Scale effects on propeller cavitating hydrodynamic and hydroacoustic performances with non-uniform inflow

Considering the lack of theoretical models and ingredients necessary to explain the scaling of the results of propeller cavitation inception and cavitating hydroacoustics from model tests to full scale currently, and the insufficient reflection of the nuclei effects on cavitation in the numerical methods, the cavitating hydrodynamics and cavitation low frequency noise spectrum of three geometrically similar 7-bladed highly skewed propellers with non-uniform inflow are addressed. In this process, a numerical bridge from the multiphase viscous simulation of propeller cavitation hydrodynamics to its hydro-acoustics is built, and the scale effects on performances and the applicability of exist scaling law are analyzed. The effects of non-condensable gas(NCG) on cavitation inception are involved explicitly in the improved Sauer’s cavitation model, and the cavity volume acceleration related to its characteristic length is used to produce the noise spectrum. Results show that, with the same cavitation number, the cavity extension on propeller blades increases with diameter associated with an earlier shift of the beginning point of thrust decline induced by cavitation, while the three decline slopes of thrust breakdown curves are found to be nearly the same. The power of the scaling law based on local Reynolds number around 0.9R section is determined as 0.11. As for the smallest propeller, the predominant tonal noise is located at blade passing frequency(BPF), whereas 2BPF for the middle and both 2BPF and 3BPF for the largest, which shows the cavitating line spectrum is fully related to the interaction between non-uniform inflow and fluctuated cavity volume. The predicted spectrum level exceedance from the middle to the large propeller is 6.65 dB at BPF and 5.94 dB at 2BPF. Since it just differs less than 2 dB to the increment obtained by empirical scaling law, it is inferred that the scale effects on them are acceptable with a sufficient model scale, and so do the scaling law. The numerical implementation of cavitating hydrodynamics and hydro-acoustics prediction of propeller in big scale in wake has been completed.     

Numerical Prediction of Tip Vortex Cavitation for Marine Propellers in Non-uniform Wake

Tip vortex cavitation is the first type of cavitation to take place around most marine propellers.But the numerical prediction of tip vortex cavitation is one of the challenges for propeller wake because of turbulence dissipation during the numerical simulation.Several parameters of computational mesh and numerical algorithm are tested by mean of the predicted length of tip vortex cavtiation to validate a developed method.The predicted length of tip vortex cavtiation is on the increase about 0.4propeller diameters using the developed numerical method.The predicted length of tip vortex cavtiation by RNG k–e model is about 3 times of that by SST k–x model.Therefore,based on the validation of the present approach,the cavitating flows generated by two rotating propellers under a non-uniform inflow are calculated further.The distributions of axial velocity,total pressure and vapor volume fraction in the transversal planes across tip vortex region are shown to be useful in analyzing the feature of the cavitating flow.The strongest kernel of tip vortex cavitation is not at the position most close to blade tip but slightly far away from the region.During the growth of tip vortex cavitation extension,it appears short and thick,and then it becomes long and thin.The pressure fluctuations at the positions inside tip vortex region also validates the conclusion.A key finding of the study is that the grids constructed especially for tip vortex flows by using separated computational domain is capable of decreasing the turbulence dissipation and correctly capturing the feature of propeller tip vortex cavitation under uniform and non-uniform inflows.The turbulence model and advanced grids is important to predict tip vortex cavitation.     

