and vertical oscillations during free-fall are negligible.