Computational study of aeration for wastewater treatment via ventilated pump-turbine

Large eddy simulations were performed on a modular pump-turbine to study oxygen dissolution inside the draft tube. Air injection was applied over the runner cone surface during turbine operation. Data regarding bubble size, void fraction and interfacial area concentration were presented to understand their influence on oxygen dissolution. Transient single phase and multiphase flow simulations were carried out to investigate the influence of air injection and dissolution within the flow field and turbine performance. Multiphase simulations were conducted by using the mixture multiphase model. The mathematical modeling of oxygen dissolution employed was validated by comparing predicted oxygen dissolution against experimental measurements performed by Zhou et al. (2013). The averaged dissolved oxygen concentration in the range of 1.2–1.4 mg/l was obtained; which is sufficient for an active aerobic microorganism activity for wastewater treatment processes. Dissolution efficiency and the amount of averaged dissolved oxygen inside the draft tube were sensitive to the inlet bubble size. The efficiency of the dissolution increases strongly as the inlet bubble size was reduced. The obtained results revealed that vortex suppression was achieved through air admission within multiphase flow simulation. Moreover, the power generation of the turbine was hardly influenced by the aeration through the runner cone.     

Swirl number based transposition of flow-induced mechanical stresses from reduced scale to full-size Francis turbine runners

At part load conditions, Francis turbines are subject to the emergence of a hydrodynamic instability in their draft tube, referred to as precessing vortex rope. It induces pressure pulsations in the water passages at the precession frequency of the vortex, leading to additional vibrations and dynamic loads on the runner blades. The prediction of both the dynamic behaviour of the vortex rope and the resulting dynamic loads over a wide operating range is of importance to improve the runner design and robustness on the one hand and to assess additional fatigue and related maintenance costs on the other hand. Such a prediction, either with numerical simulation or reduced scale physical model tests, remains however challenging. The present paper aims at introducing a methodology to assess the vortex behaviour, the related pressure fluctuations and the resulting dynamic strains on the runner over the complete part load operating range. It is based on reduced scale physical model tests of a Francis turbine, including the measurement of the pressure and the load on the runner with instrumented blades. It is shown that the influence of both the discharge factor and speed factor on the vortex dynamics behaviour and related pressure fluctuations can be represented by a single parameter; the swirl number. The correlation with the swirl number is further extended to the dynamic strains induced by the vortex rope on the runner blades. Similar mechanical load and pressure measurements are finally performed on the full-scale machine during a power ramp-up and the results are compared to the empirical correlations established on the reduced scale physical model.     

On the Capability of PIV-Based Wall Pressure Estimation for an Impinging Jet Flow

A PIV-based pressure estimation methodology is used to compute the wall pressure from the velocity field of a turbulent impinging jet flow. A simplified formulation (2D-2C) is applied to velocity fields issued from PIV data. The ability of the method to qualitatively estimate the wall pressure signature of a 3D unsteady impinging jet flow using only two velocity components in a plane is demonstrated. Nevertheless, the 2D flow assumption used in the context of planar measurements involves an underestimation of the wall pressure values all along the radial direction. The formulation based on the full integral formalism (3D-3C), computed from DNS data without any assumption on the flow, provides a reference solution. The contributions of the surface and volume integrals to the pressure coefficient are assessed. It is shown that the most important contribution to the wall pressure comes from the volume integral. Then the underestimation observed for the simplified formulation is mostly linked with the assumptions considered for the source term computation. The effect of each assumption is quantitatively analysed with the help of the DNS data and some ways to improve the simplified methodology are finally proposed.     

Analysis of Head Losses in a Turbine Draft Tube by Means of 3D Unsteady Simulations

In this paper, Unsteady RANS (URANS) simulations and Large Eddy Simulations (LES) in the draft tube of a bulb turbine are presented with the objective to understand and locate the head losses in this turbine component. Three operating points of the turbine are considered. Numerical results are compared with experimental velocity measurements for validation. Thanks to a detailed analysis of the energy balance in the draft tube, the physical and hydrodynamic phenomena responsible for head losses in the draft tube are identified. Head losses are due to transfer of mean kinetic energy to the turbulent flow and viscous dissipation of kinetic energy. This occurs mainly in the central vortex structure and next to the walls in the draft tube. Head losses prediction is found to be dependent on the turbulence model used in the simulations, especially in URANS simulations. Using this analysis, the evolution of head losses between the three operating points is understood.     

