Applications of URANS on predicting unsteady turbulent separated flows

Accurate prediction of unsteady separated turbulent flows remains one of the toughest tasks and a practi cal challenge for turbulence modeling. In this paper, a 2D flow past a circular cylinder at Reynolds number 3,900 is numerically investigated by using the technique of unsteady RANS （URANS）. Some typical linear and nonlinear eddy viscosity turbulence models （LEVM and NLEVM） and a quadratic explicit algebraic stress model （EASM） are evaluated. Numerical results have shown that a high-performance cubic NLEVM, such as CLS, are superior to the others in simulating turbulent separated flows with unsteady vortex shedding.     

Nonlinear turbulence models for predicting strong curvature effects

Prediction of the characteristics of turbulent flows with strong streamline curvature, such as flows in turbomachines, curved channel flows, flows around airfoils and buildings, is of great importance in engineering applications and poses a very practical challenge for turbulence modeling. In this paper, we analyze qualitatively the curvature effects on the structure of turbulence and conduct numerical simulations of a turbulent Uduct flow with a number of turbulence models in order to assess their overall performance. The models evaluated in this work are some typical linear eddy viscosity turbulence models, nonlinear eddy viscosity turbulence models （NLEVM） （quadratic and cubic）, a quadratic explicit algebraic stress model （EASM） and a Reynolds stress model （RSM） developed based on the second-moment closure. Our numerical results show that a cubic NLEVM that performs considerably well in other benchmark turbulent flows, such as the Craft, Launder and Suga model and the Huang and Ma model, is able to capture the major features of the highly curved turbulent U-duct flow, including the damping of turbulence near the convex wall, the enhancement of turbulence near the concave wall, and the subsequent turbulent flow separation. The predictions of the cubic models are quite close to that of the RSM, in relatively good agreement with the experimental data, which suggests that these models may be employed to simulate the turbulent curved flows in engineering applications.     

空化、超空化流动的数值模拟方法研究

基于结构化网格，运用可压缩流N—S方程及k-ε湍流模型对流场进行求解，在低压区域引入一种基于混合密度函数的空化模型对轴对称体的空化、超空化流动进行了数值模拟．通过将半球圆柱的计算结果与实验数据和前人的计算结果进行对比，验证了所发展的数值方法的可靠性．最后，采用非定常的数值方法，研究了钝头体射弹的空化、超空化流动特性，并模拟了其超空泡的发展过程．     

基于动力学模态分解法的绕水翼非定常空化流场演化分析

空化是船舶和水下航行体推进器中经常发生的一种特殊流动现象,它具有强烈的非定常性,空化的发生往往会影响推进器的水动力性能和效率. 为探究绕水翼非定常空化流场结构,本文基于 Schnerr-Sauer 空化模型和 SST $k$-$\omega $ 湍流模型,开展绕二维水翼非定常空化流动数值预报与流场结构分析. 通过将数值预报的空泡形态演变和压力数据与试验结果对比,验证了建立的数值方法的有效性. 并基于动力学模态分解方法对空化流场的速度场进行模态分解,分析了各个模态的流场特征. 结果表明,第一阶模态对应频率为 0,代表平均流场;第二阶模态对应频率约为空泡脱落频率,揭示了空泡在水翼前缘周期性地生长与脱落,第三阶模态对应频率约为第二阶模态的 2 倍,揭示了两个大尺度旋涡在水翼后方存在融合行为. 第四阶模态对应频率约为第二阶模态的 3 倍,具有更高的频率,表征流场中存在一些小尺度旋涡的融合行为. 最后对不同空化数下的空化流场进行了模态分解分析,发现脱落空泡的旋涡结构随着空化数的减小而增大,第二阶模态频率随着空化数的减小而减小.      