Numerical investigation of three-dimensional cavitation evolution and excited pressure fluctuations around a twisted hydrofoil

Unsteady cavitating turbulent flow around a twisted hydrofoil was analyzed to illustrate the physical mechanism of the cavitygenerated pressure fluctuations. The numerical simulations of cavitating flow were based on the Partially-Averaged Navier-Stokes (PANS) method and a mass transfer cavitation model. The validity of PANS model has been evaluated and confirmed in cavitation simulations by present authors using three different cases, 2D hydrofoil (Ji et al. 2012 [37]), 3D hydrofoil (Ji et al. 2013 [31]) and marine propeller (Ji et al. 2012 [38]), which shows that the PANS model with f _k = 0.2 and f _ε = 1 can obtain more accurate estimates of unsteady cavitating flows with large-scale fluctuations at a reasonable cost. In present paper we intended to shed light on the physical process responsible for the pressure fluctuations excited by cavitation. The cavity volume was analyzed to illustrate the relationship between the cavitation evolution and the pressure fluctuations. The results show that the cavity volumetric acceleration curve tracks remarkably well with the main features of the time-dependent pressure fluctuations except for the high frequency component. Thus, the cavity volumetric acceleration is the main source of the excited pressure fluctuations by cavitation. It is noted that the cavitation induced pressure fluctuations are transmitted along the suction surface of the hydrofoil and are synchronized with those on the pressure surface at the midplane of the twisted hydrofoil. Further, the pressure fluctuations on the pressure surface decrease towards the center from both the leading and trailing edges of the hydrofoil, with a minimum at 60% chord length from the leading edge.     

改进空化模型和修正湍流模型在螺旋桨空化模拟中的评估分析

为评估改进Sauer空化模型和修正切应力输运湍流模型联合使用时在螺旋桨空化模拟中的效果,以及"当σ>σi时,叶梢截面压力系数分布相对不再改变"的空化初生判定准则的适用性,以E779A螺旋桨为对象,对轻度(Ac/A0<0.1)、中度(0.1≤Ac/A0<0.25)和重度(0.25≤Ac/A0<0.5)空化程度下的桨叶空化形态、空化面积、叶截面压力系数分布、推力和力矩崩溃性能曲线以及初生空化数进行校验和分析。结果表明,在轻度空化下模拟空化面积较试验值略小;中度空化下与试验值吻合很好,模拟精度明显高于同类文献;在重度空化下因包含了泡空化面积而较试验值要大。在设计和非设计进速系数下,预报因空化引起的推力下降起始点均与试验值吻合很好,但推力衰减指数较试验值要大。应用空化初生判定准则得到J=0.77工况下初生空化数为3.25,较试验值仅偏差0.6%。由此表明,所采用的数值模型对于螺旋桨轻度和中度空化程度下的空化性能模拟具有较高的精度,所提出的空化初生判定准则是可信而且适用的。应用该准则,在求取0.88R(低侧斜桨)或0.7R(大侧斜桨)截面的初生空化数后,可较准确地预报螺旋桨空化斗图谱,进而预报舰艇空化初始航速。     

半浸式螺旋桨水动力性能的数值模拟研究

针对半浸式螺旋桨的水动力性能问题,应用CFD方法对其流场进行了数值模拟研究,并把结果与实验进行比较。通过求解雷诺平均方程(RANS)来模拟流场,采用SST k-ω湍流模型来计算RANS方程中的雷诺应力。利用Fluent中的明渠流动(Open Channel Flow)功能模拟空泡水筒中的气液两相流动,采用VOF方法捕捉自由液面。应用滑移网格法完成搅拌桨的转动,实现了对一个五叶右旋半浸式螺旋桨的数值模拟。研究结果表明,桨的尾流场形态与实验结果吻合地较好,证明了CFD方法预测半浸式螺旋桨性能的有效性。在较低浸入深度时,数值模拟可以很好地预测半浸式螺旋桨的性能。随着浸入深度的增加,推力系数和效率的预测结果基本准确,扭矩系数的预测结果有一定偏差。从数值计算结果中,可以获得宏观力的脉动曲线和完全入水桨叶的压力分布,并且可以对桨叶出水和入水过程进行详细的研究。     