Lattice Boltzmann simulation of flows in bifurcate channel at rotating inflow boundary conditions and resulted different outflow fluxes

The Lattice Boltzmann method(LBM) is used to simulate the flow field in a bifurcate channel which is a simplified model of the draft tube of hydraulic turbine machine.According to the simulation results,some qualitative conclusions can be deduced.The reason of uneven flux in different branches of draft tube is given.Not only the vortex rope itself,but also the attenuation of the rotation strength is important in bringing on the uneven flux.The later leads to adverse pressure gradient,and changes the velocity profile.If the outlet contains more than one exit,the one that contains the vortex rope will lose flux because of this adverse pressure gradient.Several possible methods can be used to minimize the adverse pressure gradient domain in order to improve the efficiency of turbine machine.     

Effect of vent opening area and arrangement on gas flow field as gas propelled cylinder exits a flow tube

The effects of auxiliary flow tube vent opening area and arrangement on the gas flow field as a gas propelled cylinder exits a flow tube were studied numerically. Configurations with a single opening of increasing size and multiple opening arrangements with equivalent opening area were considered for comparison to a baseline no-opening system. The openings are positioned near the end of the flow tube. The intended use of the openings is to reduce the pressures of the gases escaping to the surroundings and thus to reduce the intensity and size of the gas expansion zone in the surroundings. The results indicated that increasing the opening flow area decreased the pressure at the axial end of the flow tube and the radial extent of the end of flow tube exit plume. However, the radially directed flow streams leaving through the side vent openings could increase the overall radial spread of the gas expansion into the surroundings. The single opening arrangement produced as much as a 95% decrease in the pressure at the end of the flow tube and a 37% decrease in the recoil force at a given time with about 95% of the exiting flow leaving through the opening. For the parameters considered, the multiple opening arrangement produced up to a 93% decrease in the pressure at the end of the flow tube and a 90% decrease in the recoil force at a given time with about 93% of the exiting flow leaving through the openings. The results showed larger single openings to be more effective at reducing end of flow tube pressure, while the multiple openings to be more conducive to a reduced recoil force.     

Analytical solution for laminar flow through leaky tube

The laminar flow through a leaky tube is investigated, and the momentum and conservation of energy equations are solved analytically. By using the Hagen-Poiseuille velocity profile and defining unknown functions for the axial and radial velocity components, the pressure and mass transfer equations are obtained, and their profiles are plotted according to different parameters. The results indicate that the axial velocity, the radial velocity, the mass transfer parameter, and the pressure in the tube decrease as the fluid moves along the tube.     

Velocity field investigation inside a bulb turbine runner using endoscopic PIV measurements

The flow in the inter-blade channels of a bulb turbine was measured using endoscopic cameras integrated to a stereoscopic particle image velocimetry (S-PIV) system. This paper presents results from the measurement campaign and also provides some key conclusions based on the dataset. The technical aspect of the measurement configuration is addressed. The main focus is on the novelties and challenges brought by the use of endoscopic cameras to achieve S-PIV measurements between the runner blades. For the first time in hydraulic rotating machinery, velocity measurements covered 62 % of a rotor inter-blade flow. After outlining the techniques used, comparison with laser Doppler velocimetry measurements allows assessing the intrusiveness of the endoscopes. Then, some velocity field analyses are shown. First, the rotor–stator interaction is outlined as the influence of the guide vane wakes on the runner flow. The size, localization, strength and dissipation of those structures are inferred from the information coming from measurements. Finally, the PIV data allow the identification of a vortex located near the suction side of the blades and originating from the corner between the leading edge and the hub when operating the bulb turbine at part-load.     

