慢扩张旋转流的稳定性分析（Ⅰ）—理论研究

本文研究了无粘不可压慢扩张旋转流的稳定性问题，采用多重尺度展开法对有慢扩张的旋转流的非对称扰动进行浅化稳定性研究，导出了零阶及一阶扰动模所应满足的微分方程及由于慢扩张引起振幅变化的控制方程，将Ｐｌａｓｃｈｋｏ关于慢扩张喷流的结果推广到具有慢扩张的旋转流情况。     

Optimization methodology assessment for the inlet velocity profile of a hydraulic turbine draft tube: part I—computer optimization techniques

In recent years, numerical and experimental investigations on the draft tube performance have confirmed the importance of the inlet swirling flow created by the runner vanes. The results indicate that it is still a challenge to get the optimal flow distribution at the draft tube inlet which gives the best machine performance over a range of operation points. Consequently, there is a need to adjust the runner-draft tube coupling to minimize the losses arising from the inlet flow distribution. This paper focus on establishing an optimization methodology for maximizing the draft tube performance as a function of the inlet velocity profile. The overall work is divides into two parts: The part one establish the inlet velocity parametrization, the numerical optimization set-up and the objective function definition. The part two validate the numerical CFD draft tube model. These steps are represented by the coupling of the commercial softwares MATLAB, FLUENT and iSIGHT. It is considered that this proved methodology will help to find a inlet velocity profile shape which will be able to suppress or mitigate the undesirable draft tube flow characteristics.     

通过有漏孔管道时的层流解析解

研究了通过有漏孔管道时的层流,并解析地求解了动量方程和能量守恒方程．由Hagen-Poiseuille的速度分布,同时定义轴向和径向速度分量的未知函数,得到了压力和质量输运方程,并根据不同的参数,画出其分布图．结果表明,管道中的轴向速度、径向速度、质量输运参数和压力,随着流体沿管道的流动而减小．     

Theorie zur Berechnung des Abströmwinkels bei Turbinengittern

Summary A simple method is given for the approximate calculation of the outlet flow angle for cascades of narrow-spaced blades of the type used in steam and gas turbines. The method is based on continuity and momentum equation and may be applied to compressible flow.      

Statistical characteristics and time autocorrelation coefficients of the turbulent swirl flow in pipe

In this paper is presented experimental investigation of the turbulent swirl flow in pipe generated by three axial fans of various geometries. One of these fans (model ZP) generates Rankine swirl, while other two, industrial fans, produce mainly solid body circumferential velocity profile. One-component laser Doppler anemometry (LDA) is employed in this research. Downstream transformations of the non-dimensional time-averaged velocity profiles are analyzed. Distributions of turbulence levels are discussed for all three fans in both measuring sections, as well as statistical moments of higher orders for fluctuations in the axial, radial and circumferential directions. Applied correlation theory revealed turbulence structure and its statistical nature. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Chaotic analysis of pressure fluctuation signal in the gas–liquid–solid slurry column

The pressure signal of a slurry column is easily obtained by using a pressure sensor, and a chaotic analysis method is used to analyze these signals in order to indicate the flow pattern of the slurry column. The slopes of the correlation integral curve indicate the flow pattern of the slurry column in various operating conditions. The flow pattern is dispersed bubble regime when the superficial velocity is low and the correlation integral curve has two slopes. The flow pattern changes into transition regime with increase in the superficial velocity, the correlation integral curve has only one slope. In the case of the flow pattern becoming a slugging regime, there are several slopes to the correlation integral curve. So it is convenient to find out the flow pattern in the slurry column by solving the slopes of the correlation integral of the pressure signal. The maximum Lyapunov exponent represents the chaos in a slurry column with various solid holdups. The maximum Lyapunov exponent is nearly similar at different heights when the flow patterns are dispersed bubble regime and slugging regime, but the maximum Lyapunov exponent at the axial height is quite different when the flow pattern is transition regime.     