ANALYSIS OF UNSTEADY CAVITATION FLOW OVER HYDROFOIL BASED ON DYNAMIC MODE DECOMPOSITION$^{\bf 1)}$

空化是船舶和水下航行体推进器中经常发生的一种特殊流动现象,它具有强烈的非定常性,空化的发生往往会影响推进器的水动力性能和效率. 为探究绕水翼非定常空化流场结构,本文基于 Schnerr-Sauer 空化模型和 SST $k$-$\omega $ 湍流模型,开展绕二维水翼非定常空化流动数值预报与流场结构分析. 通过将数值预报的空泡形态演变和压力数据与试验结果对比,验证了建立的数值方法的有效性. 并基于动力学模态分解方法对空化流场的速度场进行模态分解,分析了各个模态的流场特征. 结果表明,第一阶模态对应频率为 0,代表平均流场;第二阶模态对应频率约为空泡脱落频率,揭示了空泡在水翼前缘周期性地生长与脱落,第三阶模态对应频率约为第二阶模态的 2 倍,揭示了两个大尺度旋涡在水翼后方存在融合行为. 第四阶模态对应频率约为第二阶模态的 3 倍,具有更高的频率,表征流场中存在一些小尺度旋涡的融合行为. 最后对不同空化数下的空化流场进行了模态分解分析,发现脱落空泡的旋涡结构随着空化数的减小而增大,第二阶模态频率随着空化数的减小而减小.     

Numerical analysis of unsteady tip leakage vortex cavitation cloud and unstable suction-side-perpendicular cavitating vortices in an axial flow pump

The objective of this work is to simulate and analyze the formations of three-dimensional tip leakage vortex (TLV) cavitation cloud and the periodic collapse of TLV-induced suction-side-perpendicular cavitating vortice (SSPCV). Firstly, the improved SST k–ω turbulence model and the homogeneous cavitation model were validated by comparing the simulation result with the experiment of unsteady cavitation shedding flow around the NACA66-mod hydrofoil, and then the unsteady TLV cloud cavitation and unstable SSPCV in an axial flow pump were predicted using the improved numerical method. The predicted three-dimensional cavitation structures of TLV and SSPCV as well as the collapsing features show a good qualitative agreement with the high speed photography results. Numerical results show that the TLV cavitation cloud in the axial flow pump mainly includes tip clearance cavitation, shear layer cavitation, and TLV cavitation. The unsteady TLV cavitation cloud occurs near the blade trailing edge (TE) where the shapes of sheet cavitation and TLV cavitation fluctuate. The inception of SSPCV is attributed to the tail of the shedding cavitation cloud originally attached on the suction side (SS) surface of blade, and the entrainment affect of the TLV and the influence of the tip leakage flow at the tailing edge contribute to the orientation and development of the SSPCV. The existence of SSPCV was evidently approved to be a universal phenomenon in axial flow pumps. At the part-load flow rate condition, the SSPCV may trigger cavitation instability and suppress the tip cavitation in the neighboring blade. The cavitation cloud on the SS surface of the neighboring blade grows massively, accompanying with a new SSPCV in the neighboring flow passage, and this SSPCV collapses in a relatively short time.     

Perturbation solution to 3-D nonlinear supercavitating flow problems

A 3-D nonlinear problem of supercavitating flow past an axisymmetric body at a small angle of attack is investigated by means of the perturbation method and Fourier-cosine-expansion method. The first three order perturbation equations are derived in detail and solved numerically using the boundary integral equation method and iterative techniques. Computational results of the hydrodynamic characteristics and cavity shapes of each order are presented for nonaxisymmetric supercavitating flow past cones with various apex-angles at different cavitation numbers. The numerical results are found in good agreement with experimental data. The project supported by the National Natural Science Foundation of China     

带尾翼水下自然超空泡射弹数值模拟研究

基于Navier-Stokes方程,考虑气液间相变,采用大涡模拟湍流模型,PISO算法及VOF方法,利用自行开发的程序对绕三维带尾翼水下自然超空泡射弹的非定常空泡流动进行了数值模拟研究.通过计算结果得到超空泡从射弹头部初生至完全包裹弹身的形成过程.在此基础上,计算不同攻角条件下的超空泡形态,并给出射弹表面空泡厚度分布曲线,分析不同攻角对超空泡形态特性的影响规律,以及在零攻角条件下,分析尾翼对空泡形态的影响.另外计算不同空化数条件下的超空泡无量纲长度和厚度,将计算结果与实验数据进行对比,两者吻合较好.研究结果为进一步研究水下高速射弹的水动力特性和弹道特性问题提供理论基础.     