环空流道液流失速水击特性及其成因的研究

环空流道与圆管的结构差异,使得其失速水击特性及其成因亦有不同。为了对其进行分析研究,利用PIV对套管环空和圆管流水击流场进行拍摄,并通过Tecplot显示流场,提取轴向速度和径向速度、等速度线等参数加以分析;同时采用高精度智能动态压力传感器采集了套管环空内、外壁及内管内壁压力,对环空中水击特性进行了进一步研究。结论是:水击发生时环空断面外壁面水击压力大于内壁面水击压力;同初速情况下环空液流水击压力大于圆管流水击压力;环空中水击压力衰减速度快于圆管中;涡流是水击压力衰减以及速度变化的主要因素;水击压力振荡变化主要是压力涡流引起的断面能量的相互转化形成的。     

基于五阶WENO格式的燃气在药床中流动过程二维两相流研究

为研究内弹道初始阶段中心点火管燃气在膛内药床中的流动特性和传播规律,设计了可视化点传火实验平台,并进行了膛内假药床的点传火实验。基于加权本质无震荡(weighted essentially non-oscillatory, WENO)格式,构造了膛内轴对称二维内弹道两相流模型,对膛内燃气在假药床中的流动过程进行数值模拟。计算结果与可视化实验结果符合较好,全局压力平均误差为5.35%。表明数值计算准确地描述了燃气流动特性,完整地呈现了点火管燃气在假药床中的发展过程。在点火初始阶段,膛内压力径向效应明显,气相沿径向传播较快,药床药粒基本不会发生运动;随着燃气逐渐在膛内传播,膛内压力呈现径向一致、轴向梯度分布的特征,在压力梯度作用下,气相轴向速度开始占据主导,径向速度在膛底和中部区域减小为零,而固相速度随气相速度变化而变化;气相在到达弹底前,由于固相颗粒的壅塞,会提前出现速度反向波动现象。     

Effective downstream boundary conditions for incompressible Navier–Stokes equations

The aim of this paper is to give open boundary conditions for the incompressible Navier–Stokes equations. From a weak formulation in velocity–pressure variables, some natural boundary conditions involving the traction or pseudotraction and inertial terms are established. Numerical experiments on the flow behind a cylinder show the efficiency of these conditions, which convey properly the vortices downstream. Comparisons with other boundary conditions for the velocity and pressure are also performed.     

Flow friction on co-rotating parallel-disk assemblies with forced through-flow

The power requirement for a rotating parallel-disk assembly with through-flow is experimentally studied. The flow velocity at the test core exit is measured using a traverse hot-wire probe, from which the exit kinetic energy is determined. A traverse pitot tube is utilized to monitor the velocity distribution in the inlet duct from which the flow rate is evaluated. The total pressure characteristics, fluid power transmission, rotor efficiency and moment coefficient (i.e. power number) are determined from the measurements of static pressures, rotational speed and torque. It is disclosed that the onset of stall propagation, a unique characteristics of shear pump, can be detected from a total pressure plot.     

Numerical modelling and flow analysis of a centrifugal pump running as a turbine: Unsteady flow structures and its effects on the global performance