离心泵蜗壳内非定常流动特性的数值模拟及分析

基于RNG k-ε湍流模型和Zwart-Gerber-Belamri空化模型,对离心泵内部非空化和空化工况下的非定常流动特性进行数值模拟,分析空化模型中凝结项经验系数对数值模拟结果的影响,并根据试验结果修正离心泵空化流动数值模拟中凝结项经验系数;数值模拟得到的离心泵扬程随有效空化余量的变化曲线与试验结果吻合较好,验证数值计算模型和方法的准确性和可靠性。数值模拟结果表明：离心泵非定常流动中,非空化、临界空化和充分发展空化工况下,蜗壳内监测点的压力脉动主频均为叶片通过频率;空化对离心泵蜗壳内压力脉动的影响较大,非空化时压力脉动最大幅值在蜗舌处,空化时压力脉动最大幅值在第1断面附近,其原因是离心泵出现空化时第1断面处旋涡强度增强,且随时间变化剧烈,对流动产生强烈扰动。     

绕水翼空化流场的数值模拟与试验研究

采用试验研究与数值模拟相结合的方法研究绕水翼ys930的非定常空化流场结构,试验采用高速数码拍摄技术观察在10°攻角下的片状和云状空化随时间的结构变化;数值模拟针对应用较多的RNG k-二方程湍流模型做适当修正,分析片状空化及云状空化时的非定常空化流场结构、流动特性及空泡演化过程。结果表明,数值模拟得到的水翼空化流动现象和试验观察到的结果基本一致,验证计算模型和数值方法的可靠性;在片状空化阶段,空泡长度变化不明显,空穴尾部边界存在小幅度波动,空穴总体相对比较稳定;云状空化阶段,空穴分为两部分:一部分为空泡主体,稳定地附着在水翼吸力面上,随时间推移逐渐长大,达到最大空泡长度后出现回缩;另一部分为空泡附体,为周期性非定常汽液两相运动区域。云状空泡的形成和发展过程均伴有压力的波动,在一个空泡生长周期内,压力面压力系数几乎不受空泡变化的影响,吸力面压力系数在空化数的负值附近小幅度波动。     

舰船螺旋桨非定常粘性流场与空化数值预报

基于粘性流理论,在均匀入流条件下,利用非结构网格和滑动网格技术数值求解非定常雷诺平均方程（URANS）来研究螺旋桨随边至下游两倍螺旋桨直径区域的尾流场压力和蒸汽体积分数等物理量。计算结果显示,螺旋桨空泡数值计算结果与INSEAN的实验观察结果基本一致,尾流场物理量的计算结果很好地预报了螺旋桨叶频和轴频等参数,梢涡对近尾流场的压力形成具有重要作用。     

柴油机气缸套冷却水空化流的三维数值模拟

基于计算流体动力学(Computational fluid dynamics,CFD)方法应用动网格技术采用两相混合流体完整空化湍流模型,对某型柴油机气缸套主推侧的冷却水空化流进行非定常数值模拟。计算结果揭示缸套空蚀发生机理和冷却水流场特性变化,预测缸套冷却水的空化部位和程度。与缸套空蚀的统计结果对比,建立的数学模型是可靠的。结果表明,缸套附近流场的绝对压力和气相体积分数均具有周期性变化特性,且与缸套的振动周期一致。缸套附近冷却水空化流的流场特性不均匀。贴近变形最大的缸套壁区(缸套壁的中上区域)处流场压力和气相体积分数波动剧烈。此局部流场脉冲压力峰值达到约350 kPa,气相体积分数在5.8%～0.4%波动。较强脉冲压力的作用导致此壁区空蚀严重。振动频率和振幅分别增大30%,变形最大壁区附近流场压力峰值分别增加55%和15%。进口流速和流向对冷却水空化特性有一定影响,最大变形壁区气相体积分数峰值随流场平均流速的增大而增加。缸套振动的加速度是影响冷却水空化流流场特性的关键因素。     

Mixed-lubrication analysis of marine stern tube bearing considering bending deformation of stern shaft and cavitation

A mixed-lubrication model has been developed to study tribological characteristics of a marine stern tube bearing. The finite difference method is employed to obtain numerical solutions of the Reynolds equation using combined Newton–Raphson and iterative relaxation methods. The differential equation of deflection curve of the propeller shaft is used to describe the bending deformation of propeller shaft. The displacement superposition method is used to solve the differential equation of deflection. The influences of cavitation and different boundary conditions, the Reynolds boundary condition and Jacobsson–Floberg and Olsson (JFO) boundary condition, as well as the bending deformation of shaft, on the Stribeck Curves are discussed in this paper.     