收缩喷嘴中的湍流Ⅰ——边界层解

应用边界层积分法,研究锥形喷嘴入口区域中湍动涡流的发展.球面坐标系中的控制方程,通过边界层的假定得到简化,并对边界层进行了积分.应用4阶Adams预测校正法求解该微分方程组.入口区域的切向和轴向速度,分别应用自由涡流和均匀速度分布来表示.由于缺乏收缩喷嘴中涡流的实验数据,需要用数值模拟对该发展模式进行逆向验证.数值模拟的结果证明,该解析模型在预测边界层参数中的能力,例如边界层的生长、剪切率和边界层厚度,以及不同锥度角时的涡流强度衰减率等.为所提出的方法引进一个简明而有效的程序,用以研究几何形状收缩设备内的边界层参数.     

Large Eddy Simulations of Swirling Nozzle-Jet Flow Undergoing Vortex Breakdown

We developed a numerical setup to simulate swirling jet flow undergoing vortex breakdown. Our simulation code CONCYL solves the compressible Navier-Stokes equations in cylindrical coordinates using high-order numerical schemes. A nozzle is included in the computational domain to account for more realistic inflow boundary conditions. Preliminary results of a Re = 5000 compressible swirling jet at Mach number M a = 0.6 with an azimuthal velocity as high as the maximum axial velocity (swirl number S = 1.0 ) capture the fundamental characteristics of this flow type: At a certain point in time the jet spreads and develops into a conical vortex breakdown. A stagnation point-flow in the vicinity of the jet axis is clearly visible with the stagnation point located close to the nozzle exit. The stagnation point precesses in time around the jet axis, moving up- and downstream. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Gauging magnetorotational instability

Previously (Z. Angew. Math. Phys. 57:615–622, 2006), we examined the axisymmetric stability of viscous resistive magnetized Couette flow with emphasis on flows that would be hydrodynamically stable according to Rayleigh’s criterion: opposing gradients of angular velocity and specific angular momentum. A uniform axial magnetic field permeates the fluid. In this regime, magnetorotational instability (MRI) may occur. It was proved that MRI is suppressed, in fact no instability at all occurs, with insulating boundary conditions, when a term multipling the magnetic Prandtl number is neglected. Likewise, in the current work, including this term, when the magnetic resistivity is sufficiently large, MRI is suppressed. This shows conclusively that small magnetic dissipation is a feature of this instability for all magnetic Prandtl numbers. A criterion is provided for the onset of MRI.     

Gauging magnetorotational instability

Previously (Z. Angew. Math. Phys. 57:615–622, 2006), we examined the axisymmetric stability of viscous resistive magnetized Couette flow with emphasis on flows that would be hydrodynamically stable according to Rayleigh’s criterion: opposing gradients of angular velocity and specific angular momentum. A uniform axial magnetic field permeates the fluid. In this regime, magnetorotational instability (MRI) may occur. It was proved that MRI is suppressed, in fact no instability at all occurs, with insulating boundary conditions, when a term multipling the magnetic Prandtl number is neglected. Likewise, in the current work, including this term, when the magnetic resistivity is sufficiently large, MRI is suppressed. This shows conclusively that small magnetic dissipation is a feature of this instability for all magnetic Prandtl numbers. A criterion is provided for the onset of MRI.     

Analytical solutions of laminar swirl decay in a straight pipe

In this work, the laminar swirl flow in a straight pipe is revisited and solved analytically by using prescribed axial flow velocity profiles. Based on two axial velocity profiles, namely a slug flow and a developed parabolic velocity profiles, the swirl velocity equation is solved by the separation of variable technique for a rather general inlet swirl velocity distribution, which includes a forced vortex in the core and a free vortex near the wall. The solutions are expressed by the Bessel function for the slug flow and by the generalized Laguerre function for the developed parabolic velocity. Numerical examples are calculated and plotted for different combinations of influential parameters. The effects of the Reynolds number, the pipe axial distance, and the inlet swirl profiles on the swirl velocity distribution and the swirl decay are analyzed. The current results offer analytical equations to estimate the decay rate and the outlet swirl intensity and velocity distribution for the design of swirl flow devices.     