The purpose of this paper is to investigate the flow patterns in a centrifugal pump when it works as a centripetal turbine, with special interest in the unsteady behavior in order to explain the shape of the performance curves. Also, we focus on the determination of the radial thrust and other mechanical loads over a pump‐designed machine. The pump studied is commercial, with single axial suction and a vaneless spiral volute casing. A numerical study has been carried out in order to obtain more information about the flow into the volute and the impeller. A numerical three‐dimensional unsteady simulation has been developed using a commercial code that solves the URANS set of equations with a standard k–ε turbulence model. The results show the non‐axisymmetric flow developed in the volute, responsible for a significant radial thrust; the interaction between the tongue and the impeller, generating force fluctuations; the velocity and pressure distributions inside the impeller; and the exit flow, characterized with post‐rotation and low‐pressure. These flow results allow us to understand the behavior of the machine by comparing it with the pump mode. Complementarily, an experimental study was conducted to validate the numerical model and characterize the pump‐turbine performance curves at constant head. Fast‐response pressure taps and a three‐hole pneumatic pressure probe were employed to obtain a complete data set of non‐stationary and stationary measurements throughout the centrifugal machine. As a result, loss of efficiency or susceptibility to cavitation, detected numerically, was confirmed experimentally. The study demonstrates that the numerical methodology presented here has shown its reliability and possibilities to predict the unsteady flow and time‐mean characteristics of centrifugal pumps working as turbines. In particular, it is shown that the commercial design of the pump allows a reasonable use of the impeller as a turbine runner, due to the suitable adaptation of the inflow distributions to the volute casing. Moreover, the efficiency for the inverse mode is shown to be as high as achieved for the pumping operational mode. In addition, it is concluded that both axial and radial thrusts are controlled, though important unsteady fluctuations—up to 25%—clocked with the blade passing frequency appear beyond the nominal conditions. In that case, a moderate use of the pump as a turbine is recommended in order to minimize risks of fatigue failure of the bearings. Copyright © 2009 John Wiley & Sons, Ltd.     

Vortical structures and pressure pulsations in draft tube of a Francis-99 turbine at part load: RANS and hybrid RANS/LES analysis

Recognizing the limitations of the conventional linear-eddy-viscosity (LEVM) Reynolds-averaged Navier–Stokes (RANS) models to reproduce complex three-dimensional unsteady flows in hydraulic machinery, we performed a comparative assessment of a second-moment (Re-stress model, RSM) RANS closure and a hybrid RANS/LES method in capturing the flow and vortical structures in the draft tube of a Francis hydroturbine at off-design conditions. Considered is a case of part load (PL) at a flow rate of only 35% of the best efficiency point (BEP) characterised by multiple unsteady vortex systems. Despite some remaining uncertainties in generating the inflow conditions, both approaches reproduced reasonably well the measured mean velocity and the rms of its fluctuations, as well as the pressure spectrum with peaks detecting the precessing vortex core. In contrast to the common LEVMs, the Re-stress closure showed sufficient receptivity to intrinsic unsteadiness and reproduced well the overall flow and vortical patterns as well as the associated pressure pulsations in accord with the experiments. The hybrid RANS/LES method gave similar predictions as the RSM, but resolving a wider range of scales, which however, showed no significant effect on the dynamics of the dominant processing vortex core and the pressure pulsations.     

Design sensitivity and finite element analysis of free surface flows with application to optimal design of casting rigging systems

A novel, fully-analytical design sensitivity formulation for transient, turbulent, free surface flows is derived and implemented in the context of finite element analysis. The time-averaged, turbulent form of the Navier–Stokes equations are solved using a mixing length model, in conjunction with the volume of fluid (VOF) method to model the free surface movement. The design derivatives of these governing equations are computed and solved to find the analytical sensitivities of the fluid position, velocity and pressure fields with respect to shape design variables. The computational efficiency produced by evaluating the sensitivities analytically is demonstrated. The design of the runner and gating system of a simple block casting is presented as an example application for using sensitivity information in design. The analytical sensitivity routine is coupled to a numerical optimizer to yield an automated method for optimal design of the casting rigging system. The results produce runner shapes which eliminate mold-gas aspiration. © 1998 John Wiley & Sons, Ltd.     

Mean flow characteristics of a turbulent plane jet with buoyancy induced curvature

An experimental investigation of heated vertical and inclined plane air jets discharged into quiescent surroundings is described. A unique feature of this data is that Pilot tube measurements were used to define the mean trajectory of the inclined jets so that subsequent hot-wire traverses could be made normal to the curved path. While the mean velocity and temperature profiles are self-similar for the range of exit conditions studied, other aspects of the mean jet development depend on the exit Reynolds and Froude numbers, or the discharge angle. It is noted that variations between this study and other published data suggest further measurements of this flow situation are needed, with particular attention to specific features of the jet apparatus and ambient surroundings, and to the exit Reynolds number. Presently with Dept. of Mechanical Engineering, University of Alexandria, Alexandria, Egypt     