Numerical calculation of the viscous flow around a rotating marine propeller

Reliable and accurate prediction of the viscous flow around a marine propeller operating at the stern is of practical importance for design and performance prediction of propellers. A computer code was developed in the present study for the full viscous flow simulation around the marine propeller at the stern and its performance was investigated using the available data. The continuity and Navier-Stokes equations with a standardk-ε model in the rotating coordinate fixed on the propeller were numerically solved using FVM. The predicted profiles of circumferentially averaged velocity and turbulent kinetic energy were in accordance with the measured data at the downstream of the propeller, while there were significant discrepancies in the near wake. The value of velocity was small in a core associated with the formation of the tip vortex and the location of maximum axial velocity on the suction side of the blade was observed in the simulation. The flow structure observed in the experiment was confirmed in the simulation, however not quantitatively. The blade wake was diffused more in comparison with the measured one.     

The effect of skew angle on the axial pressure distribution between flexible rubber-covered rollers

This work presents a simplified means to determine the axial contact pressure distribution between two pinched, flexible, rubber-clad, cylindrical rolls that are aligned with axes skewed. Of particular interest is the effect of the skew angle on the axial contact pressure distribution. A finite element model is used with beam elements to model the bending of the roll cores and spring elements to model the load-indentation relationship between the rubber coatings. Numerical results of contact pressure and contact width vs axial location are presented for varying amounts of skew, and these are compared with experimental results.     

Experimental investigation of inception cavitating flows around axisymmetric bodies with different headforms

Experiments have been performed to study the inception cavitation phenomena in the separated flows adjacent to two axisymmetric bodies whose forebodies are blunt and conical, respectively. A high-speed video camera was used to visualize the dynamic process of incipient cavitation, and the PIV (Particle imaging velocimetry) technology was applied to measure the velocity field, the vorticity and turbulence fluctuations under non-cavitation and inception cavitation conditions. Observations suggest that incipient cavities around the two axisymmetric bodies have the similar onset appearance but different development patterns and cycles with different inception cavitation index. Also, it is found that incipient cavities are always located within the separated vortex upstream the reattachment point during the whole dynamic process, and the scale of separation vortex greatly influences the positions where incipient cavities generate and collapse. Measures of the turbulence fields show that the distribution of vorticity can be changed by unsteady incipient cavities, and inception cavitation causes slight uniformity of velocity in shear layer and conspicuous increase of turbulent fluctuations. Compared to that of the conical headform, inception cavitation around the blunt headform presents more vortical traits and turbulence fluctuations.

     

Numerical investigations on cavitating flows with thermodynamic effects in a diffuser-type centrifugal pump

A cavitation model with thermodynamic effects for cavitating flows in a diffuser-type centrifugal pump is developed based on the bubble two-phase flow model. The proposed cavitation model includes mass, momentum, and energy transportations according to the thermodynamic mechanism of cavitation. Numerical simulations are conducted inside the entire passage of the centrifugal pump by using the proposed cavitation model and the renormalization group-based k-? turbulent model coupled with the energy transportation equation. By using the commercial computational fluid dynamics software FLUENT 6.3, we have shown that the predicted performance characteristics of the pump, as well as the pressure, vapor, and density distributions in the impeller, agree well with that calculated by the full cavitation model. Simulation results show that cavitation initially occurs slightly behind the inlet of the blade suction surface, i.e., the area with maximum vapor concentration and minimum pressure. The predicted temperature field shows that the reduction in temperature restrains the growth of cavitating bubbles. Therefore, the thermodynamic effect should be treated as a necessary factor in cavitation models. Comparison results validate the efficiency and accuracy of the numerical technique in simulating cavitation flows in centrifugal pumps.     