Cavity induced vibration of flexible hydrofoils

The objective of this work is to investigate the influence of cavity-induced vibrations on the dynamic response and stability of a NACA66 hydrofoil at 8° angle of attack at Re=750 000 via combined experimental measurements and numerical simulations. The rectangular, cantilevered hydrofoil is assumed to be rigid in the chordwise direction, while the spanwise bending and twisting deformations are represented using a two-degrees-of-freedom structural model. The multiphase flow is modeled with an incompressible, unsteady Reynolds Averaged Navier–Stokes solver with the k–ω Shear Stress Transport (SST) turbulence closure model, while the phase evolutions are modeled with a mass-transport equation based cavitation model. The numerical predictions are compared with experimental measurements across a range of cavitation numbers for a rigid and a flexible hydrofoil with the same undeformed geometries. The results showed that foil flexibility can lead to: (1) focusing – locking – of the frequency content of the vibrations to the nearest sub-harmonics of the foil׳s wetted natural frequencies, and (2) broadening of the frequency content of the vibrations in the unstable cavitation regime, where amplifications are observed in the sub-harmonics of the foil natural frequencies. Cavitation was also observed to cause frequency modulation, as the fluid density, and hence fluid induced (inertial, damping, and disturbing) forces fluctuated with unsteady cavitation.     

Influence of cavitation on the hydroelastic stability of hydrofoils

This work numerically examines the effect of turbulent and cavitating flow on the hydroelastic response and stability of a hydrofoil. A cantilevered, rectangular, chordwise rigid hydrofoil is modeled as a 2-degrees-of-freedom structure for its spanwise bending and torsional flexibilities. The fluid flow is modeled with the incompressible, Unsteady Reynolds Averaged Navier–Stokes equations using an eddy-viscosity turbulence closure model that is corrected for the presence of cavitation, and with a transport equation based cavitation model. The results show that, in general, massive cavitation tends to: (i) reduce the mean lift, (ii) increase the mean drag, (iii) lower the mean deformations, and (iv) delay static divergence, while unsteady sheet/cloud cavitation promotes flow induced vibrations. Such vibrations and load fluctuations could be as large as (and even greater than) the mean values for cases with unsteady cavitation, so dynamic and viscous fluid–structure models are needed to simulate flexible hydrofoils in cavitating flows. In general, the flow induced vibrations, and hence the drag force, are higher with decreasing stiffness. For small leading edge partial cavitation, increasing foil flexibility increases the maximum cavity length and reduces the cavity shedding frequency; however, the influence of foil flexibility is limited for cases where the maximum cavity length is near or beyond the foil trailing edge, because of the relocation of the center of pressure at the elastic axis, near the mid-chord. The results show that the mean deformations are generally limited by stall, and by the quasi-steady linear theory predictions at the fully-wetted and supercavitating limits. Furthermore, frequency focusing can occur when the cavity shedding frequency is near the fundamental system resonance frequencies, and broadening of the frequency spectrum can occur due to excitation of the sub-harmonics and/or modulation induced by the fluctuating cavities, if the cavity shedding frequency is away from the fundamental system resonance frequencies.     