Elongated bubbles in microchannels. Part I: Experimental study and modeling of elongated bubble velocity

The velocity of elongated vapor bubbles exiting two horizontal micro-evaporator channels with refrigerant R-134a was studied. Experiments with tube diameters of 509 and 790 μm, mass velocities from 200 to 1500 kg/m² s, vapor qualities from 2% to 19% and a nominal saturation temperature of 30 °C were analyzed with a fast, high-definition digital video camera. It was found from image processing of numerous videos that the elongated bubble velocity relative to that of homogeneous flow increased with increasing bubble length until a plateau was reached, and also increased with increasing channel diameter and increasing mass velocity. Furthermore an analytical model developed for a diabatic two-phase flow, has been proposed that is able to predict these trends. In addition, the model shows that the relative elongated bubble velocity should decrease with increasing pressure, which is consistent with the physics of two-phase flow.     

On shear thinning fluid flow induced by continuous mass injection in porous media with variable conductivity

A new formulation is proposed to examine the propagation of the pressure disturbance induced by the injection of a time-variable mass of a weakly compressible shear thinning fluid in a porous domain with generalized geometry (plane, radial, or spherical). Medium heterogeneity along the flow direction is conceptualized as a monotonic power-law permeability variation. The resulting nonlinear differential problem admits a similarity solution in dimensionless form which provides the velocity of the pressure front and describes the pressure field within the domain as a function of geometry, fluid flow behavior index, injection rate, and exponent of the permeability variation. The problem has a closed-form solution for an instantaneous injection, generalizing earlier results for constant permeability. A parameter-dependent upper bound to the permeability increase in the flow direction needs to be imposed for the expression of the front velocity to retain its physical meaning. An example application to the radial injection of a remediation agent in a subsurface environment demonstrates the impact of permeability spatial variations and of their interplay with uncertainties in flow behavior index on model predictions.     

Three-dimensional analysis of the flow in a curved hydraulic turbine draft tube

The three-dimensional turbulent flow in a curved hydraulic turbine draft tube is studied numerically. The analysis is based on the steady Reynolds-averaged Navier–Stokes equations closed with the κ-ε model. The governing equations are discretized by a conservative finite volume formulation on a non-orthogonal body-fitted co-ordinate system. Two grid systems, one with 34 × 16 × 12 nodes and another with 50 × 30 × 22 nodes, have been used and the results from them are compared. In terms of computing effort, the number of iterations needed to yield the same degree of convergence is found to be proportional to the square root of the total number of nodes employed, which is consistent with an earlier study made for two-dimensional flows using the same algorithm. Calculations have been performed over a wide range of inlet swirl, using both the hybrid and second-order upwind schemes on coarse and fine grids. The addition of inlet swirl is found to eliminate the stalling characteristics in the downstream region and modify the behaviour of the flow markedly in the elbow region, thereby affecting the overall pressure recovery noticeably. The recovery factor increases up to a swirl ratio of about 0˙75, and then drops off. Although the general trends obtained with both finite difference operators are in agreement, the quantitative values as well as some of the fine flow structures can differ. Many of the detailed features observed on the fine grid system are smeared out on the coarse grid system, pointing out the necessity of both a good finite difference operator and a good grid distribution for an accurate result.     

Pressure-sensitive paint measurements in a shock tube

 Surface pressures were measured in the short-duration, transient flow environment of a small-scale, low pressure-ratio shock tube using thin-film pressure-sensitive paint (PSP). Issues regarding coating formulation, measurement uncertainty, optical system design, and temperature and illumination compensation are discussed. The pressure measurements were acquired during steady flow conditions following the passage of normal shocks and expansion regions along a flat sidewall and a wedge sidewall. The PSP characteristic response time was 3 to 6 ms. Overall pressure uncertainty for the shock tube measurements ranged up to 5% over one atmosphere and compared well with theoretical estimates of uncertainty. Received: 20 April 1998 / Accepted: 9 September 1998