Numerical simulation of pressure fluctuations in a large Francis turbine runner

The pressure fluctuation caused by unsteady flow in runner is one of the main reasons of vibration for a large Francis hydraulic turbine. It directly affects the steady operation of the hydraulic turbine unit. The existing research of the pressure fluctuation in hydraulic turbine mainly focuses on the unsteady flow in draft tube. Accurate distribution of pressure fluctuations inside a runner is not very clear. In this paper, the numerical method for predicting the pressure fluctuations in runner is investigated and the numerical simulation is performed for a large Francis hydraulic turbine. It is proved that the combination of shear-stress transport(SST) k-w turbulence model and pressure-implicit with splitting of operators(PISO) algorithm could give more reliable prediction of pressure fluctuations in runner. The frequencies of pressure fluctuations in runner are affected by the flow in guide vane and the flow in draft tube. The first dominant frequency is significantly determined by the flow in draft tube, especially at part load condition. This frequency is approximately equal to one-third of the runner rotating frequency. The evident second dominant frequency is exactly equal to the guide vane passing frequency. The peak-to-peak amplitudes of pressure fluctuations in runner at small guide vane open angle are larger than that at large open angle at the same operating head. The amplitudes at points on blade pressure surface are generally greater than that on suction surface. The research results could be used to direct the hydraulic design and operation stability improvement of a large Francis hydraulic turbine.     

Study on unsteady tip leakage vortex cavitation in an axial-flow pump using an improved filter-based model

The aim of the present investigation is to simulate and analyze the tip leakage flow structure and instantaneous evolution of tip vortex cavitation in a scaled axial-flow pump model. The improved filter-based turbulence model based on the density correction and a homogeneous cavitation model were used for implementing this work. The results show that when entering into the tip clearance, the backward flow separates from the blade tip near the pressure side, resulting in the generation of a corner vortex with high magnitude of turbulence kinetic energy. Then, at the exit of the tip clearance, the leakage jets would re-attach on the blade tip wall. Moreover, the maximum swirling strength method was employed in identifying the TLV core and a counter-rotating induced vortex near the end-wall successfully. The three-dimensional cavitation patterns and in-plain cavitation structures obtained by the improved numerical method agree well with the experimental results. At the sheet cavitation trailing edge in the tip region, the perpendicular cavitation cloud induced by TLV sheds and migrates toward the pressure side of the neighboring blade. During its migration, it breaks down abruptly and generates a large number of small-scale cavities, leading to severe degradation of the pump performance, which is similar with the phenomenon observed by Tan et al. [35].     

The cavitation behavior with short length blades in centrifugal pump

A CFD code with 2-D cascade model was developed to predict the cavitation behavior around the impeller blades of impeller in a centrifugal pump. The governing equations are the two-phase Reynolds Averaged Navier-Stokes equations in a homogeneous form in which both liquid and vapor phases are treated as incompressible fluid. To close the model, a standard k-ɛ turbulence model is introduced. And the mass transfer rates between liquid and vapor phases are implemented as well. The validations are carried out by comparing with reference data in impeller of a centrifugal pump impeller. The cavitation characteristics of current centrifugal pumps is tested at an ondesign point (V=8 m/s) and two off-design points (V=20 m/s and V=30 m/s), respectively. The criteria of cavitation and flow instability around blades are presented. The results show that the current centrifugal pump can safely operate without cavitation at on-design point. Also, the simulation shows cavitation develops inhomogeneously among the blades at off-design points. Moreover, the effects of additional blades in the impeller are studied as well. From the numerical results, it is expected that a half-length blade is the optimum configuration as additional blades in cavitation point of view.     