The flow simulation of a low-specific-speed high-speed centrifugal pump

In this paper a general three-dimensional simulation of turbulent fluid flow is presented to predict velocity and pressure fields for a centrifugal pump. A commercial CFD code was used to solve the governing equations of the flow field. In order to study the most suitable turbulence model, three known turbulence models of standard k–ε, RNG and RSM were applied. The complex flow configuration required us to use around 5,800,000 cells, and 12 computational nodes (processors) for parallel computing. Simulation results in the form of characteristic curves were compared with available experimental data, and an acceptable agreement was obtained. Additionally, effect of number of blades on the efficiency of pump was studied. The number of blades was changed from 5 to 7. The results show that the impeller with 7 blades has the highest head coefficient. Finally, it was observed also that the position of blades with respect to the tongue of volute has great effect on the start of the separation. Thus, to analyze the effect of blade number on the characteristics of the pump, the position of blade and tongue should be similar to each other. Investigations of this kind may help to reduce the required experimental work for the development and design of such devices.     

Uniform Slip Flow on a Cylinder

In this paper, we determine the shear stress along the entire length of a stationary cylinder having radius a, under uniform axisymmetric flow, with velocity U0, in the slip regime. Investigating motion at small and large axial distances, we employ asymptotic series techniques to obtain the shear stress coefficient in non-dimensional form. For intermediate regions, we obtain a solution using the Rayleigh approximation method. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

环形扩压通道内有旋绕流动的研究

本文计算了环形截面的扩压通道内带进气旋绕的流动.在小横向流假定下.用三维边界层积分方程法求解内外壁面附近的流动.通过对子午面上与流线子午投影准正交方向的速度梯度方程和流量不变方程的迭代求解得出边界层外的势流场.计算与实验结果基本符合.本研究可用于分析环形扩压器内带进气予旋的流动.     

Linear analysis and energy budget of viscous liquid jets in both axial and radial electric fields

In their countless industrial applications, axisymmetric and non-axisymmetric instabilities are respectively responsible for electrospraying and electrospinning. A linear method and energy budget have been applied in this study to investigate the instability of viscous jets under both the axial and radial electric fields; the liquid was taken to be a leaky dielectric and the gas a perfect dielectric; the effect of a parabolic velocity profile was considered and compared to that of a uniform velocity, and the energy analysis explained the physical mechanisms to an extent. The liquid viscosity and parabolic velocity profile had a combined effect on jet instability. Work induced by the parabolic velocity profile consisted of two parts: the energy transferred from the basic flow to the disturbances, and the influence of the corresponding shear stresses. At low viscosities, these influences were positive enough to prevail over the viscous dissipation, enhancing axisymmetric instability. However, the parabolic velocity profile functioned differently in small and large wavenumber regions, and the response to the axial electric fields varied in different regions, accounting for the dual effects of axial electric fields on axisymmetric instability. Also, under the interplay between the strong axial electric fields and the parabolic velocity profile, two distinct unstable regions emerged for the non-axisymmetric mode. The effects of the radial electric fields were less sensitive, whether or not the parabolic velocity profile was considered. In summary, the parabolic velocity profile was significant–especially for charged jets with weak viscosity and strong axial electric intensity. The effects of axial electric fields in the atomization zone, and the effects of fluid permittivity coupled with the axial electric fields, were also investigated here.     

Mesures et calculs relatifs au couple de pivotement agissant sur les aubes de turbines Kaplan

Résumé Dans la présente étude, nous donnons tout d'abord un aper?u des couples de pivotement tels qu'ils ressortent de mesures typiques sur différentes installations. Puis nous intercalons un complément pour le calcul du couple d'origine centrifuge. Le rapport entre ce couple et celui d'origine hydraulique est ensuite discuté, et illustré par les valeurs établies pour une gamme d'installations. Des essais faits dans le laboratoire de mécanique des fluides des Ateliers des Charmilles sont présentés, en particulier la technique employée pour mesurer les couples de pivotement. Les résultats de mesures de couple sur une turbine dont on a varié le nombre de pales sont présentés sous la forme habituelle aux constructeurs. Le dépouillement est poursuivi pour permettre une comparaison avec les coefficients de l'aérodynamique. Des calculs schématiques des deux cas limites du profil isolé et de la grille très serrée montrent les caractères des forces hydrauliques dans les cas extrémes de la faible chute et de la haute chute, respectivement d'une vitesse spécifique élevée et faible. Entre ces limites, l'effet de grille sur le couple de pivotement est illustré par un dépouillement des diagrammes qu'a publiés le professeurSchlichting. Un calcul typique de profil Kaplan, faisant aussi ressortir l'influence du pas relatif et de l'épaisseur sur le couple de pivotement, est effectué au moyen de la méthode du professeurAckeret.