Recent progress in nonlinear eddy-viscosity turbulence modeling

This article presents recent progresses in turbulence modeling in the Unit for Turbulence Simulation in the Department of Engineering Mechanics at Tsinghua University. The main contents include: compact Non-Linear Eddy-Viscosity Model (NLEVM) based on the second-moment closure, near-wall low-Re non-linear eddy-viscosity model and curvature sensitive turbulence model. The models have been validated in a wide range of complex flow test cases and the calculated results show that the present models exhibited overall good performance. The project supported by the National Natural Science Foundation of China (10232020), the National Key Basic Research Special Fund of China (2001CB409600) and the National High-Tech Development Program (2002AA311240)     

Prediction of Flow and Heat Transfer through Stationary and Rotating Ribbed Ducts Using a Non-linear <Emphasis Type="Italic">k</Emphasis>−<Emphasis Type="Italic">ε</Emphasis> Model

The present paper deals with the prediction of three-dimensional fluid flow and heat transfer in rib-roughened ducts of square cross-section, which are either stationary, or rotate in orthogonal mode. The main objective is to assess how a recently developed variant of a cubic non-linear k−ε model (proposed by Craft et al. Flow Turbul Combust 63:59–80, 1999) can predict three-dimensional flow and heat transfer characteristics through stationary and rotating ribbed ducts. The present paper discusses turbulent air flow and heat transfer through two different configurations, namely: (I) a stationary square duct with “in-line” normal and (II) a square duct with normal ribs in a “staggered” arrangement under stationary and rotating conditions, with the axis of rotation normal to the flow direction and parallel to the ribs. In this paper the flow and thermal predictions of the linear k−ε model (EVM) are also included, as a set of baseline predictions. The mean flow predictions show that both linear and non-linear k−ε models can successfully reproduce most of the measured data for stream-wise and cross-stream velocity components. Moreover, the non-linear model is able to produce better results for the turbulent stresses. The heat transfer predictions show that both EVM and NLEVM2, the more recent variant of the non-linear k−ε, with the algebraic length-scale correction term, overestimate the measured Nusselt numbers for both geometries examined. While the EVM with the differential length-scale correction term underestimates heat transfer levels, the Nusselt number predictions with the NLEVM2 and the ‘NYP’ term are in close agreements with the measured data. Comparisons with our earlier work, Iacovides and Raisee (Int J Heat Fluid Flow, 20:320–328, 1999), show that the NLEVM2 thermal predictions are of similar quality to those of a second-moment closure.     

绕水翼超空化流动形态与速度分布

为揭示超空化流场结构特性,利用高速全流场显示技术,观察了绕hydronautics水翼的超空化流动形态,并利用数字粒子图像测速仪(DPIV)测量了其速度分布. 在测量空穴内部流速分布时,采用空化流场中的空化泡作为示踪粒子来显示流动结构. 结果表明:随着空化数的降低,超空化流动显现出了明显的阶段特征,其中水汽混合相和汽相的分布决定了空化区域的形态与流速分布;空化区和主流区的汽液交界面处存在着较大的速度梯度;低速分布区域随着空化数的降低由水翼吸力面中后部向水翼下游移动;在空化区域内部,水汽混合区的速度相对较低,而汽相区则与主流区有着相近的速度分布.关键词超空化水翼、DPIV、高速摄像、空化形态、流速分布      

An improvement to the Kunz preconditioner and numerical investigation of hydrofoil interactions in tandem

ABSTRACT

Numerical simulations of the tandem-system flow are widely conducted because of the complex interactions of the configuration. The cavitation phenomenon is an important factor that affects the hydrofoil in tandem. In this paper, we developed a new parameter for the Kunz preconditioner based on the local cavitation volume fraction. To assess this parameter, a type of Fourier footprint analysis and numerical test of the hydrofoil are adopted. The preconditioning method is also conducted in hydrofoil turbulent cavitation flows with RANS turbulence models, to prove that this method has good stability and convergence. Based on this, a tandem Clark-Y hydrofoil configuration is investigated. The results show that the distance of components has a strong influence on the cavitation and lift coefficient of the tandem hydrofoils. Therefore, the purpose of this study is to provide guidance on the design of marine vehicles that have tandem configurations.     