Numerical calculation of thermal effect on cavitation in cryogenic fluids

A key design issue related to the turbopump of the rocket engine is that cavitation occurs in cryogenic fluids when the fluid pressure is lower than the vapor pressure at a local thermodynamic state. Cavitation in cryogenic fluids generates substantial thermal effects and strong variations in fluid properties, which in turn alter the cavity characteristics. To date, fewer investigate the thermal effect on cavitation in cryogenic fluids clearly by the numerical methods due to the difficulty of the heat transfer in the phase change process. In order to study the thermal effect on cavitation in cryogenic fluid, computations are conducted around a 2D quarter caliber hydrofoil in liquid nitrogen and hydrogen respectively by implementing modified Merkle cavitation model, which accounts for the energy balance and variable thermodynamic properties of the fluid. The numerical results show that with the thermal effect, the vapour content in constant location decreases, the cavity becomes more porous and the interface becomes less distinct which shows increased spreading while getting shorter in length. In the cavity region, the temperature around the cavity depresses due to absorb the evaporation latent heat and the saturation pressure drops. When the vapour volume fraction is higher, the temperature depression and pressure depression becomes larger. It is also observed that a slight temperature rise is found above the reference fluid temperature at the cavity rear end attributed to the release of latent heat during the condensation process. When the fluid is operating close to its critical temperature, thermal effects on cavitation are more obviously in both the liquid nitrogen and hydrogen. The thermal effect on cavitation in liquid hydrogen is more distinctly compared with that in liquid nitrogen due to the density ratio, vapour pressure and other variable properties of the fluid. The investigation provides aid for the design of the cryogenic pump of the liquid rocket.     

Assessment of a turbulence model for numerical predictions of sheet-cavitating flows in centrifugal pumps?

Various approaches have been developed for numerical predictions of unsteady cavitating turbulent flows. To verify the influence of a turbulence model on the simulation of unsteady attached sheet-cavitating flows in centrifugal pumps, two modified RNG k-? models (DCM and FBM) are implemented in ANSYS-CFX 13.0 by second development technology, so as to compare three widespread turbulence models in the same platform. The simulation has been executed and compared to experimental results for three different flow coefficients. For four operating conditions, qualitative comparisons are carried out between experimental and numerical cavitation patterns, which are visualized by a high-speed camera and depicted as isosurfaces of vapor volume fraction α _v = 0.1, respectively. The comparison results indicate that, for the development of the sheet attached cavities on the suction side of the impeller blades, the numerical results with different turbulence models are very close to each other and overestimate the experiment ones slightly. However, compared to the cavitation performance experimental curves, the numerical results have obvious difference: the prediction precision with the FBM is higher than the other two turbulence models. In addition, the loading distributions around the blade section at midspan are analyzed in detail. The research results suggest that, for numerical prediction of cavitating flows in centrifugal pumps, the turbulence model has little influence on the development of cavitation bubbles, but the advanced turbulence model can significantly improve the prediction precision of head coefficients and critical cavitation numbers.     

红外探测中潜艇冷热尾流的传热传质特性

本文采用有限体积法建立了1/72龙鲨Ⅱ号核潜艇的三维计算模型,结合动参考系、用户自定义函数和物性多项式函数等实现了高速旋转螺旋桨和海水温度密度分层的仿真。基于该模型,探讨了螺旋桨高速旋转、海水温度密度分层和高温热尾流喷射等因素对潜艇冷热尾流传热传质特性的影响,所得结论如下:高速旋转螺旋桨促使热尾流后向延迟距离增大、海表温差减小,忽略旋转时海表温差的绝对误差和相对误差分别为3.23mK和52.7%;水下航行潜艇扰动温度密度分层海水浮升形成冷尾流温差信号,与温度密度均匀海水相比,海表温变区域显著增大、尾流温差由6.13mK增大到84mK;通过海表上游冷尾流特征判断是否存在水下航行潜艇,若存在,再结合海表下游热尾流特征实现潜艇位置的精确反演。上述结论可为优化潜艇冷热尾流的数值仿真精度提供参考与借鉴。