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Summary The knowledge of the twisting moment acting on the blades of turbines is particularly important for the construction of Kaplan water turbines. The moment due to the centrifugal forces is shown to amount to as much as 30% of the maximum hydraulic moment. Moments of rotation were measured at the Charmilles Engineering Works on a model runner with various numbers of blades. Measurements on radii upstream allow a computation similar to the one used in aerodynamics for isolated aerofoils. The character of governing forces measured in various plants can easily be explained by the behaviour of cascades in both limit cases of a very rapid and very slow runner, i. e., cord/pitch=0 and ∞. Pressure distributions calculated bySchlichting on actual cascades show an intermediate tendency of the pitching moment in function of the stagger angle. Calculations made with the Ackeret method show the influence of thickness when the distribution of the vortices is unchanged.

     

On the Stability of Compressible Swirling Flow

The linear stability to axisymmetric perturbations of compressible non-dissipative swirling flow is shown to be insured if a suitably defined “Richardson number” depending on the basic velocity, temperature and density fields everywhere exceeds 1/4. This result combines and generalizes in a natural way some known results for incompressible swirling flow and stratified parallel flow.     

Active Flow Control Implemented in a Multi-Stage High-Speed Axial Compressor

The decrease of fuel consumption is a main objective in the development of modern aircraft engines and heavy-duty gas turbines. Especially at off-design conditions, one promising approach to suppress flow losses and to increase the efficiency of the compressor is Active Flow Control (AFC) by aspiration or injection. Aerodynamically, the compressor flow of a gas turbine responds more sensitively to volatile flow conditions than the turbine flow because of the positive pressure gradient in a compressor achieved by flow deceleration. In a decelerating flow, particularly at off-design operating conditions, the compressor flow tends to separate from the blade surfaces. This flow separation causes unstable operating conditions inside the flow path resulting in low overall engine efficiency. Thus it is obvious that counter-measures against increased flow losses at off-design operation should be concentrated on the compressor. Considering industrial objectives, both the performance increase and the operating range enhancement are subjects of current compressor research, as is a reduction of vanes or even entire stages. While a reduced vane count reduces cost, even greater benefits can be gained if entire stages could be eliminated and thus the number of rotor discs reduced, which further reduces cost along with reducing the length of the rotor which could also improve rotor dynamics. For all of these purposes, different AFC approaches were implemented in a four stage axial compressor (4AV) and were experimentally examined. This paper presents an overview of the past and ongoing AFC research at the Institute of Turbomachinery and Fluid Dynamics (TFD). (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the Bödewadt–Rosenblat flow

Fluid motion induced by the torsional oscillations (of angular velocity bΩcosω T) of an infinite disk in contact with an incompressible viscous rotating (with angular velocity aΩ) fluid of semi-infinite extent is analysed when the amplitude parameter α( = b/a) varies from zero to infinity. Composite solutions valid over the whole of the flow regime and specific expressions for the shearing stress components at the disk and for the axial flow in the far region are obtained for low and high frequencies of torsional oscillations. Using the method of matched asymptotic expansions, we find that the region of the mean flow increases with α and reaches a maximum before settling down to the Rosenblat profile. Series expressions (for α < 1) are deduced for physical quantities of interest when the fluid in the far field and the disk are rotating with different angular velocities (in the same or in the opposite sense), which agree well with the known numerical results. (Received: April 7, 2003; revised: September 29, 2005)