绕水翼空化流动多尺度数值研究

空化的多尺度效应是一种涉及连续介质尺度、微尺度空化泡以及不同尺度间相互转化的复杂水动力学现象, 跨尺度模型的构建是解析该多尺度现象的关键. 本文基于欧拉-拉格朗日联合算法, 通过界面捕捉法求解欧拉体系下大尺度空穴演化, 通过拉格朗日体系下离散空泡模型求解亚网格尺度离散空泡的运动及生长溃灭. 同时, 通过判断空泡与网格尺度间的关系判定不同尺度空化泡的求解模型. 基于建立的多尺度算法对绕NACA66水翼空化流动进行模拟, 将数值结果与实验进行对比, 验证了数值计算方法的准确性. 研究结果表明, 离散空泡数量与空化发展阶段密切相关, 在附着型片状空穴生长阶段, 离散空泡数量波动较小, 离散空泡主要分布在气液交界面位置; 在回射流发展阶段, 离散空泡逐渐增加并分布在回射流扰动区; 在云状空穴溃灭阶段, 离散空泡数量增多且主要分布在气液掺混剧烈的空化云团溃灭区. 在各空化发展阶段, 离散空泡直径概率密度函数均符合伽玛分布. 空化湍流流场特性对拉格朗日空泡空间分布具有重要影响, 离散空泡主要分布在强湍脉动区、旋涡及回射流发展区域.      

Turbine vane film cooling: Heat transfer evaluation using high-order discontinuous Galerkin RANS computations

A high-order accurate CFD solver, based on the Discontinuous Galerkin (DG) finite element method, is here employed to compute the heat transfer, with and without film coolant injection, around a turbine vane extensively tested in a wind tunnel. The numerical solution makes also use of a high-order polynomial representation of the airfoil curved boundary in order to minimize the numerical sources of error, leaving possibly only those related to the physical model adopted. The objective of the work is therefore twofold: on the one hand to provide a detailed investigation, often beyond the reach of the experiments, of the complex flow field arising in a film-cooled gas turbine cascade, on the other hand to ascertain the limits of the Reynolds-averaged Navier-Stokes (RANS) approach and its associated turbulence model when using high-order accurate methods. The DG formulation is briefly reviewed, as well as the experimental apparatus and the measuring technique, and then the code is applied to the computation of various test cases characterized by different reference Reynolds and Mach numbers. Two-dimensional results (up to seventh-order accurate) obtained both with the high- and low-Reynolds version of the k-ω model employed are presented. Reasonably good agreement between experimental and numerical results is obtained, even though the outcomes are far from being completely satisfactory especially for flow regimes in the low Reynolds number range. This is due to the lack of suitable modeling of the laminar-turbulent transition process taking place around the blade leading edge. Such a complex phenomenon is out of reach of the modeling capabilities of the high-Re k-ω model, while can be roughly mimicked by the low-Re version of the model, which is able to provide a delayed onset of the turbulence quantities along the blade surface.Third-order accurate computation of the three-dimensional turbine vane are also presented in this work and compared with available measurements to investigate the relevant fluid flow phenomena occurring and to discuss significant issues related to an accurate prediction of the turbine wall heat transfer.     

On the performance of sudden‐expansion pipe without/with cross‐flow injection: experimental and numerical studies

The paper explores the possibilities that different turbulence closures offer, for in‐depth analysis of a complex flow. The case under investigation is steady, turbulent flow in a pipe with sudden expansion without/with normal‐to‐wall injection through jets. This is a typical geometry where generation of turbulence energy takes place, due to sudden change in boundary conditions. This study is aimed at investigating the capability of a developed computational program by the present authors with three different turbulence models to calculate the mean flow variables. Three two‐equation models are implemented, namely the standard linear k ? ε model, the low Reynolds number k ? ε model and the cubic nonlinear eddy viscosity (NLEV) k ? ε model. The performance of the chosen turbulence models is investigated with regard to the available data in the literature including velocity profiles, turbulent kinetic energy and reattachment position in a pipe expansion. In order to further assess the reliability of the turbulence models, an experimental program was conducted by the present authors also at the fluid mechanics laboratory of Menoufiya University. Preliminary measurements, including the surface pressure along the two walls of the expansion pipe and the pressure drop without and with the presence of different arrangements of wall jets produced by symmetrical or asymmetrical fluid cross‐flow injection, are introduced. The results of the present studies demonstrate the superiority of the cubic NLEV k ? ε model in predicting the flow characteristics over the entire domain. The simple low Reynolds number k ? ε model also gives good prediction, especially when the reattachment point is concerned. The evaluation of the reattachment point and the pressure‐loss coefficient is numerically addressed in the paper using the cubic NLEV k ? ε model. The results show that the injection location can control the performance of the pipe‐expansion system. It is concluded that the introduction of flow injection can increase the energy loss in the pipe expansion. The near‐field turbulence structure is also considered in the present study and it is noticed that the turbulence level is strongly affected by the cross‐flow injection and the jet location. Copyright © 2011 John Wiley & Sons, Ltd.     

Fourier neural operator approach to large eddy simulation of three-dimensional turbulence

Fourier neural operator (FNO) model is developed for large eddy simulation (LES) of three-dimensional (3D) turbulence. Velocity fields of isotropic turbulence generated by direct numerical simulation (DNS) are used for training the FNO model to predict the filtered velocity field at a given time. The input of the FNO model is the filtered velocity fields at the previous several time-nodes with large time lag. In the a posteriori study of LES, the FNO model performs better than the dynamic Smagorinsky model (DSM) and the dynamic mixed model (DMM) in the prediction of the velocity spectrum, probability density functions (PDFs) of vorticity and velocity increments, and the instantaneous flow structures. Moreover, the proposed model can significantly reduce the computational cost, and can be well generalized to LES of turbulence at higher Taylor-Reynolds numbers.     

Research progresses and prospects of unsteady hydrodynamics characteristics for cavitation

空化作为一种重要的复杂水动力学现象,具有明显的三维流动特征与剧烈的非定常特性,在水力机械、船舶推进器、水利工程中广泛存在,且通常会带来不利的影响,长期以来一直是水动力学领域研究的重点与难点课题之一.本文首先从实验测量和数值模拟两个角度,综述了空化水动力学非定常特性研究的发展概况, 分析了当前存在的问题.在空化实验研究中,主要介绍了空化水洞、空化流场测量以及多物理场同步测量等方面所取得的进展.在数值模拟方法中, 对目前的空化模型和湍流模型进行了分类介绍,并重点讨论了大涡模拟、验证和确认等在空化流模拟中的应用.之后以附着型空化为主, 同时兼顾云状空泡、空蚀、涡空化等,梳理了其研究中存在的几个关键科学问题,包括空化演变、空化流动的三维结构、失稳机制、空化不稳定性及其与低频压力脉动的联系、空化与旋涡的相互作用、空化与弹性水翼的流固耦合、空化对尾流场影响等.最后展望了空化水动力学的研究方向和未来发展趋势.     

空化水动力学非定常特性研究进展及展望

空化作为一种重要的复杂水动力学现象,具有明显的三维流动特征与剧烈的非定常特性,在水力机械、船舶推进器、水利工程中广泛存在,且通常会带来不利的影响,长期以来一直是水动力学领域研究的重点与难点课题之一.本文首先从实验测量和数值模拟两个角度,综述了空化水动力学非定常特性研究的发展概况, 分析了当前存在的问题.在空化实验研究中,主要介绍了空化水洞、空化流场测量以及多物理场同步测量等方面所取得的进展.在数值模拟方法中, 对目前的空化模型和湍流模型进行了分类介绍,并重点讨论了大涡模拟、验证和确认等在空化流模拟中的应用.之后以附着型空化为主, 同时兼顾云状空泡、空蚀、涡空化等,梳理了其研究中存在的几个关键科学问题,包括空化演变、空化流动的三维结构、失稳机制、空化不稳定性及其与低频压力脉动的联系、空化与旋涡的相互作用、空化与弹性水翼的流固耦合、空化对尾流场影响等.最后展望了空化水动力学的研究方向和未来发展趋势.